THESIS -._4 LIBRARY E“ Michigan Sate This is to certify that the thesis entitled SOLAR WATER HEATING FOR THE FOOD INDUSTRY IN THE UNITED STATES presented by Petros Z. Mintzias has been accepted towards fulfillment of the requirements for Ph.D. Agr. Engineering degree in 4% <14 / Major professor 4/4/30 0-7 639 OVERDUE FINES: 25¢ per day per item RETURNING LIBRARY MATERIALS: Place in book return to remove charge from circulation records © 1981 PETROS Z. MINTZIAS All Rights Reserved SOLAR HATER HEATING FOR THE FOOD INDUSTRY IN THE UNITED STATES by Petros Z. Mintzias A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Agricultural Engineering 1980 ABSTRACT SOLAR WATER HEATING FOR THE FOOD INDUSTRY IN THE UNITED STATES by Petros Z. Mintzias The engineering and economic potential of solar water heating in the food industry in the United States has been the subject of this study. The energy consumption in selected meat and dairy plants was analyzed and five energy use patterns which take into consideration the variability of the energy usage encountered in food processing plants were obtained. Based on the energy consumption and distribution at the Michigan State University milk processing plant a pilot plant solar water heater was built to supply approximately fifty percent of the total energy demand in the plant. The daily energy use in the dairy plant was found to be about 2,000,000 KJ. The experience gained by operating the pilot plant solar water heater was useful in the design and simulation of a wide variety of solar systems for the food industry. The Transient Simulation Program (TRNSYS) and the f-chart program, both developed at the University of Wisconsin, were used. Experimental results from the pilot plant solar water heater were utilized to verify TRNSYS. The agreement between experimental and numerical data was found to be excellent. Petros Z. Mintzias The f-chart program was modified in order to be used in the design and evaluation of industrial type solar water heaters. The NUAIN program and subroutine CALC of the f-chart were modified to account for the variability of the yearly energy usage in various 'foods processing plants. Results from f-chart were checked against those obtained by TRNSYS and the agreement was found to be satis- factory. The daily energy use pattern in a food processing plant and the time at which the plant starts operation during the day does not affect the long-run performance of a solar water heater. Solar collectors exhibit higher efficiencies in food processing plants operating seven days per week than in plants with six or five work day weekly schedules. The effect of the geographic location on solar system thermal output and life-cycle costing of solar water heating was investigated. A series of sensitivity tests of various economic parameters was per- formed to demonstrate the significance of each parameter on the economics of solar water heating. Annual fuel price escalation and annual nominal discount rate were identified as the most sensitive parameters for the economic analyses of solar water heaters. A solar water heater with an optimized collector area results in positive savings for most of the locations in the United States. Positive savings will be realized when the alternative is oil and electricity, the solar system costs 150 $/m2 of collector area, the annual | inflation rate is eight percent and price of the conventional fuel escalates at an annual rate of ten percent over the period of the Petros Z. Mintzias economic life of the solar system which was assumed to be twenty years. The amount of the yearly hot water needs in a food process- ing plant which can be economically supplied by solar is thirty to ninety percent depending on the location under consideration. Solar water heating shows higher potential in the western states of the United States than the eastern and midwestern states. Dedicated to my wife, Katherine and to our children -- Zacharias and Elena ii ACKNOWLEDGMENTS The author is grateful to Alvin L. Rippen and Pericles Markakis, Professors of Food Science and Human Nutrition; James Beck, Professor of Mechanical Engineering; and James Steffe, Assistant Professor of Agricultural Engineering, for serving on his Ph.D. committee. Special appreciation is due to the United States Department of Energy for its financial support of this study. The encouragement, enthusiastic support and constructive criticism during the course of this study by Dr. Lloyd E. Lerew, colleague, once academic advisor, and friend are gratefully recognized by the author. The completion of this study has been greatly encouraged by the courteous help and brilliant counsel of Dr. Fred H. Bakker-Arkema, Professor of Agricultural Engineering and academic advisor to the author. It was the special relationship the author developed with Fred H. Bakker-Arkema that made this work possible. TABLE OF CONTENTS Page LIST or TABLES ................................................ vi LIST OF FIGURES ............................................... XI LIST or SYMBOLS ............................................... xvi Chapter l. INTRODUCTION ........................................... 1 2. OBJECTIVES ............................................. 3 3. JUSTIFICATION OF THE STUDY ............................. 5 4. LITERATURE REVIES ...................................... 10 4.1 Energy as a Global and Multidimensional Problem ... 10 4.2 The United States Energy Situation ................ 12 4.3 The Solar Energy Option ........................... 15 4.4 Collection of Solar Energy ........................ 21 4.4.1 Solar Radiation Fundamentals ................ 21 4.5 Flat Plate Collectors ............................. 22 4.5.1 General Description ........................ 22 4.5.2 Absorber Plates and Selective Surfaces ...... 24 4.6 Evacuated Tube and Concentrating Collectors ....... 26 4.7 Solar System Analysis: Components ................ 27 4.7.1 Energy Storage and Controls ................ 29 4.8 Economics ......................................... 33 4.8.1 The Present Value Concept .................. 33 4.8.2 The Life-Cycle Costing Method ............... 35 4.9 Computer Models for Solar System Design ........... 37 4.9.1 The TRNSYS Program ......................... 37 4.9.2 The f-chart Design Method ................... 39 4.10 The Food Industry from an Energy Point of View .... 41 4.10.1 Energy Utilization ........................ 41 4.10.2 Energy Conservation in Food Processing .... 44 4.10.3 Applications of Solar Energy in Food Processing ................................ 49 iv Chapter 5. 10. 11. 12. 13. FLAT PLATE COLLECTOR HEAT TRANSFER ANALYSIS AND PERFORMANCE ............................................. SOLAR SYSTEM DESIGN ..................................... 6.1 Energy Audit ...................................... 6.2 Solar System Sizing ............................... 6.2.1 Application of the f-chart Program ........ 6.2.2 Space Requirements ........................ 6.3 Solar System Modeling ............................. 6.3.1 Description of TRNSYS ..................... 6.3.2 System Modeling ........................... 6.4 Solar Hater Heater Characteristics ................ ESTABLISHMENT OF HOT WATER DEMAND IN FOOD PROCESSING PLANTS .................................................. VERIFICATION OF THE TRNSYS PROGRAM ...................... TRNSYS RUNS ............................................. MODIFICATION OF THE f-CHART PROGRAM ..................... RESULTS AND DISCUSSION .................................. ll.l Solar Water Heater Performance .................... 11.1.1 Hourly Performance ........................ 11.1.2 Daily Performance ......................... 11.1.3 Weekly Performance ........................ 11.1.4 Monthly and Yearly Performance ............ 2 Effect of Work Schedule and Operations on Solar System Performance ................................ 11.3 Load Quantity and Solar System Performance ........ 11.4 Stratified Tank, Heat Exchanger, and Pump Requirements ...................................... 5 Long-Term Solar Water Heater Performance in Selected Cities of the United States .............. 6 Economics of Solar Water Heating .................. 7 Discussion of the Results by Thomas and Singh et a1. ...................................... CONCLUSIONS ............................................. SUGGESTIONS FOR FUTURE RESEARCH ......................... BIBLIOGRAPHY ................................................. APPENDICES ................................................... V Page 52 92 103 122 129 137 137 137 159 159 163 172 182 188 195 209 230 235 238 239 249 LIST OF TABLES Table . Page 3.1 Processing temperatures of various food process operations ........................................... 6 3.2 Percentage of process heat required at different temperature ranges in an Australian Coca-Cola plant ................................................ 7 3.3 Total energy requirements in a dairy plant: one week (average) ............................................ 8 4.1 Energy distribution usage in the United States ....... 15 4.2 Consumption, production, and net imports of energy in the United States and the rest of the world x 1015 BTU ............................................. 16 4.3 Collector material comparison ........................ 24 4.10.1 Percentage distribution of the energy used in the United States food system ............................ 42 4.10.2 Consumption of purchased fuels and electric energy in the United States industrial sector .................. 42 4.10.3 Energy consumerd for heat and power in the United States food industry and value of shipments of food products for 1972, 1974, 1975, and 1976 .............. 43 4.10.4 Energy consumed, energy use rank for 1976 and energy efficiency improvement goals for 1980 among twenty energy leading food industries ....................... 45 4.10.5 Food industry fuel usage ............................. 46 ‘4.10.6 Total energy used for selected processed foods (input) .............................................. 47 (5.1.1 Weekly energy consumption for cheese processing at MSU Dairy Plant ...................................... 67 vi Table (5.1. (5.2. (5.2. (5.2. (5.2. (5.2. (5.3. (5.3. (3.1 2 ...: 0'1wa Weekly energy consumption for ice cream processing at MSU Dairy Plant ................................... Weekly energy consumption for yogurt processing at MSU Dairy Plant ...................................... Economic criteria used to size the solar system ...... Questions asked by the f-chart program ............... Description of parameters used by f-chart ............ Value change of various parameters of the f-chart .... Thermal and economic analysis performed by f-chart ... Parameter values used in solar system design ......... Solar system monthly performance ..................... Storage tank water temperature heater on September 27, 1979 ......................... Storage tank water temperature heater on September 28, 1979 ......................... Storage tank water temperature heater on September 30, 1979 ......................... Storage tank water temperature heater on October 4, 1979 ............................ Storage tank water temperature heater on October 29, 1979 ........................... Storage tank water temperature heater on October 30, 1979 ........................... Storage tank water temperature heater on October 31, 1979 ........................... of the of the of the of the of the of the of the MSU MSU MSU MSU MSU MSU MSU solar water solar water solar water solar water solar water solar water solar water Comparison of the energy delivered to the delivery load calculated by TRNSYS to that calculated from the measured temperatures and flow rates of the MSU solar water heater and relative percentage error of the numerical results ............................... vii Page 67 68 72 74 75 76 77 85 86 107 108 109 110 111 112 113 121 Table 9.1 9.2 9.3 9.4 11.1. 11.1. 11.1. 11.1. 11.1. 11.1. 11.1. 11.1. 11.1. 11.1 .10 Page Relationships used in TRNSYS to estimate the size of a solar system .................................... 123 Parameter values independent of the size of the solar system used in solar system simulation with TRNSYS ... 125 Solar System sizes used per CASE in solar water heating simulation by TRNSYS ......................... 126 Heat exchanger sizes used in solar system Simulation with TRNSYS ........................................... 127 Difference between collector outlet and inlet temperature during a typical day in July ............. 152 Difference between collector outlet and inlet temperature during a typical day in December ......... 153 Difference between collector inlet and ambient temperature during a typical day in July ............. 157 Difference between collector inlet and ambient temperature during a typical day in December ......... 158 Daily efficiency of a 150 m2 solar collector for food processing plants exhibiting various energy use pro- files (July) in Michigan ............................. 160 Daily efficiency of a 150 m2 solar collector for food processing plants exhibiting various energy use profiles December) in Michigan ...................... 161 Weekly efficiency of 150 m2 solar collector for food processing plants with different energy use profiles . 162 2 Percentage of weekly load delivered by a 150 m solar collector system for food processing plants for different energy use profiles .................... 164 Monthly efficiency for various size solar collectors for food processing plants exhibiting energy use profile as in Case A in East Lansing, Michigan ....... 165 Yearly efficiency of various size solar collectors for food processing plants exhibiting different energy use profiles in East Lansing, Michigan ........ 169 viii Table 11.1. 11.1 11.1 11.2. 11.2. 11.2. 11.3. 11.3. 11.4. 11.4. 11.4. 11.5. 11 .12 .13 Percentage of monthly load supplied by various size solar systems for food processing plants exhibiting energy use profiles as in Case A in East Lansing, Michigan ............................................. Percentage of yearly load delivered by various size solar systems for food processing plants with differ- ent energy use profiles in East Lansing, Michigan .... Yearly performance and thermal output per collector unit area of solar water heater in food processing plants with various energy use profiles .............. Yearly thermal output and performance of solar systems for food processing plants operating five, six or seven days per week in East Lansing, Michigan . Yearly and monthly collector efficiencies for solar systems in food processing plants exhibiting differ- ent energy use profiles and different processing schedules (500 m2 collector) in East Lansing, Michigan ............................................. Percent of load supplied by solar under different hot water delivered temperatures in East Lansing, Michigan ............................................. Percentage of monthly load supplied by a solar system in processing plants with different hot water demand . Yearly performance and thermal output of a 1000 m2 collector solar water heater for food processing plants with different daily hot water demand in East Lansing, Michigan ............................... Yearly and monthly collector efficiency and percent by solar of solar systems and stratified and fully mixed storage tanks (L/D = 2.16) ..................... Monthly collector efficiency at reduced heat exchanger areas ...................................... Monthly and yearly pumpingzrequirements of a solar water heater with a 1000 m collector area ........... Percent of monthly and yearly load provided by solar calculated by TRNSYS, and the original and modified versions of f-chart .................................. ix Page 170 171 173 177 178 183 189 190 191 193 194 196 Tab1e 11. . 11. . 11. . 11. . 11. . 11. . 11. . 11. . 11. 11. . 11. . Solar system yearly performance and thermal output for selected cities of the United States ............. Yearly thermal output of solar system in selected cities of the United States under various water set temperature conditions ............................... Yearly thermal output of a solar system in selected cities of the United States under various operating days per week ........................................ Economics of a 1000 m2 collector solar water heater in selected cities of the United States .............. Economic scenario used in life-cycling costing analysis of various solar systems .................... Present worth of cumulative solar savings (103 S) of a 1000 m2 collector solar water heater in selected cities of the United States and food processign plants operating various days per week ............... Present worth of cumulative solar savings (103 S) of a 1000 m2 collector solar water heater in selected cities of the United States under various set temperatures ......................................... Optimal collector area, and thermal output, per- formance economics of an optimized solar water heater in selected cities of the United States for a food processing plant ..................................... Percent by solar and savings/investment ratio (in parenthesis) for various collector areas in selected cities of the United States with constant hot water demand (1,514,000 Kg/week) ........................... Effect of scale up on solar system thermal output and economics in East Lansing, Michigan .............. Savings/investment ratio at various fuel prices for solar systems in selected cities of the United States ............................................... Page 200 205 207 210 211 214 215 216 221 229 231 Figure 4.1 bh-h-b 0'1wa LIST OF FIGURES Historical growth of energy consumed in the United States and several projections for the period 1975 to 2000 .............................................. Total United States energy consumption ............... Total United States gross energy production .......... Evolution of solar energy budgets .................... Possible projection for the supply of energy in the United States during the period 1970-2000 ............ Solar installations for the seven highest states by the year 2000 ........................................ Schematic diagram of a solar water heater ............ Stratified water storage tank with each section at uniform temperature .................................. Cross section of a solar collector ................... Temperature distribution of absorber plate ........... Flow chart for yogurt manufacture in the MSU dairy plant ................................................ Flow chart for ice cream manufacture in the MSU dairy plant ................................................ Flow chart for cheese manufacture in the MSU dairy plant ................................................ Hot water consumption during cheddar cheese processing ........................................... Hot water consumption during acid cheese processing Hot water consumption during cheese or ice cream processing ........................................... xi Page 13 14 14 17 19 20 28 32 54 59 64 65 66 69 7O 71 Figure Page 6.3.1 Solar system component, instrumentation, and con- troller description .................................. 80 6.3.2 Block diagram of TRNSYS subroutines and MAIN program . 81 6.3.3 Subroutine and information flow diagram of the TRNSYS solar water heating model ..................... 83 6.4.1 Schematic diagram of the collector array ............. 88 6.4.2 Component arrangement in the storage house ........... 91 7.1.1 Distribution of the daily energy consumed in the Wisconsin dairy plant ................................ 93 7.1.2 Distribution of the daily energy consumed in the Wisconsin dairy plant ................................ 95 7.1.3 Approximated distribution of the daily energy con- sumed in the Wisconsin dairy plant ................... 96 7.1.4 Approximated distribution of the daily energy con- _sumed in the Lansing, Michigan dairy plant ........... 97 7.1.5 Distribution of the daily energy consumed in the Indiana meat processing plant ........................ 98 7.1.6 Approximated distribution of the daily energy con- sumed in the Indiana meat processing plant ........... 99 7.1.7 Approximated distribution of the daily energy con— sumed in the Michigan State University dairy plant ... 100 7.1.8 Representative hot water demand distribution in the food industry ........................................ 101 8.1 Total radiation on a horizontal plane in East Lansing, Michigan on September 27, 1979 ....................... 104 8.2 Total radiation on a horizontal plane in East Lansing, Michigan on September 28, 1979 ....................... 105 8.3 Daily load distribution for the experimental and simulated case on September 27, 1979 ................. 115 8.4 Tank temperature and load distribution on October 2, 1979 ................................................. 117 xii Page Stratified storage tank with four sections which can be used to estimate the four tank temperatures on October 2, 1979 ...................................... 120 Average residential water heating demand distribution. 130 Data points and regression line for Equation [10.8] . 135 Non-stratified tank temperature change during a typical day in July in Michigan ...................... 138 Tank temperature change during a typical day in July (Case A) ........................................ 140 Tank temperature change during a typical day in July . 141 Tank temperature change during a typical day in July (Case 8) ............................................. 142 Tank temperature change during a typical day in July (Case 0) ............................................. 143 Tank temperature change during a typical day in July (Case E) ............................................. 144 Tank temperature change during a typical day in December (Case A) .................................... 145 Tank temperature change during a typical day in December (Case 8) .................................... 146 Tank temperature change during a typical day in December (Case C) .................................... 147 Tank temperature change during a typical day in December (Case 0) .................................... 148 Tank temperature change during a typical day in December (Case E) .................................... 149 Overall heat loss coefficient change during a typical day in July in Michigan .............................. 154 Overall heat loss coefficient change during a typical day in December in Michigan .......................... 155 Monthly efficienty and percent of load supplied by solar ................................................ 166 xiii Fi gure 1‘1. 1.15 11.2.1 11.2 -2 11.2 .3 11.2.4 11.2.5 11.3.1 11.3.2 Monthly average daily total radiation on a horizontal plane and average temperature in East Lansing, Michigan ............................................. Storage tank temperature during a typical weekend in July for solar systems in processing plants operating five, six or seven days per week ..................... Storage tank temperature during a typical weekend in December for solar systems in processing plants operating five, six or seven days per week ........... Monthly collector efficiency of solar systems in Processing plants operating five, six or seven days per seek ............................................. Percent of monthly hot water supplied by solar in pro- cessing plants operating five, six or seven days per week ................................................. Percentage of yearly load supplied by solar under different temperatures of hot water delivered ........ Tank temperature of a 1000 m2 collector system under different load quantities ............................ Overall heat loss coefficient of a 1000 m2 collector under various daily load conditions .................. Monthly efficiency of a 1000 m2 solar collector under various daily load conditions ........................ Location of cities investigated in this study ........ Percent by solar for various cities under different water set temperatures ............................... Collector area and present worth of solar savings relationship ......................................... Collector cost and solar savings relationship in Kansas City, MO ...................................... Solar system life time and solar savings relationship in Kansas City, MO ................................... xiv Page 167 175 179 180 181 184 185 186 187 201 208 219 223 225 Fi gure Page 11 .6.4 Yearly fuel price escalation and solar savings relationship in Kansas City, MO ....................... 226 11.6.5 Annual discount rate and solar savings relationship in Kansas City, MO .................................... 227 11.6-6 Inflation rate and solar savings relationship in Kansas City, MO ....................................... 228 XV LIST OF SYMBOLS Area, m2 Control function with value of zero or unity 14 W-cm2 Constant in Eq. 4.5.3, 0.595 x 10' Constant in Eq. 4.5.3, 1.438 cm-°K Bond conductance, KJ/h-m-°C Specific heat, KJ/Kg-°C Tube diameter, m Spectral distribution of hemispherical emissive power, KJ/h-mz-Im Fraction of total heating load supplied by solar energy Collector heat removal factor defined in Eq. 5.20, dimensionless Collector efficiency factor defined in Eq. 5.17, dimensionless Collector-heat exchanger efficiency factor, dimensionless Flow rate per unit area, Kg/h-m2 2 Rate of direct or diffuse radiation per unit area, KJ/h-m Instantaneous solarzradiation incident on the collector surface per unit area, KJ/m Thermal conductivity, KJ/h-m-°C Total load, KJ Water mass, Kg Flow rate, Kg/h Number of glass covers Rate at which energy is delivered to load, KJ/h xvi -l¢-r 4549’ O ...; ...I '5 ..| 3 U1 -4 -4 -4 M U .3 -1 xi H U' C '0 -< 0‘ >< <: c: c: c: r Rate at which useful energy is collected, KJ/h Factor to convert total radiation to that on the plane of the collector, dimensionless Collsctor incident radiation over a finite period of time, KJ/m time Ambient temperature, °C Absolute temperature, °K Collector temperature, °C Temperature of make up water entering the tank, °C Water mains temperature, °C Storage tank water temperature, °C Stratified tank temperature with n-sections, °C Water set temperature, °C Temperature ratio defined in Eq. 10.3 Over all loss coefficient, KJ/h-m2-°C Collector bottom loss coefficient, KJ/h-m2-°C Collector upper loss coefficient, KJ/h-m2-°C Wind speed, m/s Dimensionless group defined in Eq. 4.9.5 Dimensionless group defined in Eq. 4.10 Dimensionless group defined in Eq. 4.9.6 xvii Greek oi Directional spectral absorbance 8 Cone angle, degrees Si Directional spectral emittance c Absorber plate effective emittance e Circumferential angle, degrees n Fin efficiency A Wavelength, time nf Collector efficiency 0 Stefan-Boltzmann constant, 5.279 x 10'12 W/cm2-°K T Glass transmittance ¢ Dimensionless temperature ratio .SUbscripts a Ambient b Bottom C Collector 1" Inlet L Load 1 Loss 0 Outlet 5 Storage u Useful up Upper ‘” Wind xviii my CHAPTER 1 INTRODUCTION For the last ten years the energy problem has absorbed the attention of the public. In the early 1970's economists, legislators 811d decision makers realized that there are physical and economic l'imits on the world's supply of oil, the most versatile and widely used energy source. As a result of this awareness, research efforts ‘tca substitute fossil fuels by renewable and essentially inexhaustible Staurces of energy have been considerably increased. Among the new energy technologies investigated, solar energy is widely expected to <2<5ntribute substantially to the future energy needs (Gustaffero, 1 979). In the mid-1970's the Energy Research Development Administra- llion established a program to demonstrate the potential of solar energy in agricultural and industrial processes. The areas included 'in the program were (ERDA, 1977): l. agricultural food processing grain drying crop drying heating of livestock shelters 01wa heating and cooling of greenhouses. A simulation study by Thomas (1977) indicated that a signifi- cant solar energy contribution can be made by replacing up to 90 percent of the electric and 20 percent of the fossil fuel energy consumption for most food processing plants over a 20-year payback period. Similar work by Singh et a1. (1978) indicated that a solar ivater heater would be able to supply about 29 to 34 percent of the “total processing energy demand in a food processing plant. The Thcansient Simulation Program (TRNSYS) was used in both studies. While solar water heaters have been successfully modeled by 'tlie above investigators, the numerical results were not verified eXperimentally. In addition, operational characteristics of solar Savstems and the effect of the daily energy usage pattern in the I>v~ocessing plant on solar system performance were not considered. This research investigates the application of solar water heating in food processing plants in the United States. A pilot Scale solar water heater has been built for the Michigan State lJniversity dairy plant. Experimental results from the pilot scale System are used to verify the results of the TRNSYS and f-chart simulation programs. The performance and thermal output of solar vvater heaters is investigated under various daily energy use scheduling encountered in food processing plants. CHAPTER 2 OBJECTIVES The primary objective of this study is to investigate the j r>catential of solar water heating in the United States food industry ifrrom an engineering and economic point of view. The specific objctives are: 1. To compare simulation results obtained by the Transient Simulation Program (TRNSYS) with experimental data from the Michigan State University dairy plant solar water heater and determine the engineering behavior of solar systems for the food processing industry. To identify daily energy use profiles encountered in the food processing industry and to investigate the effect of the energy use pattern on the long- and Short-run performance of solar water heaters. To examine the effect of the work schedule and energy demand in food processing plants on the performance of solar hot water systems. To modify the f-chart program in order to investigate the long-run engineering and economic performance of industrial type solar water heaters. 5. To evaluate the economic feasibility of solar retrofit in the food industry. CHAPTER 3 JUSTIFICATION OF THE STUDY The objective of thermal food processing is to destroy pathogenic and toxin-forming microorganisms and food enzymes. In addition to microorganism and enzyme destruction, heat is also detri- mental to organoliptic and nutritive properties of foods as well. These observations emphasize the principle that no more heat should be applied or required by regulation than the minimum necessary to free foods of mircoorganisms which may deteriorate the foods or endanger the consumer. In practice very few food processes occur at temperatures above 121°C (250°F). Most food products are thermally processed b910w 100°C. This is illustrated in Table 3.1 where various food pr‘OCIessing temperatures are listed. In a food processing plant heat is typically generated in a Central power station (boiler) at temperatures higher than those FeQUired by the processes in the plant. The heat is then distributed as 99°C water or steam at 90 psia (125°-170°C) to the individual pr‘Ocesses, most of which operate at lower temperatures. Such heat generation and distribution systems are convenient and assure aCkequate heat to specific operations. ‘11ABLE 3.1.--Processing temperatures of various food process operations. Operation Temperature , °C ——— Milk pasteurization - Batch 63 - HTST 72 (Itjice pasteurization 77-87 (:I1eese manufacture - Milk pasteurization 28-31 - Curd cooking 38-50 Beer manufacture - Hashing 38-77 - Pasteurization 60 Meat processing - Scalding 60 - Smoking 125-135 Canning 115-130 San itation - Hand washing 66 - Equipment cleaning 60-82 From an energy efficiency point of view, the above practice has serious disadvantages. A typical boiler efficiency for many p1 ants is about 75 percent (Casper, 1977). Heat losses to the environment from steam pipes and process equipment are increased 5‘1 Qnificantly with increasing temperatures. Finally, steam can hJse as much as 68 percent of its heat because of improper condensa- tion (Singh, 1979). qude et a1. (1975) investigated the energy consumption and sslnpply at the Campbell Soup Plant 2. The conclusions of the study <:c>uld be summarized as follows: (1) 65 percent of the energy needed I2)! the plant is at temperatures below 93°C (200°F) and 20 percent at temperatures between 121°-132°C (250°-270°F); (2) 75 percent of the eer1ergy supplied is at a temperature above 121°C; (3) 43 percent of 1:!1e energy supplied by the boiler (or 52 percent of fuel oil energy) 1::5 the processes is wasted in the form of hot water from the parrocesses. A more detailed study of an Australian Coca-Cola plant showed that over 40 percent of the total heat required was in the form of hot water at 60°-80°C (140°-176°F) (Proctor and Horse, 1977). Percentages of the heat used at different temperatures in the plant are shown in Table 3.2. TABLE 3.2.--Percentage of process heat required at different temperature ranges in an Australian Coca-Cola plant. \ Temperature Range, °C Percent of Total Heat Consumed \ O - 20 0.5 20 - 4O 7 40 - 60 13 60 - 80 43 80 - 100 8 100 - 125 20 125 - 150 8 150 0.5 SOURCE: Proctor and Morse (1977). A similar work by Singh et a1. (1978) in a Wisconsin milk processing plant indicated that more than 75 percent of the process- ‘ing energy requirements in the plant is at 80°C. Energy require- ments in the dairy plant at different temperatures are listed in Table 3.3. TABLE 3.3.--T0ta1 energy requirements in a dairy plant: one week (average). Energy Percent Load Requirements, GJ of Total 801' 1er feed make-up (100°C) 2.41 0.33 Pa steurization make-up water (81°C) 546.20 75.35 Case water and rinsing (49°C) 82.50 11.38 (:1 ean-up (71°C) 54.00 7.45 HTST clean-up (79°C) 0.87 0.12 Bottie washer (93°C) 39.90 5.37 SOURCE: Singh et a1. (1978). Meat processing plants utilize large amounts of hot water at te'Tlperatures between 60° and 72°C (140°-160°F). To heat and maintain the temperature of the water at 60°C in scald and dehairing tanks in an Indiana Meat plant, a daily amount of energy equal to 50 x 106 KJ 13 required (Wilson et a1., 1978). Evaluation of various research and demonstration programs has revealed that solar water heating is one of the most promising solar energy technologies (Anonymous, 1978a). Among the various types of solar collectors, flat plate collectors are the least expensive devices. They also are simple, require little maintenance and can be easily installed into retrofit designs. The efficiency of a flat plate collector below 100°C is about 50 percent. Further, at moderate temperatures (<60°C) flat p'late collectors could be as efficient as evacuated tube collectors (Grimer and Moore, 1977). Preliminary simulation work by the author has shown that $01 ar systems operating at a temperature range of 60°-80°C and assisted by a conventional water heater can supply a substantial amount of the energy needs in most food processing plants. For these reasons the author felt that a study of solar Water heating will be beneficial to the food industry in overcoming 1:l‘l‘ture difficulties related to energy cost and availability. CHAPTER 4 LITERATURE REVIEW 4.1 Energy as a Global and Multidimensional Problem Assuming a balance between births and deaths, the United Nations (1979) projects the global population in 2075 to be about 1 1 .5 billion. To maintain such a population at a reasonable standard of living with present practiced technologies, the petroleum-oriented societies must undergo major changes (Ridker and Cecelsky, 1979). Changes such as slow-down in population and economic growths are not sufficient to maintain long-run sustenance 01’ life on earth (Ridker and Watson, 1980). The side effects of the skyrocketing prices and predicted Shortages in the near future are difficult to evaluate, particularly when the problem is viewed as a global rather than a regional one. Industrial and oil importing nations such as the United States have 1081: their freedom of political maneuvering due to oil imports (The ROCkefeller Foundation, 1978). Because of a sluggish world economy and oil price increases, the developing Third World countries have famen $258 billion in debt (World Bank, 1979). Furthermore, petroleum exporting countries have begun exercising their energy "elated power in different directions (Corradi, 1979). 10 11 T0 delay and further avert a tight energy supply and shortage Situation, conservation and development of new energy alternatives is urgent and essential. Conservation itself is a very complex and controversial case. The complexity arises from the fact that its potential and constrains vary widely among countries and among sectors (WAES, 1977). Within the business and the industrial world it is also feared that conservation might slowdown growth and destroy economic balance (Meador, 1978). One of the main reasons conserva- tion has not yet made an impact, is because of the short payback time private energy consumers demand from cost saving measures (Beijdorff, 1979). While the urgency for developing new energy technologies is widespread, the direction of a new energy policy has to follow is at issue. Shale and tart sands, which are found in large quantities around the world, could extend the role of oil considerably longer, assuming their adverse environmental problems can be solved (Ridker and Cecelsky, 1979). Coal liquefaction technology might prove too costly and environmentally degrading if improper planning and manage- ment prevail over comprehensive and well-coordinated objectives (Lewis and Muller, 1979). Renewable energy sources such as nuclear fusion, solar energy and wind power appear to be associated with minimal environmental constraints. However, the economic cost of utilizing the renewable energy sources is difficult to evaluate (Ridker and Cecelsky, 1979). 12 4.2 The United States Energy Situation Since the Arab oil embargo of 1973, the United States energy outlook has become a major public and governmental issue. The embargo, associated with indigenous factors such as declining pro- duction of gas and oil, diminishing mine productivity and environ- mental legislation, has drastically affected domestic energy costs. For the period 1973 to 1975, the cost of energy in the United States increased much faster than the overall inflation rate. While the consumer price index has increased 21 percent, the price of energy increased by 84 percent (Decker, 1977). The price of oil has been constantly rising since 1973 and it is estimated that the price increase of petroleum adopted by OPEC in December, 1979 will add at least $25 billion to the 1980 oil import bill, thus increasing the total value of the imported oil to $76 billion (Anonymous, 1979). A broad breakdown of the energy distribution usage in the United States is shown in Table 4.1 and indicates that the industrial sector is the largest energy user. For the period from 1900 to 1970, the energy consumption in the United States has grown at a rate of about 3 percent per year (Dorf, 1978). In Figure 4.1, the growth of the energy consumption in the United States is shown for the 1900- 1975 period. Extrapolation of the curve to the year 2020 yields a total of 316 x 1015 KJ energy_consumed. The case for linear and zero growth is also shown in Figure 4.1. The strong dependence of the United States on petroleum products and natural gas is evident in Figure 4.2, where the total U.S. energy consumption is presented (U.S. Department of Commerce, 300 K N o o —l O C Energy Consumption, x 1015 13 l T l l O 0 O 0 0 o o o o o o o o o o o I o o O o o o 0 I Exponential growtn \} 0 Zero growth 4 i l i ”i i 1900 1920 1940 1960 1980 2000 2020 Year Figure 4.1.--Historical growth of energy consumed in the United States and several projections for the period 1975 to 2000 (Dorf, 1978). 15 Energy Consumption, x 1015 Energy Production, x 10 70 60 50 40 30 20 10 .. ‘.tt"“‘———-”T‘T—N;tura1 gas 14 1 Nuclear Total Consumption Petroleum / Hydropower and Geothermal a L J 1 I L L F I 1951 ' 1955 1959 ' 1973 Year Figure 4.2.—-Total United States energy consumption 60 ‘ 50 40 30 20 10 (U.S. Department of Commerce, 1976). / Nuci'ea Hydropower and Geothermal Petroleum Natural gas A I -M 1951 ' 1955 ' 1955 ' 1973 Year Figure 4.3.--T0tal United States gross energy production (U.S. Department of Commerce, 1976). 15 TABLE 4.1.--Energy distribution usage in the United States. Sector Energy Percent Usage Industry 32 Generation of electricity 27 Transportation 24 Residential & Commercial 17 SOURCE: Quillman, 1977. 1976). Disturbances related to the supply and availability of those two energy sources is expected to cause deleterious effects on the economic and social status of the United States, since their contribution to the total energy supply is well over 70 percent. The relationship which exists between standard of living and energy consumption is one of the reasons the United States has become a large oil importer. The United States' total energy production, shown in Figure 4.3, started lagging behind consumption during the beginning of the 1960's, the period which also produced an all time high industrial output (Dorf, 1978). Although a large energy importer, the United States is far less dependent on foreign oil than Western Europe and Japan (Table 4.2). 4.3 The Solar EnergyOption Approximately 25 percent of the total energy consumed world- wide comes from solar resources such as windpower, waterpower, 16 TABLE 4.2.--Consumption, production, and net imports of energy in the United States and the rest of the world x 10 Btu. Region Consumption Production Imports % Imports United States 74 63 ll 15 Western Europe 53 19 34 64 Japan 14 2 13 86 Sino-Soviet Block 67 70 -- -- Rest of the World 40 100 -- -- SOURCE: U.S. Department of Commerce, 1976. biomass and direct sunlight; by 2025, solar energy could possibly account for about 75 percent of the energy used in the world (Hayes, 1977). The transition to a solar era will probably be associated with social changes and certainly with yet undetermined economic efforts, but its benefits will far outweigh the costs and sacrifices. A sharp decrease of the oil consumption in the United States will occur sometime between 1985 and 2000 (Gustaffero et al., 1979). The direct involvement of the federal government in the promotion of solar energy research and development indicates that solar technology is expected to make a significant contribution to the future energy needs. The national solar budget has risen from $1 million in 1971 to approximately $600 million in 1980 (Rice, 1979). The evolution of the United States' solar budget is shown in Figure 4.4. The six basic areas where solar research and development is active are (Gilman, 1978): Solar Energy Budgets, millions 17 600" ‘ ‘ 4009» F .— 200‘- 0 t 5 I 1971 '72 '73 '74 '75 '76 '77 '78 '79 '80 Year Figure 4.4.--Evolution of solar energy budgets. 18 1. Heating and cooling buildings Solar thermal conversion Photovoltaic conversion Biomass conversion Wind conversion, and O‘Ul-DOQN Ocean thermal conversion. Evaluation of federal research, development and demonstration pro- grams has shown that solar heating of buildings, biomass, wind power and photovoltaics are the most promising solar energy technologies (Anonymous, 1978a). For solar energy to emerge as a significant energy alter- native, a consolidated national solar policy is necessary. On June 20, 1979, the White House announced that the nation should commit itself to a goal of meeting 20 percent of its energy needs with solar and renewable resources by the end of the century. The formation of a national solar bank to provide interest subsidies has also been proposed. These announcements do not constitute a well- defined solar policy. The solar acts of 1974 which encourage and support development and demonstration of practical means to employ solar energy on a commercial scale, still remain the only coherent energy policy (Rice, 1979). The projection of the future energy supply in the United States (shown in Figure 4.5) indicates that a 20 percent contribu- tion by solar is attainable by 2000. The rapid increase of solar installations shown in Figure 4.6 also indicates the possibility of a significant solar output in the near future. Enerby Consumption, x 1015 KJ/year 19 150 4- " Solar 100‘_ Nuclear ~1- Hydroelectric Coal and Geothermal 50. " Natural gas -L Petroleum 0 i if i i i 1970 1980 1990 Year Figure 4.5.--Possible projection for the supply of energy in the United States during the period 1970- 2000 (Dorf, 1978). 2000 20 o o . om .. MM 00 jfi S p. “a om .: p d m“ owe .. A m .4 omF T ow_ .. op x opus .Amemp ..Pe So eeoeeeemeav ooom Lees one me 0002 9861 9£61 q >2 4; xp <0 ...Jijdl 1 l J F l mmpmum ummgmw; cm>mm meg cow meowuappmumcw capom--.o.e mczmwa #0 room room ..oom .oomp . comp :.oomp . ooHN suolaelleasul Io spuesnoul 21 4.4 Collection of Solar Energy 4.4.1 Solar Radiation Fundamentals The energy generated in the interior of the sun by fusion is transferred to its surface and then radiated into space. The amount of solar radiation intercepted in space by a surface perpendicular to the radiation at the earth's mean distance from the sun, is called the solar constant. Its value is 1353 W/m2 (Thekaekara, 1971) and varies by :3 percent due to the elliptical sun-earth orbit and the variations in the total energy emitted by the sun. The solar energy reaching the earth is greatly reduced compared to the rate of the extraterrestrial solar constant. Air molecules, water vapor and dust particles present in the atmosphere cause the attenuation of the sun's radiation. A detailed analysis of the various factors contributing to the reduction of the solar intensity has been pre- sented by Thekaekara (1974). Radiation is classified as direct and/or diffuse. Direct radiation is received from the sun without change of direction. Diffuse radiation reaches the earth after its direction has been changed inside the atmosphere. The pyranometer and the pyrheliometer are the instruments most commonly used to measure solar radiation. The pyranometer measures total radiation while the pyrheliometer measures normal incident direct radiation. In the absence of radiation data, meteorological data on percent of possible sunshine can be used to estimate radiation. For design purposes, an hour by hour system performance is often required. Availability of solar radiation data on an hourly basis exists for only a few locations in 22 the United States. As a result, hourly values have to be estimated from daily values. A description of the methods used to calculate hourly solar radiation is presented by Duffie and Beckman (1974) and Kreith and Kreider (1978). Thomas (1977) investigated the models available to predict solar radiation and found the ASHRAE weekly model to be the best for simulating long-term performance of solar systems. Measured and estimated insolation is reported as data on horizontal surfaces. However, radiation incident on surfaces of various orientation is often required. Duffie and Beckman (1974) describe the various equations used to convert solar radiation on a horizontal surface to radiation on a tilted surface. 4.5 Flat Plate Collectors 4.5.1 General Description The present principal applications of flat plate collectors are in water heating systems and in building heating/air condition- ing. Flat plate collectors are distinguished by their low cost, simplicity, low maintenance and ability to capture both direct and diffuse radiation. These features make flat plate collectors attractive devices from an engineering and economic point of view. This is especially true when energy is desired up to 100°C above ambient temperatures. Flat plate collectors have a high net energy yield. A conventional collector returns the energy utilized in its manufacture in less than one year. 23 Flat plate collectors are simple in concept. An absorber plate acts to absorb the solar energy and to convert it into heat. One or more covers are placed over the absorber to reduce the con- vective and reflective heat losses. The heat collected from the absorber is transferred to a working fluid which is either gas or liquid. In liquid systems, tube-like channels are thermally bonded to the absorber to conduct heat from the plate to the tube wall. Conductive heat losses through the back are reduced by means of thermal insulation. Because of diurnal and seasonal motions, a solar collector should face south (or north in the southern hemisphere). In addition, the collector must be tilted from the horizontal so that a maximum amount of absorbed solar radiation is intercepted. The present practice is to specify the collector slope as a function of latitude only. In cases where a solar system is designed to supply a fraction of the yearly heating load, the surface should be inclined at an angle of about 0.9 times the latitude (Morse and Czarnecki, 1958). If a solar system is designed to supply the total heating load during the year it should be inclined at 1.5 times the latitude angle (Lof and Close, 1967). Although the collector tilt has a significant effect on hourly system performance, deviations of latitude 120° have a small effect on the annual system performance (Duffie and Beckman, 1974). 24 4.5.2 Absorber Plates and Selective Surfaces The main functional part of a collector is the absorber plate. In Table 4.3 a comparison is made of the most common metals used in manufacturing absorbers. TABLE 4.3.--Collect0r material comparison. Modulus of Cost Energy to Produce Material Elasticity, psi $/1b BTU/1b Mild steel 29 x 10° 0.12 7,500 Copper 15 x 106 0.29 42,000 Aluminum 10 x 10° 0.47 54,000 SOURCE: Grimer and Moore, 1977. The absorber efficiency of a collector is greatly increased by painting the metal plate black. Common black paints have a high absorbance. According to Kirchhoff's law, the directional spectral absorbance is equal to the directional spectral emittance: a; (A.B.e.TA) = a; (A,B.e.TA) [4.5.1] I I where EA and ox emittance and absorbance, respectively, A the are the directional spectral wavelength, 8 the cone angle measured from the directional normal to the surface, 0 the circum- ferential angle and TA the surface absolute temperature. 25 The heat losses due to radiation and convection from an absorber can be considerable: 4 ) [4.5.2] _ 4 qg - h(T - TS) + ceo(T - TS where q2 is the heat loss between the absorber and the nearest glass cover, T and TS are the absolute temperature of the absorber and the nearest cover, h is the convective heat transfer coefficient, 0 the Stephan-Boltzmann constant, and 8e the effective emittance of the absorber. The functional properties of spectrally selective surfaces can be explained by the equations described in detail by Siegel and Howell (1972). The distribution of the emissive power of a black body is governed by Plank's law: -5 I C e 2/AT_1 C eAb(A) = [4.5.3] where eAb(A) is the spectrial emissive power, C1 and C2 are constants, I is the wavelength and T the absolute surface temperature. Equation [4.5.3] is a humped curve with a peak value at Amax given by Wien's displacement law: 26 _ 2898 Amax --—T—— [4.5.4] where A is given in microns and T in °K. For calculation purposes, the sun can be considered a black body emitting energy at about 5500°K. Its peak intensity is at 0.52 micron. Allowing for absorption in the atmosphere, the solar radia- tion is almost entirely confined to wavelengths between 0.3 and 2.0 microns. Objects emitting radiation at earth temperatures exhibit their peak radiation at about 8.0 microns. Thus, the solar spectrum and that of an object on the earth do not overlap. If a material can be manufactured which differentiates its absorption, reflection or transmission characteristics between wavelengths above two microns and below two microns, the absorption of solar energy would be maximized and its emission minimized. Such surfaces have been designed. They are called spectral selective surfaces. A comprehensive discussion on selective surfaces has been presented by Tabor (1967). Until a few years ago selective surfaces were too costly to be used for inexpensive solar applications. Recent technological improvements in synthesizing the materials has considerably reduced their cost. Today selective paints have the same price as common black paints (Schreyer, 1979). 4.6 Evacuated Tube and Concentrating Collectors Evacuated tube collectors are a compromise between flat plate collectors and concentrators. They collect both direct and diffuse radiation like the flat plate collectors and operate at high 27 temperatures like the concentrators without tracking the sun. At moderate temperatures (i.e., less than 60°C) flat plate collectors are as efficient as evacuated tube collectors. Tubular collectors are not as easily incorporated into retrofit designs (Grimer and Moore, 1977). In addition, they require sophisticated controls and higher initial capital investments (Graham, 1979). Although their applicability has been demonstrated (Louie and Miller, 1978; Trice, 1979), tubular collectors have not yet penetrated the solar market (Graham, 1979). The basic design concepts of flat plate collectors also apply to tracking concentrators or focusing collectors. Additional problems such as stacking the sun, higher optical losses and possible structural damages from high winds complicate the design process from an engineering point of view. Most of the concentrating collector designs can only use beam radiation. A family of compound parabolic concentrators developed by Winston (1975) and Rabl (1976) collect both beam and diffuse radiation. With focusing collectors temperatures as high as 1500°C can be achieved (Dorf, 1978). Operating problems and high maintenance and initial costs have restricted the application of concentrating collectors for purposes other than furnaces and experimental studies (Duffie and Beckman, 1974). 4.7 Solar System Analysis: Components A schematic diagram of a typical solar water heater is shown in Figure 4.7. The performance of the collector is only the first 28 .cmumm; Lopez capom a $0 Emcmmwu ovumEmsom--.m.e mczmwu Lopez an axe: Pocucou xcme mmecopm cmmcazuxu paw: .08.. 2. A _ L38: — sgwwpwxs< L couomppoo 29 step of the design process as evidenced by the additional system components shown in Figure 4.7. The long-term performance and the reliability of solar systems depends upon properly coupling a collector with the other components. 4.7.1 EnergygStorage and Controls Energy can be stored by utilizing phase change materials (Telkes, 1974), rock beds (Lof et al., 1964), and hot water storage (Duffie and Beckman, 1974). Water is non-toxic, has a high specific heat and is readily available. The water in a storage tank is heated by the working fluid that circulates through the collector. The hot water from the storage tank is used to supply the load at various flow rates. An energy balance for a nonstratified tank gives (Duffie and Beckman, 1974): de _ MCp'_TT - Qu - L - (UA)S (Ts - Ta) [4.7.1] where M is the mass of water in the tank, T5 and T6 are the tank and environmental temperatures, Qu is the rate of energy added to the collector, L is the load, U is the tank loss coefficient and A is the area of the tank. The rate of energy added by the collector, Qu in equation [4.7.1] can be expressed as: 3O 0u = 3(5 op) (10 - T ) [4.7.2] 5 where m is the flow rate of the working fluid, To is collector outlet temperature and B is a control in a function equal to unity when the pumps operate and zero at other time. One of the targets of solar system design is to maintain a high degree of stratification inside the tank. The efficiency of the collector in a stratified tank system is greatly improved. The ratio of tank height to tank diameter (L/D) strongly effects the maintenance of stratification. The higher the ratio, the more stable the stratification. Structural and costs constraints limit the value of L/D. An L/D between 3 and 4 is a reasonable compromise between cost and performance (Lavai and Thompson, 1977). The objective of the control strategy, is to maximize the value of Qu in Equation [4.7.1]. A control device senses and com- pares the temperatures of the tank, Ts’ and the collector, Tc, whenever TC > T5 the working fluid is allowed to circulate through the collector. Schlesinger (1977) has described the type of controls used in solar applications. By properly choosing and installing a control device, the area of the collector required for a specific process can be reduced by 35 to 40 percent (Newton, 1978). In a stratified tank, the water temperature is not uniform over the vertical dimension of the tank. Under stratification condi- tions energy balances as in Equation [4.7.1] can be written for several sections in the tank. Each section is assumed to be at 31 uniform temperature. A two section tank is shown in Figure 4.8. An energy balance for the upper section (TS 1) can be rewritten as (Duffie and Beckman, 1974): dTS’l = 1 [F (50 ) (T - T ) dt (1me)s 1 1 p c c,o s,1 + (me)L (Ts,2 ' Ts,1) ' (UA)S,1 (Ts,1 - T )] a [4.7.3] where 1 if Tc,o > 15,1 F1 = { [4.7.4] 0 1f Ts,1 > Tc,o T’s,2 For the lower section (TS 2) the energy balance is dT s,2 = 1 _ dt (50 ) [F1(me)c (Ts 1 Ts,2) p s,2 + (1 ' F1)(me)c (Tc,o ' Ts,2) + (me)L (TL,r ' Ts,2) - (UA)s,2(Ts,2 ' Ta)] [4.7.5] Depending on the nature of the application, predicted system performance using Equations [4.7.3] and [4.7.5] may be significantly higher than the performance of an unstratified tank system (Equation 32- .AeNN .aa .eemp ..<.3 .cmExomm ace .<.w .wwmmaov mcaumcmaemp ecoewca um cowpuwm 50mm new: xcmu mmmcopm Lopez umwwwumcpm11.w.e weaned mmoa Peacmnp Louomppou V e Loam: . v . an axe: ... N we ‘ 4h 45 o F . e A a-Pv mmoa Peacock eeos _.m eh Louomppou 50cm e. u oeu 33 [4.7.1]) (Duffie and Beckman, 1974). This is more evident when a two or three section tank is substituted for a one-section tank. 4.8 Economics 4.8.1 The Present Value Concept Once a capital investment has been implemented, its conse- quences cannot be altered. Capital commitments, particularly those that influence the long-run flexibility and earning power of an investor, should be based on sound economic indices and criteria. Judging the economic desirability of a capital expenditure on the payback period fails to recognize the time value of money and invest- ment profitability (Bierman and Smidt, 1970). The time values of money arise from the fact that because of uncertainty, inflationary trends and alternative uses of money, a dollar in hand today is more valuable than a dollar to be received sometime in the future (Nelson et al., 1973). The interest rate charged by financial institutions represents the time value of money since the speculative motive is one of the principles behind a money lending process (Keynes, 1936). When an accumulated amount of money under compound interest is determined, the present sum of money is known. The amount of money received sometime in the future by investing and allowing com- pound interest to accrue is determined by advancing forward in time. When the present value has to be determined, the sum of money to be received in the future is known. The objective of discounting is to determine the present worth of that future sum by retreating in time (Aplin and Casler, 1973). 34 The practice of discounting incorporates the time value of money. The discount rate is cost related to the value of money with respect to the timing of its receipt and disbursement. This cost is established during a normal investment activity based on both debt and equity sources of capital. Usually, a company sets a minimum discount rate which is between 10 and 15 percent (Horwitz, 1980). In a discounting process cash flow receipts and disbursements are adjusted by the discount rate for the period of time funds are in use. The result of discounting is called the present value which is expressed as: C C C PV = C + 1 + 2 + ... + ___fl__.+ 5V -————- [4.8.1 ° (1+1) (1+i)2 (1+i)" (1+1)" 1 where PV = present value of net cash inflows CO = investment C1,C2,Cn = cash inflow after taxes in years 1,2,...n, i = the discount rate n = expected economic life of asset SV = salvage value of the asset in year n The present value is a powerful technique to judge several cash flow alternatives in terms of today's dollars (Aplin and Casler, 1973). 35 4.8.2 The Life-Cycle Costing Method In general, solar systems require higher initial and lower operating costs than conventional electric or fossil fuel fired systems. As a result, a solar system financially examined on a basis of short-term return of investment will be put at a disadvan- tage. Solar systems are more attractive if the life-cycle costing method is used (Hayes, 1977). The objective of the life-cycle costing method is to minimize the present values of a summation of costs arising both now and in the future (Corcoran, 1978). The method is an evaluation process suitable for the economic comparison of alternative projects and for the selection of the most cost-effective design for a specified application. The federal government is employing life-cycle costing in the Federal Energy Management Programs. The National Energy Conservation Policy Act (NECPA), passed in the fall of 1978, requires that "practical and effective" life-cycle costing methods and procedures are to be used in evaluating energy conserva- tion and solar energy programs for federal buildings and facilities (Ruegg, 1978). Reynolds et a1. (1976) provided guidelines for the applica- tion of the life-cycle method as a decision making process. The following components comprise the fundamental considerations of the method. 1. Initial capital investment cost 2. Annual operating and routine maintenance costs 3. Major repairs and component replacements 36 4. Complete item or system replacement 5. Residual values 6. Time, The time factor is used to determine when costs or benefits occur and when replacements are required. Reynolds et a1. expressed the economic viability of a life-cycle optimized solar system in terms of the following statistics: (1) savings/investment ratios, (2) discounted payback period, and (3) BTU savings/investment dollar. Although life-cycle costing is accepted by most economists as the soundest approach in a decision making process (Ruegg, 1975), its application involves some serious assumptions. The method assumes a period of study equal to the life of equipment under investigation. However, for solar systems this life is unknown. As a result, an equipment life must be assumed. An erroneous assump- tion can lead to serious miscalculations (Boer, 1978). Fuel cost, term of mortgage, collector area cost and annual nominal discount rate were found to be the more sensitive economic parameters of an optimized solar system (Singh et al., 1979). Another study indicated that duel escalation and maintenance are the most critical factors (ERDA, 1976). Solar hot water and space heating were found to be economically attractive when the alternative is electric energy (Butt, 1976). For a payback of 20 years, it was shown that solar energy could replace 30 to 40 percent of the electric energy demand for water heating in milk processing plants (Thomas et al., 1977). Assuming a constant fuel cost equal to $l3/106 BTU, a solar water heater in Lansing, Michigan will pay for 37 itself in 9.5 years, if the capital is borrowed at 7 percent and the collectors cost $300/m2 (Zapp. 1979). 4.9 Computer Models for Solar System Design Solar systems operate in a transient fashion subject to time changes in all forcing functions. In addition, many solar component models are non-linear. Therefore, computerized models are necessary tools for solar system design. Various solar simulation models and their status were dis- cussed by Graven (1974). Buchber and Roulet (1968), Lof and Tybout (1972), and Butz et a1. (1974) have developed quasi steady-state solar system models which are the predecessors of the widely used simulation model TRNSYS. 4.9.1 The TRNSYS Prggram The transient system simulation, TRNSYS, has been developed at the University of Wisconsin Solar Energy Lab for the design and simulation of a wide variety of solar energy systems. The computer program has been thoroughly described by Klein et a1. (1979). A typical solar system consists of interconnected components such as solar collector, energy storage unit, heat exchanger, pumps and temperature sensing collectors. TRNSYS models the transient behavior of a solar system by collectively simulating the performance of the interconnected components. TRNSYS is written in FORTRAN and is composed of a main pro- gram and various subroutines which model the function of a specific solar system component. Additional subroutines are used to perform 38 tasks such as data reading, printing, plotting and numerical integration. The flow of information in TRNSYS is either of acyclic or recyclic type. Recyclic flow occurs whenever information is flowing from a component to one or more other components of the system and then back to the starting component. In acyclic flow the information does not return to the starting component. The recyclic type flow necessitates a numerical integration algorithm which in TRNSYS is the Modified-Euler method. Predicted values of the dependent variables are corrected by the trapezoid rule. In the recycle loop, simultaneous differential and algebraic equations are solved by successive substitution iteration until all the outputs converge to within tolerance limits specified by the user. TRNSYS will best model solar systems if hourly isolation and temperature data is used. For locations where hourly data is unavail- able, the ASHRAE weekly insolation model is satisfactory for deter- mine 10ng-term solar system performance (Thomas, 1977). Experimental results have indicated that simulating systems with average meteoro- logical data, the performance of the system tends to be too optimistic (Klein et al., 1975). Such a performance overestimation was stated to be the result of the nonlinear operation of solar systems. The negative contribution of cloudy days is not propor- tional to the positive contribution of sunny days. Oonk et a1. (1975) used TRNSYS to model the Colorado State University heating and cooling system. The efficiency of the system was found to be lower in the summer than in the winter but both seasons exhibited higher efficiencies than in the spring and fall. 39 TRNSYS was used to model the demonstration solar systems described by Rippen et a1. (1978) and Key (1979). At the present time, the systems are in operation and the validity of the TRNSYS program is being investigated in both cases. 4.9.2 The f-chart Design Method The f-chart program is a fast simulation program for solar heating systems. The method correlates two dimensionless variables of a solar system to its long-term performance. It was developed at the University of Wisconsin Solar Lab by correlating hundreds of Simulations of solar heating systems. A complete description of the program is presented by Hughest et a1. (1978). The authors also discuss the assumptions under which the design procedure is valid. The identification of the dimensionless variables in f-chart has been described in Beckman et al. (1977). Assuming the energy change in the storage tank to be small, the fraction of the monthly total heating load supplied by solar energy, f, is f = Qu/L [4.9.1] where L is the monthly total load. The useful energy, Qu’ collected during the month is Q = FRAc [S - UL (Tin - Ta)] At [4.9.2] U where At is the number of days in a month. 40 A dimensionless temperature, 0, can be defined: ) [4.9.3] 6- III (tin ' Ta) / (Tref ' Ta where Tref is a reference temperature equal to 100°C. Equation [4.9.l] can be written as: -—Tf— [It (55) - UL (T - Ta) oAt] [4.9.4] ref where It is the instantaneous solar radiation incident on the collector surface per unit area and (TS) is the monthly average transmittance absorbance product. In Equation [4.9.4], f may be determined using the following two dimensionless parameters: F'UA(T -T)At x s R L Eff a [4.9.5] F' (55): Y: R L TA [4.9.5] Equations [4.9.5] and [4.9.6] are the basis of the f-chart method design technique. The f-chart program is written in FORTRAN for use in inter- active mode. It can be used to determine annual performance of resiential type solar systems for approximately 270 cities in the United States. Besides the thermal analysis, the program also 41 performs an economic assessment of a specified or an economically optimized collector area for a given location. The optimized area is the one which minimizes the present value of cumulative costs with the solar-assisted system over the period of analysis. The life-cycle coSting method is used for the economic analysis. The economics of solar water and space heating for thirteen cities has been examined by the f-chart method (ERDA, 1976). For the same values of X and Y air heating systems outperformed liquid systems, particularly for systems designed to supply a large fraction of the heating load (Klein et al., 1977). A more detailed description of TRNSYS and f-chart will appear in Chapter 6. 4.10 The Food Industry from an Energy Point of View 4.10.1 Energy Utilization Approximately 16 percent of the total United States' energy consumption is attributed to the food system (Pierotti et al., 1977). This accounts for food production, processing, distribution and food preparation. The percentage distribution of the energy used among different stages in the food system is listed in Table 4.10.1. The Food and Kindred Products industrial group, SIC 20 (Standard Industrial Classification 20) ranks sixth among all major industries (Table 4.10.2) and as such, it has been the subject of numerous energy related studies. After the oil embargo of 1973, the United States food industry has become energy cautious. The result of this cautiousness is shown in Table 4.10.3. Table 4.10.3 indicates 42 TABLE 4.10.l.--Percentage distribution of the energy used in the United States food system. Functional State Percent Production 18 Processing 33 Transportation 3 Wholesale and retail trade 16 Households 30 SOURCE: Hirst, 1973. TABLE 4.10.2.--Consumption of purchased fuels and electric energy in the United States industrial sector in 1976. Quantity Percent SIC Description Trillion KJ of Total All Industries . 13,320 100 28 Chemicals and Allied Products 3,183 23.9 33 Primary Metals 2,511 18.8 26 Paper and Allied Products 1,366 10.2 29 Petroleum and Coal Products 1,362 10.2 32 Stone, Clay and Glass Products 1,287 9.6 20 Food and Kindred Products 989 7.4 All Other Industries 2,622 19.9 SOURCE: Annual Survey of Manufacturers, 1976. 43 chap .mgmczpommzcmz eo sm>cam pazcc< ”mumzom O.OF O.__ 0.0_ O.N N.OO N.OO m.mm O.OO OOOOa OOOOOOFPOOOPZ OON O.OP _.OF 0.0P O.NP N.OO_ 0.00P O.OF_ 0.0N_ OOOOLOOOO OON N.NP O.NF N.OF O.O O._PF N.NOF O.OOF O.ONF OP_O Oee mama NON N.OF N._P O.NP O.O _.NOF O.OOF N.OOF O.NN_ OOOOOOLO NOOOO_OOOOOOO LOOOO OON N.OF 0.0P N.O O.O O.Om N.Om N.NO N.FN OOOOOOLO LOOOO OON O.ON 0.0P 0.0_ O.PF O.NOF N.OOP N.NOP N.OOF OOOOOOLO __ez Oee OPOLO OON O.OP 0.0_ N.OP N.O_ O.FOF O.OOF O.OOF N.NO_ OO_OOOOOO> Oee OOPOLL Oo>eomoea OON O._N P.ON 0.0_ O.OF O.NO N.OOP 0.00_ O.OF~ OOOOOOLO sLeOO NON N.NO O.OO N.OO N.ON O.OOP O.NO_ O.FNF O.OOP OOOOOOLO pee: .ON 0.00P 0.00. O.OOF N.OO_ O.OOO O.eOO O.FPOP 0.00_. OOOOOOLO Oeeeeex OOO OOOO ON ONOP ONOP ONOP NNOP ONO_ ONO, ONOF NNOP OnuwwemmwmmumH oOOO O OOP x Ox OP x mucmeawnm eo mapm> togamcoo smcmcm .mnmp new .mmmp .emmp .Nump so» muuzuoxn voom we mucweawsm we wapm> ace scumsucw nooe magnum coupe: me» :e cmzon ten new; ace amazmcoo smcmem1-.m.op.e m4m4 40 1; 330 3 Sq.) _ -; 20 l 3 10 _ 7 8 9 10 ll 12 13 Time Figure 6.1.6.--Hot water consumption during cheese or ice cream processing. 72 6.2 Solar System Sizing The optimum size of the solar system was assumed to be the one which will meet the hot water requirements in the dairy plant established by the energy audit. However, economic constraints may limit the size of the system to a point where only a fraction of the hot water could be attributed to solar energy. Further increase of the system size would be financially unjustifiable. Based on the parameters determined by the energy audit and the economic scenario presented in Table 6.2.1, the f-chart program was used to obtain the size of the solar system. TABLE 6.2.l.--Economic criteria used to size the solar system. Period of economic analysis 20 years Collector cost 200 $/m2 Collector indepencent cost 2000 $ Down payment (percent of original) 10 percent Interest rate of mortgage 8 percent Discount rate 8 percent Inflation rate 6 percent Fuel cost 10 $/GJ Annual fuel rise 20 percent 73 6.2.1 Application of the f—chart Program The f-chart program is programmed to be used in an inter- active mode program. The computer asks the user yes or no questions followed by a branch point. The user answers with "Y" or "N", followed by a branch point. The nature of the questions asked are presented in Table 6.2.2. At the branch point the user has the following options: A. To list the parameter values which describe the solar system under investigation. By typing "L" the parameters presented in Table 6.2.3 are listed. 8. To change the value of the parameters. The value of a parameter will change by typing the parameter code followed by a comma and the new value. Table 6.2.4 shows change of value of various parameters. C. Entering "R" the program performs a thermal analysis like the one shown in Table 6.2.5 and unless the user specified otherside, an economic analysis will follow. 0. Execution of the program is terminated by entering "S". Other options such as listing weather data, adding weather data, returning to the beginning of the program and changing units are also offered. f-Chart is composed of a MAIN program and the subroutines CALC, ECON, YESNO RADIN, TAUALF, RBAR, CYREAD, and DATAIN. Weather and location data used by the program are in the form of five data 74 4034c) 302 02¢ «00:32 0000 2H 0m>h >wamuz00nm0a c #020 0ZH04H30 02H0300¢m 0:002H zc math mu >wmum>4cz¢ 00:02000 zc 3000000 0h 3000000 02h 0¥H4 30> 04303 >vah203 44¢ «00 N.o 0h #00 002¢h00400z 023000 01h 03¢: 0b 10H: 30> 00 .Ibzoz 10¢0 000 034¢> c 2H um>h >¢x 30> 10 thzot 44¢ «00 N.o 0h #00 002ch004000 023000 01> 03¢: 001h00 >¢t 30> >w>000200 >¢0100¢000 0th 003 0b 10H: 30> 00. .Ihzoz :0c0 000 0¢04 02Hh¢01 00¢mm 4 2H 00>h >¢t 30> 00 #000200 >c01000000 01b 0sz3 0¢04 02H>¢01 00¢am 01> 4000: >¢x 30> . 2&00ct 00 z¢0 020H>¢4304¢0 10H13 000 020Hh¢004 L0 ozuhmm4 c 0204 30> 04303 >wthZ3 mm 003 0b 10H: 30> 00 .mhnz3 IwH4020 00 00 muthnm 003 >¢z 30> zwa «0 za>vwz0H>03¢>mzH 0002 30> 00 .eOcmocO ucegorm 0;» an umxmm meowummao-u.m.~.o m4m<~ TABLE 6.2.3.--Description of parameters used by f—chart. 75 CODE QID\JOCIOJHHJH VARIABLE DESCRIPTION AIR SH+UH=19LIO SH+UH829AIR OR LIO UH ONLY=3. IF IvUHAT IS (FLOU RATE/COL.AREA)(SPEC.HEAT)? IF 2'UHAT IS (EPSILON)(CHIN)/(UA)?00ooooooooo COLLECTOR AREAooooooooooooo000000000oooooocoo FRPRIME-TAU-ALPHA PRODUCT(NORMAL INCIDENCE).. FRPRIHE-UL PRODUCTooooooooooooooooooooooooooo INCIDENCE ANGLE MODIFIER (ZERO IF NOT AVAIL.) NUMBER OF TRANSPARENT COVERS................. COLLECTOR SLOPEoooooooooooooooooooooooooooooo AZIMUTH ANGLE (E.G. SOUTH'O! UEST=90)........ STORAGE CAPRCITYOoooooooooooooooooooooooooooo EFFECTIVE BUILDING UAoooooooooo00000000000000 CONSTANT DAILY BLDG HEAT GENERATION.......... HOT HATER USAGEoooooooooooooooooooooooooooooo HATER SET TEMP.(TO VARY BY MONTHvINPUT NEG..) HATER MAIN TEMP(TO VARY BY MONTHOINPUT NEG.0) CITY CALL NUMBERooooooooooooooooooooooooooooo THERMAL PRINT OUT BY HONTH=19 BY YEAR82...... ECONOHIC ANALYSIS T YES'I' N032.............. USE OPTMZD. COLLECTOR AREA819 SPECFD. AREA=2. SOLAR SYSTEM THERMAL PERFORMANCE DEGRADATION. PERIOD OF THE ECONOMIC ANALYSIS.............. COLLECTOR AREA DEPENDENT SYSTEM COSTS........ CONSTANT SOLAR COSTSooooooooooooooooooooooooo DOUN PAYMENT(PERCENT OF ORIGINAL INVESTMENT). ANNUAL INTEREST RATE ON MORTGAGE............. TERH OF HORTGAGEooooooooooooooooooooooooooooo ANNUAL NOMINAL(MARKET) DISCOUNT RATE......... EXTRA INSUR.9MAINT. IN YEAR 1( PCT ORIG.INV.) ANNUAL PERCENT INCREASE IN ABOVE EXPENSES.... PRESENT COST OF SOLAR BACKUP FUEL (BF)....... BF RISE: PERCENT/YRSIvSEOUENCE OF VALUES'Z... IF 1! UHAT IS THE ANNUAL RATE OF BF RISE..... PRESENT COST OF CONVENTIONAL FUEL (CF)....... CF RISE: PERCENT/YR=IVSEGUENCE OF VALUES=2... IF 1! UHAT IS THE ANNUAL RATE OF CF RISE..... ECONOMIC PRINT OUT BY YEAR‘I' CUMULATIVE=2... EFFECTIVE FEDERAL-STATE INCOME TAX RATE...... TRUE PROP. TAX RATE PER 0 OF ORIGINAL INVEST. ANNUAL PERCENT INCREASE IN PROPERTY TAX RATE. CALC.RT. OF RETURN ON SOLAR INVTMTTYES=19NOI2 RESALE VALUE (PERCENT OF ORIGINAL INVESTMENT) INCOME PRODUCING BUILDING? YES'ITNOB2........ DPRCO: STR.LN=19DC.BAL.SZvSM-YR-DGT=39NONE=4. IF 2! UHAT PCT OF STR.LN DPRC.RT.IS DESIRED?. USEFUL LIFE FOR DEPREC. PURPOSES............. TYPE IN CODE NUMBER AND NEH VALUE VALUE 2.00 12.23 2.00 50.00 .70 4.72 0.00 2.00 43.00 0.00 315.00 24000.00 0.00 300.00 60.00 11.00 132.00 2.00 1.00 2.00 0.00 20.00 100.00 1000.00 10.00 8.00 20.00 8.00 1.00 6.00 6.00 1.00 10.00 6.00 1.00 10.00 2.00 35.00 2.00 6.00 2.00 0.00 ' 1.00 1.00 150.00 20.00 UNITS U/C-M2 M2 U/C-M2 DEGREES DEGREES KJ/C-M2 KJ/C-DAY KJ/DAY L/DAY C C PERCENT/YR YEARS 0/M2 COLL. O PERCENT PERCENT YEARS PERCENT PERCENT PERCENT OIGJ PERCENT C/GJ PERCENT PERCENT PERCENT PERCENT PERCENT PERCENT YEARS TABLE 6.2. 76 4.--Va1ue change of various parameters of the f-chart. TYPE TYPE. TYPE TYPE TYPE TYPE TYPE TYPE TYPE TYPE TYPE TYPE TYPE TYPE TYPE .TYPE .HHAT CODE CODE CODE CODE CODE CODE CODE CODE CODE CODE CODE CODE CODE CODE CODE CODE NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER AND AND AND AND AND AND AND AND AND AND AND AND AND AND AND AND NEH NEH NEH NEH NEH NEH NEH NEH NEH NEH NEH NEH NEH NEH NEH NEH VALUE193. VALUE59.75 vALUE6.3,5 VALUE119275. VALUE149532000. UALUE15.72. VALUE17962. VALUE1821. VALUE2091. VALUE2392OO. VALUE2492OOO. VALUE31p10. VALUE34g10. VALUE3721. UALUE91.1. VALUER ' THE COLLECTOR MODULE SIZE(FT2 OR M2)?2 77 TABLE 6.2.5.--Therma1 and economic analysis performed by f-chart. 0.00THERMAL ANALYSISOOOO TIME PERCENT INCIDENT HEATING HATER DEGREE AMBIENT SOLAR SOLAR LOAD LOAD DAYS TEMP (GJ) (GJ) (GJ) (C-DAY) (C) JAN 24.8 54.62 0.00 62.19 730. -5.0 FEB 50.1 78.23 0.00 56.17 638. -4.0 MAR 64.4 106.78 0.00 62.19 553. 0.0 APR 63.4 98.70 0.00 60.18 308. 8.0 MAY 77.4 123.10 0.00 62.19 156. 13.0 JUN 84.2 127.50 0.00 60.18 27. 19.0 JUL 86.1 133.32 0.00 62.19 5. 21.0 AUG 83.5 127.88 0.00 62.19 15. 20.0 SEP 79.3 117.74 0.00 60.18 74. 16.0 OCT 65.5 101.55 0.00 62.19 234. 10.0 NOV 31.7 57.34 0.00 60.18 443. 3.0 DEC 23.3 51.53 0.00 62.19 653. ~2.0 YR‘ 61.2‘ 1178.30 0.00 732.25 3836. OOOOECONOMIC ANALYSISOOOO OPTIMIZED COLLECTOR AREA 8 218.0 M2 INITIAL COST OF SOLAR SYSTEM = 4 45600. THE ANNUAL MORTGAGE PAYMENT FOR 20 YEARS = S 4180. END PROP INC BACKUP INSURv COST SAVNGS PH OF INTRST OF YR DEPRC TAX TAX FUEL MAINT HITH HITH SOLAR YR PAID PRINC DEDUCT PAID SAVED COST COST SOLAR SOLAR SAVNGS 0 0 41040 0 0 0 0 0 4559 -4559 -4559 1 3283 40143 2280 911 3420 2841 455 4969 -209 -194 2 3211 39174 2280 966 3523 3126 483 5232 3 2 3 3133 38128 2280 1024 3636 3438 512 5519 239 190 4 3050 36998 2280 1086 3759 3782 543 5832 503 369 5 2959 35778 2280 1151 3894 4160 575 6173 795 541 6 2862 34461 2280 1220 4042 4576 610 6545 1120 706 7 2756 33037 2280 1293 4204 5034 646 6950 1481 864 8 2643 31500 2280 1371 4381 5537 685 7393 1881 1016 9 2520 29840 2280 1453 4575 6091 726 7876 2325 1163 10 2387 28048 2280 1540 4787 6700 770 8404 2818 1305 11 2243 26112 2280 1633 5020 7371 816 8980 3365 1443 12 2088 24021 2280 1731 5275 8108 865 9609 3970 1576 13 1921 21762 2280 1835 5555 8918 917 10295 4641 1706 14 1741 19323 2280 1945 5862 9810 972 11046 5385 1833 15 1545 16689 2280 2061 6198 10791 1030 11866 6208 1957 16 1335 13844 2280 2185 6567 11871 1092 12761 7120 2078 17 1107 10772 2280 2316 6972 13058 1158 13741 8129 2197 18 861 7454 2280 2455 7416 14364 1227 14811 9246 2313 19 596 3870 2280 2603 7903 15800 1301 15981 10481 2428 20 309 0 2280 2759 8438 17380 1379 17261 11848 2542 THE RATE OF RETURN ON THE SOLAR INVESTMENT( PER CENT)= 23.8 YRS UNTIL UNDISC. FUEL SAVINGS I INVESTMENT 10. YRS UNTIL UNDISC. SOLAR SAVINGS = MORTGAGE PRINCIPAL 13. UNDISCOUNTED CUMULATIVE SOLAR SAVINGS = 3 76797. PRESENT HORTH OF YEARLY TOTAL COSTS HITH SOLAR I S 84032. PRESENT HORTH OF YEARLY TOTAL COSTS H/O SOLAR 8 $ 105515. PRESENT HORTH OF CUMULATIVE SOLAR SAVINGS = S 21484. TYPE IN CODE NUMBER AND NEH VALUES GOOD-BYE STOP 1.117 CP SECONDS EXECUTION TIME 78 blocks, namely CITYDATA, SOLDATA, DDDATA, TADATA, and TEXT. The data contain city labels and latitudes, monthly average total radia- tion on a horizonatal surface, monthly average degree days, and monthly average ambient temperature. Data is available for 266 cities in the United States and Canada. Notations and symbols used by the original program had to be changed to a certain extent to be recognized by the MSU CDC 6500 computer, since the program was originally developed to run on a UNIVAC lllO computer. The core requirement of f—chart is 32,000 words decimal (Hughes et al., 1978). For thermal analysis the execution time is 1.044 CP sec and the cost is $l.90. If economic analysis is performed, the time is l.lll CP sec and the cost is $2.27 (l980 MSU rate). Tables 6.2.2 through 6.2.5 represent the run made to size the solar water heater for the dairy plant. In Table 6.2.5 an optimized area of 218 m2 is shown. The thermal analysis of this size system indicated that 6l.2 percent of the hot water needs in the plant could be supplied by solar. 6.2.2 Space Requirements The roof of the plant was considered the original site to install the solar collector. Its area is large enough for installing a 2l8 m2 solar collector. Evaluation of the roof strength revealed that reinforcement was necessary. Solar retrofit, under these cir- cumstances, was rejected on the basis of economics. The collector was finally installed on the ground approximately 60 m (200 ft) away from the dairy plant. 79 Space availability limited the area of the collector fo 2 2 116 m . The area of the proposed solar collector was about 100 m smaller than the optimum area (218 m2) determined by f-chart. . 6.3 Solar System Modeling 6.3.1 Description of TRNSYS Modeling of the solar system shown in Figure 6.3.l was con- ducted by developing a simulation model where the system and its components were sized in accordance to the energy requirements in the dairy plant. The model together with measured hourly weather data were combined with the TRNSYS program to form an executable element. The functional properties of TRNSYS are explained in the diagram shown in Figure 6.3.2. The MAIN program contains the alsorithm for solving differential equations. Subroutines PROC, CLOCK, EXEC, and PRINT are called by MAIN. PROC reads and processes the user's model. Subroutine CLOCK contains the time clock and the print/reset timers for the output producing components. Subroutine EXEC calls the component subroutines and checks the input/output connections for convergence. Subroutine PRINT handles the output producing components. The BLOCK DATA is a non-executable subroutine and it is used to initialize variables in common. The TRNSYS deck, consisting of control and data cards, con- tains the information required to simulate a solar system. A description of each card can be found in the TRNSYS manual (Klein et al., l979). A sample TRNSYS deck is listed in Appendix A. 80 g; $§§ §E 535 .cowuawgomwv gmppocpcou new .cowumucmE:cumcw .ucmcoaeou smumxm Empomuu.F.m.m mcamwm m>Fm> Pocpcou pmcowugoaogm pocpcou Fm>mp gmgmz m>_m> m>pm> gang umumoEsth gmmcmzoxm Ham: xcmu cowmcmaxm scams zopu mmzmm mgammwca mpazouosgmgh ”PF Hmdédémmmo ,. 81 .Emgmoga zH¢<£Dm H *S- ---- '0 .' .--- --.. H #0461 *B'- --.. § ---- H zmH .---I HHHHH -- 0.--- '1... thmm § " ---- -.-- H +... ---- -§-' H +- -- ---- ---- H+HHHHHHHHH ucm mmcwpzognzm m>mzmk mo Emgmmwu xuon--.N.m.o mczmwm +IIIInI+ +IIIIIII|+ H ehh,n H HNH H H H mzmH mg» Ho Emgmmwu 3oHH coHHmELoH:H new mcwuzognsmnu.m.m.o mgzmwu Esta :qu in! g 15.5 >65 in 45m 53 «NEHRH—z. «HERE: RENE: : a azHcH ate: E38?! 653:: mgmzfi cum—£82.: : H t H a c a: t H 5554.3 5633; mun—fins... HHEHHHE u x H 0::sz gs «Er—«=5 84 Design parameters already established during system sizing, which was discussed earlier, were used to determine the value of the remaining parameters. The objective was to achieve operating conditions which wuld allow a temperature rise across the solar collector of 8° to 10°C (15°-20°F). This temperature range is recom- mended for maximum thermal output from a solar system (U.S. Depart- ment of Commerce, 1977). Hourly weather data for the year 1974 in East Lansing was used by the program. A number of preliminary runs were conducted to determine the value of the parameters used by TRNSYS. Their numerical values are presented in Table 6.3.1. Based on the parameter values, a TRNSYS run resulted in solar system performance as shown in Table 6.3.2. 6.4 Solar Water Heater Characteristics The solar collector array was built in the Department of Agricultural Engineering at MSU. It has an effective collective area of 116 m2 (1250 ftz). The two transparent covers of the collectors are tempered glass with low iron content and with reflectivity and transmissivity values of 0.08 and 0.80, respectively, at normal incident. The absorber plates are manufactured by Tranter, Inc. (Lansing, Michigan). The plates are full-flooded with a 90 percent internally wetted surface. The size of each plate is 209 cm by 87 cm (82.2 x 34.2 in.) providing an effective surface area of 1.83 m2 85 TABLE 6.3.1.--Parameter Values Used in Solar System Design. RADIATION PROCESSOR UNIT 16 TYPE 16 2. 3. 4. 5. SOLAR COLLECTOR mmNafim-§WNH PUMP CONTROLLER Parameter: l. 2. 3. Mode Day of year of start of the sinulation Latitude Solar constant Shift of solar time angle UNIT 1 TYPE 1 Mode Area Fl Specific heat of fluid Collector absorbance Number of glass covers Collector plate emittance Back loss coefficient Transmittance of glass UNIT 2 TYPE 2 NSTK Upper dead band difference Lower dead band difference COLLECTOR PUMP UNIT 3 TYPE 3 Parameter: 1. Maximum flow rate HEAT EXCHANGER UNIT 5 TYPE 5 Parameter 1. 2. 3. 4. Mode 2 US Specific heat of hot fluid Specific heat of cold fluid HEAT EXCHANGER PUMP UNIT 13 TYPE 3 Parameter: 1. Maximum flow rate STORAGE TANK UNIT 4 TYPE 4 Parameter: 1. 2. 3. 4. 5. Tank volume Tank height Specific heat of fluid Fluid density Loss coefficient AUXILLARY HEATER UNIT 6 TYPE 6 Parameter: l. 2. 3. Maximum heating rate Set temperature Specific heat of fluid 1 1 42.7°C 4871 KJ/m 0 2-hr ..a 0'1 3 N .95 .64 KJ/Kg-C .90 .10 2 .5 KJ/hr-min -C .82 OOONOWOd-fl 4 10°C 3°C 15000 Kg/hr counterf1ow 12000 KJ/hr-C 3.64 4.186 15000 Kg/hr 7.6 m2 3 4.186 1000 Kg/m3 1 106 KJ/hr 74°C 4.186 TABLE 6.3.2.--Solar system monthly performance. 86 Percentage of Load Month Efficiency Supplied by Solar January 43.1 22.0 February 43.3 37.5 March 43.1 40.4 April 46.5 55.3 May 45.0 44.5 June 48.6 57.4 July 48.8 66.0 August 50.0 62.0 September 48.0 56.5 October 48.7 45.4 November 46.9 25.9 December _§;4 gggs YEAR 47.0 44.7 87 (19.6 ft2). The plates are constructed of 18 gauge (0.048 psia) carbon steel. The pressure drop through one plate is 2 psia at a flow rate of 2.3 Kg of water per minute (0.6 gpm), which assures satisfactory uniform flow distribution over the plate. The spacing between the glass cover directly above the adsorber of each collector is 2.54 cm (l in.), with another inch between the lower glass plate and the top cover glass. Six inches of fiberglass insulation (R19) is placed under the absorber plates. The absorber plate, glass covers, and insulation are assembled as a module into a wooden frame box with a total depth of 16.5 cm (6.5 in.). Black silicone paint constitutes the non-selective absorber plate coating. The solar absorbance of the coating is 0.92, the emittance is 0.86. The total set of collector plates is 64. Four plates are assembled in one large module. The modules are assembled side by side to form an array of south facing collectors. The tilt of the collector is variable. Figure 6.4.1 is a schematic diagram of the collector array. Ethylene glycol at a concentration of 30 percent is used as the collector fluid. A nitrate base corrosion inhibitor is added. The collector modules are mounted on A frames and the system is designed to withstand a maximum of 100 mph wind. A 2200 gallon cylindrical fiberglass storage tank functions as the energy storage device. This results in 1.8 gal per ft2 collector (73.3 kg/mz). The maximum design water temperature of the 88 .nggm LouumHHoo mg“ Ho Emgmmmu uHHmEmsomuu.H.¢.u mgzmpu 89 tank is 82.2°C (180°F). The dimensions of the tank are 1.82 m (72 in.) diameter by 3.05 m (120 in.). The tank is insulated by cellulose insulation (R20). The storage tank is not pressurized. A float valve provides make-up water. The solar water heater is a dual liquid system, employing a heat exchanger for the transferring of energy from the working fluid to the service water. One pump (1.5 HP) circulates the solution from the solar collectors to the liquid-to-liquid heat exchanger and back. A second pump (0.5 HP) circulates water from the storage tank through the heat exchanger and back to the tank. A 0.5 HP pump supplies the load requirements. A small make-up water tank with a vent to the atmosphere is placed in the collector loop to allow steam escape in case of power failure. A plate type heat exchanger manufactured by Tranter, Inc., is used in the system. The exchanger consists of 16 plates fabri- cated of 31655 and has a total heat transfer area of 5.3 m2 (56.5 ftz). At a flow rate of 190 l/min (50 gpm) of glycol and 190 1/min water, the rated heat exchange (at a AT of 11.l°C between the solar heated glycol solution and the water) is about 242,000 KJ (230,000 BTU) per hour. The pressure drop under these circumstances is 9 psia in each loop. Figure 6.3.1 is a schematic presentation of the solar system. It shows the location of system components, controls, valves, meters, and other instrumentation. The controllers are solid-state with thermistor inputs and solid state switches and relays producing the electric impulses to 90 the motors and valves. A differential thermostat is used to sense the difference in temperature between the collector array outlet and the bottom of the storage tank. The sensor which measures the fluid temperature at the collector is located on the manifold pipe which collects the heated fluid from the collector array. The sensor in the storage tank is located in the bottom fourth inside the tank. The differential thermostat will eventually be replaced by a Dynabyte microprocessor (Model 280). The unit is designed to act as a control, data acquisition, and load simulation device. The microprocessor contains 4K of RAM, 4K of EPROM, a keyboard input port, 300 BAUD audio cassette interface with file handling capabili- ties. The Dynabyte is programmed in BASIC. Temperatures, pressure and flow rates are measured and checked as it is shown in Figure 6.3.1. Six additional thermocouples not shown in the figure have been attached to the collector array. The temperature recording system consists of an Esterline Angus digital thermocouple recorder (Model PD 2064, Key programmable system) and a paper tape puncher. The temperatures at 22points on the solar system are being recorded at hourly intervals. Storage tank, heat exchanger, pumps, controllers, and temperature recorder, are all located in a specially built storage house. The arrangement inside the house is shown in Figure 6.4.2. EXPANSION TANK HEAT EXCHANGER 91 l—STORAGE TANK ngement in the storage house. Figure 6.4.2.-Component arra CHAPTER 7 ‘ESTABLISHMENT OF HOT WATER DEMAND IN FOOD PROCESSING PLANTS In general, load requirements in food processing plants are variable. Two or more operations of different temperature and flow rate can likely occur at the same time in a plant. Examination of the load requirement of a number of processing plants indicated that the load distribution is unique for each plant. To generate representative energy demands, four selected food processing plants will be investigated: a milk plant in Wisconsin (Lund, 1977), a milk plant in Lansing, Michigan (Rippen and Mintzias, 1977), a meat plant in Indiana (Wilson et al., 1978), and the Michigan State University Dairy Plant. Processes and energy requirements for the Wisconsin milk plant are shown in Table 3.3. Expressing the daily energy demand in the plant in terms of flow rate and temperature the daily energy demand distribution shown in Figure 7.1.1 is obtained. Each line in Figure 7.1.1 corresponds to a specific process. For example, the solid line is the energy consumed in the pasteurizer. To input the information of Figure 7.1.1 in TRNSYS is a time consuming process. In addition, a representative total energy demand is difficult to obtain from Figure 7.1.1. Expressing the energy demand in KJ/hr 92 93 :8.3 x 106 1 energy at 81°C 12 x 105‘” .. I I 10-- !.__..__I..I—.—! energy at 49°C I 1 I | I 1 I I u l.__ —"'""".' 8.. | ' I I 3. .1 |- l l -r- I; ' I ‘2 Is I ' I 8 6. : I 51 I 5 ”7| -1'__ _Ienergy at 93°C 6 I I N". “‘3 '" I s I I ,. ............. I, — ' I 1.......... .....-........ .1 I" C _.————energy at 71°C ...-.T- o—L: : .L 1 F : : : 5 9 13 17 21 Time, hours Figure 7. l. 1. --Distribution of the daily energy consumed in the Wisconsin dairy plant. 94 instead of in terms of flow rate and temperature, the daily energy demand shown in Figure 7.1.2 is obtained. The demand in Figure 7.1.2 was approximated for the TRNSYS runs by Figure 7.1.3. Similarly, the energy demand in the Lansing, Michigan milk plant was appr0ximated as shown in Figure 7.1.4. It should be noted that the Wisconsin and Lansing, Michigan plants are both pasteurizing milk and orange juice, but their daily energy demand distribution show no similarity (see Figures 7.1.3 and 7.1.4). In the meat processing plant the steam consumed to heat a 11,190 gallon dehairing tank was analyzed. The daily energy demand and distribution for the two processes are shown in Figure 7.1.5. The solid line in the Figure is the total energy. The load in Figure 7.1.5 was approximated by the graph (histogram) of Figure 7.1.6. This corresponds well with the relatively constant demand common in meat processing plants (Thomas, 1977; Lund, 1977). The energy demand in the Michigan State University dairy plant (see Figures 6.1.4 and 6.1.5) was approximated as shown in Figure 7.1.7. This type of demand is common in small food processing plants with one working shift where cleaning floors and equipment is the last operation of the day. The investigated plants resulted in five representative loads encountered in the food industry. The approximated loads are summarized in Figure 7.1.8 (Case A-d). Case E is assumed to account for a load with variable daily energy distribution. Canning plants are not considered in this study. Canaries show seasonal operations and as a result a solar water heater does Energy Consumed 95 _I— l l l L l L l L l l l L I I I r j I I I T I I r 2 4 6 8 10 12 14 16 18 20 22 24 Hour Figure 7.1.2.--Distribution of the daily energy consumed in the Wisconsin dairy plant. Energy Consumed 96 db _1 4. .1- ‘ d J I 1 1 l I l L l I I I I I I T I I I 1 1 0 8 12 18 24 Figure 7.1.3.--Approximated distribution of the daily energy consumed in the Wisconsin dairy plant. 97 ‘U Q) E 3 U) C O 0 db 3 d S. d) C m db db lLlLllllll_l [TIITIIITI I 0 12 24 Hour Figure 7.1.4.--Approximated distribition of the daily energy consumed in the Lansing, Michigan dairy plant. 98 .ucmHa mcwmmmooga Home mcmwucH msp cH umssmcou ngmcm HHHmu ng Ho cowpznwgumwoun.m.H.H mcamHL mgao; .mEHH mH NH 0 m [m - b n - P P b P P b a db 1- 1:94.14... HJiL _ . Fir- 1 rJl ono pm ngmcm womm pm Hucmcm ngmcm HmuoH ‘- d A O O") O ‘0 py 901 x ‘pawnsuoo Abuaug Energy Consumed 99 —/£1 1 1 1 1 1 1 1 1 1 1 1 14 1 6 8 10 12 15 Hour Figure 7.1.6.--Approximated distribution of the daily energy consumed in the Indiana meat processing plant. 100 fl 3 1, E l— 3. c o u a 3.. cu LE 1 ll L 1 1 1 1 I 1 I II _I— I I fl fir I 2 6 8 10 12 14 16 18 20 Hour Figure 7.1.7.--Approximated distribution of the daily energy consumed in the Michigan State University dairy plant. 101 U 31 D 61 ...J S. 0.1 If) 1_1 CASE A CASE B 1 1 1 l 1 1 1 1 l L l r I I I r T I I T I I 0 12 24 0 12 24 Hour Hour 1) B D 3 CASEC L (D .13 12 24 0 Hour F 1-1 6 n g F' D . _F 3.. 0: 5 __H I _J‘ Ind CASE 0 CASE E . 1 ‘1 1 1 ‘51 1* 1 1 1 1 4 0 12 24 0 12 24 Hour Hour Figure 7.1.8.--Representative hot water demand distribution in the food industry. 102 not seem compatible with a canning operation. In canaries a solar heating system could be used for water heating during the operating season and for space heating the rest of the year. CHAPTER 8 VERIFICATION OF THE TRNSYS PROGRAM To demonstrate the validity of TRNSYS, the MSU dairy plant solar water heater was simulated under various hot water loads and weather conditions. The ambient temperature was measured at the site of the solar system. Solar radiation was measured at the MSU weather station with an EPPLY Pyronometer. The instrument records total radiation on a horizontal plane. A sample of solar radiation recorded is shown in Figures 8.1 and 8.2. The average hourly radia- tion was estimated by calculating the area under the curve. The wind speed was measured at the Lansing city airport which is located less than 10 miles from Michigan State University. The temperature of the water in the storage tank was chosen as the criterion for the reliability of the TRNSYS results. Four thermocouples were installed at various depths inside the tank (see Figure 6.3.1) to measure the tank water temperature. Three TRNSYS runs were made. The first run was for September 27 and 28, 1979, the second for September 30 - October 2, 1979 and the third for October 29-31, 1979. October 2 was a day with low solar radiation. On October 30 the solar system operated under zero load conditions. 103 104 .mHmF .HN Lunempamm :H cmmngHz .mcwmcmg umom :H mcmHa HmpcoNHLo; o co coHumHumL HmuoH--.H.w mcamHL HH mgso; .mEHH mm NH ¢H 4» o.o 1.m.o +.m., o.N sKalfiue1 105 ‘b .mHmH .wm Lmnewpqmm :H cmmngHz .mcwmch ummm cH mcmHa HmucoNHLo; m :0 cowumvaL HmuoHuu.N.m mczmwm d) 0H {1 HH 4? NH 1) .3 1 ¢.o A Lr w.o N.H o.N sfialfiue1 106 In Tables 8.1 through 8.7 the hourly experimental and theoretical tank water temperature are presented. The experimental temperature was measured by the four thermocouples inside the tank. Since the tank of the MSU solar system is fully mixed, the four thermocouples were recording the same temperature. The difference between numerical and experimental values (AT) is shown in column four of each table, the TRNSYS temperatures are sometimes higher and sometimes lower than the measured ones. A small disagreement between the two temperatures was expected because the simulated solar system and the MSU solar water heater operated under slightly different circumstances. Equation (4.7.1) for a finte period in time can be written as: _ AT Ts,new - Ts,old + (mc)S [qu ' L ' (UA)s (Ts,old ' Ta) [8.1] TRNSYS estimates the tank temperature numerically according to the above equation. In TRNSYS, the energy collected by the solar col- lector (qu) is calculated assuming a constant value of collector incident solar radiation for a finite time increment (one hour). Under experimental conditions, however, qu will change according to the total radiation shown in Figures 8.1 and 8.2. The deviation of the instantaneous radiation, about the averaged hourly value, is sometimes substantial. For example, at 14-15 on September 27 (Figure 8.1) the average radiation is 1.15 langleys (1 langley = 107 TABLE 8.l.--Storage tank water temperature of the MSU solar water heater on September 27, 1979. Tank Measured Temperature, °C Solar Radiation Hour Measured 'Simulated AT°C KJ/m2 Load Kg 0- 1 58.0 58.0 0.0 -- -- l- 2 58.0 58.0 0.0 -- -- 8- 9 57.8 57.0 -0.8 251.0 -- 9-10 57.9 58.4 1.5 853.7 960.0 10-11 59.4 55.8 -3.6 1456 0 970.0 11-12 54.8 56.5 1.7 1958.0 760.0 12-13 49.7 55.0 5.3 2310 0 1650.0 13-14 49.4 51 6 2.2 1506.0 2433.0 14-15 42.2 44.7 2.5 1908.0 15-16 45.6 47.0 1.4 1757.0 16-17 49.2 49.0 -0.2 1205 0 17-18 50.0 49.3 —0.7 954.0 18-19 50.0 49.3 -0.7 301.0 108 TABLE 8.2.--Storage tank water temperature of the MSU solar water heater on September 28, 1979. Tank Measured Temperature, °C Solar Radiation Hour Measured Simulated AT°C KJ/m2 Load Kg 0- 1 49.5 49.1 0.4 -- -- 1- 2 49.5 49.1 0.4 -- -- 8- 9 48.9 49.0 0 1 100.0 -- 9-10 45.7 41.6 -4 1 630.0 2300.0 10-11 39.4 40.6 1.2 900.0 700.0 11-12 37.7 41.0 3.3 1506.0 850.0 12-13 37.2 39.9 2.7 1760.0 2000.0 13-14 42.5 44 6 2.1 2410.0 -- 14-15 48.9 48.7 -0.2 2270.0 -- 15-16 53.0 51.2 -1.8 1958.0 -- 16-17 54.0 52.0 -2.0 1506.0 -- 17-18 54.0 52.0 -2.0 803.0 -- 18-19 54.0 52.0 -2.0 401.0 -- 109 TABLE 8.3.--Storage tank water temperature of the MSU solar water heater on SeptembeF 30, 1979. Tank Measured Temperature, °C Solar Radiat'on Hour Measured Simulated AT°C KJ/m Load Kg 0- 1 71.5 71.5 0.0 -- -- l- 2 71.5 71.5 0.0 -- -- 8- 9 71.1 71.3 0.2 301.3 -- 9-10 71.0 71.3 0.2 752.2 950.0 10-11 68.3 66.6 -1.7 1355.8 950.0 11-12 59.6 60.4 0.8 703.8 950.0 12-13 57.0 54.0 -3.0 577.5 950.0 13-14 54.7 49.7 -6.0 828.6 950.0 14-15 47.2 45.7 -1.5 1130.0 950.0 15-16 45.6 45.2 -0.4 1581.0 950.0 16-17 46.1 44.0 -2.1 703.0 950.0 17-18 45.5 44.2 -l.3 125.0 -- 23-24 44.5 44.0 -0.5 -- -- 110 TABLE 8.4.--Storage tank water temperature of the MSU solar water heater on October 4, 1979. Tank Measured Temperature, °C Solar Radiation Hour Measured Simulated AT°C KJ/m2 Load Kg 0- 1 44.5 44.0 -0.5 -- -- l- 2 44.5 44.0 -0.5 -- -- 8- 9 43.3 44.0 0.7 276.0 760.0 9-10 44.4 42.1 -2.1 753.2 450.0 10-11 41.7 42.9 1.2 1481.4 450.0 ll-12 40.3 45.6 5.3 2008.7 450.0 12-13 42.6 48.0 4.4 2058.9 2044.0 13-14 41.1 44.5 3.4 2008.7 1703.0 14-15 41.0 41.2 0.2 1556.7 -- 15-16 45.0 43.3 -l.7 1531.7 -- 16-17 48.0 45.0 -3.0 828.6 -- 17-18 48.0 45.0 -3.0 703.0 -- 111 TABLE 8.5.--Storage tank water temperature of the MSU solar water heater on October 29, 1979. Tank Measured Temperature, °C Solar Hour Measured Simulated T°C Raggigéon Load Kg 0- 1 25.0 25.0 0.0 -- ~- 1- 2 25.0 25.0 0.0 -- -- 8- 9 24.8 24.7 -0.1 502.0 -- 9-10 24.7 33.5 8.8 1255.4 2040.0 10-11 25.5 34.1 8.6 1556.7 1470.0 11-12 28.0 37.0 9.0 1858.0 910.0 12-13 33.3 40.0 6.7 2109.0 1470.0 13-14 35.1 38.0 2.9 1757.6 2044.0 14-15 35.0 39.0 4.0 1456.3 970.0 15-16 34.5 38.0 3.5 853.0 970.0 16-17 32.4 35.1 2.7 376.0 970.0 17-18 31.7 32.4 0.7 -- 970.0 18-19 31.6 30.0 -1.6 -- -- 112 TABLE 8.6.--Storage tank water temperature of the MSU solar water heater on October 30, 1979. Tank Measured Temperature, °C Solar Hour Measured Simulated AT°C Ra233;§on Load Kg 0- 1 31.6 30.0 1.6 -- -- l- 2 31.6 30.0 1.6 -- -- 8- 9 32.0 31.0 -l.0 1004.3 -- 9-10 32.7 33.1 0.4 1506.5 -- 10-11 35.8 36.1 0.3 1757.6 -- 11-12 40.5 41.5 1.5 1858.0 -- 12-13 46.1 46.5 0.4 1757.6 -- 13-14 50.0 51.4 1.4 1858.0 -- 14-15 55.3 55.5 0.2 1757.6 ~- 15-16 57.9 57.9 0.0 1781.0 -- 16-17 57.9 58.3 0.4 753.0 -- 17-18 57.9 58.2 0.3 301.0 -- 113 TABLE 8.7.--Storage tank water temperature of the MSU solar water heater on October 31, 1979. Tank Measured Temperature, °C Solar Hour Measured Simulated AT°C Raggaggon Load Kg 0-1 57.1 58.2 1.1 -- -- l- 2 57.1 58.2 1.1 -- -- 8- 9 56.4 60.0 3.6 502.0 -- 9-10 57.0 61.6 4.6 828.6 1610.0 10-11 53.3 56.6 3.3 1355.8 1930.0 ll-12 44.4 51.2 6.8 1632.0 2044.0 12-13 44.0 46.0 2.0 1556.0 1022.0 13-14 40.0 45.0 5.0 1456.3 1533.0 14-15 38.9 42.0 3.1 1130.0 510.0 15-16 39.4 40.0 0.6 470.0 -- 16-17 39.1 40.0 0.9 276.0 -- 17-18 39.1 40.0 0.9 -- -- 114 4.186 J/cmz). At 14 15 the radiation is 1.15 langleys, whereas at about 14:28 it is 0.4 langleys. To what extent the change of the instantaneous qu will affect the average over the hour qu is not known. Since over a finite period of time both, experimental and numerical results will be based on approximately the same amount of solar radiation, the effect of the instantaneous change of solar radiation on the tank temperature is not expected to be serious. The disagreement between the numerical and experimental results is at least partially due to different hourly load conditions. The hourly load used in TRNSYS is shown in columns 6 of Tables 8.1 through 8.7. In actuality, the hourly load distribution was differ- ent than the one shown in the tables. During the experiments the load distribution was changing according to the water demand in the dairy plant. Most of the time the hot water supply was not changing hourly. For example, on September 27 the actual daily load dis- tribution (see Figure 8.3) shows zero load between 10:20 and 11:20. In TRNSYS the amount of water from 10:00 to 10:20 was distributed over a 60-minute period (10:00 - 11:00) because changes occurring at time intervals of less than one hour are not recognized by TRNSYS under circumstances of hourly data input. The two parts of Figure 8.3 demonstrate the differences between the actual load distribution is different for the experimental and the simulated cases, the total daily load is the same for both. In Tables 8.1 through 8.7 it can be seen that in the beginning and the end of each day the temperature differences are not as great as during the day. This indicates that the energy supplied by the system to the load is approximately the 115 25.. 201* TRNSYS input 01 M m S? x 15 Jr 15‘ f6 0 _l 101- 5.. 15«- Actual Load Distribution .52 m 52 X 10 I). u" (U 0 _J 5 db .‘1 9 10 1'1 1% 1‘3 171 Time, hours Figure 8.3.--Dai1y load distribution for the experimental and simulated case on September 27, 1979. 116 same in both the experimental and the simulated situations. The effect of the load distribution is better shown in Table 8.6 where the two temperatures are very similar. On October 30 (Table 8.6) the system operated under zero load conditions. The temperatures in the tank on October 2 are shown in Figure 8.4. An important phenomenon is shown in Figure 8.4. October 2, 1979 was a rainy day. The solar radiation was very low. The temperature in the tank was considerably higher than that of the collector (see Figure 8.4). Therefore, no energy had been supplied to the tank from the collector. At 8:30 a.m. removal of hot water from the tank began in order for the load to be met (see upper part of Figure 8.4). In the meantime, cold city water started replacing the hot water removed. Because of the higher density of the cold water, the cold water remained in the lower sections of the tank. Under these circumstances, a cold water front developed close to the bottom of the tank. The solid lines in Figure 8.4 represent tempera- tures measured at different depths in the tank. At approximately 9:00 a.m. the thermocouples nearest to the bottom of the tank indi- cated a sudden temperature drop (from 47° to 13°C). The same is observed for the next nearest thermocouple at 10:00 a.m. Finally, at 1:00 p.m. the temperature of the upper tank section began to drop. At about 4:00 p.m. the temperature in the tank became uniform (12°C). Each of the four lines representing the sudden temperature drop inside the tank, indicates the position of the cold water front at various times during the day. The front moves to the top of the tank as time advances. 117 4 .. £2 3 1‘" 00 {-———Load 2 2 X 13 1‘ :3 “...—...J I 0 Storage tank 50 .. :::::: . Temperature, °C ’ TRNSYS Tank Temperature \. “5"...“ 10 ‘9/‘I--—---Collector Temperature 0 L . . . . 7 9 11 «r 1 l l 1 1 I I I 13 15 l7 19 Time, hours A T Figure 8.4.--Tank temperature and load distribution on' October 2, 1979. 118 In Figure 8.4 it can be seen that despite the low temperature in the lower tank sections, most of the water removed to meet the load was at a much higher temperature (48°C). The dotted line in Figure 8.4 is the temperature of the tank from the TRNSYS run. It can be seen that TRNSYS underestimated the temperature in the tank. Under these conditions, Equation [8.1], which is used by the TRNSYS algorithm, cannot describe the tempera- ture in the tank. The energy of the load (L) in the equation is based on a temperature which corresponds to the total water mass (M)S in the tank. From Figure 8.4 it can be seen that this is not true. The behaviorcfi'the water temperature inside the tank, shown in Figure 8.4, can be explained by assuming a stratified tank with four sections (see Chapter 4). By this assumption, Equation [8.1] will be replaced by four differential equations. Figure 4.8 and Equation [4.7.3] and [4.7.5] are an example of a stratified tank with two sections. For a four section tank with zero energy supplies from the colar collector, the tank will be as in Figure 8.5. An energy balance for section 1 will result in: T =1 =AT [-m(T-T)-1ii(T-T) 1,new 1,01d (mlc) L 1 2 1 1 2 + m6 (T2 - T1) - (UA)s,1 (T1 - 1a)] [8-2] Similar equations can be written for the other tank sections. 119 A stratified tank was not assumed during the verification of TRNSYS because the tank of the MSU solar system was fully mixed for all days indicated in Tables 8.1 through 8.7, except for October 2, 1979. If a stratified tank would have been assumed, then, as will be discussed in Chapter 9, the long-run performance of the solar system would have been substantially overestimated. The energy supplied to the load by the solar system is pre- sented in Table 8.8. The relative percent error of the numerical results indicates that with the exception of October 2, the error is relatively small. As was explained above, on October 2 TRNSYS could not describe the temperature in the tank. Modeling a solar system is a complex procedure. The transient behavior of the various components of a solar system is determined by solving simultaneously sets of algebraic and/or differential equations. Accounting for the complexity of solar water heating from a system modeling point of view, the differences observed in Tables 8.1 through 8.8 can be considered small. T T ___).. 1 To Load 1 “IL 1111 1116 T2 "'2 "'5 T3 h T4 Make up water “‘L Figure 8.5.--Stratified storage tank with four sections which can be used to estimate the four tank temperatures on October 2, 1979. 121 TABLE 8.8.--Comparison of the energy delivered to the delivery load calculated by TRNSYS to that calculated from the measured temperatures and flow rates of the MSU solar water heater and relative percentage error of the numerical results. Energy Delivered to the Daily Load, KJ Relative Error Date Actual TRNSYS Percent September 27 1,040,581 1,101,411 5.84 September 28 727,978 695,036 -4.40 September 30 1,411,111 1,387,409 -1.63 October 1 810,060 844,223 4.19 October 2 1,251,148 750,219 -39.96 October 29 1,083,104 1,356,147 6.74 October 31 1,356,870 1,449,560 6.85 CHAPTER 9 TRNSYS RUNS The purpose of the FORCING-FUNCTION subroutine (unit 14 type 14) in TRNSYS is to generate a time dependent forcing function which has a behavior characterized by a repeated pattern. The pattern is established by a set of discrete data points indicating its values at various times through a cycle. Generation of continuing forcing functions is obtained by linear interpolation between the discrete data points. The forcing function in the TRNSYS runs is the hot water consumed inthe processing plants. Cases A-E in Figure 7.1.8 are the repeated patterns characterizing the forcing functions used in this study. Each function was repeated 5, 6 or 7 times per week depend- ing on the time schedule in a plant. In Figure 7.1.8 each discrete data point represents a fixed percentage of the daily load. Deter- mination of this percentage value allows calculation of the flow rate of the water being supplied to the plant at various times during the day. To scale-up the Michigan State University dairy plant solar water heater, the parameters related to the size of the solar system were generated according to the figures presented in Table 9.1. By assuming the volume of the storage tank to be equal to the daily hot 122 123 .cOpomHHou Lapom prmeeseea apaem eamweu_z 6;» e_ new: Amy .HHmH .mucmeeoo Ho ucmspcmamo .m.: HNV .HHV m umoH Loam: no; HHHmo ASL e.HFV a.m SL-L.-L;\:Hm may «5-8.-Lg\e¥ om_ ANSL-L;\_am Hm.PV Ne-ee\pp em a . . Ape \NSL mom ov me\me m m_ mazHo> mmmcogm Heaven See» Amy mmcm LouumHHoo\.m.: H<=V HNV amen LopumHHoU\mme 30H; HHV wasHo> mmmcopm\amcm LopomHHou .Emumzm LmHom a $6 m~Hm ecu mpmewumm o» mHmzmH :H cum: mQHmeoHumHmzuu.H.m u4m><+1>8 r l 1 T 4 8 12 , 16 18 Time Figure ll.l.l.--Non-stratified tank temperature change during a typical day in July in Michigan 24 139 The hourly supply of hot water, however, varies in the five systems according to the energy use profiles established in Chapter 7 (Figure 7.1.8). In Figure 11.1.1 can be seen that before any solar energy is collected the temperature in the storage tank drops due to hot water usage. As soon as the sun strikes the solar collector the hot water temperature increases. The water temperature in the tank in Case A reaches the lowest point. This is because at 7 a.m. when the temperature begins to rise approximately 20,000 Kg of hot water is supplied to the processing plant. During the same period the processing plant of Case 0 has used only approximately 5,000 Kg of hot water. The water temperature rise in the tank stops either because of decreased insolation (late in the afternoon) or because of the energy removed from the tank becomes greater than that absorbed by the solar collector. In Figure 11.1.1 the temperature of the tank in Case 0 begins to decrease around noon due to the fact that approximately 50 percent of the daily water delivery occurs between 12 and 2 p.m. Figures 11.1.2 through 11.1.6 represent the daily variation of the tank temperature for the five use patterns in July in Michigan (Lansing). The distribution of the daily hot water supply is also shown in the figures. Figures 11.1.7 through ll.l.ll show the tank temperature and the same loads during a day in December. As expected, the water temperature in December remains considerably lower than in July. Temperature, °C 140 70 "- Daily Efficiency: 54.9°C 65‘[ Tank Temperature Relative 60 “' Load 55‘r 50" 45‘- 40-- 35 : i i f; f: i i f % f’*i *1 : i f i 4% 0 4 8 12 16 20 Time, hours Figure ll.l.2.--Tank temperature change during a typical day in July (Case A). Temperature, °C 141 659- Daily Efficiency: 54.98°C 60., Tank Temperature 55-- 50.. Relative Load 45“ 40" 35 f i 4. + ‘ fl: #1 4 6 8 10 12 14 16 18 20 Time, hours Figure 11.1.3.--Tank temperature change during a typical day in July. °C Temperature, 142 65 «1- 60.11- Daily Efficiency: 54.77°C Tank Temperature Relative Load 35 6 8 10 12 14 16 18 20 Time, hours 22 Figure ll.l.4.--Tank temperature change during a typical day in July (Case 8). Temperature, °C 143 65" Daily Efficiency: 55.5°C 60 d)- 55 1)- Tank Temperature 0'! O 1 .h U1 1 401r .‘ Relative Load «11- I d 35 Time, hours Figure ll.l.5.--Tank temperature change during a typical day in July (Case 0). Temperature, °C 144 65 4» Daily Efficiency: 54.75°c .. Tank 60 Temperature 55" 'F'H' L Relative F Load 1—1 50-4 45-lb 40 “- 7 35 5, : f 1 1 l : 0 2 4 6 8 10 12 14 16 18 20 Time, hours Figure 11.1.6.--Tank temperature change during a typical day in July (Case E). Temperature, °C 145 45 Daily Efficiency: 49.83°C 40 -> Tank Temperature 35 «- II Relative 0ad 30 25 b 20 L -r— 4 : 4‘? 0 4 8 12 16 20 24 Time, hours Figure 11.1.7.--Tank temperature change during a typical day in December (Case A). Temperature, °C 146 5011 Daily Efficiency: 500°C 45" .. Tank 40 Temperature 351' ‘ Relative Load 30.1 25 n 20 f f f i i 0 4 8 12 16 20 24 Time, hours Figure 11.1.8.--Tank temperature change during a typical day in December (Case 8). Temperature, °C 147 504. Daily Efficiency: 50.3°C 45-» 40" Tank Temperature 35" 30‘- Relative Load 1 ~ 25-~ 20 t t : : 0 4 8 12 16 20 24 Figure 11.1.9.--Tank temperature change during a typical Time, hours day in December (Case C). Temperature, °C 148 5° " Daily Efficiency: 50.7°c 45 - 40 ‘ Tank Temperature 35 - 30 " ""1 Relative “"_Load 25 " 20 t i i i . 0 4 8 12 16 20 24 Time, hours Figure 11.1.10.--Tank Temperature change during a typical day in December (Case 0). Temperature, °C 50 45 4O 35 30 25 20 149 Daily Efficiency: 50.2°C Tank Temperature ‘ R 1 t' Hgag 1ve 1H1 4 8 10 16 20 Time, hours Figure ll.l.ll.--Tank temperature change during a typical day in December (Case E). 150 The temperature rise in the water tank of a solar water heater system exhibits an exponential profile. The nature of the exponential profile appears to be a function of the amount of hot water removed from the tank (see Figures 11.1.2 through 11.1.11). Other factors such as amount of insulation and degree of mixing in the storage tank will also affect the temperature profile. The hourly efficiency of a solar system cannot be determined by TRNSYS. This is because at times of zero incident radiation the TRNSYS run will terminate since a division by zero will be performed. As was discussed in Chapter 5, efficiency is calculated by dividing the energy absorbed by the total incident radiation (see Equation 5.25). The hourly performance of the solar systems is expressed in terms of the over-all heat loss coefficient of the collector, the temperature rise across the collector, and the collector inlet and ambient temperature differences. As was discussed in Chapter 5, collector efficiency, thermal losses and thermal output of the collector are directly related to the above quantities (see Equations 5.19 and 5.25). In Appendix 81 and 82 the simulated collector inlet and outlet temperature for the five solar systems during the same day of July and December in Lansing, Michigan is presented. The collector inlet temperature varies for the five systems. For an individual system the hourly variation is in accordance to the temperature in the tank. A similar variation in the collector outlet temperature is observed. Despite the above differences, the temperature rise 151 across the collector, presented in Tables 11.1.1 and 11.1.2, is approximately the same for all solar systems. As was mentioned previously, each system represents a certain food processing plant with characteristic energy use profile. A significant difference in the temperature rise across the collector during the day is observed, but there is little variation among the five systems during a specific time interval (i.e., 10-11 a.m. in July). This indicates that the thermal output of the solar collector is hardly affected by the hourly amount of hot water removed from the tank. It seems that considerably larger differences in inlet temperature among the five systems than the ones which occurred during the two days investigated, are required for a significant difference in thermal output to be noticed. The overall heat loss coefficient of the collector for the five solar systems is shown in Figures 11.1.12 and 11.1.13. The variation of the loss coefficient among the five systems is small. According to Equation [5.22] for the same ambient temperature a 20°C rise of the plate temperature will increase the loss coefficient about 0.5 KJ/hr-m2-°C. In the figures it can be seen that the range of change is relatively narrow (6.7 to 8.4 KJ/gr-m2-°C). The loss coefficient is mostly dependent on characteristics such as number of glass covers, absorbance, and emittance of the plate, transmittance of the glass and amount of insulation. For a simulation period equal to one year the maximum and minimum values observed are 6.1 and 9.2 KJ/hr-m2-°C. The majority of the values are about 2 8 KJ/hr-m -°C. Thus, it seems that by treating the overall loss 1 52 TABLE 11.1.1.--Difference between collector outlet and inlet temperature during a typical day in July. (Tout ' Tin)’ 0C Hour Case A Case 8 Case C Case 0 Case E 7- 8 1.8 1.7 0.7 1.5 1.7 8- 9 3.7 3.6 3.6 3.5 3.6 9-10 5.6 5.5 5.5 5.4 5.5 10-11 7.1 7.0 7.0 7.0 6.9 11-12 8.0 8.0 8.0 8.0 8.0 12-13 8.2 8.2 8.3 8.2 8.2 13-14 7.5 7.7 7.7 7.8 7.7 14-15 6.2 6.4 6.5 6.8 6.5 15-16 4.9 5.0 5.2 5.2 5.0 16-17 3.0 3.2 3.3 3.4 3.2 17-18 1.3 1.4 1.4 1.6 1.5 153 TABLE ll.l.2.--Difference between collector outlet and inlet temperature during a typical day in December. (Tout - Tin)’ °C Hour Case A Case 8 Case C Case 0 Case E 8- 9 4.6 4.6 4.6 4.5 4.6 9-10 3.0 3.0 3.0 2.9 3.0 10-11 4.5 5.0 4.4 4.4 4.4 11-12 6.2 6.2 6.2 6.2 6.2 12-13 5.5 5.6 5.6 5.5 5.6 13-14 6.8 6.9 6.9 7.0 6.9 14-15 4.3 4.4 4.4 4.7 4.4 15-16 1.3 1.5 1.5 1.7 1.5 UL, KJ/hr-m2-°C 154 O 012‘ (n- O V m-i ., C) aégaagii’d' A O “'7 CC. C) ‘9 'c~7 60 CASE A O ‘:‘_ 7 A CASE B l" /’ _ + CASE C (9 X CASE 0 .6- <2) CASE E O V ‘02 O C3 c6 1 F 1 _ 1 fl 8 12 16 18 20 Hour Figure 11.1.12.--0verall heat loss coefficient change during a typical day in July in Michigan. UL, KJ/hr-m2-°C 60 13.40 $3.00 '7L80 .60 155 69 CASE A .1 A CASE 8 ./ -1- CASE C q ' )< CASE 0 4:)” CASE E f I 1 l l 8 10 14 16 18 20 Hour Figure ll.l.l3.--0verall heat loss coefficient change during a typical day in December in Michigan. 156 coefficient as a design parameter rather than an operational characteristic, the error introduced in determining the long run performance of a solar system is relatively small. The difference between the collector inlet and ambient temperature for two days in July and December is presented in Tables 11.1.3 and 11.1.4. As was explained in Chapter 5, the heat losses of a solar collector are calculated based on this temperature difference since the plate temperature is difficult to estimate. From Tables 11.1.1 and 11.1.3 and Figures 11.1.1 and 11.1.12 it can be seen that higher tank temperatures will result in a higher loss coefficient, a higher difference between the collector inlet and ambient temperature and a lower temperature rise across the collector. The difference in magnitude of the above quantities among the five systems is not large enough to result in significant varia- tion of the daily solar system performance. The daily collector efficiency shown in Figures 11.1.2 through ll.l.ll does not vary significantly among the five systems. In December a slightly smaller daily efficiency is observed because of the higher differ- ences of collector inlet and ambient temperature observed in December (Table 11.1.4) compared to July. As will be discussed in the next pages, the long-term performance of a solar system is slightly better in the summer than in the winter because of the higher differences between collector inlet and ambient temperature observed in the winter than in summer (Tables 11.1.3 and 11.1.4). 157 TABLE 11.1.3.--Difference between collector inlet and ambient temperature during a typical day in July. (Ti - Ta), °C Hour Case A Case 8 Case C Case 0 Case E 7- 8 17.1 18.5 20.2 24.8 20.4 8- 9 22.2 23.5 24.0 27.9 23.7 9-10 26.4 27.8 28.2 31.5 28.9 10-11 31.0 32.6 32.5 32.1 34.4 ll-12 38.3 38.1 37.3 38.6 39.9 12-13 44.2 42.0 40.3 43.6 43.9 13-14 47.6 43.6 42.1 39.8 42.8 14-15 49.9 44.0 41.7 34.2 42.4 15-16 50.2 44.3 41.4 36.2 42.9 16-17 48.5 44.0 41.0 37.1 42.5 17-18 43.6 42.4 41.0 37.1 29.4 158 TABLE ll.l.4.--Difference between collector inlet and ambient temperature during a typical day in December. (Ti - Ta), °C Hour Case A Case B Case C Case 0 Case E 8- 9 32.0 33.2 33.7 35.6 32.8 9-10 30.2 31.6 31.7 33.4 31.4 10-11 35.4 36.2 36.7 36.7 37.3 11-12 44.0 44.2 43.9 44.9 44.5 12-13 46.7 45.7 45.3 46.9 46.0 13-14 53.9 52.0 50.8 49.5 51.4 14-15 52.2 50.3 49.2 43.2 49.6 15-16 50.3 47.1 45.3 40.2 45.7 159 11.1.2 Daily Performance In Table 11.1.5 the daily collector efficiency of solar systems operating in food processing plants with different energy use profiles is presented. A small variation of the efficiency among the various processing plants is observed. The table is divided in weekly sections. The processing plants were assumed to operate five days per week. The last two rows of each weekly section represent days at which the plants do not operate. During such days the temperature in the tank constantly increases, reaching its peak the last day of the week. The result of this operational characteristic of food processing plants is expressed directly in lower collector efficiencies for the last two days of the week. The first operating day of the week in the plant which follows the two idle days is also exhibiting lower efficiencies because of the relatively high water temperature in the storage tank. During this day the effect of the energy profile on collector efficiency is more pronounced than during the rest of the days. Table 11.1.6 contains the same information as Table 11.1.5 for the month of December. For reasons mentioned previously, lower efficiency values are observed in December than in July. 11.1.3 Weekly Performance The weekly collector efficiency in December and July for various food processing plants is presented in Table 11.1.7. There is no significant effect of the energy use profile on the efficiency 160 TABLE 11.1.5.--Dai1y efficiency of a 150 m2 solar collector for food processing plants exhibiting various energy use profiles (July) in Michigan. Efficiency, percent Day Case A Case 8 Case C Case 0 Case E 1 40.1 38.4 42.4 39.8 40.9 2 30.1 29.4 31.5 30.2 30.3 3 44.1 47.6 40.8 45.4 43.3 4 54.4 55.4 54.0 54.3 54.4 5 46.9 47.9 46.9 47.8 47.7 6 53.6 54.7 54.4 55.1 54.4 7 52.6 53.5 53.3 53.4 53.4 8 42.3 41.5 44.9 42.7 42.9 9 28.8 28.1 30.4 29.2 29.8 10 43.8 45.3 40.9 43.3 42.6 11 47.5 45.2 44.1 45.3 45.0 12 54.0 54.8 54.4 55.0 54.4 13 52.5 53.2 52.9 53.1 52.8 14 52.7 53.0 52.8 53.4 53.1 15 44.2 42.9 46.9 44.5 44.9 16 31.2 31.0 32.7 31.6 32.0 17 43.8 44.5 41.3 42.6 42.1 18 49.3 47.6 46.9 45.4 47.1 19 56.0 56.4 56.0 56.0 56.0 20 54.9 55.3 55.0 55.2 55.0 21 53.0 53.1 53.0 53.0 53.6 22 43.0 42.1 45.2 43.2 44.0 23 0.0 0.0 0.0 0.0 0.0 24 42.4 43.5 40.4 41.8 41.3 25 52.9 53.1 51.6 52.7 52.4 26 48.1 47.9 48.0 42.8 43.4 27 54.6 55.5 55.2 56.2 55.6 28 43.5 42.9 45.7 44.6 44.4 29 28.9 28.5 29.9 29.2 29.2 30 38.9 40.4 36.7 38.4 37.6 31 45.0 44.9 45.1 45.0 44.7 161 TABLE ll.l.6.--Dai1y efficiency of a 150 m2 solar colelctor for food processing plants exhibitng various energy use profiles (December) in Michigan. Efficiency, percent Case 8 Case C Case 0 Case E Case A Day 21:5 680 2 5 072 870 2 5 357 780 2 5 449 759 2 4 A94 7.].0. 2 123 2241203 3535134 0796043 8031095. 2535 24 4567890 1 It$5kmfl 43123 2 8645406 43123 5580607 7685306 431123 42.13928 5214828 4105938 0909750 3352235 Amounm7unmnwon 3352234 4890950 3342235 162 TABLE ll.l.7.--Neekly efficiency of l50 m2 solar collector for food processing plants with different energy use profiles. Efficiency, percent Month Case A Case B Case C Case D Case E July 46.6 46.6 46.9 46.6 46.8 46.7 47.3 47.3 47.4 47.2 46.6 46.7 46.8 46.8 46.7 48.3 48.3 48.1 47.8 48.0 46.2 46.6 46.4 46.5 46.5 December 45.0 45.3 45.0 44.9 44.9 43.3 44.4 43.7 44.3 43.8 38.3 38.2 37.6 37.6 37.6 43.2 43.7 43.5 43.5 43.5 163 of the collector. The efficiency in December is slightly lower than in July. Table ll.l.8 shows the percentage of the weekly hot water load supplied by a solar system. The processing plants have been supplied by the same amount of solar heated water. There is a dif- ference among the various weeks and among the two seasons but not between cases. As will be explained in later pages, this is due to the seasonal variation of the solar radiation available. ll.l.4 Monthly and Yearly Performance The monthly collector efficiency of a solar system operating in a food processing plant is shown in Figure ll.l.l4. The minimum and maximum efficiency is reached in December (42%) and August (49%), respectively. The lower efficiency of the winter months shown in Figure ll.l.l4 is the result of the low ambient temperature in the winter (Figure ll.l.lS). In Table ll.l.9 the monthly collector efficiency for various size solar systems operating in food processing plants exhibiting energy use profile as in Case A is presented. Collector areas up to 4000 m2 show no change in efficiency because each solar system has been scaled according to the procedure described in Chapters 6 and 9. For collector areas larger than 3000 m2 the efficiency is slightly lower. Lower efficiency for these sizes was expected since the heat exchanger of the systems was considerably smaller than the one determined by the scaling procedure (see Table 9.l). 164 TABLE ll.l.8.--Percentage of weekly load delivered by a 150 m2 solar collector system for food processing plants for different energy use profiles. Percent of Load Supplied by Solar Month _ Case A Case 8 Case C Case D Case E July 83.6 82.2 84.7 85.5 85.2 78.5 76.9 79.1 79.8 80.2 81.3 81.1 82.5 83.3 83.1 78.7 78.5 79.4 81.3 80.3 73.4 78.9 74.4 75.1 74.7 December 31.6 33.0 32.0 32.7 32.4 38.7 39.5 30.0 40.4 39.4 23.1 24.2 23.2 24.1 23.6 14.0 14.2 14.4 14.8 14.4 165 o.o¢ m.o¢ o.~¢ N.P¢ ¢.N¢ o.m¢ o.me a.me m.~¢ gmnsmuma n.~¢ n.m¢ n.m¢ o.¢¢ m.m¢ P.o¢ p.0v o.oe a.me Lmnem>oz m.m¢ m.¢e m.ee p.me o.m¢ m.n¢ m.me m.me m.o¢ Lmaouuo n.m¢ m.¢¢ m.¢v m.e¢ ¢.oe m.o¢ m.o¢ c.5e m.o¢ LmnEwpamm m.m¢ m.m¢ a.mv w.o¢ m.me «.me N.m¢ N.m¢ n.w¢ umsmz< e.m¢ m.¢e e.¢¢ ~.¢¢ p.0e m.m¢ n.o¢ m.m¢ N.o¢ apza o.¢¢ m.¢¢ m.¢¢ ~.m¢ ~.m¢ m.~¢ m.n¢ ¢.n¢ w.e¢ 0:36 ¢.N¢ m.m¢ ¢.m¢ m.m¢ P.m¢ m.m¢ a.me a.me m.me >.mz —.N¢ a.me p.me e.me m.¢e m.m¢ ¢.me ¢.m¢ a.me nga< “.mm o.o¢ m.oe N.p¢ m.~¢ m.~¢ a.me a.mv e.~¢ coca: ¢.mm m.o¢ m.o¢ m.o¢ a.me ~.N¢ n.~¢ m.~¢ m.~v xungnmu o.mm a.mm a.mm ~.o¢ m.~v m.P¢ m.p¢ m.Pe m.Fe zgmzcmw ooom ooom ooo¢ ooom ooom coop com omm omp zucoz NE .m~_m Louumppou pcmugma .zucmwuwwem .cmmmcuwz .mcwmcmg pmmw cw < mmmo cm mm mpwmoca mm: zwcmcw mcwuwawcxw mpcmpa mcwmmmuogn uooe com mgopomppou empom muwm mzowgm> com aucmmuwwwm argucoz--.m.p.Fp m4m

m ucm mcmpa Pmuco~wcos m :o cowpmwumg page» xp_mc mmmgm>m zpsucoz--.m~.P.p_ mg=m_m 28:02 a z o m < a a z < z m a o O at 1F¢ 1. .3 .. =o_pmwumm .1NP WM meom w7c CF11 110p R x ..r ATQF m8 mczumcmasm» If LION o~.. ..em uo;1e;pea aelos 168 The monthly collector efficiency for other type food process- ing plants is tabulated in Appendices 83-86. The yearly collector efficiency presented in Table 11.1.10 does not change with the collector area and type of food processing plants. Large areas (3 3000 m2) exhibit lower efficiency values because of the smaller size heat exchanger used in the simulation. The percentage of the hot water load in a processing plant supplied by solar energy is presented in Table 11.1.11. The varia- tion of the percentage among the different size solar systems is small. Collectors with large areas (1 3000 m2) exhibit lower per- centage values because of the smaller size heat exchanger used in the simulation. The variation of the percentage among the months in the year shown in Figure 11.1.14 follows the same change as the monthly average daily total radiation on a horizontal plane described in Figure 11.1.15. From Figures ll.l.l4 and 11.1.15 can be concluded that the monthly collecor efficiency will vary within a relatively narrow range. The percentage of the hot water demand supplied by a so1ar system, hwoever, will depend to a large extent on the amount of solar radiation available. Percentages for other type processing plants are tabulated in Appendices 87 through 810. Again, there is no considerable varia- ‘tion in percentage among the food processing plants. This is also illustrated in Table 11.1.12 where the yearly percentage of various size solar systems operating in different type food processing ‘plantats is presented. 169 TABLE 11.1.10.--Year1y efficiency of various size solar collectors for food processing plants exhibiting different energy use profiles in East Lansing, Michigan. Efficiency, percent Collectgr Area m Case A Case B Case C Case 0 Case E 150 45.5 45.5 45.6 45.6 45.6 250 45.9 45.5 45.5 -- -- 500 45.9 45.9 46.0 46.2 46.0 1000 45.9 45.9 46.0 46.1 46.1 2000 45.3 45.3 45.3 -- -- 3000 43.8 43.3 43.9 43.5 43.8 4000 43.6 43.0 43.6 -- -- 5000 43.5 43.5 43.5 -- -- 6000 42.6 42.1 42.6 42.2 42.6 170 o.m~ m.m~ m.m~ m.o~ F.5N «.mm ¢.n~ m.m~ ~.mm Lmnemumo “.mm m.om N.om m.om w.om m.om w.om n.0m m._m LmaEw>oz P.~m p.mm a.mm a.mm N.¢m m.¢m ¢.¢m F.¢m a.mm Lmaopuo o.¢o ~.mo m.¢o a.mm N.om ¢.oo N.mm a.mo ¢.mo Lmnsmuawm o.o~ m.on ¢.om m.o~ m.PN p.mu m.~n o.pu m.mn um3m3< m.mn m.mn a.mu P.nn ¢.wn a.mn m.wm P.mm m.mn zpzw ~.mo P.mw a.mo «.mm m.mc a.mo m.mm ~.mo o.Pn wcsa n.~m ¢.mm ¢.mm m.mm m.¢m m.¢m o.em N.¢m w.mm an: «.mm «.mm ¢.mm m.mm a.mm v.5o «.mm N.no n.mm nga< ¢.m¢ «.me F.m¢ m.u¢ ¢.w¢ m.w¢ o.we N.m¢ m.m¢ :ugmz N.me o.¢¢ o.¢¢ F.¢¢ p.me m.m¢ «.me m.m¢ m.o¢ xgmagnmu a.mm P.0N p.0N p.mm u.cm m.m~ n.o~ o.m~ m.mm Agmacwa coon ooom ooo¢ ooom ooom ooo— com omN omp gpcoz ms .mNPW Louumppou cmpom an umgm>PFmo vac; mo pcmugmq .=.m_;uwz .mcwmcmg pmmm cw < ammo :_ mm mmywmogn mm: xmcmcm mcwuwnwnxm mucmpa mcwmmmuogn uoom com memumxm go—om m~wm mzowgm> an vmwpaazm coop apgucos to mmmucmugma--._P.F.p_ m4mwpmo Excwmo ~E\»mgmcm an ~3ng N 3.8:”. N335 “532.: «:3me xcmh .mmpmmogn mm: augmcm maowgm> new: mpcmpa mcwmmmuoca woo; cw guano; smug: gmpom mo mmgm awe: gouumppou Lon paapao pmsgmgu ucm mucosgomgma apgmm>uu.mp.P.Pp u4mmm Lo xwm .m>ww mcwumcmao mucmpa mcwmmmuoga cw memumxm gmpom so. xpzw cw ucmxmmz quwaxu m mcwgsu mgaumcmasmu xcmu mangoum--.~.N.P— mgzmw. o 0 w. we mg: g «2.. .N 0 cc b q Amuse: xmccsm Amugaumm i/RS N ..e 4.0m 3\ m .T 33 m Jr - _ 3° ‘aunneuadwal xuel ~.mm e..e ¢.m¢ .coz N.em m.m¢ ~.om .cam ..om. m.¢m m.em ..ec .pam 3\o . 3\o m 3\o m Nmm. L. aucmwuwtcu l .oep 176 The daily collector efficiency of the solar system corre- sponding to different operating days in the plant is tabulated in Figure 11.2.1. The variation of the efficiency among the three situations is obvious. On Sunday, for example, the 5 o/w and 7 D/N efficiencies are 30.2 and 54.2, respectively. The tank temperature difference between the two cases is about 50°C. The inlet tank temperature will differ by about the same magnitude. Therefore, a large difference between the efficiencies is to be expected (see Equations [5.19] and [5.25]). In December the temperature behavior in the three tanks is shown in Figure 11.2.2. Because of lower insolation in December, large temperature differences as in July are not observed. The same can be said for the efficiency (see Figure 11.2.2). The monthly efficiency and percent by solar for the three scenarios (5 DIN, 6 o/w, 7 D/N) are shown in Figures 11.2.3 and 11.2.4. From the figures is it clear that high efficiencies cor- respond to low percentages and vice versa. The yearly thermal output and performance of the three systems is presented in Table 11.2.1. In Table 11.2.2 the yearly and monthly collector efficiency of solar systems with the energy use profiles shifted backward in time is presented. From Tables 11.2.2, and 11.1.9 and Appendices 83 through B6 can be seen that the long-run performance is not affected by changes in the daily water use schedule in processing plants. 177 TABLE ll.2.l.--Yearly thermal output and performance of solar systems for food processing plants operating five, six or seven days per week in East Lansing, Michigan. Collector Energy Energy Day per Efficiency Percent by Gained/m Delivered/m Week percent Solar (105KJ) (KJ) 5 46.0 54.9 2.17 1,998,360 6 48.5 50.5 2.31 2,187,517 7 51.1 45.2 2.41 2,269,040 178 TABLE 11.2.2.--Yearly and monthly collector efficiencies for solar systems in food processing plants exhibiting different energy use profiles and different processing schedules (500 m2 collector) in East Lansing, Michigan. Efficiency, percent Processing Schedule Moved Forward, hours Case A Case 8 Case C Case 0 Case E Month 8 4 9 6 4 January 41.8 41.4 41.8 41.6 42.0 February 43.0 43.1 42.8 42.9 43.1 March 42.7 42.8 42.2 42.5 42.9 April 45.8 45.7 45.5 46.1 45.9 May 45.5 45.5 44.9 45.6 45.8 June 47.6 47.5 47.6 48.2 47.7 July 46.3 46.3 46.1 46.7 46.7 August 48.4 48.3 48.2 48.9 48.9 September 46.8 46.5 46.9 47.0 47.0 October 47.1 47.1 47.0 47.4 47.3 November 46.5 46.4 46.5 46.8 46.6 December 42.3 42.6 42.0 42.1 42.6 Yearly 45.8 45.8 45.5 46.0 46.0 179 mgao; .wswh ..mmz .ma mama cm>mm Lo x_m .m>w$ m:_umgmqo mpcmpq mcwmmwuoga cw mamumAm Loyom Low .mnsmumo cw ccmxmmz Pmuwaa» m mcwgzu wgaumgmasmu .cmp mmmLoum11.N.N.Fp mgzmw. Nu we em o .4 + u . xmocoz amucsm xmcgzumm o.Pm m.w~ m.n¢ .coz m.om m.~¢ m.¢¢ .czm m.wm a.mm m.Pm .pmm 3\a . 3\o m 3\o m .xmm au=a_u_..m 3\o n z\o o 2\o m op cm on oc 3° ‘aunneaadwal xuel 180 .xmmz gmg mxmu :m>mm Lo xwm .m>ww mcwumcmqo mpcmpn mcwmmwuoLa cw mamumxm gmfiom mo aocmqummm Louumppou >.;uco:--.m.m.- mgzmw. 3\o o 3\o m .1 oe .1 cm nuaouad ‘Kouatotgga Percent by Solar 181 80 ~- 70 -- 5 D/w 6 D/w 60 -F 7 D/w 50 di- 40 -~ 30 -- 20 ; 'r i : : + t t : 1r i J F M A M J J A 0 N 0 Month Figure 11.2.4.--Percent of monthly hot water supplied by solar in processing plants operating five, six or seven days per week. 182 The percentage of the monthly load supplied by solar systems delivering hot water at different temperatures is shown in Table 11.2.3. The percentage varies linearly with the temperature (Figure 11.2.5) since the hot water load is a linear function of temperature. The slope of the two parallel lines in Figure 11.2.5 is expected to remain constant for a certain location assuming the design parameters of the solar system do not change. 11.3 Load Quantity and Solar System Performance In Chapter 9 a constant ratio (19.8) of collector area to the daily hot water load was assumed (see Table 9.1). For a constant collector area (1000 m2) the performance of the solar system was observed by increasing or decreasing the amount of the daily load. In Figures 11.3.1 and 11.3.2 the tank temperature and loss coefficient, respectively, for various loads is shown. The dashed line in the figures corresponds to a load determined by the ratio in Table 9.1. Smaller loads exhibit higher tank temperatures and loss coefficients. The daily efficiency presented in Figure 11.3.2 increases with increasing loads because of lower loss coefficients and tank temperatures. The monthly efficiency presented in Figure 11.3.2 increases with increasing loads because of lower loss coefficients and tank temperatures. The monthly efficiency shown in Figure 11.3.3 changes according to the daily efficiency. 183 TABLE ll.2.3.--Percent of load supplied by solar under different hot water delivered temperatures in East Lansing, Michigan. Percent by Solar Hot Water Temperature, °C Month 50 60 70 74 80 January 44.4 35.4 29.3 27.4 25.0 February 71.9 59.4 49.6 46.6 42.5 March 73.5 62.5 52.8 49.6 45.4 April 91.1 83.4 73.2 69.1 63.4 May 81.1 69.4 59.2 55.8 51.1 June 95.7 87.1 75.6 71.2 62.3 July 89.3 93.0 83.9 80.0 74.5 August 96.4 88.2 77.7 73.7 68.2 September 92.5 83.1 72.0 68.1 62.7 October 84.3 70.7 59.7 56.1 51.4 November 51.8 41.2 34.1 31.9 29.1 December 45.3 36.0 29.8 27.9 25.4 184 80 :1- U 0 'U Q) L G) > w- F m ‘5 c3 70 L Q) 1.) (U 3 q. 0 w +- ‘_ 60 3 .p (U ‘- m D. E a) ... 50 ‘b1.5 60 76 80 Percent by Solar Figure 11.2.5.--Percentage of yearly load supplied by solar under different temperatures of hot water delivered. (1/3) otnea p901 JBAO uotiegqeu auaptoul 185 mp .mmwuwgcmaa cmop ucmgwmmwv Lmuc: swamam Lopumprou op mesa; .me?h «F Np or m N dr- P d «1!- db ‘\v‘|unl. nip-go d' de db E o.oan|\\w-r E o.mm lu' m m I, 1 E coop m mo mgzpmgmaemp xcmh--._.m._F mgzmwm oe on D co ‘aunqeuadmal xuel 2: % ONH 186 Overall Loss Coefficient, KJ/hr-m2-°C n l n I l n I . 7 8 9 10 ll 12 l3 14 15 Time, hours Figure ll.3.2.--Overall heat loss coefficient of a 1000 m2 collector under various daily load conditions. 187 60-r 106 "I3 80 m3 53 m 40 m 26.5 m 13.2 m ...: C 8 L L .1 m 20 a. >3 U C OJ .P U .P u- e - q_ 10 LIJ Figure ll.3.3.--Monthly efficiency of a lOOO m2 solar collector under various daily load conditions. 188 The monthly percentage of the load supplied by solar decreases by increasing the load (Table ll.3.l). For small loads (12.6 m3), the percentage is over 100 percent. The yearly perform- ance and thermal output presented in Table ll.3.2 indicates that the thermal output and efficiency are improved by increasing the daily load. Since the percentage is decreasing under the same circum- stances, higher efficiency and higher thermal output become a dis- advantage above a certain value from a practical point of view. ll.4 Stratified Tank, Heat Exchanger, and Pump Requirements In Chapter 4 the effect of tank stratification on the per- formance of the solar system was discussed. In a stratified tank the water temperature is not uniform over the vertical dimension of the tank. In this situation the tank is divided in sections or seg- ments each one assumed to be at uniform temperature. A fully mixed or one section tank is assumed to be at uniform temperature over the vertical dimension. For a solar system with 1000 m2 collector three runs were made. In the first run, the tank temperature was assumed to be uniform. For the second and third runs two and three sections in the tank, respectively, were assumed. The performance of the solar system under various tank strati- fication conditions is shown in Table ll.4.l. Under the tank strati- fication condition the fluid motion in the tank is due to density changes arising from the water heating process. 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v=um mes“ :_ umummwumm>cv mmwuwu 4o cowumoobii.p.m.~P weaned w. .9. A: = m I. ¢ N... w. .fl w. nnu a. m. Nu. 202 Table ll.5.2. A collector area of l000 m2 was assumed for the run. The weekly load and water set temperature were 264,960 Kg and 74°C, respectively. The water main temperatures was different for each city according to the values reported by Collins, 1925. The collector slope was assumed to be equal to the local latitude. The water use schedule was not taken into account because as was dis- cussed previously it has no effect on the preformance of the system. The parameter values used for the runs are shown in Table ll.6.2. The incident solar radiation, shown in the second column of Table ll.5.2, varies considerably among the cities. For example, in Denver, Colorado, the incident radiation is about twice as large as in Buffalo, New York. The percent by solar varies according to the incident radiation. In addition, cities with high insolation have higher water main temperatures. In spite of the same amount of hot water consumed by the processing plants in the various cities (264,960 Kg/week), the yearly energy load in Table ll.5.2 varies among the cities as a result of the different water main temperatures employed for each city. The fifth column of Table ll.5.2 can be considered as an index of the efficiency of the solar collector. The values of the column are calculated by multiplying the yearly load by the per- centage of solar. The result gives the amount of energy supplied by the solar system. The energy absorbed by a solar collector is partially lost from the pipes, the heat exchanger, and the tank and partially delivered to the load. Assuming the losses to be constant among the various cities, division of the energy supplied by the 203 incident solar radiation gives the values of Column 5 which can be considered as an indication of the efficiency of the solar collector. The index is relatively constant among the various cities in Table ll.5.2. The lower values for cities like Phoenix, Arizona and Los Angeles, California are because in cities of high insolation the solar system supplies more energy than is required by the load. Under such circumstances the percent by solar is higher than 100. f-Chart does not print values higher than 100 percent. As a result, in situations of l00 percent by solar the energy delivered to the load will be partially wasted and the efficiency index will be based on a fraction of the energy delivered. The relatively constant efficiency index values among the cities indicate that the yearly efficiency of a certain solar collector does not vary considerably from one location to the other. The energy supplied to the load per in2 shown in the last column varies also according to the incident radiation. As was discussed previously, the overall loss coefficient is dependent on the design parameters of the solar system. The co- efficient is an input for f-chart. The effect of the ambient temperature on the system's performance is taken into account by f-chart. The values of the efficiency index in Table ll.5.2 indicate that the different ambient temperatures among the various locations has minimal effect on the index. This is because for places with high ambient temperature the insolation is also high and this will reSult in higher tank temperature than in places with low insolation. Previously it was stated that high tank temperatures result in higher 204 collector inlet temperatures. As a consequence, the difference between the collector inlet and ambient temperature remains relatively constant among various locations. Therefore, the yearly collector efficiency does not depend to a large extent on the location. Design parameters such as the number of glass covers, transmittance of the glass, amount of insulation of the collector, emittance and absorbance of the absorber plate, storage capacity, effectiveness of the heat exchanger, collector fluid flow rate, and amount of hot water sup- plied by the solar system are the ones affecting the long-run solar system performance. Table ll.5.3 presents the thermal output of a solar system under changing water set temperature conditions. The cities on Table ll.5.3 represent cases of high, low and medium insolation (see Table ll.5.2). By increasing the set temperature the percengage by solar decreases and vice versa. The relationship between set tempera- ture and percent by solar is approximately linear (see Figure ll.2.5) because the thermal output of the solar system remains the same regardless of the set temperature while the load changes linearly with the set temperature. The non-linear relationship shown in Figure ll.5.2 is due to the wasted energy delivered by the system (discussed earlier) in situations where the solar system supplies more energy than that required by the load. The yearly performance and thermal output of a solar system supplying hot water to food processing plants operating five, six or seven days per week is presented in Table ll.5.4. The cities in the table are of low, medium and high insolation. 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CODE VARIABLE DESCRIPTION VALUE UNITE 1 AIR SH+KH=I.LIO SH+NH=2-AIR OR LIQ NH ONL‘u3 3 00 2 IF I,HHAT IS (FLOW RATE/COL AREA)'SPEC HEAT) 12.;3 NYC W“ 3 IF WHAT IS (EFSILON)(CMINI£(UA) , . . 2 OH 4 COLLECTOR AREA . .. , . 2000 00 M2 5 FRPRIME- -TAU- AL.PHA PRODUCTi NORMAL INCIDENCE) 0J 0 FRPRIME- UL PRODUCT . . . . 2.00 H/C0Mg 7 INCIDENCE ANGLE MODIFIER (ZERO IF NOT AVAIL ) 0 GO 8 NUMBER OF TRANSPARENT COVERS , . . .. 2 DO 9 COLLECTOR SLOPE ....... .. .. . 41.09 DEGREES AZIMUTH ANGLE (E G SOLTH- O NEST=SO) 3.09 DEGREES - O OO KJ/C'MZ CJ MJ’C-UAV 00 MJFDAY O I STORAGE CAPACITY 2 EFFECTIKE BUILDING UA 3 C'NSTANT DAILY BLDG HEAT GENERATION :1 5 b P 4:: C! 0. C) L) O . . 5 I I O 1 HOT WATER USAGE. . .. . 204950 00 L/VVEEK 1 WATER SET TEMP (TO VARY BY MONTH.INPUT NEG #' 74 00 C I HATER MAIN TEMP(TO VARY BY MONTH,INPUT NEG N: 12 00 C I CITY CALL NUMBER .. . . ..... 207 00 IS THERMAL PRINT OUT BY MONTH=I- BY YEAR=2 2 00 IR ECONOMIC ANALYSIS 7 YES=1. NO= .. . ...... 1 00 20 USE OPTMZD. 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O .C 4., S. O 3 4.; C 3 0 d) 3: -501P 0 100 200 Collector Cost, $/m2 Figure 11.6.2.--Collector cost and solar savings relationship in Kansas City, MO. 224 A linear relationship between the life time of a solar system and solar savings for Kansas City is shown in Figure 11.6.3. A solar system with a life time of less than 12 years will result in negative savings under the assumed scenario values of Table 11.6.2. The effect of the annual price escalation of the conventional and backup fuels is presented in Figure 11.6.4. The exponential relationship shown in Figure 11.6.4 indicates that fuel price esca- lation is a very sensitive parameter in the life-cycle costing analysis. In Figure 11.6.5 the relationship between the annual dis- count rate and the savings for Kansas City is shown. The exponential relationship indicates that the annual discount rate is also a sensi- tive parameter in life-cycle costing analysis. In Figure 11.6.6 the relationship between the inflation rate and the savings for Kansas City is shown. It can be seen that to obtain more than $100,000 savings the inflation must be negative (deflation). Thus, inflation is also a sensitive parameter in the life cycle costing analysis. In Table 11.6.7 the economics of scale for East Lansing, Michigan is presented. Collector areas and water consumption rates in a processing plant are increased by the same order of magnitude. From Table 11.6.7 it can be seen that the solar savings are scaled up according to the collector area and water consumption. There is no change on the percent by solar and the other indices. The effect of the conventional and back up fuel price on the 2 savings investment ratio of a 1000 m collector solar system in Present Worth of Solar Savings, 1000 $ 225 1601b 120 4. 80 .L 40 « -40 «~ -80 .. o 16 26 ' 30 Life Time of Solar System, Years Figure 11.6.3.--Solar system life time and solar savings relationship in Kansas City, MO. 226 300.. Jr- {A O O S 200» .3 U) .S > :3 .. S. m 153. ‘8 _c 100 ‘- 4.: S. O 3 4.: C 0) q]- 8 L. O. o -100 : : : o 5 10 15 20 Annual Fuel Escalation, Percent Figure ll.6.4.--Year1y fuel price escalation and solar savings relationship in Kansas City, MO. 227 Y 200‘ 1001’ Present Worth of Solar Savings, 1000 $ 0 1 L I V db- 17 0 5 10 15 Annual Discount Rate, Percent Figure ll.6.5.--Annua1 discount rate and solar savings relationship in Kansas City, MO. 20 228 150-- 69 O CD 52 J; 100 .. U) C '5 3 L ,2 8 50 cu- q. 0 .: ...) L O :3 -g 0 8 Q) L O. -40 4: : i i 0 5 10 15 20 Inflation Rate, Percent Figure 11.6.6--Inflation rate and solar savings relationship in Kansas City, MO. 229 owpmg.pcmsumm>cw\mmcw>mm u m » coop .m:m>mm meom mo cage: acommgm u e Fmawucwga mammucoe u mmcv>om Empom umuczoumvucs pvuca mgmm» u m pcmspmm>cm u mmcw>mm pmaw umucsoumwuca pwuc: mgmw> u N “nausea .ucmsumw>cp Empom mg“ no cgzpmg mo man: n F k. NNe.o N.m¢~ mp m a.mp m.om mwF.N oom.mmo.P oooe NN¢.o m.FF_ m— m m.mp m.om mmF.N omm.emN ooom NNe.o m.¢N mp o m.mp m.oe mmp.N oom.mNm OOON NNe.o m.Nm m_ m a.mp m.oo mmF.N omm.¢mN coop NNe.o a.mp mp m w.m_ m.om mm_.N mm¢.NmF com m e m N «H Lm_om aw .Ne\omop ou we .mmg< An . mm: Loam: oaumppou ucmugma .cmmmzumz .mcwm:84 ummm cw mowsocoum use paguzo Fmsgmsu Emumxm gmpom :o a: mpmom Co uumCmmuu.N.o.P~ m4m<~ 230 various cities of the United States is shown in Table 11.6.8. At the present, the prices for natural gas, oil and electricity are approximately 2.5, 9.0 and 15.0 $/GJ, respectively. Solar water heating is economical in all cities investigated when the conven- tional fuel is electricity. Under a natural gas scenario, the solar savings are negative in all cities studied. With oil the SIR index was higher or lower than 1.0 depending on the geographic location under consideration. 11.7 Discussion of the Results by Thomas and Singh et a1. The results by Thomas (1977) and Singh et a1. (1978) are discussed here. In both studies TRNSYS was used to investigate the feasibility of solar water heating in food processing applications. I. Thomas (1977) categorized dairy and meat processing plants according to size as shown in the chart on page 232. This author disagrees with the procedure of classification shown because there is not consistancy among the sizes. For example, a medium meat plant is smaller than a medium dairy plant, while a small meat plant is larger than a small dairy plant. The energy audit on which Thomas based the classification of the processing plants is questionable. The large difference of the water temperature among the sizes is not clear. Since in all plants water is used for cleaning, the temperatures are expected to be approximately the same. Geographic location was found by Thomas to have a definite effect on economic solar water heating feasibility for food TABLE 11.6.8.--Savings/investment ratio at various fuel prices for solar systems in selected cities of the United States. Fuel Cost, $/GJ City 2.5 9.0 15.0 Buffalo, NY - - 1.248 Chicago, IL - 0.460 2.049 Denver, CO - 1.495 3.774 East Lansing, MI - 0.404 1.955 Kansas City, MO - 0.719 2.480 Los Angeles, CA - 0.981 2.917 New York, NY - 0.215 1.641 Phoenix, AZ - 1.385 3.594 232 Water Use Operating Water Plant Size Kg/day days/week Temperature, °C DAIRY PLANTS Small 1,940 3 65 Medium 6,456 5 66 Large 25,000 6 79 MEAT PLANTS Small 3,026 5 60 Medium 5,410 5 71 Large 42,000 6 71 processing plants. Similar observations about the geographic location are made in this study (see Table 11.5.2). The observation by Thomas that a plant operating six days per week showed better economic performance than a plant operating five days per week is confirmed by Table ll.6.3 of this study. According to Thomas, a significant solar energy contribution can be made byreplacing up to 90 percent of the fossil fuel energy consumption for most processing plants over a 20-year payback period. Whether the payback or the life time of a solar system is 20 years is not clear from the above statement. If the payback was 20 years, positive solar savings would have never been realized according to Table ll.6.l of this study. 233 The conclusion of Thomas that solar energy can supply up to 90 to 100 percent of the annual energy demand is correct according to Table ll.5.2 of this study. 11. The principal results by Singh et a1. (1978) are: I. The more sensitive parameters for economic analysis in life cycle costing are: a. total yearly demand b. location c. conventional fuel cost d. annual discount rate e. collector area cost. Similar observations about the above parameters have been made in this study (see Figures ll.6.l through 11.6.7). In addition to the above parameters, annual fuel escalation price and inflation rate are found to be sensitive parameters. 2. The percent by solar in three cities found were identified as shown on page 234. According to this study and results by Thomas (1977), the above figures are wrong. In East Lansing where the insolation is considerably lower than in Fresno, California, a solar system will supply approximately 50 percent of the energy needs, under approxi- mately the same load as used by Singh et a1. (1978) (see Tables 11.2.1 and 11.5.2). According to the authors, "The contribution of solar energy in Fresno and Charleston was slightly greater than that in Madison 234 Collector Load Percent by City Area, m2 GJ Solar Madison, WI 1000 3,080 8.5 4000 10,500 28.9 Fresno, CA 1000 2,580 71.0 4000 7,960 34.1 Charleston, VA 1000 2,820 11.2 F 4000 7,960 32.5 i because both Fresno and Charleston have warmer climates than Madison and subsequently less heat loss in the collector system." This is not true. The higher contribution by solar in Fresno and Charleston is largely due to higher insolation in Fresno and Charleston than in Madison rather than to the warmer climates as the authors claim. CHAPTER 12 CONCLUSIONS 1. The engineering behavior of a solar water heater for a food processing plant is accurately predicted by TRNSYS. Numerical results have been compared with experimental results obtained by the Michigan State University dairy plant solar water heater and the agreement was found to be more than satisfactory. 2. The f-chart program modified to accept weekly instead of daily water loads can be satisfactory used in the design of industrial type solar water heaters. Predicted values of solar system performance by the f-chart method were found to be in satis- factory agreement with the results obtained by TRNSYS. 3. Energy use profiles encountered in food processing plants have been identified and the effect of each on the performance of solar water heaters has been determined. The hourly and daily solar system performance have been found to be slightly effected by the daily process energy distribution in a food processing plant. The weekly, monthly, and yearly solar system performance, however are not effected as a result of the energy use pattern in a food processing plant. 235 236 4. The time a food processing plant assumes daily operation has been determined to have no effect on the performance and thermal output of a solar water heater. 5. The number of work days per week in a food processing plant has been found to have a significant effect on the engineering behavior and performance of a solar water heater. A solar water heater in a food processing plant operating seven days per week was found to have higher collector efficiency and thermal output per . collector unit area than a solar system of equal size in a food processing plant operating five or six days per week. The solar -ln. water heater in a food processing plant operating five days per week contributed more to the yearly hot water load than in cases of six or seven operating days per week. 6. The yearly efficiency of a specified solar collector design was found to be relatively constant among the varius cities of the United States investigated by this study. The thermal output per collector unit area and consequently the fraction of the yearly hot water attributed to solar energy has been found to vary signifi- cantly among the various cities of the United States. 7. Depending on the yearly hot water load in a food processing plant and the geographic location, a solar water heater with storage tank capacity equal to the daily hot water load and the collector area sized according to the volume of the tank can supply up to 49 percent in Buffalo, New York and up to 94 percent in Phoeniz, Arizona of the yearly hot water needs. 237 8. A sensitivity analysis of the economic parameters has indicated that conventional fuel escalation costs over the period of the economic analysis, annual nominal discount rate and geographic location have the greatest effect on the economic performance of a solar water heater. 9. Solar water heating for food processing plants is economically feasible in most of the locations of the United States when oil and electricity is the alternative, the nominal discount rate is 10 percent, the solar system costs 159 $/m2 of collector area, the inflation rate is 8 percent, the fuel cost escalates at an annual rate of 10 percent and the economic life of the system is 20 years. In the Western states solar water heating is more cost effective than in the Eastern, Midwestern and Southern states. CHAPTER 13 SUGGESTIONS FOR FUTURE RESEARCH 1. Investigate the engineering behavior of solar water heaters in food processing plants in geographic locations with different insolation. 2. Design an experiment to determine the validity of TRNSYS over a longer period of time. 3. Perform TRNSYS runs in selected geographic locations to modify the f—chart program under various amounts of solar radiation. 4. 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Efficiency, Percen Collector Size, m Month 150 500 1000 3000 6000 January 4l.9 42.2 42.2 40.2 39.2 February 42.7 43.0 43.0 40.9 39.7 March 42.5 43.0 42.9 40.8 39.7 April 45.3 45.8 45.8 43.6 42.4 May 45.3 45.8 45.8 43.6 42.4 June 47.0 47.5 47.3 45.2 44.0 July 46.3 46.9 46.9 44.6 43.3 August 48.7 49.1 48.9 46.7 45.4 September 46.7 47.2 47.2 45.0 43.7 October 46.9 47.3 47.3 45.l 43.9 November 46.1 46.3 46.3 44.4 43.0 December 42.6 42.6 43.0 4l.2 40.1 259 APPENDIX B4.--Monthly efficiency for various size solar collectors for food processing plants exhibiting energy use profile as in Case C. Efficiency, Percent Collector Size, m Month l50 500 1000 3000 6000 January 4l.9 42.2 42.2 39.9 38.8 February 42.6 42.9 , 42.9 40.3 39.2 March 42.6 43.0 43.0 40.5 39.3 April 45.0 45.5 45.5 42.8 4l.5 May 45.3 45.7 45.7 43.l 41.9 June 46.8 47.2 47.2 44.5 43.2 July 46.5 46.9 46.8 44.0 42.6 August 48.7 49.2 49.2 46.3 44.9 September 46.4 47.0 46.9 44.3 43.0 October 46.6 47.2 46.9 44.5 43.4 November 45.8 46.0 46.0 43.7 42.4 December 43.0 43.3 43.3 4l.l 40.0 260 APPENDIX BS.--Monthly efficiency for various size solar collectors for food processing plants exhibiting energy use profile as in Case D. Efficiency, Percen Collector Size, m Month 150 500 1000 3000 6000 January 42.0 42.5 42.5 40.2 39.l February 42.7 43.2 43.1 40.6 39.4 March 42.5 43.1 43.l 40.5 39.2 April 45.l 45.6 45.6 42.9 4l.5 May 45.5 46.0 46.0 43.4 42.l June 46.8 47.4 47.4 44.7 43.3 July 46.3 47.l 47.0 44.3 43.0 August 48.5 49.2 49.2 46.3 44.9 September 46.5 47.2 47.l 44.6 43.0 October 47.0 47.5 47.5 44.8 43.5 November 46.1 46.6 46.6 44.l 42.8 December 42.8 43.3 43.3 4l.l 40.0 A... m 261 APPENDIX 86.--Monthly efficiency for various size solar collectors for food processing plants exhibiting energy use profile as in Case E. Efficiency, Percent Collector Size, m Month 150 500 1000 3000 6000 January 42.0 42.2 42.l 40.3 39.2 February 42.6 43.1 43.0 40.8 39.6 March 42.5 43.0 42.9 40.9 39.7 April 45.3 45.6 45.6 43.4 42.2 May 45.4 45.8 45.7 43.6 42.4 June 46.9 47.4 47.4 45.2 44.l July 46.3 47.0 46.9 44.6 43.4 August 48.6 49.l 49.l 48.8 45.5 September 46.6 47.2 47.1 45.0 43.6 October 46.8 47.3 47.2 45.0 43.8 November 45.8 46.2 46.2 44.2 43.0 December 42.7 43.l 43.0 4l.3 40.2 262 APPENDIX B7.--Monthly percent by solar for various size solar collectors for food processing plants exhibiting energy use profile as in Case 8. Efficiency, Percent Collector Size, m2 Month l50 500 1000 3000 6000 January 28.0 27.3 27.3 27.6 26.9 February 47.5 46.4 46.5 46.1 45.5 March 50.7 49.5 49.6 50.l 48.8 April 68.9 67.8 67.8 68.0 66.7 May 56.0 54.9 54.9 55.6 54.7 June 70.8 69.3 69.4 69.9 68.6 July 78.9 77.7 77.8 78.5 77.5 August 73.6 72.2 72.2 73.2 71.9 September 68.4 67.3 67.3 67.7 66.6 October 56.8 55.5 55.4 55.6 54.5 November 32.6 3l.8 31.8 32.1 31.4 December 28.9 28.1 28.1 28.4 27.8 263 APPENDIX B8.--Monthly percent by solar for various size solar collectors for food processing plants exhibiting energy use profile as in Case C. Efficiency, Percent Collector Size, m2 Month l50 500 1000 3000 6000 January 28.3 27.4 27.5 26.7 26.2 February 47.6 46.5 46.6 45.l 44.l March 50.4 49.2 49.3 47.9 46.9 April 70.2 68.3 68.9 66.9 65.4 May 56.2 55.2 55.4 54.0 53.2 June 72.0 70.3 70.4 68.7 67.3 July 80.6 79.6 79.7 78.2 76.9 August 74.3 72.8 72.9 7l.2 70.0 September 68.8 67.4 67.5 65.9 64.8 October 57.0 55.7 55.8 54.4 53.2 November 32.6 31.7 3l.8 30.9 30.2 December 28.5 27.7 27.7 27.0 26.4 264 APPENDIX 89.--Monthly percent by solar for various size solar collectors for food processing plants exhibiting energy use profile as in Case 0. Efficiency, Percen Collector Size, m Month 150 500 1000 3000 6000 January 28.9 28.1 28.1 28.3 31.1 February 49.2 47.8 47.9 48.0 48.5 March 51.8 50.4 50.6 51.0 52.7 April 71.7 70.2 70.6 70.3 69.5 May 57.7 56.4 56.6 56.9 57.0 June 73.0 71.5 71.6 71.3 70.1 July 81.3 80.0 80.1 80.2 79.1 August 75.5 74.0 74.2 74.1 73.0 September 70.1 68.7 68.8 69.2 68.2 October 58.6 57.3 57.4 57.3 56.8 November 33.4 32.3 32.6 32.9 35.0 December 29.5 28.7 28.7 29.0 31.6 265 APPENDIX BlO.--Month1y percent by solar for various size solar collectors for food processing plants exhibiting energy use profile as in Case E. Efficiency, Percent Collector Size, m2 Month 150 500 1000 3000 6000 January 28.3 27.4 27.4 26.7 26.1 February 47.9 46.6 46.9 45.3 44.3 March 50.8 49.6 50.0 48.3 47.3 April 70.6 69.1 69.l 67.7 66.1 May 56.9 55.8 55.9 54.8 53.9 June 72.8 71.2 71.3 69.7 68.3 July 81.1 80.0 80.3 78.8 77.6 August 75.2 73.7 73.7 72.3 7l.l September 69.4 68.1 68.3 66.6 65.5 October 57.5 56.1 56.0 54.7 53.5 November 32.8 31.9 32.0 31.0 30.4 December 28.7 27.9 28.1 27.2 26.5