. if“. q 3 ‘3‘ w‘ v A l ' ;m*‘~*' JJMM ' ; 3 so". .A ‘A_‘ - «f on -1»;- J . . I'¥ Q '0'.‘ ’2'. ’ .Z , ~ . \ _ . A‘I C, A-AAA HI IA" ISA I In I A.AA: I'I‘ . Kv' " l "I i" -' | I-“" ah... I‘ '.I ‘7' :(I I' I. ”1:9 VE:;II%IOII';ZIOI- : I 'EIA'II' ! ‘:E._ mkfl". . o'A MI |, . -: 7.“ I‘ A} ItA‘L'fimlhu (Liv-M. AAAAAA AAAI:A . $41-ng 'It-A'l'Wm‘.‘ I .1. ' I‘IH' 'II H1. «(KWN‘ WII‘ 1? r. r‘ ‘. AYA$AK1TET3 . f A _k: Cart: I I :l “-fi; 1’ g \ P Vh_§- ' f. . . L At? . “1-: L " . 2-3 5394:; I.» - 1 5 {.A". nrw (it 1 ' {is _ ~ -;‘.;:{:’+:;:} .53 “E? .l I u . J . 115 I 3,; I ' “v' . . gamut; ‘2‘: 5.‘ Ic" fl"."£icn‘ ‘ ” I. PW .4333; . if? - A :9? 1-7.5: z if: A}: d. . . I . . . - . " It N'vI "Tlr ‘- ‘4? ~. - ”Fag: $415?» .3; £1"; “' [Aili- “ .‘ "fifi‘ I.) ’ J - - ’. . . - I. ’ . ‘ n’ L‘ {kmdffi‘ u . fifl I i 3" “A“: " -» ' ’ ' '- - . » f . ' H‘x. i '«ii 4:; 1' afir‘nm "‘3' \( ' fiAMI».J L' ;...'L \LA. . M . :l‘:':', ~ ‘ng . c “R.“‘L‘l‘w ‘ ”n" u. ,A'xA..\t.“:0 . I :6. 12%;“. . ‘.l . :AAA'IIJ , :r'TB-fl A.I ‘ H ,. .I ‘AAfJ'.A.AA, ~7ng 351‘,” L.‘ ”I“ --.'-.-A ~ ' - AL}: ~ 5‘ .‘ I I ...' ‘ "mtg. AA, I '. 4‘ A ,. I. A ' A . A. . 'I" 15:31. Q‘A'I‘AA IA "4', ' ' .I ' A! ‘. , . ‘. ‘ ‘ I I . "‘-' . . ' ': ‘9;+"‘:?'.‘I¢1§-Iflt.‘¢'lfi- A A A " AAA AA A I .‘ A J " ‘ ”AI I ‘. I A I. . ll ..' J31!" r"'l;"‘v\":” }:"r!' c fix all? " i ‘I ‘I I " fit: :".'.‘:"::.c‘:+"}‘v:‘r I“ (I. '13 ‘s. I I _ I I \' I".II ‘u 'I 1‘: ." . 1" )1":h'.. ‘I‘ ' . ‘m ' A “V4 ' - A» lt‘ .' t - J .n‘ . DAIIK "J 9: -A I I P A 'I' ’4 I." [A u’I’AJ 55."? Am lin't'! I”... . I I I. I '4 '.l'.\‘ . --,A I‘ ,' LA 1 ‘Q I , I I“ ‘.' '1 O': ‘A'.\‘ 'l‘;""( (I: “ ‘V . <| .‘ A A', A I \ I1! I II I AI I A”? I”? "A‘""A\:‘;:"AAAA H .A >(AA A‘AAAIA A A A A.A V. . I”. AAAAA.,.‘ I II . I- .- . A . , ‘ fl II‘, ‘ I . J ‘ . . A4 y- I ' I I! k I ' I. | I I‘ l . I ' . ' ' ' ‘ L p -. I I A I I "fifth. L J“ I:'AII II A IA . l‘ ‘ 1‘ f' I A ‘II #3:}: . I : r "I: I. r' I I' I ' II . . A: I ‘A 'I, A,I. ', ‘ , III c‘? I" k‘.’ . ' l‘ ‘AII 1| ‘) I H I I I .. 'l" I‘I’ I AIA' ’ I I | .A I, II I I f -:I‘ I I ‘_ ' ‘I m in, ,. "7 W ‘ I I ‘ ' I ‘ l ‘ I 4| I d + ,‘A’lh I ‘I I ‘ I I I I!- I I 'I‘ ' . ' I‘ ‘ J I ”II was» ' ’ M E 4. " 1. .~'.;; i: J" Vt“ 734‘: “ ’ ‘ "'1 FIGURE 1-5. The Novelty Locomotive by Ericsson to Compete with Stephenson's Rocket, 1929. By 1830 Ericsson had invented the screw propeller, fire engine and wrought iron cannon, but at that time, he could not find investors. He had also invented the hot air engine. Many of his inventions were before their times. It was in 18”9 that Joules established the mechanical equivalent of heat. Joules discovered that one BTU was equivalent to 778 foot-pounds of work. Also, heat was explained with the caloric theory. In other words, thermodynamics was in its infancy. In those days, few could understand Ericsson's hot air engine or caloric engine. The caloric engine is shown in Figure 1-6 (3). Professor Michael Faraday did not accept the condemna- tion of Ericsson by the leading scientific community of that day. The general opinion was that Ericsson's engine was Ericsson's Caloric Engine. FIGURE 1— 6 . based on unsound scientific principles. A large audience attended the Royal Institution in London to hear Faraday supposedly explain and support the engine. Ericsson was disappointed when Professor Faraday opened the lecture by stating he did not know how the engine worked and would direct his lecture to how the regenerative apparatus functioned. The theoreticians of 1833 could not accept Ericsson's theories and claims as sound, yet because of a lack of understanding in thermodynamics, they could not explain their skepticism. Ericsson attracted attention when he published his paper on a solar motor. In his paper, he said "Adverting to the insignificance of the dynamic energy which the entire exhaustion of our coal fields would produce, com- pared with the incalculable amount of force at our command, if we avail ourselves of the concentrated heat of the solar rays. Already Englishmen have estimated the near approach of the time when the supply of coal will end, although their mines, so to speak, have just been opened. A couple of thousand years dropped in the ocean of time will com- pletely exhaust the coal fields of Europe, unless, in the meantime, the heat of the sun be employed." It seems John Ericsson could foresee the energy crisis coming at the beginning of the fossil fuel age (3). Ericsson ran experiments that showed he could evaporate ”89 cubic inches of water per hour with a collecting surface of 100 square feet, which he stated would be over one 10 horsepower (3). By assuming 300 BTU/hour with a collector efficiency of 70%, the engine efficiency would be twelve per cent. The efficiency is calculated by converting one horsepower to BTU/hr by multiplying by 25”5 BTU/hr-hp and dividing by the collector area, the insolation (solar radiation) and the collector efficiency. 1 hp x 25u5 BTU/hr hp 100 ft2 x 300 BTU/hr ft2 x .70 The Ericsson sun power plant shown in Figure 1-7 must have been approximately 12% efficient. The engine which had a six inch diameter piston with an eight inch stroke was driven with steam. The engine operated a five inch diameter pump. The engine could also operate a mill running off the flywheel. The average speed was 120 rpm with 35 psia pres- sure on the piston. There was a steam condenser in a closed system. Therefore, the engine of Figure 1-7 was probably a basic rankine cycle. 1.” Other Solar Engines In 1876, W. Adams ran a steam engine from the sun in Bombay, India with a ”0 foot diameter hemispherical collector formed from many 10 inch by 17 inch plane mirrors. The water boiler ran a 2.5 hp steam pump (1). Calculating the overall efficiency assuming 310 BTU/ftzhr and 70% collector efficiency: 2.5 x 100 x 25”5 310 x %C4MF'JFUZ 7< 7U SIC-«U "UF'FUHZW IIIUU3>3>ITJ Inventor(s) .W. White et al .H. Schwartzman .G.U. Granryd .W. Yates Daniels Knoos Hartmann, et a1 .0. Schur .A. Kelly Dix Bell 2!.“ Cowans Horton . Arthur Burnett, et a1 Powell Newland Bentley Siegel Spector .A. Kelley .J. Brinjevec 223: May 1, 1 Nov. 17, June 2”, Jan. 27, Feb. 17, Oct. 10, Oct. 17, May 21, Nov. ”, May 25, June 29, 962 196” 1969 1970 1970 1972 1972 197” 1975 1976 1976 Jan. 25, Feb. 8, March 8, June 28, July 5, July 5, July 5, 1977 1977 1977 1977 1977 1977 1977 Aug. Aug. Aug. Sept. 15, 15, 30, 13, 1977 1977 1977 1977 22 /3—’--]/ w, \ . ,1/5 // .‘ TE,“ :/ ‘\. 4E374V7 ,0 'I/ V/ \g :— L2. ,. 1913;; a .r-1 can-5:822 :7 Efr‘” ///9 111‘2; / 2],?“ V / l \- \/ V‘—_"_ FIGURE l-l”. W.W. White Radiation Turbine. The side 19 is transparent. Air enters at 17 and leaves at 18 (31). There are some unique features, but the perfor— mance is questionable. Another turbine type invention is shown in Figure 1—15. Elwood Newland has a patent on an air turbine operating from a flat plate collector. The Newland device would probably have a low efficiency and would perhaps be used in connection with heating. The inventor was sensitive to cost effective- ness in the claims of the patent (31). The inventions of Figures 1—1” and 1—15 are attempting to move air with the sun and then extract energy with an engine (31). In the earth's atmosphere, winds are formed by the same solar process. These inventions would have to compete effectively with windmills. .——.-...... FIGURE 1—15. Newland Solar Energy Device. Patent No. ” 033 126. Another class of inventions would be based on the thermal expansion of metal when heated. Such a device is shown in Figure 1—16 by Peoples and Kearns of the Marshall Space Flight Center in Alabama. Sun hitting the aluminum rod would cause thermal expansion. Work can be extracted from the motion. Patent No. ” 006 59” by Paul Horton uses a complex system based on the heating and cooling of members to produce rotation. Two wheels at an angle to each other have con— necting bars alternately heated and cooled, which supposedly produced motion. The device is pictured in Figure 1—17. 2” PULLEY'FIXEO " " HW'W ATENOOF TAKEOFF ALUMWUMROD SHAFT SPWNG ALUMINUM ROD FIXED END OF PRIME MOVER CHINESE WINDLASS DIRECTION OF SEPARATE!) FROM ITS ROTATION COMMON SHAFT FIGURE 1—16. Solar Engine Based on Thermal Expansion. ll 25' 22' 27 42 3/ 34 A /0 FIGURE 1-17. Horton Solar Power Plant. 25 A heat engine using air is presented in Figure 1-18. The engine by Arthur Bentley was designed to be heated by the sun (31). '00,. "."..;. v'.'¢.oo ".000 a, I; 00"."...._ 46 "‘v-'0"’ FIGURE 1-18. Bentley's Heat Engine. Patent No. ” 033 13”. Another novel idea connected with producing power using the traditional Rankine Cycle engine is given in Figure l-19. In Bell's arrangement, photovoltaic cells using gallium arsenide convert light to direct current electricity. The waste heat from the cell area produces power from a Rankine Cycle engine (31). 26 IN: I n I” FIGURE 1-19. Bell's Solar Energy Converter with Waste Engine. Patent No. ” 002 031. 27 1.7 Summary It is technically possible to produce mechanical power from the sun. There have been many workable engines. l-2 gives a chronological order of developers. TABLE 1—2. Solar Engine Developers 5222 Solar Work Solomon de Caux (France) 1615 H.E. de Saussure (Sweden) 1766 Sir John Herschel (England) 1836 C.S.M. Pouillet (France) 1838 C.L. Althaus (Germany) 1853 Carl Giinter (Austria) 185” August Mouchot (France) 1860 John Ericsson (U.S.A.) 186” C.H. Pope (U.S.A.) 1875 William Adams (England) 1876 Abel Pifre (France) 1878 S.P. Langley (U.S.A.) 1881 J. Harding (England) 1883 Chas. Louis Abel Tellier (France) 188” A.G. Eneas (U.S.A.) 1900 H.E. Willsie (U.S.A.) 1902 C.G. Abbott (U.S.A.) 1905 Frank Shuman 1906 Charles Fery (France) 1906 G. Millochau (France) 1906 Frederico Molero (Russia) 19”l M.L. Ghai (India) 1950 M.L. Khanna (India) 1950 Date of First Table There has been little systematic development of solar machines. Past developers have been accused of ignoring economic considerations so that the solar engine systems of the past were not cost—effective. Perhaps economics had always been a consideration of the early inventors. These inventors were pioneers and were enthusiastic about free solar power and probably realized that equipment depreciates. Fossil fuels were abundant and cheap. The demise of each 28 product, that was a technological success, was a result of the solar engines inability to compete with fossil fuel engines. With increasing difficulty in obtaining cheap fossil fuel, solar engines will continue to become more competitive. If the design of solar engines is approached with the proper economic perspective, then cost effective designs will result. From the data of these historic engines, a level of expectation can be established. The areas (collector efficiency, engine efficiency, power output and collector area / one brake horsepower) are given in Table 1—3. Table 1-3 gives an excellent guide to use in feasi- bility studies. Shuman and Boys, in the author's opinion, conducted reliable experiments. One of the problems of determining overall efficiency is the problem in deter- mining the solar insolation. Many of the investigators had no way of being certain about the quantity of sunlight striking their collectors. However, the determination of horsepower is easily done, and the best information can be obtained in the value of collector area per one brake horsepower. It will be assumed that these solar enthusiasts published only the best results which would be recorded at solar noon on a clear day. It would also appear that: l. 100 ftZ/lbhp is a goal that will be somewhat challenging to reach. (Willsie, Boyle and Ericsson claimed to have reached this.) 2. 150 ft2/lbhp should be an easily obtainable figure with modern systems. 29 TABLE 1-3. Past Performances of Solar Engines and Collectors INVESTIGATOR COLLECTOR COLLECTOR OUTPUT AREA ENGINE 8 DATE 8 SIZE EFFICIENCY bhp bhp EFF. Mouchot 5.22 m2 099 (1878) Truncated Cone ° Ericsson Parabolic (1868— trough in 72% 1870) series Ericsson Parabolic l bhp IIMIft2 12% trough l bhp 16" x 11' Adams Hemisphere 70% 2,5 bhp 503 2.3% (1876) ”0 ft. d1a. 1 bhp Pifre Parabolic .065 bhpl538 0.5”% (1880) bhp Eneas Truncated (1901) Cone2 79.6% 6”2 ft Eneas Truncated (1903) Cone2 73.3% 700 ft South Truncated _ Pasadena Cone Claimed 2 7 329 Ostrich 33'6" major 10 hP 1£31££_ ' ° Farm diameter. Probablel bhp (1901) 15' minor ”~25 hH diameter. Willsie Flat Plate 50% (1902) Double glass Willsie Flat Plate 85% 6 hp 100 12% Boyle 600 ft 1 bhp (190”) Shuman Flat P1 te 100 50% 3.5 h 5% (1907) 1200 ft? p l bhp Willsie Double glass 303ft2 Boyle Flat Plate 50% 15 hp 1 bhp 25% (1908) 1000 ft2 30 TABLE 1-3 (Cont'd) INVESTIGATOR COLLECTOR COLLECTOR OUTPUT AREA ENGINE 8 DATE 8 SIZE EFFICIENCY bhp bhp EFF. Shuman Trough with 9 (1911) sides 2 30° %E%E— 10,295 ft p Shuman— Parabolic 55.5 Boys Tracked ”0.1% bhp 183 8.6% (1913) East-West 63 max 1 bhp 13,269 52.” min C.G. Abbott Parabolic 1/2 hp (1936) Trough The apparent engine efficiency from history range from 1/2% to 25%. The average engine efficiency would be 10%. For example, if a parabolic concentrator has 70% efficiency and the solar engine has 12% efficiency, the overall effi- ciency is: n 3 .12 X .70 = .08” : 8.”% Calculating the overall efficiency of an engine with a 100 ft2/lbhp ratio: 1 bhp X 100 x 25”5 _ 100 X 300 l (D 0 (fl o\° The 300 BTU is the assumed average solar insolation per hr ft2 at solar noon. From the example, it takes a 70% efficient collector coupled to a 12% efficient engine to equal a 100 ft2/1bhp efficiency ratio. FOr economic 31 feasibilityistudies, 10% efficiency overall seems possible if the assumption is made that past systems can be duplicated with minor improvements. 1.8 Objectives There has been a need demonstrated for such research. The author received numerous letters from researchers in the third world countries asking for more information in response to a paper published at the Second World Hydrogen Conference in Zurich (5). The most important application of solar mechanical power is in water pumping applications in developing countries. After searching the literature, and the United States patent office, it became obvious that solar engine technology needs additional research efforts. Solar engine development appears to be a near virgin research area with immediate applications. The objectives of the research were to: 1. Establish from the literature an expected level of performance. 2. Make economic judgments as to the feasibility of solar mechanical power. 3. Assemble the necessary theoretical tools to help produce a solar engine. ”. Build and analyze a demonstration model. CHAPTER 2 SOLAR INSOLATION 2.1 Solar Constant and Surface Insolation Solar insolation is the energy per unit area per unit time that hits a specified location. This value is essen- tially a constant in outer space. The distance between the sun and earth varies with the seasons, and there is some minor variation of the solar constant (solar radiation in space). The present accepted value is 1353 watts/m2, but variation ranges from 1390 to 1310 watts/m2 (6). However, the energy that reaches the earth's surface is significantly different. Shown in Figure 2-1 is the solar insolation versus time at the ”00 North Latitude on February 21 (10). The total area under this curve (Figure 2-1) would represent the daily normal solar insolation, and it equals 29,981 kJ/m2 day (2,6”0 BTU/ft2 day). For most practical applications, the solar insolation can be read from the ASHRAE tables included in the appendix. A sample has been included and is presented in Figure 2-2. Radiation received at the earth's surface is attenuated by atmospheric scattering and absorption. The sun-earth distance varies, and the air mass is constantly changing. ' These factors must be considered if a mathematical model is to be developed for the surface insolation. 32 33 BTU/HR—rr2 308-e- 30 5 :“"““‘-*-‘-----—-- 295 ‘F-~----------- 27” "*-----do-. 22”.. 69a J l I l I l j l 1 l l 6 7 8 9 10' ll. 12 l. 2 3 ” 5 6 TIME O'CLOCK FIGURE 2—1. Solar Insolation ”00 North Latitude - February 21. 3” . . 1. - . .., 1 _ 3. [SOLAR POSITION AND INSOLATION, 40°19 LATITUDE FI M75 SOLAR TIME a EOLALPPSIUON Elm. ‘7. TOTAL INSOLATION ON SURFACES ' A79 PM . AU 1.. [11‘3" gourifé'ansufifir thlmfif—T ___109n_A_L_, 110912. 30 1'0 S’.‘ I _ i _. .11 3" unfl : 9 SJ s3 M2 n EI'MTLsiiSE 291 10 g 16.8 uu.o 239 83 155 171 182 187 171 . ”8 M9 7» H7 n8 n7 7w ,nu n3 1L 1 mm m0 n9 1% 2w 2n ”012% 53 12 SUQFAES g 0.0 2239___0_159__j_2701 291 303 305 253 1 .1 amnm111u_fisim NOCT‘”F‘ ' nan 7 5 98 727 59‘ m’wnwlfi“wl%44%tme%%7 g g 13.3 32.2 229 73 119 177 125 I 127 107 ' 1n 2 3 . .2 77a 132 195 205 709 709 157 2.8 35.9 295 178 755 757 271 757 710 11 1 38.1 18.9 305 205 293 305 310 309 235 1-... '1LIZUREAE'2'Q‘ __,__7 0.0 J 12308.1 _215fi__3,05_,_319_g__323 317 295 ‘ _. g __ 13111111719755 ‘ 6”O 141” 2060 2 6 MAR 21 g I“ 5 11.9 80.2 171 95 55 155 2253 215? 1732 9 g g; $5 50 1m 1m 1m 38.1n 89 10 2 “g 93 M2 in 25 2V n3l2m 1m 11 . 91.9 297 218 273 775 771 . 258 175 1 97.7 22.5 305 217 310 313 307 ; 293 700 12 50.0 0.0 .__.101_ 1.2.5.2.. .322 __32_5_ 320 2 305 208 . squgge p.113 TOTALS . 2915_, 1852 72308—1 2330 ‘1‘2286 "*‘2174‘ ” 198C FIGURE 2-2. ASHRAE Tables. 2.2 Transmittance of Solar Radiation through the Air Mass Radiation is equally absorbed or scattered in the earth's air envelope. Dust, air molecules, and water vapor attenuate the sun's energy. The amount of attenuation depends upon the mass of air the radiation must pass through. The quantity of air between the surface of the earth and the sun varies with time and terrestrial location. This amount of air is directly proportional to the air mass index. The air mass is defined as (6) m = 1 (2.1) Cos ez where m is the air mass ratio and 82 is the angle between the zenith (perpendicular to the earth's surface) and the sun's rays. If the sun is directly overhead, the cos 82 is one and m equals one. If the sun is 600 from the zenith, then m 35 equals two because the cos 62 is one-half. In other words, the path that the solar radiation must traverse is twice as long at 82 = 600 as it is at 82 = 00. The intensity of the radiation at the surface varies according to the zenith angle 92. A sunset can be observed with the naked eye because the path length of radiation through the atmosphere is long as compared with path length when the sun is directly overhead. There are two types of radiation received at the earth's surface. Beam radiation is the solar radiation that is received from the sun without direction change. This is the radiation that enters the earth's atmosphere. Diffuse radiation is the solar radiation after its direction is altered. The reflecting and scattering of the beam radiation by the atmosphere produces diffuse radiation. Flat plate collectors can use diffuse radiation, but solar collectors that concentrate the rays, generally, cannot utilize this small component. As can be seen from the previous discussion on the air mass, the longer the path through the atmosphere, the greater is the attenuation of the terrestrial insolation. Using Bouger's law equation (9) I = I e'km (2.2) where Ib is the terrestrial insolation of beam radiation, I0 is the solar constant, "m" is the air mass, and "k" is a constant that represents the absorption constant. If m were 36 zero in (2.2), and Ib would equal the extraterrestrial radiation, which is the solar constant. The definition of the average atmosphere transmittance, Tatma is the ratio of the radiation received on the collector to the solar constant fatm : Ib / IO (2.3) In Figure 2-3, a schematic representation is given of the quantities involved. ZENITH J °$ ‘kamrubz FIGURE 2—3.’ Air Mass. 12 is the zenith angle, a is the altitude of the sun, Iatm can be found using (2.”) for clear and dry air. 37 + e-.65 m(z) (2 9) 2 e-.095 m(z) Tatm ' where m(z) = [[1229 + (519 sin (1)2]16 - 519 sin a]%%%% (2.5) and P(z) equals the atmospheric pressure at elevation Z feet above sea level, P(o) is the atmospheric pressure at sea level, a is the angle of the sun. To approximate P(z) in Equation 2-5, an aviator's rule of thumb, which states that pressure changes one inch of Hg per 1000 feet of elevation, can be used. Equation 2.” does not account for particulates and water vapor. Hottel (8) has developed an equation to correct for non—clear day transmittance. ‘k/COS 02 (2.6) Tatm : a0 + a1e where the constant a al, and k are compiled in table form. 03 Some values are given in Table 2-1. a0, a1, and k are a function of the altitude and visibility. To illustrate the use of (2.6), for an air mass equal to l and 2 at 23 km haze model at sea level is calculated: m = 1 r = .1283 + .7559e"3878(1) 1:.6” m = 2 T = .1283 + .7559e-'3878(2) 1:3.”8 38 TABLE Coefficients of a0, a1, and k Altitude above sea level (km) 0 05 1 L5 2 (15V 23 km haze model Visibility a. 0.1283 0.1742 0.2195 0.2582 0.2915 (0.320) a, 0.7559 0.7214 0.6848 0.6532 0.6265 (0.602) k 0.3878 0.3436 0.3139 0.2910 0.2745 (0.268) 5kmhaz£model Visibility a. 0.0270 (0.063) 0.0964 (0.126) (0.153) (0.177) a, 0.8101 (0.804) 0.7978 (0.793) (0.788) (0.784) (0.573) 0.4313 (0.330) (0.269) (0.249) k 0.7552 _—-—.. ,..._ 2.3 Solar Geometry The Ib found in Section 2.2 is the direct normal beam radiation. Section 2.2 is sufficient. another important factor must be considered. For tracking solar collectors, the Ib found from However, for fixed collectors, The collector does not face the sun at all times, and therefore, the projected normal area will change. projected area in Figure 2-” is: FIGURE 2-”. PROJECTED AREA A2 = A1 cos 0 Projected Area. As an example, the (2.7) 39 As can be seen in this simple example, A2 approaches zero aséiapproaches 900. (6 is measured from the vertical.) It becomes obvious that for fixed collectors, this geometric projection in the path of the beam radiation must be deter— mined. To calculate the magnitude of the energy incident upon a horizontal surface, four quantities must be evaluated. These quantities are found from equations 2.8, 2.9, and 2.10. The angle of declination is given by 6 = 23.95 sin {360 (2§fl_i_g) (2.8) 365 where n is the day of the year. The angle of declination, 6, is the angle the sun's rays make with the plane of the equator. The equinox is the time of the year when the sun is directly over the equator. At this time, the angle of declination, 6, equals zero. The sunrise hour angle, W can be calculated from 8’ cos ws : —tan 6 tan 6 (2.9) where WS is the sunrise hour angle, 6 is the latitude with north positive, and 6 is the angle of declination obtained from (2.8). The hour angle W is the angle of the sun off the meridian. Solar noon would be zero. Each hour, the hour angle would move 150 with mornings as positive. In Figure 2-5, the hour angle, latitude, and angle of declination are shown. ”0 6 (1.5711005) ‘7) 111551 UATO R) ‘ PO 5:. ‘\ - (oecuumow '5 INERTDUWI U0 HOUR RME 5m: mew 01- TOP mew or EARTH . EARTH SSLHV FIGURE 2-5. Angles Defined. The length of the day, N, can be found from the equation: _ 2 N — 15 WS (2.10) where the units on N are hours. The final value needed is the daily extraterristrial solar energy falling on a horizontal surface in kJ/mz-day £12 11 360m 0 7.6” 10 [[1 + .033 cos( 365)][A + B]] A = cos 6 cos 6 sin WS 2 W . . B = S"s1n 6 s1n 6 (2.11) 360 where I0 is the solar constant per hour, n is the day of year from 1 to 365. 6 is the latitude, 6 is the angle of declin- ation, and WS is the sunshine hour angle. 91 The average horizontal radiation can be calculated from Hav = HO (a + bx /100) (2.12) where X is the percentage of sunshine and a and b are values related to meteorological conditions. Values of "a" and "b" for some locations are given in Table 2.2 (12). To determine the hourly radiation from the daily, Hav’ use Figure 2-6 from Liu and Jordan (1963) (7). The total hours from sunrise to sunset is found from (2.10). Reading upward from the total hours to the intersection of the proper "hour from solar noon" line, the ratio of hourly radiations on a horizontal surface to the daily radiation on a horizontal surface from Figure 2.6 will determine the amount of hourly radiation on a horizontal surface. The values obrained thus far are for horizontal surfaces. To obtain the interterrestrial insolation on a tilted surface, (2.13) is used (6) cos at = H__ (2.13) Hav R = ______ b cos 92 where H is the hourly or daily radiation depending on the un1ts of Hav and cos 0t = cos(6 - 8) cos 6 cos W + sin(6 - s) sin 6 and cos 82 = cos 6 cos 6 cos W + sin 6 sin 6 All the angles have been previously defined except "S" 92 TABLE 2-2. Constant for Equation 2-ll* Location Average X a b Albuquerque, New Mexico 78 .”l .37 Atlanta, Georgia 59 .38 .26 Blue Hill, Massachusetts 52 .22 .50 Brownsville, Texas 62 .35 .31 Buenos Aires, Argentina 59 .26 .50 Charleston, South Carolina 67 .”8 .19 Darien, Manchuria 67 .36 .23 El Paso, Texas 8” .5” .20 Ely, Nevada 77 .5” .18 Hamburg, Germany 36 .22 .57 Honolulu, Hawaii 65 .1” .73 Madison, Wisconsin 58 .30 .3” Malange, Angolia 58 .3” .3” Miami, Florida 65 .”2 .22 Nice, France 61 .17 .63 Poona, India 37 .30 .51 (Monsoon Dry) 81 .”1 .3” Stanleyville, Congo ”8 .28 .39 Tamanrasset, Algeria 83 .30 .”3 * Where X = 0, the value of "a" would be representative the diffuse radiation. When X = 100 percent, the value of a + b would have to equal the atmospheric transmittance. of ”3 FOR TOTAL RADIATION I FOR DIFFUSE RADIATION HOUR FROM SOLAR NOON 9.0000 p 0.04 'DAILY RADIATION 071.71 HORIZONTAL SURFACE 0.02 RATIO' HOURLY RADIATION ON A HORIZONTALSURFACE HOURS FROM SUNRISE T0 SUNSET L 1 1 4 L 60 75 90 I05 IZO SUNSET HOUR ANGLE .0, 6097.“ FIGURE 2-6. Hourly Radiation Chart ( 7). which is the angle of the collector with respect to the ground. Rb is applicable only to beam radiation. Diffuse radiation is not directional to any extent and will not be as important in concentrating collectors. So the hourly or daily value is obtained from (2.13) where Hav is either the daily or hourly horizontal insolation, Rb is the factor to correct for orientation. 2.” Solar Time Equation 2.1” gives a relationship between solar time and the local time: Solar time = Standard time + E + ”(LS - L1) (2.1”) "E" can be estimated from Table 2-3, LS can be found in Table 2-”, and L1 is the local longitude. It should be noted that the published "E" values vary with time and must be read from current published charts. 99 TABLE 2-3. Equation of Time "E" MONTH MINUTES January 1 — 5 February 1 - 13 March 1 - 13 April 1 - 5 May 1 + 3 June 1 + 3 July 1 - 3 August 1 - 6 September 1 0 October 1 + 10 November 1 + 16 December 1 + 10 TABLE 2-”. Standard Meridian for Local Time Zone (6) ZONE 1?: Eastern 750 West Central 900 West Mountain 1050 West Pacific 1200 West CHAPTER 3 SOLAR COLLECTORS 3.1 Introduction There are two broad categories of solar collectors, concentrators and flat plate collectors. Most of the engines of past times used tracking concentrators. Shuman and Willsie—Boyle engines both operated from fixed flat plate collectors. Ether and sulphur dioxide were heated from hot water flowing through a flat plate collector (1). In Table 1.3, the efficiencies for engines using flat plate collectors were, in general, higher than the concentrating type. Some of these quantities should be questioned, but the author has verified what Shuman reported. Shuman, in 1907, had 50% efficiency with a flat plate collector and ”0.1% with a parabolic concentrator. The author has had similar results. Earlier investigators may have not known the correct amount of interterrestrial insolation. Published discussions on concentrating collectors expect higher efficiency because of a smaller absorber area. However, radiation losses are very high from non-selective absorber surfaces as can be determined. It is difficult to look at an operating absorber with the unprotected eye which indicates large radiation losses. The author believes that flat plate collectors and concen- trating collectors, under test, will have comparable efficiencies. The re-radiation losses are to the fourth ”5 ”6 power of the absolute temperature. Unless special consider- ation is made in the absorber design, it may be difficult to exceed flat plate collector efficiency. A design to lower re-radiation is shown in Figure 3—1. This invention by William R. Powell is included in the appendix (31). Flat plate collectors will be the least expensive of the two types. If actual working models have comparable efficiencies, then the selection of the collector type will be made based on economics and engine efficiency. The concentrators have much higher temperatures. The efficiency of the engine is directly proportional to the peak operating temperature, and, therefore, engines operating from concentrating collectors will have higher efficiencies. This is verified with the Carnot engine principle: T 0C = l-Ji (3.1) arnot TH As the temperature, TH’ approaches infinity, the efficiency would approach 100%. Of course, the concentrator temperatures are limited. The absorber temperature is limited theoretically by the sun's temperature. The second law of thermodynamics would be violated if the absorber temperature exceeded 5,762OK., the average sun temperature. The technological aspect would further limit the absorber temperatures. ”7 «aw-.0 .......- 5...... .. w '- . . u ' . 26 .......... ‘ ." o ' ' - . t\\‘-. 0 Paroboloid Mirror 4 FIGURE 3-1. Patent No. ” 033 118 by Powell. Receiver for Collecting Solar Energy. ”8 3.2 Flat Plate Collectors Flat plate collectors have powered solar engines in the past and their analysis should be discussed. The application of solar engines may initially be centered in warm sunny regions or used in summers for agricultural purposes in colder climates. The treatise will be for single transparent covers which are more efficient than multiple covers in warm climates. An analysis of flat plate collectors goes as follows. The first law of thermodynamics states that: Energy in = Energy out + Change in stored energy. E- = E + AE (3.2) In most flat plate collectors, the AE, stored energy, is negligible. In the flat plate collector analysis, the objective is to analytically measure the energy leaving the system. The first law applied to a collector is (6) Bi = A[[H(Ia)]b + [H(ra)]d (3.3) E = m(hé - hi) + UBA(T o ' Tair) +.UTA(T cover ' TSky) (3.”) plate ”9 where A = transparent cover area in m2. ‘ normal (Equation 2.13) insolation. m U” 1 Hd = diffuse insolation. (To) = transmittance-absorptance product. m = mass rate of flow through collector kg/hr. hé = enthalpy of fluid out of collector kJ/kg. hi = enthalpy of fluid into collector kJ/kg. UB = the overall heat transfer coefficient out the back. kJ/hr m2°C. UT = the overall heat transfer coefficient out the top cover. kJ/hr m2OC. sky = the temperature of the sky in ° K. _ 1 ° ' O Tcover - the temperature of the a1r in K. The energy that is used to produce work in the solar engine is: Ew = m(he - hi) (3.5) In a testing situation, (3.5) is obtained by direct measure- ments. If the collector is an air system, (3.5) becomes Ew = 90.2 CMM(Te — Ti) (3.5) where CMM is the volume rate of flow of inlet air in cubic meters per minute. Te and Ti are the respective exit and inlet temperatures. For water systems, (3.6) becomes E = 139.9 LPM(Te - T ) (3.7) w i 50 where LPM is the liters per minute of water flow. The incoming radiation, A [[Hb + HdJ], can also be measured with a solarometer. The efficiency could be easily found by direct measure- ments using (3.9): 0 = m(hé — hi)/A(Hb + Hd) (3.9) If the collector system is a new design, then the quantities of (3.3) and (3.”) must be solved, and the numerator of (3.9) would represent the unknown quantity in (3.3) and (3.”). In Figure 3-2 is a small hand-held solarometer useful in measuring the denominator of (3.9). FIGURE 3-2. Solarometer Measuring A(Hb + Hd). 51 The value of Ub’ the overall heat transfer coefficient through the back of the collector can be determined from 1 Ub : l/hi + Xl/kl + X2/k2 + l/hO (3'10) where hi = convective heat transfer coefficient inside the collector BTU/hr—ft2 ° F.or kJ/hr-m2° c. h0 = convective heat transfer coefficient outside the collector. x = thickness of material in feetcm1meter. k = thermal conductivity of material in BTU/hr-ft ° F. The convective heat transfer coefficient can be found for a vertical surface using (16) h = .99 + .21 Vel (3.11) where "Vel" is the air velocity in ft/second. Table 3-1 gives some simplified convective heat transfer coefficients. As can be seen, Ub is easily obtained from (3.10). Ut is much more tedious to calculate, and is an iterating process. The problem is evident from Figure 3-3. Ut’ the heat transfer coefficient through the cover plate, has radiation and convection in parallel. The temperature of the cover must be known to be able to determine the value of the radiation resistance. TABLE 3-1. 52 DESCRIPTION Air-Forced Convection Vertical Plane with air velocity from 16 to 100 feet/sec and approximately 70° F. Vertical plane with air velocity less than 16 feet/sec and air temperature approximately 70° F. Convective Heat Transfer Coefficients (16) EQUATION BTU/hr-ft2 °F. .5(V)0'8 = .99 + .21 V ----------------------------------- db—--------—----——-- Air-Natural Convection with L a characteristic length in feet and AT the temperature difference between the surface and the fluid Small Vertical Plates Large Vertical Plates Small Horizontal heated facing Large Horizontal heated facing Small Horizontal cooled facing Plates being upward Plates being upward Plates being upward = .29(AT/L)0'25 = .19(11'1')°333 = .27(AT/L)0'25 = .22(AT)°333 = .12(AT/L)0°25 53 -rAIR I I ‘27' 13‘C. I <3 .1 CIDVTZFK R T? Tzr- C .1-P LATE FIGURE 3-3. Heat Transfer Through Cover. r’ the resistance to radiation flow, is (l - el)/el + l/F1-2 + (l - E2>Al/€2A2 (3.12) 0(T22 + T12) (T2 + T1) where Emittance of surface 1. m |,_.1 II Emittance of surface 2. ('0 I\) II Fl-2 = Shape factor from surface 1 to 2. Area of surface 1. 11> H 11 ' Area of surface 2. 11> 1x) 1 The resistance from the absorber plate to the trans- parent cover would have 59 and (3.12) is simplified to 1/8 - l + 1/8 p C (3.13) Rr(Plate-Cover) = 2 2 0(TC + Tp ) (TC + Tp) where TC and T are the respective temperatures of the cover P and the absorber plate. The resistance to convective flow is _ 1 RC(Plate - Cover) - H; (3.1”) where hi is the convective heat transfer coefficient inside the collector. The sum of the resistances across the system would give the overall heat transfer coefficient (Ut) which is given by: l Ut : 1/ + / l_3*l_ + ep - 1 1/sC + 1 ep h- h 2 2 2 2 1 O OCTC + Tp )(TC + Tp) 0(1‘sky +TC )(Tsky+TC) (3.15) l Ut = — ZR (The last term in the denominator comes from assuming Esky = 1.) If the cover temperature, Tc’ were known, (3.15) could be solved. To obtain TC simply write the first law of thermodynamics around the cover plate. The system is shown in Figure 3-”. 55 /’ ‘\ I \ 1 1 cryvzn? \ I \ .. , 4- SYSTEM ~ _ ~ _ _ / ELI FIGURE 3-”. Energy Balance on Cover. Equation (3.16) gives the Ei and (3.17) gives E O. o(T§+-Tcu) Ei : hi(Tp - TO) + (3.16) 1/ep + l/CC-l ._ 9 9 LO - hO(TC - Tsky) + oeC(TC - Tsky ) (3.17) Equating (3.16) to (3.17) is the equivalent of stating that the heat into the cover equals the losses from the cover. Everything is known in the equation except TC (temperature of the transparent cover). The best method of solving TC in (3.18) is by trial and error. 0(T 1* - TC”) h.T+T+ p l( p C) 1/8p + l/eC- u e 9_ l hO(TC-T8ky) +O€C(TC Tsky ) (3.18) 56 When the left side equals the right side of (3.18), the correct balue of TC is known. This value of Tc is then substituted into (3.15) where Ut can be determined. The temperature of the sky, T is found from sky’ T = T - - 6 (3.19) where TSky and Tair are 1n C. In determining Ub and Ut’ some fixing of design para- meters was necessary. The plate temperature, Tp, was established. The plate temperature is equal to where Ti equals the inlet temperature of the collector and Te equals the outlet temperature. From (3.20) and normal expected conditions placed upon Ti and Te’ Tp can be deter- mined. Re-examining (3.”) will show that the quantity m is the only unknown in the equation. The energy coming onto the plate is found from (3.3) which is the next item to discuss. Then, (3.3) is equated to (3.”) which is shown in (3.21) A[[H(arflb'*[H(raHd]‘:m(hé"hi)'+UBA(Tp"Tair)'iUTA(Tc"TSkY) (3.21) where the subscripts are b beam radiation d diffuse radiation. 57 The Hb is determined by methods of chapter two. The Hd’ the diffuse radiation, is not precisely obtained. Three assumptions can be made: 1. The diffuse radiation comes from around the sun and the angular correction factor Rb would equal Rd. (Rb = Rd applicable on a clear day.) The diffuse radiation is uniformly distributed across the sky. (Rd = 1 in this case and would be applicable on cloudy days.) The diffuse component is not used with concentrating collectors and is usually small and can be neglected for a conservative approach. (The system will work better than predicted.) The (10) product is equal to (to) = Id n (1-a)pd] = Ia/[l - (l - a)pd] (3.22) ll M8 I 0 where T isthe transmittance through the glass and the a is the absorption of the absorber plate, ad is the diffuse reflectance, n is the number of covers and pd can be deter- mined from Table 3—2. TABLE 3-2. Diffuse Reflectance pd (6) Number of Covers 3g 1 .16 2 .2” 58 T of equation 3.22 is determined from Figure 3-5 and a from Table 3-3. TRANSMITTANCE O 20 4O 60 80 ANGLE 0F INCIDENCE FIGURE 3-5. Transmittance, r, Neglecting Absorption (6). TABLE 3-3. Absorption Emissivity of Various Surfaces (16) Surface Material 0 e "Nickel Black" (Selective Surface) .90 .10 Flat Black Paint .96 .88 Green Paint .50 .90 Concrete .60 .88 Dry Sand .82 .90 Black Tar Paper .93 .93 Green Rolled Roofing .88 .9” Water .9” .96 White Paint .20 .91 Aluminum Foil .15 .05 59 It can be seen that all the quantities of Equation 3.22 can now be calculated except the mass flow rate m. Being the only unknown, 5 can be determined from (3.22). The collector efficiency can then be calculated from (3.9). 3.3 Simplified Analysis for Flat Plate Collectors The method of this section has been verified by tests from solar installations. The solar module designed by the author is shown in Figure 3-6. Another vertical air system was designed by R.C. Schubert and the author (5). This vertical unit is pictured in Figure 3-7. Both of these systems use air as the medium of energy transfer. Both have air flowing between the inside of the cover and the absorber face. A comparison is made between this simplified analysis and actual test results. Fluid enters the inlet of a flat collector at Ti and leaves at Te. The simplification comes in assuming that the temperature in the fluid is equal to the discharge temperature throughout the collector. As an example, if the inlet temperature is 90° F and the discharge temperature is l”0° F, the procedure assumes that the entire fluid temperature is l”0° F. In the operating region for flat plate collectors, this simple modification has been quite accurate. The radiation component through the cover is neglected, and the increased fluid temperature increases the convective losses. This modification adjusts for the radiation losses which were not considered. 60 FIGURE 3-6. Solar Test Module. FIGURE 3—7. Vertical Solar Collector. 61 Figure 3-8 shows the electrical analogy of this concept. -TAN< “‘31—— '/h¢ \7 1_I (ZCNUEHK T?:=r’b/AQ( FINTE FIGURE 3-8. Heat Flow From Collector (Simplified). The Ut of the cover becomes 1 = 3.23 Ut l/hO + k/Ax + l/hi ( ) which is much simpler than (3.15). Equation 3-10 is still used to calculate the back losses. In Figure 3-9 is shown a small 3 ft x 2 ft flat- plate solar collector. Test data taken from this panel include Ti = 3.3° C (Temperature in) Te = 21° C (Temperature out) m = 1.17 kg/min (Mass flow rate) I = 3567.1 kJ/hr-m2 (Solar insolation) A = 0.557 m2 (Area) Veli = 12.95 m/sec. 62 The actual efficiency is: n z m C2 AT : 1.17 x 50 x 1.012(21 - 3.3) = 53 = 539 IaA 3557.1 x 0.557 Using the simplified method of analysis, proceed as follows: Using Table 3—1 to find hi and ho, with 3 ft/sec inside air velocity. hi = .99 + .21(92.99) = 9.9 BTU/hr-ft2 °F‘= 202.9 kJ/hr-m2°C ho = .99 + .21(22) = 5.51 BTU/hr-ft2 °F = 119.57 kJ/hr-m2°(3 U _ 1 t l/hi +11x1/kl + l/hO U _ l t ‘ l/202.” + .003/1.05 + 1/119.7 U = l = 50 29 kJ/hr-m? °C t .0099 + .003 + .0087 ° Qcover : Ut A AT Qcover = 50.29 x .557 x (21 - 3.33) 0cover = 592.9 kJ/hr Note, the temperature outside equaled 3.33° C. Assumed panel temperature was at 21° C throughout. 1 .00”9 + 0.213 + .0087 Ub = = 9.917 kJ/hr-m? °c Qback = Ub A AT 9.917 x .557(2l - 3.33) = 93.97 kJ/hr Qinsolation = 3557.1 kJ/hr2 x 0.557 m2 = 1985.9 kJ/hr 63 Quseful : Qinsolation - Qlosses Q 1986.9 - (592.9 + ”3.”7) useful Quseful = 1350.5 kJ/hr 1350.5 : ———— : 9 D 1986.9 67.90 This calculated efficiency is 67.7% as compared with actual efficiency. For the few test comparisons made, this simplification worked reasonably well. However, the tests were made on air systems operating with relatively low temperatures and should be used with caution. The tedious procedure of Section 3.2 shows a need for an apparent temperature. The apparent temperature would be elevated high enough to account for radiation losses without actually having to include the traditional radiation equations. The general form that the relationship might take is T = T apparent + K exit where K would be assumed constant over a certain range and would increase with elevated temperatures. By further development, this concept could be used for other types of collectors such as concentrators. 3.” Solar Concentrators Because of the potential for increased enginesafficiency, as was discussed in Section 1.1 and 3.1, solar concentrators 6” will play an important role in the production of mechanical power. The concentrators are not necessarily more efficient than flat place collectors. There is potential for lower efficiencies. The author has found that a concentrator can have a poor efficiency. The reasons for this poor efficiency were not always obvious. An analysis is developed here to show the ratios of concentration must be larger than one to have the flat plate and concentrating collectors equal in efficiency. AR = AC: nC nO An energy Actual receiver area that is white from concen- trated solar rays. Aperture of collector. Projected area normal to the collector. Instantaneous collector efficiency. Optical efficiency. The fraction of specularly reflected radiation that strikes the absorber. This quantity will, in general, be unknown because it is a function of the quality of the surface. A prudent engineer would use a value less than 100%. Collected solar energy. Beam solar radiation at the collector aperture. Overall heat transfer coefficient. balance on a collector would give: Qu : nOIbAC ' UL(TC - Tair>AR (3'2”) 65 The inSIantaneous efficiency is: Qu (3.25) IbAC n : By substituting (3.2”) into (3.25), another form of the efficiency is l (3 26) I1) 0 where the concentration ratio C equals one for a flat plate collector and C> l. or a concentrator. If the values of UL’ I? and lb are ignored, then the efficiency of a C’ concentrator would be higher than a flat plate collector. However, Ib, the beam solar radiation, is less than the solar insolation for a flat plate collector which includes Ib and Id, the diffuse radiation. Also chis much higher in a concentrator, and UL is a function of the cube of the higher TC' As an example, compare the efficiency of a flat plate collector to a concentrator where the assumptions are: 1. Temperature of concentrating absorber is twice as hot as the temperature of the transparent cover on the flat plate collector. 2. Optical efficiency is 100% in both. 1 3. U = L l/hwind + l/eoT3 ”. Assume both are receiving the same insolation. 5. e = l for both the cover and the concentrator absorber. 66 With these assumptions, equate the efficiency of both and calculate the necessary concentration ratio, C. 0flat plate : nconcentrator l T ' Tair _ l l/ - + 1/ T3 I - hWind 8C0 b I 1 (2T - TA) 1 l - 3 _ l/hwind + €AU8T I Ib C I 1 (T T ) i 1 ‘ (2T - TA) 3 - ' = 3 l/h ind + l/OT I a1r Kl/hwind + 1/80T c C l/hwind + l/oT3 2T _ TA = 3 -—-———— \l/hwind + 1/80T T - TA (3.27) In (3.27), the first quantity on the right is larger than one. The second quantity is also larger than one. Therefore, the concentration ratio must be larger than one to have the efficiency of a flat plate collector equal to a concentrating collector. It becomes obvious that solar concentrators do not have necessarily an inherent efficiency advantage. The analysis of solar concentrators follow the same general approach as given in Section 3.2 for flat plate collectors. Writing an energy balance on the receiver gives Energy in = Energy out + Change in stored energy. The energy in would depend on the reflectance of the concentrator's surface, and the amount of reflected radiation that is intercepted by the absorber surface and would affect 67 the "energy in" quantity. The equation for the energy into the receiver is Ei = Aalbpnoa (3.28) where Aa is the aperture area, Ib is the beam radiation, 0 is the specular reflectance of the mirrored surface, 00 is the optical efficiency, a is the absorption of the receiver. Equation (3.28) is for a tracking collector. I is found from (2.3) and (2.6) These equations are b rewritten here for convenience. -k/cos 02 e If the concentrator is fixed or partially fixed, the "energy in" would be 5i = AaH noao (3.29) where H, the hourly radiation, is found from (2.13). The energy leaving the receiver would occur from heat losses through the walls of the absorber and from the useful energy transported to the engine. Equation 3.30 gives the analytical relationship as E0 = m(he - hi) + U Ar (Tr - T ) (3.30) L a where m is the mass flow rate, hé and hi are the respective enthalpies out and in, Ar is the area of the receiver, UL is the overall heat transfer coefficient, Tr is the receiver 68 temperature, Ta is the environmental temperature. The change in stored energy, AE, within the receiver equals AB : m2U2 - mlUl (3.31) where m2 and ml are the masses inside the receiver at the end and beginning of the analysis. U2 and U1 are the inter- nal energies of the fluid inside at the end and beginning of the consideration. Solar systems never obtain a steady state condition where AE = 0, but for a short period of time, this value will be very small. Therefore, "AE" can be neglected in most cases. Equating "energy in" to "energy out" gives: AaIbpnod = m(he - hi) + ULAR(TR — Ta) (3.32) The specular reflectance is reflectance where the angle of reflection equals the angle of incidence. Values for specular reflectance are given in Table 3-”. TABLE 3-”. Specular Solar Reflectance Surface 0 Aluminum Foil .86 Back-aluminized 3M Acrylic .86 Back-silvered White Glass .88 Electroplated Silver .96 69 The optical efficiency represents the percentage of energy that leaves the reflective surface and contacts the receiver. Because of poor alignment, small irregularities and manufacturing tolerances, some of the radiation will miss the receiver. The optical efficiency is defined as: n : Actual Radiation Flux on Receiver (3 33) 0 Total Radiation Flux Possible ' These values have been obtained theoretically, but because of the large number of variables experimental measurements are preferred. The optical efficiency should be part of a construction specification and therefore established by the solar engine system designer. Values should be greater than 0.9 for most smaller systems. The absorption, 0, can be easily found from the litera— ture. Table 3-3 gives a few values that are applicable. Cavity absorbers should be used whenever possible where the value of a would approach unity. A large range of temperatures are possible with a solar concentrator. By adjusting the flow rates through the receiver, the temperature in and out can be controlled. The enthalpies are a function of the temperatures. Referring to (3.32), the designers trial values would be: Aa = Aperture size of collector. p = Specular reflectance. ”0 = Optical efficiency. 70 a = Receiver absorption. Area of the receiver. 3> II r h; = Exist enthalpy. hi'= Entering enthalpy. The above values are chosen by the solar engineer and would be selected by various design requirements. The environ- mental terms in (3.32) that are determined by time and location would be: Ib Beam component of solar insolation. Ta Air temperature. The values that require further calculations are: UL Overall heat transfer coefficient. T r Temperature of the receiver. The unknown that must be computed from (3.32) is the mass flow rate, m. The electrical-thermal analogy of heat flow in the receiver is presented in Figure 3-9. I —' c. 011'} +Tg-x'rrrrqx T .——_b [EWFLU‘D p ‘ 1 T R:.AXIR 'RaJ/h; 'R-.-.-. I/h, A559“? FIGURE 3—9. Heat Transfer into Receiver. 71 The value of heat flow through the receiver wall must equal m(h; - hi). The heat flow through the wall is: (T - T - ) m(hé — hi) = Ar r f1Uld (3.3a) AX/k + l/hi UL of (3.32) becomes: u = l (3.35) L 2 2 1/h0 + l/erO(Tr + Ta )(Tr + T ) a Equation 3-3H has been simplified by neglecting radiation. Also, the value of hi’ if the liquid is boiling, is usually large. Substituting (3.3M) and (3.35) into (3.32) gives Ar(Tr - Tfluid) Ar(Tr - Ta) 0 _ AaIbpnO ‘ A + 2 2 X/k + 1/hi 1/h0 + l/EPO(TP + Ta )(Tr-+Ta) (3.36) where Tfluid is the mean fluid temperature inside the receiver, AX is the receiver wall thickness, k is the thermal conductivity of the receiver wall, hi is the convective heat transfer coefficient on the inside of the receiver. The other terms have been previously defined. If the temperature of the surface, Tr’ can be found, the mass flow rate can be solved and the efficiency can be determined from (3.25) or (3.26). To calculate Tr’ use (3.36). Every term in (3.36) is known except Tr' Because of the fact that Tr cannot be factored out easily, a trial and error solution becomes necessary. The correct value of Tr will equate the left side of (3.36) to the right. CHAPTER 4 ACTUAL COLLECTOR TESTS COMPARED WITH ANALYSIS ”.1 Parabolic Collector Test and Comparisons In any science, it becomes important to compare the theoretical analysis to actual test data. Assumptions and simplifications can produce invalid theory. The material presented in Chapter 2 and Chapter 3 can be used to predict performance and then be compared with collected data. Shown in Figure u-l is the spherical dished concentra- ting collector used to generate the data in Table u—l. The four-wheeled cart in Figure H-l held the supply water that was kept at a fixed height manually. A tube coming out of the tank entered into a vertical cylinder. The face of the tube was white from the radiation flux. At the bottom of the tube is a discharge line that drained into a bucket. FIGURE u-l. Testing System for Table u—l. 72 TABLE H-1. 73 Data for Solar Concentrator (Condensed from Data in the Appendix) TIME SOLAR WIND TEMP TEMP TEMP FLOW EST METER 2 VEL AER .AIR OUT RATE DATE BTU/HR-FT FT/MIN F F 0F ML/SEC 1:55 270 MOO 78 78 86.5 6.25 May, 1978 2:00 270 600 75 76 86 6.6 May, 1978 2:05 275 600 76 76 86 6.6 May, 1978 2:10 270 600 76 77 87.5 6.6 May, 1978 2:32 150 150—300 58 7O 79 3.31 May 17, 1978 2:39 125 150—300 58 70 75 3.21 May 17, 1978 2:37 100 300 58 70 75 -- May 17, 1978 2:”0 150 300 58 70 76 -- May 17, 1978 2:”5 160 350-300 58 70 75 3.25 May 17, 1978 1:30 265 100 86 77 98 2.38 June 1, 1978 1:35 265 200 87 77 10H 2.39 June 1, 1978 1:38 265 350 87 78 10M 2.37 June 1, 1978 1:55 265 400 87 79 118 2.3 June 1, 1978 1:58 268 350 87 79 120 2.07 June 1, 1978 2:00 265 50 86 80 12H 2.03 June 1, 1978 2:03 265 300 86 80 122 2.11 June 1, 1978 2:05 205 350 86 80 122 2.03 June 1, 1978 74 The hand-held solarometer is shown in Figure u-z. Measurement must be made at the site to accurately determine the solar insolation. The methods of Chapter 2 can be used to determine the solar radiation, and this method can be used to compare with the hand-meter readings. FIGURE H-2. Hand-Held Solarometer. Insolation Calculations On June 1 from 1:30 - 2:00 p.m., the solarometer was reading 265 BTU/hr-ftz. From (2.3), (2.u), and (2.5), the solar insolation can be determined. However, the solar time must be known and the sun altitude must be found. The solution is as follows (located at 86° W longitude): 75 Solar Time Standard Time + E_ ”(LS - LL) (2.1”) Solar Time = 12:”5 + 3 minutes + ”(75 - 86) Solar Time 12:”5 + 3 minues + (-””) Solar Time 12:”5 - ”1 minutes Solar Time = 12:0”. The angle of declination from Equation 2.8 is: 6 = 23.”5 sin [360 (28” + n)/385] June the first is the lSlst day of the year (n = 151). 6 = 21.9° The hour angle is easily calculated by multiplying the number of hours from solar noon by 15°. W = 15 (1:”5 - 12:00) W = 15 (1.75 m) W = 26.25 From (2.13b) (Latitude ”2.25 N) Cos 82 = cos

sin 6 Cos 62 = cos ”2.25 cos 21.9 cos 26.25 + sin ”2.25 sin 21.9 Cos 62 = .616 + .25 = .8668 6 = 29.916° Z a = 90 - 29.916 = 60°. m(z) = [[1229 + (61” sin 60°)2]l/2 - 61” sin 60 %%g% (2.5) _ P(z) _ 1”.21 _ m(z) - (1.15) W - (1.15) m - 1.11 76 e-.095 m (z) + e —.65 m (z) Tatm = 2 = .693 (2.”) Ib : Io Tatm (2.3) 1b = ”860.6 x .593 = 3368.” kJ/hr-m2 CALCULATED: Ib = 3368.” kJ/hr—m2 MEASURED: Ib = 265 BTU/hr-ft2 = 3009.5 kJ/hr-m2 By Equation 2.6 Tatm = a0 + ale—k/COS 6z (1.5 km alt) :atm = .2582 + .6523‘°291/°866 = .725 CALCULATED: I = 352” kJ/hr-m2 b As can be seen, the calculated values were higher than the measured values; but from an engineering viewpoint, there were correlation. What appears to be a clear day can be deceiving. Had the 5 km haze model been used for Equation 2.6, the results would have been: -.330/.866 Ta = .26 + .793e = .667 lb = .667 X ”860.6 _ 2 I — 32”2 kJ/hr-m 77 Efficiency Calculations From the measured data, using the 2:05 time on Table ”-l . : kg 3600 sec : kg m 6.6 ml/sec x g/ml 1000 g ___HF-__ 23.76 hr Qu = m (h; - hi) = 23.76 5% u.19 kJ/kg"C (30-2u.u)° C Qu = 557.5 E; AaIb : 1.1195 x 32u2 AaIb = 3629.” %% measured efficiency is n = Qu/AaIb = 557.6/3629.” E .16 o\° Testing n = 16 For calculating purposes: Aa = 12.05 ft2 = 1.1195 In2 o=9 no=8 a = .96 _ 2 _ 2 Ar - .02778 ft — .0026 m (hé - hi) = 10 BTU/1bms = 23.23 kJ/kg 78 275 BTU/ftZ—hr = 3123 kJ/mZ-hr 1b = Ta = 750 F = 29.990 C k = 229 BTU/hr-ft O F = 1330.9 kJ/m O C AX = .125" = .00318 m hi 2 550 BTU/hr-ft2 O F = 11995.9 kJ/hr—m2 O C ho = 3.09 BTU/hr-ft2 O F = 53.15 kJ/hr-m2 O C m = 53.3 1b/hr = 29.2 kg/hr. Substituting the above into Equation 3.36 and T (Temperature on outside of receiver) gives: P A (Tr - T P fluid) Ar (Tr, - solving for Ta) AaIbpno“ : Ax/k + 1/hi + The first step in analyzing the efficiency is from the above equation. If the receiver has —— > 0.6 (Threlkeld) where Di and D0 are the respective inside and diameters, the linear forms of the resistance tion can be used. limits, the conduction becomes: Q = [29k (Tl - T2)]/[ln (Do/Di)] 2 1/hO + 1/ero (Tr + Ta2)(Tr~+Ta) to solve T r a outside to conduc- If the walls are thicker than the stated 79 Every element of (3.36) is known except the convective heat transfer coefficients hi and ho. With these values calcu- lated, Tr, the surface temperature of the absorber, can be evaluated. To determine ho’ use h0 = .99 + .21 vel (”.l) where vel is in ft/sec and is less than 16 ft/sec. This equation (Jinges), which is applicable for air flowing parallel to a vertical plate, is h = a + b m“ (9.2) The values for (”.2) come from Table ”-2. TABLE ”-2. Factors for Equation ”-2 (l6) Surface Vel l6 ft/sec let/secvel 100 ft/sec a b n a b n Smooth .99 .21 1.0 0 .5 .78 Rough 1.09 .23 1.0 0 .53 .78 The focal point of the concentrating collector covered an area of approximately 2" x 2". For all practical purposes, this could be considered a vertical plain area. The hi is found from (”.3) (16). This equation is applicable for water flowing down the inside of a vertical 80 tube having inside diameters<_ . i + _1_ . 1 k hi hO era (Tr? + Ta7)(Tr + Ta) Equation 3.36 with higher receiver temperatures becomes _ Ar (Tr - Tfluid) Ar (Tr - Ta) Achpnoa ‘ (AX)/k + l/(hi) + 1/hO + 0 (9.9) 81 Substituting the values of this real problem gives (1.1195) (32”2) (.9) (.8) (.96) = .0025 (Tr - 300.2) + .0025 (Tr — 279.9) .00318 + 1 1 1330.9 11””6” 63.16 The mass flow rate by (3.2”) would be . , _ 9 _ Ar (Tr “ Tfluid) m (he hi) ' ITAX)/k + lfhi m = 109.3 kg/hr. The efficiency by (3.25) will become 0 = (Qu)/(ACIb) = (10”.3 x 23.23)/(1.ll95 x 32”2) o\° n = 66.6 The actual measured efficiency was 16 % which indicates some fundamental problems with the test apparatus. The value of optical efficiency was essentially unknown, but the discrep— ancy between the actual and the theoretical seems too large for such a simple explanation. Examining (”.”), it appears that the convective air film insulates the receiver regardless of the receiver temperatures. The l/hr term approaches zero at high tempera- tures. By trying to solve (3.36) with an iterating process, '(98'8) UT aoaas pus {stag Aq punog st J; '(9'fi) moag punog st Tn sasqm I , -Q/I + X/(XV) _ 0 q 0 (9e 5) (£981 - J1) 10 JV + (ptnIgL _ al) av - 0 U0 I v ssmoosq 98'8 uotienbg 9 - - 1 = 5131 '(6I'6) moag PUHOJ St 0X8; sasqm (9'9) _[(91 + J1) (35181 + ZJL) o 3/I] = 70 I smoosq ITEM Tn pus ‘sssso; uotiosAuos sqi ueqi JsBJe; qonm sas sssso; uotietpea ieqi spew sq III“ uotidwnsse sq; '(AXSI + J1) (32381 + 3J1) 0 3 = J9 sasqm (9'9) I_(*19/I + PUIMQ/I) = 10 (9) st asAtsosa sqi go iustotggsoo asgsueai issq IIPJBAO sq; °&;uo AitootsA ate go uotioung 9 SEN Oq was; sAtiosAuoo sqi isqi pus ‘Atsnosueitnmts psaansoo uotietpea pus uotissAuoo go moIg issq ISIIPJPd ieqi sasm (99:9) qitm uotiosuuoo ut pssn suotidmnsse sq; 'psstoasxs sq ptnoqs uotineo inq ‘stqsidsoos pus stqeuosssa AasA sq pInom % 9°99 go GHIPA psisInsteo sq; °sanisasdmsi go uotioung e iou psmnsss sem was; Oq sq; °uotietpsa uodn pssodmt uotieitmt; stqi go saeme smeosq Joqine sqi Z8 83 The temperature of the receiver is around 833 °K by these assumptions, and the efficiency is practically the same as before. The theoretical analysis is, therefore, valid if the receiver will actually absorb .96 % of the radiation flux. It appears that in actual installation, the receiver should be concaved to improve the absorptivity. The receiver used in the test had a convexed surface. The low efficiency of 16 % was produced, in part, by the improper angle of incidence of the radiation on the absorber surface. ”.2 Flat Plate Collector Tests and Comparisons Flat plate collector analysis as presented in Chapter 3 agrees well with actual data. Shown in Figure ”-3 is an auxilliary space heating system designed by the author. FIGURE ”-3. Auxilliary Space Heating System. 8” The collector is an air system with a single glass cover and a black cloth absorber glued onto fiber glass insulation. In Figure ”-” is shown another air collector. This vertical flat plate collector uses a Sun—Lite cover with a black painted aluminum foil absorber that is glued to insulation. The covering is undulated to provide for thermal expansion. This system was designed by R.C. Schubert and the author. Efficiencies have reached 63 % with snow reflection. FIGURE ”—”. Vertical Solar Collector at Western Michigan University, 85 A small solar test panel is shown in Figure ”-5. The student is measuring the exit temperature and the solar insolation with a hand-held solarometer. Solar Test Panel. FIGURE ”-5. Tests were conducted on two identical panels with different absorbers. In Table ”—3 is a summary of the results. The entire test results are included in the- Appendix. The panel is 2' x 3' and is described in the Appendix. TABLE ”-3. Absorber Tests (March 25) Mass Flow Rate lb/min Temperature In Temperature Out Collec- Collec- Oollec- Collec- Collec- Collec- tor A tor B tor A tor B tor A tor B fi1=2.750 fi1=2.5”6 ”0° F ”0° F 71.1° F 71.9° F 86 The efficiency of Collector A and B at 12:12 solar time on March the 25th from the test data of Table ”-3 is Q/A = (m Cp AT)/A (Q/A)A = (2.750 x 60 x .2” x 31.l)/6 = 205.25 ”A = 205.25/31”.1 = 65.3 % (Q/A)B = (m Cp AT)/A (Q/A)B = (2.5”6 X 60 X .2” X 31.9)/6 = 19”.92 nB = 19”.92/31”.1 = 62.06 %. Using the long form for flat plate collectors in Chapter 3 gives the following results from the test data of Table ”-3 (compared with Collector A) by TP 2 (90 + 71.1)/2 : 55.5°F = 13° C by ho = .99 + .21 Vel = .99 x .21 (19.5) ho E 9 hi = .99 + .21(13.5) = 35 by T =T -6=”.””-6=-l.55°C=27l.5°K. 87 Solving for Tc’ temperature of cover, by Equation 3.18 9 9 _ hi (Tp - TC) + [o (Tp - TC )]/(l/ep + 1/eC - l) - . ) + o s (T 9 — T 1+) P C C h (T - T o c a1 ll (0 U is solved from (3.15). Assume a = .88 and e p c T 10 kJ/hr—m2° C. II C. From (3.21) m = 85.25 kg/hr _ m CDAT _ _ n - (.557)(3557) - (85.25 x 1.012 x l7.3)/1986.9 — .75 o\° 71:75 The calculated efficiency by the methods of Chapter 3 gives: 75 o\° . Actual efficiency is: 65.3 %. .3 II By careful examination of the process, it is seen that hi and ho’ the convective heat transfer coefficients, effect the calculation greatly. Also, the sky temperature equation has much to do with the final results. The biggest factor 88 comes in using clear day insolation. The actual test was run under unknown solar insolation. CHAPTER 5 SOLAR ENGINE ECONOMICS 5.1 Introduction Some very conclusive truths can be obtained from an economic analysis of solar engines. The fact that solar engines are not part of modern technology indicates past problems, since their development can be traced back to 1615. Ericsson in 1883 built a solar engine that will be a rival to modern developments, and he realized that his solar engine system could not compete with cheap fossil fuel. John Ericsson could see the demise of the fossil fuel era when heavy use of fossil fuel had barely started. As fossil fuels become more difficult to obtain, solar engine tech- nology will become more competitive. Yet, fundamental changes in the engine design are necessary to eventually have working models that are cost effective. Cost effective design means that the cost to obtain power from the sun is equal to or less than the cost of power from fossil fuel engines. Chapter 6 deals with design problems to reduce cost and increase brake horsepower. 5.2 Simple Payback Costing The diesel engine has an overall efficiency of approx- imately 33%. There are ”0,1”0 kJ/liter in diesel oil. Assume the engine's purchase price is Cl and the yearly cost for maintenance is C2. The total annual cost per horsepower 89 90 for a diesel engine would be (5.1) C1 + C + (bhp)d 2685 kJ C3 X t [Cost] = N— 2 .33 X hr-hp X 90,190 kJ bhp diesel IiEer engine (bhp)d where C3 is the cost per liter and t is the number of hours annually of operation. To compare the solar and the diesel engine, the bhp/hr of each engine must be equal. A diesel engine could run 2” hours while a solar engine might operate 6 hours. Therefore (bhp)d x 2” = (bhp)S x 6 (5.2) (bhp)d = l/”(bhp)S where the "d" and "s" are subscripts for diesel and solar respectively. To compare systems, the solar engine will need to be four times larger at best because of its intermittant operation. The annual cost of a solar engine is Ci/N + C; (COSt/bhp)SOlaP : 39(bhp)S , , (5.3) ”(Cl/N + C2) (Cost/bhp) = SOlaP (bhp)d where C1 is the cost of the system depreciated over "n" years. CE is the annual maintenanCe cost. 91 To determine a cost effective design, equate (5.1) to (5.3): Cl/N + C2 + (bhp)d x 1750 x C3 = ”(Cl/N + C2) (5.9) Assume maintenance cost such that C2 = ”C5. Assume equal life of 20 years. For one brake horsepower, Table 5-1 gives the comparison of diesel engine cost to solar engine cost. Equation 5-” with the assumptions becomes: ci = k(Cl + 35,200 C3) (5.5) As an example, consider a small 1 hp diesel costing $600 with a fuel cost of $0.”0 per liter. What can the solar engine system cost? Move to the left horizontally on the 0.”0 line until the vertical $600 column is intersected. Read the solar engine maximum cost at $3,671.30. The procedure of this section is called the simple payback method. The value of the energy is used to pay back the added investment in a solar engine system. The example given shows that $3,671.30 could be invested in a solar device. The difference in the price between diesel and solar engines is about $3,000. The simple payback method fails to take into account returns on the $3,000 if it were invested. Considering the yearly inflation rate, the returns on the invested $3,000 would have difficulty in matching the increased appreciation on the solar equipment. Therefore, 92 cowvmamoo mo mhmow om co ommwm « m.~:mh m.sH:s m.mmms m.m:ms m.NmHs m.m:fis m.mmos ms.om o.mmHm o.osom o.m:m: o.mmm: o.m:m: o.mms: o.m:s: mm.om m.Hmo: m.mmmm m.Hssm m.HNsm m.Hsom m.Hmwm m.Hsmm o:.om 3.:mjm :.momm 3.:mHm 5.:mam 9.:mom 9.:mom 9.5mmm mm.ow m.s:mm m.mmsm m.smmm 0.5:mm m.sm:m m.s::m m.smmm mm.om Doom coma OOOH com com so: com mamHHoo as mpmpflq Lozomomaom\pmoo maawcm Hmmmwa pom “moo Hmdm «mafiwdm memfim mom§m> ocwwcm pmaom pow pmzommmpom\00flam .Hlm mam 23 CC»!D£&¢S€HZ «vvvvm—v )5 1! FIGURE 6-5. Rankine Cycle Schematic. 103 the best choice in certain cases. The hot air engine would have higher engine efficiencies but it would be difficult to capture the rejected heat. The Rankine efficiency is (15) m(h - h ) n = l 2 (6.7) where the enthalpies, h, are references in Figures 6-” and 6-5. There are a number of ways to improve the Rankine cycle efficiency with such devices as reheaters or regenerators. These changes in the basic system must be justified economically. Since many of the engines are relatively small, it appears that the simple cycle without the frills should be used, and the condenser heat will be utilized for heating in cold climates. 6.3 Ericsson Cycle The Ericsson cycle and the Stirling cycle are similar in design. The literature seems conflicting on how the engine worked, but actually Ericsson built one engine after another. It is possible to explain these discrepancies in the fact that details of operation on one engine may not fit another and good business practice protected trade secrets. In New York in 1870, Ericsson built his first "sun motor". The engine was steam driven and used a Rankine cycle. Another engine of different construction was designed and two or three experimental engines were built in 187” (Churchill, 1935). 10” In a letter Ericsson wrote to a business associate, Harry Dilamater, he enthusiastically described how small caloric engines were unreliable because of valve adjustment. He then designed an air engine without valves. "Having found, by long experience, that small caloric engines cannot be made to work without fail, on account of the valves getting out of order, the above solar engine is operated without valves, and is therefore absolutely reliable" (Churchill). In Figure 6-6 is one of Ericsson's hot air engines. FIGURE 6-6. Solar Engine Adapted to Use Hot Air in 1880 ( 3) 105 In Figure 6-7 is a schematic of an Ericsson Engine using valves. The engine also resembles a Brayton cycle. The charging piston pumps air into the heating chamber where, with valves closed, the heat is added at constant volume. (The Brayton cycle adds heat at constant pressure.) The valves open and the pressure produces work on the piston. The work piston would then vent the air through the regenerator (not shown) and out. HEATER K—k (‘IIAIIG 1m Cnxnnxxn ~..» ».1 ..... PISTON "* L- hORK 1.90 PISTON I . L—a— PUHGING ‘ A CHIRGING PISTON Emsmxc L l._ WW2 ‘l W 0 III III I 11“.: j_ if umzmm '” "IT-3 PISTON \ J FILLING — ~-- -mm FIGURE 6-7. Schematic of One Type of John Ericsson's Hot Air Engine (Mernel). The exact thermodynamic cycle that Ericsson's engine followed is uncertain. Most texts accept Figure 6-8. However, the engine of Figure 6-7 would not follow this cycle. 106 The engine has an isothermal compression from 1 to 2, an isobaric heating of the gas in the regenerator from 2 to 3, an isothermal expansion from 3 to ”, and an isobaric cooling in the regenerator from ” to l. The efficiency of this cycle is the same as a Carnot efficiency. SH-SB:Sl-SZ (6.8) 19 TH (Ericsson Cycle Efficiency) P...c.o us-mN‘r I I Job, 3' ’4- 01mg. 0 was. 2. l I on + FIGURE 6-8. Ericsson Cycle. 107 6;” Stirling Cycle The Stirling cycle, developed by Robert Stirling (1870-1878), is being studied for automotive applications using fossil fuel because of high theoretical efficiency (17). The engine has potential in reducing exhaust emissions that are associated with internal combustion engines. The Stirling cycle consists of isothermal expansion and compression, and a constant volume addition and rejec- tion of heat. The theoretical cycle shown in Figure 6-9 is an isothermal addition of heat from 1 to 2, and a constant volume rejection of heat from 2 to 3. This is accomplished by pushing the heated gas through a regenerator with high heat storing capacity. There is an isothermal rejection of heat from 3 to ”. A constant volume addition of heat from ” to 1 is accom- plished by passing the cooled gas through the hot regenerator which adds energy back into the system. I f /VOL=C. /VOL=C. O 'K :3-p FIGURE 6-9. Stirling Cycle. 108 The Stirling efficiency is: _ Qs -- Qr n _._______ 03 Q8 = TH(82 - 31) Qr = TL(S3 ‘ S (5.9) Since July of 1972, N.V. Philips of Holland and Ford Motor Company have been trying to develop the Stirling engine for automotive applications (17). Ford's primary concern at that time was emission control which the Stirling could provide. Recently, Ford has abandoned the project temporarily because of other priorities, but not until tests were conducted on a 170 hp engine. One engine was tested on a dynamoter and one in a Torino test vehicle (17). There was also a Ford/ERDA feasibility study made on an 80-100 hp Stirling engine. The car used was a 1976 Ford Pinto. The noise level was 10 dB below their current cars, but the fuel economy was 25 miles per gallon, lower than the desired 30 mpg. Engine friction and auxiliaries were blamed for the low efficiency. Emission objectives were not met either (17). CHAPTER 7 A SOLAR ENGINE DESIGN 7.1 Economic Comparison of Solar Designs A new concept of design must precede the advent of solar mechanical power. Design technology used for fossil fuel engines cannot successfully be used on solar engines. Solar energy is essentially low density power. Fossil fuel is high density energy. The typical frictional horsepower of fossil fuel engines might exceed the brake horsepower of a solar engine. Solar engines are relatively slow and must be as frictionless as possible. One of the prime consider- ations is to introduce methodology to minimize friction. Another criteria in solar mechanical conversion is to use simple concepts. Simple concepts produce inexpensive engines which are necessary in order to have a cost-effective design. The investment in the capital must be recovered from the value of energy collected. The value of the energy collected would be based on a particular fossil fuel. If the logical competitor is diesel engines, then diesel oil would be used as an equivalent solar energy value. Solar engines must be low cost, efficient, and, as previously stated, as frictionless as possible. The ideal engine would be cheap and efficient, but there are relation- ships between these platitudes that are important. If an engine were very efficient and very expensive, this engine might be rejected and an inexpensive low efficiency engine 109 110 chosen. The relationship between efficiency and cost is determined by cost—effectiveness. This concept was discussed in Chapter 5, but must be constantly stressed. The break-even cost of a solar engine as compared to a diesel engine was given by Equation 5-5. This equation related equivalent power from each engine. In this selection of one solar engine design versus another, (7.1) is applicable. Equation 7.1 gives the savings over N years. Savings = (nIbACC3N).009 - C - C (7.1) 1 2 where n = overall efficiency. ID = beam radiation (kJ/mzday). AC = aperature area of concentrator (m2). C3 = cost of fuel oil/liter ($/liter). N = number of years of life. Cl - initial cost. C2 = total maintenance cost. Equation 7-1 is based on simple payback, and no investment consideration was made. The eggine design that would give the maximum savings from (7.1) should be the preferred design. From this equation, it is easily seen that at higher fossil fuel costs (C3), the more probability that a solar engine will be cost effective. The cost of the engine (Cl) and the reliability whiCh shows up as maintenance costs (C2) enter logically into this relationship. 111 7.2 Engine Design to Minimize Cost One major factor in the success of getting mechanical power from the sun is to start with a simple concept. Ericsson and Stirling cycles have operated from the sun. Both engines will reveal one fault. The engines were not simple. A displacer moves back and forth pushing a gas into and out of the hot zone, and in general, both engines are somewhat complex. The Rankine cycle (steam engine) is simpler in design, but becomes more complex when a boiler, condenser, and pump must be added. The three cycles, Ericsson, Stirling, and Rankine cycles, should not be excluded from consideration, but these systems should be viewed as maximum in complexity. Successful solar engines will need to be simpler whenever possible. Solar engines may find their initial application in pumping water in arid climates. A very simple device for pumping water is shown in Figure 7-1. Savery's ( ”) steam pump is operated by opening the steam valve which pressur- izes the top of the tank forcing the water out and up through the discharge line. The steam valve would be shut and cooling water would flow over the tank. As the steam condensed, a vacuum would form allowing water to be pushed by the atmosphere into the tank. By exploiting the idea of Savery's steam pump, a low cost solar pump concept can be developed. Since there are heating and cooling cycles in the steam pump, two complete systems are needed with a means of shifting the heating and 112 COOLING WATER :' / FORCE PIPE FIGURE 7-1. Savery's Steam Pump. 0 cooling modes at the proper time. Two identical tanks with check valves in the inlet and outlet area are required. Attached to the side of the main tanks are receivers. The receivers absorb solar energy and produce pressure by boiling water trapped in the chamber. Flexible hoses connect the receiver to the main tank. The two receivers are insulated from one another, but they are mechanically fastened together. A one-way hydraulic cylinder with a spring return is attached to the two receivers. When the pressure builds up high enough, the hydraulic cylinder will shift the heating-cooling mode. The system is sketched in Figure 7-2. The simplicity of the system will result in a cheap pump. The four check valves and the spring loaded hydraulic cylinders are standard pieces of hardware. The rest of the apparatus is built by the fabricator of structural steel components. There would be a minimum of machining and very 113 .aazm smaom .mIs mmame ‘ n cofiwosfi / 3 r m7 ’ ImCMHooo Mame % LDUCHH>U oefidmhozm . mafipmom Mame mmhwgomflo 11” little precision fabrication. Most of the structure would be assembled by welding and punching operations. A lower cost pump would be difficult to perceive. The recharging of the receivers with water could be done by the proper location of the flexible hoses on the side of the tank. Another type of design developed by the author is the rotating air or gas engine. It became obvious that valves and displacement pistons were items that contributed greatly to the cost. The design goals were to eliminate both of these elements. Shown in Figure 7-3a is a section through the new rotating engine. The construction consists of a fixed crank ghgft with opposed pistons. The housing rotates and power is extracted from a gear or sprocket (not shown) attached to the housing. The solar concentrator hits an energy con- ducting ring that is something less than half a circle. One ring is being heated which pressurizes tha gas inside the ring. The other ring is being air or water cooled since the ring is outside the focal point of the solar concen- trator. A frontal view is shown in Figure 7-3b. Each heat conducting ring is divided into two parts. From A to B the ring surface is transparent or very readily conductive. With the energy being quickly added to the ring while the piston is near top dead center, the effect of adding energy at a constant volume is achieved. From B to C the rate of heat transfer is lessened by alterations in the energy 115 "’l a? /:olar Radiation P. A I ' iston .W II >{K\\Energy Power From Here EEEEUCtlng .:===£==q Housing Aff.Rotates I‘I Fixed Shaft . ~ . I r 9 g F SJ M\n Piston ”0 Energy Conducting Ring FIGURE 7-3a. ‘Solar Engine Front View. 116 A -Energy‘Conducting:Rings HI'HII' .«jj " p . f . { 511823.30 . I Conducting K vRingS‘ " * 3' s‘ FIGURE 7-3b. Solar Engine Side View. 117 conducting ring. The surface could be thickened to reach the isothermal addition of heat which is necessary to have the theoretical efficiency equal to a Carnot cycle. The cooling cycle would be more difficult to regulate for a tracing of a theoretical Stirling cycle. A coolant sprayed at one point 180° opposite the solar concentrator would produce the desired results. Having the engine retrace a Stirling cycle would produce a theoretical cycle efficiency equivalent to the Carnot cycle. However, practical considerations must be made when using solar power. The sun cannot be regulated. If surfaces of the heat ring are operating at controlled temperatures just to proclaim high theoretical efficiency, it is obvious that available solar power would not be used. This would decrease the overall efficiency regardless of the theoretical analysis. The theoretical analysis considers only the temperature of the gas inside the engine. This analysis assumes the source is controllable. The future heat rings may just absorb the maximum energy over a some- what shortened heat ring. The rotating solar engine is conceptually simple. There are two power strokes per revolution. There are no mechanisms to displace air from the hot and cold zones. There are no valves. The simplicity of the engines meets the solar engine criteria of being non-complex. In modifying the heat ring in the development process of the rotating engine, another useful element was 118 discovered. A new type of engine fulfilling the concept of being simple became possible. The details are discussed more thoroughly in Chapter 9. The engine is operated from a flat plate collector which is sealed and charged. The collector is connected to a piston of the design discussed in the following section. The cooling cycle can be accom- plished in a number of ways. One possible system is shown in Figure 7-”. Another would be to use the pumped water to cool the collector. Solar energy enters the collector. The temperature and the pressure increase. The piston moves down which pumps water. A cable attached to the piston arm pulls a shade over the collector for the necessary cooling cycle. The pressure drops. The shade is removed. The system returns to the starting point where the process can be repeated. 7.3 Minimizing Friction in Solar Engines Frictional losses must be reduced to a very low level in solar engines. The method of design used for fossil fuel engines will not in general be accepted in solar technology. Friction is developed in several areas. The largest and most difficult to overcome is the piston friction against the cylinder walls. Another source is the piston rod guide bushing that keeps the piston and cylinder concentric. Friction is also developed in the main bearings and the ,connecting rod bearings. All of this discussion assumes that reciprocating machinery is being used. Rotating machinery is a choice that is possible, but it is believed 119 pom QEdm .wcwmcm hmaom mpme swam Loyooaaoo smaom .jlb mmame c..- ”.odb—~ 120 that cheaper equipment can be manufactured using recip- rocating devices. Also,— Tensvle sIIengIh 70,000 psi oI RT I . | Tenmle sIIengIn —' IZO.COO as: 0' 8"- 40— Fahque lumiI, IOOO psi 7- Tens-le sheanh ' $0,000 nsi a! RT ' -200 9200 6 0 IOCO Teslinq Iempemlure. F FIGURE 7-ll. Effect of Temperature on the Fatigue Limits of Steels (26). 13” The last material characteristic to consider is thermal conductivity. Thermal conductivity is of prime importance in and out of the engine. Without successful transfer of energy, the engine will not operate. Therefore, top prior— ity must be given to thermal conductivity. In Table 7-3 are given thermal conductivities of various metals. TABLE 7-3. Thermal Conductivities of Various Metals (26) k in BTU/hr-ft F METALS 68° F 212 392 572 752 1112 Pure Aluminum 118 119 12” 132 ll” Al-Cu (95%, 5%) 95 105 112 Al-Si (86.5%, 12.5%) 79 83 88 93 Carbon Steel ' 0.5% 31 30 28 26 2” 20 1.0% 25 25 2” 23 21 19 1.5% 21 21 21 20 19 18 Nickel Steel 20% Ni 11 ”0% Ni 6 Chrome Steel 1% 35 32 30 27 2” 21 5% 23 22 21 21 19 17 Pure Copper 223 212 216 213 210 20” The solar receiver, the heat ring, has to withstand much higher temperatures. There is always the possibility of an engine held in the static operational mode. Without work being extracted, temperature much higher than normal will be encountered. With production engines, all the ques— tions of this section must be answered. The prototype that is discussed in the next chapter is a prototype that was 135 built to prove the principle of operation. Some of the design was based on expediency of fabrication. The selection of material used in future solar engines will be a challenge to the science of metallurgy. At the present level of technology of the rolling diaphragms, the operating temperature is somewhat limited. If pure alumi- num were to be used, the temperature should be under 182° C (360° F) to keep from having creep problems. This tempera- ture would be acceptable as an operating temperature for the diaphragms. The 1100 alloy, commercially pure aluminum, has a yield stress of approximately 9000 psi at 360° F with an H1” temper. This material has good corrosion resistance, but the most important physical property is the high thermal conductivity. The information for each material is easily found in the "Metals Handbook" (26). 7.5 WorkinggMedia in Solar Engines The engine design is an integrated process. One com— ponent affects the next which affects the next, and so goes the procedure. The weakest link in the chain becomes the principle criterion for the design, and satisfying this limiting factor will help fix the design. In the rotating hot air engine, the temperature was fixed at 182° C (360° F) in the cylinder because of creep, and the temperature limits placed on the rolling diaphragms. It can be assumed that the operating media could operate at approximately 182° C (360° F) and 882,530 N/m2 (128 psi) (lbs. per square inch 136 gage) from the working stresses allowed in the rolling diaphragm. (See Section 7.3.) With the temperature and pressure fixed, the working media can be intelligently chosen. Rankine cycles would utilize condensing vapors. The rotating engine will require highly superheated gases. Condensation could cause trouble with the operation. To insure that condensation will not occur, a sketch of the temperature-entropy diagram is helpful. A T-S diagram of water is shown in Figure 7-12 (15). 1- P=qeszeo III/mz (I40 95:) Isz'c. I360) 013'6 (3533' s FIGURE 7-12. T-S Diagram of H O. 2 137 The pressure and temperature maximums would be about 965,266 N/m2 (1”0 psia) and 182° C (360° F) which, as can be seen in Figure 7-12, is just barely in the superheated region. In Figure 7-13, vapor pressures for various working media are given ( 2). To the left the substance would be a liquid. As an example, by locating the point 360° F and l”0 pressure, the materials listed to the left would be in the superheated region given the two properties. It can be seen from this figure that NH3, F22, Methyl Chloride, 802, N-Butane, etc., would not stay in the super- heated phase during the engine heating and cooling cycles. However, these materials are more applicable to the Rankine cycle since condensation is expected in the condenser. The proper substance would be selected from Figure 7-13. In the rotating hot gas solar engine an ideal gas should be used. Air would make an acceptable gas if it were not for the corrosiveness of the oxygen, particularly at higher temperatures. Hydrogen is commonly used in Stirling engines. The ideal gas equation —— = MR = Constant (7.12) shows that there is theoretically no advantage of one gas over another, since (7.12) equals a constant. The main consideration would be the chemical reaction of the gas with the machine components. Inert gases such as Helium and 138 .Am V 0e©02 mcwxsoz smaom pom m0&59090aE0B mSOHsm> mo 0QSmm0sm soa0> .mHIh mmame “8d - 380883“ 139 Argon should be considered. It was found that Freon had definite advantages. This is discussed in Chapter 9. 7.6 Design of Machine Elements It is not the intention of the author to cover topics in machine design that are readily found in texts on the subject. There are some unique areas in solar hot air engines that will require special treatment. Two of these areas are: 1. Thin wall cylinder design. 2. Guide Bushing and Transmission Angle. The cylinder must both heat and cool. With the heat ring, less will be required of the cylinder for heat trans- mission, but in general the cylinder should be as thin as possible. The guide bushings were installed so that rolling diaphragms could be used to eliminate friction. Certain restrictions are involved to prevent the guide bushings from becoming a major source of friction. The two basic problems are illustrated in Figure 7-1”. GUIDE TBUSHle IN WALIS 0" u o 1 # # _ Q I w .— _ —_o FIGURE 7-1”. Hot Air Engine. 1”0 When the transmission angle, 5, becomes large, heavy side loads are put on the bushing. Cylinder Design The objective is to design the cylinder walls as thin as possible for good heat transfer. The first step to achieve this goal is to determine the working temperature using (7.9) ”A .3Tm (7.9) 0 where Tm C is the melting temperature of the metal and T° C would be the maximum working temperature. Equation 7-9 defines the working temperature that is acceptable from a creep perspective. From this equation the yield stress is found at that particular temperature and with a suitable factor of safety, a working stress can be established. (See Table 7-”.) As an example, assume 1100 alloy aluminum is used because of its superior thermal conductivity. From the "Metals Handbook" (26), the melting temperature is: Tm = 1215° F = 6570 C The operating temperature would be: T = (.3)1215 = 3650 F 2 185° C The yield strengths for untempered 1100 aluminum is given in Table 7-”. 1”1 TABLE 7-”. Properties of 1100 Aluminum Alloy At Various Temperatures When Heated for 10,000 hr. (26) TEMPERATURE YIELD STRENGTH 75 F 23.9 C 5,000 psi 3”,”7” kPa 300 l”8.9 C ”,500 psi 31,026 kPa ”00 20”.” 3,500 psi 2”,132 kPa 2,000 psi 13,789 kPa 600 315.5 F F 500 E 250.0 E 1,500 psi 10,392 kPa E 0000 700 371.1 1,000 psi 6,895 kPa Interpolation of the l82.2° C (360° F) would give from Table 7-” a yield stress of 3900 psi. With a factor of safety of an arbitrary 1.5, the working stress would equal: Working Stress = 17,926 kPa (2600 psi) From the rolling diaphragm discussion in Section 7-3, the maximum pressure is 883 kPa (128 psi) inside the cylin— der to avoid using a special diaphragm. The side wall thickness is calculated from the simple thin walled cylinder theory which is given in (7.13). -132 8x 7 2t (7.13) For a ” inch cylinder the example described would give: 17,926.” = 883 x .106/2 x t t = .00261m = 0.1 inch The cylinder top thickness would be determined by using 1”2 the circular plate equation with clamped edges. The equation for stress at the center is (27) 3Pr2 2 (7.19) ”t S : where t is the plate thickness, P is the pressure in kPa, r is the radius of the cylinder. The maximum stress determined by Equation 7-1” is at the edge. In our example the cylinder top is: 17,925.9 = 3 x 883(.10612)2/”t2 t = 0.01019m = .” in Guide Bushing The initial step in designing the guide bushing is to determine the reactions at the extremities of the bushing. If the forces are excessive, two bushings are needed with the proper spacing. The piston pressure in general is known, as is the piston area. The reaction force would be the pressure multiplied by the area. The vector relation- ship is shown in Figure 7—15. The downward reaction on the end of the piston rod is Fy = PA Tan 62 (7.15) where P is the piston pressure, A is the piston area and 62 is the angle between the piston center line and the connecting link. The reaction R on the outside of the 1”3 bushing would be given by summing the moments R = F —- (7.16) where X1 and X2 are the length of rod extension and the bushing length respectively. Fy is found from Equation 7.15. The value of R is the force that the guide bushing sustains without binding. Bearing loads are determined mainly by experience. In Table 7-5 is a table of current practice for rotating shafts. The application is somewhat different in that there is linear motion through the bushing. However, the same wedging mechanism that keeps the rotating shaft supported on an oil film is present to a certain degree in a linear bushing. The pressure in a linear bushing would range from minimum on the outer edge to zero somewhere internally. Using the rotating hot air engine as an example, the connecting link is ”.5 inches and the pitman arm is 2 inches. At a rotational angle of ”5 from the machine center line, the angle 02 defined in Figure 7-15 is 18.31. The Fy, from (7.15) using a ” inch piston with 883 kPa (128 psi) pressure, is 2366N (532 lbs). Assuming a force distribution as shown in Figure 7-16, the average force would be R/2. 199 TABLE 7-5. BearinggDesign Pressure (29) DESIGN PRESSURE TYPE OF BEARING IN PSI Diesel Engine Mains 800-1500 Connecting Rods 1000-2000 Wrist Pins 1800-2000 Electric Motor 100-200 Marine Lineshaft 25—35 Steam Turbine and Reduction Gears 100-250 Automotive Gas Engine Mains 500—700 Connecting Rods 1500-2500 Air Craft Connecting Rods 700-2000 Centrifugal Pumps 80-100 Railway Axle 300-350 Light Lineshaft 15-25 Heavy Lineshaft 100-150 1”5 FIGURE 7-15. Forces on the Guide Bushing. FIGURE 7-16. Force Distribution in Bushing. 1”6 The average pressure in the example would be p = ——3—— = 5— (7.17) 2D X L/2 LD where L is the bearing length, D is the diameter, and R is the reaction from (7.16). The pressure from the example is calculated to be: P = ——§§3—— = 7335 kPa(106” psi) 1 x 1/2 This amount of pressure caused metal to metal contact in the bushing, and excessive friction made the first engine inoperative. The bronze bushing was replaced with a Thomson ball bushing. It appears that pressures in a standard bronze bushing must be much less than 689 kPa (100 psi). Further research is needed in this area if this design is to be used. Considering Table 7—5, it would be expected that pressures under 689 kPa would be required. This lower pressure can be achieved in several ways. The bushing length "L" can be increased. If the length is excessive, two bushings can be used with a space between them. The stroke length could be shortened, which would decrease the angle ez, or r2 could be lengthened. It appears that the best solution would be to use linear ball bearings. A picture of the ball bushing is presented in Figure 7-17. 1”7 FIGURE 7-17. Typical Ball Bushing. The engineering procedure to size a ball bushing is as follows: 1. Find the minimum allowable bushing size using (7.18). Use Figure 7—16 to find K in (7.18). L Locate the bushing from the sample Table 7—6. 2. Compute the allowable load capacity from (7.19). 3. Predict the travel life expectancy from (7.20). ”. Find the minimum allowable shaft hardness from (7.21). The minimum allowable bushing size is (25) Rav R = (7018) R KI X KH where RR is the rolling load rating, R is the average av load capacity and KL and KH are found from Figures 7-19 and 7-20 respectively. 1”8 LOAD CORRECTION TACTOR, K; I 2 3 5 7 IO 20 30 SO 70 100 200 400 IOOO 2000 TRAVEL LIFE IN MILLIONS OF INCHES FIGURE 7-19. Ball Bushing Design Chart (25). Lbb'ain'oQi-Io'o IL-j. I I Lj—DJ I .. l l J I . 60 50 JO 30 20 IO O SHAFT HARDNESS, ROCKWELL C LOAD CORRECTION EACTOR, Kn FIGURE 7-20. Ball Bushing Design Chart (25). 1”9 The allowable load capacity is calculated from (7.19) RA = KL x KH RR (7.19) where RA is the allowable load capacity and RR iS‘Uu3r01ling load rating from (7.18). KL and KH are found from Figure 7-19 and 7-20. The difference between the allowable load capacity, RA, and therolling load rating, RR, is based on a travel life of 2 x 106 inches with a Rockwell 60C shaft hardness. The allowable load capacity is an adjustment for any variations from these initial specifications. By reading the proper KL which is found from (7.20), the travel life can be estimated. Rav KL = -————-— (7.20) RRXKH where Rav is the average load capacity actually on the bushing, RR is the rolling load rating and KH is selected from Figure 7-20. The shaft hardness can be computed from: R av KL : _____—— (7.21) KH is used in Figure 7-20 to select the proper shaft hard- ness. The terms of (7.21) were previously defined. A sample bearing table is shown in Table 7—6. 150 TABLE 7-6. Ball Bushing (25) Bushing Number Bore I .005 Length Rolling Load Rating Normal (RI) Maximum Super 8 .5000 1.250 180 lbs 255 lbs Super 12 .7500 1.525 970 500 Super 15 1.000 2.250 780 1050 Super 29 1.500 3.000 1550 2000 Frictional force on the ball bushing is found from F = 0N (7.22) where u is the coefficient of friction from Table 7-7 and N is the applied load. N can be either equal to RR or RA' The frictional horsepower can be claculated from hp friction = FV/33.000 (7.23) where F is found from (7.22). The velocity, "V", in feet per minute, must be determined from the length of pitman arm "r" (see Figure 7-15), and the revolutions per minute of the engine. The velocity of the rod through the bushing would be Vel = 2n rl n sin 62 (7.2”) where n is the rpm of the engine, rl is the pitman length in feet, and 62 is the angle in degrees between the pitman arm, r1, and the piston centerline. The form would be a constant found from (7.22), but the velocity will vary according to (7.2”). 151 TABLE 7-7. Coefficient of Friction (25) . . - -.- —. Coefficients of Rolling Friction (fr) of Ball Bushings P fr 2 — where P equals frictional resistance and L equals applied load LOAD m 95 or ROLLING LOAD RATING BUSHING IIIJIIELE: CONIZITION (for 2,000,000 inches of travel life) '0' CIRCUITS lUBRICATION 12595 10095 7535 5095 2595 Ia'n 95". 3 8 4 No Lube .0011 .0011 .0012 .0015 .0025 1/2". 52'8” Grease Lube .0019 .0021 .0024 .0029 .0044 on Lube .0022 .0023 .0027 .0032 .0045 99'2 1" s No Lube .0011 .0011 .0012 .0015 .0022 Grease Lube .0018 .0019 .0021 .0024 .0033 OII Lube .0020 .0921 .0023 .0027 .0036 110" 5 No Lube .0011 .0011 .0012 .0014 .0019 19:0 4" Grease Lube .0015 .0015 .0017 .0018 .0022 OIILube .0018 .0018 .0019 .0021 .0027 Coefficients of Static Friction (to) of Ball Bushings LOAD IN % OF ROLLING LOAD RATING 125% 100% 75% 50% 25% .0028 .0030 ' .0033 .0036 .0040 Values are based on use of shafts of recommended dIameters. hardened to Rockwell 58-630. The unique features of solar engine technology are: 1. High temperature exposure of the engine. 2. Frictionless piston sealing by rolling diaphragms and ball bushings. The design of the other engine components such as bearings, gears and structures can be found in traditional texts on design of machine elements. The engine designer will build prototypes with the theory presented here and in other machine design texts. Actual working commercial, engines will result from the experience gained on experi- mental engines. No amount of analysis can replace the 152 art of applied engineering which simply makes the theor- etical model work by trial and error techniques. CHAPTER 8 ENGINEERING ANALYSIS OF A ROTATING SOLAR ENGINE 8.1 Introduction and Engine Description In Section 7.2, three engines were described. They were invented by stimulation from past experiences. By understanding how Savery's water pump works, hundreds of variations of this design could be imagined. Finally, the mind conceives of what the inventor perceives as the simplest design. The result is a "new invention". Later, added gadgets to overcome something overlooked often com- pletely disguise the idea source. This new machine will help foster an idea in someone else, and so goes the process. The rotating hot air solar engine came from the same series of events. Heat must be applied externally to a piston after top dead center, and so as not to violate the second law, heat must be rejected after bottom dead center. This engine idea was born in understanding the Carnot engines. (See Section 6.1.) The Stirling engine was also partially responsible. The mental creativity began to think of ways to add and subtract heat to the cycle. The rotating engine with a fixed crank came forth. The heat ring was added as a gadget to solve the adding and rejecting heat problem. An engine was born. From this engine better and simpler for— mulation may result. Therefore, with this solar engine design selected, the theory was applied. The design was 153 15” analyzed and the performance of the engine was predicted. Many practical "lessons" were learned in building three models. The design material of Chapter 7 resulted in part from Sun Engine I and Sun Engine II which never were totally completed. Problems encountered often found subjective solutions and finally Sun Engine III resulted. The rotating engine, Sun Engine III, frame is pic— tured in Figure 8-1. The lower cylinders and the fixed crank are shown fastened to the frame. FIGURE 8—1. Solar Engine Frame. 155 In Figure 8-2, an exploded assembly photograph of the lower cylinder, the piston, the rolling diaphragm, washer, and the upper cylinder can be seen. The piston, the diaphragm and the washer are slipped over the piston rod where a nut secures the components. The lip on the diaphragm is clamped between the upper and lower cylinders. FIGURE 8-2. Solar Engine Piston Assembly. 156 The assembled engine is displayed in Figure 8—3. The stand holds the crankshaft in a fixed position. The entire engine rotates acting as a flywheel. Power is extracted from a sprocket fastened to the frame. The circular heat rings rotate in and out of solar concentration focal point. FIGURE 8-3. Solar Engine Assembly. 157 8.2 Cycle Analysis of the New Engine Since the Ericsson and Stirling cycles have efficien- cies theoretically equal to the Carnot cycle, it becomes important to achieve this efficiency in any new engine. To have the efficiency equal to the Carnot engine, simply make the engine expand and compress the gas at a constant temperature with the entropy difference equal for each isothermal process. This process is shown in Figure 8-” (15). FIGURE 8-”. Cycle Diagram. 158 Heat is added in the Stirling cycle from the regener- ator between 1 and 2. Heat is added isothermally between 2 and 3 and rejected to the regenerator from 3 to ”. Finally, heat is rejected to the environment from State ” to l. The process where heat is added and rejected, excluding the isothermal processes, could be constant entropy, volume, pressure, or any process. The important relationship is L, (8.1) and that heat is added or rejected to regenerators during the non-constant temperature processes. With this condi- tion, heat is added or rejected outside the engine only in the isothermal processes. As an example, prove that a constant volume process from State 1 to 2 and 3 to ” does satisfy Equation 8.1. From State 1 to 2, dQ/T = mcvdT/T ds U) I (D II 1 m cV (1n T2 - 1n T1) 82 - S1 = m c 1n TH/TL V From State 3 to ”, ds dQ/T - mc dT/T V U) I U) II 3 m cv (ln TL — 1n TH) 159 S” - S3 = m C 1n TL/TH Cl) (1) I U) 4: II S c 1n TH/TL which gives: Rearranging (8.2): With Equation 8-1 satisfied, the efficiency of this cycle is easily shown to be 0 = Work/QS = Q8 — Qr/Qs n = l - TLAS/THAS TI : l-TL/TH which is identical to the Carnot efficiency. Note the heat rejected to and from the regenerators is internal shifting of energy and does not enter into the efficiency calculation directly. This cycle analysis is relevant to this section because the design concept was centered around making any new engine follow approximately a Stirling cycle. The solar engine can be made to follow a Stirling cycle. The heat ring can have varying thermal conductivities such that the objectives are achieved. The schematic of Figure 8-5 will help to illustrate this cycle. 160 93 FIGURE 8-5. Solar Engine Schematic. A curved tube called an energy conducting tube (a) is attached to the cylinder. This tube (a) is connected to the space above the cylinder (f). Concentrated solar radiation strikes this hollow energy conducting tube and transfers its energy to the gas that is above the piston (b). This tube spans an arc of 180 degrees, but it is divided into two parts, 01 and 62. During the 61 portion of the tube, solar energy can readily transfer into the enclosed gas, but as the engine rotates, the focal point strikes the 02 section where thicker walls restrict the energy transfer. Since the piston is near top dead center at 51, there is little volume change. If radiation from 161 the sun can be added quickly, then this portion of the cycle would approximate a constant volume process. Likewise, in 02 by proper selection of the materials and thickness of the wall of the tube, expansion of the gas could take place isothermally. The opposite end has identical hardware, and there are two power strokes per revolution. The crank- shaft (0) is locked between supporting brackets. The entire engine rotates, and power is taken from the rotating engine by such means as attaching a sheave to the engine housing. The pistons (b), (d) are 180 degrees apart. Since the engine rotates, the heat rings and cylinder heads alternate— ly rotate into and out of the focal point of the solar concentrator. While one end is being heated, the other end is being cooled by convection and radiation. The energy conducting heat rings (a), (g) can receive energy by conduction through a thin opaque surface or the side facing the solar concentrator can have a reinforced transparent cover. The process would start with piston (b) nearing top dead center and piston (d) approaching bottom dead center. The cylinder head and heat ring with piston (b) moves into the focal point of the solar concentrator. If this section of the energy tube were transparent, the pressure would rapidly increase with little change in the volume. Pressure above piston (b) produces a reactionary force on the engine housing that causes rotation. After a rotation of 01, the construction of the energy conducting tube could be altered to an opaque surface with varying 162 materials or thickness so that during 02 the expansion could take place isothermally. During 03 the volume changes very little through a relatively large engine rotation. As before, this portion of the process could be considered to transfer heat at a constant volume. The remaining isother- mal compression would occur during 0”. The basic cycle is complete in one revolution with two power strokes per revolution. The cyCle is divided into four segments: 1. 01 is the rotational section when the piston is near top dead center. The energy tube admits energy quickly during a time when little volume change occurs. The process is assumed constant volume. 2. 52 is the rotational period when a lesser amount of energy is added to the energy conducting ring. This is accomplished by changing the material of the energy ring. An isothermal process is obtained by adding a controlled amount of energy such that the internal energy remains constant. In other words, work is extracted in an isothermal process. 3. 63 is the rotational period where the energy con- ducting ring moves out from under the solar concen- trator. Cooling begins. It is assumed that the process is constant volume because the piston is at bottom dead center where a small volume change occurs within a relatively long period of time. 163 ”. an is the rotational period where the process is cooled isothermally. This is done by transferring heat at the same rate that work is performed in compressing the gas as the piston returns to top dead center. 51 + 82 + 83 + 8H = 350 (8.3) The described processes follow the relationship q/dt = mcvdT/dt + W/dt (8.9) where internal energy term is zero during the isothermal processes and the work term is zero during the assumed con- stant volume processes near the bottom dead centers and the top dead centers. The thermal efficiency would be: Work _ QA ' QR Heat Supplied QA Efficiency = The heat added is QA : Q1-2 + Q2-3 where Q1-2 is heat added during the constant volume process near top dead center and Q2_3 is the heat added during the isothermal expansion. The heat rejected is 16” where Q3_u is the heat rejected during the constant volume process near bottom dead center and Q”-l is the isothermal compression. Q _ Q (Q _ + Q _ ) - (Q _ + Q - ) Eff.=A R: 12 23 39 91 QA (Ql-2 + Q2_3) (8.5) Writing (8.”) over the constant volume process 1-2 gives: q = mcvdT Q1_2 = ch(TH - TL) (8.6) Writing (8.”) over the isothermal process, the internal energy term is zero and: Q2_3 = f Pdv = MRTHln V3/V4 (8.7) Writing (8.”) over the constant volume process 3-” with work equal to zero and: q = chdT Q3-” = mCV(TH - TL) (8.8) It should be noted that (8.6) equals (8.8). Writing (8.”) over the final isothermal compression with the internal energy term zero, Q”-l becomes: 9 = W 165 Q4_l = f Pdv = MRTLln vu/vl (8.9) Substituting (8.6), (8.7, (8.8), (8.9) into Equation.8—5 gives: (Q - + Q - ) - (Q _ + Q _ ) Eff. : l 2 2 3 3 9 9 1 = (Q1-2 + Q2-3) ch(TH - TL) + MRTHln V3/V9 - ch(TH - TL) - MRTLln V”/Vl : ch(TH - TL) + MRTHln V3/V2 THln V3/V2 - TLln V”/Vl THln V3/V2 Referring to Figure 8-”: V1 z V2 v3 = vu v3 v, so —- = —— v2 V1 v3 v, Therefore, 1n __ = ln-—— v2 v1 T T and Eff. = H ' L TH (8.10) Equation 8.10 is the efficiency of a Stirling engine and the approximate thermal efficiency of the new modifi- cation as described. This same equation is the equation of 166 the Carnot efficiency. The Stirling engine also has indicated mean effective pressure comparable to the Diesel and Otto cycle. Because of the isentropic processes in the Carnot cycle that are replaced with constant volume processes in the Stirling cycle, the Stirling engine becomes a practical possibility as compared with the Carnot engine. 8.3 Solar Insolation To determine the solar insolation falling on the aper- ture of a solar concentrator, solve for the beam radiation in (2.3): (8.11) I would equal ”28 BTU/hr-ft2. is the transmittance o Tatm through the atmosphere and is best given by (2.6): e-k/(cos 02) T = a + a1 (8.12) atm o The constants in (8.12) are found from Table 2-2. The value of cos 02 is found by solving first the angle of declination "6" from (2.8) which is rewritten here as 6 = 23.”5 Sin [360 (28” + n)/365] (8.13) where n is the number of days. The hour angle, W, is next required. After calculating the solar time from (2.1”), Solar time = Standard time + E + ”(.LS - LL) (8.1”) the number of hours, N', away from solar noon is needed. 167 W is found from: W = N' x 15° (8.15) Solve for the cos 92 from: Cos ()z = cos 4) cosS cosW + sin¢ sin S (8.16) where 0 is the local latitude. Equation 8.16 is then sub- stituted into Equation 8.12. With the T solved, the atm beam radiation can be found. A June 1 calculation was made in Chapter ”. The results for the 5 km haze with 1.5 m altitude are: 1b = 285 BTU/hr-ft2 8.” Energy Transferred to the Gas In Section 8-3, the procedure for determining the energy striking the outside surface of the energy tube was reviewed. From Chapter ”, a sample calculation using June 1, km haze, and a 1.5 m altitude was made. The results for 92° N latitude at solar noonvnnma285 BTU/hr-ft2. This theoretical value will be used to analyze the engine. For stationary receivers, the procedure of Section 3-” is applicable. The solution of (3.36) gives the temperature of the receiver surface. Equation 3.36 is rewritten for convenience. ArcTP — Tfluid) + Ar(Tr - Ta) ’ AX/k + l/hi 1/h0 + T/eru(TP2+ Ta2)(Tr + Ta) a AaIbpnO (3.36) 168 Once the surface temperature Tr is known, the mass flow rate is calculated using: Ar(Tr - Tfluid) AX/k + l/hi m(hé -h§) = Qu (8.18) The efficiency is calculated from (3.25) which is: Q n = u (8.19) Sections 3-1 and ”-1 should be reviewed if there are questions on this method. The fundamental problem of this section is to modify the procedure described above to fit the energy tube that is essential to this design. The solar concentrator has the energy tube moving through its focal point which makes the heat transfer problem unique. The surface receives a transient application of solar radiation. The non-steady state conduction is affected by both the varying solar radiation on the outside and the changing temperatures inside the tube resulting from the work of the piston. Several assumptions can be made without affecting the analysis appreciably. These assumptions are: l. Conduction is one dimensional. The heat flow is normal to the tube surface. 2. The tube temperature follows the theoretical diagram as shown in Figure 8-”. 3. Reradiation will be a minimum. Most of the losses The 169 from the surface of the tube will result from convection. problem is best illustrated discretely in Figure 8-6. The heat ring is divided into elements. The The The The For energy in the top of the element is: QZ = kA BT/Bz energy out the bottom of the element is: QZ + dZ = AIk aT/BZ + 8/3X(k 3T/32)dx] change in internal energy is: AU = pCA 3T/3T dx. differential equation becomes: B/BZ(k BT/BZ) = 00 3T/3T constant thermal conductivity: 32T/322 = (pc/k)3T/31 (8.20) which applies internally in the energy tube's wall. The boundaries have radiation and convection losses which require energy balances at the boundaries. “For the areas where convection is involved, which is the entire inside and the outside except for the brief period where the focal point is on the element, the energy balance gives: kA aT/az = -hA(Twall - Tm) (8.21) FIGURE 8- 6 . 170 Energy Balance on Heat Ring. 171 The energy balance while the focal point is on the element is: -kA aT/az = hA(Tw — T”) + AIbpnO° (8.22) The remainder of the time, the energy balance is: -kA aT/az = hA(Tw - T ) (8.23) on The last term in (8.22) would be considered a constant over the time interval AT which is equal to AT = Ax/rw (8.2”) where Ax is the length of the element, r is the mean radius of the heat ring and w is the angular rotation in radians per second. The problem can be approached using finite difference techniques. The 32T/BZ2 is approximated by aQT/aZ2 =(l/AZZXT - 2T + T ) (8 25) n+1 n n-l ' where AZ is the thickness of the element and Tn is the nodal temperature with Tn+1 and Tn-l representing the temperature on each side respectively of the elements temperature. The aT/ar is also approximated by the equation aT/a: =(Tfi - Tn)Mm (8.25) where T5 is the next transient temperature after the time AT. To ensure convergence of the numerical solution: 172 (AZ)2/0AT 3 2(hAZ/k + 1) (8.27) Substituting (8.25) and (8.26) into (8.20), (8.21), and (8.22) gives the respective finite difference equations: Tn+1 - 2Tn + Tn_l = (AZzpc/kAT)(Tfi — Tn) (8.28) For any particular problem: AZQpC/kAT = constant n+1 - Tn = (hAZ/k)(Tn+l - Tm) (8.29) Tn+1 - Tn = (hAZ/k)(Tn+1 - Tm) + AZIbpnOa/k (8.30) where the last term is a constant applied over one interval. Equation. 8.28 is applicable inside the conducting wall. Equation 8.29 is used at the boundaries of every interval except when the focal point strikes the element. At this point, (8.30) is valid. The T00 is assumed equal to the cycle temperature and varies with the crank rotation. As can be seen, the described approach is very tedious. The convective heat transfer coefficients, "h", on the tube inside as well as the outside are difficult to compute. Therefore, a simplified analysis is essential to find the gas temperature. The analysis can be simplified by writing the general energy equation: (8.31) 173 where T is the time for the ring to move through the focal point in hours. The tube surface temperature can be con- servatively assumed to equal: T + T H L The terms in (8.32) which were not previously defined are: P1 = Initial pressure. Vl = Initial volume. V2 = Final volume. CV = Specific heat for air at constant volume which equals £171” BTU/lbm° RJ(3.717 kJ/kg° K Time for half a revolution. r-i ll Gas constant for air. 70 ll Assuming the rotating hot air engine has approximately Pl = 101.35 kPa v1 = 0.0003 m3 v2 = 0.00113 m3 h = 511.1 kJ/hr-m2° C At = .0278 m2 A = 1.119 m2 o =.9 no = .8 a = .96 T = .6 sec 1.67 x 10"1t hr r-l II 17” The resulting high temperature is 325° K which is obtained by substitution into (8.31). TL was assumed to be 38° C. 8.5 Engine Efficiency The simplified method of Section 8.” resulted in a high temperature of 325° K. The calculation was based on the prototype engine that reflected an attempt at having an operational engine and not a totally optimized design. It was assumed that the low temperature was at 38° C, and that the tube and the film offered no resistance to heat flow. The efficiency is: 1 - TL/TH (8.33) .3 l which would equal: n = 1 - 311/325 The resulting efficiency could be improved by increas- ing the compression ratio V2/Vl coupled with other design changes. From a prototype design viewpoint, 5% efficiency would be an acceptable beginning. Ericsson achieved a claimed 12% engine efficiency which will be a challenging goal for modern solar engines. The actual test results are given in Chapter 9. 175 8.6 Mechanism and Stress Analysis Since the solar engine is a relatively slow moving engine, dynamic loading will, in general, be of minor inter- est. Efficiency improvements can be made by increasing the compression ratio, and the stroke length should be adjusted to maximize the V2/Vl value. Lightweight pistons and con- necting rods will keep forces small. The dynamic forces are related by: F = ma/gC (8.3”) II It is obvious that the mass "m is equally as important as ", in dynamic forces. the acceleration, "a The design of the cylinder was discussed in Section 7.6. In Chapter 7, consideration was given to stresses. In general, the engine application will fix the factor of safety used in the design which will establish the stresses. If the market develops for agricultural irrigation engines, then lower factors of safety and higher stress levels will be encountered. However, if critical industrial applica- tions are developed for the engine, where safety is in- volved, lower stress levels will be used. Basically, outside the heat ring and cylinder, there is little that is unique with this engine. General machine design procedures will be sufficient to solve the necessary details. 8.7 Servicing and Engine Life The design presented in this text is extremely simple. Little difficulty was found in repairing the engine. The 176 failures will be obvious to the mechanic. Engine life will be determined primarily by the diaphragm and at present levels of technology, two years of operation seems possible with the diaphragms. The guide bushing and the main and connecting rod bearings also require preventive and pro- gressive maintenance. It is percieved that servicing and engine life will be a developing art with this engine design, and with competitive manufacturers, improvements can be expected with time. CHAPTER 9 OPERATION OF THE SOLAR ENGINE 9.1 Discussion of thg Rotating Engine It became apparent from the development process that the rotating heat ring was theoretically sound, but tech— nically difficult from a functional viewpoint. During part of the cycle, heat had to be added with minimum losses. The remaining 180 degrees of revolution had to allow the heated gas to expand and to minimize heat losses. The return stroke required heat to be transferred away. These requirements of adding heat and extracting heat during different portions of the cycle produced the design shown in Figure 9-1. {ITI— FIGURE 9—1. Solar Engine Schematic with Revised Heat Ring. 177 178 The design was changed by utilizing the greenhouse effect of a transparent or translucent cover. Kalwal, the trade name for a fiberglass reinforced plastic material, was used. The heat ring was moved toward the inside of the circle to minimize surface areas. Short wave radiation passed through the cover and was turned to longer wave radiation which was trapped. The gas was heated and the pressure increased. The pistons moved downward. This movement of the piston exposed the cylinder walls, which are finned for heat transfer purposes. With this design, the criteria of controlled losses can be achieved. The heat ring has a transparent cover. Tests were con- ducted on a small test chamber with a transparent cover. The results are discussed in Sections 9.2and.9.3. The test showed that insulation placed beneath commercially available selective surface was necessary. Reinforcement of the cover became important because of the pressure increase. The supply line from the heat ring was relatively large and insulated. Pictures of the large four inch bore engine are shown in Figures 9e2and 9—3. A smaller model is shown in Figure 9-”. The entire engine rotates. Power is taken off a pulley on the crank center line which is fixed to the frame. The engine sits vertically on the ground. Manual cranking is required to start. The dished concentrator is focused on the heat ring, which is difficult with high sun altitude 179 FIGURE 9-2. Four Inch Bore Engine. angles. The general arrangement of engine to concentrator is rather awkward and tends to lower the collector effi- ciency. In other words, the engine is in the way of the collector. If the concentrating mirror is placed to one side, a distorted focal point results. Not all of the energy impinging upon the dished mirror can strike the heat ring because of the physical arrangement of mirror to engine. Another problem is found in the concentrating collector. The optical efficiency of the collector was low enough to be rejected by the manufacturer. The mirror was purchased by the author with limited funds and this reject was all that was affordable. The actual test data presented in Chapter ” gave a sixteen percent efficiency for the collec— tor, which verifies some optical efficiency problems. 180 FIGURE 9-3. Four Inch Bore Engine. FIGURE 9-”. 181 Small Model of Solar Engine. 182 The determining of the engine efficiency of both rotating engines with several built in "problems" became meaningless. The engines of Figurgg 9-2, 9—3, and 9-” simply proved thg: the concept was feasible. 213 Results of Tests When it became apparent that radiation through a cover into the heat ring was the only way to meet the design ob- jectives, tests were conducted upon a small chamber. The chamber is shown in Figure 9—5. The body of the test chamber was machined from aluminum. A .0”0 inch premium Kalwal cover was attached. FIGURE 9—5. Test Chamber. 183 Two ports were located on each end which were used to purge and charge the test chamber. Two mediums, air and Freon-12, were used. A 150 watt flood light was place eight inches from the face. Pressure in inches of water was recorded as a function of time in seconds. The'hma gases were tested with different pressures. The result is shown in Figure 9-6. At first the system failed to respond. The aluminum acted as a heat sink and also reflected out much of the radiant energy. The results of Figure 9—6 came after in- sulating the inside to the test chamber and covering the insulation with a selective surface (black chrome). Probably the most significant finding of the entire thesis came in this simple test. The results of the tests indi- cated that an engine can be operated from the increased pressure developed inside a transparent covered enclosure that is exposed to solar radiation. By transferring energy through a transparent cover onto a selective surface, the enclosed gas pressurized according to the ideal gas laws. The increase in gas temperature with its resulting pressure increase can be made to occur rapidly. Other engine designs can use simple flat plate collectors similar to the test chamber. The flat plate collector can be connected to a piston using the techniques of Section 7.3 with various methods of producing a cooling cycle. A simple water seal piston (inverted can over water) could produce a cost 18” mQZOOMm 2H MZHB .mPHSmwm #009 .mlm mmeHm as em as s: cm ON OH O 4 1 d 14 a a .. . 03 as N.HI comps m 03 as mN.N 0N< a N was: NN.OI comes 0 0590 co0sm m 03 as N.m comps < s e m 0H NH \\ ) \\+ :H uw.du: \ 0 \\ t. \\ ma 0 .0 \IIID \ rs RI on .zH mmDmmmmm 185 effective design. Shown in Figure 9—7 is a small model engine operating from the test chamber. FIGURE 9-7. Flat Plate Collector Engine. From Figure 9—6, several important facts can be ascer- tained. Increased mass of gas increased the pressure rise in a given time. This just verified the ideal gas law. PV/T = mR Freon-l2 responded better than air. Not only was the initial rate of pressure increase higher in Freon than air, 186 but the rate of change of the slope was less in Freon. The air curves tended to decrease their slope. In other words, the air charge test chamber began to reach a steady state condition more rapidly than Freon. When steady state conditions are reached the pressure remains constant. The energy going in will equal the energy coming out. Such a condition cannot produce work. The Freon had faster pres- sure increases and would reach steady state conditions at a much higher pressure than air. The non-ideal gas, Freon 12, is a better solar engine medium than the ideal gas, air. Other gases should be tested and compared. This is certainly a future research project in developing solar engines. 9.3 Proposed Solar Engine Design The initial design of the rotating solar engine was influenced by the Stirling and Ericsson engines. In these engines, heat applied externally was transferred through solid walls by conduction. This method did not work well in the rotating engine design. To overcome the problem, the heat ring was designed with a transparent side toward the tracking collector. The focal point was concentrated on the absorber inside the heat ring. The cover stopped most of the losses and solved the problem. The ease with which the gas pressure could be increased with radiation resulted in a simple source of power for engines of the type shown in FiguresSL¥7and 7-”. The choice of this engine over the 187 rotating engine was verified by the ease of building models. Many attempts were made before the rotating engine produced power. Complex machining was also required on this engine. The flat plate engine was easily fabricated and was opera- tional with little effort. The necessary theoretical tools are very simple. The compression ratios must be low. (Vl/V2==compression ratio.) The temperature near the top dead center cannot exceed the temperature of the gas being heated from the sun. The logic can be seen from (9.1) T2 = T1n’l (9.1) where T1 is the initial temperature, T2 is the temperature at the top of the stroke, Vl/V2 is the compression ratio and n is a function of the process. If the process of returning the piston to the top of its stroke were assumed reversible and adiabatic, then n would equal 1.” for air. If the temperatures were assumed to be T2 equal to ”3.3° C and T1 equal to 37.7° C, the compression ratio would be: vl/v2 = 1.095 (9.2) A system with a 9.29 m2 (100 ft2) collector could have l27.”2 liters (”.5 ft3) of displacement with a deep solar panel. The collector size and piston displacement from this example have values that make the system feasible to construct. From the author's experience, a static temperature of 93.3° C (200° F) is quickly obtainable in a flat plate 188 collector. Using the ideal gas relationship a pressure increase of 13.8 becomes obtainable. The flat plate collector would be charged with an initial pressure of P1. The gas would be Freon. T2 would reach a stagnation temperature of 93.3° C. Tl would be somewhat larger than the environmental temperature. Vl/V2 would be designed close to unity by having the surface area of the collector large as compared to the piston area. The stroke would be as short as practical. The end objective is to have P2 = P1 + 13.8 kPa(2 psi). With the final pressure P2, a force can be developed by applying the pressure to a relatively large piston area. The piston is a rolling diaphragm with a ball bushing or an inverted barrel in water. The piston is attached to one end of a lever. The other end could be a pump rod. When the piston pushes downward, the lever pulls the pump upward. Through a mechanism shading is provided for the cooling cycle cm'water from the reciprocating pump could produce the necessary intermittent cooling. In this resulting design, the cost of equipment will justify the decrease in engine efficiency. The rotating engine served its purpose. Instead of being the reported design to pursue, the rotating engine caused the research which fostered a simpler engine. The efficiency of this flat plate collector engine is easy to determine. The pressure-volume diagram can be a 189 rectangle when lifting water. The work is W = APAV where AP is the pressure change and AV is the volume change. The efficiency is n = W/QS = (APAV/T)/(IaAn) (9.9) where T is the time in hours per cycle, 1a is the actual solar insolation, and A is the collector area with an effi— ciency of 0- There are many ways of achieving a cooling cycle with the flat plate engine. If the engine is pumping water, the discharge water provides the necessary cooling. Or, the motion of the piston closes the shutter to allow cooling. Another possibility is to have the absorbing surface reflec- tive on the back. Through a mechanism, the absorber flips over to the mirrored surface to reject the incoming energy 190 so that cooling takes place. A more direct approach is to use valves. By inclining the collector, natural flow is possible if valves in the top and bottom are opened. Cool- ing can also be accomplished through the cylinder walls. As the piston is pushed downward, the walls that are finned are exposed. To determine the efficiency from (9.”), the time, I, must be determined. If T is large, then the efficiency is small. This can be seen from (9.”). On the heating cycle it becomes important to have the collector well insulated. On the cooling cycle the opposite is required. Valving is one of the most certain ways to solve the problem of reducing the time of the cycle. However, engine cost must be weighed against efficiency. Shading with a simple device might be the proper solution in some instances. Another related problem is the presence of energy sinks. Mass that is thermally conductive should be avoided. The less mass used in the collector, the better is the efficiency. The absorbing surface is a future area of research. The surface requires extensive contact with the gas to be heated. A black cloth undulated for maximum contact gives good results. 9.” Failures There is a learning experience in failure. Solar engine technology reached its peak of development one hundred years ago. With the advent of low cost energy came the demise of solar engines. The state of the art has, in 191 general, been buried with its inventors and entrepreneurs. It seems prudent to publish the errors the author made. Had Ericsson, Pifre, or Shuman been alive and consulted, many hours of development time could have been saved. The very first rotating engine was designed using piston rings. The frictional energy consumed was larger than the available power. Consequently, this engine sat motionless when heated. The first challenge came in developing a frictionless piston. Close fitting brass pistons in aluminum cylinders were tried. The height of the piston versus the diameter was too small in one case. This caused the piston to bite into the cylinder walls. Close fitting pistons can be made to work satisfactOrily if the skirt length is larger than the diameter, but the process holds little promise for mass production. The use of rolling diaphragms became the simplist solution (30) and was the topic of discussion in Section 7-3. To use the diaphragms the piston is held away from the cylinder wall. This is accomplished by using linear bushings. If rotary motion is desired, a crank mechanism is used. Large piston displacements will place proportion- ally large side loads on the bushings. The second engine had a ” inch stroke. The piston through a link was connected to a crank. The large dis- placement caused the piston rod to lock in the bronze bushings and the second engine could not be rotated. (See Section 7.6.) 192 The second engine with the ” inch stroke had too much compression. The temperatures in the engine were being elevated above the source temperature. The stroke was shortened to two inches, which lowered the compression temperature and allowed the engine inertia to smoothly rotate against the compression. Finally, the initial heat:nhng,which was a one inch copper tube formed into a semi-circle, transferred heat away as fast as it was added. Conduction heat transfer was inadequate. The problem was solved by using the "greenhouse effect". The heat ring was given a transparent cover facing the sun. Radiation passed through the cover and was trapped. Heat was then rejected in the piston which needed fins. CHAPTER 10 CONCLUSION The scope of the thesis was to investigate the possi— bilities and methodology of converting solar radiation to work. Some technology had been developed a century ago. From this early development, it appears that one brake horsepower can be extracted from 100 square feet of collec- tor area. (See Chapter 1.) Patent and literature searches indicate these past inventions were, in general, too complex to be cost effective. Solar engine development requires competency in collec- tor analysis and evaluation of solar insolation. Collected energy is a function of time, location, orientation and type of collector. An important aspect of solar development is cost effective design. To be cost effective, a design must com- pete with fossil fuel engines economically. With fuel prices of $0.53/liter ($2.00 a gallon), solar engines could cost approximately $5,000 per horsepower and be cost effec- tive. Concentrators could cost $562.00 more per square meter than flat plate collectors. With rising fuel costs it appears that solar engines can be used principally in applications such as water pumping. (See Chapter 5.) Contrary to many publications, it was found that theoretically, flat plate and concentrating collectors have nearly the same efficiency. Under actual tests the flat 193 19” plate collectors had higher efficiencies. The absorber used in testing the dished mirror concentrator reradiated large amounts of solar energy, and special design efforts must be made to stop these losses. However, with assumed equal efficiency of concentrating and flat plate collectors, the engine efficiencies are higher with concentrators. The efficiency of the engine follows: Efficiency = l - TL/TH for the Carnot, Stirling and Ericsson cycles. With assumed equalcmdlectorefificiency and higher engine efficiency using concentrators, the overall product efficiency will be higher using concentrators. Economic considerations may cause the flat plate with its lower overall efficiency to be the best choice because of lower capital investment. Thermodynamics was in its infancy when Ericsson and Stirling developed their engines. Most theoreticians criticized Ericsson's engines as being unsound. These critics were silenced when Ericsson's engines were seen producing power. Theoretical thermodynamic cycles follow the development of the engines. Initially, the author concentrated on having a new engine follow a particular cycle such as the Stirling cycle. It was soon realized that the cost per horsepower is more important than having the engine follow a particular cycle. Deviation from a cycle may soon become necessary to build a cost effective engine. There are many possible cycles that a solar engine 195 could use. The Rankine cycle can be used if the rejected heat from the condenser has some use. In northern latitudes a solar steam engine could pump water and the condenser could heat domestic water. The added cost of this cycle could be justified by using the waste heat. The Ericsson and the Stirling cycles have promise, but tend to be ex- pensive engines. The salient principle is to inexpensively add and reject heat during the cycle. Cycle tracing is of lesser importance when compared with capital investment in the engine. Chapters 7, 8, and 9 discuss the methods necessary to accomplish the conversion of radiant energy to work inexpensively. Solar engine design centers around building friction- less pistons. Turbine type devices were not considered because it appeared to be difficult to compete with the oldest type of solar engine called a wind mill. The piston design uses a rolling diaphragm with a roll ball bushing. This type of construction requires a minimum of machining with liberal tolerances. Aluminum alloy pistons and cylin- ders will meet the other requirements of heat transfer, strength, and product life. Initially, a rotating engine using a heat ring and a concentrator was investigated. By rotating the engine, a means of adding and rejecting heat became possible without valves or displacement pistons. An analysis of the engine was made theoretically and with the assumptions made in Chapter 8, an efficiency of ”.”6% was determined. 196 The engine described in Chapter 8 was not operational initially. The problem of adding heat to the rotating heat rings was solved by constructing semi-circular flat plate collectors. A concentrating mirror focused its energy inside the flat plate collectors. Before building the new heat rings, tests were conducted on a small test chamber filled with varying pressures of Freon-12 and air. The most important findings of the project came from these tests. A flat plate collector could be designed to rapidly change the pressure of the trapped gas. By insulating the inside of the chamber and covering this surface with a black selective surface, significant pressure changes could be obtained. For most simple applications, 13.8 kPa (2 psi) pressure increase is possible inside a flat plate collector. These changes occur rapidly and follow the ideal gas relationships. With the redesigned heat rings, the rotating engine became operational. Because of equipment limitations, no efficiency measurements could be made. The small model shown in Figure 9-” was the model completed at the time of thesis publication. The mirror available is too large for this engine. The model was operated from a light bulb. With a 13.8 kPa(2 psi)increase possible in an enclosed flat plate collector, many new possibilities exist. Relatively large diameter pistons connected to even larger flat plate collectors are able to produce significant forces. The motion of the piston can provide shading through a 197 mechanism or water pumped could cool the collector. The rotating engine is novel, but somewhat complicated to build. The engine that operates from a simple flat plate collector can be very simple. A thirty gallon barrel with the end cut out makes a piston. By inverting this smaller barrel into a fifty gallon drum, a simple piston is made. A flexible hose is attached to the flat plate collector. A simple lever arrangement fastened to a fixed.postand the top of thetflfi1d3rgallon barrel completes the system. The end of the lever is fastened to a pump rod. As the pressure builds up in the collector, the water is displaced out of the thirty gallon barrel. The lever pushes upward lifting water which flows through coils in the collector. The water provides the cooling cycle. Such an engine will find an application in third world countries. Other more sophisticated engines are possible using the techniques described in previous chapters. The extraction of mechanical power from the sun has been proven possible. The results of this work should show the potential of producing cost effective solar engines using elementary thermodynamics and simple designs. The initial research and development must produce engines that have a place in the free market. If high efficiency engines require costly technology, then perhaps the prudent designer will find simple, cost effective engines with lower effi- ciency that shall be classified as appropriate technology for our times. CHAPTER 11 RECOMMENDATIONS Several research and development projects can develop from this work. Tests should continue on flat plate collectors designed to produce pressure. The design of the absorbing surface to produce pressure will be different from the surfaces used in typical heating applications. Only two gases were used in this study. Many other gases should be tried. Curves relating the type of gas, surface, initial pressure, and final pressure to time need to be developed. Methods of alternating the heating and cooling cycle should be studied in the flat plate collector engine. Both the rotating and the flat plate collector engines require further development. 198 BIBLIOGRAPHY 10. BIBLIOGRAPHY Ackerman,.A.SgE.,The Utilization of Solar Energy. Government Printing Office, fiAnnual Report of the Smithsonian Institution, 1915". Jordan, R.C., Mechanical Energy from Solar Energy. N.Y. Johnson Reprint Corporation. "World Symposium on Applied Solar Energy Proceedings". Church, W.C., John Ericsson. Charles Scribner 8 Sons, New York. Walton, H., The How and Why of Mechanical Movements. Popular Science Publishing Company, E.P. Dulton 8 Company, New York. Ryan, L.D., "The Theoretical Design of a Solar Engine for the Production of Hydrogen", 2nd World Hydrogen Energy Conference Proceedings, August 1978. Duffie, J.A., Solar Energy Thermal Process. John Wiley 8 Sons, 197”. Liu, B.Y.H., Solar Energy, ”, No. 3, (1960), "The Interrelationships and Characteristic Distri- bution of Direct, Diffuse, and Total Solar Radiation". Hottel, H.C. "A Simple Model for Estimating and Transmittance of Direct Solar Radiation Through Clear Atmospheres", Solar Energy, Vol. 18, pp. 129-13”, 1976. Krieth, F., Principles of Solar Engineering. McGraw-Hill Publishing Company, 1978. ASHRAE Handbook of Fundamentals, American Society of Heating, Refrigeration, and Air Conditioning Engineers, New York, New York, 1972. 199 11. 12. 13. 1”. 15. 16. 17. 19. 20. 21. 22. 23. 2”. 200 Hottel, H.C., Transactions of the Conference on The Use of Solar Energy, 12, Part I, 7”, Univ- ersity of Arizona Press, 1958. "Evaluation of Flat-Plate Collector Performance". Ryan, L.D., Fundamentals of Solar Energy. Prentice- Hall, 1981. Cherenusinoff, P., Principles and Applications of Solar Energy. Ann Arbor Science Publisher, 1978. Gupta, A., "Digital Simulation of a Solar Collector", Paper presented to the Honors College, Western Michigan University, Kalamazoo, Michigan, 1978. Wark, K., Thermodynamics. 2nd Ed., McGraw-Hill, 1971. McAdams, W.H., Heat Transmission. 3rd Ed., McGraw- Hill, New York, 195”. "Automotive Stirling Engine Development Program", Contractors Co-ordination Meeting Report, Ford Motor Company, Engineering and Research Staff, Dearborn, Michigan, October 1978. "Fatigue at High Temperature", ASTM Special Tech- nical Publication ”59, A symposium presented at 71 annual meeting, American Society of Testing and Materials, San Francisco, California, June 23-28, 1968. Colangilo, V.J., Analysis of Metallurgical Failures. John Wiley 8 Sons, New York, New York. Dorn, J.E., Editor, Mechanical Behavior of Materials at Elevated Temperatures. McGraw-Hill, New York, New York, 1961. Greenfield, P., Creep of Metals at Higher Temperatures. Mills and Boon Limited, London, 1972. Sully, A.H., Metallic Creep. Interscience Publisher Inc., New York, New York, 19”9. Kachanov, Translated by E. Bishop, Theory of Creep. National Lending Library for Science and Techno— logy, Boston, 1967. 25. 26. 27. 28. 29. 30. 31. 32. 201 "Thomson Ball Bushings for Linear Motion", Thomson Industries, Ind., Manhasset, New York. American Society for Metals, Metals Handbook. Vol. 1, 8th Ed., Metals Park, Ohio. Roark, R.J., Formulas for Stress and Steam. 3rd Ed., McGraw-Hill, New York, 195”. Spotts, M.F., Design of Machine Elements, ”th Ed., Prentice-Hall, Inc., Englewood Cliffs, New Jersey. Kent, W., Kent's Mechanical Engineers Handbook. 10th Ed., John Wiley 8 Sons, New York, New York, 1923. "Design Manual Bellofram", Burlington, Massachussetts, 1962. U.S. Patents. United States Patent Office. Klein, R.S. "John Ericsson: The Successful Failure", Industrial Education, Vol. 52, pp. 63-6”, 1978.