SIMULATION OF le HOUSE DRYING OF CHICKEN EXCRETA Haggis far the Degree of Wt a. WCWGAN STATE UNEVEQSFW GERRY DEWETT Wills 193’ " A} LN” _ m I JIll!WIll'llmllfilmfllmliflmlfilflllL if ’5 3" " ~ 3 1293 01070 3241 This is to certify that the thesis entitled SIMULATION OF IN-HOUSE DRYING 0F CHICKEN EXCRETA presented by GRANT DEWI TT WELLS has been accepted towards fulfillment of the requirements for @204 i Mnjor professor .Date 1/71/72— 0-7639 ABSTRACT SIMULATION OF IN-HOUSE DRYING 0F CHICKEN EXCRETA by Grant DeWitt Wells Fresh chicken excreta contains 88 percent moisture on the wet weight basis. Partial drying of chicken excreta within a few hours after deposit reduces odor production considerably. Handling characteristics are also improved by partial drying. The ventilation air exchange through a poultry house evaporates moisture from the exposed wet surfaces of the droppings. Improved ventilation patterns and supplemental heat sources within the excreta deposit area increase the rate of drying. Basic information concerning water movement within the material and over-all drying rates are needed for economical design of in-house drying systems and for systems analysis of poultry house environments. This study was undertaken to develOp drying rate equations for deposited chicken excreta. Laboratory drying tests were made with uniform samples (l0 cm wide by l0 cm long) of three thicknesses (0.32, 0.64 and 0.96 cm). Environmental conditions similar to those found in windowless poultry laying houses were simulated. Supplemental energy was supplied in the form of electrically heated floor panels. Two drying rate periods were observed. As long as surfaces remained saturated, constant rate drying took place. Grant DeWitt Wells The constant rate period was followed by an extended period of falling rate drying. It was found that the constant drying rate was a function of free stream velocity, wet-bulb depression and ambient air temperature as it effects vapor pressure at the saturated surfaces. Process variables of increased surface area and conducted heat source also increased the drying rate. The constant drying rate was predicted on the basis of surface film resistance and concentration gradient terms. More than half of the removable moisture was evaporated from the body surface at a constant rate. Because the rate of shrinkage was not measured, the end of the constant rate period could not be accurately defined, but break points were estimated for each sample tested. The rate of change in moisture during the falling rate drying period was roughly proportional to the removable moisture remaining. The proportionality constant was estimated as a function of the constant drying rate and the sample thickness. The free stream conditions were found to be of major importance throughout both the constant and falling rate drying periods. Indications are that most of the non-hygrosc0pic water moves to the surface in liquid form and is evaporated there. The experimental drying rates were compared to some in-house drying data and were shown to predict the in-house Grant DeWitt Wells drying rates if a measure of the mean boundary layer thickness and area of wet surface was approximated. Wimp/é i Mafior Professor ,5 ,4 3w artment Chairman SIMULATION OF IN-HOUSE DRYING OF CHICKEN EXCRETA By Grant DeWitt Wells A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Engineering l972 To Pixie ACKNOWLEDGMENTS The author wishes to express his appreciation and thanks to: Dr. M. L. Esmay for serving as committee chairman and for his guidance, encouragement and patience; Dr. F. W. Bakker-Arkema for his extra help and encouragement; Drs. A. M. Dhanak and R. Hamelink for their help and support; and the Agricultural Engineering Department for support that aided in the completion of this study. TABLE OF CONTENTS ACKNOWLEDGMENTS LIST OF TABLES LIST OF FIGURES LIST OF APPENDICES. LIST OF SYMBOLS Chapter I. Introduction . l.5 General Remarks. Objectives Some Properties of Chicken Excreta . Typical Environments Encountered in Poultry Enterprises. . . . . . Rate of Excreta Production . 2. Review of Literature: Heat and Mass Transfer. 2.l 2.2 2.3 2.h 2.5 2.6 Introduction . . . . . . . . . . . . . . . Boundary Layer Concept and the Convective Transport Coefficients . . . . . . . . . . Vapor Transfer From the Wet Body to the Surrounding Envinznment. . . . . . . . . Surface Heat and Mass Balance. Surface Constant Rate Drying . Heat of Vaporization and Capillary Potential as They Effect Surface Drying Rates. ll ll l3 IS 16 18 2I Chapter 3. Material Drying Characteristics 3.] 3.3 Falling Rate Drying Periods. . . . . . 3.la Description. 3.lb Modes of moisture movement within the porous body. 3.lc Approximate drying equations for ‘falling rate periods Characteristics of Biological Materials Related to Drying. 3.2a Physical structure, moisture and the hygroscopic phenomena. 3.2b Shrinkage, case-hardening and distortion . . . . . . . . . . Characteristics of Chicken Excreta Related to Drying. . . . . . . . . . . . . . . Selecting the Empirical Model for Drying Chicken Excreta . . . . . . . . . . h.l 4.2 4.3 4.1+ General Comments and Assumption. Assumptions and Development: Constant Rate Period. Continuity Between Periods Assumptions and Development: Falling Rate Drying. . . . Experimental Design and Procedures. 5.l 5.2 5.3 Controlled Environmental Variables Material and Process Variables Collection of Sample Material and Prepara- tion of Test Samples . . . . . . . . . . . Brief Description of Experimental Test Chamber. . . . . . . . . . . . . Experimental Apparatus Test Procedures. . . . . . . . . . . . . . Page 23 23 23 26 28 3] 3l 32 36 38 38 no 1.1 1+2 LIL. an as A6 48 51 5h Chapter Page 6. Regression Analysis and Deve10pment of Drying MOde] . C O O C C O C O I O C O O O O O O O O O C O 58 6.1 Data Summation and Limitations . . . . . . . 58 6 2 Analytical Techniques. . . . . . . . . . . . 67 6 3 Initial Drying Constants . . . . . . . . . . 67 6.4 Initial Constant Drying Rates. . . . . . . . 69 6 5 Conducted Heat Sources and Utilization Efficiencies . . . . . . . . . . . . . . . . 74 6.6 Analysis of the Falling Rate Data. . . . . . 77 6.7 Critical Moisture Ratios and Time. . . . . . 8O 7. Discussion of Methods and Results. . . . . . . . . 85 7.1 Drying Rates as a Function of Time and Moisture Content . . . . . . . . . . . . . . 85 7.2 Factors Influencing Rate of Drying . . . . . 88 7.23 Temperature, Humidity and Air Velocity . . . . . . . . . . . . . . . 88 7.2b Material and Process Factors . . . . . 92 7.3 Volumetric Shrinkage, Shrinkage Water and Stresses . . . . . . . . . . . . . 9h 7.h The Falling Rate Drying Constant and Internal Diffusion . . . . . . . . . . . . . 96 7.5 Some Comparisons with Drying Rates in Existing Housing Units . . . . . . . . . . . 99 7.6 Utilization Rates of Energy Inputs . . . . . 102 8. Summary and Conclusions. . . . . . . . . . . . . . 107 8.1 Summary. . . . . . . . . . . . . . . . . . . 107 8.2 Conclusions. . . . . . . . . . . . . . . . . 108 8.3 Suggestions for Future Research. . . . . . . 109 LIST OF REFERENCES. . . . . . . . . . . . . . . . . . . . lll APPENDICES. . . . . . . . . . . . . . . . . . . . . . . . 116 Table 6.1 6.3 A.l 8.1 8.2 8.3 8.4 8.5 8.6 LIST OF TABLES Experimental and estimated laminar flow drying rates. . . . . . . . . . . . . . . . Experimental and estimated drying rates for heated samples. . . . . . . . . Utilization factors and efficiency. . . . Heat deficits Experimental test-run conditions. Experimental sample data: Initial conditions Constant rate analysis: Unheated samples Constant rate analysis: Heated samples Falling rate analysis Summary . Page 72 76 77 121 125 126 129 132 133 137 Figure 3.1 4.1 5.1 6.1 6.2 6.3 6.4 6.5 6.6 6.7 7.1 7.2 7.3 7.4 7.5 A.l LIST OF FIGURES Equilibrium moisture content of chicken excreta (Sobel, 1969) The basic drying system . Sketch of the experimental test chamber . Drying curves for test-run 1000 . Semi-logarithmic drying curves for test-run lOOO. . . . . . . . . Drying curves for test-run 0300 . . . . Semi-logarithmic drying curves for test-run O300. . . . . . . . . . . . . . . . . Sample temperatures for test-run 0300 . Heated sample temperatures for test-run 1000. . 95 percent confidence limits of estimate for sample No. 1003 . . . . . . . . . . . . Estimated drying rates for runs 0300 and 1000 . Critical moisture ratios with more than one falling rate period . Influence of wet-bulb depression on constant rate drying . Influence of thickness on falling rate drying . Utilization efficiencies. Boundary layer and velocity profile deve10pment along chamber floor . viii Page 33 40 49 61 62 63 64 65 65 84 86 88 9O 90 104 119 LIST OF APPENDICES Appendix Page A.l Hydrodynamics of experimental chamber . . . . 117 A.2 .Evaporative surface heat balance. . . . . . . 120 A.3 Example of normal shrinkage . . . . . . . . . 124 8.] Tables. . . . . . . . . . . . . . . . . . . . 125 LIST OF SYMBOLS Meaning Intercept of linear regression eq. 6.1 Exposed surface area of sample sample dimension Sample dimension Skin friction coefficient Cubic centimeters Specific heat at constant pressure Characteristic length, flow path length of air over sample Diffusion coefficient Nominal thickness of sample Effective depth (Vol/AS) Time derivative Equilibrium moisture content wet basis Exponential Shape factor (a'2 + b“2 + d‘z) Absolute humidity Convective heat transfer coefficient Convective mass transfer coefficient Convective mass transfer coefficient Laminar convective mass transfer coeff. Heat of evaporation Radiation heat transfer coefficient Initial moisture content percent wet basis Units C1112 C111 cm cm3 cal/gm-OC cm cmZ/min cm CITl % cm2 gm/gm cal/hr-cmz-OC gm/cmZ-hr cm/min cm/min cal/gm cal/hr-cm2~OC % Symbol 3 F XL" Re rH Sc Meaning Colburn j factors Drying constant Thermal conductivity Moisture content ratio (m - mel/(mo- me) Moisture content percent wet basis Moisture content Total initial weight (mo + ms) Initial moisture content Dry weight of solids Drying rate Drying rate per unit area Nusselt number Power coefficient of equation 6.3 Barometric pressure Prandtl number (Cpfl/k) Saturater vapor pressure Partial vapor pressure of air Heat flow per unit area Heat flow rate Gas constant for water vapor (4.55) Reynolds number Relative humidity Schmidt number (A /f Del Absolute temperature (273 + t) Temperature Units l/hr cal/hr-cméoc atm atm cal/hr-cm2 cal/hr atm-cc/gm-mole-OK Symbol Meaning Units U Heat utilization factor cal/kgm Ueff Heat utilization efficiency % u Local boundary layer velocity cm/sec V Mean free stream velocity cm/sec Vol Volume cm3 wb Wet basis -- Greek Symbols °< Coefficient of linear shrinkage l/gm X Specific volume cc/gm 6' Boundary layer thickness cm A Difference -- 6 Emissivity -- R Constant of equation 2.19 -- 9 Time hours 14 Viscosity gm/cm-sec 'V Kinematic viscosity cmZ/min ,f Density gm/cc Subscripts a Air b Body, bulk c Constant rate, convection, characteristic cr Critical d Position distance from surface dp Dew point e Equilibrium Subscripts f Falling rate h Supplemental heat i Initial 1 Lower 0 Initial, free stream r Radiation s Solids, surface, saturated v Vapor u Upper wb Wet bulb x . At position x Superscripts and Overscores ' Falling rate ” Flux Rate Mean /\ Estimated xiii 1. INTRODUCTION 1.1 General Remarks A common practice in poultry production systems is to let the chicken excrement drop directly to the floor or pit where it remains until removed. Frequency of removal depends on the type of facilities. After removal, further handling and condi- tioning operations are necessary before the material is finally disposed of, the exact nature depending on the overall operating facilities and the desired end product. Water is a major component of fresh excreta and in most operations, outside those specifically designed for liquid processes, it is a hindrance. Any amount removed from the droppings, even if it is only a small percentage of the initial volume, is desirable in reducing volume and weight of material to be handled. Partial drying of poultry excreta minimizes odor production and air pollution. Still another advantage of moisture removal is that it results in overall improvement of handling characteristics. The situation is favorable for partial excreta drying at the drOpping site within the poultry house. The volume of ventilation air exchange provides sensible heat energy for evaporation, and its ability to absorbe moisture also provides the carrier by which moisture can be removed after evaporation. The random deposition of poultry droppings both in time and space provides surface areas for heat and mass exchange. Supplemental energy inputs may be desirable to enhance the drying situation. Such inputs might include electrical energy in the form of heat (conductive or radiative), mechanical energy in the form of stirring and mixing the droppings to increase exposure, and/or electrical current to expell water from the droppings by the electro-osmosis phenomena as investi- gated by Cross (1966). Preliminary research reports have shown that the use of electrical energy input in floor panels under the collection area in combination with bed stirring can economically reduce the moisture content of the droppings to such a degree that it is seriously being considered as a recommended management practice (Bressler, 1958; Esmay and Sheppard, 1971). However, due to a lack of basic information concerning water movement within the material and over-all drying rates, the optimum solution to each situation must be deve10ped more or less by trial and error. Phillips (1969) found this lack of basic knowledge to be one difficulty in his systems analysis of summer environment for laying hens. Free moisture evaporation from the droppings had to be estimated more or less arbitrarily. He recommended for future research that the actual mass transfer coefficient for evaporation of moisture from the surface of the droppings be determined. 1.2 Objectives It was the purpose of this research to determine quanti- tatively the rate of drying of chicken excreta under the influence of moderate environments such as those found in poultry houses. Complete drying involves several phases or periods of drying as different mechanisms of drying dominate at different moisture contents. Although some sample material was completely dried, the emphasis of this research was on the initial drying phases. Specifically, the objectives were to: (1) Obtain sufficient experimental data to determine drying rates for the initial drying phases. (2) Evaluate drying rates as influenced by environ- mental, geometrical and excreta conditions. (3) Determine the duration of time in which each rate holds and how much water is removed during each period. (4) Develop a semi-empirical mathematical model to predict drying rates in the initial phases. 1.3 Some Properties of Chicken Manure The prOperties of chicken excreta can be classified as physical, chemical and biological. Each class has some effect on drying characteristics of the material. The following discussion is quite general with emphasis on those preperties believed to have the most influence on drying. Unlike most animals, urine and feces formed in the digestive processes of the bird are voided into the cloaca and passed from the rectum in a conglomerate mass. Excrement leaves the body at body temperature (41.90C, 107.50F), but quickly cools to room temperature due to relatively high thermal conductance values, moisture contents and surface to volume ratios. The percentage of water depends on the type and breed of chicken, feed quality and quantity of intake, health of the bird and environmental factors. Environmental factors are important in determining feed and water intake requirements. Fecal water output per pound of feed consumed is directly related to ambient air temperature resulting in excreta of higher moisture content (Esmay, 1969). The range of moisture content has been reported to be from 72 to 80 percent wet basis by weight. Seventy-five percent was the average value used by Sobel (1966). Although reported to be fresh values, it would appear that the samples were collected after some exposure to the atmosphere. Similar values were obtained by such methods of collecting samples for this research project. However, Esmay and Sheppard (1971) and Dixon (1958), report values of 88 percent moisture by collecting samples in oil covered pans. The physical and chemical properties of chicken excreta are known to be affected by the physiology of the bird, the feed ration and the environment. The digestibility of the feed ration, the protein and fiber content and the nature of the other feed elements affect the composition of the excreta, which basically consists of undigested protein, fat, nitrogen free extract, minerals and crude protein. Sturkie (1965) states that a high percent of fecal matter will be cellulose, lignin and other fiberous materials because chickens can digest but very little of these substances. In confinement housing, the waste found in the collection area will also contain feed and water spilled, egg shells and contents from broken eggs, feathers and other ingredients in addition to excreta passed by the chicken. According to Sturkie (1965), the urine of birds contains thick muciod material, and is abundant in uric acid (approximately one part per 100). A number of other complex molecular substances are also present. Sturkie also states that the pH of chicken urine ranges from 6.22 to 6.7, decreasing with increasing consistency, and that the specific gravity is 1.0025. Dixon (1958) reports that urine contains between 95 and 96 percent water. Therefore, the liquid portion of the excreta is often referred to as water and its gaseous state as vapor. Microbiological organisms that actively digest, metabolize and grow in the sub-environment of heat, oxygen, nutrients and water are always present in the excreta collection areas. The oxidation processes are involved and complex. Heat and moisture is produced as a result of this activity, whether the process is aerobic or anaerobic. Exact quantitative values can be determined only by experiment as they will vary depending upon the specific environment. Chicken excreta is composed of discrete organic and bio- logical particles bound together by water in a semi-solid state. The term semi-solid is a consistency term used to indicate that the material does not flow under the force of gravity but at the same time does not exhibit elastic properties of a solid. Excreta with moisture contents of 80 percent or more, approach a semi-liquid state where some flowability can be observed. Sobel (1966) found the particle size of fresh chicken excreta to range from 2.34 mm to minuscule dissolved solids. Approximately 50 percent of the solids were found to pass a 200 mesh screen. This inc1uded dissolved solids. The average particle density ranged from 1.75 to 1.85 grams per cc.** Sobel also reported that bulk density varies from 65 to 67 pounds per cubic food (1.04 to 1.07 grams per cc) with the variation of moisture content from 75 to 80 percent. A quick calculation shows that for these values, fresh excreta contains from two to eight percent void space by volume. Thus, there are three basic components of the material: voids, water and solids. Build-up and settling in the collection pits will reduce the void space and increase the density if little or no water is removed by evaporation. 1.4 Typical Environments Encountered in Poultry Enterprises Successful poultry housing systems provide Optimum environmental control at minimum housing cost per production **Verified by this author. unit. The trend is to the windowless house with mechanical ventilation systems. The birds may be confined to cages, small pens or allowed free movement within the confines of the house. The bottom of the confinement space is usually made of woven wire so that excreta droppings fall through to a storage area below. The storage area may be shallow or deep pits depending on the planned frequency of cleaning. Optimum ambient temperature control is obtained mainly by regulating the ventilation rate. Fifty-five degrees fahrenheit (13°C) is considered optimum housing temperature for cold weather (Esmay, 1966). Ventilation rates are kept to a minimum to reduce heat losses. However, rates of approximately 1/4 cfm (1/2 m3/hr) are recommended by Esmay (1966) to keep moisture from condensing within the structure and to keep down accumulations of dust and odors. Under these conditions, air velocities over the droppings will be very low, approaching static conditions. Relative humidities may be as high as 80 to 85 percent. Summer conditions present different environmental control problems. House temperatures will be approximately those of outside temperatures. However, 2 to 5 degrees of heating are not uncommon. House temperatures that exceed 80°F (27°C) affect production considerably. Temperatures of 100°F (38°C) or above may be lethal (Esmay, 1966). Hot weather ventilation rates are greatly increased to minimize house temperature increases above outside values. From 4 to 6 cfm (6-10 m3/hr) per bird are rec6mmended by Esmay (1966). Lilleng (1969) found that with similar ventilation conditions, the air velocities above the droppings are of the order of 30-60 feet per minute (15-30 cm/sec). Relative humidities are approximately equal to outside conditions with little change in bulk air values within the building. Research by Esmay, et a1. (1966) indicates that the psychrometric change of ventilation tends to follow lines of constant relative humidity. The absolute humidity will increase as the ambient air tempera- ture increases. In Michigan, summer climatic relative humidities vary roughly from 50 to 80 percent. Deep pits offer the Opportunity for increasing the ventilation rate over the droppings independently of the house proper. In such a case, Bressler (1968) utilized air velocities up to 750 feet per minute (380 cm/sec) in the pit area. Electrical energy input through heating cables or panels placed in the floor of the dropping pits are another source of energy input used specifically to speed up in-house excreta drying rates. Energy input rates up to 40. watts per square feet (37 cal/hr-cmz) have been used by Bressler (1968). This high rate was applied only to areas where extra moisture was apt to collect, such as beneath the waterers. Esmay and Sheppard (1971) used heating panels with energy input rates of eight and sixteen watts per square foot (7.4 and 14.8 cal/hr-cmz) in a cage housing situation. Increased drying rates can be obtained by exposing more surface area to the air. Temporary retention of droppings on a fine mesh wire screen suspended between the cages and pit has been used. Thus, the droppings are completely immersed in the drying fluid. The screens must be cleaned at least once daily to avoid build-up which quickly reduces drying efficiency. Droppings from the screens may be moved directly from the house or simply allowed to fall into the pit area. Stirring the drOppings in the pit increases the total surface area exposed at one time by roughing the surface and more importantly it exposes previously covered material. Manually, stirring is usually done once a day, but with automation it could be done as frequently as thought desirable. The simplest form of stirring is by pulling some sort of toothed implement through the droppings. Research by Esmay and Sheppard (1971) indicated that once a day stirring accounted for up to 20 percent increase in water removed by natural ventilation. 1.5 Rate of Excreta Production The magnitude of the drying problem depends on the rate of excreta production. As summarized by Loehr (1969), wet excreta production in pounds per day has been found to vary from 0.03 to 0.08 pounds per pound of live weight or in terms of each 4-5 pound chicken, 0.12 to 0.40 pounds (54-180 gms). Population densities are approaching 1/2 square foot (465 cm2) of floor area per chicken over the excreta collection area. This means that up to 0.8 pounds (360 gms) of excrement is deposited on each square foot (929 cm2) of pit area each day. 10 This amount of excreta contains more than 1/2 pound (225 gms) of moisture that can be removed by drying. Eight tenths pound Of excreta spread uniformly over one square foot would have a mat thickness of approximately 0.144 inches (0.366 cm). Because of the semi-solid state of chicken excrement, the bed thickness will not be uniform under typical housing conditions. The degree of surface roughness depends on the initial moisture content of the droppings, the amount Of drying in the pit area, the time since the area was last cleaned and the system Of chicken confinement. Cones of droppings have been observed to reach the height of two feet in certain cage operations with good distribution Of ventilating air. These cones increase the drying rate because of the increase in dropping surface area exposed to the air stream. Excrement is deposited intermitently throughout the day. It would be helpful to know the average volumetric size of each separate deposition, the frequency of deposition, the randomness of location where dropped and the average surface area exposed to air after being dropped. Perhaps this type of information sounds rather superficial, but as will be noted later, relatively large amounts of water can be removed in periods of hours rather than days. In addition, it is a well known fact that the thinner the material to be dried, the greater the drying efficiency. It would seem that Optimum drying efficiency would be Obtained if each new deposition were dried to the desired moisture content before being covered by a subsequent one. 2. REVIEW OF LITERATURE: HEAT AND MASS TRANSFER 2.1 Introduction The phenomena involved in drying biological, porous syStems are inherently dynamic and complex. However, by reducing the problem to components, it is found that although still complex, some aspects of the problem can be handled with relatively simple physical and mathematic analysis. Drying a moist body always involves the movement of a quantity of water away from that body. For purposes of analysis this process involves two successive phenomena of: (1) migration of water within the moist body to the surfaces in the form of liquid and/or vapor, and (2) conveyance of the vaporized water away from the body surfaces. The factors that control the rate of transfer of vapor from the body to its surroundings are determined by the characteristics of the environment and not by the conditions within the body. 0n the other hand, the rate of moisture movement within the body can be regarded as independent of the external conditions to the extent that boundary values are known or assumed. Some of the important external factors are: ambient air temperature (ta), absOlute humidity or concentration (HO), atmospheric pressure (P), mean free stream velOcity (V0) and a scale of turbulent intensity. Internal factors are less 11 easily separated and defined. Moisture content (m), porosity, density (P), thickness (d), body temperature (tb), and equilibrium moisture content (me) are a few of importance. These variables are not necessarily completely independent of each other. For example, ambient air temperature affects the body temperature and density is related to porosity. Analytically, the phenomena of surface evaporation and internal moisture movement are quite different in terms of controlling factors and complexity. In this chapter, the surface phenomena will be reviewed, in the main, independently Of the drying material. Chapter 3 will be devoted to the phenomena of internal moisture movement with emphasis on hygrOSCOpic, biological materials and specifically with reference to chicken excreta. The rate of transfer of any substance or energy depends on the driving force or potential and the conductance of the media to that substance or energy through which it must pass. In the words of Ohm's law: rate equals conductance times potential. Thus for heat energy Q = hc(tl - t2) (2.1) where he is the conductance coefficient and the temperature difference is the driving potential. A similar expression for mass transfer is m” = hd(H] - Hz) (2.2) where the absolute humidity difference is the driving potential. 13 Keys (1966) states that the transfer coefficients are essentially aerodynamic properties of the system, whereas the terms within the parenthesis, the potential differences, are essentially thermodynamic properties. 2.2 Boundary Layer Concept and the Convective Transport Coefficients The hydrodynamic boundary layer theory as extended to include heat and concentration boundary layers is well docu- mented by Eckert and Drake (1959), among others. The transport coefficients depend on the characteristics and interactions of these boundary layers. Mean transfer coefficients may be Obtained by exact analysis when the flow over a simple geometric surface is laminar. The nature of turbulent flow caused by higher velocities and rough or blunt Obstructions greatly increases the complexity of exact solutions. Analogies between momentum, heat and mass boundary layer formation and transfer mechanisms are often used to relate one coefficient to another. One such analogy has been deveIOped by Chilton and Colburn (1934). The complete heat and mass transfer Chilton-Colburn analogy as given by Welty et a1. (1969) is jH = jD = cf/z (2.3) where: jH = hC(Pr)2/3/JPaVOCp and in = h.($e)2/3/J°avo 14 By this analogy, the mass transfer coefficient is related to the friction factor by hd = cf/gvo/z Sc2/3 (2.4) This analogy is exact for flat plates and satisfactory for other geometric forms provided form drag is not present. For systems with form drag, jH = jD, but does not equal Cf/Z. The evaluation of the mass transfer coefficient from the heat transfer coefficient is possible, and visa versa. This is valid for gases and liquids within the ranges of 0.6‘3x106) is approximately (Eckert and Drake, 1959) Cf = 0.376/Re1/5 (2.6) Thus, the mass transfer coefficient can be calculated using the Chilton-Colburn correlation and equations 2.5 and 2.6 depending on whether laminar or turbulent conditions prevail. Where the body presents an obstruction to the air stream such that form drag is present, the resulting flow patterns 15 around the Object are much more complicated and highly a function of the body geometry. Even where laminar flow prevails there may be points Of stagnation, separation and reattachment which makes it difficult to estimate an over-all mean transport coefficient for the body. However, the form of the skin friction equations suggest the following: hd = (fave/ZSCZ/B’Hm/Re”) (2.7) where m and n are constants depending upon the flow system and must be determined by experiment. 2.3 Vapor Transfer from the Wet Body to the Surrounding Environment The rate of evaporation, m, for a body with evaporative surface, A, is a = hd A(Hs - HO) (2.8) where H5 and Ho are the concentrations immediately adjacent to the surface and in the free stream, respecitvely. For a fluid with nearly constant properties, the mass concentration can be converted to partial densities. In addition, according to Eckert and Drake (1959), if the density can be assumed approximately constant and the temperature difference in the field small as compared with absolute temperature, Dalton's equation is obtained. Thus, R" = hD(pS - Po)/RT (2.9) The mass diffusion coefficient, hD, is equal to the mass transfer coefficient, hd, divided by the density,_fg. The rate of evaporation from a saturated surface is completely determined by the rate at which water vapor can be transferred through the film layer Of air adjacent to the wet Surface and mixed with the main air stream. Thus, for a time the rate of evaporation is independent of the kind of material of the body. The concentration of vapor pressure in the free stream is determined by the thermodynamic properties of the free stream air. The corresponding value at the saturated surface is somewhat more difficult to determine. ’If saturation is complete and no heat is conducted or radiated to the surface, the layers immediately adjacent will be saturated at the thermodynamic wet-bulb temperature of the free stream. The actual surface temperature is influenced by the heat transfer rates and is therefore not solely a function of the air state. 2.4 Surface Heat and Mass Balance Evaporation of moisture from the surface of a wet body involves two processes: (1) a transfer of heat to evaporate the liquid, and (2) a transfer of mass as vapor away from the surface. Heat is required at the surface to change the state Of the moisture., If the only source Of heat energy is supplied as convected heat from the air stream, evaporation is adiabatic. The heat and mass balance for such a steady state is hfgm” = hfghd(HS - HO) = hc(tO - t5) (2.10) where hfg is the latent heat of vaporization. This may be greater or less than that for a free water surface depending 17 on surface effects and liquid properties to be discussed later. To account for heat radiated to the wet surface from the surrounding walls of the enclosure, a second heat flux term must be added to the right hand side of equation 2.10 as follows: hfghd(Hs " 1‘10) = hc(to - ts) + hrItr - t5) (2.11) where hr is the radiation heat transfer coefficient and tr is the temperature of the radiating walls. Threkeld (1970) states that for the case of a small body completely enclosed by a larger body, the radiation coefficient may be estimated by hr = 4.876 ([(Tr/IOO)1+ - (Ts/100)L’]/(tr - t5) (2.12) where {is the emissivity of the wet surface and the temperatures are absolute. Heat may also arrive at the evaporating surface by conduction of heat through the body. In this case, the heat and mass balance of equation 2.11 must include an additional term, such as: k(ts - td)/d, to account for the conducted heat source or sink. Ideally, for the evaporative surface temperature to equal the theromodynamic wet-bulb temperature the heat and mass transfer process must involve pure turbulent mixing only (Threkeld, 1970). At a finite air velocity, the two temperatures, are identical providing that Leg + [hr(tr - ts)]/[:hc(to - tsfl}= I, (2.13) or in the case where the radiating wall temperatures are equal to the dry-bulb temperature of the air, l8 Le(1 + hr/hc) = l (2.14) where the Lewis number, Le - hC/hd. At finite air velocities, radiation heat transfer may compensate for the Lewis number being less than unity. At low velocities, the Lewis number is approximately equal to tne thermal diffusivity,o<, divided by the mass diffisivity, DV, of the air. Rewriting equation 2.11 with equations 2.13 and 2.14 in mind we have HO - HS = K(to - t5), (2.15) where K is the psychrometric wet-bulb coefficient and equals the left hand side of equation 2.13 or 2.14 divided by hfg. In estimating surface temperatures, equation 2.15 can be solved by trial and error or graphically from the psychrometric chart assuming the coefficient, K, can be reasonably estimated. 2.5 Surface Constant Rate Drying Basically, there are two major periods Of drying materials initially saturated. In simple terms, they are called the constant and falling rate periods. During the first, the moisture content of the body changes at a constant rate. The temperature of the body remains nearly constant and as a rule, it equals the wet-bulb temperature of the environment (Harmathy, 1969). Drying takes place from the surface of the body by evaporation of moisture similar to evaporation from a free water surface. The rate is affected largely by the surroundings and little by the material being dried (Hall, 1958). 19 Moisture diffuses or moves to the surface in some manner as fast as the air stream is capable of removing it. In the porous body, it is Often assumed that there are continuous threads of moisture. Harmathy (1969) refers to this as the funicular state. It is characterized by high moisture mobility. There has been much research done on the drying of porous solids and on the drying of hygroscopic porous bodies. It is generally accepted that if a constant rate drying period exists, it takes place at a rate depending only on external conditions. This has been shown to be true with a wide variety of materials and further, the rates differ little from that of a free body of water. See, for example, Gilliland (1938). Most research has dealt with the constant- rate dyring period only in passing (Pearse et al., 1949; Harmathy, 1969; Nisson et al., 1959). Equations 2.8, 2.9 and 2.10 all are suitable for predicting the rate of drying during the constant rate period. The parameter least likely to be known is the convective transfer coefficient. Estimates are usually made based on aerodynamic flow characteristics as suggested in section 2.2. However, in most cases there are certain constants that must be determined experimentally for the particular system in question. In calculating mass transfer coefficients from drying experi- ments, the partial pressure at the surface is usually inferred from the measured or calculated temperatures of the evaporative surface. 20 The use Of the heat transfer coefficient is preferred in estimating drying rates because they are usually more reliable (Bagnoli et al., 1963). Small errors in temperature have negligible effect on the heat-transfer coefficient, but do introduce relatively large errors in partial pressure estimates and hence in the mass transfer coefficient. In the absence of applicable specific data, Bagnoli et. a1. (1963) suggest the following equation for estimating the heat-transfer coefficient for flow parallel to plane plates: hC = 0.01 00-8/0C0-2 (2.16) where G is the mass flow rate of air and Dc is the characteris- tice dimension of the system. The value Of the exponent Of G has been selected to conform with the Colburn j factor for turbulent flow. Krischer, as reported by Luikov (1966, page 143) suggests the introduction of a universal characteristic dimension to be the length of flow round the body. He recommended the following single formula for heat transfer in the flow of air streams with low velocities over bodies of different shapes: NuDC = 0.8 ReDc”2 (2.17) with DC as the length of flow around the body and with ReDc within a range of values greater than 10 but less than 105. FOr mass transfer he recommends: Nud,DC = 0.662 Prl/3ReDCI/2 (2.18) Thus, using the idea of a characteristic dimension of flow around the body, equation 2.7 can be written as follows: 21 hd = QYol-n/Dcn (2.19) q = fam(v)”/2362/3. 2.6 Heat of Vaporization and Capillary Potential a§_They Effect Surface Drying Rates Sobel (1969) found that water evaporation rates from chicken excreta surfaces in still air are not equal to those from a similarly situated body of free water. If in fact the manure surface is saturated and the surface factors control the rate of evaporation, this would indicate that the liquid exhibits characteristics somewhat different from those of a pure water surface. The constant drying rate may be somewhat different than the free water evaporation rate because the liquid surface tension of the urine with all of its soluble contents is different from that of water. It is known that the latent heat of vaporization Of a liquid is related to its surface tension. However, it is not known how much the surface tension of urine differs from that of water. The simplest theory relating heat of vaporization to surface tension is Stephan's equation as given by Paddy (1969): b’(Mo-)2/3 = hfg/Z (2.20) where: the surface tension 0" M the molecular weight of the liquid and U = the specific volume of the liquid. 22 Other equations have been deveIOped to include temperature effects. There are several methods for determining surface tension. In many cases, measurement of the height of capillary rise of the liquid in a small tube has been found satisfactory (Paddy, 1969). A second possible reason for a drying rate different from a pure water surface is that the vapor pressure at the surface may not be the same. Slayter (1967) states that the vapor pressure is increased by a positive pressure exerted on the liquid and decreased by suction. The effect is only appreciable for comparatively large absolute values of pressure, however. As shown by Slayter, capillaries with radius Of curvature of 10'5 cm reduce the relative vapor pressure approximately one percent. 3. MATERIAL DRYING CHARACTERISTICS 3.1 Falling Rate Drying Periods a. Description The rate of moisture diffusion to the surface from within the material eventually falls below the surface evaporation potential. At this time constant rate drying ends and the falling rate drying period begins. The moisture content at the surface of the body is called the critical moisture content and is a characteristic of the material. The average moisture content of the entire body is called the mean crticial moisture extent and as Luikov (1966) points out, is a function Of size and shape, as well as material and drying air characteristics. The moisture content changes at a continuously, decreasing rate during the falling-rate period and the temperature of the body increases (Luikov, 1966). The mechanisms limiting the rate of moisture removal for the two periods are distinct, although all mechanisms may be present to varying degrees throughout. In fact, the transition from the constant rate to a well defined falling rate period may not be sharp. Harmathy (1966) saw need for defining upper and lower critical values for porous systems. The upper was defined as the mean value at the time when the rate of drying first deviated from constant, i.e., the usual definition of critical moisture 23 24 content. The lower was more arbitrarily taken to be at the time when all wet spots disappeared from the surface, indicating that from then on the drying rate would be primarily a function of internal characteristics. For a non-shrinking porous body, the moisture distribution is basically constant until the upper critical point-is reached, then the surface areas rapidly dry to the lower critical point causing the formation of steep moisture gradients at the surface with nearly constant values in the center regions. As the zone of evaporation retreats deeper into the body Of a non-hygroscopic material, the rate continues to decrease as the distance over which the water vapor must diffuse, increases. The rate remains finite.until the last moisture is evaporated from the bottom. For hygroscopic solids the pheno- mena are more complex. The rate of weight loss typically falls Off as drying progresses, but Often not in a single, continuously smooth curve. Distinct break points are often discernable. For example, Gorling (1958), found two break points in the drying ofla potato slice. The first break was interpreted to signify the beginning of evaporation within the porous body and the second occuring when no part of the sample piece contained moisture above the hygroscopic limit. Newitt and Coleman (1952) also discerned two break points in the drying rates Of china clay, a material that shrinks with drying. They postulated that the first period of constant 25 rate drying ends when surface layers have reached a moisture content equal to that of the material with the shrinkage water removed. The moisture gradient was then approximately linear with depth. During the first falling rate period the moisture gradient began to flatten as interior shrinkage water moved to the surface. Newitt and Coleman postulated that most of the shrinkage water was removed before the pore water was affected. During this period, the drying rate decreased at a constant rate as the distance the moisture traversed to reach the surface increased. The surface moisture content was considerably above equilibirum during this period. Eventually, the path became so toturous and the capillary potential so great that the minisci were drawn from the surface and the second falling rate drying period began. The surface moisture rapidly approached equilibrium and the moisture gradient within the material became parabolic. Eckenfelder and O'Connor (1961) comment on the air drying Of sludge from waste treatment plants. These beds initially contain as much as 95 percent water. They state that the drying process occurs in three stages, namely: a constant rate period, a falling rate period and a subsurface drying period. During the constant rate period, the sludge is completely wetted and the rate Of evaporation is independent On the nature of the sludge and approximately the same as evaporation from a free liquid surface. 26 b. .flgggs of Moisture Movement Within the Porous Body The moisture is transferred through the membranes and porous structure of the material as liquid and/or vapor. Hall (1958), lists five possible mechanisms that may control internal movement of moisture in agricultural products: (1) Diffusion as liquid and/or vapor (2) Capillary action (3) Shrinkage and vapor pressure gradients (4) Gravity (5) Vaporization of moisture. Gorling (1958), also pictures five physical mechanisms as being involved during the drying of materials such as wood, potato or macaroni. They are: (1) Liquid movement under capillary forces (2) Diffusion of liquid caused by a difference in concentration (3) Surface diffusion in liquid layers adsorbed at surface interfaces (4) Water vapor diffusion in air-filled pores, caused by a difference in partial pressures and (5) Water vapor flow under differences in total pressure, as for example in vacuum drying under radiation. These are a little more specific and not quite the same as those listed by Hall because of the nature Of the materials and drying processes involved. Number 4 would exist if a temperature gradient existed in the moist body. 27 Fresh chicken excreta contains a very high percentage of moisture and exhibits high volumetric shrinkage. Therefore, liquid movement and retention by the forces of osmotic inhi- bition and capillary suction are of the most interest here. Gravitational forces are considered to be relatively unimportant. The physical unbalance of forces at an interface between a liquid and a gas or vapor produces the effect of a suction on the liquid. A wetting liquid will rise in a small tube due to this suction. Liquid will move from a region of lower potential to one of a higher potential. In a porous body, a narrow pore will draw water from a larger pore. Water will distribute itself in this manner until all potentials are equalized. Thus the porous structure of the system is very important in analysis of water movement by this method. Pore water is dependent upon the inter-molecular attraction between solid and liquid and is common to all solids when wet. A certain class of porous solids exhibit an additional potential of electrochemical suction. These solids can imbibe osmotically an amount of water depending upon a quantity known as the base exchange capacity. Coloidal particles and organic humus material exhibit very high base exchange capacities (Slayter, 1967). These materials exhibit shrinking and swelling phenomena with desorption and sorption of water. 28 Newitt and Coleman (1952) do not consider capillary action responsible for the swelling and shrinking because of the required presence of a gas phase. They found that no such phase was necessary for clay to develop imbibitional suction. Newitt and Coleman consider pore-water to be substantially immobile because Of its adsorbed nature and postulate that it vaporizes in situ. 0n the other hand, electrochemically adsorbed water is much more loosely bound and more likely to move to the surface under the influence of osmotic potential before evaporating. Therefore, Newitt and Coleman feel that it is this water that is associated with shrinkage and is referred to as shrinkage water. In any case, it is a potential difference that causes water to move from one point in the system to another. When water is removed from the surface of a shrinking body, the discrete particles move closer together. The pore space between the particles thus exhibit a greater suction potential and are capable of drawing water from the larger pores within the material. Water is drawn from the interior through the narrowing channels at rates dependent upon the strength of force and viscous resistance Of moisture to flow. This process can continue as long as there are continuous threads of liquid. c. Approximate Drying Equations for Fallinijate Periods The falling rate can frequently be expressed with fair accu- racy by the following equation (Lapple et al., 1955; Hall, 1957); dm/dO =-Kf(m - me) (3.1) 29 The value of the drying constant, Kf, depends on factors affecting rates of internal and external moisture movement. If the initial moisture content is above critical so that a period Of constant rate drying proceeds the falling rate period, by continuity, the falling rate drying constant is a function of the constant rate as follows (Lapple et al., 1955; Bagnoli et al., 1963): -Kf(mcr - me) = dm/de)f = dm/d0)C (3.2) where 9 = ch. Thus: Kf = (dm/d0)C/(mcr - me) (3.3) This approximation is especially suited for the period of unsaturated surface drying where the entire evaporative surface can no longer be maintained saturated by moisture movement within the material. The drying rate decreases for the unsaturated portion and hence the rate for the total surface decreases. Internal moisture movement is controlled by capillary flow and drying time varies inversely as thickness (Bagnoli et al., 1963). For drying periods governed entirely by internal moisture diffusion, Fick's Law is applicable. It states that the flux is a product of the gradient of the concentration and the effective diffusion coefficient, De. It can be shown (Jason, 1958; Carslaw and Jaeger, 1959) that the solution for a three dimensional slab is 30 m - m 8 2 D D D e 2:172 exp [-77 ( X41- y+ 2)]9 (3.4) D D D 90—-717;(X+__y_+_f- (m-m.) (3.5) de 4 23-2. b2 (:12) If the medium is isotropic, 0x = Dy = 02 = De- Equation 3.5 is identical to equation 3.1 with Kf = 717308 F, where F is the shape factor and equal to (l/az) + (l/b2) + (1/d2). The diffusion coefficient has been regarded as a constant. Thus, Kf should be proportional to the shape factor, or inversely as the square of the thickness in situations where a and b are much greater than the thickness, d. Thus far, it has been tacitly assumed that shrinkage does not occur. Calculations are based on initial dimensions. Danckwerts as reported by Fish (1957) handled shrinking systems by allowing the coordinates to shrink with the solid portion of the system. He has shown that where it can be considered constant, the diffusion coefficient is invarient with body size and shape and the shrinkage factor can then be ignored. 31 3.2 Characteristics of Biological Materials Related £2 Drying a. Physical Structure, Moisture and the Hygrosc0pic Phenomena Biological substances are characterized by complex and heterogeneous physical structure, of which water is an ubiquitous and fundamental part. Moisture contents of the different consti- tuents may differ widely at equilibrium even though temperature and vapor pressure may be equalized throughout. In the course of drying shrinking materials the distance through which water must travel to reach the surface is decreasing, but if the material contains cellular tissues, the number Of cell walls through which the water must pass does not change. In view Of these complex relationships the term ”moisture content'I must be defined in terms of the exact procedure used to physically determine the quantity. The hygroscopic point has been defined by Lewis (1921) as the product moisture content corresponding to a relative humidity of 100 percent. In general, a body with greater mois- ture content is saturated. The term ”free moisture” isused to mean that moisture not bound to organic particles as chemical or adsorbed water, or in other words, water contained above the hygroscopic limit. IIRemovable moisture” refers to all moisture that will be removed from the material upon drying to its equilibrium moisture content (Van Arsdel, 1963). It is represented by the expression, m - me, where m is the amount of moisture present in grams and me is the amount of moisture contained in its equilibrium state. 32 Physically, if the material is saturated, it is a two- component system of water and solids, and if not, a three- component system of water, solids and gas (air). A hygroscopic material exhibits a surface phenomena called sorption. Water bound to the body in this manner is called adsorbed moisture. The bonding may be physical, chemical, or both. The amount of water held in this manner is described empirically as a function of pressure and temperature. The relationship between the amount of vapor adsorbed by a solid and the vapor pressure is represented by the moisture equili- brium isotherm. Moisture sorption isotherms of biological materials are noted for their striking S-shape and the phenomena of hysteresis. Hysteresis is the difference between equilibrium moisture content at a given vapor pressure according to whether the equilibrium point was reached from higher or lower moisture contents (Van Arsdel, 1963). A limited number of equilibrium moisture isotherms have been determined for chicken excreta by Sobel (1969) and are included here in Figure 3.1. Values obtained from this figure were used extensively in analyzing the data of this research. b. Shrinkage, Case-hardenfgg and Distortion By analogy with the definition of the coefficient of thermal expansion, the linear shrinkage with uniform moisture distribution has been characterized by the coefficient of linear shrinkage (Gorling, 1958) as follows: I T fi I I 48 32 . 4 4 30 fl 40 28 36 26 , a 2 32 24 m >~ 23 22 4, g 13 g 20 ~ 24 S 8 6118 1 I M E g: 20 16 I E 16 g 1“ (0:27 ca 1 E 0.. 00 000° / 8 12 gas- ,1}. / 12 O E 10 .1 31 0 9° . 1'5; / . 1100?) s 8‘-———7I “3. GK 2 8 “ 6 «1 4 4 2 .1 ‘ A ‘ ‘ L L ‘ 0 10 20 30 40 50 60 70 80 90 RELATIVE HUMIDITY - rH - PERCENT Figure 3.1 Equilibrium moisture content of chicken 33 excreta (Sobel, 1969) 100 34 °<=(1/ao)(Aa/Am). (3.6) As long as this relation holds, the shrinkage is called ”unrestrained” or “free”. Where additional forces caused by adherence or friction are present, the shrinkage is restrained. During drying processes, the material layers next to the surface dry more quickly, so that the tendency to shrink is higher there but is restrained by the adjacent layers due to inner friction. Thus, shearing stresses appear along layers parallel to the surface, and at right angles there are either compressive or tensile stresses (Gorling, 1958). These stresses may cause deformations or, if the tensile strength is exceeded, surface cracks. The tensile strength Of materials composed of discrete particles is relatively low. Increased drying rates cause greater moisture gradients and more cracking. Chen and Rha (1971) investigated the shrinkage in dehydration of grapes and found that volume change was an exponential function of drying time in much the same manner as was moisture content. It was not stated how this would effect the diffusion model for high moisture foods. Volume change of shrinking materials can follow different patterns for different moisture ranges. Philip and Smiles (1969) use the terms ”normal“, ”residual” and “zero” to 35 describe patterns of volume change in collodiul soils. In the normal range, the material behaves as a two-component system and shrinks in direct proportion to the amount Of water removed. The zero range is the other extreme where no volumetric change occurs upon drying, and residual refers to that range in between. Formation of a crust like shell may occur while the interior of the body is still wet. This is sometimes called ”case hardening” (Van Arsdel, 1963) and is a result of structural change and/or bonding by solute constituents. Soluble constituents such as sugars may migrate within pieces as drying occurs and be separated from the water by membranes. In addition to increasing the resistance of water flow through the membrane they may act as bonding agents as the shrinking system forces the particles together. The result is that resistance to moisture movement through these layers become much greater. A drastic decrease in drying rate will occur even though the mean moisture content of the body is relatively high. Van Arsdel (1963) states that if migration Of solutes or a chemical reaction does not change the character Of the surface there is no advantage to preventing surface structure formation by slowing the initial drying rate. The moisture in the body always distributes itself through the solid in such a way that a low diffusivity in a zone of low-moisture content is compensated by a steeper moisture gradient in that zone. 36 Van Arsdel also states that the existance of a ”wet center“ is a condition which favors the most rapid further drying. 3.3 Characteristics of Chicken Excreta Related to Drying The main points of the following discussion are taken from the article “Removal of Water from Animal Manures,” by Sobel (1969). Drying relationships established for agricultural products such as hay and grains, and for sewage sludge cannot be applied directly to animal manures because of their empirical nature. However, it has been established by Sobel and others that chicken manure has drying characteristics similar to other agricultural hygroscopic materials, such as, for example, equilibrium moisture contents and drying rates. The following conclusions were made by Sobel: a) Removal of water from chicken excreta results in a reduction in weight and volume. b) The offensiveness of the odor of chicken excreta decreases with a decrease in moisture content. c) Equilibrium moisture content of chicken excreta is comparable with other agricultural hygroscopic materials. Typical values for equilibrium moisture content at 70 F (21°C) are 19% w.b. at 90% rH and 9% w.b. at 10% rH.** d) Drying times for chicken excreta under minimum velocity or “static” conditions are in terms of days. Typical drying times to equilibrium for the standard sample used at 80°F (26.70C) were 45 hours at 35% rH and 70 hOUrs at 56% rH.*** **For shelled corn equivalent values are: at 77OF(250C), 19.6% at 90% rH and 5.1% at 10% rH (Hall, 1958). ***Standard sample thickness was 1/4 inch (0.635 cm). 37 e) Variation within samples has more effect on drying than humidity variation within a t 15% range of relative humidity. f) Reducing the thickness of the droppings has significant effect on the drying characteristics. The droppings must be thin, e.g. 1/4 inch, to enhance drying. g) The.loss of water from excreta surfaces are less than that from a free water surface. Constants required for determining drying rates depend on environmental conditions, excreta characteristics and inter- action between the material and its media. Parameters such as diffusivity and heat conductivity are difficult to establish for any biological material and especially so for materials Of extreme heterogenity and biological variability as in the case of chicken excreta. In all likelihood, material parameters will vary with moisture content. No numerical values have been reported for chicken excreta. Sobel also found that chicken excreta exhibited considerable shrinkage upon drying, as much as 50% when air dried from 75% w.b. to equilibrium moisture content. In addition, he found considerable cracking occuring as drying proceeded, cracking similar to that of cohesive soils. 4. SELECTING THE EMPIRICAL MODEL FOR DRYING CHICKEN EXCRETA 4.1 General Comments and Assumptions Most drying models are empirical, or at most, semi- empirical in nature, based on experimental data and verified by how well they predict actual results. They are phenomeno- logical in that they predict what will happen but not how. The reason for any mathematical drying model is to predict moisture contents at a given time (or the amount of moisture removed Over a period of time) or the time required to reach a given moisture content. Drying data are most frequently presented in the form of drying rates, dm/dO. The rate of drying can usually be quite accurately described as a function of the moisture content of the drying body. Rate equations are straight forward in compu- tational procedure but strictly empirical in nature. Drying constants must be determined by experiment for each new system. Direct integration of drying rates is theoretically allowable only if the rate of drying is strictly determined by the value of its mean moisture content and not at all by its previous drying history (Van Arsdel, 1963). This is never exactly true and further empirically restricts the methods. Break points in drying rate curves indicate different dominating mechanisms involved in moisture movement. Better drying estimates are possible if distinct drying constants 38 39 are determined for each apparent period of drying. However, transition from one period to another is Often gradual and the break point itself must be estimated. As stated in the Objectives, this research will be primarily concerned with the initial phases of drying of fresh chicken excreta including constant and initial falling rate periods. Rate equations will be used for prediction. Because of the distinct difference in mechanisms of drying and the factors involved, two distinct prediction equations are anticipated. However, drying is a continuous process. The equations must be compatable at the critical time when the rate changes from constant to falling. This compatability may be Obtained through establishing initial conditions for each period based on the final conditions Of the previous period. The basic drying system to be analyzed is sketched in Figure 4.1. The drying body was dimensiOns of: a, the length parallel to the flow of air; b, the width perpendicular to the air flow; and d, the thickness. The surfaces are assumed hydraulically smooth and laminar flow conditions are assumed to prevail in the free stream. The top and four sides of the body are unrestricted and exposed to the air stream. The bulk free stream prOperties are maintained constant throughout the drying process and are unaffected by the process. 4O drying body (£11 / / Figure 4.1 The basic drying system 4.2 Assumptions and Develppment: Constant Rate Period The term, constant rate drying suggests that, during this period the rate will be constant and that it is simply a matter of evaluating this constant in terms of those factors that control the mechanisms of heat and mass transfer to and .from the body. The basic assumptions are that the body surface remains saturated and the adiabatic evaporative process prevails throughout the period. It is further assumed that no period of conditioning is required before the beginning Of the constant rate period. Under these conditions, equation 2.9 can be used to _predict the rate of moisture removal. Equation 2.9 is reproduced below for convenience. m“ = hD(Pa - PS)/RT (4.1) The transfer coefficient, ho, takes the form of equation 2.19 with the characteristic length equal to a + 2d. Integration of 4.1 gives 41 m - m0 = [hD(Pa - Psl/RT] 0 (4.2) In terms of moisture ratio this is equivalent to M = 1 - KCQ (11.3) The drying constant, KC, is equal to the absolute value Of [hD(pa - ps)As/RT(mO - mei], and is dependent on the ambient air temperature, the wet-bulb depression, the free stream velocity and the body characteristic length. In the development of equation 2.19 it was tacitly implied that the drying bodies were located far enough from the walls of the experimental chamber to be unaffected by the develop- ment of the momentum boundary layers along these walls. This is not the case for the situation depicted in Figure 4.1. However, it will be assumed that the basic factors affecting the deve10pment of the drying equations still hold and that the experimentally determined constants will allow for the differences in the systems geometry. The momentum boundary layer thickness at the wall of the experimental test section is estimated in Appendix A.l. Equations 4.1 and 4.2 apply for all drying times between zero and the critical time when the mean critical moisture content is reached and the falling rate drying period begins. Thus, as long as the surface is saturated, the rate Of moisture removed per unit area is constant. 4.3 Continuity Between Periods The transition from constant to falling rates will be gradual. Theoretically the constant rate period will end 42 when the first water miniscus recedes into the body. Because of the shrinking nature of the material there is a time difference between the first deviation from constant rate drying and the complete disappearance of the surface pore water [)ower critical point of Harmathy (19697] . Therefore, the critical break point between constant and falling rate periods will not be well defined. To satisfy the condition of continuity pw=pgate=ep (40 where the critical time, 9cr, is the time of the first deviation from constant rate. The critical time is directly related to the critical moisture ratio by equation 4.3 as follows: Gcr = (1.0 ' MCF7/KC (4.5) 4.4 Assumptions and DeveIOpment: Falling Rate Drying Definition of conditions during the falling rate period are much more difficult. Physical shape and internal charac- teristics make the problem extremely complex. The aim will be to develop a phenomenological rate equation of the type of equation 3.1, where the rate is a function Of the mean moisture content of the material. Equation 3.1 is dm/dOf = -Kf(m - me) (4.6) As shown in Section 3.1c, the drying constant, Kf, is a function of the constant rate and the critical moisture content as follows: 43 Kf = Kc/Mcr (4.7) Thus, by this relation, the break point between the two periods of constant and falling rate is not as physically defined in the previous section but exactly determined by the ratio of drying constants. This more accurately defines the break point in analytical terms in the case where the transition is not well marked. Shrinkage occurs throughout the drying process. However, original dimensions will be used as a basis. Shrinkage causes internal changes, but it will be assumed that these changes are a function of moisture content and not shape. From previous discussion, it would be logical to expect more than one distinguishable falling rate phenomena. However, only the first falling rate constant will be determined. 5. EXPERIMENTAL DESIGN AND PROCEDURES 5.1 Controlled Environmental Variables The controlled environmental factors were: ambient air temperature, thermodynamic wet-bulb temperature (absolute humidity) and free stream velocity. The barometric pressure was assumed constant at one atmosphere. Air flow was assumed laminar. The range of air temperatures and velocities used for the experiments were somewhat higher than those anticipated in summer housing conditions in order to Obtain better control and measure of these variables. It was difficult to maintain high humidities at lower temperatures with existing laboratory room temperatures. Higher temperatures were advantageous in that faster drying rates were obtained, thus decreasing the time required for each test. Velocities of less than 25 cm/sec (50 ft/min) were difficult to maintain constant and the air conditioning unit was designed to best handle some- what greater mass flow rates. Ambient air temperatures were controlled at values of 70 (21.1), 80 (26.7), 82 (27.8), 85 (29.4) and 90 (32.2) degrees fahrenheit (centigrade). Velocities were maintained at 50 (25), 150 (76), 240 (122) and 290 (147) feet per minute (centimeters per second). Absolute humidities ranged from 44 45 74 to 136 grains per pound of dry air (0.0106 to 0.0194 gm/gm or Ib/lb). Corresponding relative humidities ranged from 40 to 76 percent and the wet-bulb depressions from 7 to 190F (4 to 1100). Selected values were held constant throughout each run. 5.2 Material and Process Variables The only two material variables measured were initial moisture content and density, and these were not specifically controlled. They were found to vary randomly between 75 and 80 percent moisture content wet basis and 1.05 to 1.25 grams per cc, reSpectively. Age was also a material variable, but harder to define in quantitative terms. Most sample material was not older than three days, but in some cases was more than one week old; old enough that biochemical changes were apparent through color and smell. Process variables include body shape and thickness, surface area and additional conducted heat input. Three primary thick- nesses were used. They were: 1/8 (0.317), 1/4 (0.635) and 3/8 (0.952) inches (centimeters). Almost each run included at least one sample of each thickness. The sample shape was basically unchanged for all tests at 4 inches (10 cm) wide by 4 inches (10 cm) long. A few were 8 inches (20 cm) long. Two levels Of surface area per thickness were obtained by placing the samples either on the floor of the test chamber or suspending them in the air stream on wire screens. The suspended samples effectively had almost twice the evaporative surface area. 46 Because of the extreme shrinking characteristics of the material, it was difficult to cover the sides such that no drying occured there and at the same time avoid effecting the normal shrinking patterns. In addition, there was the problem of keeping the top layer flush with the protective sides. It was decided to leave the sides exposed to the air stream and increase the tOp surface area to reduce the relative edge effects. The top to side area ratios were: 7.9, 4.0, and 2.6 for the respective thicknesses. The thinnest thickness possible was about 0.3 cm due to the fiberous content of the material. Larger body dimensions of length and width insured a more representative material sample but, on the other hand, increased the difficulty Of forming a continuous sample. Also, the experimental apparatus limited the sample size. The experimental apparatus included two test sections. One section was provided with an electrical heater to supply additional heat input. The range of additional heat supplied was from 30.6 Btu/hr-ft2 (8.4 cal/hr-cmz) to 100 Btu/hr-ft2 (27.1 cal/hr-cmz). 5.3 Collection 2i Sample Material and Preparation gfi Test Samples Chicken excreta was collected from one of the caged laying houses at the Michigan State University Poultry Research Farm. All material was collected from the same group of hens over a period of one month. The environment was typical to that 47 encountered in mild summer weather. Most of the sample material was collected within three days after deposit in plastic bags to prevent drying by natural ventilation. The rest was collected directly from the open pit area. The amount of spilled water and feed in the sample material was minimized by the collection techniques. The material was stored as collected in sealed bags at refrigeration temperatures of approximately 7°C for one day to allow for moisture equalization throughout the material. The material was removed from the refrigerator 2-3 hours before the test samples were made. Samples were formed by spreading 1/8 inch (.31 cm) layers within a 4 by 4 by 1/8 (10 x 10 x .317 cm) form. The 3/8 inch samples were composed of three such layers. The resulting density ranged from 1.10 to 1.25 gm/cc. It will be noted that this was considerably greater than the fresh excreta values reported by Sobel (1966). There was no correlation between thickness and material density or initial moisture content. Some samples were formed using minimum disturbance techniques. The material was collected on plates with the excess material trimmed away to form the test samples. The fiberous nature of the material made it difficult to obtain smooth surfaces of constant dimensions. The density of these samples were approximately 1.05 gm/cc. One additional sample was tested completely undisturbed. In this case the surface area could only be roughly estimated. 48 The object of molding the samples wasto Obtain hydrauli- cally smooth surfaces of known area. All samples, except the two surface drying samples, rested on l/8 x 5 x 5 inch (.31 x 12.7 x 12.7 cm) plexiglas plates. These plates were required so that the samples could be removed from the experimental chamber for weighing. The two surface drying samples rested on screens of approximately 40 gage wire were 0.3 cm Openings. The two surface samples were somewhat thicker than nominal dimensions because some of the material was squeezed into the grid openings upon forming. 5.4 Brief Description g£_§xperimental Test Chamber The following discussion will be clarified by referring to Figure 5.1. The experimental chamber consisted of a settling chamber, two test sections and an exit section. Conditioned air entered the settling chamber through a 10 cm diameter pipe. The air was spread by diverging walls and screens into a 12 x 26 inch (30.48 x 66 cm) plenum chamber. Then it passed through a converging throat, two screens and a honeycomb flow straightener into the main test chamber measuring 4 inches (10.1 cm) deep and 26 inches (66 cm) wide. The flow straightener was 1.4 cm thick with 0.25 cm Openings and was located approximately 30 cm from the leading edge of the samples in the first test section. 49 LOnEmzu ummu _mucoe_coaxe ecu wo cubmxm _.m OL:m_u muocmunwamuuw 30am N .02 ”OH” H .02 60H“ can wcwaooo coauuuo Ocauoou mcweuon no wawumeaillIII/ri sane uaou unsn umou MHIAWMWI p/v Own/r / M0 L1 .w HO OH m A ///////1/// /(f///y/Jh//Q///A~VA w Pmuuom 36006 W 7/ / / / / doauwaamcfi mo an m a“ cowuuum uuau anOHOOO Message Ouauam 3MH> A¢onHoum1mmomu mon —\I n r 4 LP AV — E0 HC ‘— EU 00—. ‘— 8 OWll /.V./r////././/////m/r// J/./,// // // z/M/r//./r/////r //;, /r;///;/;/ / / / / A1 uno A115” “Hm ’///A p,‘_._ um 99__._. v ////.//////// ///// /////// // manna; uonv Hum r. IILr I») cofiuoem OHxO_waHumuOHOOOO coauoem umau Gama Alp/I II I! 1! Kl— ( L Hensmno wnaauuwm SMH> Aczo mc_>co _.o Ocam_m ammo: a O 1 NZHH wszmn m¢ ¢¢ CO @m an mu «m ON ea NH w w o 61 11d] / / Hoo 9 . lfillxr/l N o I as l/rA” mnmo.$ 6.0 sec. Oaumm oupumwozpawowufiuo o m.o . memo. m .8 3.0 u a 83 62 625m x .8 3.0 u 6a 82 .oz 6353 o N801H:\HOO N.Na u a “OOHAEOO vmumem lem w .8 3.0 u 6 82 .oz 6268 4 so m~.o u 66 mood .oz mfiaawm o 00m\:~0 “N u > 33 m a a ooaH n u 00mm n u "msowuavcov HHfllSION OILVH N 62 00 000. c301um0u to; mO>Lau meOS I 0 I NZHH quwmn 00 N m «a ea 0 0 00 00 mm=0= 1 O I HZHH wzHrmn um «N as w ./ H _ 0 0 a .— ucaoe couuoeamaa 0 .~.0 unawum you on mama “unawumuoa 0cm ecoauwwaoo 000. nma~.0 H0. HHHISION «0.. 00. OILVH 00. 00. Amuse. ~.0 N m:_>cn O_E;u_cmmo_-_EOm ~.0 Ocsm_u N0. 00. 00. H.0 N.0 «.0 0.0 0.0 0.H HHHISION OILVH ‘N M RATIO MOISTURE 0.5 (.0470 .0728 0.114 0.4 \ 0.3 \ \ 0.2 \ 0.1 \ 0 4 8 63 Conditions: ta - 32°C, twb - 26°C, V - 122 cm/aec Sample NO. de (cm) 0 0301 0.28 A 0302 0.51 D 0303 0.69 x 0308 0.21 (2-surface) 0 Critical Moisture Ratio O . 0340 Figure 6.3 DRYING TIME - 9 - HOURS Drying curves for test-run 0300 64 0N 0N oomo CDLIOmOu Lo» mo>cso mc_>cv O_E:u_cmmo_1_EOm :.0 OL:m_u mMDOS 1 0 1 MZHH UZHNMG 0N 0H 2 a 6 a 4 d 1 unwom acuuooamcw O _ «00. mmoA 000. / 8. mum. N0. «0. H.0 ~.0 «.0 w r/ 65 _ 0.H HHDLSION OIIVH N. / 0N «N mMDOE I 0 I MZHH wszmn 0N 0H NH 0 T P _ fl .m.0 ou:m«m “Om we made "meowuauO: van macaufivaoo a 05H. namo t «0. 00. H.0 0.0 0.0 0.0 0.H HHfllSION OIIVH N 65 32 1 1 I 33 Temperature sample effective , thickness - 0.28 cm. 5930 F— Conditions: ta 8 32°C, I 3 0 .fl twb 26 c, g V - 122 cm/sec 91 28 g r >4 5:26 in O 4 8 12 16 20 24 28 C BODY TEMPERATURE - tb - ° DRYING TIME - O - HOURS Figure 6.5 Sample temperatures for test-run 0300 l I 7‘ Temperature sample effective thickness - 0.51 cm. 0 Conditions: t8 = 27 C, 36 --- U b O 1———- twb 19 C, V = 25 cm/sec W N DJ 0 28 26 0 32 40 48 DRYING TIME - 9 - HOURS Figure 6.6 Heated sample temperatures for test-run 1000 66 Bias may result through the data recording time sequence relative to the beginning Of the falling rate period or through undetected nonrandum measurement error. In some cases it is possible to combine data from more than one sample to improve on the reliability of the estimates. These are also noted. Another minor limitation arose from the fact that, in order to shorten the time required for experimentation, most samples were not dried to equilibrium. Equilibrium moisture contents are assumed using the results reported by Sobel (1969). (See Figure 3.1) Low values of the moisture ratio, M, are extremely sensitive to small errors in equilibrium moisture content, but relatively insensitive to such errors at high values. Immediately evident from Figures 6.1 and 6.3 is the presence Of an initial period Of constant rate drying, or at least a period that can be approximated by a constant rate model. Therefore, as suggested in previous chapters, the analysisfbr the initial period will be separated from the following falling rate period or periods. Determining the break or critical point between the constant and falling rate periods is a major problem. Preliminary tests indicated that uncontrolled sample variability could cause as much as plus or minus five percent variation from the mean in drying rates. This variability becomes Of primary concern in the analysis Of the falling rate period because of its dependence on material characteristics. 67 6.2 Analytical Techniques Drying rates for each sample were approximated by straight lines fitted to the drying data by the least-squares method. For the constant rate period this line was linear with respect to time and for the falling rate period the rate was assumed expOnential with time (See Figures 6.2 and 6.4). TO relate the drying constants and rates to the inde- pendent environmental, process and material variables, multiple regression and least squares elimination procedures were used where other methods and theories could not be applied. For all of the statistics calculated, it was assumed that the dependent variables are normally distributed random variables with (1) mean based on the value of the independent variables for each observation, (2) constant variance over all Observations, and (3) independence between observations. Michigan State University computer facilities as well as those Of the Agricultural Engineering Department were used for these calculations. The Michigan State University Agricultural Experiment Station routines for the CDC 3600 computer were used extensively. The computer programs used are relatively straight forward. 6.3 Initial Drying Constants The initial portion of the drying curves can be approximated very well by straight lines fitted by the least- squares method. There slopes are the bulk drying constants, 68 KC, of the sample for the constant rate period. The initial portion of the drying curves are straight lines without correc- tion for change in surface area, even though some volumetric change was observed during this period. The regression equation is M: A - KCO (6.2) The number Of points used were determined by trial, using the standard error Of estimate and confidence limits to indicate at what time the drying rate deviated significantly from constant. In most cases, the plotted data quite clearly indicated where the experimental measurements began to deviate from the initial straight line. It was a simple matter to calculate the linear regression using those points that fell on the line and check the correlation between the two variables. Then one additional data point was added to the number of Observations used in the analysis and again the correlation checked. Often two calculations were sufficient to find significant deviation. The standard error of estimate did not exceed 0.005 and the confidence limits at the 95 percent level were well below plus or minus five percent of the estimated value in most cases. At the beginning Of the drying period, the moisture ratio is ideally equal to one. This point was not used in the analysis because of possible non-linear conditioning periods. In all cases, the first data point used occured between one and two hours after the beginning of drying. Even so, the 69 estimated straight line passed very close to one at zero time. Often, the value of one fell within the 95 percent confidence intervals of the estimated intercept. These results are shown in Table 8.3 for unheated samples and Table 8.4 for heated samples. Ninety-five percent confi- dence limits are listed in column (5) in terms of percent of the calculated value recorded in column (4). In column (6) are the intercept values, A, of the regression analysis. It should be noted here that although the correlation between the moisture ratio and time (better than .999) is very good, close examination of the regression equations, its intercept and SIOpe, their conficence limits and change as data points are added one by one, indicate a very slight concave tendency. There is some evidence of a change in surface area by body shrinkage. However, the straight line estimate fits the data so well that the initial drying period will be considered constant without correction for surface area changes. 6.4 Initial Constant Drying Rates To obtain the constant drying rates, equation 6.2 is differentiated with respect to time. The resulting rate equation for the constant rate period is m = -KC(mO - me) (6.3) Dividing by the evaporative surface area gives the rate per unit area or dividing by the weight of solids in the sample, 70 ms, gives the rate per unit solid. These two rates are listed in Table 8.3 in columns (7) and (8) and in Table 8.4 in columns (10) and (11) for the heated samples. The rates per unit area are nearly the same for all sample thicknesses within any given run. Thinner samples tend to show rates less than the thicker because they are more affected by the hydrodynamic boundary layer of the test chamber walls. The theoretical thickness and the local velocities within this layer are calculated in Appendix A.l. It was shown in Chapter 2 that surface evaporation rates from free water bodies are a function of convective transfer coefficients and a concentration potential difference. Combination of equations 2.9 and 2.19 gives the following relation between drying rate and the independent variables that effect drying during the constant rate period: rin" = q(V]'”/DC”)(Pa - P5) (6.4) Laminar flow over a flat plate with length equal to sample length will be considered first. The coefficientsriand n are 25.0 and 0.5, respectively. The vapor pressure at the surface is assumed to be the saturated vapor pressure at 1/2°C above the thermodynamic wet bulb temperature of the air. This value of vapor pressure is selected for two reasons. First, experimental temperature measures indicated body temperatures approximately 1/2 degree higher than the measured wet-bulb temperature of the air during the initial drying period. 71 This, in itself does not demand that the surface temperature also be higher. However, surface heat and mass balance equations using the Colburn analogy to estimate the convective heat transfer as a function of the mass transfer coefficient, show a heat deficit. (See Appendix A.2 for details). It is assumed that there is either heat production within the body or that heat is conducted through the body, thus raising the average body and surface temperatures. In Table 6.1 are shown the average evaporation rates per unit area for each run, the estimated value by laminar flow conditions as described above, and their difference. Even with the assumed surface temperature increase, the laminar flow estimation is almost always less than the experimental value. This is also true for the 2-surface samples suspended in the air stream and unaffected by the experimental chamber wall boundary layers. For high mass transfer rates, the transfer coefficients depend on the mass transfer rate. Using methods outlined by Bird et al., (1965) it was found that the mass transfer rate was small enough not to affect the transfer coefficients as developed by the laminar boundary layer theory. Because of the thickness of the sample and its blunt leading edge, there will be local regions of flow disturbances. The experimental values of the drying rates of the unheated samples are now used to evaluate statistically the coefficients 72 Table 6.1 Experimental and estimated laminar flow drying rates Average Estimated Percent Run Value Laminar Estimated Difference Number Experimental Flow Minus Based on Rate Rate Experimental Experimental Value (qm/hr-cmz) (qm/hr-cmz) (gm/hr-cmzj 0200 .0156 .0169 +.0013 8 0300 .0188 .0182 -.0006 3 0400 .0205 .0185 -.0020 10 0500 .0065 .0053 -.0012 23 0600 .0156 .0132 -.0024 16 0700 .0110 .0072 -.0038 35 0800 .0332 .0318 -.0014 4 0900 .0127 .0127 0 0 1000 .0108 .0090 -.0018 17 1100 .0092 .0092 0 0 1200 .0058 .0048 -.0010 23 2-surface samples 0300 .0202 .0192 -.0010 5 0900 .0146 .0129 -.0015 10 1200 .0108 .0092 -.0016 15 samples with 8 inch length 0304 .0192 .0182 -.0010 5 0501 .0054 .0053 -.0001 2 1104 .0087 .0092 +.0005 6 *cooled samples of test section 2 73 qand n. Only the first sample of each group listed in Table 8.2 is used to avoid weighting in favor of those runs with repeated samples. The characteristic dimension, DC, used is the path length of flow over the sample, that is the top length plus two times the thickness (two times one-half the thickness of the 2-surface samples). The vapor pressure at the surface is assumed as before. Velocity adjustments based on the calculations of Appendix A.l are made for the 0.31 cm thick samples in runs 0200, 0300, 0400, 0800 and 0900. Rate differences of these runs with higher air velocities seemed to be more marked than those of lower velocities. With these assumptions and adjustments, the parameters of equation 6.4 are calculated to be: n = 0.6 andrl= 55.6. The multiple correlation coefficient of this estimate is 0.9637. The estimated results are tabulated in column (12) of Table 8.3. In column (13) of this table are listed the percentage differences between the estimated and experimental values. The standard deviation of the differences is 9.27 and the 95 percent confidence limits are t 20 percent of the experimental values. The main conclusion of this section is that the initial drying of wet chicken excreta is controlled by environmental conditions and the rate can be predicted if the hydrodynamic boundary layer conditions and surface temperatures can be estimated. 74 6.5 Conducted Heat Sources and Utilization Efficiencies Additional heat sources greatly increased the drying rates as is seen by comparison of the results of heated samples with non-heated samples. Under steady-state conditions, the summation Of convective and conductive heat sources at the surface equals the latent heat required to evaporate the moisture being removed. In mathematical terms hc(ta - ts) + k(td - ts)/d = hfghD(p5 - pleT (6.5) where p5 is a function of the surface temperature, ts, and td is the temperature at distance d from the surface. The second term on the left hand side of this equation is the heat flow through the material and to estimate its value requires knowledge of several unknown factors. Although the conductivity of wet excreta can reasonably be assumed approximately equal to that Of water, heat flow estimation by temperature measurement is impossible because of the necessity for accurate sensor placement and response beyond that Obtained in this experiment. The most reasonable estimate of heat input is obtained by calculating the electri- cal energy input and assuming conversion to heat evenly distributed over the hot plate with no heat loss through the floor Of the test chamber. Disregarding slight differences in density and moisture content, the only variable difference between the heated and 75 unheated samples is the heat input. Heat and mass balance for the unheated samples is hfgm" = hc(ta - ts), (6.6) and with conductive heat input hpganh = hc(ta - tb) + 0 (6.7) where tb is the measured body temperature and also assumed _tO be the surface temperature of the heated sample. 0 is the heat input as tabulated in Table 8.1. The ratio of heated to non-heated drying rates is then sub/a" = [(ta - tb)/(ta - twb)] + (Q/hfga") , (6.8) Estimated drying rates of heated samples based on this equation are presented in Table 6.2. The estimates range up to 25 percent greater than the experimental values indicating that the original assumptions of no heat loss and uni-directional heat flow are not quite true. A measure of the utilization efficiency of the additional heat input is the heat energy required to causethe observed increase in evaporation rate compared to the amount of heat ideally required to evaporate the same amount of water under the same environmental conditions. The utilization factor, U, in heat energy per unit weight may be stated as follows: 0 = Q/ [(hc t/hfg) + (Q/hfg) - (ho p/RT)] (6.9) In many cases, with moderate heating, the temperature difference 76 Table 6.2 Experimental and Estimated drying rates for heated samples Average Average Rate Estimatad Run Drying Drying Ratio Drying Percent Number Rate Rate Heat to Rate b Difference No Heat With Heat No heat Eq. 6. (gm/hr'cmz) (gm/hr-cmz) (gm/hr-cmz) 0200 .0156 -- ~- 0300 .0188 -- -- 0400 .0205 .0305 1.5 .0370 +14 0500 .0065 .0222 3.4 .0236 + 2 0600 .0156 .0312 2 0 .0428 +24 0700 .0110 .0161 1.45 .0180 + 7 0800 .0332 .0472 1.4 .0607 +19 0900 .0127 .0339 2.7 .0389 + 9 1000 .0108 .0184 1.7 .0222 +14 1100 .0092 .0226 2.5 .0251 + 6 is nearly zero and the term, h t, is small relative to the c other terms in the denominator. Thus 0240/ [(Q/hfg) - (hDAp/RT)] (6.10) The utilization efficiency, Ueff’ in percent is ”eff = (hfg/U)100 (6.11) In Table 6.3, the following results are shown: utilization factor of equation 6.10; the convective heat transfer coefficient, hc, estimated by the Colburn analogy based on the experimental value of hp for the non-heated samples of each run; the 77 Table 6.3 Utilization factors and efficiency Utilization Convective Utilization Utilization Run Factor by Heat Transfer Factor by Efficiency Number Eq. 6.10 CoefficienE Eq. 6.9 by Eq. 6.11 (cal/kgm) (cal/hr-cm -°C) (cal/kgm) 0400 1485 1.38 1350 43 0500 712 0.66 925 63 0600 950 0.58 907 64 0700 2480 0.58 1575 37 0800 1880 1.24 1270 46 0900 780 1.32 949 61 1000 1215 0.59 1150 50 1100 796 0.85 1004 56 utilization factor of equation 6.9; and the utilization efficiency. Discussion of utilization efficiencies will be continued in Section 7.6. 6.6 Analysis 2: the Falling Rate Data As has been stated, the data did not show any distinct period during the falling rate drying process. On rare occasions, portions of the data did form a locus for a straight line on semi-logarithmic coordinates but, in general, the curves were 78 S-shaped as clearly shown in Figures 6.2 and 6.4 Indications are that for complete drying analysis, more than one falling rate drying constant is needed. Only one will be considered here to estimate the falling rate drying period between the critical moisture ratio and a moisture ratio of approximately 0.1. As pointed out in Section 4.4, falling drying rates for thin layers frequently can be expressed in terms of the mean moisture content of the layer as follows a, = (dm/dQ')f = -Kf(m - me) (6.12) The falling rate time, 0', is the total drying time minus the time at which the falling rate period began. Integration Of equation 6.12 leads to an equation describing the drying curve in terms of moisture ratio: M = Mcr exp(-Kf9') (6.13) Regression equations of this type approximated the falling rate data with fairly high correlation. All eXperimental falling rate data was used to estimate the falling rate drying constant, Kf. Deletediwere those points beyond the inflection point (see Figures 6.2 and 6.4) that greatly reduced the correlation between the moisture ratio and time. I The 95 percent confidence interval of the drying constant, Kf, is given in terms of its estimate in column (5) of Table 8.5. Even though some of these intervals seem relatively 79 large, examination of the curves (see, for example, figure 6.4) suggest that this is not due to random measurement errors and that, at least qualitatively, the estimate can be considered meaningful. The fact is that a linear estimate is being made of what is in reality non-linear. A more serious limitation insofar as general model deve10p- ment is concerned is the fact that the relative segment of the falling rate drying curve being estimated by linear regression varies from sample to sample. This can be seen by comparing the drying curves of samples 0303 and 0301 in Figure 6.4. The observations of sample 0303 cover only the beginning of the falling rate period while those Of 0301, although limited in number, cover the entire period. The true falling rate drying constant of 0303 may be somewhat different from the estimated value even though the correlation of those Observations available are good. Those samples that did not reach a moisture ratio of 0.1 by the end of the test- run are marked with an asterisk to the right Of Table 8.5. Upper and lower values of confidence at the 95 percent level are given for the estimates of the moisture ratio at critical time (see next section for method of calculation) and at the time Of the last ovservation used in the analysis, which in some cases is also the last Observation of the test-run. These are tabulated in Table 8. 5 in columns (8) and (9), and (13) and (14), respectively. If the lower limit is negative, zero is tabulated because, physically, the moisture 80 ratio will not be less than zero if the equilibrium moisture content has been assumed or calculated correctly. The confidence band over the midrange of the analysis will be less than at the two end points so that what is tabulated is the worst situation for each sample. As much as 84 percent of the variation In the falling rate constant can be accounted for by the variation in the constant rate drying constant. For 24 estimates under adiabatic conditions Kf = 0.12 + 3.2 KC - 0.25 (:18 (6.14) with a multiple correlation coefficient of 0.938. For the 18 estimates with added heat input Kr = 0.25 + 3.8 KC - 0.37 de (6.15) with a multiple correlation coefficient of 0.966. Including the variable of heat input did not improve on this correlation. These relations and their significance will be discussed in Section 7.4. 6.7 Critical Moisture Ratios and Time Continuity is assumed between the constant and falling rate periods. Thus, at critical time, 0 = 0 the falling cr’ drying rate, 6“,, must be equal the constant drying rate, m”c. Setting equation 6.12 equal to equation 6.3 and substituting mcr for m, gives -Kc(mO - me) ='Kf(mcr - me) (6.16) From this it can be seen that the ratio of the constants are equal to the critical moisture ratio: 81 Mcr = (mcr - mel/(mo - me) = Kc/Kf (6.17) The critical time, 9cr: is calculated by rearranging equation 6.3 and setting M = Mcr= ecr = (1 - Merl/KC (6.18) The critical values calculated by this method can be found in Table 8.5. They do not affect the falling rate constant if the same data are used for the estimation of Kf, but they do affect the upper and lower limits of moisture ratio confidence intervals and thus, are necessary for the compilation of Table 8.5. The assumption is that the constant rate period ends when the moisture content at the surface reaches a specific value. Since the critical moisture ratio is the average through the material, its value depends on the rate of drying, the thickness of the material, and the factors influencing moisture movement and resulting gradients within the solid. As a result it is to be expected that the critical moisture ratio increases with increased drying rate and with increased thickness of the mass of material being dried. The drying rates of the adiabatic drying situation do not cover a sufficiently broad range to significantly change the critical moisture ratio within the sensitivity of this experiment. The critical moisture ratio could only be related to the thickness as follows: Mcr = 0.68 de (6.19) where the multiple correlation coefficient is 0.826. 82 In the case of the heated samples, surface temperatures are higher resulting in increased drying rates. But heating also increases the material temperatures and temperature gradients within the body, thus increasing the rate of internal moisture movement. The overall result is an increased amount of moisture removed at the constant rate, lowering the critical moisture ratio. However, no correlation could be made with any of these variables. The presence Of conducted heat input did lesson the effects of depth, however, as indicated by comparing the following relation for the heated samples with equation 6.19. Mcr = 0.1 + 0.19 de (6.20) The multiple correlation coefficient for equation 6.20 is 0.925. To determine the critical time from the relation of continuity rather than the critical moisture ratio, such as: A exp(-ngcr) = 1 - KCOcr (6.21) (where A is the exponential moisture ratio intercept at drying time of zero), in many cases resulted in an initial falling rate higher than the constant rate because of the inexact determination of the falling rate constant. The critical time solution determined by trial, (the left hand side of the above equation is not linear), resulted in two, one or no solutions depending on the pre-calculated values of the drying constants. Table 8.6 summarizes the estimated drying constants and critical ratio by sample thickness and rank of the constant 83 rate drying constant from low to high values. Environmental variables are also included for convenience. Because of the method of deveIOpment, this model will slightly underestimate moisture ratios during the transitional period from the constant to falling rate periods by over extending the constant rate time period. This is illustrated graphically for a typical sample in Figure 6.7. The experimental data are plotted, and the falling rate estimate and confidence limits of the estimate are shown. The error Of the estimate during the transitional period reaches a maximum at the critical time and decreases as falling rate drying progresses. The estimated experimental value (estimated because experimental data are seldom recorded at the exact critical time) is shown in the last column of Table 8.6 beside the estimated critical moisture ratio in column (13). Greater error usually occurs with the more rapid drying situations. A difference of 0.01 in the moisture ratio represents approximately one percent difference in percent moisture content for the experimental sample sizes and less than five percent estimated error in total moisture removed. 84 . q ..:.;1\\11110111 m. _, 4w . H.o ~ _ 1&1 oueawumo mum» 953mm V 1 awesome sump 053mm mo 638.3 LT ‘7 Owumubusumuoa N.0 moo. .oz 6_ae6m 000 OumE_umO mo mumE__ oocov_mcoo DCOOLOQ mm 5.0 Ocsm_m $503 I 0 I MZHH 02:55 .3 00 00 Nm 0N 0N 0N 0H NH 0 0 , 1 lb . 0 11 / £.Hooaaauu a 05.: Hmowuau . _ m.0 0.0 . 0.0 OumEHumO mumu ucmumaoo mo muwfifid $0.0 MISION OLIVE N 7.- DISCUSSION OF METHODS AND RESULTS 5 §_function gj_Time and Moisture Content 7.1 Drying Rates The process of complete drying Of fresh chicken excreta was expected to be complex. However, large portions of moisture are removed by the relatively simple process of constant rate drying because of the extremely high initial moisture contents and because a large portion is free (non-hygroscopic) moisture. It was shown in the previous chapter that the falling rate can be estimated as a linear function of the moisture content of the material. Figure 7.1 graphically shows the drying rates as a function of time and moisture ratio as derived from the analysis of Chapter 6. Average constant rate values are used for the run. The experimental data points are estimated by m”f = Kf(mo - me) M/As (7.1) where the moisture ratio M is the experimental value and Kf is the falling rate constant of Table 8. 6. There is some descrepency between the solid curves and experimental data points because the curves are based on average values for the run and the points are calculated using individual sample data. The lepes of the falling rate portion of the right hand drying curves are: K,c(mO - me)/A5, so that the falling rate equation 7.1 applies. This is equivalent to equation 6.12, 85 000— can Como meat to» mOumL mc_>co UOumE_umw _.N Ocsm_m z I 02.; gHmHOZ $50: I 0 I NEH“. 02:30 86 a 0 0.0 N0 00 0 00 am 00 00 .a 0N S 0 0 H O E n / i, m on m 2.0 0000 x 3 00.0 0005 o 4 r . H0. Awoumocv m... (1 008.0141 . «1 - . Wafo 82 4 _ 30 002 o M ““ AEOVOU .oz OHQEmm .x 1.0:. my. 1 020.0 _ _ _ _ 020.0 ".400. 1 z 1 0:8 $5382 $500 - 0 .. 0:3 02:55 .0. 0 .A I N nu M AwommusmiNv a 2.0 0000 x - 48 .0 0000 o u 3.0 N000 4 _ 30 800 o 0 W 080 0 .62 3080 m Z .111- N 0 1—4 0 Jq-zmo/ulfi - “151 - 3.1.178 ONIAHO Jq-sz/mfi - “131 - Elva SNIAHQ 87 namely, mf = -Kf(m - me). Note that this is a linear relation with zero intercept because the equilibrium moisture content, me, is chosen to be the final dried moisture content. This relation then assumes zero drying rate at zero moisture ratio and precludes any secondary falling rate period. A more general expression would be dm/dO = Kf(m - ml), (7.2) where m] is the moisture content at zero drying rate if the material continued drying at the same rate (with drying constant Kf) and would be different from me if there were secondary falling rate drying periods. Writting equation 7.2 in terms of equilibrium moisture content and moisture ratio gives dm/dO = Kf(mo ' me)(M ' Ml) Kf(mo ' me)M ' $1 (7.3) where M] = (m] - me)/(mo - me) and m]: Kf(mo - me)M]. Graphically, the situation is sketched in Figure 7.2 The critical moisture ratio would then be adjusted by the amount M]. This would allow for a second falling rate period, but since the experiment was not aimed at distinguishing fafling rate drying periods, no values are available to estimate the necessary adjusting parameters. The selection of equilibrium moisture content as the lower limit Of the falling rate drying period could effectively be used within the range of analysis because most Of the moisture ratios are little affected by small changes in the selected value of the final dried moisture content. 88 1 ,. l H I .1: I \ 1 8 1 . 1 OS I I 1 E11 + I 2 T : l A g 0 IT 1'.o g, 1 o - MOISTURE RATIO - M ——>- Figure 7.2 Critical moisture ratios with more than one falling rate period 7.2 Factors Influencing Rage,g£ Dryigg a. Temperature, Humidity, 25g_AjL_Velocity The most important single factor correlated with constant rate drying is the absolute humidity or wet-bulb depression of air flowing past the wet surface (Van Arsdel, 1963). The drying rate is a function Of the vapor pressure differential and if the air is saturated, no drying can take place by convection. The saturated vapor pressure is a function of the absolute temperature while the partial vapor pressure of the air is, by definition, its saturated vapor pressure times the relative humidity (Brooker, 1966). 89 In Figure 7.3, the constant drying rates for the ten experi- mental conditions are plotted against the wet-bulb depression. Only two points at any one condition of constant velocity and ambient air temperature are available. Although the psychrometric relation between vapor pressure difference and wet-bulb depression at different ambient air temperatures are not exactly linear, it is nearly so within the narrow range of these tests and straight lines are drawn through those points of similar experimental velocity to clarify their possible association. The wet-bulb depression is a very simple measure Of the drying potential of the stream of air, but has little effect on the falling rate period where internal diffusion rates are controlling. It is, in the main, a surface phenomena. The material temperature has the most affect on the localized vapor potential within the body during the falling rate period. It has been shown that for similar hygroscopic materials the critical break points between surface and internal evaporation at different temperatures of the substance can be predicted according to the change in ratio of surface tension tO the viscosity of the liquid of the product (Gorling, 1963). In this research there is insufficient evidence to indicate what the temperature effects are except tO note that the heated samples did exhibit lower critical moisture ratios. However, this may have been caused by the temperature gradient rather than the sample temperature, per se. 9O Run NO. t ( C) V(cm/sec) 3. O 0 03 __ 0500, 1000 26.7 25 L O A 0600, 0700 32.2 25 D 0400, 0900 26.7 147 X 0200, 0300 32.2 122 O 0800 32.2 147 O 1100 21.0 76 0.02 n C 61/ D 15 10.00123 0.01 if ° 0 2 4 6 8 10 WET-BULB DEPRESSION - °c CONSTANT DRYING RATE - gm/cmZ-hr Figure 7.3 Influence of wet-bulb depression on constant rate drying 0.3 \e“?¥‘\‘ 5 '\AN ,3 ‘9 , 0.2 <3 | I 8 E”- q, I (‘1 . O 0.1 u 01 'O FALLING RATE DRYING CONSTANT -'Kf - l/HR 0 0.2 0.4 0.6 858 1.6"'J' SQUARE ROOT OF SHAPE FACTOR - (F)§ - (1‘! Figure 7.4 Influence of thickness on falling rate drying 91 In the low moisture range, drying is so slow that the cooling effect of evaporation is inappreciable and the material assumes very nearly the dry-bulb temperature of the air as shown in Figure 6.5. The internal redistribution Of moisture, which is the rate determining factor at this stage," is accelerated by a rise of the material temperature. Free stream air velocity affects the constant drying rate through its hydrohynamic effects on heat and mass transfer. These effects have been demonstrated to be a fractional exponential function of velocity. For laminar flow, it is a function of the square root of the velocity. In such a case, an increase of velocity by 4 times should double the drying rate. This is roughly the case as shown in Figure 7.3 even though pure laminar boundary flow was not attained in the experiment. The velocity associated with the upper line is approximately 5-6 times that of the lower and the lepe is approximately the square root of 5 times that of the lower. That the velocity, as well as the wet-bulb depression has some combined affect on the falling rate period because of larger heat transfer coefficients is demonstrated by the close correlation of the constant and falling rate drying constants. However, the real controlling factors of falling drying rates are those that control the rate of moisture movement to the surface. It is prophesized that further 92 analysis would indicate that of the three environmental factors only ambient air temperature, as it affects body temperature, will affect falling rate drying. b. Material and Process Factors 0f the many possiblefactors associated with the biological and physical material characteristics, and sample size and shape, only the thickness and the ratio of volume to evaporative surface area were studied in any detail. The rate of drying per unit area is a function of the environmental factors and thus the rate of drying per unit dry solid is a function of how much surface area can be exposed to the drying air. For a given mass of material, an increase in surface area also decreases the internal path length the moisture must traverse to reach the surface. Thus, not only is the rate per unit mass increased, the moisture content at the critical level is decreased, or in other words, the amount of moisture removed at the faster constant drying rate is increased. Exposing both surfaces Of a mat Of material to the drying air as was done in three experimental runs by suspending samples on wire screens, effectively doubled the rate of moisture removal and also decreased the critical moisture ratio. By referring to Figures 6.1 and 6.3, it will further be noted that drying time varies approximately inversely as the thickness. This is true for most Of the falling rate period 93 as well as the constant rate period. In situations where internal vapor diffusion is the controlling drying mechanism, the rate varies inversely as the square of the thickness and it would take nine times as long to dry a sample three times as thick to the same moisture content (Van Arsdel, 1963). The linear relation of falling rate constants to the thickness is illustrated in Figure 7.4. Supplemental conductive heat sources will be discussed in more detail in a later section, but it will be noted here that drying rates are increased by increasing the material and surface temperatures. During the constant rate drying period the increase in surface temperature increases the vapor pressure potential difference, as the partial pressure of the air remains the same. Internal moisture movement is increased not only through increased material temperature, but also due to an increase in the temperature gradient across the body. It has been shown by several researchers (Cary and Taylor, 1962; Luikov, 1966; among others) that liquid phase moisture diffusion is affected by thermal gradients as well as by concentration and pressure gradiets. Luikov also states that liquid transfer by means of selective diffusion such as an osmotic pressure gradient is a function of moisture content and temperature. 94 7.3 Volumetric Shrinkage, Shrinkage Water and Stresses Chicken excreta contains a high percent of shrinkage moisture, moisture that results in body shrinkage when removed. However, the rate of shrinkage apparently is not directly related to the rate of moisture removal during the constant rate drying period. This is shown by the simple fact that a bulk constant drying rate does exist without adjustment for volumetric and surface area changes. Considerable amounts of moisture are evaporated before any apparent change in drying rates are noted. For example, one calculation predicted a 35 percent surface area change (see Appendix A.3) if the sample should shrink in prOportion to the amount of moisture removed during the constant rate period. Volumetric changes of this magnitude were not observed during the constant rate drying period. There are two possible explanations for this phenomena. The first is that as water is evaporated, the mean pore diameter decreases through surface shrinkage and structural changes resulting in an increase in the osmotic and capillary moisture potential in the surface layers. Water is drawn from interior regions of lower moisture potential leaving air pockets. If the liquid threads remain continuous through- out the drying period, most of the non-hygroscopic water will be removed by surface evaporation. The second possible reason that little shrinkage occurs during this period is that water is ”manufactured” through biological and enzimatic breakdown of the fats and starches 95 present in the material. There is no data to support this statement because there is no measurable difference in the calculated moisture content of samples dried quickly and those dried slowly. Part of the change of drying rate during the early part of the falling rate period is because no correction is made for reduction in evaporative surface area through shrinkage. The real beginning of the falling rate drying period cannot be determined until accurate measurements Of shrinkage rates are made. Surface area change does not account for the entire falling rate phenomena, however. In addition to the associated surface area changes, shrinkage creates stresses causing surface cracks to form. Shrinkage stresses are discussed more fully in Section 3.2b and by Gorling (1958). It is to be noted here that the first signs of surface fissures and cracks did not appear until near the end of the constant rate drying period. This would indicate that steep moisture gradients did not develop until near the beginning of the falling rate process. In addition, thinner samples developed many hair line cracks while the thicker samples formed fewer but wider cracks as drying progressed. This would indicate steeper moisture gradients in the thinner samples. It might be asked, does cracking expose new evaporative surfaces to compensate for the volumetric shrinkage such that apparent constant bulk drying rates are maintained? Probably 96 not, because these cracks are at first so small in width that moving air does not penetrate and moisture would have to diffuse in the Vaporous form through still air, or affectively through a thicker boundary layer. This was demonstrated with one sample (#1001) in which were scored V-cuts the thickness of the sample and approximately 1/4 cm wide at the surface at the beginning Of the test. The increase in exposed surface area was nearly 10 percent, yet the bulk drying constant was not significantly different from the unscored counterparts. Further research involving drying, associated shrinkage rates and linear shrinkage coefficients are needed to further the understanding of drying of chicken excreta. 7.4 The Falling Rate Drying Constant and Internal Diffusion During the falling rate period, evaporation may be at or near the surface or it may occur below the surface. The relative resistance to the movement of water and heat through the surface gas film and through the solid determines the position Of evaporation. Thus, if liquid water moves easily through the solid and the rate of evaporation is low, the water will be able to equalize throughout with only a small concentration gradient within the drying material, and evaporation will take place mainly near the surface. The falling rate constant is highly correlated tO the initial drying constant indicating that the surface film 97 resistance still plays a part in limiting drying rates. That this is so is not surprising considering that the raw data are weighted in favor of the early phases of drying and that the material still contains large amounts Of non- hygrosc0pic water at the beginning of the falling rate period. That falling rate drying has not reached the stage where internal diffusion rates are the sole controlling factor is shown by the relation of the drying constant, Kf, to the shape factor, F. As shown in Section 3.1c Kf will equa117zDeF/4 if the medium is considered isotropic and the diffusion coefficient, De, constant. The drying constant is not a linear function of F but rather of the square root of F, or if the dimensions of a and b are much larger than d, a linear function Of the inverse of thickness, l/d. This linearity is shown graphically in Figure 7.4. The temperature difference between the top and bottom of the sample will help indicate whether or not the plane Of evaporation is retreating within the material (Gilliland, 1938). If the evaporation continues to take place at the surface, the resistance to heat transfer will be largely in the film layers around the body and the temperature difference across the body will remain essentially constant. Sample temperatures are shown in Figures 6.5 and 6.6 for a heated and unheated case. The adiabatic unheated sample showed no significant temperature difference across the body thickness. The heated sample showed nearly constant differences until near the end 98 of the drying process. Because of the limited sensitivity and relative size of the sensors, this does not conclusively support the hypothesis of surface evaporation during the initial stages of the falling rate period, but does suggest the probability. Although there is insufficient data with which to examine the mechanisms Of internal moisture movement, it appears that the so-called falling rate period dealt with in this study is largely transitional in nature, the true limits being the upper and lower critical moisture ratios Of the transition period as defined in Section 3.1a. At the upper critical point, surface shrinkage begins to have an effect. Dry patches begin to show on the surface in the form of surface cracks. In these regions, the funicular state (Harmathy, 1969) begins to break down, greatly reducing moisture mobility. Over the remaining surface regions, constant surface evapora- tion rates continue. The SCOpe of this research does not warrent a discussion of the falling rate period in great detail. Owing to the lack of raw data, the rate data obtained for this period cannot be considered equally reliable as those obtained for the constant rate period and further data are desirable before an accurate analysis is attempted. However, indications are that large proportions of the non-hygroscopic water are removed from the material by the time the lower critical point is reached where the internal moisture movement takes place predominately 99 in the gaseous phase. This is particularly true for thinner drying layers of the material. 7.5 Some Comparisons with Drying Rates jg ExistingHousing Units Esmay and Sheppard (1971) recently reported results of their research involving in-house drying of poultry droppings. Some of the data from that report are used to evaluate the possibility of extending the methods of drying analysis of Chapter 6 to cover the more general case of existing drying situations. Several assumptions must be made regarding the environmental conditions in the pit area. It immediately becomes apparent that not enough is known about the boundary layers along the surface of the droppings. Surface roughness, mean path length of surface flow and fluctuations in flow patterns caused by obstructions in the house favor turbulent boundary layer development. On the other hand, extremely low velocities support fiIick laminar boundary layers. In any case, undulated surfaces and wet and dry regions would preclude uniform boundary layer deve10pment and transfer rates. A measure of the mean mass transfer film thickness is needed,based on some simple measure of free stream air movement and possibly, some measure of surface roughness. Esmay and Sheppard reported summer removal rates of 95 grams of water per hen-day (4 gms/hen-hr) which converts to 0.0128 gm/hr-cm2 where the population density is 3 hens per 100 929 cm2 (1 square foot). Assuming a vapor pressure differential Of 0.068 atm (0.1 psi) and a room temperature of 26-1/20C (80°F), the convective mass transfer coefficient for the above drying rate is 43 cm/min (85 ft/hr). Summer ventilation rates are 132 m3/min (4650 cfm) through a room with cross-sectional area of 21.4 m2 (320 ftz). Velocities beneath the cages are assumed to be three times the room average. The result of 30.8 cm/sec (60 ft/min) is of the same order of magnitude as those reported by Lilleng (1969). Under these conditions, the transfer coefficient of 43 cm/min is approximated by laminar flow conditions over a 10 cm (4 in) smooth surface. On the other hand, if the pit surface area is assumed saturated over its entirety and the mean path length is assumed to be the width of the pit (122 cm or 4 ft), there would be turbulent transfer conditions with a mean coefficient of 71 cm/min. Assumption of laminar transfer would decrease the transfer coefficient to 13 cm/min. This would indicate that neither pure laminar or turbulent flow conditions can be assumed. This analysis completely neglects the random dropping patterns and the possibility of initially faster drying rates followed by slower falling rate periods. 1 Total production of excreta was reported to be 220 grams per hen-day. At a density of approximately one cc per gram, this would cover 310 cm2 (1/3 ftz) approximately 0.95 cm 101 (3/8 in) deep. At 88 percent initial moisture content, 26.5 grams are dried solids and 3-5 grams of moisture are not removable under these drying conditions. With these conditions the constant rate drying constant, K is 0.0208/hr. c’ It would take 48 hours to dry to equilibrium at a constant rate. The estimated critical moisture ratio is 0.5. The constant rate drying period would last 24 hours and the moisture content at the end of this period would be 78-1/2 percent wet basis, approximating the reported values of moisture content in dropping pits during the summer. The initial drying rate of 0.0128 gm/hr-cm2 is matched by test-runs 0700 (V = 25 cm/sec, ta = 32°C), 0900 (V = 147 cm/sec, t8 = 26-1/200) and 1000 (v = 25 cm/sec, ta = 26-1/2°C), of which only run #1000 closely matches the above in-house environmental conditions. In run 1000, the wet-bulb depression is 7.30C (13°F), the relative humidity 52 percent, and the vapor pressure differential at the saturated surface 0.0544 atm (0.08 psi). Although direct comparisons cannot be made, indications are that a prediction model of this type does have potential in predicting in-house drying providing a mean boundary layer thickness or convective transfer coefficient can be determined for each particular housing situation. Because ofthe lack of fresh, wet-weight fecal production figures, similar calculations could not be made for winter conditions. Increases in moisture removal rates with heating panels are discussed in the next section. 102 7.6 Utilization Rates 9f Energy Inputs The rate equations indicate the following five alterna- tives available for increasing drying rates and decreasing drying times: (1) increase air temperatures, (2) increase wet bulb depression (decrease humidity), (3) increase the air flow rate, (4) increase material evaporative surface area (decrease effective depth), and (5) increase evaporative surface temperature through material heating. There is little opportunity to use the first two alternatives to advantage as there limits are narrowly determined by environ- mental conditions required for optimum production. Opportunity for increasing the air velocity is also somewhat limited unless the pit area is deep and the air flow . can be partially confined to this region. However, local increase of the circulation rate without increasing ventilation rates would be quite beneficial. Increasing the evaporative surface area would be very effective for decreasing drying times. The initial rate per unit area remains constant but the amount of moisture removed from a given mass of material is directly proportional to the surface area. Not only is the bulk drying rate greater, as seen in Figure 6.3, but generally lower moisture contents are reached before the falling rate period begins as indicated by the discussion of critical moisture ratio in Section 6.7. 103 This simple alternative does require rather complex handling systems to maintain thin layers. Energy inputs are required for whatever scraping, mixing and handling called for. Stirring the bed to expose new surfaces without breaking up the structure of the conglomerate masses would not be of much help as long as all surfaces are saturated. However, chickens confined to cages will tend to concentrate their droppings near the center of the floor area beneath. Stirring will spread the wet surfaces more uniformly over the pit area. Esmay and Sheppard (1971) reported that approximately 10 percent more moisture was removed from areas with once a day stirring over those without any. The final alternative to increasing drying rates is the addition Of heat sources. Conductive heat panels beneath the manure are considered here. King and Newitt (1955) studied drying of granular materials with heat transfer by conduction. An initial constant drying rate was observed, the rate of evaporation largely determined by the flow of heat through the material. Since the heat conductivity of the material is a function Of its moisture content, decreasing as the bed dries, the flow of heat will gradually diminish, resulting in a progressive reduction in drying rates. The increase in drying rate due to conducted heat is a complex function of existing environment conditions and rate of heat input. Figure 7.5 shows the heat utilization 104 1 (D S p. Z H F--1 4; 6% 0.6 \ 53 H E—4 U B a Z O U 0.4 o g 7\ m , l-0.0163 > I—I 53 O E U 0.2 O \ 122.. O E: E—1 ii 0 68.2 30 40 50 60 UTILIZATION EFFICIENCY - Ueff - PERCENT Figure 7.5 Utilization efficiencies 105 efficiency as a function of convective to conductive heat source ratio for the 8 runs with heated sub-sections. The equation of best fit is linear with slope and intercept as shown, although over a broader range of values the relation may not be linear. As the ratio of convective to conductive heat sources increases, the efficiency decreases. Utilization efficiencies at a given level of conductive heat input decreases as the convective source, or in other words, convective drying potential increases. This is because by increasing the surface temperature, the convective heat potential is decreased, eliminated or even turned into a sink depending on how much the surface temperature is raised. Thus, some Of the conducted heat input is potentially lost for moisture evaporation in replacing the convective heat source. The greater this source, the less efficient will be the conducted heat source. The average heat utilization Of 8 runs was 50 percent. Esmay and Sheppard (1971) reported similar efficiency figures for in-house, winter drying conditions with somewhat lower efficiencies under summer conditions. In-house summer conditions generally consist of higher air temperatures, greater wet-bulb depressions and higher ventilation rates, all creating more favorable convective drying conditions. Assuming heating sources well insulated from the ground beneath, summer utilization efficiencies would be lower because of the greater drying potential of the air itself. 106 In conclusion, for moderate drying requirements, greater efficiency will be Obtained with more efficient use of the heat energy already available in the air, with conducted heat used as a supplementary source to increase drying rates where convective drying is insufficient, such as wintertime conditions.' This would require improved circulation patterns of air over the droppings. Although, with laminar flow, air velocities must be increased four times to double the convective transfer rate, the total increase in power would not be great because only that air near the surface is involved in the transfer of heat and moisture. Bulk vertical mixing is required to bring more air into contact with the surface. 8. SUMMARY AND CONCLUSIONS 8.1 Summary Ninety-five samples of chicken excreta were dried in eleven laboratory controlled environments, simulated to typify those found in poultry houses. Samples of three basic thicknesses were used. Drying rates Of some samples were increased by supplemental heat inputs and by increasing the exposed surface area per unit mass by suspending thesample on a fine mesh wire screen. The results are summarized in Table 8.6. Basically, it was found that the drying rates were a function of free stream velocity, wet-bulb depression and ambient air temperature as it affects the saturated vapor pressure. Process variables of increased surface area and conducted heat source also increased the drying rate. More than half of the removable moisture was evaporated from the body surface at constant rates which can be predicted by film resistance and concentration gradients. Because the rate of shrinkage was not measured, the end of the constant rate period could not be accurately defined, but critical moisture ratios were calculated for each sample tested. The free stream conditions were found to be of major importance throughout the drying periods analyzed. Falling rate drying was predicted as a function of moisture content. 107 108 The falling rate drying constant was estimated as a function Of the initial drying constant and the sample thickness. Indications are that most of the non-hygroscopic water moves to the surface in liquid form and is evaporated there. Although only two drying periods are clearly defined by this researCh, it is hypothesized that, because chicken excreta is hygroscopic at lower moisture contents, drying to equilibrium consists of one or more falling rate periods. Vapor diffusion is expected to control drying rates when the surface moisture content falls below the hygrOSCOpic limit. Drying rates were compared to some in-house drying data. It was shown that constant rate drying will predict the in-house drying rate if a measure of the mean boundary_layer thickness and area of wet surface can be approximated. 8.2 Conclusiais The following four conclusions have been supported by this research dealing with drying of chicken excreta in thin layers of less than 1 cm (1/2 inch): (1) The initial drying rate of fresh chicken excreta is constant. Falling rate drying periods follow the constant rate period. (2) The constant rate is a function Of the boundary layer thickness and boundary layer concentration gradients with the surface at saturated conditions. (3) Falling rate drying periods can be identified and the rate predicted as a function of removable moisture content as in thin layer drying. _ o I" 1.114 ‘\ 109 (4) In-house drying of fresh chicken excreta can be predicted on the basis Of constant drying rates. In addition, there is some support for the following: Non-hygroscopic moisture moves to the surface in liquid form at a rate nearly equal the surface evaporation potential until the surface falls below the hygrosc0pic limit. 8.3 Suggestions for Future Research Based on this study, there are two major areas of research of concern to in-house drying that need to be pursued. Basic research is needed to determine material properties and their relation to such parameters as heat and moisture conductivity, specific heat and etc. Also, the degree of micro-biological activity and its affects need to be studied in more detail. The hygroscopic limit needs to be determined as well as shrinkage rates and coefficients. Applied research is needed in the area of micro-environ- mental conditions in the pit area and along the manure surfaces. Parameters physically describing manure surfaces and its interaction with the enviornmental ventilation air are needed. A systems approach to develop an economically optimum system for in-house drying would be of great practical value. Specifically, it is felt that the following three suggestions would reap the most immediate benefits: (1) Determination of the volumetric shrinkage rates with drying. (2) (3) 110 Develop some one basic measure of air movement in the region immediately above the manure surface that would satisfactorily pre- dict the effective mass transfer film thickness and/or coefficient. Determine heat conduction and moisture diffusion coefficients as a function of moisture content. LIST OF REFERENCES REFERENCES Bagnoli, E., F. H. Fuller and R. W. Norris (1963). Humdifica- tion and drying. Section 15, in J. H. Perry, et. al., Ed. Chemical Engineers Handbook. 4th Ed. McGraw-Hill Book Company, New York. Bird, R. 8., W. E. Stewart and E. N. Lightfoot (1960) Transport Phenomena. John Wiley and Sons, Inc., New York, New York. Bressler, G. O. (1968). Preliminary report on drying poultry manure inside a poultry house. ASAE Paper NO. NA 68-502. Brooker, D. B. (1966). Mathematical model of the psychro- metric chart. ASAE Paper No. 66-815. Carslaw, H. S. and J. C. Jaeger (1959). Conduction gj Heat jfl_So1ids. Oxford, Clarendon Press, London. Cary, J. W. and S. A. Taylor (1962). The interaction of the simultaneous diffusion of heat and water vapor. Soil Sci. Soc. Proc. 26:413. Chen, C. S. and C. K. Rha (1971). Investigation of shrinkage in dehydration of grapes. ASAE Paper NO. 71-387. Chilton, T. A. and A. P. Colburn (1934). Mass transfer (absorption) coefficients: Prediction from data on heat transfer and fluid friction. Ind. Eng. Chem. 26:1183. Cross, 0. C. (1966). Removal of moisture from poultry waste by electr-osmosis (Part 1). pp. 91-93, in Proc. Nat. Symp. Animal Waste Management. ASAE Pub. N‘_§o. 135366. Dixon, J. M. (1958). Investigation of urinary water reabsorp- tioz in the cloaca and rectum of the hen. Poultyy Sci. 37: IO. Eckenfelder, W. W. and D. J. O'Connor (1961) Biologjcal Waste Treatment. Pergamon Press, New York. Eckert, E. R. G. and R. M. Drake, Jr. (1959). Heat and Mass Transfer. McGraw-Hill Book Company, Inc., New York, New York. Esmay, M. L. (1966). Poultry Housing for Layers. Extension Bulletin 524. Cooperative Extension Service, Michigan State University, East Lansing, Michigan, 16. pp. Esmay, M. L. (1969). Principles of Animal Environment. AVI Publishing Company, Westport,_Connecticut. 112 113 Esmay, M. L. , M. Saeed, and G. D. Wells (1966). Psychro- metrics of summer- -venti1ization air exchange in window- less poultry houses. ASAE Paper No. 66- 912. Esmay, M. L. and C. C. Sheppard (I971). In-house drying of poultry droppings. ASAE Paper No. 71-917. Fish, B. P. (1957). Diffusion and equilibrium properties of water in starch gel. Food Investigation Technical Paper No. 5. Gilliland, E. R. (1938). Fundamentals of drying and air conditioning. Ind. Eng. Chem. 30:506. Gorling, P. (1958). Physical phenomena during the drying of foodstuffs. Fundamental Aspects of the Dehydration of Foodstuffs. Society of'Chemical Industry, LonHOn. Hall, C. W. (1957). Dryinngarm Crops. Agricultural Consulting Associates, Inc., Reynoldsburg, Ohio. Harmathy, T. Z. (1969). Simultaneous moisture and heat drying. |8EC Fundamentals. 8:92. Jason, A. C. (1958). A study of evaporation and diffusion processes in the drying of fish muscle. pp. 103, in Fundamental Aspects of Dehydration of Foodstuffs. SECIety of’Chemical Tfidustry, ’London. Kays, W. M. (1966). Convective Heat and Mass Transfer. McGraw-Hill Book Company, New York, New Yor . King, A. R. andD. M. Newitt (1955). The mechanism of drying of solids. Part 7. Drying with heat transfer by conduction. Trans. Inst. Chem. Engr. 33: 64. Lapple, W. C., W. E. Clark and E. C. Dybdal (I955). Drying design and costs. Chem. Engr. 62:11: 77 Lewis, W. K. (1921). The rate of drying of solid materials. Ind. Eng. Chem. 13: 427. Lilleng, H. (1969). An investigation of How the Inlet Air Velocity, Direction and Temperature Affect Air Flow Patterns and Temperature Distribution in Cage-Laying Houses. AE class 899 Research Report, Michigan State University, East Lansing, Michigan. Loehr, R. C. (1969). Animal wastes - a national problem. J. San. Engr. Div. , ASCE. 95:189. 114 Ludington, D. C., A. T. Sobel and B. Gormel (1971). Control of odors through manure management. Trans. ASAE. 14:177. Luikov, A. V. (1966). Heat and Mass Transfer in Capilla_y- Porous Bodies. English translation. Pergamon Press Ltd., London. Newitt, D. M. and M. Coleman (1952). The mechanism of drying of solids. Part 3. The drying characteristics of china clay. Trans. Inst. Chem. Engr. 30:28. Nissan, A. H., W. G. Kaye and J. R. Bell (1959). Mechanism of drying thick porous bodies during the falling rate period: I. The pseudo-wet-bulb temperature. A.l.Ch. E. Journal. 5:1:103. Padday, J. F. (1969). Surface Tension. Part 1. The theory of Surface Tension in E. Matijevic, Ed. Surface and- Colloid Science. Vol. 1. Wiley-Interscience‘Uiv. of JothWiley and'Sons, Inc., New York. Pearse, J. F., T. R. Oliver and D. M. Newitt (1949). The mechanism of the drying of solids. Part 1. The forces giving rise to movement of water in granular beds during drying. Trans. Inst. Chem. Engr. 27:1. Philip, J. R. and D. E. Smiles (1969). Kinetics of sorption and volume change in three component systems. Aust. J. Soil Sci., 7:1. Phillips, R. E. (1969). A Systems Analysis of Summer Environ- ment for Laying Hens. Unpublished Thesis, Michigan State University, East Lansing, Michigan. Schlichting, H. (1968). Boundar La er Theor 6th Ed. English Translation. McGraw- HI 11 Book Company, Inc., New York, New York. Slayter, R. 0. (1967). Ejant-Water Relationships. Academic Press, New York, New York. Sobel, A. T. (1966). Some physical properties of animal manures associated with handling. pp. 27- 32, In Proc. Nat. Symp. Animal Waste Management. ASAE Pub. No. SP- 0366. Sobel, A. T. (1969). Removal of water from animal manures. pp. 347-362, in Animal Waste Management. Proceedings of the Cornell UnTVersity Conference on Agricultural Waste Management. 115 Sturkie, P. D. (1965). Avion Physiology. 2nd Ed. Cornell University Press, Ithaca, Nengork. Threlkeld, J. L. (1970). Thermal Environmental Engineering. 2nd Ed. Prentice-Hall, Inc., EnglewoodCIiffs, New Jersey. Van Arsdel, W. B. (1963). Food Dehydration. Vol. 1. Principles. AVI Publishing Company, Inc., Westport, ConneCticut. Welty, J. R., C. E. Wicks and R. E. Wilson (1969). Fundamentals 9f_Momentum, Heat and Mass Transfer. John Wiley and Sons, Inc., New York, New York. APPENDICES APPENDIX A.l Hydrodynamics of Experimental Chamber Figure A.l is a sketch of the physical situation and the assumed hydrodynamic boundary layer development between the point of air entry at the flow straightener and the test section, as well as the assumed velocity profile near the leading edge of the test samples. The distance between the straightener and samples is approximate because no attempt was made to position the samples exactly each time. Air is assumed to leave the straightener at uniform velocity. Non-uniformities caused by momentum boundary layer development through individual passages of the straightener and minor turbulence caused by rough edges will quickly dissappear with the low flow rates used in this experiment. The momentum boundary layer along the test chamber wall is assumed to begin immediately following the flow straightener. The samples are located well within the hydrodynamic entry length far removed from the theoretical region of fully developed duct flow. Therefore, boundary layer deve10pment along the chamber floor is considered to be that of laminar flow over a flat plate. The length Reynolds number at the leading edge of the sample location is, at the maximum test velocity of 147 cm/sec, approximately 27800, well below the turbulent transition Reynolds number of 2x105. 117 118 The momentum thickness,({, at this point is calculated by equation A.l (Eckert and Drake, 1959) and the results are tabulated below along with the ratios of sample top surface position to the momentum thicknes,c{. (Refer to figure A.l.) d/= 4.64(x)/(Rex)l/2 where x = 30.5 cm. dl/d .1526 V (cm/sec) Rex ({(Cm) 25.4 4628 2.080 76.3 13888 1.200 122.0 22222 0.948 147.5 26850 0.829 A velocity profile of u/us = (3/2)(d/a) - 0.5(d/a)3 .2644 .3347 .3677 is assumed (Eckert and Drake, 1959). at support plate and sample heights are tabulated below: V(cm/sec) u] ”2 25.4 5.8 11.2 76.3 29.5 55.4 122.0 59.0 88.0 147.5 77.8 136.0 JT'NV-i \lem I O O O U'IONUJ dz/o/ .3053 .5290 .6695 .7355 .L‘NVN \INO\O U‘IOWCD d3/J .4580 .7935 1.004 (A.l) dq/J .6106 1.057 (A.2) The resulting velocities 119 3r sample support plate «low straightener esample . (Sketch not drawn to scale) u = velocity in boundary layer u = velocity at d (d - 0.32 cm plate thickness) - velocity at d (d I .32 cm plate + .32 cm thick sample) u 8 velocity at d3 (d - .32 cm plate + .64 cm thick sample) n ' velocity at d4 (d4 .32 cm plate + .96 cm thick.ssmple) u = velocity at J - V cm/sec Figure A.l Boundary layer and velocity profile development along chamber floor APPENDIX A.2 Evaporative Surface Heat Balance The adiabatic heat balance at the evaporative surface of the sample is, according to equation 2.11, hfgm“c = hc(ta - ts) + hr(tr - ts). The radiation coefficient, hr, is estimated by equation 2.12 with the surface emmisivity assumed to be 0.95. The tempera- tures of the radiating walls of the chamber are equal the air temperature. So calculated, the radiation heat transfer coefficient value is approximately 3 to 4 percent that of the convective heat transfer coefficient. The convective transfer coefficient is calculated in the same manner as in Section 6.5. Evaporative surface temperatures are assumed equal the wet bulb temperature plus l/ZOC as before. The following table includes the heat required to vaporize the moisture at the experimental rate assuming latent heat of vaporization equal that of free water, the calculated value of available heat through convection and radiation, and the heat deficit. The deficit is approximately 1/3 to 1/2 the value of the combined heat source and averages 3.1 cal/hr-cmz. There are at least four possible reasons for the calculated heat deficit of this magnitude. First, it is 120 121 Table A.l Heat deficits Run Evaporation Evaporation Combined Combined Heat Number Rate Heat Heat Convective Deficit fim' Required Transfer Heat (gal r-cmz) (cal Coeff. Source hr-cmz) F??em2) (cal (cal hr-cm -°C)hr-cm2) 0200 .0156 9.2 I.Is 6.25 3.0 0300 .0188 10.9 1.30 7.2 3.5 0400 .0205 11.9 1.54 7.1 4.8 0500 .0065 3.8 0.72 2.0 1.8 0600 .0156 9.15 _0.64 6.4 2.8 0700 .0110 6.4 0.72 4.0 2.4 0800 .0332 19.4 1.32 3.1 6.3 0900 .0127 7.u 1.37 3.8 2.6 1000 .0108 6.3 0.70 4.7 1.6 1100 .0092 5.35 0.90 3.0 2.3 possible that the latent heat of vaporization of the contained water is less than that for free water. There seem to be no solvents contained in the urine that would be expected to I reduce the surface tension of the solution to any extent, and in fact, Sobel (1969) observed lower evaporation rates from a manure surface compared to a free water body in the same environment. Until it is shown that the surface tension is less than that of water this possibility will be discounted. 122 Secondly, there is the possibility of heat production within the sample. Based on work by Minor (1969), it is estimated that active digestion rates may produce as much as one cal/cc-hr. The temperature increase caused by this internal heat source will be maximum at the wall and equal to (Eckert and Drake, 1959) t = Q'dz/Zk + Q'd/hc where Q' is the internal heat source and the thermal conduc- tance is assumed to be roughly that of water, i.e., 0.0014, cal/sec-cm-OC. For a 0.64 cm thick sample, the increase in temperature is approximately 0.04OC at the wall and progressively less toward the surface. This is quite insufficient to account for the calculated heat deficit. The third and most reasonable possibility is that ideal adiabatic conditions are not achieved. The heat source from outside the experimental chamber is minimal due to the thick insulated walls and the fact that in most cases the laboratory air temperatures were nearly the same as the thermodynamic wet-bulb tempectures of the experimental chamber. A more real source is heat conducted through the edges of the sample support plate and through the walls of the experimental chamber directly from the air as shown in the sketch below. 123 In any case, a temperature differential of less than l/2°C across a 1/4 inch sample thickness is sufficient to make up the heat deficit assuming conductivities of the order of water. It has previously been assumed that the body temperature was uniform. However, a slight difference in temperature was measured, but it was felt that the precision of the measurement was not good enough to justify reporting exact values. Finally, the fourth reason for the deficit is in the calculations. First, the convective mass transfer coefficient calculations are based on the vapor pressure differential. This differential, in turn, is not measured directly but is calculated from measured and assumed temperature values and is extremely sensitive to variations in these values. Thus, the estimated mass transfer coefficient may be in error. Secondly, the Colburn analogy does not hold exactly for gases with a Schmidt number less than 0.6. The calculated Schmkit number in this case is 0.51. APPENDIX A.3 Example g:_Normal Shrinkage The example referred to on page 94 is sample number 0301. Its drying curve is shown in Figure 6.3 where it will be noted that after 8 hours of drying, has reached a moisture ratio of 0.4 at constant rate drying. This means that 18 (0.4x30) gms of water have been removed at this time. With initial sample volume of approximately 33 cc, this would mean approximately 50 percent volumetric change under normal shrinkage conditions. If unstrained shrinkage is assumed, dimensional change will be proportional to length and physically independent of the 3-dimensional shape. By the coefficient of linear shrinkage (see Section 3.1c) 0<= (l/aO)(Aa/Am) or a/ao= (l -Amo<) =c-b/bo=d/do c2; Vol/VolO = c3 (Vol/V010)“3 and A/AO Thus: A/AO With these assumptions, the evaporative surface area after 8 hours should be 65 percent of the initial surface area. Individual dimensions would be approximately 0.8 of their original value. As noted, such dimensional changes were not observed. 124 APPENDIX B.1 Tables Table B.l Experimental test-run conditions Test sub- section Test sub-section two one _— a twb H V ENC a th a tb Q 8» "a 3 “a 2 Run 0 o o s; __ £1; _qn_ . o. o . a. o cal Btu No. F C C u. min sec %wb o 5 C o 8 C hr-cm hr-ft 00 Z no 2 In (1) (2)(3) (4) (5) (6) (7) (8) (9) (10)(11) (12) (13) (14) 0200 82 27.8 22.2 102 240 122 11.0 5 22.8 4‘ 22.8 -- -- 0300 90 32.2 26.1 134 240 122 9.5 5 26.7 8 26.7 -- ~- 0400 80 26.7 21.1 94 290 147 11.0 5 21.7 3 26.1 19.5 72 0500 80 26.7 23.3 117 50 25 13.0 5 23.9 4 32.2 19.5 72 0600 90 32.2 21.7 84 50 25 9.0 4 22.2 4 31.1 23.0 85 0700 90 32.2 26.1 136 50 25 10.0 5 26.7 3 30.6 8.4 31 0800 90 32.2 21.7 84 290 147 8.0 4 22.2 6 28.9 27.1 100 0900 80 26.7 23.3 117 290 147 12.5 5 23.9 7 29.4 27.1 100 1000 80 26.7 19.4 80 50 25 10.0 5 20.0 5 26.1 12.2 45 1100 70 21.1 17.2 75 150 76 11.0 4 17.8 4 25.0 19.5 72 1200 70 21.1 17.2 75 150 76 11.0 3 17.8 2 16.1 cooled samples 125 2 126 Table 8.2 Experimental sample data: Initial conditions a E d de Dc A8 m1 m8 mo-me m0 )3 Age g g {in cm cm cm gm gm gm Zwb 'gn/ cc 0‘! Cements (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) 0202 1/8 .282 10.8 116 39.0 10.0 27.6 74.2 1.19 0 0205 38.8 10.0 27.5 74.2 1.18 0 0208 39.1 10.0 27.8 74.5 1.19 0 0203 1/4 .508 11.4 129 77.4 20.1 54.8 74.0 1.18 0 0206 77.1 20.5 54.1 73.5 1.18 0 0209 78.1 20.0 55.6 74.5 1.19 0 0204 3/8 .692 12.1 142 117.1 32.7 80.2 72.0 1.19 0 0201 116.7 32.2 80.6 72.5 1.19 0 0207 119.8 31.5 84.4 73.7 1.21 0 0301 1/8 .282 10.8 116 41.6 10.2 30.3 75.4 1.27 0 0305 43.5 11.0 31.5 74.9 1.33 0 0313 36.1 10.0 25.0 72.1 1.10 0 0302 1/4 .508 11.4 129 80.0 18.8 59.2 76.5 1.22 O 0312 76.1 17.7 56.5 76.7 1.16 0 0304 .535 21.6 245 152.7 34.8 114.2 77.2 1.16 0 8" length 0303 3/8 .692 12.1 142 120.4 30.3 86.9 74.8 1.22 0 0310 125.2 30.3 91.8 75.8 1.27 0 0311 109.9 25.6. 81.6 76.7 1.12 0 0308 1/8 .213 10.5 225 56.1 15.8 38.6 71.8 1.17 0 2-surface 0307 1/4 .336 10.8 238 94.8 24.2 68.1 74.5 1.18 0 " 0309 94.1 27.8 63.3 70.5 1.18 0 " 0306 3/8 .440 11.1 250 135.1 33.1 98.5 75.5 1.23 0 " 0402 1/8 .282 10.8 116 36.1 8.2 26.9 77.4 1.10 1 0406 35.2 7.7 26.5 78.1 1.07 1 heated 0401 1/4 .508 11.4 129 76.5 16.6 57.9 78.3 1.17 1 0407 73.2 14.9 56.4 79.6 1.12 1 heated 0403 3/8 .692 12.1 142 115.8 24.4 88.4 78.9 1.18 1 0408 111.6 23.5 85.2 ,79.0 1.14 1 heated 0405 1/2 .845 12.7 155 148.2 30.1 114.5 79.7 1.13 1 0404 -- .852 12.2 135 117.8 23.1 91.8 80.4 1.05* 1 undisturbed 0503 1/8 .282 10.8 116 37.1 6.1 30.0 83.5 1.13 1 0507 35.9 6.3 28.7 82.5 1.10 1 heated 0502 40.9 10.0 29.4 75.6 1.25 0 0501 .290 20.9 226 75.0 12.7 60.4 83. 1.14 1 8" length 0504 1/4 .508 11.4 129 78.1 12.9 63.2 83.5 1.19 1 0508 82.5 15.2 65.2 81.6 1.26 1 heated 0505 3/8 .692 12.1 142 116.8 21.0 92.7 82.0 1.19 1 Table B.2 (1) 0603 0606 0602 0604 0605 0608 0601 0607 0704 0708 0705 0707 0701 0703 0702 0706 0801 0805 0806 0807 0808 0803 0809 0804 0810 0802 0903 0905 0901 0902 0904 0907 0906 0909 0908 0910 0911 0912 (2) 1/8 1/4 3/8 1/8 1/4 3/8 1/8 1/4 3/8 1/8 1/4 1/8 (3) .282 .508 .692 .282 .508 .692 .282 .508 .692 .282 .508 .213 cont. (4) (5) 10.8 116 11.4 129 12.1 142 10.8 116 11.4 129 12.1 142 10.8 116 , 11.4 129 12.1 142 10.8,,116 11.4 129 10.5 225 127 (7) NLDU‘IONUIUImN O \OCDUIOkflmOUO NNI—‘I—‘l—‘H O 0.. UUNU-L‘U’IQN s s o s hDhDhthh‘h‘ O UIHIBJO\\JBJUJG> P‘F‘ O O O O hthhDh‘hd NU‘UU‘IONNI-‘I-‘mo .0 O hfihl\lu>o\\lc>m>hih‘ memO‘INmmN O bNOxNNmH-I-‘m HI—‘I-‘l-‘H (8) 28.3 27.0 60.8 61.1 60.6 61.6 93.3 90.3 31.5 32.8 59.1 59.6 56.2 51.3 88.2 90.9 33.6 31.3 31.1 29.2 28.7 51.8 62.1 92.5 90.9 55.4 30.8 31.2 31.7 28.8 56.1 60.8 59.1 63.4 46.1 43.0 42.1 38.8 page 2 of 3 (10) (11) 1.11 1 1.09 1 heated 1.19 1 1.19 1 1.19 1 heated 1.20 1 " 1.22 1 1.18 1 heated 1.22 l 1.28 1 heated 1.16 1 1.16 1 heated 1.26 0 1.05* 1 undisturbed 1.16 1 1.19 1 heated 1.33 1 1.22 l heated 1.34 0 " 1.25 0 " 1.13 1 " 1.22 1 1.21 1 heated 1.20 1 1.20 1 heated 1.05* 1 individual droppings 1.21 1 1.25 1 1.25 1 1.15 1 raised 1/8" 1.14 1 1.21 1 heated 1.21 l " 1.28 l " 1.05* 1 heated and undisturbed 1.28 0 2-surface 1.25 0 " 1.14 0 " Table 8.2 (1) 1003 1008 1010 1005 1001 1002 1004 1006 1007 1009 1102 1106 1109 1101 1105 1104 1103 1107 1201 1202 1203 1204 1205 (2) 1/8 1/4 3/8 1/8 1/4 3/8 1/8 1/4 3/8 1/8 1/4 (3) .282 .508 .692 .282 .508 .535 .692 .231 .349 .444 .282 .508 cont. (4) 10.8 11.4 (5) 116 129 142 116 129 245 142 225 238 250 129 128 (6) 41.1 40.0 42.1 80.5 81.5 73.3 79.3 83.0 77.5 121.6 39.5 39.5 38.1 81.4 78.7 157.8 119.4 118.9 57.5 99.5 134.3 (7) 9.0 9.2 10.5 18.0 17.6 12.6 18.9 18.2 15.4 N U‘ o oo UIUII—‘Chmflmm s O‘HmUNl-‘UIN NNUI—‘H (8) 31.1 29.7 30.4 60.5 61.9 59.3 58.2 62.8 60.4 92.9 30.1 29.8 29.9 62.8 60.0 121.3 90.6 89.4 43.4 75.3 102.7 29.6 Page 3 of 3 (10) (11) 1.25 l 1.22 1 heated 1.28 0 " 1.23 1 1.24 l scored 1.05* 1 undisturbed 1.21 0 1.27 1 heated 1.05* 1 heated and undisturbed 1.24 l heated 1.21 l 1.21 1 heated 1.16 1 " 1.24 1 1.20 l heated 1.20 1 8" length 1.22 l 1.21 1 heated 1.19 1 2-surface 1.20 l " 1.21 1 " 1.21 1 cooled 1.22 1 " * Estimated density 2 {{ Age: Nominal thickness (1/8 in. = 0.317 cm., 1/4 in. = 0.635 cm. and 3/8 in. = 0.952 Cm.) 0 - sample material collected after remaining in the pit area 72 hours or longer. 1 - sample material collected within 24 hours of being deposited in the pit area. 129 Table 8.3 Constant rate analysis: Unheated samples 2 3 8 o -.-I u A A t: d H K a. Rate Rate 0 3 8 e ‘3 ° E 1’: h” 11“” 53 9~° E .7. .3 831. 21281. .29. as .22 {se. 2 f: fig cm g' 1/hr -‘7 f; hr/cm gm/hr min min min hr/cm : (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)(11) (12) (13) 0202 .28 6 .0581 3 1.007 .0138 .160 " 0205 7 .0580 1 1.010 .0138 .160 0208 6 .0612 2 1.011 .0147 .171 202,5,8 18 .0590 3 1.009 .0141 69 80 85 .0156 +6 0203 .51 7 .0378 1 1.007 .0161 .103 0206 7 .0398 1 1.005 .0168 .105 0209 7 .0383 1 1.006 .0165 .106 203.6,9 21 .0386 3 1.006 .0165 80 87 85 .0174 +5 0204 .69 6 .0292 2 1.003 .0165 .0715 0201 7 .0285 2 1.001 .0162 .0714 0207 7 .0267 1 1.004 .0160 .0715 204,1.7 20 .0278 3 1.001 .0162 82 85 85 .0168 +4 0301 .28 5 .0728 2 .984 .0190 .215 0305 5 .0677 4 .999 .0184 .194 0313 5 .0736 2 .996 .0158 .182 301,5,13 15 .0714 4 .991 .0177 87 80 87 .0175 -1 0302 .51 6 .0470 1 .992 .0216 .148 0312 6 .0387 1 1.003 .0170 .124 .0193 97 87 87 .0193 o 0303 .69 5 .0340 2 .993 .0208 .0975 0310 7 .0304 1 .997 .0196 .0920 0311 7 .0312 1 .998 .0179 .0992 3.10.11 19 .0278 16 .947 .0194 94 85 87 .0186 -4 0402 .28 4 .0707 4 .992 .0164 .235 85 91 94 .0180 -10 0401 .51 6 .0493 2 .996 .0221 .172 116 94 94 .0186 -16 0403 .69 6 .0370 2 .997 .0230 .134 116 91 94 .30180 -22 0405 .85 6 .0335 2 .997 .0247 .128 0404 5 .0403 3 .993 .0274 .160 -l ‘ dun—m '3'}! 130 Table B.3 cont. page 2 of 3 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)(11) (12), (13) 0503 .28 9 .0243 3 .979 .0063 .112 50 48 39 .0066 +5 0502 6 .0250 5 .982 .0063 .0736 0504 .51 14 .0138 4 .990 .0068 .0676 50 47 39 .0064 -6 0505 .69 14 .0103 l .989 .0067 .0454 52 45 39 .0062 -7 0603 .28 4 .0628 2 1.014 .0153 .244 45 48 40 .0165 +8 0602 .51 7 .0340 1 1.014 .0160 .131 47 47 40 .0159 -1 0604 6 .0337 1 1.012 .0159 .132 0601 .69 9 .0231 1 1.009 .0152 .090 44 45 40 .0154 +2 0704 .28 6 .0408 3 1.002 .0110 .165 50 48 40 .0106 -3 0705 .51 7 .0254 1 1.007 .0117 .099 0701 5 .0215 1 1.005 .0094 .051 0705 6 .0262 1 1.005 .0103 .062 705,1.3 18 .0247 7 .991 .0110 53 47 40 .0102 -7 0702 .69 7 .0179 2 1.008 .0112 .0688 51 45 40 .0099 -11 0801 .28 4 .0964 4 .977 .0297 .356 84 88 96 .0300 +1 0803 .51 4 .0660 3 .986 .0316 .245 92 94 96 .0322 +2 0804 .69 5 .0589 2 .985 .0383 .230 112 91 96 .0311 -19 0802 -- 3 .0821 5 .971 .0337 .264 0903 .28 3 .0440 4 .976 .0117 .174 0905 5 .0448 6 .970 .0121 .167 0901 5 .0470 12 .983 .0128 .184 0902 3 .0487 10 .922 .0121 .186 3.5.1.2 16 .0481 10 .984 .0122 77 88 93 .0122 0 0904 .51 5 .0347 4 .981 .0151 .120 109 94 93 .0130 -14 1003 .28 5 .0405 1 .993 .0108 .140 44 48 39 .0118 +9 1005 .51 7 .0233 l .996 .0109 .0783 1001 7 .0230 1 .999 .0110 .0809 1002 7 .0240 1 .995 .0110 .113 1004 6 .0227 2 .991 .0103 .070 05.1.2.4 27 .0232 2 .990 .0108 45 47 39 .0114 +4 1102 .28 6 .0362 1 .986 .0094 .133 65 75 66 .0108 +15 1101 .51 11 .0181 1 .990 .0088 .070 61 72 66 .0105 +19 12 .0150 1 .994 .0096 .0544 66 70 66 .0101 +6 1103 .69 131 Table B.3 cont. page 3 of 3 (1) (2) (3) (4) (5) (6) (7) (3) (9) (10)(11) (12) (13) samples with 8 inch (20.3 cm) top surface length I 1 0304 .53 6 .0412 1 .997. .0192 .135 87 71 87 .0157 -18 0501 .29 12 .0201 3 .994 .0054 .096 39 32 39 .0045 -16 2-surface samples 0308 .21 4 .1141 6 .962 .0196 .279 89 99 87 .0220 +12 0307 .34 4 .0731 7 .989 .0209 .206 95 97 87 .0217 +4 0309 4 .0697 3 .974 .0185 .159 0306 .44 4 .0549 5 .988 .0216 .163 98 96 87 .0213 -2 0910 .21 2 .0775 - 1.004 .0148 .256 0911 2 .0800 - .992 .0150 .275 0912 2 .0810 - .990 .0140 .291 910.11.12 6 .0797 9 .995 .0146 116 99 93 .0137 -6 1201 .23 5 .0544 3 .996 .0105 .193 73 76 66 .0111 +5 1202 .35 6 .0346 1 .998 .0109 .123 75 75 66 .0109‘ 0 1203 .44 7 .0265 2 .993 .0109 .099 75 74 66 .0107 -2 cooled samples 1204 .28 5 .0227 1205 .51 8 .0125 1.008 .0058 .0782 78 76 66 .0056 -4 .998 .0059 .0457 79. 74 66 .0054 -7 Idro 132 Table 8.4 Constant rate analysis: Heated samples ‘3 . c. 8 o u u 3 /\ a (1 '1-1 K ----I a. K H R t R t 0 . a e t: eah .5 8 .541: q a. a . . . 8 .4 0 E .4 H K u IH fig 0) +7 3 c Real 3" 59.1.. 2 E. E. 2 3.1 m 2. cm "3 l/hr - o g -- hr C hr/cm gm/hr hr/cm G o as (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13 0406 .28 3 .1413 6 .983 2.00 2.00 5 .0323 .487 .0365 +8 0407 .51 5 .0668 2 1.003 1.35 .0292 .253 .0371 +18 0408 .69 5 .0500 2 1.002 1.35 .0300 .182 .0372 +16 0507 .28 4 .0959 2 .985 3.94 2.00 8 .0237 .436 .0239 -é3 0508 .51 7 .0411 1 1.000 2.97 .0208 .177 .0220 +6 0606 .28 3 .1367 23 1.127 2.18 2.37 9 .0318 .463 .0427 +23 0605 .51 5 .0658 1 1.030 1.94 .0309 .250 .0428 +25 0608 5 .0599 2 1.030 .0286 .237 0607 .69 5 .0487 1 1.023 2.11 .0310 .192 .0427 +25 0708 .28 5 .0554 2 1.004 1.36 0.86 4 .0157 .219 .0180 +9 0707 .51 7 .0367 2 1.022 1.44 .0169 .148 .0183 +4 0706 .69 5 .0260 1 1.018 1.45 .0166 .101 .0182 +5 0805 .28 3 .1804 11 .936 1.87 2.79 7 .0487 .697 .0595 +15 0806 2 .1910 - .973 .0512 .499 0807 3 .1611 18 .943 .0405 .429 0808 2 .1990 - .990 .0493 .743 5,6,7,8 10 .1777 6 .955 .0474 0809 .51 4 .0948 3 .985 1.44 .0457 .371 .0600 +21 0810 .69 4 .0748 3 .998 1.27 .0479 .271 .0624 +20 0907 .51 4 .0728 4 .988 2.10 2.79 6 .0343 .273 .0368 +3 0906 4 .0728 5 .993 .0334 .245 0909 4 .0692 1 .989 .0340 .242 0908 4 .0822 5 .978 .0294 .283 907,6,9 12 .0716 4 .987 1008 .28 4 .0772 1 1.015 1.91 1.26 7 .0198 .249 .0221 +7 1010 4 .0695 2 .995 .0182 .202 1006 .51 5 .0362 1 1.009 1.55 .0176 .125 .0222 +17 1007 6 .0416 1 1.015 .0195 .163 1009 .69 8 .0259 1 1.011 -- .0170 .094 .0222 +20 1106 .28 4 .0898 5 .994 2.48 2.37 8 .0231 .316 .0249 +3 1109 3 .0885 8 .965 .0228 .373 1105 .51 5 .0504 1 .999 2.78 .0234 .185 .0255 +5 1107 .69 7 .0335 1 1.002 2.24 .0211 .117 .0247 +11 1 33 Table B.5 Falling rate analysis Moisture ratio estimates at: Timeof last w Critical time observation used d 1.1 Kf E .0 M 9 MC M 9 MC .218 e “’ :1 .51 “7 1.4.. Cl” ‘1' 1.41. ' an E +2 3 gag 7° cat-kg 7. g; cm él/hr -/°§ -- g 3 hr wb -- .3: 3 hr wb (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)(11) (12)(13)(14)(15)(16) 0202 .28 4 .196 27 .992 .30 .42 .18 12.0 49 .03 .15 0 24.0 18 0205 4 .210 28 .991 .28 .39 .16 12.5 47 .03 .15 0 24.0 17 0208 4 .222 2 .999 .28 .28 .27 12.0 47 .05 .05 .04 20.0 20 202.5,8 11 .2025 11 .986 .29 .32 .24 12.2 48 .03 .07 0 24.0 16 0203 .51 7 .0946 2 .999 .40 .41 .39 16.0 54 .05 .06 .02 40.0 20 0206 8 .103 7 .998 .39 .43 .34 15.5 53 .03 .07 0 40.0 17 0209 7 .107 5 .999 .36 .38 .34 16.7 53 .03 .05 0 40.0 18 203.6,9 22 .102 5 .994 .38 .41 .35 16.0 53 .03 .06 0 40.0 18 0204 .69 10 .0387 5 .998 .75 .79 .72 8.5 67 .16 .19 .13 48.0 33 * 0201 10 .0415 2 .999 .68 .69 .67 11.0 65 .15 .15 .14 48.0 33 * 0207 10 .0387 1 .999 .68 .69 .68 12.0 66 .17 .18 .16 48.0 37 * 204,1,7 30 .0397 3 .998 .70 .72 .68 10.8 66 .16 .18 .14 48.0 35 * 0301 .28 4 .273 23 .994 .27 .38 .16 9.7 48 .02 .15 O 20.0 14 0305 4 .273 33 .988 .25 .37 .13 11.0 45 .02 .19 0 20.0 13 0313 4 .228 38 .985 .32 .50 .14 9.0 47 .03 .23 0 20.0 15 301,5,13 12 .258 12 .983 .28 .33 .22 10.0 48 .02 .08 0 20.0 14 0302 .51 4 .170 10 .999 .28 .31 .24 15.3 49 .04 .07 0 28.0 17 0312 4 .1575 22 .995 .25 .29 .20 19.5 48 .06 .13 0 28.0 22 302,12 8 .1635 29 .949 .26 .36 .19 17.2 48 .05 .14 0 28.0 20 0303 .69 5 .0595 4 .999 .57 .58 .56 12.5 64 .23 .24 .21 28.0 43 * 0310 4 .0639 9 .999 .48 .49 .46 17.0 61 .24 .26 .21 28.0 45 * 0311 4 .0633 9 .999 .49 .51 .47 16.0 63 .24 .25 .21 28.0 46 * 3.10.11 12 .0625 6 .996 .51 .53 .49 15.2 61 .23 .24 .21 28.0 43 * 0402 .28 4 .320 23 .994 .22 .30 .13 11.0 46 .03 .11 0 17.3 17 0401 .51 5 .158 12 .996 .31 .36 .26 13.9 55 .04 .09 0 27.3 20 0403 .69 6 .0720 2 .999 .52 .53 .51 13.0 67 .14 .15 .13 31.3 28 * 0405 .85 6 .0610 1 .999 .55 .56 .54 13.3 69 .18 .19 .17 31.3 45 * 0404 6 .0787 4 .999 .51 .53 .49 12.0 68 .11 .13 .09 31.3 37 * Table 8.5 cont. (E>(2) CD (4) (5) U» 0503 .28 4 .0967 16 .997 0502 f 0504 .51 3 .0262 10 .999 0505 f 0603 .28 3 .3475 94 .992 0602 .51 3 .0933 32 .999 0604 3 .0936 33 .999 602.4 6 .0934 7 .998 0601 .69 f 0704 .28 5 .1635 7 .994 0705 .51 5 .0502 6 .999 0701 5 .0327 4 .999 0703 5 .0514 7 .999 705.3 10 .0510 5 .999 0801 .28 3 .311 82 .994 0803 .51 5 .202 9 .999 0804 .69 5 .1335 3 .999 0802 -- 7 .144 2 .999 0903 .28 5 .154 13 .996 0905 5 .184 18 .992 0901 5 .165 14 .995 0902 5 .202 13 .996 03.5.1.2 20 .176 19 .925 0904 .51 5 .0855 8 .997 1003 .28 9 .1935 13 .987 1005 .51 6 .0725 9 .997 1001 6 .0687 9 .997 1002 6 .0865 13 .993 1004 6 .0606 8 .997 05.1.2.4 24 .0721 12 .963 1102 .28 7 .224 15 .987 1101 .51 4 .0580 13 .998 1103 .69 2 134 (7) .52 .18 .36 .36 .36 .25 .50 .65 .50 .50 .31 .33 .44 .57 .28 .25 .28 .24 .26 .40 .21 .32 .33 .28 .37 .32 .16 .31 (8) .53 .34 .40 039 .37 .28 .51 .66 .51 .51 .47 .37 .45 .59 .32 .29 .33 .28 .31 .27 .34 .35 .30 .39 .35 .21 .33 (9) .51 .02 .33 .33 .35 .22 .49 .64 .49 .49 .15 .28 .43 .55 .25 .20 .24 .19 .21 .14 .30 .31 .25 .35 .30 .10 .29 (10)(11> 30.0 58 33.7 73 44 60 60 60 53 67 63 69 5 68 55 57 64 . 66 56 51 56 51 53 61 46 54 56 58 56 56 42 57 page 2 of 4 (12)(13)(14)(15)(16) .09 .43 .04 .23 .24 .06 .34 .45 .33 .33 .11 .03 .08 .05 .06 .04 .05 .03 .04 .01 .10 .11 .07 .14 .04 .17 .11 .44 .28 .27 .28 .08 .35 .45 .34 .35 .32 .07 .09 .06 .10 .10 .09 .07 .10 .10 .12 .13 .10 .16 .07 .18 .05 41.7 .42 41.7 0 17.7 .19 23.7 .20 23.7 .03 0 34.0 .08 45.0 .09 45.0 .04 45.0 .11 45.0 0 31.2 .14 47.2 37 69 * 20 50 * 51 * 27 59 55 60 60 31-31'31'1- 33 16 28 20 27 22 25 19 23 44 * 13 31 34 32 35 22 46 * 135 Table B.5 cont. page 3 of 4 (1) (2) (3) (4) (5) (6) (7) (8) (9) (101(11) (12)(13)(14)(15)(16) samples with 8 inch (20.3 cm) top surface length 1' '2': _ .a_-- n! 0304 .53 4 .195 26 .993 .21 .27 .16 10.0 44 .04 .12 0 28.0 18 0501 .29 4 .0566 12 .998 .35 .37 .34 31.7 65 .20 .22 .18 41.7 52 * 1104 .53 4 .0515 10 .999 .34 .35 .33 37.0 59 .20 .21 .19 47.2 48 * 2-surface samples 0308 .21 4 .4025 27 .992 .28 .46 .10 6.0 44 .01 .23 0 16.0 11 0307 .34 5 .2455 11 .997 .30 .38 .22 9.5 49 .01 .10 0 28.0 11 0309 5 .235 10 .997 .30 .37 .23 9.5 44 .01 .10 O 28.0 10 307.9 10 .240 6 .997 .30 .34 .26 9.5 45 0306 .44 5 .169 15 .995 .33 .40 .24 12.0 52 .03 .10 0 28.0 16 0910,0911,0912 .21 6 .1775 28 .971 .45 .49 .41 6.9 61 .28 .33 .23 9.5 51 1201 .23 4 .409 30 .990 .13 .22 .04 16.0 38 .01 .12 0 25.2 14' 1202 .35 4 .159 40 .983 .22 .31 .13 22.5 48 .04 .14 0 33.2 23 1203 .44 6 .1125 13 .993 .24 .27 .20 28.6 51 .03 .08 0 47.2 21 heated samples 0406 .28 7 0407 .51 4 .360 44 .979 .18 .32 .05 12.2 45 .04 .19 0 17.3 21 0408 .69 4 .183 31 .990 .27 .35 .19 14.0 53 .05 .15 0 23.3 24 0507 .28 3 .428 28 .999 .22 .27 .18 7.9 54 .09 .13 .05 10.0 36 0508 .51 4 .200 40 .983 .21 .27 .14 19.3 51 .05 .15 O 25.5 26 0606 .28 f 0605 .51 3 .472 -- .988 .14 .33 0 13.5 39 .05 .32 0 15.0 22 0608 3 .278 78 .994 .21 .34 .09 13.6 49 .06 .30 0 17.7 26 605.8 6 .375 59 .909 .17 .25 .08 13.7 45 0607 .69 4 .213 30 .990 .23 .30 .16 16.2 50 .04 .13 0 23.7 21 0708 .28 4 .452 25 .993 .12 .19 .05 16.0 37 .01 .06 0 23.5 12 0707 .51 5 .145 16 .994 .25 .27 .23 21.0 53 .09 .12 .07 27.5 33 0706 .69 4 .0630 9 .999 .41 .42 .40 23.2 63 .31 .32 .30 27.5 57 0805,0806,0807,0808 .28 8 .865 46 .881 .20 .40 0 4.2 41 0809 .51 4 .381 28 .992 .25 .34 .16 7. 52 .02 .16 0 14.2 14 0810 .69 4 .250 27 .992 .30 .38 .22 9.3 54 .05 .15 0 16.2 22 136 Table B.5 cont. page 4 of 4 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)(11) (12)(13)(14)(15)(16) 0907 .28 4 .389 37 .985 .18 .28 .09 11.0 45 .02 .15 0 16.7 16 0906 4 .379 41 .982 .19 .30 .08 11.0 44 .02 .17 o 16.7 16 0909 4 .406 41 .982 .17 .30 .04 11.7 42 .01 .14 0 18.7 15 0908 3 .539 -- .986 .15 .43 0 10.0 40 .01 .42 0 14.7 15 906.7.9 12 .370 15 .973 .20 .24 .15 11.0 44 1008,1010 .28 4 .476 67 .954 .15 .29 .02 11.5 36 .09 .17 0 14.0 27 1006 .51 6 .191 22 .981 .19 .24 .14 22.7 44 .07 .10 0 30.0 26 1007 5 .191 19 .991 .22 .25 .19 19.0 49 .06 .09 .02 26.0 26 1009 .69 6 .103 12 .993 .25 .28 .22 29.3 50 .05 .08 .02 45.0 23 1106,1109 .28 3 .438 71 .995 .20 .31 .09 8.7 50 .06 .22 o 11.2 26 1105 .51 4 .2085 35 .987 .24 .31 .17 15.0 51 .05 .17 0 21.2 26 1107 .69 5 .121 13 .996 .28 .30 .25 21.0 53 .09 .11 .06 31.2 32 cooled samples 1204 .28 5 .0623 7 .998 .36 .38 .34 28.5 58 .12 .13 .09 47.2 37 * 1205 .51 5 .0204 5 .999 .61 .62 .60 31.0 70 .44 .45 .43 47.2 64 * * Value at end of test-run, end of falling rate drying period not reached. { Insufficient data. **‘ Confidence limits at the 95 percent level. 137 Table B.6 Summary t: a rH V Q de F Kc X f Met MC! Run 0 o _EEH_£E .22; 2 exp** No. F C % sec sec hr/cm cm cm l/hr 1/hr -- -- (1) (2) (3) (4) (5) (6) (7) (3) (11) (12) (137(14) 1 0500 80 27 67 25 1 -- .0245 .0967 .25 .28 2 1100 70 21 68 76 2% .0362 .224 .16 .20 3 1000 80 27 52 25 1 .0405 .1935 .21 .24 4 0700 90 32 64 25 1 .0408 .1635 .25 .27 5 0900 80 27 76 147 5 .0460 .176 .26 .32 6 0200 82 28 62 122 4 .0590 .196 .29 .31' 7 0600 90 32 40 25 1 .0628 .3475 .18 .21 8 0400 80 27 60 147 5 .0707 .320 .22 .25 9 0300 90 32 63 122 4 .0714 .273 .28 .28 10 0800 90 32 40 147 5 .0964 .311 .31 .32 11 0500 80 27 67 25 1 .0138 .0262 .52 .53 12 1100 70 21 68 76 2% .0181 .0580 .31 .31 13 1000 80 27 52 25 1 .0232 .0725 .32 .34 14 0700 90 32 64 25 l .0245 .0502 .50 .50 15 0600 90 32 40 25 1 .0340 .0933 .36 .36 16 0900 80 27 76 147 5 .0347 .0855 .40 .43 17 0200 82 28 62 122 4 .0386 .102 .38 .41 18 0300 90 32 63 122 4 .0415 .170 .26 .30 19 0400 80 27 60 147 5 .0493 .158 .31 .31 20 0800 90 32 40 147 5 .0660 .202 .33 .34 21 0500 80 27 67 25 1 .0103 -- -- '- 22 1100 70 21 68 76 2 .0150 -- -- ~- 23 1000 80 27 52 25 1 -- -- -- -- 24 0700 90 32 64 25 l .0179 -- -- -- 25 0600 90 32 40 25 1 .0231 -- -- -- 26 0900 80 27 76 147 5 -- -- -- '- 27 0200 82 28 62 122' 4 .0280 .0387 .70 .71 28 0300 90 32 63 122 4 .0315 .0625 .51 .50 29 0400 80 27 60 147 5 .0370 .0720 .52 .51 30 0800 90 32 40 147 5 .0589 .1335 .44 .45 31 1200 70 21 67 76 2% .0227 .0623 .36 .37 32 0700 90 32 64 25 1 .0554 .428 .12 .15 33 1000 80 27 52 25 1 .0733 .476 .15 .16 34 1100 70 21 68 76 2 .0890 .438 .20 .24 35 0500 80 27 67 25 1 .0959 .428 .22 .23 138 Table B.6 cont. page 2 of 2 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)(14) 36 0600 90 32 40 25 -1 23.0 .28 .10 .1367 -- -- -- 37 0400 80 27 60 147 5 19.5 .1413 -- -- -- 38 0900 80 27 76 147 5 27.1 -- -- -- ~- 39 0800 90 32 42 147 5 27.1 .1800 .865 .20 .23 40 -- 41 1200 70 21 67 76 2% * .51 .39 .0125 .0204 .61 .61 42 0700 90 32 64 25 1 8.4 .0367 .145 .25 .28 43 1000 80 27 52 25 1 12.2 .0390 .191 .19 .23 44 0500 80 27 67 25 1 19.5 .0411 .200 ..21 .22 45 1100 70 21 68 76 2% 19.5 .0504 .2085 .24 .26 46 0600 90 32 40 25 1 23.0 .0630 .375 .17 .17 47 0400 80 27 60 147 5 19.5 .0668 .360 .18 .22 48 0900 80 27 76 147 5 27.1 .0716 .389 .20 .22 49 0800 90 32 42 147 5 27.1 .0948 .381 .25 .30 50 -- 51 1200 70 21 67 76 2% -- .69 .85 -- -- -- ~- 52 0700 90 32 64 25 1 8.4 .0260 .0630 .41 .42 53 1000 80 27 52 25 1 12.2 .0259 .103 .25 .28 54 1100 70 21 68 76 2% 19.5 .0335 .121 .28 .31 55 0500 80 27 67 25 1 19.5 -- -- -- -- 56 0600 90 32 4O 25 1 23.0 .0487 .213 .23 .26 57 0400 80 27 60 147 5 19.5 .0500 .183 .27 .31 58 0900 80 27 76 147 5 27.1 -- -- -- -- 59 0800 90 32 42 147 5 27.1 .0746 .250 .30 .30 60 -- 2-surface 61 1200 70 21 67 76 2% -- .23 .0544 .409 .13 .16 62 0900 80 27 76 147 5 .0795 .1775 .45 .45 63 0300 90 32 63 122 4 .1141 .4025 .28 .33 64 1200 70 21 67 76 2% -- .34 .0346 .159 .22 .25 65 0900 80 27 76 147 5 -- -- -- -- 66 0300 90 32 63 122 4 .0715 .240 .30 .36 67 1200 70 21 67 76 2% -- .44 .0265 .1125 .24 .27 68 0900 80 27 76 147 5 -- -- -- -- 69 0300 90 32 63 122 4 .0549 .169 .33 .38 * cooled sample ** Experimental value at estimated critical tum98 CI' MICHIGAN STQTE UN 111111111 IV. LIBRARIES IIIIIIIIIIIIIIIIIIIIIIII 03241 I 7