Illllllllllllllll”Illllllllllllllllllllllllllllllll 9’?” A R Y 3 1293 10462 0848 “’1" “3’3“ Jude . University This is to certify that the thesis entitled ENERGY CONSERVATION IN GRAIN DRYERS USING HEAT PIPE EXCHANGERS presented by Shahab Sokhansanj has been accepted towards fulfillment of the requirements for Ph.D. . Ag'ri ltural En ineerina degree in cu g " Major professor Date/’/'-77 07639 “a »—_-\ A .. .. ‘2 .m— ‘WW ~ ..) .- . ,— “r—" ‘ O . ‘_ “'. I —t 111‘ ENEMY (INSERVATICN IN GRAIN DINERS USIIB HEAT PIPE W By ShahabSokhansanj A DISSERTATICN Suhnitted to Michigan State Universtiy in partial fulfillment of the requimts for the m of WWW Agricultural Engineering Deparhnent 1977 PLEASE NOTE: Dissertation contains computer print-outs that have broken and indistinct print. Filmed best way possible. UNIVERSITY MICROFILMS 4mm mNSERVATIQ‘i IN GRAIN DRYERS USING HEAT PIPEEXCHAMERS By SiahabSokhansanj Grain drying is a major energy consuner in the processing of agricultural prochcts . A heat exchanger med to recover the waste heat from exhaust air is one way to increase the energy efficiency of the pro- cess. However, gas to gas heat recovery is a low efficiency heat transfer process and, consequently, a large and expensive heat exchanger is required to transfer a certain annunt of heat. The newly developed heat pipe exchangers are mre efficient than the conventional types. Transpor- taticn of heat by evaporation and condensat ion of a liquid in an mclcsed pipe is the principle of heat pipe operation . In this investigation the heat pipe characteristics important in a grain dryer application are considered. The performance of a coupact heat pipe exchanger is analyzed when both sensible and latent heat are present. A nonlinear optimization technique is used for an optiml design. Also the possibility of using a linear optimization schare is investigated. The profitability of heat pipe exchanger as influenced by the annual fuel escalation, inflation, interest, and tax rates is investigated. A 5-year and a lO-year service life and 750 hours of operation per year are the asampticns used in the economic analysis. Shahab Sokhansanj Experimental results show that up to 18 percent of the energy can be saved in a ccncurrait-flow dryer by the use of a heat pipe exchanger. Fouling in a heat pipe exchanger results in increased pressure drop rather than in decreased heat transfer . To prevent the heat ex— changer blockage, particles larger than .6 mn must be filtered out of the grain dryer exhaust air prior to entry into the heat exchanger. At least twice a year cleaning is recomnended for the heat exchanger surface area. Heat recovery with and without a heat pipe exchanger was investigated by sinulation. Results show that direct recirculation in concurrent-counter- flow dryers yields camarable savings to those obtained when recycling is performed throrgh a heat pipe exchanger. A ccubination of direct recycling of the cooler exhaust and, indirect recycling of the dryer exhaust through a heat pipe exchanger , reduces the energy consunpt ion to about 2964 kj per kg of water renoved, as compared to 3488 kj for a concurrent-flow dryer witmut recirculation and use of a heat pipe exchanger. Sinnlation results also straw that the heat pipe exchanger in crossflow dryers is less profitable than in concurrent-flow dryers . The annual fuel escalation, inflation rate, interest rate and the rate of taxation have significant effects on the profitability and the net present value of a heat pipe exchanger . Approved /’ ii! 4/4! ’1 ‘ or ' ens?- -77 W, Min»... Department (hairunn 'lhe author expresses his deep appreciation to his acadanic advisor Dr . F . W . Bakker-Arkem . Professor Wer-Arkeua' s friendship and generous advice made the graduate study a joyful experience, and the presmt work possible . Sincere appreciation is extended to Dr. L. J. Segerlind, Agricultural Engineering Department, Dr. M. C. Smith, Mechanical Engineering, Dr. J. R. Black, Agricultural Econanics Department, and Dr. J. V. Beck of the Mechanical Engineering Department for their valuable advice during the author's academic program and this research. The author appreciates the opportunity of being associated with the very special people of the Agricultural Engineering Department and particularly benefited from the processing group: Mitch Roth, Lloyd Ierew, Roger Brook, Edison Rugunayo, Larry Walker, Steve Kalchik, Damis Kline, and Ralph Gygax. Thankful acknowledgment is extended to the people of Iran who supported and inspired the author throrgh the ministry of higher educatim to continue a profession in food production. 'Ihe financial support of the Andersons, Maunee, (bio, is deeply appreciated. ii To Gity TAHEG‘CINTHWI‘S HSTOFTAHLES LISTOFFIGURES LISPOFSYMHIS WEN CBJEIII‘IVES l. REVIEWOFLI'IERA’IURE 1.1 Graindrying. 1.2 Heatpipe . 1.3 Heatpipeexchangers 2. REVIEWCFHEATPIIEPRII‘CIPIES 2.1 Introduction. . 2.2 Heat pipe construction. 2.2.1 Pipe 2.2.2 Wick . . . . . 2.2.3 Fluid . . . . . 2.3 Heat pipe therml transport capability. 3. HEAT PIPE EXCHANGE ANALYSIS. 3.1 Introduction . . 3.2 Heat pipe exchanger effectiveness. 3.2.1 Finite differences . . 3.2.2 Finite elemnts . . . . 3. 3 Heat transfer coefficient and friction factor 3.4 Fouling factor . . . . . . 3.5 Profitability nodel 3.6 Sinulation . iv ii vi viii 16 83888 8383 SN N 4. EXPERIMDJTAL. . . . . . . . . . 69 4.1 Introduction. . . . . . . . . 69 4.2 Heat pipe exchanger . . . . . . . 69 4.3 Chain dryer . . . . . . . . . 71 5. HEAT PIPE W (PI‘DIIZATICN. . . . . . 78 5.1 Introduction. . . . . . . . . 73 5.2 Linear optimization . . . . . . . 79 5.3 Nonlinear optimization. . . . . . . 88 5.3.1 Application to heat pipe exchanger. . . 89 5. 3. 2 Results . . . . . . 91 6. MILTS AND DISCIJSSKNS . . . . . . . 101 6.1 Introduction. . . . . . . . 101 6.2 Laboratory test results . . . . . . 101 6.3 Sinnlation resmlts . . . . . 105 6.4 Economies of heat pipe exchanger. . . . . 112 6.4.1 Heat pipe exchanger and concurrentflow dryer . 114 6.4.2 Heat pipe exchanger and cannercial crossflow dryers . 119 6.4.3 Heat pipe exchanger and batch type dryers 126 6.4.4 The effects of fouling on heat pipe exchanger. economics . . . . 127 7. (INIIIJSIQB . . . . . . . . . . 132 8. SHEETKNS 1m MIKE m. . . . . . . 134 9. LIST (1' mm . . . . . . . . 136 APPENDIX A . . . . . . . . . . . . 143 APPENDIX B . . . . . . . . . . . . 172 Table 1-1 2—1 2—2 2-3 3-1 3-2 3-3 4—1 4—2 4-3 5—1 5—2 5—3 5—5 LIST OF TABLES Energy requirerents of different types of dryers to evaporate one kilogram of water from wet grain. (berating tenperature range, melting and boiling points of some comnercial heat pipe fluids. Physical and thermal properties of sane of the commercial heat pipe fluids. . . . . . . . . Typical resistances against the heat flow in a water- operated heat pipe . . . . . Carparison of high temerature heat recovery Imits . Correlations for predicting the heat transfer coefficient - and the pressure drop in a heat pipe exchanger. Dimensional specificat ions of finned tube heat exchangers, utilized in the camarison of heat transfer coefficient and pressure drop correlations . . . . Perfomance characteristics and the construct ion of the experimental heat pipe exchanger, ISO-FIN, as specified by the nanufacturer . . . Settings for the concurrent-counterflow dryer utilized in the soft meat drying experiment . . . Settings for the concurrent-counterf low dryer utilized in the corn drying experiment . . . Tabulation of the sanple linear progranming problem. The output of the linear programing optimization using the inputs of Table 5-1 . . A camarison between an optiml design of heat pipe exchanger with Im-FIN unit . . . . 'Ihe Westelaken grain dryer specifications. 'Ihe inputs for optinal design of heat pipe exchangers for various nodels of Westelaken grain dryers . Oonparison of different values of the convergence criterion for the optimal designed heat pipe exchanger vi 17 18 22 26 52 7O 75 77 87 87 92 95 97 Table 5-7 6-1 6—2 6-3 6-7 6-10 6-11 6-12 6—13 The optical designed heat pipe exchangrs for various nodels of Westelaken gain dryers . . . . . . 99 'Ihe effect of fouling resistance on the optimal asigned heat pipe exchanger for the Westelaken gain dryer Ibdel 810-A . . . . . . 100 Heat pipe exchanger performance test results . . . 102 Test results of wheat drying in a concurrent-cormterflow dryer equipped with heat pipe exchanger . . . . 106 Test results of corn drying in a concurrent-counterflow dryer . . . . . . . 107 Settings for simlat ion of the concm'rent-comterflow gain dryer. lbdel 8lO—A . . . . . . . 109 Sinnlated test results, using a heat pipe exchanger in the concurrent-cormterflow dryer, the Westelaken Model 810—A. . . . . . . 110 Sinnlated test results, using direct recycling, in the concurrent-comterflow dryer, the Westelaken Ibdel 810-A . . . . . 111 ’Ihe effect of drying tenperature on the savings, as a result of sinulating the use of a heat pipe exchanger in the concurrent-comterflow dryer Model 810-A . . . . 113 Present (first year) costs and savings chta for use in the profitability analysis of heat pipe exchangers, used in different nodels of the Westelaken gain dryers . . . 115 Cashflow and net present value analysis of different sizes of heat pipe exchangers, used in the Westelaken gain dryers 116 Some typical dinensions and process values of a camercial crossflow dryer nnnufactured by Ferrel-Ross Co. , Saginaw, Michigan. . . . . . . 123 Input for the optimal design and output specifying the optimal designed heat pipe emhanger for use in the Ferrel-Ross crossflow dryer . . . . . 124 Annual cashflow and net present value analysis of the optiml heat pipe exchanger, used in the Ferrel-Ross crossflow dryer . . . . . . 125 Particle size and the weigt percentage in a typical exhaust air fran a crossflow dryer . . . . 130 Figure 2-1 'Ihe principle of heat pipe operation . 2-2 A tubular heat pipe construction and operation . 2-3 A thernosyphon construction and operation . 2—4 Heat path through a heat pipe and its analogy to an electrical resistance network . 3—1 A bmdle of heat pipes in a housing LIST OF FIGUM'E 13a 13a 13a 21 25 3-2 A cross section of heat pipe exchanger parallel to the 3—3 Specific hunidity of the air-vapor mixture in the eleuent and on the fin surface in a heat pipe exchanger 34 'Ihe psychrouetrics of the air—vapor mixture in a heat pipe 3-5 A section of the heat pipe (or a solid bar) for which eqmtion 3-41 is written . 3—6 Division of a heat pipe exchanger into square gids . 3—7 A typical elanent with the specified nodes . . 3—8 Heat transfer coefficient predicted by diffeer correla- tions for various surface configurations . . . . 3—9 Pressure drqa predicted by different correlations for various surface cmfiguratims . . . . 3-10 Heat transfer coefficient versus airflow for surface G (Table 3-3), predicted by different correlations 3-11 Pressure drop versus airflow for surface G (Table 3-3) predicted by different correlations . . . 3-12 Fouling resistance versus time for systems in which the deposition rate predaminates (Curve A) and in which the removal rate increases with the fouling thickness (Curve B) viii Figure 3-13 4-1 4—2 4-3 5—1 5—2 6-1 6-2 6-3 6-4 3323 6-7 A flow chart of the subroutine "PMS". Experimental set up for the performance tests of the heat pipe exchanger . . . Schenatic of the concurrent- cormterflow dryer used in the wheat drying experinents . . . . Schematic of the concurrent-counterflow dryer used in the corn drying experiments . . . . . . Box (MEX AIGGII'IHM) logic diagram Westelaken gain dryer Deviations of the predicted energy saving fran the experimental values; (0 line). Net present value as a function of fuel escalation and tax rate, for a heat pipe exchanger life of 5 and 10 years of ' service; and 750 hours of operat ion per year. Net present value as a function of fuel escalation and inflation rate for a heat pipe exchanger life of 5 and 10 years of service; and 750 hours of operation per year Net present value as a frmction of fuel escalation and discounted cashflow rate of return (IIFR), for a heat pipe exchanger life of 5 and 10 years of service; and 750 hours of operation per year. . . . . Ferrel-Ross recirculating crossflow dryer 'Ihe effect of fouling thickness on the total anmnl costs and mvings of a heat pipe exchanger specified for the Westelaken gain dryer Model 810—A. . . Time required for the fouling thickness to reach to the critical thickness for various values of ramval rate (K2); see equation 3-103 . . . . . . -67 .74 . 76 .104 . 118 .120 . 121 . 122 .128 .129 gamwgmppkgwabddxawggao”>f58?0>> LISP OF srms Heat transfer area Mininun free flow area Finned area Annual operating cost Annual fuel saving Wick cross sectional area. Pipe or a solid bar cross sectional area Specific heat Duct concentration Cashf low at year k (ash incone at year k Pipe diameter Diffusion coefficient Depreciation Discounted cashflow at year k Discounted cashflow rate of return Hydraulic diameter Enthalpy Electricity unit cost Friction factor Annual fuel escalation First costs Friction power kWhr =7 D‘ 09 f8 "U ’U 0H2 EH2 :3 8 2° t-* g 5‘ 3:: p: pr; La. (.1. p. a: :1: Fuel unit cost Mass velocity Minn nass velocity based on the minimun free flow area Gravity acceleration Convective heat transfer coefficient Heat of vaporization Fin height (berat ing hours per year True interest rate Energy Rate of inflation 'Ihernal cmduct ivity Constant Constant Wick permeability Kilowatt hours Pipe length Heat exchanger depth Flow rate Nmber of years of service life Nunber of fins per an Net present value Nurber of rows (berating costs at year, k Perineter Pmssure P1, P2, P3 (bustants xi $/million kg kg/hr - m2 kg/hr - 1112 9.8 m/s2 W/mz - °C kj/kg m hr decimal joule decimal W/m - °C Its/hr years deciml L'U 3310 law?) U) Heat transfer rate Resistance against heat flow Eadiaust ratios Wick pore radius Seconds Distance between fins longitudinal pitch Transverse pitch Slope of the condensation line Fuel savings at year, k Terperature t Time t Fin thickness t Tax rate U Overall heat transfer coefficient Um Convective mass transfer coefficient V Volune Vc Free volume v Velocity W. Humidity ratio WB Wet basis xf Fouling thickness Subscripts a air side b bare pipe (without fin) c cold side ci cold side inlet co cold side outlet 107 hr °C/W deciml °C d dust f fin, fluid, fouling eff effective g air-vapor mixture h hot side hi hot side inlet ho hot side outlet 1 inlet , inside 3 year 3 k year k 9. liquid in metal , mixture 0 outlet , outside r radial s saturation t pipe, tube uf unfinned v vapor w wick, wall Greek synbols A Difference 5 Heat exchanger performnce effectiveness n Heat exchanger surface effectiveness 9 Wetting angle degrees 11 Viscosity kg/m - hr 9 2 Density kg/III’ 0 Liquid surface tension N/m xiii 1 Rear stress (1’ Heat pipe tilt angle (pd Rate of deposition or Rate of renoval Dimensimless nmbers Eu Euler umber Nu Nusselt umber Pr Prandtl umber Re Reynolds Sc Schnidt nunber xiv INIRCUJCI‘ICN The gain drying process consumes more ttnn 65 percent of the total energy used for on-farm corn production. To dry 100 kg of corn from 25 percent to 15 percent moisture content (WB) , an energy expenditure of 3500 to 8000 kj is required in a conventional dryer. 'Ihe United States produced more than 1.58 x 108 tons of corn in 1976. Assum'ng that 75 percent was artificially dried for safe storage, it can be estimated that 7.15x.10 7 m3 of LP gas was consuned for the drying process. As the fuel availability decreases and its price escalates, the proportion of drying to the overall production cost will increase. 'lb preserve the gain quality, to keep the costs down, and to match up with a high capacity harvesting operation, improved or new drying methods must be devised. Considerable research and developumt are carried out to improve the energy utilization of grain dryers. 'Ihe advent of the new, continuous flow concurrent gain dryers is the result of such endeavors. Pre- liminary investigations have shown that concurrent flow dryers are more efficient in energy utilization than the conventional dryers. 'Ihe efficiency may further be improved by using a proper heat recovery unit to capture the exhausted heat . Applications of heat exchangers in grain dryers have always been of interest . The low efficiency of air to air heat transfer results in large surface areas and high initial costs which are the two main obstacles 2 in the heat exchanger application . Heat pipes capable of transporting a large amount of heat are promising devices for the heat recovery applications in gain dryers. A heat pipe is a closed pipe into which a mall amount of fluid has been introduced. When heat is applied to one end of the pipe the fluid evaporates and the vapor travels to the other end of the pipe where it condenses. 'Ihe condmsate flows back to the evaporator by either gavitational forces or capillary pumping or both. Because vaporization and condensation take place at a constant terperature, the rate of heat transfer along the pipe will be high. As a result, the heat pipe becomes an excellent thermal conductor. A bundle of these pipes equipped with fins in a housing forms a carpact heat exctmnger that is referred to here as "heat pipe exchanger". 'Ihe heat pipe exchanger is able to exchange heat between the supply and exhaust air streams in a gain dryer. CBJECI‘IVES 'Ihe objectives of this study are to evaluate the technical and economic aspects of the heat pipe and to investigate the future potential of this device in gain drying operations. 'Ihe following steps are to be followed in the analysis: a) b) e) d) the heat transfer coefficient, pressure drop and fouling in a heat pipe exchanger along with the performance of the individual heat pipes will be analyzed and the proper netherat ical relat ion- ships will be developed; a profitability analysis of the hat pipe exchanger will be performed in conjunct ion with commercial concurrent flow gain dryers, and the analysis will include the effects of interest rate, inflation rate, and fuel escalation on the project profitability; an optimization procedure for weigh and analysis of an optimum heat pipe exchanger will be deve10ped and utilized; a set of experimarts will be performed to validate the computer progame . 1. REVIEWQFLITHIATURE 1.1 Grain drying Artificial gain drying in the United States was first practiced in 1947 using World War II barber engine heaters (Foster _e£_a_l_.1 1976) . Since then commercial grain dryers have been manufactured to dry large quantities of wet gain harvested with big capacity combines. 'Ihese dryers dry large volumes of gain by using a big terperature and a high airflow rate. Grain exposed to high temperatures is susceptible to breakage in subsequent handling, and may not be suitable for some end uses (Brooker M. , 1975). Serious quality probl- have prompted researchers to look for new ways of grain drying which not only ensure a big capacity, but also result in a better quality grain. 'Ihe big rate of mergy consurption in gain dryers becomes a serious problem as energy prices increase. Theoretically 2258 kj is required for one kg of water at 100°C to evaporate at atmospheric pressure . '1b the above energy, an additional amount has to be added in the gain drying process for sensible heating of the grain, and moving the gain and the air. Depending on the design, commercial dryers consume from about 3500 to about 8000-k1 of heat energy to extract 1 kg of water from the gain. Table 1-1 shows energy requirements of different types of dryers. (he type of dryer that shows promising features is of the concurrent type. In this dryer the gain and drying air flow in the same direction. cooler Table 1-1. Energy requirements of different types of dryers to evaporate one kilogam of water from wet gain. Type of Dryer 511155 Specific Source Conditions Layer drying 4290 Inlet air 32°C Woodforde 15 cm - Inlet humidity and Lawton deep (wheat) 8350 Ratio .0085 kg/kg (1965) Batdr drying 2845 Inlet air Clark and 61 cm - Imnd (1968) deep (wheat) 5194 15°C lbdified 3700 Air partially Converse cross-flow recycled (1972) Modified 3000 Corn dried from Lerew et a1 . cross-flow 22 to 15.5% (1972) Concurrent 3387 Corn dried fron Anderson flow with 21.7 to 16.4% (1972) counterflow (Anderson design) cooler Crossflow 5803 5-point removal Morey and (conventional) optimized conditions Irreschen ( 1974) Fixed—bed 2456 Heat pipe and Lai et al heat pump (1975) Concurrent 4062 5-point reroval flow with (Westelakm design) Westelaken counterflow (1977) 'Ihe air and gain reach an equilibrium temperature well below the inlet air temperature within a few centimeters from the top. Therefore, high temperature air with high flow rates can be used without damaging the gain due to excessive heat . 'lhis dryer not only preserves the quality of the gain, but also proves to be efficient in energy consumption (Graham, 1967). Becker and Isaacson (1971) simulated a concurrent- flow dryer in a wheat drying experiment and reported favorable results in energy consumption and in gain quality. Carano £131. (1971) built a laboratory size concurrent gain dryer with a counterflow cooler; the dryer was tested for quality and drying performance. Anderson (1972) reported the experimental results of a commercially sized concurrent dryer and confirmed the favorable energy and quality characteristics. Bakker-Arkema 91:_a_1_. (1972) after an evaluation of different gain dryer types stated that "the concurrent flow dryer should be considered more seriously in future designs because of its favorable quality characteristics". 'Ihe majority of the commercial continuous dryers are of crossflow type. In these dryers a moving layer of gain about 30—45 cm thick is exposed to the drying air. Iheven drying and short residmce time for the air in the bed makes the crossflow dryers the least efficient dryer as far as energy and gain quality are concerned. A number of modifications have been done to improve crossflow gain dryers. Converse (1972) conducted a series of tests with a recir- culating crossflow dryer (the Hart-Carter Model), and reported a 50 percent decrease in energy consumption. However, the resulting quality of the dried gain was not investigated. Lerew M. (1972) reported a value of 3084 kj per kg of water removed when a modified crossflow was 7 simulated. In these analyses the recirculating air is a mixture of the exhaust air from the middle and the bottom sections of a three-stage crossflow column. New commercially available recirculating crossflow dryers such as the ones manufactured by Ferrel-Ross (Anon, 1977) and Beard Industries (Noyes, 1977) have beau claimed to improve the energy efficiency and to preserve the gain quality. Much of the on-fanm gain drying takes place in a fixed-bed type gain dryer. In these operations a stationary layer of grain with a depth from .3 to several meters is dried using heated or natural air. There have been many changes and improvements both in fixed-bed drying equipment (circulating grain, stirring, fluidized, etc.) and the drying process (dryeration, low temperature drying, etc.) to make the operation economical in terms of energ consumption and quality gain. Brooker fl. (1975) presented a comprehensive review of these innovations and listed the advantages and disadvantages of each system. Definition of a dryer's efficiency is expressed differently by various researchers. In order to standardize this definition, Bakker- Arkema ial. (1973) proposed a new dryer performance evaluation index (DPEI). 'Ihe index is a measure of the total energ required by a dryer to remove one kg of water from gain dried under a set of specified conditions . Later Bakker—Arkema 3131 . (1974) introduced a variety of couputer programs to evaluate the design parameters affecting the "DPEI" values. Although the concurrent dryers are more efficient than the other types, the exhausted air temperatures are high enough to motivate further investigations to recycle the waste heat back into the system. Both gt_a_1_. (1973) simulated a heat exchanger in conjunction with a closed 8 loop recirculating coumterflow heater and coumterflow cooler . They showed that the theoretical WEI can be reduced to almost zero under ideal conditions. Roth and DeBoer (1973) optimized a concurrent-counter- flow gain dryer with and witl'out the use of a heat exchanger. 'Ihey found that utilizing a heat exchanger reduces the DPEI by more than 20 percent. Additional work on the same type of dryer by Bakker-Arkema gt__a_1_. (1974) and Sokhansanj (1974) showed that fluids other than air in the heater section improve the efficiency of the heat exchanger. Althoug heat exchangers proved to be effective in improving the energy efficiency of gain dryers, the problems of size and initial costs remained a question. Lai and Foster (1975) conducted preliminary investigations on the use of heat pipes in a batch type gain dryer. 'Ihe dryer consisted of a cylindrical bin of .75 m diameter and a height of 1.2 m. 'Ihe heat pipe exchanger was of a 6—row plate-finned type with a face area of .30x 38 m on each side. 'Ihe heat pump consisted of a 3/4 hp compressor and a 3/4-ton refrigerator. 'Ihe dryer ethaust was directed to the heat exchanger and then over the heat pump evaporator coil . 'Ihe simulation results showed that with 21°C ambient air temperature and 49°C drying temperature energy saving of up to 30 percent with heat pipe only, and up to 55 percent with both heat pipe and heat pump can be obtained. However, the reported saving as a result of experiments were in order of 10 and 40 percent for heat pipe and for heat pipe and heat pump, respectively. Part of the discrepancy between the experimental and simulated results may be due to the inaccuracy of the simulation models. Bakker—Arkema M. (1975) optimized a system of heat pipes and cmwrrentflow dryer based on minimizing a cost objective function. An energy saving of 21 percent was obtained for a set of optimized conditions 9 (45 ma/minlm2 airflow, 230°C drying air temperature, and 5 percent moisture removal); the present study is a follow-up to this study. 1.2 Heat pipe According to NASA (1975) the first technical paper on the heat pipe was publiged by Grover M. (1964). Since then a large number of references have appeared in the literature on all aspects of this device. Feldman and Whiting (1968) reviewed the commercial applications of the device. Excellent reviews on the technology of the heat pipe were publidued by Winters and Barsch (1971). Asselman and Green (1973) gave details on the heat pipe theory and the principles of operation. Ibhani (1974) reported the limits of heat pipe operation when noncondensable gases are present in the pipe. The most recent publication on the heat pipe are books by Dumn and Reay (1976) and Chi (1976). In both books the design relationships, limitations, and manufacturing aspects of the heat pipes are discussed. Parallel to the development of heat pipes, thermosyphon technology was investigated. A thermosyphon is a simple version of the heat pipe where condensate flows by gravity forces to the evaporator. Therefore , the wick is eliminated and as a result the construction of the pipe is simpler. The review by Japikse (1973) on the advances in thermosyphon technology is of practical interest . Streltsov (1975) presented simplified equatims for calculating the heat transfer and the amount of working fluid in a thermosyphon. 10 1.3 Heat pipe exchangers In spite of the commercial availability of heat pipe exchangers, not much research has been published in the open literatuure. Amode and Felduan (1975) reported the resuults of a test and an analysis of a heat pipe exchanger made from arterial 1 type heat pipes . Aronson (1976) and Ruch (1976) reported the application of heat pipes as heat recovery umits, but did not give any specific data or relationships. Their report contains a detailed description of a heat pipe exchanger operation. At presa‘ut the only available data is that published in the sales literatuure on some specific heat pipe exchangers . One of the major problems in a heat pipe exchanger operation is fouling. There is not much reported research on the subject of fouling. The investigations usually are carried out by the manufacturing and process industries. However, in recent years some investigators have classified different modes of fouling and have proposed mathematical models. Among these investigations those by Friedlander and Johnston (1957) , Kern and Seaton (1959), Beal (1970) , and the excellent reviews by Taborek fl. (1972a, 1972b) are of practical interest . lbst of these studies are on industrial fouling where the process fluids are of a liquid type. The proposed models are of a specific nature and cannot be applied to general cases. The characteristics of dust particles emitted from gain dryers have not been investigated extensively . Converse (1971) , expressed the need for removing dust particles from the gain dryer exhaust to comply to the state and federal regulations . Johnson (1976) recommended specially designed duust collectors for gain dryers . Meiering and Ibefkes (1976) 1Heat pipes with a grooved inside wall. 11 investigated the type and size of the dust particles emitted from a number of crossflow gain dryers. Avant (1976) reported analysis and performance test results of a sorghum dust collection system. 2. REVIEW OF HEAT PIPE PRINCIPLES 2.1 Introduction (he way of transferring a large amoumt of heat with a small temperature difference is throuugh a phase change process. Energy that is used for the evaporation of a liquid is transported through a duct by the vapors, and is released uupon condensation . I In order to perform the operation continuouusly the condensate must be returned to the evaporator. A completely closed container in which this process takes place is called a heat pipe or thermosyphon, depending on the way the condmsate returns from the condenser to the evaporator. 'Ihe principle of heat pipe operation is shown in Figure 2.1. In the steady state, the temperature of the liquid in the condenser and the evaporator approximate the terperature of the heat sink (cold side), and the heat source (hot side), respectively. The difference in terperature results in difference in vapor pressure; consequently the vapor travels from the evaporator to the condenser. The depletion of the liquid by evaporation causes the vapor/liquid interface in the evaporator to retreat inward. 'Ihe pressuure of the liquid in the condenser is slightly higer than that in the evaporator. This pressure difference causes the liquid to travel from the condenser to the evaporator throuugh the capillary structure of the wick. Since the temperatuure remains constant during the phase change, theoretically a considerable amouunt of heat can be transported with no or a very small tauperature difference between the condenser 12 13 and evaporator. As a resuult the heat pipe has a hig thermal conductivity. Figuure 2.2 shows a tubular heat pipe construction and operation. The heat pipe is equipped with circular fins to extend the heat transfer area. The pipe's external area is divided into a suupply side (heat sink), and an exhaust side (heat source). The average pressure inside the pipe is the saturation pressure of the working fluid at the operating taupera- tuure. The performance of a heat pipe is often expressed in terms of equivalent thermal conductivity. A tubular heat pipe of the type illustrated in Figuure 2.2, using water as a working fluid and operating at 150°C has a thermal conductivity several humdred times more than copper (Asselman and Green, 1973). 'Due thermosyphon is a simple version of the heat pipe in which the wick has been eliminated. Thermosyphons are used in a vertical position where the gravity facilitates the return of the condensate to the evaporator (Figuure 2.3). To wet the wall evenly the inside wall of a thermosyphon is usually grooved. Except for capillary pumping, other features of the thermosyphon are identical to those of the heat pipe. 2 . 2 Heat pipe construction There are three main components in a heat pipe: (1) the pipe, (2) the wick, and (3) the fluid. 133 float mace g Y LighUfir“““"‘\\\ Chmmaser ‘\\’ vapor Evaporator \\ Li uid Capillary structure A Heat sink Figure 2-1. The principle of heat pipe operation XHAUST $U__P___PLY COLD COLD "Lo: 3": no ocvepopem'o'.’o'o' .\ AL-Wca. .M l/ Mt‘m Raw» ‘3’” watt- - .- ‘ an: ”m" ummn 1". .4l., mam» H07 H07 Figure 2-2..A.tdbular heat pipe construction and operation. W/ Condenser. ntummg / I under the action at 9'0"” Figure w ‘ 4‘.»- A ' fl if uvuvu uuuuuu «a... 2-3. A thermosyphon construction and operation. 14 2.2.1 Pipe The pipe separates the working fluid from the surrounding environ- ment. 'Ihe pipe is usually equipped with circuular or plate fins on the outside to increase the heat transfer area. The pipe material must be compatible with the wick and fluid. Generation of non—condensable gases and subsequent corrosion of the pipe is a result of the incouupatibility of the pipe material and the fluid. Non-condensable gases in the pipe also block the transfer of the fluid and vapor along the couplets length of the pipe and sharply reduce thermal conductivity and the effective length of the pipe. Cbpper, aluminum and stainless steel are the most common materials used in heat pipe construction. The pipe diameter is usually in the range of 15 to 25 mm. The pipe wall thickness is about 1.25 mm. 'Ihe length of the heat pipes used in thermal recovery devices ranges from 30 cm to 125 cm. The circuular or plate fins on the external suurface of the pipes range from 2 to 6 fins per cm. The height and thickness of the fins is 30-50 mm and .3—.5mrm, respectively. 2 .2.2 Wick The wick is a porous layer that forms the capillary structuure of the Pipe. The prime function of a wick is to generate a capillary pressure sufficient to transport the working fluid from the condenser to the evapora- tor. The wick also provides a means of spreading the working fluid evenly thhouguout the pipe. The wick performance geatly depends on the construction material and the geometry of the pipe. Usually, the most expensive and hard to 15 manufacture part of a heat pipe is the wick. Materials such as monel beads, nickel powder, and fiberglass have been developed for heat pipes. A layer of this material is bonded to the inside suurface of the pipe wall. The selection of the wick depends on the type of operation and performance expected from the heat pipe. Wicks with a large pore size are suuitable for gavity assisted flows, while wicks with small pores have inherently hig capillary pumping capability. The wick thickness depends on the type of wick. A typical value for a wick made from wire mesh is .058 cm for a 1 cm pipe diameter. Sometimes, the inside wall is gooved for the condensate return (arterial wicks). By this method the amount of wick material is either reduced or totally eliminated. A combination of arteries and porous materials usually improves the performance of the heat pipe. The overall cost of a heat pipe depends largely on the structure, materials, and manufacturing practices of the pipe and its wick. It is important not to choose pipes with expensive wicks for applications Where gravity may be used. A simple and cheap arterial structure Probably will serve the purpose. 2 .2.3 Fluid The fluid is the medium through which the energy is transferred from One end of the pipe to the other end. A proper fluid must have a big latent heat, big surface tension, and high thermal stability. Quanical Wtibility between the fluid, the wick and the pipe material, is the prime requirauent. To prevent fluid degradation a high thermal stability is needed. Often it is necessary to keep the operating temperature of a heat pipe below a specified value to prevent fluid breakdown. 16 A high surface tension is required in order to enable the heat pipe to work against gravity, and as a result the fluid can flow uphill from the caldalser to the evaporator. It is necessary for the fluid to wet the wick and the pipe in order to generate a high heat transfer coefficient and to spread heat evenly throughout the pipe surface. A high latent heat of vaporization is desirable to transfer large amounts of heat with a minimun amolmt of liquid in the pipe. 'Ihermal conductivity of the fluid should be high to reduce the radial temperature gradient and the possi- bility of nucleate boiling at the interface of the wall or the wick and the fluid. 'Ihe anemt of fluid in the pipe should be sufficient to wet the wick plus a small amount to flow freely for safe and efficient operation. 'Ihe pipe is vacuumed thoroughly prior to the filling. Tables 2—1 and 2—2 list some of the characteristics of some commercial working fluids used in heat pipes. 2.3 Heat pipe thermal transport capability 'Ihe maximun heat that a heat pipe is able to transport depends on the rate of fluid flow inside the pipe: Q = 111 big (2-1) Where m is a function of the working fluid properties such as density, Viscosity, and surface tension, and of the wick properties such as Doha radius, permeability, and thickness. 'Ihe expression for m can be developed from a pressrre balance in the pipe. 'Ihe result is given by Dunn and Reay (1976): 17 Table 2-1. (berating temperature range, melting and boiling points of some commercial heat pipe fluids. 1 Melting Boiling Useful Operating Point Point Range °C °C °C Amnonia -18 -33 -60 to 100 Freon 113 -35 48 -10 to 100 Methanol -98 64 10 to 130 Water 0 100 30 to 200 Source: Dunn and Reay (1976) 1For cmplete'properties of the fluids, see Table 2-2 18 833 zoom one :85 ”consom H04 86 mwé RH. wmo. owe. om. wmm mmww 8H .8de SA mwé 54 HS. 38. HON. 3.4 03. mon E. Hogans m5 m. mad and owe. ammo. m5. moé web can ow I seem em . ma mmm . H ma . N m: . omo . mum . o . NH 0mm 83 ca flea—5. “S x as «S x 82 cougar NS xsémz Nsinz cos; .3? mafia mi? 0. > A o >0 >3 a: an >Q ac wan ooawcop H8: .980 gunman comma . comm doom? . meow? agony 53:3 5356 pace 3&5 3:34 nag nag egos 3qu 33> 3.453 poops..— . 959 .eau as :2 3.23 a. t a... a menace asses as see .2 as 19 = 92 kw Aw (2 °2 “2. I"eff rc m 0060 - on g Leff sine) (2—2) For a typical water heat pipe of 2 an bore size and 30 cm long, operating at 100°C, the values of m and Q will be calculated for hori- zontal heat transport lmder the following conditions: (1) 'Ihe wick is made of a 4-1ayer, loo—mesh wire with a diameter of .0045 cm; the thickness of the 4-layer is .036 an, (2) 'Ihe pore radius of this wire mesh, rc is .002 an and the permeability kw, is 1.52 x 10"” m2 = 2.256 x 106 is kj/kg and the assmption of perfect wetting, equation (.2-2) ( 3) Using the water properties at 100°C with h becomes: 958 x 1.52 x10-10 x .226 x 10"“ (2 x .0589 .283 x 10.; x . 3 .02 x 10" = 2.28 x 10’“ kg/s and Q = 2.28 x 10‘” x 2.256 x 10*3 = 51.2 j/s or W 'Ihe heat transport capability of a thermsyphon reported by Streltsov ( 1975) is: h 3 a a 3 V" Qagnn 39,3 I<,, hc’ and to that of the cold side if h > bh’ c 3. HEAT PIPE W ANALYSIS 3- 1 Introduction 'Ihe heat pipe exchanger consists of a bundle of finned heat pipes placed in a housing (Figure 3—1) and separated into two sections by a. partition. The hot air flows througl the exhaust side while the cold air passes through the supply side. 'Ihe evaporator section of the heat pipes is located in the exhaust side and the condenser in the supply side 'Ihe pipes are either individually equipped with circular fins, or they are bundled in a series of plate fins. 'Ihe arrangaxent of the pipes is usually staggered forming several rows. 'Ihe typical distance between 13m pipes in a row is about 6.4 cm, center to center, and the longitudinal distance between two rows is about 4.4 cm. 'Ihe camercially available heat pipe exchangers usually have 4 to 8 rows and the face surface area 1"Bulges. frcm2800 can2 to 30,000 am. A heat pipe exchanger is similar in construction to circular and plate type carpact heat exchangers. In the operation, a heat pipe e"K'Zihanger is similar to a liquid-coupled heat embanger. 'Ihe cooling system of an automobile engine is an example of a liquid-coupled heat e"Ichanger. A comparison between different types of heat exchangers 1mlluding the heat pipe is given in Table 3—1. Heat pipes are more etji'icient than other types of heat recovery units, because of low pressure drops and high overall heat transfer coefficients , as is indicated in 24 r’i Figure 3-1. A bmdle of heat pipes in a housing Source: Isothermics (1976) 38.3 gamers egg Seesaw we? nween—ow... cmE oz oz no: sea 38 $3 prom 35E so: oz new cmE 38 33 5:88 cmE has oz oz swam on: 33 handbag 38 oz oz 8: sea sea tea. a dorm swam no» new swam sea on: mnoefiosmmmm 8.39 E30338 non no.2 seaweed—a pcoo Hosea SHE e95 Hmwmg mug Efiflg ”58 Hmnwg 960m gag meat ”:5 mtg 2888 9.8: genomes ES .8 83.398 .3 can 27 Table 3-1 . 'Ihe partition separates the supply side and the exhaust side to prevent cross contamination. In the following sections the parameters and relationdiips which govern the performance of a heat pipe exchanger are identified. 'Ihe performance relationships will be coded in RETRAN and the predicted results will be canpared with experimental data. 3 - 2 Heat pipe exchanger effectiveness The effectiveness of a heat exchanger is measured by determining its ability to transfer heat fmn the hot side to the cold side. 'Ihe alas-{inn heat available to be transferred in a comterflow arrangenent can be written: Qmax = “‘min (ehi " eci) (3'1) wh - - ere n‘ i is the minimum flow rate, the snaller value of mu and mo. 'Ihe ratio of the heat gain by the cold side or the heat loss by the hot Side to q (whichever has the minimum value of m) is called the eiffeectiveness: (3-2) min c (3.3) (3-4) 28 Q = "‘h (ehi ' eho) (3'5) and the enthalpy (e) is: e=419W+CT (3-6) (3-7) where C=Ca+CvW ’Ihe heat exchanger effectiveness (2) , has been related to the ratio of UA/ (m)m by Kays and Lombn ( 1964). 'Ihe ratio is called the umber of transfer units (NTU) . 'Ihe e - NI'U relationships for a counterflow heat exchanger is: 1 a exp[-NTU(1- (m)min/(nc)m)] 5 = 1 - (mom/(mom exp [-fifi: o"- (fi)m/(mc)mn (3'8) For the case of (mam/(mom = 1, equation (3—8) reduces to: E = TNi‘P‘m-fi (3‘9) To Obtain the rate of heat transfer, Q can be written as: (3-10) Q=UAAT1n mel'e AT , the log mean tanperature difference, is obtained from: (T -T )-(T --T) ho ci hi co (3_11) ATln = 1n[(Tho ’ TciV (Th1 " Too” 29 Equatims (3—1) through (3-5 ) are written based on the overall enthalpy difference rather than the teuperature difference. 'Ihe reason for the ethics is that the exhaust air from the dryer usually contains large quantities of water vapor that will condense on the exchanger upon cooling. However, the enthalpy difference reduces to the tenperature difference if there is no condensation . For the evaluation of Um’ ASHRAE (1974) and McQuiston ( 1975) suggested to use: Uh (3—12) for the situations where the diffusion rates of the water vapor to the wall is low. When the rate of diffusion is high due to excessive anounts of vapor in the air stream, Mizushina (1974) suggested nodification of equation (3—12) to: Um = 3%- x 10‘3 (3-13) where: P - P 1/2 a = 59—75:; (1%) (3-14) ASHRAE (1974) gave a value of .845 for Sc/Pr ratio in case of air-water Vapor mixtm'es. Pst’ the saturation vapor pressure is evaluated at the pipe tenperature. 'Ihe pipe tenperature is obtained using equation (2‘7), for each element. Ch, can be evaluated by using equation (3-7). The overall heat transfer coefficient (U) is defined as: (3—15) = 1 + 1% +Rf+3m alt-4 U 0 :5 0 up 30 The fin surface effectivenesses, nh and nc, are developed based on the effectiveness of the individual fins. 'Ihe effective surface area of a finned tube heat exchanger is: Aeff = Auf + A:f nf (3—16) Equation (3—16) can be used to define the extended surface area effective— ness: A A A eff _ uf _f A - A + A nf (3—17) also, Af n=1-r(1-nf) <3—18) Where nf, the individual fin effectiveness is the ratio of the actual heat transferred fran a fin to the heat that would be transferred if the entire fin area was at the base temerature. For a long square fin of uniform thickness, the fin effectiveness is: g tanh bh nf bh (3-19) where 1/2 _ 2 h b - (Kf t) (3.x) Equation (3-19) can be used for circular fins with less than 8 percent error (Holmn, 1976) . 'me effectiveness of a wet surface is affected by the condensate film. Meriston ( 1975) added the latent heat to the heat balance over a fin and consequently nodified equation (3-20) to: 31 2h 8 b e [at (1 + -a—C- hfg)]1./2 (3-21) 'Ihe slope of condensation line (S) will be discussed in the next section. Equation (3—21) reduces to (3—20) when there is no condensation (S = 0). 'me value of nf for a wet fin is 2 to 3 percent lower than that of a dry surface. Rich ( 1973) expressed the metal resistance Rm by: R = (Jr—2.11) R + (3—22) m n a BM Equation (3—8) will be used to calculate the effectiveness of the heat exchanger when the hunidity ratio of the exhaust air is low (this will be discussed in Chapter 6). Knowing the effectiveness, the heat transfer rate is calculated fran equations (3-2) and (3—3), and the outlet cmditions from equations (3—4) and (3—5). Although the foregoing procedure is fast and sinple, it fails to predict the effectiveness and the outlet conditions correctly since the exhaust air hunidity is sufficiently high (nore than .05 kg/kg) to release large anounts of latmt heat upon condensation. For such cases the heat exchanger mist be divided in snaller segments for the analysis. In the following sections two such analysis methods are developed. 3.2.1 Finite differences A cross section parallel to the airflow in a 6—row heat pipe exchanger is shown in Figure 3—2. 'Ihe heat exchanger is divided into 6 elements each containing one row of heat pipes. Assuning a constant flow rate in the Exhaust Cold air Partition an TW fill..." I'll—HII*I"J . '|""I-+I'|-"|l o 1" I‘l'|'_'| It- "'I unuucnnnfiiltlnu. Il'"‘|'|nl_'||" [I "l Hot air Supply Figure 3-2. A cross section of heat pipe exchanger parallel to the airflow. I-hnu‘dity ratio 33 Air vapor mixture Wall who Wtho Area -—-—§ Fig. 3-3. Specific hunidity of the air-vapor mixture in Fig. 3-4. the element and on the fin surface in a heat pipe exchanger. 1 1 . .2 ‘ '1 Wm _ I I I ZZZ-.1 Ill—.2": I'LL-L: who a :r m : i Tth Th) ‘ Th Thi 'Ihe psychranetrics of the air-vapor mixture in a heat pipe exchanger. Point 1 depicts the inlet air, and point 1' represents the air at a point where the wall tamerature is below the air dew point temperature; point 2 approximates the outlet air condition, and point 2’represents the condition of the air close to the wall at the exit. 34 heat exchanger the energy balance on each of the elements can be written: for the hot side: cn=mhchdrh+mhdwhfg (3-23) = ”m“ (Wh ' wth) hfg + uhdA (Th " Tth) and for the cold side: (n = mc Cc ch (3—24) Uch (th _ Tc) Equation (3—23) for the hot side is based on the total enthalpy since the possibility of condensation exists. In equation (3—24) the terns associated with the heat of condensation are absent because the air at the cold side is gaining sensible heat. dA is the average surface area of the row of heat pipes (and fins) in each element. dW is the annunt of water condensed from the hot air in an elanent. In a counterflow arrangenent the inlet tenperatures, Thi and Tci and hunidity ratios W hi In order to find the tenperatures and hunidities, equations (3—23) and Wei are the known values (Figure 3—2). and (3-24) mist be written for every elenent of the exchanger and then solved simultaneously. Before writing these equations, proper relation- ships are required for expressing hunidities in terns of teuperatures. 'Ihe hunidity ratio of the air and the humidity ratio at the wall in an element are shown in Figure 3—3. As the figure shows the humidity ratio of the air decreases continuously and approaches a value close to that of the wall. In Figure 3-4 the state of the air is shown on a psychro- metric chart, as the air proceeds through an‘ element.. Point 1 depicts 35 the tenperature and humidity ratio of the air at the entrance point of an element. The air cools down as it reaches a point where the wall surface teuperature is below the air dew-point teuperature (Point 1’). Point 2 approximates the state of the leaving air at the exit point of the element. 'Ihe condition at the wall surface corresponding to the outlet air is depicted by Point 2’. Mizushina (1974) and McQuiston (1975) showed experimentally that the broken line 1-1’-2-2’ can be approximated by a straight line, or: - w h th or: wh ‘ wth = s (Th ' Tth) Also Whi who = S (Thi ' Tho) or: dwh = s dTh (3-26) Substituting equations (3-25) and (3-%) in (3-23) and (3-24) gives: (”I = (mu Ch + me She) “Th (34”) Rearranging equations (3-27) and (3—24) gives: 1 dT=dQ( ) h thh+nlialfg (3-29) _ 1 dTc-(n(mC cc ) (3—30) Ooubining equation (3—29) and (3—30) results in: 1 1 h c mn (Ch + Sifg) mc Cc ( 3-31) Fquatim (3-28) and the second part of equation (3-24) are coubined to give the teuperature differences: Th - Tth = (Um S hfg + Uh) dA (3-32) T _ 'r =_Q_ (3-33) Assuning the heat pipe is isothermal, addition of equation (3-32) to equation (3—33) and solving for (Q) gives: dQ = U dA (Th - Tc) (13-348.) where : 1 1 = + —— (3—34b) Um S hfg + Uh Uc CilH Substituting (Cu) from equation (3—34) into equation (3-31) yields: (1 (Th - To) = U dA 0 (Th - Tc) (3—35) where: l m = 1 + mh (Cb + alfg) c Cc C 37 An overall energy balance also holds on the two air stream in the element . Equating equations (3—2A) and (3-27) yields: d'l‘h = R ch (3-3) where: R = mc Cc .1. mtr (Ch Shfg) Equations (3-35) and (3-36) are the two main relationships to be written for the elements. 'Ihe quantities Uc’ Uh, hfg’ mc, Inn, and Cc are assumed to be constant throughout the heat exchanger. Um’ the convective mass transfer coefficient, Ch the heat capacity of the mixture of air-vapor, and S the slope of condensatim line have to be evaluated in each element. Equations (3—35) and (3-36) will be solved by finite difference techniques: (T -T)-(T-T) =dAUc(T -T) h C:x h c:x+Ax h cx-I-l/ZI'ix (3—37) and Thx Thx+Ax-R(Tcx Tcx+Ax) (3-38) where (T -T) c x + 1/2 Ax can be approximted by: (T -T)+(T -T) h cx h cx+Ax 2 38 Equations (3—37) and (3-38) can be simplified and rearranged: Thx(l—b)+Tcx(—1+b)+Thx+AX(—l+b)+Tcx+Ax (3-39) (l+b)=0 Thx (+1) +Tcx (-R) +Thx+Ax(-l) +Tcx+Ax(R) =0 (3—40) “here b=dAU , l 1 + ——1 2 Lmh(Ch+Shfg) mcCc Equations (3-39) and (3—40) are written for all elarents and after substi- tuting for the known temperatures '11); and T07 (Figure 3—2) the resulting matrix can be solved for the rest of temperatures. An iteration schare is utilized to calculate the constants in case of condensation and to reconstruct and evaluate the natrix. 3.2.2 Finite elements In the foregoing discussion the assumption was made that the pipes are isothermal and thus the temperature stays constant along the pipe. This tenperature can be calculated from equation (2-7). For the cases where an effective thermal conductivity can be defined for the heat pipe or where some other means of heat transport such as a solid copper bar replaces the heat pipe, the assumption of isothemality is not valid. For a solid bar which gains or loses heat in a stream of air, the tempera- ture profile in the axial direction is found fran the following 39 differential equation: (12 Ti: KAy dyz =Up(T-Tt) (3—41) Equation (3—41) is derived by writing a heat balance on an element of the pipe shown in Figure (3-5). When there is condensation on the pipe an additional term, which represents the heat released by the condensed vapor, is added to the equation (3-41): dzT 1:. KAy dyz -‘Up(T-Tt)+Ump(W-Wt) (3—42) Simplifying equation (3-42) by using equations (3-13) and (3—%) and rearranging results in: dz'r 12:31.2 _ _S__ dyz Myer Tt) (1+ac hfg A theorem from the calculus of variations states that the points ) (3-43) that satisfy equation (3—43) will also minimize the following integral: CH‘ 2 x= “(3313) dv+ §U(Tt-T)2ds (3.44) S Fbr the case of equation (3—44) where (U) contains more than one term: X= 13K (353-)2 dv+§U (1+§_5h_) ('1‘ -'l‘)2ds V dy ~a -fg 8 t (3-45) 4O \ KN / Heat pipe or a solid bar Tt _h__. T i. Y T Fig. 3-5. A section of the heat pipe (or a solid bar) for which equation 3-41 is written. 41 'Ihe exchanger is divided into square elements (Figure 3-6). Each element contains a smell segment of the pipe in the middle. 'Ihe nodal points are located in the middle of each side. Equation (3-45) must be written and evaluated for each element . Nodesland3inFigure3-7areonthepipeandnode62and4represent the state of the process stream at the inlet and outlet locations. The section of the tube in the element depicts a one-dimensional element. It will be assumed that temperature changes linearly over the length of the pipe in this element (Segerlind, 1976): T = C1 + C2 Y (3'46) with the following bomdaries: T (Y1) = T1 (3'47) T (Y3) = T3 (3-48) Applying the boundary conditions, solving for C; and C2 , and substituting back in equation (3-46) will give: T=N1 T1+N3 T3 (3'49) where Y _ N1 = 3 L Y (3-50) N3 = Y i Y‘ (3-51) N1 and N; are called shape functions. Y‘f 42 Exhaust 9 4p 0 0 4} 0 0 ° 4 : t L Air out 0 W 0 0 a (p 0 c—-—-—’. (b 1) 1) (D (b ‘P u f t t - ; Partition 4? 1P 1) 0 (i 0 0 : : 3 3 : Air in 0 1+ 0 0 0 (P H h A 0 4) o (p u + Supply X Fig. 3-6. Division of a heat pipe exchanger into square grids. Y+AY _ T1 T r * 7r Ai t _._ JL T3 ‘1 —> Ax J y x + Ax l‘ TI , Fig. 3—7. A typical element with the: specified nodes. 43 'Ihe temperature profile in the element can be written in terms of the four hows; T=N1T1+N2T2+ N3T3+ NhTu (3-52) 'Ihe shape ftmctions associated with nodes 2 and 4 do not enter into the coordinate system, so their values are zero: T=N1T1+ OT2+ N3T3+ 0T1. (3-53) In matrix notation, (3—53) becanes 3 T = [N] {T} (3—54) where [N] is a row mtrix: [N] = [N1 0 N3 0] (3-55) and {T} is a colum matrix: {T} = 2 (3-56) cfl‘ dN a—Y" if {T} (3-57) Let [g] = [-331 (3-58) and [B]=[-?‘d§-1=——od—Y—01 <3—59) 11:31 (3-57) can be written: [a] = [B] {T} (3-60) and its transpose [ng = of [BIT <3-61) Sutstituting (3—54), (3-57), (3-60) and (3—61) in (3-45) will give: X =f Q‘K [g]T [g] dV + QUCI. + is? hng{[T - '1‘le [T — T2] 8 V + ['1‘ - TulT [T - mus (3-62) where [T-Til=[N1T1+ 0T2+ N3T3+ OTn‘Tz] = [NiTr'T2+N3T3+0TIo] or [T-T2]=[N1-1N30] “r. 4%: I“ let [¢]= [NI-1N30] then ['1‘ - T2] = [o] {T} (3—63) and [T - '1‘le = of MT <3—64) Similarly it can be written for [T- T.,]: let [ID] = [N1 0 Na - 1] (3-65) 45 thar [T - Tu] = [lb] {T} (3-66) and [T - MT = mT MT <3—67) Substituting equations (3—63), (3-64), (3-66) and (3-67) in equation (3—60) and expanding, gives: x=J ax m“ [13]T [B] {T}dv +iU<1+§hfgn v . I {T}T [MT M {T} d82 +J {T}T MT [W {T} dS-o} (3-63) 2 Sn s2 and s“ refer to each half side of the pipe surface area exposed to the nodes 2 and 4, respectively. Equatim (3-68) is the one to be minimized with respect to the temperatures in order to find stationary points where the differential equation (13-43) will be satisfied. Differentiation of X in equation (3-68) with respect to {T} and equating the result to zero will give: h ax = T fg arr} Kim] [B] {T}dv +U(l+Cp S){ I MT [a] {T} as. J MT [w] m ds.} = o m '3 .3 '2 .3 $2” 0000 T. Cp 3430-36 T. (3—86) -§A; let C,-L h and c2=% U(1+E‘—-'ES) 'mal (3—86) can be written C1 + 4C2 -3C2 -C1 + 2C2 -3C2 T1 0 -3C2 5C2 -m2 0 T2 0 = (3'87) ‘C1 + 2C2 -3C2 C1 + 4C2 —3C2 T3 0 ’302 0 "302 6C2 Ti. 0 L .J or [k] {-T} = {f} (3—88) The matrix [K] and {f} are called the elenent stiffness matrix and the element force vector respectively. The vector {T} contains the unknown temperature. Similar equations are written and then evaluated fortrevery e16.L ment . All elemental. equations have to be assembled into a global matrix. The method of "direct stiffness" as explained by Segerlind (1976) is efficient method of performing the assembling process. 'Ihe force matrix initially has zero term, but when the boundary conditions are applied, the global system will be modified to incorporate the known tameratures. As a result of this modification same of the zero term in the foroe matrix 50 are replaced by non zero values, and the system of equations becanes non-homogenous. 3.3 Heat transfer coefficient and friction factor 'Ihe performance of a heat pipe exchanger greatly depends on the heat transfer coefficient and friction factor. 'Ihese values in turn depend on the Reynolds number and other process variables such as temperature and hunidity of the process stream. Rays and London (1964) reported their extensive investigations on the performance of compact heat eamhangers for some specific sin-race configurations. Further investigations by Mchiston and Tree (1972), Guillory and mister: (1973) and Rich (1973 and 1975) analysed the effect of desigi variables on the performance of the cmpact heat exchangers. It is customary to approximate a heat exchanger surface by models for which the performance data is available. here are no mathematical models to cover the wide range of variables and to calculate the heat transfer coefficient and friction factor for different values of the Reynolds nmber. 'Ihe arpirical models are usially limited to a specific type of heat exchanger and the predicted values by the empirical relationship are often within 1 20 percent of the actual values (Rohsenow and Hartnet, 1973). Siephard (1956) showed that for air at low velocities of about 1 m/s the heat transfer coefficient is about 28 to 34 W/m2-°C, and a pressure drop of 3 nm of water. 'Ihe manufacturers (Hughes, 1975; Isothermics, 1975; Q-Dot, 1976) of the heat pipe exchangers usually require a face velocity of about 2.54 m/s for an efficient design 51 resulting in an h value of about 60 W/m’-°C. 'Ihe pressure drop resulting from the specified velocity is about 5 mm of water. Table 3—2 contains sure of the equations found in the literature that have been applied to the design and analysis of finned tube heat exchangers. In order to choose the proper correlations for heat transfer and pressure drop, eight different sizes of circular finned tubes were chosen from Kays and Iondon (1964). Table 3-3 contains the dimensions of the selected heat exclnngers along with a given alphabetical designation. 'Ihe pressure was calculated by using the following equation: AP = f g: 1%; (3'39) A program that was written for the WANG 2200 Omputer facilitated the generation of data for different surfaces by different correlations . 'Ihe results are presented in grafirical form in Figures 3—8, 3-9, 3-10, and 3—11. An airflow of 53 m3/mi.n--m2 was used for Figures 3-9 and 3—10. For Figures 3-11 and 3-12, airflows of 23, 53, 230 and 530 m’lmin-mz were chosen. Figure 3-8 slows the heat transfer coefficients as predicted by different correlations for different heat exchanger sizes. 'Ihe pre- dictions follow a similar pattern indicating that each variable has similar effects on the correlation . 'Ihe heat transfer coefficient varies from 17 i 6 to 80 1- 12 W/m2-°C. Commercial heat pipe exchangers have specifications similar to the groups D and G in Table 3—3. For these groups the heat transfer coefficient is between 15 and 30 W/m2—°C. 'Ihe data from Kays and Iondon (1964) fall somewhere in between; Mirkovich's correlation predicts the lowest and muston's the bignest. Perry's 52 Table 3-2. Correlations for predicting the heat transfer coefficient and the pressure drop in a heat pipe exchanger. Winston (1972) and Schmidt (1949) : Nu = hb n. - .217 < - R Rohsenow P —— K Kays ”\M P Perry up A B C I) E F G Model designation (Table 3—3) Figure 3-8. Heat transfer coefficient predicted by different correlations for various surface configurations. 16. mmof water Pressure drop m Fig. 3—9. Mirkovich Watch Rohserm Kays and London Jameson Mo\ Airflow 54 m3/‘ruin-m2 371‘ m\ Temperature 38°C \19 \ N; V“ R 'I— at: \,,M ’j \\a"‘a a v V v v V A B C D E F G H Madel designation (see Table 3—3) oxwgfi Pressure drop predicted by different correlations for various surface configurations . '20‘ Heat transfer coefficient W/m2 -°C 100 ‘ 50 J 57 1...: O v a j v 50 100 200 500 Airflow ma/min-m2 Fig. 3-10. Heat transfer coefficient versus airflow for surface G (Table 3-3) , Predicted by different correlations. Pressure drop mm of water 10.0‘ 30 MI Mirkovich ‘ ‘ Mc McQuistcn ,1 R Rohsenow 50‘ K Kays and London 5 J Jameson R 40 Taperature 38°C " 20 ‘ {K i 10 . 8 . “ lb 6 . 4 . 2 d “I 1 - 5 a no 10 50 100 200 500 Airflow ma/iminmm2 Fig. 3-11. Pressure drop versus airflow for surface G (Table 3-3) predicted by different correlations . 59 and Rohsenow's values are consistently in the mid-range. Although both Perry's and Rohsenow's correlations are valid in a wide range of heat exchanger dimensions , Rohsenow' s correlation contains most of the variables explicitly. Figure 3-9 slows the pressure drop as predicted by the correlations of Table 3—2 for the different models listed in Table 3—3. Although a large variation between the predicted values is indicated, the overall pressure drop in a heat pipe exchanger is small . 'Ihe difference between the McQuiston's and Rohsenow's relationships for a D surface is about 2.54 mm of water and for the G—surface is even smaller. Jameson's correlation also seems to be valid over the range of surfaces. Figures 3—10 and 3-11 show the effect of airflow rate on the heat transfer and pressure drop. Both figures indicate that for various airflows the correlations follow each other rather closely. The variation in heat transfer values as indicated before is less than that for pressure drop. Figure 3-11 shows that for normal flow rates between 20 and 50 ma/min-m2 the pressure drop is very small. 'Ihe correlations given by Ibhsenow and Hartnet (1974) are chosen for the performance evaluation of the heat pipe exchanger, because the resulting heat transfer and pressure drop values are in the mid-range of other correlat ions' predicted values . 3.4 Fouling factor 'Ihe process by which dust particles are deposited on the heat exchanger surface area is called fouling. Fouling increases the resis- tance against the transmission of the heat from the pipes to the process 60 stream. Fouling also increases the pressure drop when there are enough deposits to narrow air passages and to block the airflow. 'Ihe constants hc’ hh’ nc’ nh’ and rim of the overall heat transfer coefficient (equation 3-15) have been considered in previous sections. 'Ihe resistance to heat flow Rf, due to the fouling is the subject of this section. 'Ihe exhaust air frcm a dryer contains a full spectrum of particle sizes and densities. Grain dust, clay dust, trash, broken kernels, stone particles, and light materials such as bees wings can be expected in the dryer exhaust air. Each of these materials foul differently and have their own specific fouling characteristics. A crust on the individual heat pipes resulting from the caking of grain dust when the air is moist and hot can be expected. Also, temporary clogging due to loose, light, and larger particles is inevitable. Bacterial growth in the heat exchanger is also another source of fouling (Anderson, 1977) . 'IWo modes of fouling may happen in a heat exdranger as shown in Figure 3-12. (he is when the deposition rate predominates the removal rate and there is a constant increase in the deposit thickness (Curve A). As a consequence of this mode there will be a build—up of sediment on the heat exchanger surface area. In the other mode, as the deposit thickness grows the rate of reroval will increase to a point where the rates of deposition and removal will be equal. Curve B of Figure 3-12 shows this second mode of fouling. Based on the foregoing discussion the change of deposit thickness with time can be written as: 3‘ 13.4) ¢ Tit-— d— r (3—103) 61 m. 8 ® 7o 3 s“ m “a 3 (a «b = 4» Q3 0° d r H \ DD ‘51" ® :1 1 -r-1 '3 e” O In Time Fig. 3—12. Fouling resistance versus time for systems in which the deposition rate predominates (Curve A) and in which the removal rate increases with the fouling thickness (Curve B). Source: Taborek et a1. (1972) 62 Depending on the type of fouling process, (cpd) and (cpr) can be formulated in a mmber of different ways. Kern and Seaton (1959) suggested the following definitions for (dad) and (or): = K1 C m (3-104) 4’d d ¢r = K2 I xf(t) (3-105) where (T), the shear stress of the air on the surface is equal to: (3-106) Substituting equations (3—104), (3—105), and (3-106) in (3—103) yields: .dx 2 at—f- = K1 Cd m - K2 f g-éP—xfm (3-107) 1 Equation (3-107) can be solved for time necessary for the deposits to * reach a value of xf #- . oxf t = T (3—108) 0 K, cdm-Kzfiz’léle‘t) v, the maximum air velocity is a fimction of time, because as the deposit thickness increases with time the air velocity also increases. After the values of K1 and K2 were defined for a particular heat exchanger, equation (3-108) can be integrated numerically. 63 K1 depends on the properties of the particles and the type of fouling. K1 can be defined as a sticking probability and expressed as a fraction of particles sticking on impact. K1 must be found experimentally, using equation (3-104) . Kern and Seaton (1959), for a fouling depicted by Curve B in Figure 3—12, proposed the following simplified relationship: Bt * .. R=R l-e f f ( ) (3—109) * Where Rf is the value of fouling resistance (Rf), at the asymptote. 'Ihe coefficient B is a removal rate expression, related to the shear stress as: B = K2 1' (3-110) :0: R 'Ihe value of B is the slope of log (1 - BI) plotted experimentally versus f time . 3 . 5 Profitability model Savings or costs resulting from an investment in the future have a different value at the presert . Factors such as the rise in energy cost, the rate of inflation, the tax rate, and the service life influence the profitability of a heat recovery system. If the annual fuel escalation is at a rate of (f), the fuel savings (Sk)’ at any year (k), can be written as: Sk=AS(l+f)k R: 0,122, °°°°°°° 3n (3‘111) where (AS) is the present fuel price, (savings) Similarly, the annual operating costs (0k), with an annual inflation rate of (j) can be written as: 0k = A0 (1 + wk (3—112) where (A0) is the present annual operating costs. Subtracting (0k) from (SK) yields the cash income (CI): CIk = Sk - q( (3—113) Assuming a straight line depreciation and a zero value for the heat exchanger after n years of service, the annual depreciation (Dk) can be written as: Dk = $110 (3—114) where (FCC) is the total first costs. The annual tax (TAXk) is calculated based on cash income minus depreciation, OI‘I TAXk = (CIk — Dk) t (3-115) ’Ihe net cashflow (CFk) results from subtracting taxes from the cashflow: ark = CIk - TAXk - FCO (3-116) In order to calculate the present value, the net cashflow must be 65 discomted at the true interest rate (1)1. In addition, the purchase power of a sum of money will decrease at the rate of 3' percent inflation. Therefore the net cashflow must be discounted at the rate of (i) and (j) as suggested by Iblland and Watson (1977a and 1977b): CFk DCF = The net present value (NPV) of the discounted cashflow can be written as: CF 11 mm = z kk k (3-118) 0 (1 + i) (1 + j) Equation (3-118) is the model used in the economic analysis of the heat pipe exchanger. Equation (3-118) can be rearranged to give, CFk (3-119) 1 (1 + 1)k (1 + j)k where dC NPV-PCO Whenever (dC) is equal to zero, the project is at the break-even point. 'Ihe values of (dC) greater than zero represent a profit, and the values less than zero indicate a loss. Setting (dC) equal to zero and solving for (i) in equation (3-119) for any particular value of (n) will give the discounted cashflow rate of return (DCFR). 1A true interest rate does not include the inflation rate. 3.6 Simulation The performance relationships developed in the foregoing sections were coded in FGH‘RAN; and the routine was called "SJBRCUI‘INE PMSS". Evaluation of the overall heat transfer coefficient and pressure drop is performed using Rohsenow's equations (3-101), (3—102) and (3—102-1) In the case of the finite element and finite difference analyses the temperature and corresponding humidit ies in each element are checked for condensation. When the overall effectiveness method (equation 3—8) is used, condensation is checked at the exit points of the heat exchanger. In case of condensation the overall heat transfer coefficient must be re-evaluated using equation (3—34b). A flowchart of the subroutine PROCESS is shown in Figure 3-13. Equations (3-39) and (3—40) were solved using a package called ”SIN", which obtains the solution of a set of simultaneous linear equations by the elimination method (Lukey, 1975). A set of subroutines developed by Segerlind (1976) for solving a one-dimensional heat transfer problem is utilized in the solution of equation (3—88). The following subroutines are used: a) ASMBLY --- constructs the global and stiffness matrices b) BDY -----— applies the bomdary conditions to the system of equations and modifies the stiffness matrix. c) DCMP ---— decomposes the global stiffness matrix into an upper triangular matrix d) SLVBD ---—-- solves the system of equations by the backward substitution method. 67 ® maximum flow , heat capacity [mflalfi'y,minimrnflow, Heat transfer coefficient ; equation 3-101 1 measure drop equations 3-102 , 3-102-1 Finned surface effectiveiess equations 3-18 , 3-19 _ Overall heat transfer coefficient equation 3-34. Mich Mass transfer coefficient ; equation 3-13 performance 1 Finite difference equations 3-39 , 3-40 analysis 1 Kays and Iondcn (1964) equations 3-3 , 3-4 ,- Pinite element equation 3-3 , , 3.503-8 3.4'3-5'3-88 Write performance results Qatain the slope (S) 3 equation 3-26 Figure 3—13. A flow chart of the subroutine PROCESS. 68 Additional subroutines for grid generation (FINITEEL) , reconstruction of matrices in case of condensation ((DNDENS) supplerent the package. A listing of the programs and samples of inputs and outputs can be found in the Appendices A and B. Parts of the analyses such as the heat transfer coefficient, pressure drop, fouling factor and economic analysis were performed on a WANG computer which utilizes BASIC. A listing of these programs can be found in Appendix A. For the purpose of drying simulation, the programs already available (Bakker-Arkema e_t___a_1. , 1974) were utilized. In order to couple the heat exchanger to the drying simulation programs a subroutine was written to calculate the properties of the air recycled to the heat exchanger and the grain dryer. 'Ihe subroutine receives the temperatures, the humidity ratios and the flow rates of the n-number of air streams to be mixed. 'Ihe enthalpy of the mixture is calculated using equations (3-6) and (3—7). Specifying the ratio of each stream (R), the final mixture properties can be written: n 2 G1 R1 ei em = n G. R. (3420) 1 1 n EIG. R. W. w = 1 1 ..1 (3-121) 111 11 G R )3 i i 1 n Gm - >13 61 R1 (3-122) Equations (3—120) through (3-122)‘ are contained in the subroutine called "INPUIMIX". A listing of ”INPUI‘MIX" can be found in Appendix A. 4. EXPERIMENTAL 4 . 1 Introduction The experimental tests were carried out to establish: a) the experimental data for the heat pipe exchanger to compare with those predicted by the simulation, and herce to validate the heat pipe exchanger computer program, and b) the experimental application of a heat pipe exchanger to a grain dryer and the investigation of the performance of the overall system. In order to fulfill these objectives, the experiments were divided into two parts: a) those related to the heat pipe exchanger, and b) those related to the performance of a grain dryer and the heat exchanger . 4.2 Heat pipe exchanger A commercial heat pipe exchanger (similar to Figure 3-1) was pur- chased frcm Isothermics, Inc., Augusta, New Jersey. The coil construction and performance characteristics of the heat exchanger as supplied by the manufacturer are shown in Table 4—1. 69 70 Table 4-1. Performance characteristics and the construction of the experimental heat pipe exchanger, Iw-FIN, as specified by the manufacturer. Performance: Nominal effectiveress % 67 1- 3 Supply air volume m3/min 2.83 Exhaust air volume m3/min 4.25 Supply inlet temperature °C -1 Supply outlet temperature °C 43.3 Exhaust inlet terperature °C 65.5 Exhaust outlet temperature °C 35.5 Supply pressure dr0p mm 4.3 Exhaust pressure drop mm 7.6 Energy recovery kj/hr 9115 Construction: Nmber of rows 6 Pipe material Aluminum Fin pitch 4.3 fins/cm Overall dimensions: width 3 m, depth .3 m, length .46 m Isothenmics, Inc., Augusta, New Jersey. 71 During the test the heat exchanger was equipped with four transition ducts and a port at the bottom for the condensate to drip out . 'Ihe asserbly was connected to an Aminco 1mit which provides airflows of different temperature and humidity (Figure 4-1). ’Ihe supply side of the heat exchanger preheated the cold ambient air before entering into the Aminco unit. The exhaust side of the heat exchanger received the conditioned air with a specific temperature and humidity from the Aminco. The outlet and inlet terperatures were measured by copper-constantan thermocouples . 'IWo thermocouples connected to a multichannel temperature recorder were used in each location. The humidity ratio of the air exhausted from the Aminco unit was adjusted using the controls provided on the wit. The humidity ratio of the supply side was measured using psychrcmetrics as follows: a thermocouple wrapped in a wick and soaked with water was installed in the air passage to measure the wet bulb terperature; using the dry bulb and the wet bulb temperatures, the humidity ratio was found from the psychrometric chart . 'Ihe airflow in each side was measured by a pitot tube. A variable speed fan was used on the Aminco unit to provide different airflows. 4.3 Grain dryer Two series of experiments were performed with the grain dryer. The first experiments were carried out in the summer of 1976 when newly harvested soft wheat was dried in a laboratory concurrent-counterflow dryer. 'Ihe second series of experiments was performed in the fall of the same year, drying shelled corn in a modified laboratory concurrent counterflow dryer. drugs mafia pace on» no memo» coaches on» you a: new 3253 .Te new 5531mm: Eugenia 3E poem nouns couscous . . ”.9585 i IIIIIII a m. L oBB IIIIIIII >396 lull! .. n-.. @l -1 I u_ as e e u... ores new 73 A sketch of the first dryer is shown in Figure 4-2. 'Ihe dryer was equipped with two airlocks to separate and direct the air passing through the cooler and the dryer. 'Ihe measuremnts for the heat exchanger were the same as the previous tests. Table 4—2 contains the dryer dimensions and the process settings for the wheat drying tests. For the second experiment the design of the grain dryer was extensively modified in order to reduce the moving parts and consequently, to eliminate the air leakage (Kline, 1977). The air locks were replaced by columns of grain to prevent the air leakage (Figure 4-3). In addition the cooler was separated from the dryer so the cooler could be bypassed whenever cooling operation was not necessary. 'Ihe method of heat exchanger application to the grain dryer in both tests was similar to the way it was used in Aminco tests. Table 4-3 lists the dryer settings used in the com drying experiment. 74 Air lock T Grain W Air D Preheated air Dryer L— Ambient air ..._.‘._._ ‘__—— Arr lock 3 J- r __,__ ____,, Cooler ' I Ambient air Fan Heat pipe exchanger Fig. 4-2. Schematic of the concurrent counterflow dryer used in the wheat drying experiments . Table 4-2. Settings for the concurrent-counterflow dryer utilized in the soft wheat drying experiment. Inlet air temperature Inlet absolute humidity Airflow rates: - Dryer -- Cooler Ambient air Inlet grain terperature Inlet moisture content Grain flow rate Length: —- Dryer -— Cooler Cross section area of the dryer and the cooler 120, 150, 177 8:. 205 .015 18.3 6.1 18 . 976 .61 kg/kg ma/min-mz ma/min-m? °c °c % (WB) tonnes / hr--rm2 76 Grain colum ... ~ ('41. n Us ‘ Q1257; . .- 5.3133388 11L ‘— WEEK-WIN Elevator " ct)- ." 'Ir 7 mm; 1! “NEW“? ’73:“ . "99 Figure 4-3. Schematic of the concmrent-couiterflow dryer used in the corn drying experiment. 77 Table 4—3. Settings for the concurrent-counterflow dryer utilized in the corn drying experiment. Inlet drying air temperature 205 Inlet absolute humidity . 005 Airflow rates: -- Dryer 42.7 - Cooler 6.1 Ambient air terperature 12 to 15 Inlet grain temperature 22 Inlet moisture content 20 to 22.5 Grain flow rate 1.5 to 2.5 Length: - Dryer 1.0 - Cooler .6 Cross section of dryer and ~09 cooler °C kg/kg m13 /min-m2 rid/1111mm2 °c °C % (WB) tonnes/hr—m2 5 . HEAT PIPE EXCI-IAI‘EER MIMIZATION 5 . 1 Introduction ’Ihe design of a heat pipe exchanger for a specified set of inputs including airflow, inlet air terperature, and humidity is discussed in this chapter. Heat exchanger optimization is a complex procedure that requires the ccmbinat ion of experience and matheratical models . Rays and London (l964)stated that "the mettodology of arriving at an optimum heat exchanger design is a corplex one, not only because of the arithmetic involved, but more particularly because of the many qualitative judgments that must be introduced". ichaust ive design requires optimization across at least 12 control variables . Multivariate search methods are typically erployed for optimization. 'Ihe product of the multivariate search method will be an optimal heat exchanger with detailed specified dimensions . However, for the purpose of cost estimates and overall planning a rough estimation of the size and performance is sufficient. For this case a cheaper and faster optimization scheme will be appropriate. 'mo optimization metrods are utilized in this investigation. One is a linear optimization that is based upon the heat exchanger's overall performance relationships. The other is a non-linear search method that utilizes the performance and dimensional characteristics of most of the control variables . 78 79 5 . 2 Linear optimization The general form of a linear optimization problem (Hillier and Lieberman, 1967) can be written as follows: n maximize: Z = X C. X. (5—1) ~=1 J J J subject to: n )3 a.. X. _<_b. (5—2) 3:1 13 j 1 X. > O 1 1:2: 3 m J — 132: r n Here equat ion (5—1) represents the net annual savings , and equation (5—2) specifies the constraints on the variables in the objective function. For the heat pipe exchanger the net annual savings can be written as: NAS=P1Q-P2KWH-P3A'5 (5—3) (Q) represents the annual fuel savings in million kj, and (P1) the price of fuel in $ per million kj . (KWH) represents the annual power expendi- ture in kilowatt—hours, and (P2) is the price of electricity in $ per kilowatt-hours. The expression (P3 A“ 6) represents the annual fixed cost of the heat exchanger. 'Ihe first cost of the heat exchanger is calculated by: ,6 “36 = ma (2'1) (5—4) a 80 Using the first cost ($320) and the surface area (7.8 mz) of the purchased heat exchanger from Isothermies, Inc., Augusta, New Jersey; equation (5-4) can be written as : -6 Feb = 320 (28—8) (5‘5) Assuming that the heat exchanger service life is 5 years, the annual fixed cost of the heat exchanger is: It " OI‘ rob = 18.7 (may6 (5.7) Thus p3 is equal to 18.7 in equation (5—3). 'Ihe constraints on the variables are obtained from the following relationships: a) to establish the constraints on the friction power expenditure, a simplified equation given by Kaye and London (1964) is used: - G3 A Hr KWH = 1.07 x 10 1" 32 ' (5-8) Equation (5-8) does not require estimates for various primary variables, whereas, the equations in Table 3—2 do. Substituting .02 and .06 as lowest and highest values for the friction factor, and simplifying; equation (58) can be written: — — 3 — KWH 1.9El6(Gmin )AHrzO (59) +3 Gmax 81 and .. 3 3 _ KWH 5.7 E—16(Gmin + Gmax) A Hr 6 O (5 10) b) The maximum heat that can be transferred theoretically in a counterflow heat exchanger can be written as: q .._ (3min do » <5—11) where Cmin = (Mnmin and do = (Th1 ‘ Tci) Multiplying equation (5-11) by a heat exchanger's effectiveness (2:) , gives the actual heat that is transferred in a given heat exchanger: Q = cmin d0 6 (5-12) = be written for Assuming that C min Cmax’ the effectiveness can a counterflow problem as follows (Kays and London, 1964): UA C e = m <5—13) 1 _ IA Cmin Substituting equation (5—13) in equation (5—12) results in: UA Q -’ 1 him do (5-14) 82 Equation (5—14) specifies a value for the surface area when the heat exchanger effectiveness is specified. 'Ihe exact value of (3) depends on the design and performance of the heat exchanger. In order to introduce the variations of the effectiveness into the optimization scheme, equation (5-12) can be written as: z = c . d e* (5-15) where (5*) is a specified value for (s) with possible variations. The objective ther will be to maximize the value of (6*) in order to maximize the net annual savings (equations 5—12 and 5—3). However, the maximum of Q cannot exceed Qmax of equation (5—11). Actually Q may be equal to the product of maximum value of 5* and Qmax' A probability is associated with this objective, that can be stated as: (5—16) where (or) is a decimal representing the odds that (6) falls somewhere between the maximum and'the minimum of (8*); (Black and Fox, 1976). A normally distributed random variable, (Q) can be converted into a standard normal distributed random variable, (A), as follows: Z - E(Q) V(Q) (5-17) where M91- A Zvar) 3* 83 V(Q) and E(Q) are the variance and the expected value of (Q), respectively. Replacing E(Q) by Q and rearranging, equation (5-17) yields: Q-Z+l V(Q) 2 0 (5—18) Q-Z-XWQ) $0 (5-19) Since (6) is a random variable, using equation (5-12), the variance of Q is written: V(Q) = v (clmin do a) = slim (13 v (e) (5-20) and the standard deviation (s.d.) of (Q) is written: s.d. (Q)=\/ V(Q = Cmin do s.d. (6) (5—21) Substituting equations (5-15) and (5-20) in equation (5-18) yields: do6*+lC dos.d.(6)20 Q‘Cmin min or Q - Cmin do [6* - A s.d. (6)] z 0 (5—22) and similarly Q - Cmin do [6* + l s.d. (6)] s 0 (5-23) Equatims (5—9), (5—10), (5-14), (5—22) and (5-23) are the constraints to the objective function (5—3). The optimization scheme can be summarized as follows: 84 Maximize: NAS=P1 Q-Pz KWH-P3 A" (5-24) subject to: 3 3 KWH-1.9E-16(Gm+Gm1n)AHr 2 0 (5—25) _. _ 3 3 KWH 5.76 16 (Gm+ijn)AHr < 0 (5-26) UA _ Q - T7314 do - 0 (5-27) Cmin Q - cmin do [6* - 1 s.d. (6)] z 0 (5-28) Q - Cmin do [6* + A s.d. (6)] <_ O (5.29) Q. A. KWH 2 0 (5-30) As can be seen, the objective function (5—24) and equation (5—27) are not linear in terms of A. In order to linearize these two equations, several points on the area domain will be assured, and then, the points will be linearly interpolated to approximate the original equation. Assuming a three-point interpolation, the function containing the surface area can be written: HA) ___ W1 f(A1) + W2 flAz) "’ W3 f(A3) (5'31) where W1, W2, and W3 are the interpolating weights, such that: 3 § w. = 1 (5-32) 85 For example the expression A' 5 in equation (5—24) is written: A°5=W1A1'° +w2 A2’5+W3A3" (5-33) After linearizing; equations (5—24) through (5—30) and equation (5-32) will be all linear in terms of the variables; and can be solved by the Simplex algorithm (Hillier and Lieberman, 1967 ) . Example: A heat pipe exchanger is to be optimized for the following data‘: Airflow 3.5 m3/m1n (supply and exhaust side airflows are 0 equal) Th1 65 C O Tci 5 C e 65 percent s.d. (e) 15 percent Hr 750 hrs/year pI 3.3 $/1o‘i k3 p2 .035_$/kWhr P3 $ 18.7 U 40 W/m’-°c a 95 percent 3 p l kg/m C 1.005 kJ/kg-°C Heat exchanger life 5 years 'Ihe calculated values: Cmin=cmnx=nc 1'Ihe data of this example are similar to the data specified for the Im-FIN, the experimental unit. 210 x 1.005 211 kj/hr~C Cmm=cmm=1117skg/m2 -m~ (based on .015 m2 of free frontal area) From a probability table for or = 95% the value of A is 1.96. Substituting the specified and calculated values in equations (5—24) through (5-29) yields: NAS = 3.3 Q - .035 KWH - 3.74 A“ (5-34) KWH - .398 A z 0 (5-35) KWH - 1.193 A _<_ 0 (5-36) Q -—-fi—‘15'38.A A = 0 (5—37) Q _>_ 3.38 (5-38) Q _<_ 9.02 Q. A. KWH a 0 (5-39) Assuming 3 points for A, as follows: A1 = 1, A2 = 10, and A3 = 100; equation (5—34) through (5-39) are tabulated in Table 5-1. A computer program developed by Harsh and Black (1975) was utilized. 'Ihe program utilizes the Simplex algorithm. Table 5—2 contains the resulting output of the program for the given inputs of Table 5-1 . Table 5-2 shows that the designed heat exchanger has an effectivnsss of 80 percent . 'Ihe designed surface area, 4.3 m2 is smaller than that of the experimental unit; and the amount of savings is higher. In fact, the algorithm obtains the mam‘mxn value of Q, and then fran equation (5-37) finds the value of A. 'Ihe friction power is found after Q and A are specified, 87 Table 5-1. Tabulation of the sample linear programming problem. Q KWH W1 W2 W3 3.3 -.035 -18.7 -74.05 -294.8 0 1 -.398 -3.98 -39.8 2 0 O 1 -1.193 -11.93 -119.3 5 0 1 0 -20.25 11.17 9.67 = 0 1 O O O 0 > 3.38 l O O O 0 S 9.02 0 0 1 1 1 = 1 Table 5-2. 'Ihe output of the linear programing optimization using the inputs of Table 5—1. (bjective function -8.71 Q 9.02 x 10‘ (12026 KWH 1.67 A 4.3 kj .’year kJ/hl') 88 because (KWH) has a small price in the objective function. 5. 3 Nonlinear optimization 'Ihe exhaustive design of a heat pipe exchanger requires a two-step optimization scheme. First , the individual heat pipes are optimized based on the properties of working fluid, structural characteristics of the wick, and the geometry of the pipe. Second, the heat exchanger is optimized for the overall performance and the core specifications . This study is concerned with the second scheme which is similar to optimal design of a conventional finned pipe heat exchanger. The objective function used in nonlinear optimization is the same as the one used in the linear optimization (see equation 5-3). Several methods can be utilized to arrive at an optimal heat exchanger. (he method is the lagrange multiplier technique by which the partial derivatives of the objective function with respect to each variable are set equal to zero. 'Ihe resulting system of equations is solved for the optimum variables. 'Ihe Lagrange method is simple and fast provided that the derivatives are defined and can be found. A multivariate method reported by Kuester and Mize (1973) and written inFCRI‘RANOode isutilizedinthis study. 'Ihemethodisbasedon the camplex procedure of Box. 'Ihe procedure consists of maximizing the function: F(X1, X2, . . . . , XN) (5-40) subject to: Gks-inflk k=1,2,...,M (5-41) ’Ihe implicit variables XN + 1, . . . , XM are dependent functions of the explicit variables X1, X2, . . . , XN.'1he upper and lower constraints “in and Gk are constants or fmctions of the independent variables. 'Ihe procedure finds an optimum solution from the carbination of the points scattered over the feasible region. The feasible points are generated by the following equation; Km. = Gr + YLJ. (Hi - oi) (5-42) 1: 1, 2, o . o o , N j: 1, 2, . . . . , 13-]. k is the umber of complex points chosen and is at least equal to N + l. Yi, j are random mnbers between 0 and l. ‘Ihe selected points must satisfy both explicit and implicit constraints. As can be seen fran the flow chart given in Figure 5-1, the convergence of the objective function to a small specified value after certain iterations provides the optimum design 5.3.1 Application to heat pipe exchanger ‘Ihe calputer program consists of three parts: (1) 'Ihe main program was that reads the inputs necessary for the optimization: a) inlet process conditions such as airflows, humidity ratios and temperatures, b) economic parameters such as fuel and electricity prices, c) initial estimates for the following primary variables: fin 90 Pick Startingfpoint (Feasible) I l Generate Point in Initial Complex of K Points \ Violation , Check EXplicit Violation Move Point in a Distance 6 Inside Constraint. Okay I the Violated Constraint heck . Implicit Okay nitial Complex Constraints Evaluate Objeciive L Function at Lach Pointj‘ Check Yes Generated 0’ Yes Convergence Replace Point With the Lowest Function Value lly a Point Reflected Through Centroid, of Remaining Points No Low Point \ \Wezrtcr Yes Move Point % Distance in Toward the Controid of the Remaining Points @ Fig. 5-1. Box (CCMPIm AIGORI'n-M) logic diagram Source: Kuester and Mize (1973) 91 diameter, pipe diameter, fin thickness, umber of fins per unit length of the pipe, hot side pipe length, cold side pipe length, mnber of pipes in a row, mnber of ram, distance between two rows (center to center) and distance between two pipes in a row (center to center), (1) maximum values for the overall heat exchanger dimensions, i.e., width, height, and depth, e) number of iterations and the convergence criteria. (2) ........ Subroutines DEI‘AIID, GNSX, (HEX, and CENTER plblidled by Kuester and Mize. 'Ihese subroutines carry out the optimiza- tion procedure until either a maximum function value is reached or the amber of specified iterations is exceeM. 1 (3) Additional subroutines are supplied to the main program as follows : 5.3.2 Ibsults . contains the constraints on the primary independent and dependent variables . contains the objective function . contains the performance relat imships . contains the relatimships to calculate the heat exchanger dimensions . output of the performance results . output of the dimensional and the core specifications A set of inputs similar to those specified for the experinmtal unit were supplied to the computer program. Table 5—3 shows a camparison between l’Ihe programs are listed in the Appendix -A. 92 Table 5—3. A comparison between an optimal design of heat pipe exchanger with ISO-FIN unit. 1 Units Optimal ISO-FIN Desig length cm 37.0 46.0 Height cm 21.0 17.0 Depth cm 29.0 29.0 Fin diameter cm 4.03 3.81 Fin thickness an .03 .04 ‘Pipe diameter cm 1.80 1.91 Fins per cm 4.40 4.30 No. of rows 6 6 No. of pipes in a row 4 4 Surface area2 m2 7.42 7.80 Efficiency 3 Percent 57 67 1- 3 Energy saved kj/hr 6928 9115 Objective function" e .373 —— 1For the input conditions see Table. 4-1. 2Total surface area including pipe and fins. 3Values for ISO—FIN is given by the manufacturer. “Based on $3.3 per million kj; 3.5¢ per KWhr, and the heat exchanger cost from equaticm (5-7). 93 the optimal design of the heat exchanger and the experimental unit, ISO-FIN. As can be seen the optimal unit with a lower efficiency has almost the same surface area and dimensions of the ISO-FIN. The optimal unit has also a larger fin diameter and slightly more fins per cm than the Im-FIN. The 1975 models of the Westelaken grain dryers manufactured by the Westlake Agricultural Engineering, Inc. , St. Marys, Ontario, Canada were used as examples of one—stage concurrent flow dryers. Figure 5—2 is schematic of the typical dryer. Table 5—4 contains the relevant dimensions and the capacity of the different dryer models. Table 5—5 lists the input conditions that remained fixed for the analyses of the convergence criterion , the optimal design of the heat pipe exchanger for various models of the Westelaken grain dryers, and the effects of the fouling factor on the optimal design. Those values which are not fixed are specified for the specific analysis. 'Ihe choice of the fixed values are arbitrary and generally are typical values in a grain drying operation. Table 5-6 shows the effect of different values of the convergence criteria on the optimal designed dimmsions for Model 810—A grain dryer, CPU time, and the carputer cost (CDC-6500, Michigan State University). 'Ihe number of iterations is also shown for each convergence value. As can be seen from the table, the objective function (equation 5—3) value increases significant 1y as a smaller convergence criteria is used. At the same time, the increase in the accuracy results in a larger nmber of iterations and hence a higher computer cost . For the purpose of this investigation, a convergence of 1.0 is chosen for further analysis. / o I. . w evJ’ 0 e .3 I / . . . q. 9 1 5., . , 4. ._ a I. \ I ' R1. . /7 .i \ 111111111 Figure 5—2. Westelaken grain dryer. 95 Table 5-4. 'Ihe Westelaken grain dryer specifications. . Model No. Cross Section Dryer Cooler Capacity’ Airflow Area length length m2 m m tonnes/hr m3 min dryer cooler’ 810-A 8.90 2.0 1.0 20 407 203 1210-11 13.40 2.0 1.0 30 612 316 3010-A 23 . 80 2 . 0 1 . 0 75 1087 543 4510-A 37 . 20 2 . 0 1 . 0 115 1700 850 Source: Westlake Agricultural Engineering, Inc., St. Marys, Ontario, Canada 1Based on 45.72 m3/min/m2 2Based on 22.86 m3/min/mz 3At 5 point moisture removal 96 Table 5—5. 'Ihe inputs for optimal desigl of heat pipe exchangers for various models of Westelaken grain dryers. 1 Inlet air temperatures - Exhaustz 62.0 °c -- Supply3 15.5 °C Inlet humidity ratios“ -- Exhaust .05 kg/kg - Supply .005 kslkg Fuel dost $/million kjs 3.31 Electricity dost $/k w hr .035 1For the airflows and the dryers dimensions, see Table 5—4. 2Airflow to the exhaust side of the heat exchanger consists of the combined exhaust from cooler and dryer. 3Airflow to the alpply side of the heat exchanger consists of the airflow to the dryer. “The cloice is representative of typical humidity ratios. 5Based on $92/m3 No. 2 fuel oil with 3.86 x 107 kj/m’ heating value and about 70 percent combustion efficiency. 97 Table 5—6 , Comparison of different values of the convergence criterion for the optimal designed heat pipe exchanger. Units Convergence Criterion 0.01 0.1 1.0 2.0 Surface area m2 7.42 7.01 9.32 8.33 adjective function 9: -.78 -l.13 -2.92 -14.25 value1 Iterations No. 716 360 124 34 CPU2 Seconds 45.4 16.9 3.9 1.4 00st’ 3 4.19 1.77 .68 .47 lij ective function value is based on annual net profit maximization . 2Central Processing Unit coo-6500, Michigan State mivemity. 3Program execution cost . 98 Table 5—7 shows the optimized dimensions of the designed heat pipe exchangers for the various models of Westelaken grain dryers. As the dryer size increases, the heat exchanger size incme is primarily in the amber of pipes. A small increase in the number of fins per unit length is also evident. More savings are realized in larger heat exchangers than in the sraller ones. Table 5—8 shows the effect of different values of thermal resistances due to the fouling on the optimal design of heat pipe exchanger. This shows that thermal fouling does not have a significant effect on the performance of the heat exchanger as far as heat transfer is concerned. hhlnh) with respect to each other do not change significantly. The choice of .02 , 1 In other words the relative values of (Rf) and (W) or ( and .002 is based on the TEMA (Tubular Etchanger Manufacturers Association) recommendations for the fouling allowance (Perry, 1974). 99 Table 5-7 . 'Ihe optimal designed heat pipe exchangers for various models of Westelaken grain dryers. 1 Grain dryer models Units 810-A 1210-A 3010-A 4510-A length on 182.0 234.0 304.0 360.0 Height cm 120.0 184.0 219.0 272.0 Depth cm 64.0 73.0 62.0 65.0 Fin diameter cm 4.54 4.61 4.87 4.88 Fin thickness cm .04 .04 .04 .04 Pipe diameter cm 1.58 1.58 1.59 1.60 Fins per an 5.27 5.17 5.24 5.51 No. of rows 7 8 7 8 No. of pipes in a row 28 43 48 48 Surface area m2 553 1264 1837 2610 Efficiency Percent 63 72 63 60 Energy savings kj/hr .78xlo‘ 1.33:»;106 2.1x10‘ 3.08x10‘ 1Recycling of carbined drying and cooling air through the heat exchanger. 100 Table 5—8. 'Ihe effect of fouling resistance on the optimal designed heat pipe exchanger for the Westelaken grain dryer Lbdel 810-A. 1 Fouling thermal resistance 01W Units 0.0 .002 .02 length cm 182.0 183 .0 178.0 Height cm 120.0 118.0 119.0 Depth cm 64.0 34.0 39.0 Fin diameter cm 4.54 4.52 4.87 Fin thickness on .04 .04 .05 Pipe diameter cm 1.58 1.58 1.59 Fins per cm 5.27 4.53 5.27 No. of rows 7 7 7 No. of pipes in a row 28 25 23 Surface area m2 553 421 510 Efficiency Percent 63 54 54 Energy savings . . kg/hr .78x10‘ .67x10'5 .67x10‘ ‘ 1Recycling of combined drying and cooling air through the heat exchanger. 6. RESULTS AND DISCUSSICNS 6.1 Introduction 'Ihe primary objective of this study was to evaluate the technical and economic aspects of heat pipe exchanger application to grain dryers. In this chapter the experimental and the simulated results will be carpared. Heat recovery by recycling the dryer and cooler exhausts, either directly or through' a heat pipe exchanger, will be investigated, using the simulation models. The economics of heat pipe exchanger application to different types of gain dryers and the effect of fouling on heat exchanger economics will be presented. 6.2 laboratory test results Table 6-1 is a list of the performance test results of the experimental heat pipe exchanger. Tests 1 to 4 are the results of using an Amrinco—Aire mit. Tests 5 to 8 represent corn drying experiments and test umber 9 is the result of a wheat drying experiment. 'Ihe last colum of Table 6-1 shows the heat pipe exchanger effectiveness obtained from the experimental data. 'Ihe average effectiveness is about 73 percent which is higher than the reported 67 1 3 percent by the heat exchanger supplier. 101 102 36.8 . 3E mum humus 8:33 TH Nunez ms So. So. mm mm s; moo. moo. mm 3 s; o so So. So. me 3 mm moo. moo. me so one o no m8. m8. mm NH or. so. oso. mm mm o4. s no N8. «Ho. 8 S on. 8o. «so. so om or o ms m8. m8. we on s.m ooo. sso. me on out o es 8. coo. S m on «so. 8o. so so od e os ooo. ooo. on a s4 o8. smo. on so as m ss ooo. coo. ss m o4. o8. omo. so on o4 m as coo. ooo. me o s; smofl moo. om mo s; H .s muss so E to as was so 5 so a NW3 8852 .53 posts canal 3633 o. 88o. sea and: 532 3683 oo 9.8. sea nuns sums Susannah uses no cosh sheen assessors sacs so coca ounces 635mm.“ one» womanhomaoc namesake 39.3 poem .Hlm canon. 103 Figure 6—1 shows a comparison between deviations of the predicted effect ivenesses from the experimentally obtained values. The horizontal line represents the experimental results. 'Ihe black circles represent the use of equation (3-11) (Kaye and Iondon, 1964). The black squares represent the use of equations (3-39) and (3—40) (finite difference). 'Ihe black triangles represent the use of equation (3-88) (finite element). Finite difference and finite element techniques are used to find outlet temperatures and humidities. Knowing the outlet conditions, equations (3—1) and (3-2) or (3—3) are used to find the heat exchanger effectiveness. Equation (3-88) predicts the temperature gadient along the pipe only. In order to use the finite element analysis a term representing the mass balancebetween thesupplyandexhaust sidemustbeaddedtoequation (3-41). The addition of the new term will complicate the finite elerent solution, because the new governing differential equation contains pipe and air temperature gadients along 11 and y, directions. Furthermore, the temperature gadient along the pipe is minimal due to the low resistance in the axial direction, and hence, the left hand side of equation (3—41) is almost zero. For these reasons finite elamalt solution was abandoned for further analysis. Figure 6-1 slows that the accuracy of the predicted values largely depends on the absolute humidity of the exhaust air . For a balanced flow, i.e. equal supply and exhaust (m C), the predictions by equation (3—11) and by the finite element method and the experimental values are in good ageerent up to a humidity ratio of .04 kg/kg. When the humidity ratio is higher tram .04 kg/kg, the results of the finite difference are slightly superior to those predicted by equation (,3-11). Kays and London's equation (3—11) is utilized in this investigation for the economic analysis of a heat pipe exchanger in conjunction with a grain dryer. 104 50 0 Equation 3-8 401 . Equations 3-1 , 3-2 , 3-39 and 3-40 30‘ A Equations 3-1 , 3-2 , 3-88 20« 10‘ . Percent devratlon O I -304 . -40 i -50 V .02 .04 .06 .08 .lo Humidity ratio kg/kg Fig. 6-1. Deviations of the predicted energy savings from the experimental values; (0 line) . ' 105 Table 6—2 shows the results of the wheat drying experiments. The savings indicated in the table are the results of recycling the dryer exhaust air through the heat pipe exchanger to preheat the drying air. The low values of percent savings (5.5 to 7.5 percent) are mainly due to the high ambient temperature and low airflows. Table 6-2 also indicates that as the drying temperature increases the percentage savings {slightly increase. Table 6—3 shows the test results of corn drying in a modified concurrent—counterflow gain dryer. The main variables were the gainflow rate and the initial moisture content . The experimental and simulated energy requirements for removing one kg of water are in good agreement . Energy savings due to different forms of recycling are between 8 and 18 percent. 'Ihe largest saving is obtained when the carbined dryer and cooler exhausts are recycled through the heat exchanger. 6.3 Simulation results A series of simulated tests were conducted using the drying programs developed by Bakker—Arkema _e_1_;__a_1_. (1974) . 'Ihe one stage Westelaken concurrent-counterflow dryer model 810-A was used as an example . For each simulation a heat exchanger surface area was calculated, assuming an effectiveness of 60 percent and an overall heat transfer coefficient of 40 W/m2 - °C. 'Ihe chosen values are based on the optimized V8.le which were between 55 to 72 percent for effectiveness and 20 to 60 W/m2 - °C for overall heat transfer coefficient. 106 Table 6-2. Test results of wheat drying in a concurrent-counterflow dryer equipped with heat pipe exchanger .1 1 Drying Dryer Outlet Initial Final kj/kg Savings Temperature Temperature MC MC 01' H20 °C °C . % WB % .WB Removed 120 43 18.0 16.5 6298 6.1 150 45 17.7 15.6 5824 5.6 177 45 15 . 7 l3 . 6 7349 6 . 1 2052 48 17.9 13.7 6007 7.4 1A schematic view of the dryer is shown in Figure 4-2; dryer settings are listed in Table 4-2. 2Airflow in this experiment was 28.6 m3/mim-m2 for the dryer section. .0603 was agoaxo menu 5 gufioeoce ads. 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Boa H 38$ 3033350052on0 3 5 035 choc Ho nuance." e89 .mlo can—fl. 108 Table 6—4 is a list of inputs to the program sinulating a corn drying process. Tables 6-5 and 6-6 show a sunnary of the output. 'Ihe recycling settings and the nomenclature are shown by a diagram on the left side of the table. 'Ihe ratios indicated in the table are provided as inputs. 'Ihe program will iterate until the final misture content reaChes within .05 percent. Table 6—5 is a list of the simulated test results, using a heat pipe exchanger to recover heat in a concurrent-counterflow dryer (Westelaken .MOdel SlO-A). Thejprogramldid not converge for a 75 percent direct recycling of the dryer exhaust, because in each iteration inlet air hunidity was increased. 'Ihe least ammmt of energy (2988 kg/kg) is used for the test in which the dryer exhaust is recycled into the heat exchanger, the cooler eXhaust is directly recycled back to the dryer, and the make up is fran the preheated anbient air. . Table 6—6 shows the savings Obtained as a result of direct recycling of the exhausts, and'byepassing the»heat pipe exchanger. The first test indicates conventional drying without using any heat recovery methods. As the table shows a 30 percent make up from the anbient air will result in a 3030 k3 per kg of water reunved which is only about 1.5 percent mre than the lowest value in Table 6—5. Tables 6-5 and 6-6 Show'that not nuch difference can'be found between a direct recycling and indirect recycling through a.heat exchanger. Holding an optinun ratio of direct recycling is a difficult taSk and usually results in a varying inlet condition. When the exhausts are indirectly recycled through the heat exchanger the inlet conditions can be controlled nore effectively. One unre point nwst be mentioned that the specified heat exchanger effectiveness 4 of 60 percent is a 109 Table 6.4 Settings for sinnlation of the condiment-counterflow » grain dryer. Model 810—A. Inlet air temperature 230°C Inlet absolute humidity .004 _kg/kg Airflow rates . .dryer 47 .72 Ina/miner? . . .cooler 22.86 :m3/Jnin-5n2 Ambient air temperature 18°C Inlet grain temperature 24°C Grain shelled corn Grain moisture content 25% (KB) Grainflow rate 2.184 tonnes/luau2 Length . .dryer 2 m . . .cooler 1 111 Cross section area of the dryer and cooler 8.9 m2 110 .0003 030 0005 .89 08508 003 0000.80 00 no 0000058030 800.308 .800 0a .85 3» 8 88.08." 83 ha 5050 .8080 08. .mp8» 0.88080 28. one 8.8 8? Hb.wH OO.DN hm.wH 00.0N hm.wH 00.0N mO.wH oo.mN 0m.mH OO.mN m®.wH 00.0N Hb.wH OO.DN HUSH HQ: 85 08080 .88 08 o . 88 88 «an as 38 88 0: Re 008 00.8280 900 30 88 84 HS SR 88 men 30 88 88 «an E 28 85 m8 0 88 88% 88 E 08.05 8E 3 .8003 «0 000009580 3 00.85 8H 80 No 8 R: No on 80 de mm mm me on on on 8 E. 8 8 8 2 80 80 0 one Em Bm 0800.00 0030." 00.300000 585 a J 0000 .8 o .9: H 00 183 I WTLJM g 8E f , i .0:on 88: 80338: 08. .85 Eagpgoonpgocoo 05 5” 805308 00.3 0.000 c 030: .0380.“ 000.... 008308 0.: .mlm 0HQNB 111 a gun emnmmm 00H0.0m 000060 omNm moan omom 000m mmflm 000m 0 COCO 00005c00 00:_000 Ham Hmm vmm mme mum O . ee.mfl oo.m~ -.m0 oo.m~ m~.m0 oo.m~ mm.m0 oo.m~ mm.m0 oo.m~ 0e.m0 oo.m~ mus .030 newonwn mmwm swam 000m hmvm movm mmvm H0m00 he 0:00:00 09500002” 00003.00 00 000 0>0§00 00 >000gm mm 0 mp 0m 0 om 0m 00 0m 0m 00d 0m 0v 00H 0H 0m 00H 00 000 0. 0 mmflfl 0000000 moflnmu mafiaoaomm 000000 “fl 000:0 e¢r0Hm H0uozflcmxma00003 05.0 .0066 8008056088008 0005 .gaomowu 00000.0 00000 00.3000 00000 0000.383 .010 0.300. 112 conservative value (it might be as much as 75 percent). 'Ihe last two tests of Table 6-5 are the repeat of the first and second tests, but with a heat pipe exchanger effectiveness of 75 percent. The resulting energy consumption is reduced by 2.8 percent. Table 6-7 shows the effect of drying temperature on the energy savings resulted from simulating the use of a heat pipe exchanger in the concurrent counterf low model 810—A, Westelaken grain dryer. As the drying temperature increases, a heat pipe will save more energy and the required surface area decreases . However, the overall energy requirements increase. 6.4 Economics of heat pipe exchanger Equation (3—119) is used to analyze the profitability of the heat pipe exchangers used in different sizes and types of grain dryers. For each grain dryer an optimal heat exchanger is designed and the following assumptions are made: (a) the purchase cost of the heat exchanger is obtained using equation (5-7). 'Ihe ducting system is calculated based on the length, the number of bends and also cross section to match the airflow and the size of the heat exchanger frontal area. The cost of the duct system is calculated based on $3.85 per kg (Goodfrey, 1977). 'Ihe first cost (PC) is the sun of the heat pipe exchanger and the ducting purchase cost, (b) the annual operating cost is obtained from the power requirement to overcome the static pressure in the ducts and the heat exchanger. The power requirement is expressed in kilowatt hours per year and is calculated based on 750 operating hours per year. The price of electricity is taken as 3.5 cents per kWhr. A 5 percent of the first cost is added to the operating cost as maintenance cost (Perry, 1974), (c) the annual savings is obtained Table 6-7. The effect of drying temperature on the savings, as a result of simulating the use of’a heat pipe exchanger in the concurrent—counterflow dryer Model 810-A.l Ding u. .143. °C Percent Percent m2 erer_ 922E.EEEE. §X§E§E. 121 25 22 509 3237 310 2927 149 25 21 508 3305 324 2981 177 25 20 506 3349 334 3015 232 25 18 503 3413 338 3075 288 25 17 500 3488 359 3138 18cc Table 6-4 for the dryer settings. The combined dryer and cooler exhaust are recycled through the heat pipe exchanger. 114 based on the heat gain by the supply side of the heat exchanger expressed in million kj. Fuel oil number 2 is chosen as a typical fuel for the dryer. ’Ihe price of fuel expressed in dollars per million kj, is calculated assuming a heating value of 3.86 x 107 kj per m3 with a 70 percent (Isothermics, 1975) efficiency and a price of $92 per m3 . 6.4.1 Heat pipe exchanger and concurrentf low dryer Table 6—8 is a list of costs and savings data for the profitability analyses of the heat pipe exchangers used in the Westelaken grain dryers. Table 6-9 is generated by using equation (3-125) and applying data of Table 6-8. A ten-year cashflow and a net present value analysis is utilized assuming typical values for interest, fuel escalation, inflation and tax rates. Table 6-9 shows that in 4 to 5 years the heat pipe exchanger will break even. The exhausts fram the dryer and the cooler must be combined and recycled into the heat exchanger, unless the heat exchanger is designed for smaller airflows. In other words a heat pipe exchanger must be Operated at its maximum potential, in order to give the desired economical results. The net present value is analyzed as a function of the fuel escalation for three different ranges of tax rate, inflation rate and discounted cashflow rate of return. For each case two different service lives, 5 and 10 years, are considered. Figure 6-2 shows that, for a service life of 5 years, an annual fuel escalation rate of 10 percent will have a net present value of about $2200 when no taxes are paid, while the same yields minus $200 if a 50 percent tax rate is to be paid. 'Ihe profitability of the heat exchanger will be altered to a large extent .8835 00 858052 .80 08 00:0 0:0 00 082% 9E” 5 1 1 $05 0 2wa . m 080 owmmm wmwm 08m «F030 8mm 0003 . m mam mgma mean $00 «7080 3mm monmmA Fe 880 >20 003 «:33 a $0 @3wa . mom Sow 0 Km mam «:05 a 000m .330 w ~8 H00.» \w .3\ .3 0000 00008500 0000 00.8 0.3.30 00500 050280 0.80 0000 80.90 E82 .0005 500.0 004300003 0:0 00 00008 000.000.0000 5 000: 0000:2000 003 000: 00 000305.. 335000.080 0:0 5 00: no.0 0000 005200 000 0008 300% 0000.3 00000.5 .010 038. 116 Table 6-9. Cashflow and net present value analysis of different sizes of heat pipe exchangers, used in the westelaken grain dryers. 810—A Interest Fuel Inflation Tax Rate Rate Rate Bate .12 .15 .05 .50 Year First Fuel Operating Cash Dep- Net .Discount Net Cost Cost Cost Income reci- Cash Cash Present at ion Flow Flow Value 0 3711 0 0 0 0 -3711 -3711 -3711 l O 1941 399 1542 371 956 813 -2897 2 O 2232 418 1813 371 1092 789 -2107 3 O 2566 439 2127 371 1249 768 -1339 4 O 2952 461 2490 371 1430 747 ~591 5 0 3394 484 2909 371 1640 729 137 6 0 3904 509 3394 371 1882 711 849 7 0 4489 534 3954 371 2163 695 1544 8 O 5163 561 4601 371 2486 679 2224 9 0 5937 589 5348 371 2859 664 2889 10 O 6828 618 6209 371 3290 650 3539 1210-A Interest Fuel Inflation Tax Rate Rate Rate Rate .12 .15 .05 .50 0 6137 0 O 0 0 -6137 -6137 -6137 1 O 3319 471 2848 613 1730 1471 -4665 2 0 3816 494 3322 613 1968 1423 -3242 3 O 4389 519 3870 613 2241 1378 -1863 4 O 5047 545 4502 613 2558 1337 -526 5 O 5804 572 5232 613 2923 1299 773 6 O 6675 601 6074 613 3344 1264 2037 7 O 7677 631 7045 613 3829 1231 3268 8 0 8828 662 8165 613 4389 1200 4468 9 0 10152 695 9457 613 5035 1170 5639 10 0 11675 730 10945 613 5779 1142 6781 Table 6—9 (continued) H H OLDCDQGDUH-waI—‘O OQDCXDQCDUIQDONI-‘O ~J no 15 000000000000 (9 (D [\3 CD OOOOOOOOOO Interest Rate 0 0 5230 692 6014 726 6916 762 7954 801 9147 841 10519 883 12097 927 13911 973 15998 1022 18398 1073 Interest Rate 0 0 7667 1269 8817 1332 10139 1339 11660 1469 13409 1542 15421 1619 17734 1700 20394 1785 23453 1874 26971 1968 117 3010-A Fuel Inflation Rate Rate .15 .05 0 O 4538 794 5287 794 6153 794 7153 794 8306 794 9636 794 11169 794 12938 794 14976 794 17324 794 4510-A FUel Inflation Rate Rate .15 .05 O 0 6398 982 7484 982 8740 982 10191 982 11867 982 13801 982 16033 982 18608 982 21578 982 25002 982 Rate —7943 2666 3041 3474 3973 4550 5215 5982 6866 7885 9059 Rate -9828 3690 4233 4861 5587 6424 7392 8508 9795 11280 12992 -7943 2267 2198 2136 2077 2023 1971 1923 1876 1832 1790 -9828 3138 3061 2989 2921 2856 2794 2735 2677 2622 2568 -7943 -5675 ~3476 -1340 736 2759 4731 6654 8531 10364 12155 -9828 -6689 -3628 —639 2281 5138 7932 10668 13346 15968 18536 S Net present value Net present value 4000 1 3000 q 2000 f 1000‘ -1000+ -2000~ -3000‘ ‘4000. 16000. 12000. 8000* 4000‘ 118 5 years service life d --— is Fuel escalation percent r"“"5-_—"— Inflation 5% 12% Interest _-- ~—--—-- I i 10 years service life I 0 -40004 -80001 -12000.. -l60004 25 Fuel escalation percent Fig. 6-2. Net present value as a function of fuel escalation and tax rate, for a heat pipe exchanger life of 5 and 10 years of service; and 750 hours of Operation per year. 119 when a longer service life can be expected from the heat exchanger. Cbnsidering similar conditions the importance of the inflation rate on the profitability is shovm in Figure 6-3. In this figure a 10 percent fuel escalation and a 5—year service life will not generate any net income unless the fuel price escalation reaches a value of more than 14 percent. Figure 6-4 shone that if a 20 percent discounted cashflow rate of return (DCFR) is the result of investment in the heat pipe exchanger, the life of the project must be at least 10 years. In summry, Figures 6-2, 6-3 and 6—4 indicate that a careful study of such parameters as fuel escalation, interest rate, tax rate, and inflation rate is necessary in the profitability analysis of a heat pipe exchanger. 6.4.2 Heat pipe exchanger and cormercial crossflow dryers Figure 6-5 shows a schematic view of a recirculating crossflow dryer manufactured by Ferrel—Ross, Saginaw, Michigan. The exhaust air from the heat levels 3, 4 and 5, and the cool level 2 is recycled directly back to the burner after it is mixed with the anbient air. Typical dimensions and process conditions are listed in Table 6-10. For the purpose of a profitability analysis, it is assuned that the recycled exhaust is directed to a heat pipe exchanger to preheat the drying air. An optimal heat pipe exchanger is specified using the non-linear optimization program, developed in the previous chapter. Table 6-11 lists the inputs for optinal design and sane of the outputs specifying an optimal designed heat pipe exchanger for heat recovery in the Ferrel—Ross crossflow dryer. Table 6-12 contains the surface area, the savings and the profitability analysis of using F‘ Net present value $ Net present value 120 1600 4 1200 ‘ Inflation 800 1 5% 400 5 years of service life _400 el escalation percent -800 -1200 -l600 {”/////' Tax 50 % Interest 12 % 8000 Inflation 6000 4000 2000 10 years of service life ~2000 1° 15 20 25 Fuel escalation percent -4000 -6000 Fig. 6-3. Net present value as a function of fuel escalation and inflation rate for a heat pipe exchanger life of 5 and 10 years of service; and 750 hours of operation per year. $ Net present value $ Net present value 2000‘ 1500‘ 1000, 5004 121 5 years of service life -500. -1000 -1500J -2000‘ Fuel escalation percent 8000‘ 6000, 4000! 2000, 0 -2000 -4000 4 -6000‘ -8000, Inflation 5% Tax 50% b——— ———_-—— 10 years of service life p——_— —-_-._-- _—--—-——-— ————‘”"' Fuel escalation percent Fig. 6-4. Net present value as a function of fuel escalation and discounted cashflow rate of return (DCFR), for a heat pipe exchanger life of 5 and 10 years of service; and 750 hours of operation per year. 122 C—_————* _——-_—‘ Li A pm“: L—.———‘ .. BILL”... ..._...._ ‘ L; ‘1 LL. ' I] :2“ ._.r —. —..- .0.de p—o—«—.- - —.——-‘ —-—---» v... P“- -——._ _, _— DRYER COOLER Figure 6-5. Ferrel-Ross recirculating crossflow dryer Source: Bauer et al.(1977) 123 Table 6-10. Some typical dimensions and process values of a commercial crossflow dryer manufactured by Ferrel- Ross Co., Saginaw, Michigan. Drying air temperature: outlet air temperature: level 8 102°C 33°C level 5 106°C ‘ 70°C level 2 23°C 52°C Ambient air temperature 18°C Ambient absolute humidity .004 kg/kg Grainflow rate 100 tonnes/hr Airflow rate: . ..Dryer 40 mS/min-m2 . .Cooler 20 m:"/min-m2 Length : ..Dryer 14.6 In ..Cooler 4.8 In Drying and cooling columns .3 x 2.4 x 3.1 m Number of column in eaCh level 6 Number of levels: Dryer Cooler 2 Holding Capacity 81.5 tonnes (Shelled corn) Source: Bauer 9£_al;11977) 124 Table 6—11. Input for the optimal design and output specifying the optimal designed heat pipe exchanger for use in the Ferrel-Ross crossf low dryer . Inglts: Airflowl m3/min Temperature2 °C Humidity3 kg/ kg Fuel price dollars/million kj Electricity dollars/kWhr Qrtputs: Overall dimensions m Fins per cm No.ofrows No. of pipes in arow Surface area m2 Effectiveness percent Savings Kj / hr Exhaust side Supply side 4813 5776 60 18 . 01 .005 3 . 31 .035 5.8x2.8x.8 5.04 10 48 4842 6.43x10" 1Based on 94.5 m /min.-tonn of grain 2An average temperature 3A typical condition Table 6-12. Annual cashflow and net present value analysis of the optimal heat pipe exchanger, used in the Ferrel-Ross crossflow dryer. First cost $ 33246 Operating cost $ 4972 Savings $ 15962 Interest Fuel Inflation Tax rate escalation rate rate .12 .15 .05 .50 Year First Fuel Operating Cash Dep- Net Discount Net cost cost cost income recia cash cashflow present -tion flow value 0 33246 0 0 O 0 -33246 -33246 -33246 1 0 15962 4972 10990 3324 7157 6086 -27159 2 0 18356 5220 13135 3324 8230 5951 -21208 3 0 21109 5481 15628 3324 9476 5826 -15382 4 0 24276 5757 18520 3324 10922 5710 -9671 5 0 27917 6043 21874 3324 12599 5601 -4069 6 0 32105 6345 25759 3324 14542 5497 1427 7 0 36921 6662 30258 3324 16791 5398 6825 8 0 42459 6696 35463 3324 19393 5301 12127 9 0 48828 7345 41482 3324 22403 5207 17335 10 0 56152 7713 48439 3324 25881 5115 22451 126 the heat pipe exchanger in the crossflow dryer. Table 6—12 shows that savings in fuel will pay back the heat pipe exchanger costs after 5 years. The heat pipe exchanger in the crossflow dryer shows a lower level of profitability than the concurrentflow dryers. However, at the present, crossflow dryers are the major types being used and the heat pipe exchanger definitely results in net savings which otherwise will be lost. 6.4.3 Heat pipe exchanger and batch type dryers Application of heat pipe exchangers to deep bed dryers largely depends on the price of fuel. 'Ihe exhaust air from a well designed and operated deep bed dryer is saturated and its temperature is low. However, when the ambient air temperature is lower than the exhaust, sensible and latent heat available in the exhaust stream can be recovered by using a heat pipe exchanger. The effectiveness of the heat exchanger will increase as the drying proceeds in the bed and more heat becomes available to be recovered. Use of heat pipe exchangers in layer drying operation is similar to the cmssf low dryer. However, layer dryers operate at lower temperatures than the crossflow dryer, and thus, a lower net present value is expected. Use of heat pipe exchangers in fluidized bed dryers is similar to concurrent flow dryers. In fluidized dryers, the total airflow is higher than in a concurrent flow dryer with the same dimensions. The absolute humidity of the exhaust air is also higher. The high airflow and available latent heat are the tm characteristics that make the heat pipe exchangers economically attractive in fluidized bed dryers. 127 6.4.4 ’Ihe effects of fouling on heat pipe exchanger econanics The effects of fouling on the economics of a heat pipe exchanger is shown in Figure 6-6 where the annual costs and the annual savings are plotted versus the thickness of fouling layer. 'Ihe analysis is for a heat pipe exchanger specified for the Westelaken grain dryer model 810-A. However, the results will be similar for other units. Figure 6-6 shows that the savings and costs intersect at a fouling layer thickness that can be considered a critical value (.44 mn)‘. Beyond this point, the heat exchanger is not economical. Figure 6-6 also indicates that the changes in savings are small compared with the changes in costs. The reason is the relative value of resistances due to the heat transfer (h) and fouling (Rf). 'Ihe fouling build up results in higher velocity air which eventually produces a high heat transfer coefficient. The relative increase in the heat transfer coefficient is the same or more than the relative increase in fouling. As a result, not much change is noted in the amount of heat transferred. However, high velocity air results in a higher pm drop which is responsible for the operating cost increases. To calculate the frequency of heat pipe exchanger cleaning in a year, Figure 6—7 has been plotted. Meiering and Hoefkes (1976) measured an average amount of 200 g/mZ/hr dust in the exhaust air of several sizes of crossflow grain dryers, and gave various quantities and sizes of the grain dust particles (Table 6—13). Meiering and Hoefkes (1976) stated that 1The thermal conductivity of fouling material is assumed to be the same as those of grains (about 1056 W/m—C). Dollars Annual costs and savings 128 3000 « Savings . ‘- i i I I 2000 . Total costs : l / I l I l I I l 1000 l i I l I l I I .0 .01 .02 .03 .04 .05 .06 Fouling layer thickness can) Fig. 6-6. The effect of fouling thickness on the total annual costs and savings of a heat pipe exchanger specified for the Westelaken grain dryer Model 810eA. 129 Critical fouling thickness Fouling thickness mm 200 400 600 Hours Fig. 6‘7- Time required for the fouling thickness to reach to the critical thickness for various values of renoval rate (K2) ; see equat ion 3—1 14 . 130 Table 6-13. Particle size and the weight percentage in a typical exhaust air from a crossflow dryer. Category Particle Size Weight mm Percentage of Total I > 1.2 44 II .6 - 1.2 19 III .4 - .6 12 IV .15 - .4 14 V <.15 ll Source: Maiering 8; Hoefkes (1976) 131 "the particles below .6 m can be assumed to have an amorphous, concentric shape with a density similar to that of many biological materials, about 1.2 g/cm3. 'Ihe particles with diameters over .6 mm have a foliar shape”. It is assured, in Figure 6-7, that the particles smaller than .6 mm stick to the heat transfer surface area.and fonm the fouling crust. This amounts to 37 percent of the total emissions (74 g/mz-hr). The remaining 63 percent dust particles have to be removed in a settling chamber or a bag house. Otherwise, these particles will block the frontal area of the heat pipe exchanger. Figure 6-7 shows the time required to build up to .44 mmlthickness with various removal rates (see equation 3-108). In about 300 hours of operation, fouling builds up to a critical value. Therefore, at least twice a year a cleaning operation is required if the heat exchanger is to be operated economfically 750 hours a year. The cost of filtering equipment has not been considered in the economic and fouling analysis, because most of the commercial dryers are equipped with some type of filtering device. 'Ihe profitability of a heat pipe exchanger will be reduced considerably, if a collection device is to be used and the costs are charged to the heat exchanger. 7. (DNCLUSIONS Based on the analyses and experiments performed in this study, the following conclusions can be drawn: 1. Energy savings from 15 to 18 percent can be obtained in grain dryers as a result of heat pipe exchanger applications. These values were obtained both experimentally and by a simulation. Simulation results showed a direct recirculation gain dryer yields savings in a concurrent-counterf low comparable to those obtained when recycling is performed through a heat pipe exchanger. A combination of direct recycling of the cooler exhaust and indirect recycling of the dryer exhaust through a heat pipe exchanger reduces the energy consumption to about 2964 kj per kg of water removed as compared to 3488 kj for a concurrentflow dryer without recirculation and use of a heat pipe exchanger. The profitability of a heat pipe exchanger depends on the annual fuel escalation, inflation, interest and tax rate. Heat pipes used on a concurrentflow dryer showed a break even point after 5 years of operation, while on a crossflow showed a pay back after the fifth year of operation (750 hours of operation per year). Particles larger than .6 mm must be removed from the exhaust air entering into the heat exchanger to prevent these particles 133 from blocking the air passages. It is recommended that heat pipe exchangers be used in the grain dryers already equipped with same type or emission control devices. Purchasing filtering devices solely for the sake of heat exchanger and charging the costs to the heat exchanger will alter the presented profitability analysis to a large extent, because the cost of filtering equipment is usually several times more than the cost of the heat pipe exchangers. Fouling results in high pressure drop and increased operating costs. 'flhe rate of heat transfer and, as a result, the annual savings remain rather constant with increased fouling thickness. This is partly because the relative values of the convective resistance and fouling resistance do not change with the layer build up. Cleaning must be performed about 300 hours of operation before the Operating costs exceed the savings. The economics of heat pipe exchangers used in either a concurrent- counterflow dryer or in a crossflow dryer depends on the exhaust temperatures and the airflows. concurrent-counterflow grain dryers have better design characteristics to use heat pipe exchangers more economically, than in crossflow and batch dryers. The high airflow in crossflow dryers will offset the large initial investments in the heat pipe exchanger equipment. The analysis and the optimization methods developed in this investigation are valid for a wide range of size and.process variables. Therefore, the computer programs can be used for future analysis and designs. 8. SUGGESTIQVS FOR FUI‘URE WCRK Based on the analyses and conclusions of this study, the following recommendations are made for further investigations: 1. To investigate the characteristics and quantities of emissions from different types of dryers. 2. To install a heat pipe exchanger on commercial grain dryers to investigate: a) fouling characteristics b) heat exchanger performance c) savings and costs under different operating conditions 3. 'Do extend the application of heat pipe exchangers to other agricultural and food process industries. 4. Tb investigate the use of thennosyphons in grain drying and other processes. 134 REFERE‘ICES 9. LISI‘ OF REFERENCES Amode, J. O. and K. T. Feldnan, 1975. Preliminary analysis of heat pipe exchangers for heat recovery. ASME Paper No. 75/WA/HT—36. The American Society of Mechanical Engineers, New York, NY. Anderson, R. J. , 1972. Comercial concurrentflow heating, counterflow cooling grain dryer. The Anderson Nbdel. ASAE Paper No. 72-846. Am. Soc. Agr. Eng., St. Joseph, MI. Anderson, R. J ., 1976. Personal communications. The Andersons. Maumee, OH. Anon., 1977. Efficient grain dryers. Sales literature. Ferrel-Ross Co., Saginaw, MI. Aronson, R. B., 1976. 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The effect of the nmber of tube rows on heat transfer performance of smooth plate fin and tube heat exchangers. ASHRAE Trans. 1:307—317. Rohani, R. A. and C. C. Tien, 1974. Minimum heat transfer limit in simple and gas loaded heat pipes. AIAA J. 4:530-532. Rohsenow, W. M. and J. P. Hartnet, 1973. Handbook of Heat Transfer. McGraw—Hill Book Company , New York , NY. Roth, M. G., F. W. Bakker-Arkema, S. F. DeBoer and L. E. Ierew, 1973. Energy conservation in grain dryers: A two-stage recirculating counterflow dryer. Paper No. 73—138. Presented at the 1973 Canadian Society of Chemical Engineering Conference. Vancouver, B.C. Sept. 9—12, 1973. Roth, M. G. and S. F. DeBoer, 1973. Cptimization of concurrent-counter- dryer with heat exchanger. A Special Report. Agricultural Engineering Department. Michigan State University, East Lansing, MI. Ruch, M. A., 1976. Heat pipe exchangers as energy recovery devices. ASHRAE Trans. 82:1008-1014. Sheperd, D. G., 1956. Performance of one row tube coils with thin-plate fins, low velocity forced convection. Heating, Piping and Air Conditioning 4:137-144. Schmidt, T. E. , 1949. Heat transfer calculations for extended surfaces. Refrig. Eng. 4:351—357. Segerlind, L. G., 1976. Applied Finite Element Analysis. John Wiley and Sons, Inc., New York, NY. Sokhansanj, S., 1974. Heating the Grain by Hot Water, "Part of a The Stage Recirculating Counterflow Dryer." Unpublished M. S. Thesis. Michigan State University, East Lansing, MI. Streltsov, A. I., 1975. Theoretical and experimental investigation of optimum filling for heat pipes. Heat Transfer, Soviet Research 1:23-27. Taborek, J., T. Aoki, R. B. Ritter and J. W. Palen, 1972a. Fouling: The major unresolved problem in heat transfer. Chemical Engineering Progress 2:59-67. 141 Taborek, J., T. Aoki, R. B. Ritter and J. W. Palen, 1972b. Predictive methods for fouling behavior. Chemical Engineering Progress 7 :69-78. Winters, E. R. F. and W. C. Barsch, I971. The Heat Pipe. In: Advances in Heat Transfer. 7. Woodforde, J. and P. J. lawton, 1965. Drying cereal grain in beds six inches deep. J. Agric. Eng. Res. 10:146-171. APPENDIXA 143 Appendix A-l. A list of the heat pipe exchanger analysis programs. PROGRAM ANALVS(INPUY.OUTPUT.TAPES oTAPE60=INPUToTAPEGI'OUTPUTI ANA YSI OF THE PERFORMANCE OF A HEAT PIPE EXCHANGER g SUB OUT HES! CALCbBPRO ESSEDFINITEL* FINITEO; KA AAsnaLv. car com o 0L6 . REPOR 6 Y5 REPORYP .REP RTC COHHON/PRIHE/EFF, NT“. 09HE9HEH, EEC 090:0”H9RECQREHQEYACé ETAH 30 za¥figsc*3SHgGH,GC:VH,VCoUOVgUOVCoUOVHgRH.RHCT,RHHY.OSOo0 SHQE¥C: PH. COMMON/DIPEN/ACC‘ A H; SP, HT w5V:::EEC,A:EAF. .AREAoAF921oZZoZ3gZ“ COHHON IE ONCHY IA COHHON inPPTV/SA.CAf CP.c v.cu G CONHON/PpY/ICCUN'oSQE 095C °C.!TPZAX.HA,601.IFLOH.COEF CCHHON/PQTY4XKP XKF PI COHHON/INLE /rINc.TiNH fiNINc HINN. Mg .NN OHHON/OUTLET/TochOH .Noc.N N.c0No §¥4532’3%E§i{”1l DATA SA.CA.CP'CV cuopancHFG/Zhaoo02‘902690969109520910000, DATA xxp xNP,Pr/iza. 120..3.1~15/ 0A7“ RI.$I.XNY.HR,FUO.EUC/.12..05.5..750..3o5o.0351 c PArnsiu. READ THE INDEPENDENT VARIAEEES 0P rue HEAT PXCNANG a 70 as § aggézzso IFIN DIAMETER. PIP orANETPn. PrN THICKNE s. PIN c PIPE {PthN IN COLD sroe. NunesaT 0P now as NUMBER 0P PIPES IN c A PoutflAXl LONGITUO INA} Pgtcn. TRANSVE R§£ Prrcu. PIPE LENGTH 8 IN HOT srné.....ALL rN EE 0 READ 101.cx11.4). J-1.1o) c INPUT INLET A o YEHPF Hors sgos rrNN. c030 s: 8 ABSOLUTE Hun frv LB/LB HOT E NINN. CLO s P fit nPAo 1:1 TINN.rrnc N1NN.NrNc PRINT 10%. TINH TIN .NrNN.NrNc 13’ F09HAT‘SCX 515 &n 1 I POQHArcaPi . i g AIR FLOHS IN La/NP. HOT 510: NH. COLD SIDE HO READ loloHva PPINT wiué CALL cAL "£4.1m gfikL PROCES 55 1.1L 1.x.1: DO omuun C”? CNS CK’AO (ND C) C) CK) CICWO C) 0 CM? {10 CM, CK) cua 90 144 SURROUTINE CALCINAHAK9X9I) CALCU AT CH OF THE CORE AHO DIMENSIONAL CHARACTERISTICS OF TH H AT PIPE EXCHANGER COHH N/PPINP/EPP NTU a HEH HEC 0Pc nPN, caREH PIAc TA gn ac. :ggbggg*gan.CN.chVN.6c’u3v .uovc.u6vu,éN.Pch% HHT. 'osc. bgm Ho: PPN. COWHBN/OIHENIACCQACH SD: HTNOQVAARE‘Cv‘REAflpAREA. AF92192292312“ OHHON/PRTY/XKP XKP.APo IHENSION xIK.NI PAaer SI/XII $0) TOTAL Nona! CF PIPES TPI9553X(Iu6’/Zo“20.x‘I.7"10, PPIPPIN'IN cstss TSP=X(I 3IPX(;.AI PIN §PAc%N, 5P=¢1./12.- SPI/xtI.AI HEAT TRAN§FER SURFACP AREA Ci=2.’°1‘(X( i} P-z. -xtf Z)"2.PX(I.1!‘X(I 3IIPXII.«I APEAC=¢C1P2.‘P chI.ZIPsPthI.AIIPx¢I,5IPIPIPPsPIz. AFEAH=APEAOIRA EXCHANGER CEPTH X‘2913’3XI .9I‘XI196, EXOHAHGER HEIGHT X(1911’3X(IQ7I‘X(IAC’ EXCHANG P L NGTH x(I.1$LEXOIA§3H:LIOIgIANC ch.1AI=snRIix(I.9IPP2.Ix§I.oIPP2./A.I PXCNANcER VOLUME vsch.1LIPxII.12IchI.13I FRONTAL AREA HOT AVA! ABLE FOR PLUIo PL ATOPZ.‘CX(I.1I‘XII.3) .2I IPSPIPXII.AIIXII? SI-XII.7IP12. ATHslTC/RA FRE‘ FLOH AP A Acc:x¢5.5IPx¢I Iii-ITO ACN=XII.IoI-xci.11I-AIN PIN AREA AP=cxPx¢I.5IPIPIP£s-12. 'TOTAL SURFAgE AREA AREAzAREACO REAH EXCHANGEP [IHEHSIONAL PAPANEIERS 21: REA/v 22=Ac3/¢x¢I SIchI.11II Z3=AFIAREAC 2A=A.Ix¢I.13IPAcc1AP£Ac PEIURN ENn suanoUIINa PROCESS «N.N.K.X.II CALCULATION 0P THE PEPPOPNANCE 0P THE NEAI EXCHANGER COMMON/PPI IEFF, NIU.0.NE.NPN. NPc OPC OPH PPc.RsN.EIAc ETAHER oc. SIfiésfiIh SN, H. cc.vu.vc.uov.uovc.uévn ,PN.Pch.PNNI.Qsc WASHgE EPN. 3833§3$§§3937ic6‘3°a‘33' .g¥0595.:gegé.m APEAN AREA AP z 22 23 26 cowaaN IPPPRTV/SA,CA:CP:V ’ ’ Puo HG ’ ' 1’ ' ' CONNON/PRI/ICCUNI.SB.PN C’ITPHAXf NA.CC1.IPL0N.005P COMMON/INLET/TINCITINH .NIN M6 .NN COHHON/OUTLET/TOCoTOHoHOC Hon. couos COMMON/PRTY/XK°.XKP PPO.° PINPNSIoN xcw.NI.eA512I.AI I12.12I.INI7I;IC¢7I,NRIII.IP¢6I 145 ’ U W T N E 0| T m s T H o , E T 2 n. m 1 E M Q 33 n a 11. E s 11 H V. C o o T E L F O O U a» E o t E 0 N 22 T I A .3. .. m . L 6 22 m C I. o O o C E N z N ¢ . 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NCI/Hflau NI, A2 9 '22 I. o 088 cl. u PTTH H O 0H] N E E U N NCluAASCE N90 01111N L. E HISAACOO 0AA 9511/] 2211‘ 33 EEHLT 11V 0 R T E T ( IO; HMO & v1AAXNHsI A1 VHCUTVOOAHH L00 T$¢(8811E((HH OZZO..RL ((01 E E I S I 0 S TTNOO: UGCCAICJH 0 V1 CCHO/HHHD 9 PH" XXXCBELTTNN E. n E o o+flNIIUT R H N U N T. V. (TI/’1. 8 .1 11d. ”India I 9 SAAIC CD 99” RD: THO ! 1186Tv.AA N o 0N11T90 o 0” E T T. T. A O 0 "CH2! NIauAAN 1:0UI Sl/XNi/IDCH R/l Aloofiflo¢NPPTT N11N¢¢CF 110. H I F P F R X 21655 THN (CH:=I§JK:0¢ AHCAI=HCPHH ICH EPZZOOHCIOQ=3 I:=I:=HV ==V1 T E O O HH:QQTAFR LXHHXNHZJHREX HHHHTAGGAgz AHH HS=:ooHHSSSCH FCHFTTQO CHO: L L L ==X==NHEU A s 2 :ATC (S I I 8 (n z 2 CH 8 8 INC: .- 8 = : SIT. AN NC: NVUV I. L L HCACHT.P To ELizkflagPT x HC =HHC 55 CH 111HCHC CHHH TT NH" 00:0 A a ‘ SSPFFPC EN QXNNCCPCHHI H CG TRV' VV 00 SPPHHHH BEPP EE 9PN UUHU C C C CQOEEPFHRE 5 1 2 C C C C C C C C C CC CCCCC CC CC C 2 146 SUBROUTINE FINITEL1N9N9X1 C N RAT ON OF THE r N N s an? CATION OF THE BOUN AR 8 CSN ITI NS. CALCUL‘TEON CF'THE ECNSTANTS OF THE STIEFNESS g NAvaIX CONNON/PRIN IEFF.Nru.O.N .NEN.NEC 0P0 DPH.R c R N.ETAC AN R. :£¥figsg*5aHQEHoGCOVHgVCoUSVQUCVCOUCVHQNNpRflcgpéN ToOSCoCELoEECQESN COHMbN/PRT/ICCUNT.SB.RH,SC ITHAXP HI.CC!.IBLOH.00EF CONNON/INLEt/TINC.TINN.HIN6 N1NN,N , N COMMON/OUTLETITOCoTOH NOC.N6N.CONO COHHON/PRTY/XKP.XKF,P1 DIMENSION 8(1001 PNCC100).HUNI1OO).ev16).IaNtal.Ierts).NE .112) V(N HD‘D(1001,N5811§1 oxNENsxoh N.111.53N1A.u1.srtu1.pntcur.Aczoo01 DATA IN/60/.Ic/61/ NCL/1/.Io1/a/.NNP£/b/.NOOF/tl.KL/b/ OnrA cc1.IFLON/1..1/ NAsNINN ICOUN =0 NNIO NP=X11QB1 NPR13’N966 NESS’NP NHN32‘NROZ C IC86 JGF=NP+NP‘ L JGSN=JGFON NCL JEND=JGSH+NF‘NBN JL‘J Nn-JGF 0013 =1‘JEND c 13 8(1180. E ASSEGN Nc THE BOUNDARY VALUEScOCUNTERFLON..IFLON-n. C CON UR ENT FLOHOOIFLON'1 IFCIFLOH.EQ.01 GO to 10 00 ii 131‘ IBM! 1:12 -11‘NR¢I BVtID=TINH 11 IBF(I)=Z’I'NROI no 12 tab IBN 1):;‘3'NROI ev¢11=1 t 12 IBF(I)=(2‘I-11‘NROI 60 T? 13 1o CONT Nu - no a 1:1 6 IaNtI)=t§‘I-1)'NR+I BV(§)=TINH IE( .68.“, BVQI1=TINC a CONTINUE CO 5 131‘6 éar1112 I’NRO! s ONTfNU 1b CONT NO 00 6 1:1 6 6 NFatlisli-s1'flflo1 no 9 1:7 1 9 NEB(I)=(1-61‘NR 35:11’357H7’1-91 c INITIAtigxuc THE STIFFNESS MATRIX CC.CCC‘§.§ D 6 I. v“ 00 i J: 5 c 26 ESH .Jrsb. g INITIALIZATION or vscroa 9 FOR use IN susnourrue CONDENS no 27 1-1 100 27 311130. ' XX- 00 (Z‘Nfloib (6.'12.1 cwqur) ONHMAH 147 C p .m N a. 9 a m X .1 J. N ”w R W F N R T v T. I R .0 B N O .J r. “w E NW N 0X ea N 9 RT; 5 a. N F “HR P. 1..1 F. m“ C. .UT N .V nu a. J _vA F. “v.1 ! To 0 .3" B. o a. M. 23' nu D. T. N I. mi. N .3 ca 71 I. I. M“ I. Ht. 0 a. m” .0 n. 0. .UN .L 1.90 N I?! N F. F N P I a 9 VV “F N NF. 8 Mn 9 N .L BB" .0 I OT. O. ’.L .v N I! X. In RT. 0 O J 11 T" 9 NE w u w u m mm mm m 1 on T K N § N II N 0 J ”T ..nh ”n 9 O! Q. a. I. .IF 0 n. 1 L|.e3: .0 T J N ( CL EN 0 N W0 N O O N 1 NC NT 5 Dr EN N 111 R N 0 F6 8 a 1 1 NT. 5 O 0N1. P. Bo..1N 8 O .1 1 n3! 2 E 1 F8. 1 0 "N TI 1 1 C 1 cc 2 P I 1 GNF) AN 9( SS J J I 01 U D. O Y: O lulu LN Pr. U 9 9 .1 ON 951 o 2 222 R F (PJI 1. N6 L S I K H HR HT oZPZPPP E 6 AN(9 1m 99 AXN ( ( 5 SP TS b93.!o.¢ P 1. OQAN .0 FI..!1N H. N .0 9.0 N 60 21.... O nu.1|.16 9.9 .bN n2KU Q. Q. 1.0V .(N :Au 0 86..... P u 901: (U NN GAL 0 . . 0 u N: E 2. ===..=:: .r HMTIrN .flHN Q.v Hnu a: 1 41.1 a 1 FBn_NQ 1 1111111 m C. SSHQQN 9 QR GP E c ,- II. 1 " flu 1 ON 0 O .1 1991121533. 0 05331U9323U .(N US: flv.J ’..J o 9 .P! 13L 0 O Occlvooin. .: N niiboanEUT. T(.1320 T 0.0 .9 T.v1 0H".1N 6 RR 3&23N341 N S ((JBETENE DH RN OLN TLK LLJ CU AA I! 1""... ((11111. 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EEEEED E CCK‘SENNNNEE;c S CFu O a. o w 0 nu.3 .911 ON 70 I P 1 1 1 1L 22 0?. u 2 9..c ’5..£¢ a. 3 . 00060 0060 2 3 0 cc 0 UPC OPH REC REN ETAC AH R 0c EVN.$N,chT.§NNTIO .65N.£¥C:EFN ONEHgNEC OVOUOVCOU E .000 VCOU N/PRT/ICCUNquagflugSCgITHIXPpNAQCC1OIFLON.COEF GC,VH IHE/EFF’NTU CONNON/PR ‘OH VSC VS oNThc N1UH CONNb 148 NN NFC HINH NC 3H6?! 1.NS(#1.EF(91.NPC(60190(NP1.NEB(121.B( r 3 "Eucéw A DENb ' x: p .YiN .OA. KL), L E T A E H E H T T s N I 1 A N G N .l E T c. R R S 0 D. P I N E P 0 a R T n 2 Z P 1 L o A A A P a ( L 0 E I H S u 20 D. I 6 H T N1 0 N lCPZ L C N I IA 1 E 69 i O S o .9 E 5 oHH .. 2 O to .1 O 1 1 11 .1 29.0 H ’- 1 as t 1 1 N 1. 1126C 1 P 1 1o 0 IIZ T o 3 IA. K1 0 G I 66.. E XN O 2 2 11/ o u 2 51HD K. v C V C ::== N AI R 11 1 .111. 1 .r U 1 1 .0 (30 A I 11:11 ( NU N 1 I a 111 a O T a 031“ 05 2 E B 1 3b11 H 1TT O O 7. o 063 T D - TI1+ H6 1 H . I '99. U OIE 2 RR 16 611561 0 E a 6 (Jr: HO T 1 I. 3:423 H T 0R o ( 1NN1 ( (111.1... C 1 T 0801" W I 2 D. 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TR: NN-Z RETURN 3 , IFTABS!SB¢CONOSD.GT.0.001) so To 5 52:19.25:- 1 .sgfiuarci T£RATION ON THE EXCHANGER svowpeo NR_OIFFEPENOE s 'Fa. NNBZ pgTURN 5 I «RN.cT 1.» GO TO 7 PRINT 6.§O.RN 6 FORMAT(‘ No CONDENSATION AT NIN TEMP IN THE EchANcER 'F6.2‘ onx RN ‘F6.6) NNaz RETURN 7 c NT‘NUE RE U N END suaROUTIN- SLvacccsn or x NP NBN «cm 10 NE Rue NN NUN NR 153 *OIBFgIBNoIC1 9 O 9 0 O o v o o o T O 8 SOLUTION TO THE GROBAL NATRIx USING THE GAUSSIAN e ININATION AND RAORNARO sues ITUTIcN. :NO OUTPUT THE RESULTIN TEHPER URES CONNON/RRIIIccUNT.sa.RN.sc.ITNAxp.NA.cc1.IFLON.OOEF COHHONIPstgIPATH CONNON/INLsT/TIN8.TINN.NéNO HINH Ng.NH CONNON/OUTLET/To .TON.NO NON cofio OINENSION GSH(NF,NBN) GF(NP ka1 chP.NcLT.RNOTNET.NUN¢N£1 OIHENSION NEB(1ZT.IBF(IC).I N( c1 13.219 1 00165KK819NCL JNaK § OEOONPOSTTION OF THE COLUNN VECTOR GF( 1 oozsora1.NR1 H IIONEN‘1 I (NJ. 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P T 7.: PO TT NCPO TEAAOFTT 5.66.0 ILU R 0 GITITHA NT TELTT3NODLKT3N0 P. ONS/AHPBONPNFQH OFOHI‘FiIN OIOHTEN NGH .tLT NCTHPRT I Z HSLI R ISHGTARA .CIUA A EI A oFEITXHSFIT IV E 9.1! ECTFIRIH ECT IPIFHNI EAAESPB D H TI .1603 AIONNN HSDTSN HSDTSNCECSFLI X7... r. 3 GMT ITu. THA o.IT/ THA QHCTSIC CXHPE C P N SNNHN POLFIO 0 F A30 9 F ASITORA .rX3 OANIYMI AAFD RHPAA3P DHPQX—KZdHO uTC C 000 R. c; HEOAO GHFL IS a Q7cIS . o ZEHAC: R. I 6F10... v r HIT RCA... T T PHHTT T 200 X9L Y 930 10278! L O 1.0 C L TTE DEIQTE a 511.4an 3. To 9 .n A. LA? J/N T ..t. : _Nr: 0T EEEHG o v 57.... GLQEST.3HHS I D 1C? TF TTNDUII. ETRDII: .zTRD L P. Y... r «.14 I T...1/c. Ev. T LLONTEY TLLONTX HIXV RAETCAPU/ UTUA OTC EEI:PDT3TT( C7 3110 ENFB: Int. XF6TSNX2I LIH NNLEELTN NNLEcHMO/c. ETTA TUTUD T301 SFULR LLAYTDI .AAPCOI oAAPCROFHflFHTv ..HA Sn. .8 NIOTIIFLBNIOTIIFLBZUL31N NOAHDSTBTO 8 .N 8 PNI NNRPUACGHHAIACEHHAIFLR. nGHRZG H 17H ICLN IOLN HF .lI ETH S BA80 00:. DNIA)IIGDO AF VR AF VP FN o oLXbH .0T1HI.FA IFENNNP o IFENNNP. oH BAA a 9H 9H 7 O o S HICHE I. a 4 a n a t s o D. ”Y E. 0.. DY : ¢ 5 ACCE? AHA../...3ZNI.U. TH». T..1...T.ETHM IIIIF T ILPF oP. 5H697639 F. T 1F TSE XX XXXXX/A9.ID.FH/ADIRFH/IRHHV/JZF/S/Z o1X13UD.BAAAvSJUPRAAAYS/c I 66 06010100. L A 16.: AP. 6:. 5:.555/CIUDOP/CIUOOP lAT 1.2X2/ l/7/5I2HIH0 RD RIZHIHOD O PI/o A2: H 7(7(7(77( o H (((GEY(((2(((((( A0 S... An. S... LTN1/6((G(/Fo..((( AACGGDD! AAGGG.DB(HHH 1 T T T TX P TTTNLTTTTMTTTTTTT IKTOTI IRIOI TI... IIPTI TATaLXLTTTH TH TBA/ 2 TATATATTAA O AAAIP AAA/AAAAAAAYLLAHAAVLLAHA. AULAAHFAALA ob. AAA9HHHHHHHA9HHHHHHHA1ZCL I. NHNHNMNNNP F NHHS NHHNHHHHHHER UETHE: UETWLFOND 1H HHHFNED oHHM12931083H12931083HXX0AX/ In In In TIP... Rod.” 6 o. D. o 10.9 P o RPHD BHAD Hn. BHAD. oHrIGo. 7. 7. Po 0 F In a. D ..9 21223129 21223129. R : IMF POFOPCFPOF 000 o OOOHOOOOOO C 06 CXXCCHOTAEOOC O 011HI1 PFPFPFPPFI FFF. FFF/FFFFFF...¢¢.F: AHAasFFu‘ 40F66FF2FF VFFF F F 000 o ++O6¢¢ +¢¢+OO AAOO+ LO 1 46* 1236:676 123&6.676 123651 3 0 3 19 0 6 0 a 1 30 9 1 5 6 7 9 601 123 he. 67 69 0 0 1 32 6 E32 0 3 0 0 0 0 000 «0 000000 3 1 1 1 1 1 2 7 7 7 7 CC C733 33 333333 3 3 3 3 3 169 o NorptNAxuNTINEsxzuAInsx3NA9$9¥3NDSL3x5NcRAIN6X2NNC 31T.geéngg}543537runsxxNNUNEngNUE:xgzzfgg?;5gugggéga¢/n=m . H N x HHP x HCTXSHKGIK H .c - . _ 31a FOSHATIIIATHTSITUATTON EN Ncounweaso NNICN CAN NOT a: MéoELEDIIA1o.2 12H FLAG SET AT LENGTH or F6.3 IN N r 319 FODNAT(1/1sx21NPEpr0fiNANCE DATA II 15x 9 ZOHSTATIC PRESSUPE BAP Axs1z.61 0 15X13HPOHER N Axs12.6/ O1FX22HENERGY INPUTS KJIKG I b 17X13HFAN 1.; EFF! bXEéZ 6/ o ’7: 11NNcA 5N6 AIR ax $5.6! o 1 x 10NN0 ? G.ATN Axs12. I . 17x 12HTOTAL ENERGY «xe12.6/ o 15x3ANuA1FR Revovso KG Nee/Kc GRAIN hXEiZ.6 I +F§§X3OHENERCV FOR EVERY ms or HATER Denovso AXE1Z.6‘ KJ 0» PgGB R31T59HQ’GQ9939T51H59 OOOO COG SUBROUTINF INFUTHXTTHXgHHééHzggu ”T1 H1 G1oR1vT29HZoGZoRZoT3gfl3 11 GA U ATION OF THE TEHP AND HUNIDITY OF THE 5 GIVEN STPEAPS BEING MIXED AT A KNOHN RATIO 2\\C1mx0u pxx vHadm O'Ha- x I 061.‘HHX)I¢CAO.65'NNXD ‘SUBROUTINE COOLEF(GAocpoTINgTNIN9XNIN,HIN,TOUTgTHOUTgXHOUT.H0UT9XL COOLER SIMULATION BASED ON ROTH AND DEBOER COOLER MODEL 0N IPQPPTV/SA.CA cp, ch cu RHOP.NFG A‘VSDB‘AITINOA65., MI HIN A‘CA)‘(1.-EXP(-1.232*XLD)‘(TIN-THINT/(GA‘OAAB.83H ‘(1o-EXPC-k.11B:XL))+.633‘GA'CA)’(THIN- TINT/(GP‘CPO 3331 p ‘XL".5“66‘¢100155‘3‘(TIN'5O.T9103‘110509E'2‘1THIN‘1 6.‘XHIN;.21,.1O,’CF"‘.Q 6132 UT-HIN’ ’GAIGP + o mflxutaddon znnnnODmrrnc> 040' C: O T I I i CZ’fin-OC I! J. 2 ll HI"-0 II 6 T (G a ‘C A = 92 + “A T HC R SUBROUTINE DERFUN coo... c.0so C""‘ 4.00. LoEo LEREH, PROGRAHPER DESCRIPTION CU...‘ C“"' ¢n¢tn co...- cuanuu USAGE SUBROUTINE T0 COMPUTE DERIVATIVES FOR RKANSUB USE” WITH PKANSUB FOR CONCUPPENT FLO“ DRYER HOOEL COMMON IPPPPTTISA CA,C°9CV HFG COWHON ICONS TNT/CO”IOCON296ONS .CONA.CON5.CON6.GA COMMON IPKAHIYTZOZ' THIH=T(1’-Y(K, 170 M S . . S L A U P E T P N D E U N R 0 0 R P 0 E H N U H C Y T T 0 A R S C E L 3 o E H M E W N . I! l. V. . a, s I 2 O M R N W I W N A .l T V E N m T. m I o Y N T U N T 0 T F 5 B I U I Y. N c A 0 N A P R T 0 T 0 N R N B N C 0 U H. C 0 G 0 o... 0 N W R O I C L C 0 A 0 A T. H I N 0 P N A 0 0 U K o A D. c 0 U L N 0 A 0 A U l. C 0 F A E N E E A l‘ E 0 F V 0 U I I R m E Y. I 1' I I N T 3 R E W T o ‘1 T T I N \I r“ T N U o 0 a I ‘ T F. 9 Y N O I P G o O 5 O. N R I. A U c 7| N I: 9 C o E Y L 0 N 0 ) N I P Y C F G N C N 0 C 0 0 I T F A I U c o I I: E M 0 HI 5 H 0 1 0 1 T O C N TO 0 T. N O K N o P A R T. A n , A c N E R R o “u TG N G 0 G 0 . F W N a N T NNT N F r! o s A N )..N.. N IRN O ’I3TWT .I B . pm 0 ) Y. NOE ‘1 o .l A .l A A . 31 ¢ IFR L M. A o 31R 3 ( M a. A no 0 (A V A R ED N3! oOCT ( I I P L R H VT 0 TLU V0 OBYOTYNE Y 50 T x F 0 R . N O NAC GR HI; I 90R 9 MI E F 20 N6 OINX VP TY1TOQCU39 Xv! T A ! 0 D E NO OF CTOOH I H. 0.206 T 6 .A N I L I G C 0 IN NC/F 0810339. 3230 0 OR E .I E f. 9 A R CE vial Er. HCC.21A3 ,90119 N L’O v A I L 0 N’N N A NRHD on. OIQGYQS 0 5 v3: ARBNG R T F N F N 011 0 U OIET 0A 206 0T SAFHOA’CR VHO 0/ A U U INT 1’? ETFIFNN (0.» .I . OI Go)/U IL .1) E R Y N o H TOU TOEN FUFNTXIYPOauOE) .0 IA’T )UAATE R .1 T G 9 ACO A‘ T IOT. A/l/PQPIIN oN’i‘ESlRO. OAN U s. I s A L9 Ut UVX. BRODLNEHI .XH 2.. .AOCYHI anEBAUX 9 I o D B 0 L 59 OIBN 00 03 B EUINA 9;EU oYH oY oXOZX +00. 0t I A5N F R9 E3U00Fq6/N WUUNSCAA Kr. A; HTCRTLIH. N 9(5AAEO I ’H . HS... 1X .1 9 NSIE NAO SIUNNRH7A LA N oAP, ZGTIC H 0 5H...- UNSN ./ N5H9 6 X0 TFXOTC I All/AIGKoHKFEHIZK OUATXX EHSCOQ FHOIUE) TERIOQ). UCLAIOCFI T. C N63C)BCTG BC(C)LD o 90!. U NY191U 1'11901U Y19Z£1 l-LUD/cHsN U NNNIB o. 305N oDHYFDANMn/cNN7083N NTT:: 0‘. NT: 39(1 T=A0 H ..T’R 0 0000 o7H.(HHOHHE(HN ..OLSW :RIEI)’XOIEA!’=Y001€T)9Y .0 03CEL0’00U R THN HAIZCYPCCPD .. ..CXRCA ..D’UTSTIZ:TTST12’I 3.17512 0.. ..T 7 L Q 1tnn MN H? .h (a ((59 (H ..n. ATN 0.19.. N 1139.8 N 11.2.5. 0 ( A ( (ENU oomAzs FH FFHN FL IA CEO (INOO (((NNOO (INNMON Y 0 Y YRES 06 0A8 I: IIXX IA TR YRC YYXGC . YYYXXGC YYPXXGE . : u . . : . ..u . a”. an a. I l O C O u u. a . :uo¢ u an u a u s« a. u C I I a C O C O I 0 l I O 0 O O O O 0 O C O O C C l O D . O 0 0 ¢ 0 § 0 C 0 C 0 cc c C cccc C CC C C C CC CC c APPENDIX B 172 .w .. mm“ m. . O .. H . 0x. 0 . 0 w. 0 . m6 0 . firm m . ~—. 9 _r ; fs 3“ O C m. ..U . “m. A. o.o¢ 0.?» 05K. W... M fem «ion. a KR. ‘. I. 0'. n'- .I. ll- IIIo .II- '0... O! .Iun sun- ol. ll. ..0- a... .1. wt. I... 1.. u... .clc III .00. 0'. nun. Ila: ‘Io 0'. o! I- -! II. '00 A. or: ..C- n A». . .F m. .. . uh m . mm. «WHO. «#0. ONO. «2 Hm. viva fl. 0...... m. O CO . ..h GOO . ..H 0.“...0 . H 1‘ Q . .fi .m ..H . W.,... x... m . m. m. mfio. ado. one. {.0n q.¢n e.em m. 000.0 ccc.fi coc.fi . o x ., o 3 ...e . . ..u. fix! M.. _u. ..n. A... BAH. .w G .. A... ._. O . manna. . . "an a, . w. J . «3.... m . coo.fi coo.fi c. an. mfmm. m... .m. m“ m n. a 3.0. NR. .. \ h! g... x. \ Bl q... f‘? ..Fw m. . 09 a . Tm A“ M, o Kb 0 w... . ..H m. N199 ..M o «H... w EGO. . w . «mg. m“ . 0 a mfnop. 0.5%,...“ Coma.“ O.CN.~ m.mofi c.0m. e.mfi_ c.0m. w.mofi c.0mfi m.eHH H.mwfi m.mofi m.omfi mmo. mac. ¢.aflfi o.a¢fi j... . . .. .50? .12? n... . .10. .F m . on. H O . W.,... C . «Lamps Axum...» w. A..\ a..,w ..C... o ... ..l. ..1 n... . we H . CM H u...3w*****¥.**************************i¥fi**%*%i***%******¥.%%**¥H.**¥%****** .mfimxamum unmEmHm mpflcwm mo mamamm <..H-m xwvcomq< 173 Appendix B-2. A sample of the perfomance analysis of a designed heat pipe exchanger . pRucrss ANALYSIS SHJFW”L-Y’ EZXf1fifljkfl .con 0..- a... 0.. o-o 0.. 0-. 3... IN OUT IN TEMPERATURE OF 50.0 62.7 130.0 AIR PLUM LB/HH .4000OOE+O3 .600000E+03 AIR FLON CFM .976123E+02 .146419E+03 FACE VELOCITY FT/MIH .252228E+03 .378342E+03 MASS UELUCITY LB/HP/FTQ .272205E+04 .408307E+04 REYNOLDS NUMBER .226755E+03 .340132E+03 PRESSURE DROP IN H30 .536520E+00 .109239E+01 PUMPING FHKHHY th/YR .120801E+02 .375947E+02 HEAT TRANSF CUFF .114100E+02 .142774E+02 BTU/HR/Fr9/OF ENERGY SAVED BTU/HR .123933E+04 .193537E+04 EFFICIENCY 158?35h+00 .2481?6E+00 174 Appendix B-S..A.samp1e of the dimensions of a designed.heat.pipe exdxmger. HEAT PIPE EXCHANGER DESIGN AE-NSU CALCULATIONS AFTER hUUNDING OFFS EXCHANGER OVFRALL DIMENSIONS IN FT LENGTH LENGTH HEIGHT DEPTH LTOTAL COLD HGT 2.695 3.30 QoUO 2.02 5531.57 CORE SPECIFICATIONS IN INLH€S FIN PIPF FIN FPI 01AM OIAM THK QTY 1:814 .62h .017 13.5u ROH °IPES PIPE Row QTY IN A Row SPACING SPACING 7.0 25.0 1.920 3.h62 DIMENSIONAL FA€AHFTERS VOLUME 48.4h ATOTfiL/JUL AFLOH/AFRCNT AFIN/ATOTAL HYD.0I#M 114.19100 .53275 .97659 .01666 175 Appendix B-4. A concurrentflow dryer analysis using a heat pipe exchanger PRAGII§N or THE cooLER to THE ExGNANGER PRAc *1 s: or THE HEATER to THE EchANGER FRABTION: or THE DRYER INPUT PRON 3 c R 3951 Egcgegsfik EXHAUST ERENANGER SUPPLY Anfigggr AIR DEPTH IINE AIR Aas REL GRAIN Nc ' tENP RUN RUN IENP Ne 00 FT BR F LG/LG osc HA5 F PERCENT GEGINAL .01 .go «01.6 .1932 . 1; 117.0 25.00 .332; 6: .6 0 9 16309 02576 .6 6 163.7 19.6. 02“ GOOLER 00tPur 1 GRA N T NP 73 5 GRATE N N (H8) 1’01 :P 1% .3 HR 00‘73 INPursu to THE EXHAUST SIDE or THE echANGER '5'"; F ”Run .35 “LE"mms INPui go THE: SUPPLY $506 or In? EXGNANGER 7 "P 2+0 "RuaooE 35R RL35.976305 e¥c31022 OUTPUT. ' 122.576 "2306 139‘362 .107 Néu INgUTF to rNé EERVER %§ AIR RLON 155F .206 676.260 DEPTH IINE AIR Ass §5L GRAIN no No IENP NUN N IENP N9 09 FT NR F LBILB oec NAL 6 PER EN DEG N 0.1 03" “01.6 020~2 o 1““ 11700 2 .0 0 3 6.0» .59 169.6 .2639 . 233 16hob 19.3 .25 c00LER OUTPUT s GRAINI 73.5 . A1?fi (H8) 1737 A R 156 0 A RN .6475 "ENERGY BILL DRYER COOLER NEAIPIPE SVSIEN FAN 736 23 33.97 a 35 775.35 E GRAIN 8. 0 .00 0 6 0.00 A AIR 10673.2 0.0 -A57.5 10015.3 TOTAL 11211.5 33.0 -953.3 0726.5 NAgER RENOVEG L IBU 4.663 1.573 0.000 6.036 StAtIc PREssuRE 5"“) mm 9:32 2313-. 3¥05N20 gIREGI £§5$3LING 323.1 ° '