THE UNIVERS I TY OF MICHI GAN COLLEGE OF ENGINEERING Department of Mechanical Engineering Student Project Reports INVESTIGATION OF DESIGN MEANS FOR HOME LAUNDRY APPLICANCES Dowell Howard Robert Handler DRDA Project 371550 supported by: WHIRLPOOL CORPORATION BENTON HARBOR, MICHIGAN administered through: DIVISION OF RESEARCH DEVELOPMENT AND ADMINISTRATION ANN ARBOR June 1974

TABLE OF CONTENTS Page Development of a Thermodynamic Actuator by Dowell Howard 1 ABSTRACT 3 PROBLEM STATEMENT 4 CONCEPT AND ANALYSIS 5 EXPERIMENTAL PROCEDURE 7 DISCUSSION OF RESULTS 8 CONCLUSIONS 9 REFERENCES 10 ACKNOWLEDGMENTS 22 APPENDIX A COMPUTER PROGRAM 23 APPENDIX B DATA REDUCTION PROGRAM 29 An Experimental Testing Procedure For Determining Heater Characteristics by Robert Handler 31 INTRODUCTION 33 THERMODYNAMIC ANALYSIS 34 EXPERIMENTAL PROCEDURE 39 Instrumentation and Experimental Design 39 Test Procedure 40 RESULTS AND DISCUSSION 41 Small Flexatherm Heater 41 Large Flexatherm Heater 41 iii

TABLE OF CONTENTS (Concluded) Page CONCLUSIONS 43 Practical Implications 43 APPENDIX COMPUTER PROGRAM FOR DATA REDUCTION 57 NOMENCLATURE 58 iv

DEVELOPMENT OF A THERMODYNAMIC ACTUATOR Dowell Howard 1

ABSTRACT This work describes the development of a linear thermodynamic actuator to replace solenoids as actuation devices in certain applications in washing machines. The investigation includes the characteristics and also considers possibility of development of a multiple-position thermodynamic actuator. 5

PROBLEM STATEMENT Whirlpool Corporation products use millions of linear actuators every year. Presently, the electromechanical device known as the solenoid is used exclusively. A solenoid offers relatively instantaneous actuation with twoposition capability, fully extended, and fully retracted. The major goal of this research project was to develop an actuation device that could replace solenoids in certain washing machine applications. One requirement was that the device should possess multiple-position capability, an option which solenoids do not offer. Since many solenoids are used each year, the development of a cheap reliable substitute might reduce costs. Even if the actuation device did not result in lower unit cost; with its multiple-position capability, it might replace several solenoids and therefore be cost competitive. 4

CONCEPT AND ANALYSIS The basic concept of the actuating device used a thermodynamic working fluid to displace a piston upon the addition of heat energy as shown in Figure 1. The working fluid was chosen for its thermodynamic properties. For two reasons, it was desirable that the working fluid operate in its thermodynamic two-phase region. By operating in the two-phase region, a large pressure change could be produced which would act against the load with a small volume change. Secondly, by choosing an appropriate working fluid whose vapor pressure-temperature curve was compatible with ambient conditions, the amount of energy input required would be minimized. After investigating the thermodynamic properties of various fluids, "Freon 11" (trichlorofluoromethane) was chosen as the working fluid. A temperature-volume diagram of "Freon 11" is presented in Figure 2. At typical ambient conditions, 75~F, the vapor pressure of "Freon 11" is 14.7 psia. The thermodynamic actuator can by analyzed by considering a control volume, as shown in Figure 1. Applying the First Law of Thermodynamics to the system gives Q = W + m(u2 - ul) where Q = heat which crosses system m = mass of fluid uI = specific internal energy of fluid before heat transfer U2 = specific internal energy of fluid after heat transfer W = work done by the system on surroundings The work relation for the system is W tt = PdV total Also the total work is sum of the work done on the spring and the work done 5

on the atmosphere. Thus W = W. + W total spring atm f k x dx + f P dV atm where k = spring constant x = the displacement of the spring Interestingly enough, by pre-loading the spring, the pressure at which actuation initiates can be controlled. Here the mechanics of the device tend to govern the thermodynamics of the system. A computer program, shown in Appendix A, was written using the above equations and the properties of the fluid to size the thermoactuator for a given set of conditions. 6

EXPERIMENTAL PROCEDURE A prototype actuator was constructed to provide information and to demonstrate the feasibility of the device. For purposes of instrumentation, the prototype was constructed larger than normal size. The cylinder is nearly 3 in. in diameter as compared with a typical installation size of about 1/2 in. diameter. Figure 3 shows the cylinder apparatus. All parts except the clamping rods, piston rod, spring sleeve, and spring are aluminum. A lip seal was used on the piston (Huva cup, Crane Co.). An O-ring seal was used in the cylinder base. The spring constant of the spring used was 147 lbf/in. Figures 4 and 5 show the test set-up. The standpipe configuration was finally used to insure that the liquid Freon was always in contact with the heating surface. A flexible heating element was wrapped around the lower portion of the standpipe as shown in Figure 6. The filling port was located at the lowest point in the system. A variable transformer (Variac) was used to control electrical power imput to the heater. This power was measured with an AC voltmeter and ammeter. Piston deflection was measured with a dial indicator gage. Each experimental run was conducted as follows: first, the system pressure was nulled along with the dial indicator reading. A vacuum of 21 in. Hg was used to reduce the amount of air in the system. Then the liquid Freon 11 was allowed to flow into the system and the system was filled with Freon to the same level for each run. Five runs were made at different power levels. The powers were 16, 37, 54, and 94 watts. For each run, the pressure and extension were recorded as a function of time. Data was also taken for the retraction condition (zero input power) with cooling natural convection. Data are presented in Figures 7-11. Figure 7 is a temperature-volume plot for the heating process and compares two data sets with the predicted results. A data reduction program, listed in Appendix B, was used to obtain thermodynamic properties from the pressure-extension data. Figure 8 is a plot of extension vs. time and Figure 9 shows pressure vs. time for various powers. Figure 10 is a plot of extension vs. time, and Figure 11 shows pressure vs. time-both plots for the cooling or retraction portion of the cycle. 7

DISCUSSION OF RESULTS Looking at the temperature-volume diagram of.Figure 7, the predicted and measured values (54 and 73 watts) are in good agreement. The extension (heating) graphs of displacement and pressure vs. time proved interesting. At first glance, it might be expected that the system response would be exponential in nature; with the initial rapid rise in output variable slowly reducing to become nearly constant with time. However, this expected trend is found only at the lowest power input, 16 watts. Higher power response appears to follow a different relationship. This apparent discrepancy may be explained by the inherent non-linear behavior of the system. Further, the experiment was run insufficiently long for the displacements to become constant with time for the higher powers. The retraction (cooling) performance of the system as shown in Figures 10 and 11 were more conventional. The exponential decay in both deflection and pressure follow classical free convective colling curves. Caution must be used in extrapolating results from these experiments to the performance of different sized (smaller) actuators. Since the performance of the actuators is primarily heat-transfer limited, no simple set of scaling parameters can be readily defined. However some general trends can be inferred. Since the dynamic response of the actuator is heat-transfer limited, then the net heat input rate to the fluid is the difference between the heat transferred to the fluid from the electrical heater and the heat lost from the fluid (and the system) via convective heat transfer effects. Suppose that the electrical heater is virtually immersed in the liquid Freon so that the amount of heat to the system is a function of the electrical power only, and not limited by heat transfer surface. The heat loss from the system, however, is a function of the surface area available for heat transfer. Consequently, a smaller actuator, for the same power input, will have a smaller heat transfer surface available for losses. Thus the net heat input to the fluid will be greater with a correspondingly increase in actuator response. Roughly speaking, scaling the actuator down by a factor of 6 in a linear dimension (3-in. diameter piston scaled to 1/2 in.) results in a reduction in area by a factor of 36. Thus response time would be reduced by a factor of 36. Additional work would include study of the scaling effects just mentioned. Analytical modelling together with the construction and testing of a smaller actuator would be useful. Various methods of forced cooling might be investigated in order to improve the retraction (cooling) response time. Alternate heat sources, other than electrical, could be considered. 8

CONCLUSIONS While this research project has not fully investigated all aspects of thermodynamic actuators, some important conclusions can be drawn. A linear thermodynamic actuator has been developed which appears to possess potential for replacing solenoids in certain application in washing machines. The prototype has demonstrated that the concept of a linear thermodynamic actuator is a feasible approach to problems in actuation. The research also showed that the theory correlates well with the experimental results, and that the computer program satisfactorily predicts the performance of these actuators. The dynamic response indicates that this type of actuator should be used for an extension application rather than retraction or rapid cycle. These conclusions suggest that additional work is warranted in the further development of linear thermodynamic actuators. 9

REFERENCES 1. Brinkworth, B. J., An Introduction to Experimentation, English Universities Press, Ltd., London, England, 1968. 2. DuPont De Nemours & Company, Inc., Thermodynamic Properties of Freon-11R Refrigerant, E.I. DuPont De Nemours & Company, Inc., Wilmington, Delaware, 1965. 3. Lipson, Charles, Design of Experiments. 4. Sonntag, R. E. and G. J. Van Wylen, Fundamentals of Classical Thermodynamics, John Wiley & Sons, Inc., New York, 1965. 5. Streeter, V. L., Fluid Mechanics, McGraw-Hill Book Company, New York, 1971. 10

Freon Piston Spring r - I Heat IO Ii isto Input I I H~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ HII H- L —-J Control Volume Figure 1. Schematic of actuator.

639. 50 psia /Critical / 3380 Point _ X 100 psia E 198 - Liquid - Vapor Liquid (Two Phase Region) / Vapor -,!& -< " 115 ~~~~ro ~, _:///B _14. 73 psia C 750 A SPECIFIC VOLUME Figure 2. Temperature-volume plot of Freon 11.

__- - - " —-- (D l-,1 - 1 I We- L —I — - I m a HzQ 1 Y \ E \ HiE r 1n I,4C F -

Dial Indicator Pressure Gauge Cylinder Fill Tower ^- ^ T-T Safety Valve Insulation /i~/ ^ ^ Ii__>'_.-, ^->. ~~Vacuum // MMML^ E (^) Pump Surge Vacuum ^! = = s ^ H e a te r - ^r T__ E^~I T a n k G a u g e Fill Valve 00 r Amp Volt ====== ====== 117 Vac Variac Figure 4. Test set-up.

**%:'/";:% """;* **' "'' *'1 -:.' *' * Figure 5. Photograph of experimental apparatus.~~~~~~~~~~~~~~~~~~~~~~~~~~~15 ~:

Figure 6. Photograph of standpipe. 16

130 o 125 0o, o x, 120 1 ^ -; 115 0o ~~z Liquefaction o - 110 - Line o' 105 - LU LU x 0 100 x0 o Predicted u 95F - 0 x Experimental 0 73 W I< _ x o Experimental ZD. ^ " o 7354 W - x 0 54W 85 X 80-x 0 75.010.015.020.025.030.035.040.045 SPECIFIC VOLUME (FT3/ I BM) Figure 7. Temperature-volume plot.

10. 0 93. 6 9.0- Watts 8...00 77.8 W atts..-' 0 0 *0* i 7.0 00 0 * 0 354 W atts I.-' 00 =! 3.0'-0 0 0.1-. 00 * LU' 16 W atts 0 OO O 3 5.0 -- 0 ~ ~ O 0 40 o~IIF e eee Et sov.~ iefrhang Jura"'6080 00 2014010010 ~~~~~~~TM OO~O' oO~O 3~~~~~~Fgr.-'reso OOO'' m'"'hat

24 93.6 22 - Watts. 22 -...0 73 Watts 016 0 ~ ~m... —.. * *. ~. * * 354 Watts 18'. ~ ~.~. 16 * 0 14 0.0 12.* 0 00 00 37 Watts L~ 0 20 0 00 0 Figure 9 Pressure vs. time for he ating 1 ~ 0 ~ ~ 0 L0 * 00 o 0 0 0.0 * 0 0. 0.00000 4:.o 0O0 ~2 *0 ~ ~ 0 200 400 600 800 1000 1200 1400 1600 1800 TIME (SECONDS) Figure 9. Pressure vs. time for heating.

100, 000.. 9. 0'0 0 0. 0. z 600 A- "*****...... * **, 94 54 Watts | *- *. 37 Watts * * *. 8.0- * -000. * * *. * * *. 0 *.. *.... * * * *0** * * 4 2.0 F x 1.02. I —' 200 400 600 800 1000 1200 1400 1600 1800 TIME (SECONDS) Figure 10. Extension vs. time for cooling. -- ~ ~ ~ ~ ~ ~ ~~~~~TM (SECNDS ~~~~~~~~~~iue1.Etnsor.tiefrclng

24 22 0 20 3. 18- *. "16 *:::.* 93 Watts 16 -' 14- * 54 * o 0. 00 ~'. S o.... Watt s' o1~2~ d W12 37 Watts-...,- OO10 * 0 LO ~~10-' * * * * * * -:0~0 0 0 w~~~ Cy- 8 37*... 816 W atts 6 -*0 0 0 0 0 * * 0 0. 4 2 20 200 400 600 800 1000 1200 1400 1600 1800 r0 201 40 TIME (SECONDS) Figure 11. Pressure vs. time for cooling.

ACKNOWLEDGMENTS I would like to take this opportunity to thank my advisor Professor Robert Keller for his suggestions and guidance. Also, I would like to thank Mr. Ray Allen and Mr. Sheldon Roll for their help in constructing the experimental apparatus. 22

APPENDIX A COMPUTER PROGRAM 25

PROGRAM VARIABLES 1 PROP (I, J) Freon-property matrix Temperature - column 1 Pressure - colume 2 VF column 3 Vg column 4 HF column 5 Hg column 6 2. DIAM - cylinder diameter (inches) 3. VINT = initial volume (inches)3 4. XINT = initial quality 5. PRESSI = initial pressure (absolute pressure) 6. SPRK = spring constant (lbf/in) 7. PRPRS = gage pressure (psig) 8. FPRE = preload force (lbf) 9. SPRY = preload distance (in) TSAT = saturation temperature (~F) SPVDL = specific volume (ft3/lbm) ITINT = initial enthalpy (Btu/lbm) VINT = initial internal energy (Btu/lbm) FREMAS = freon mass (Ibm) EXTEN(I) = extension (inches) DELTAV = delta volume (inches)3 VOL = new volume (inches)3 X = quality H = Enthalpy (But/lbm) v = internal energy (But/lbm) CAPU(I) = internal energy (Btu) 24

CAPVINT = initial internal energy (btu) W = work VF = specific volume (saturated liquid) VG = specific volume (saturated vapor) HF = enthalpy (saturated liquid) HG = enthalpy (saturated vapor) UF = internal energy (saturated liquid) UG = internal energy (saturated vapor) 25

$LIST WHIRL 1 C THIS PROGRAM WILL DETERMINETHE REACTION OF THE ACTU2 C ATOR UPON THE ADDITION OF HEAT. THIS ANALYSIS ASSUMES 3 C THAT NO HEAT IS TRANSFERED TO OR FROM THE SURROUNDINGS 4 C READ INITIAL CONDITIONS, FREON 11 PROPERTIES 5 DI NSION PROP(22 6) CAPU(22) EXTEN(22) 6 REAL INTERP 7 DO 5 1=1,22 8 5 READ (5,100) (PROP(IJ),J=1,6) 9 100 FORMAT(6F10.6) 10 WRITE(6,106) ( PROP I J),J=1,6),I=1,22) 11 106 FORMAT(',6(2X,FIO. 6)) 12 DO 81 K=1,40 13 READ(5,101) DIAM,FLENG,XINTPRESSI,SPRK 14 WRITE(6,88) 15 88 FORMAT(' i'2X,'THE DATA SET FOR THIS RUN IS: ) 16 WRITE(6,44) 17 44 FORM AT ( O,5XD, I AMETE R'3X, *FREELENGTH',2X,' INT.QUAL 18 1,2X,'INT.PRESS',2X,'SPRING K' ) 19 WRITE(6, 107) DIAMFLENGXINT,PRESSI,SPRK 20 107 FORMAT( O',2X5 (F1O.4,1X)) 21 101 FORMAT(5F10.4) 22 AREA=3.1459*DIAM**2/4 23 VI NT=ARE A FLENG/1728 24 PRPRS=PRESSI-14.70 25 FPRE=PRPRS*AREA 26 SPRX=FPRE/SPRK 27 CALL GIV(PRESSI,PROP,XINT,TSAT,SPVOL HINT,UINT) 2 8 FREMAS=VINT/SPVOL 29 WRITE (6,50) 30 50 FORMAT ('4'IX,tEXTEN',2X,'VOL',2X, PRESS' 3X' TSAT' 31 13X,' X',3X'ENTHALP',lX,' INTENER',2X,' SPECVOL', 3X, 32 2'WORK',3X,'HTTRAN' ) 33 WRITE(6,52) VINT,PRESSI,TSAT,XINT,HINUINTSPVOL 34 WRITE(6,55) FREMASFPRE,SPRX 35 55 FORMAT('',3X,'FREMAS=',F7 4, 3X'PRELOAD FORCE=m 361,F 7.4,3X,PRELOAD X =',F5.3) 37 52 FORMAT( O',6XF 5.4,F7.3,1 XF 6. 2,IXF 4. 3, X,F7.3, 38 IX,F7.3,X F9.6,2X) 39 C UINT IS THE INITIAL INTERNAL ENERGY 40 C NOW DETERMINE CHANGE AS VOLUME IS INCREASED 41 INCREMENTALLY 42 W=O 43 Q=0 44 DO 6 1=,20 45 EXTEN(I )=I0.05 46 DELTAV=AREA*EXTEN )/1728 47 VOL=VINT+DELTAV 48 SPVOL=VOL/FREMAS 49 PRESS=PRESSI+EXTEN( I )*SPRK/AREA 50 C DETERMINE PROPERTIES 51 CALL DETERM(PRESSPROP,SPVOL,TSAT,X H, U) 52 CAPU( I)=FREMAS*U 53 IF(I.GT. 1) GO TO 12 54 CAPUNT=FREMAS*UINT 55 U2U1=(CAPU( I )-CAPUNT) 56 GO TO 13 57 12 U2UI=CAPU( [)-CAPU( I-1)+U2U1 58 13 CONTINUE 26

59 WORK DETERMINATION 60 C IF YOU DESIRE THE INCREMENTAL W3RK BETWEEN ANY TW3 61 C EXTENSIONStSIMPLY CMI T HE +W ON THE END OF THE 62 C THE STATEMENTS FOR BB AND CC. 63 X1=SPRX 64 PATM=14.70 65 BB=PATM*AREA*EXTEN( I ) +W 66 IF (I.GT. 1) GO TO 14 67 W=.5*SPRK* ( X1+EXTEN( I) )**2-( X) **2)+BB 68 GO TO 15 69 14 ZZ=.5*SPRK*IX1+EXTEN(I-1))**2-.5*SPRK*Xl**2 70 CC=PATM*AREA*(EXTEN( I)-EXTEN(I- 1) )W 71 W=.5*SPRK*XI+ XEXTEN(I) )**2-X*1*2)-ZZ+CC 72 15 CONTINUE 73 Q=U2U1+W/(12*778) 74 WRITE(6, 51) EXTEN I ) VOtL,PRESSTSAT TX,H U,SPVOLt W Q 75 51 FORMAT ('', IX F4.2,1X,F5.4~F7.3, IX, F6. 2, 1XtF4.3 76 1 1X,F7.3 lX,F7.3 tlX F9.6,lX,F7.3, lX, F7.4) 77 6 CONTINUE 78 81 CeNTINUE 79 END 30 SUBROUTINE DETERM(PRESSPROPSPVOLTSAT,XH,U) 81 DIMENSION PROP(22,6) 82 REAL INTERP 83 TSAT=INTERP(PRESSPROP 2, 1) 84 VF=INTERP(PRESS,PROP,2 3 ) 85 VG=INTERP PRESSPROP,2,4) 86 HF=INTERP(PRESSPROP, 2, 5 87 HG=INTERP(PRESS PROP,2,6) 88 UF=HF-144*PRESS*VF/778 89 UG=HG-144*PRESS *VG/778 90 X=( SPVOL-VF)/(VG-VF) 91 H=HF +X* ( HG-HF) 92 U=UF +X* ( UG-UF 93 RETURN 94 END 95 REAL FUNCTION INTERP(VALUEPROP,IX,IY) 96 DIMENSION PROP(22t 6 97 DO 10 1=,t22 98 IF(PROP(IIX).LT. VALUE) GO TO 9 99 GO TO 11 100 9 CONTINUE 101 10 CONTINUE 102 11 YL=PROP ( I-1t IY 103 YH=PROP(, tIY) 104 XL=PROP ( I- 1, IX) 105 XH=PROP ( I,IX) 136 I NTERP=YL+ (YH-YL) * (VALUE-XL)/( XH-XL 107 RETURN 108 END 109 SUBROUTINE GIV(PRESSPROP, XI NT, TSAT SPVOL,HtU) 110 DIMENSION PROP(22,6) 111 REAL INTERP 112 TSAT= INTERP(PRESSPROPt 2 1) 113 VF=I NTERP(PRESS,PROP,2,3 ) 114 VG=INTERP(PRESSPROP,2,4) 11.5 HF=INTE RP (PRESS, PROP, 2, 5 ) 116 HG=I NTERP(PRESS,PROP,2,6 ) 117 UF=HF-144*PRESS*VF/778 118 UG=HG-144*PRESS*VG/778 27

119 SPVOL=VF+XINT*( VG-VF ) 120 H=HF+XINT (HG-HF) 121 U=UF+XINT*(UG-UF) 122 RETURN 123 END END 3F FILE 28

APPENDIX B DATA REDUCTION PROGRAM 29

$LIST PROPCALC 1 C THIS PROGRAM IS FOR THE REDUCTION OF THE TEST DATA OBTAINED 2 ED. THE PRESSURE IS FEED IN AS GAUGE AND EXTENSION IN IN. 3 DIMENSION PROP(22,6) 4 REAL INTERP 5 DO 5 1=1,21 6 5 READ (5,100) (PROP(I,J),J=1,6) 7 100 FORMAT(6F10.6) 8 WRITE(6,106) ((PROP(IJ),J=1,6),I=1,21) 9 105 FORMAT',6( 2X,F10.6 ) 10 WRITE(6,39) 11 39 FORMAT('4',2Xt'EXTEN',2X,'VOLUME',3X,'PGAUGE',3X, 12'PABSOL',4X'TSAT',3X,'SPECVOL', IX'QUALITY',2X, 13 2'ENTROPY' 14 C NOTE THAT ON THE'DO 81' STATEMENT THAT 100 IS THE 15 C LIMIT ON THE NUMBER OF DATA SETS. 16 DO 81 K=1,100 17 READ(5,333) PRESSI,EXTEN 18 333 FORMAT(2F10.5) 19 DIAM=2.875 20 AREA=3.1459*DIAM**2/4 21 VINT=1.96/1728 22 FREMAS=0.103 23 C FOR THIS SPECIAL CASE DIAM=2.875;VINT=1.96 IN3;AND 24 C FREON MASS EQUALS.103LBM. 25 VOL=VINT+AREA*EXTEN/1728 26 SPVOL=VOL/FREMAS 27 PRESS=PR ESS I+14.696 28 CALL DETERMIPRESS,PROPSPVOL1TSAT,X,S) 29 WRITE(6,92) EXTEN,VL,tPRESSI,PRESS,TSAT,SPVOL,XtS 30 92 FORMAT ('',2XF5.4,2X,F6.5 2 2XF7.4,ZX,F74,2X,F7.3 31 1,2X,F8.7,2X,F5.4,2XF8.7 32 81 CONTINUE 33 END 34 SUBROUTINE DETERM(PRESS,PRUP,SPVOLtTSAT X,S) 35 DIMENSION PROP(22,6) 36 REAL INTERP 37 TSAT=INTERP(PRESS,PROP 2,1) 38 VF=INTERPIPRESS,PROP,2,3) 39 VG=INTERP(PRESS PROP 2,4) 40 SF=INTERP(PRESS,PROP,2,5) 41 SG=INTERP(PRESSPROP,2,6) 42 X=( SPVOL-VF )/( VG-VF) 43 S=SF+X( SG-SF) 44 RETURN 45 END 6b REAL FUNCTION INTERP(VALUEPROPt IX, IY) 47 DIMENSION PROP(22,6) 48 DO 10 1=1,22 49 IF(PROP(I,IX).LT. VALUE) GO TO 9 50 GO TO 11 51 9 CONTINUE 52 10 CONTINUE 53 11 YL=PROP (I-1, IY) 54 YH=PROP( IIY) 55 XL=PROP( I-1,IX) 55 XH=PROP(I, IX) 57 I NTE RP=YL+ (YH-Y L)* ( V ALUE-XL ) / (XH-XL) 58 RETURN 59 END END OF FILE 3o0

AN EXPERIMENTAL TESTING PROCEDURE FOR DETERMINING HEATER CHARACTERISTICS Robert Handler 31

INTRODUCTION Recent advances in the development of heating elements have allowed new design approaches to drying devices for clothes dryers. An important problem is the determination of heater performance characteristics. Once these characteristics are known, then the effect on performance caused by changes in heater configuration must be found. The purpose of this research is to develop a testing procedure which can be used to determine heater performance characteristics. Three major characteristics described the effectiveness of a heater. These are: (1) thermodynamic heater efficiency, nth (2) velocity profile at heater exit, V2(x,y) (3) temperature profile at heat exit, T2(x,y) It should be noted that for some applications, only one of these characteristics may be important while in others all three may be important. It will be shown, for instance, that all heaters have high thermal efficiency (greater than 90%) and hence efficiency may be relatively unimportant factor in the selection of any particular heater. Once a method has been developed to determine these characteristics, changes can be made to improve one or more of these characteristics. For instance, altering the heater element configuration will change T2(x,y) and V2(x,y) while leaving qth unchanged. Insulation or holes placed in the side of the heater box will change rth but leave T2(x,y) and V2(x,y) unchanged. 33

THERMODYNAMIC ANALYS IS The system analyzed is shown in Figure 1. Air flows past the heating element from the inlet, station 1, to the outlet, station 2. The electrical input power, E, acts to heat the air while the heat loss rate, L, represents the losses across the walls of the duct. The energy equation, for steady state conditions, simply states that the difference between the heat input rate and the heat loss rate is equal to the difference between the leaving and entering enthalpy flux. Then E - L = H -H (1) 2 1 where H = entering enthalpy flux H = leaving enthalpy flux Since the fluid passing through the heater is a mixture of dry air and water vapor, the expression for the leaving enthalpy flux is the sum of the enthalpy flux of the'dry air, HA2, and the water vapor, H2 H2 = A2 +HV2 (2) Now the leaving enthalpy flux of the dry air is written as H2 = h2 dm A A where h2 = enthalpy of dry air A dm = differential mass flux But enthalpy is the product of the specific heat at constant pressure, CPA2 and the temperature, T2(x,y). Note that the exit temperature is a function of position at the duct exit station. Thus ho C= A T2(x,y) 54

The mass flow rate, in differential form, is the product of the density of the air, PA2 its velocity,V2(x,y), (velocity is also a function of positions at the duct exit station) and the differential area, dA2. Combining these several expressions results in the expression for the enthalpy flux of the air at the exit station as H2A= fA CP2 T2(x,y) pA2 V2(x,y) dA2 () In a manner similiar to that used for air, the enthalpy flux of the water vapor is written as the H = f h dm 2V h 2V V2 But now the definition of absolute humidity, c, is introduced as the ratio of the mass flow rate of water vapor and the mass flow rate of dry air as tV mA then the differential mass flow rate of water vapor is related to that for air as dmav = c) d And the enthalpy of water vapor is written in terms of the specific heat of water vapor, CPV, and the temperature, T2(x,y) as y = CPV2 T2(x,y) v V2 2 Combining these several equations then results in the expression for water vapor ethalpy flux at the exit station as HV = A CPV2 T2(x,Y) X2 pA2 V2(xy) dA2 (4) 35

Since as described, in equation (2), the total exit enthalpy flux is the sum of the vapor and air enthalpy fluxes, equations (3) and (4) are combined to give H = ft [CPA Tt(xy) PA^ V2(xy) + CPV2 T2(x,y) pA V2(x,y)] dA which is simplified to CPyv 2= (+ C2 ) A T2(y) V2(y 2 (5) A similar approach is used to develop an expression for the entering enthalpy flux at station 1. The problem is considerably simplied by the assumption of uniformity of both the velocity and temperature profiles at the inlet station. Thus the enthalpy flux is the sum of the enthalpy fluxes of the air and water vapor as 1H = HA + And the air enthalpy flux, HA1 is written as the integral of the enthalpy and the mass flow rate HA = f^ h diiA1 A A1 A1 where the differential for the mass flow rate is the product of the density, velocity, and differential area as dA = pA1 V1 dA1 Thus the expression for the enthalpy flux of the entering air is A = j CPA T1 PA^ V1 dA1 but since none of the variables are a function of position station 1 the integral can be written directly as 36

HA - CPA T1 Pq V1 A1 1 1 1 Note that the mass flow rate, mA1, is the product of density, velocity, and area, mA = pA V1 A Then CAl T1 mA (6) A1 CPA 1 Now the expression for the enthalpy flux of the entering water vapor is written as HV = CP1 Ti C' (7) 1 Combining equations (6) and (7) for entering enthalpy flux gives H =CPA T A +CPv T1 (ninA 1 1 1 C1 1 or / CPV. H, T= CPA 1 C+ a1 (8) 1 mA1 A 1CPA Finally equations (5) and (8) for the enthalpy fluxes at both inlet and exit stations can be combined with the first law of thermodynamics, equation (1), to yield E-1 2 C PA PA2 T2(xy) V2(xy) dA' / 22CP 1 - mAlT1 CPA + ( CPA 37 57

Some further simplifying assumptions are now made concerning the constant specific heats of both air and water vapor along with the realization that the water vapor content of the air, as it passes through the heater remains unchanged and hence the absolute humidity is also constant. Thus = CP CPA = CPA 2 cPv = CPv = CP CPv2 - L = CP = A V So that a final expression can be written for the first law which is: E - L =CA + f CPA f PA2[T2(xy) - T1] V2(x,y) dA2 (9) The humidity term can be interpreted as a correction term sinc.e its value is generally quite small as compared with unity. Thermal efficiency Bth can be defined as H - lHi rth = (10) Thermal efficiency can them be written in terms of enthalpy fluxes using equation (9) as CP CP P A A pA2[T(x,y) - T1] V 2(,) dA2 Trth = 38

EXPERIMENTAL PROCEDURE INSTRUMENTATION AND EXPERIMENTAL DESIGN Following the directions indicated by the thermodynamics analysis, a system was designed and constructed to evaluate the various terms of the thermal efficiency definition. A system schematic is shown in Figure 2, a photograph of the installation in Figure 3. Air is drawn into the inlet, through the heater box, and finally through the blower. The inlet ducting is used to develop uniform flow uniformity. A "Flexatherm" resistance heating element was used in the heater. A measuring station is located downstream of the heater to obtain air velocity and temperature information as a function of position. The inlet temperature, T, is measured with a mercury thermometer, the exit temperature, T2(x,y), and velocity, V2(x,y) are measured at various x and y positions by means of probes mounted on a traverse mechanism as shown in Figure 4. The mechanism consists of a moveable upper plate, used to vary the x-position, and a gear system used to vary the y position of the probes. Figure 5 shows the inside of the traverse. A total head tube and an ironconstantan thermocouple are located so that velocity and temperature-can be measured at'the same location. Read-out devices are shown in Figure 6. The three principal measurements Y, T2 and AP2 are taken to a three-position switch. The thermocouple signal, in millivolts, is amplified so that all three signals are in the 0- to 1-volt range. Voltage and current delivered to the heating element are measured by voltmeters and ammeters as shown in Figure 6. Regulation of current and voltage for the low power heater (approximately 1 kw) was accomplished by use of a variable transformer. Figure 7 shows the actual instrumentation used. A H-P 3440A digital voltameter was used to measure the output signals. An instrumentation amplifier was used for the thermocouple signal. A sensitive manometer (Baraocell electronic manometer, CGS Corp.) was used to measure the difference in total and static pressure heads of the velocity signal. Figures 8 and 9 show methods used in the measurement of temperature and position. Temperature can be measured as a differential quantity as indicated in Figure 8. The digital voltmeter then indicates the temperature differential, T2 - T1. The vertical or y position of the velocity and temperature traverse was measured as shown in Figure 9. The shaft on the traverse mechanism is attached to a potentiometer and a change in shaft position then changes the output voltage. This voltage is then converted into a y-position value. The velocity, Vx, of the air at station x if found from the difference between the total and static pressures according to Bernoulli's equation as 39

V = /40 T APP where T = the absolute temperature measured at station x, deg. R. *xI AP = the pressure difference between the total and static pressures, psi P = the static pressure at station x, psia x TEST PROCEDURE The procedure for obtaining data for a typical run is outlined: (1) Turn on blower (2) Turn on flexatherm heater and wait until temperature has stabilized (3) Record heater current, and voltage (4) Record static pressures at inlet and exit (5) Record barometric pressure, wet and dry bulb temperatures (6) Proceed to take temperature and velocity reading at the outlet of the heater by setting the x-position and varying y. This procedure, assuming 20 to 30 measurements of outlet velocity and temperature are taken, takes approximately 15 to 20 min to complete. It should also be noted that due to the turbulence of the flow, the velocity and temperature at the outlet are both periodic functions of time. Thus, T2(x,y,t) = T2 (x,y) sin (cot + ) AV V2(x,y,t) = V2 (x,y) sin (ot + i) ~~2 V 2AV Since only the average or steady value of these measurements is desired, they can be obtained by removing the oscillatory position of the signal using a highly damped meter. 40

RESULTS AND DISCUSSION SMALL FLEXATHERM HEATER Data were taken for the small heater in 0.1-volt increments in the vertical or y-direction at the heater exit for values of x-locations of 0.125, 0.25, 0.50, 0.75, 1.0, 1.25, 1.75, 2.0, 2.25, and 2.375 in. Since the computer program is written for data at 16 arbitrary locations at the heater exit, and y-readings used for the computer input were those at 0.4, 0.7, 1.0, and 1.3 volts, and x-values of 0.5, 1.0, 1.5, and 2.0 in. Using these values of temperature and velocity, then enthalpy fluxes/ft2 for each x-station are found. A linear integration of these values then gives an approximation to the threedimensional volume as indicated in Figure 10. The linearization, particularly near the wall, of the temperature and velocity profiles, resulted in a considerable error in the final determination of thermal efficiency as indicated in Figure 11. The actual enthalpy flux profile is probably as shown; while the linear interpolation between two adjacent points gives a lower value than is acutally the case. Thus the thermal efficiency of 520/ for the small heater as found from the computer calculations is clearly erroneous. A better approximation to the actual efficiency can be obtained by realizing that: net enthalpy flux = pAVAV CP(TAV2 - TAMBIENT) or LBM 2.75 x 4.50 T2 FT net enthalpy flux = (0.073 FT3 ( 144 FT ) (19.5 E-) (.24 ) (110.7 - 80) = 0.91 B/SEC Then; Tth = NET ENTHALPY FLUX.91 0 Then; ~th =0.99 E.92 More accurate values of thermal efficiency can be obtained by developing a computer program which will take into account all data taken (as well as that in the thermal boundary layer near the walls of the test section). Typical plots of velocity and temperature versus vertical position for X - 1.0 in. are shown in Figures 12 and 13. LARGE FLEXATHERM HEATER Various runs were made with the large flexatherm heater. One run was 41

taken with no insulation, another run was also made with holes punched in the sides of the heater box. Computer output is shown in the Appendix for these runs. Again, Compute calculated efficiencies are seen to be about 50%. These erroneous values of efficiency are easily corrected when the assumption about the thermal boundary layer is recognized. Corrected calculations reveal efficiencies well above 90%. Methods used in such corrected calcualtions are shown in the Appendix. 42

CONCLUSIONS It is evident that from an examination of the.plots of Figure 12 and 13 that there is considerable variation in velocities and temperatures at the outlet of the heater. Velocities are seen to vary as much as 15 ft/sec over the full range of y-positions. Similarly, temperatures are seen to vary as much at 30~F over the range of y-positions. The implications are clear: (1) That experimental velocity and temperature profiles, because of the complex nature of the system under consideration, must be obtained in order to develop accurate values for the thermal efficiency; (2) The irregularities in temperature and velocity fields indicate that flow blockage is occurring and that hot spots are present at the exit of the heater. PRACTICAL IMPLICATIONS The practical implications of this study are these: (1) That such a well-defined, accurate, and quick procedure as developed and described in this report should be of aid in the design and improvement of heating elements. (2) That the criterion of thermal efficiency as a basis for the judgment of heater performance may be erroneous as it appears that heaters are by nature extremely efficient heat transfer devices. (3) That the use of velocity and temperature profiles will clearly be of more use to the practicing engineer than efficiency determinations as they will indicate where, for example, the heater is likely to fail during prolonged use. (4) Such a procedure will enable the engineer to use techniques of trial and error to determine optimum heater configurations (i.e., that which gives uniform temperature and velocity profiles). In conclusion, it is hoped that this procedure will be of use to those engineers interested in the improvement of heating elements. 43

Electrical Input Control Volume2 I 1 2 = Air1 / \ / i\'I Air In | _ _ 4____ ________ Air Out Heater Element Figure 1. System schematic.

Traverse Mechanism A. C. Input r Inlet Duct | Outlet Duct ____ I \ I I [7~~~~ t^~~~ ~ ~Blower Flexatherm Heater Figure 2. Experimental system.

i-:.i::~:;i.--:j;::::::-::::::ii::::::1:::-::r:::'`F::'""'a:B:ilis:-:i:::::: i-:'i::~::_i:lc:';:::il::.:i:::::: i.- -::::i,:i:i::'i::~'.::'::: —''':::: alii~'::c;:::::::::.:::::,j:i::"3ii:,:::::;:_i::::::::::::`::: ~::i::::I::i:::: I::j::;:: j':5:;Rliii:i"-:i:i:::::...::x ~i: """':''i:_:."":':i'i:ii::i::-::~-:l::i.;:.-.:x::::::. I':lci::::'": -''-'-";::('9'':::::i:: -_ _:,:::::::~:: "'i.l""::i:::::i::1~:: —:::::_:~::::::IO:: ii::i::::': isi:;:l:_2_:..:,i':::ig::::::r:::i::::':l:l~:::J::U:i'is:i::-::: l:-i:i: i:::::::i'l;il:-::,.:::::-::-:::::.:::i: —j::Si,'r',i'4~ ly; * isi:::-i:::::i i:::":-:::::-;:':':'r:i:iiii~p':::'::::::j::'~...::::"':l:i: :i':ii-:B''i::~:i:::=::;:;::::i::C:~:::::-.:,::.:\:.::::,:,il:i-i:::::~:-a: :i::44_::-:si: — g:::::j:::"t"',g p, _':::::.: amge fF B: -~~ ~` i::: i:~::::::~::;:::_-:: -:I.::i::::::i:::::::i~i-i: ~~c~e:cl ~ -" g'p Figure 3. Overall view of experimental installation.

L ~ ~~ Jl 1;^::.54.Ma:*l^ -*...:-~~~~~~~~~~~~~~~~~~~~~~~~~~...... Figure 4. Trave-rse mechanism. i:-:::

':::b'::I —:;: iiiii~~~~~~~~~~~~~~~~~~~:r::**/^a iA ^^ I~~~~~~~~~~~~~~~~~.**.-.^'S M -Lii~::-is:iiil Figure —:::: 5-Coeu ie fpoe atace totaes ehnss i:::::.:i:::i::8

Y'-1 y O(xy) Switch T (x, y) AMP. D. V. M. tatPress. Trans. Static Press. Trans. Total Press. From Outlet 0-120 V O-10A 0-250V 0-25 A Variac tA.C. A.C. A.C. A.C To ~~^12~V 00~^ ^~^ C-\ ^\ iHeater 0" 120V A.. C.R Figure 6. Read-out devices.

Figure 7. Instrumentation. 50

b&+ /\ \ 1 2 — P+ m I I FE Const. y FE Const. H \ + G - Amplifier D. V. M. Figure 8. Temperature measurement.

Pot Attached to Traverse, VN < No V Vy Figure 9. Vertical position transducer.

>. E a) X Horizontal Direction Duct Width Figure 10. Sketch illustrating three-dimensionality of temperature and velocity field at heater exit.

- Actual Profile -1 // L-Computer xI /f|,Approximation I/l \\ X X2 X3 X4 Figure 11. Example of the difference between actual profile and the linearized profile used in the computer program. 54

26 2422 20- 0 0 18| | \ ~E = 0.97 KW 18 - \ X= 1.0 Inches Ie~ ~ ~ ~ ~~\ ~ Small Heaters 16 14 12 0 0. 0. 0. 0. 0. 0I I I I I I 10 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 Y (Volts) Figure 12. Typical velocity profile at heater exit. 55

130 125 E = 0.97 KW X= 1.0 Inches Small Heater 120 T(OF) 115 0 110 105 100 I I I I I I I I I I 0 0.2 0.3-0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 Y (Volts) Figure 13. Typical temperature profile at heater exit. 56

APPENDIX COMPUTER PROGRAM FOR DATA REDUCTION In order to facilitate and to formalize the data reduction procedures, a computer program was written. Since the program was written after hand calculations had been made; the sequence and methods used in the program closely follow the conventional data reduction methods and procedures. Certain tables were put into the program: steam tables (for determining humidity calculations), thermocouple voltage-temperature calibrations, and the calibration information for the y-position of the transducer as a function of the potentiometer voltage reading. Then all of the data was read into the computer-the atmospheric conditions, electrical quantities, inlet conditions, along with the temperature and pressure quantities for each of 16 locations, in terms of voltages. Data reduction then followed; first thermocouple voltages were converted into temperatures, y-position voltages converted into displacements in inches, the pressure differences between total and static pressures, in voltages, were converted into a velocity in ft/sec. Humidity calculations were next, followed by determinations of the enthalpy fluxes at the 16 stations at the heater exit. Next integration of these local enthalpy fluxes into a single, average or overall value was found. Finally electrical quantities were used to find the heat supplied to the heater, and then thermal efficiency was found. After printing the majority of the information found, reduced, and calculated, the next set of data was read in and the calculation procedure repeated, until all input data had been processed. A copy of the computer program, together with a set of data for the small heater is included. A list of the nomenclature follows. 57

NOMENCLATURE Variable Computer Units AP in PR psi Y YV Volts X X in. TV Volts Amps Amp Amps Volts Volts Volts Wet bulb WB ~F Dry bult DB ~F Baro Baro in. Hg PStatic exit PSE psi PS in PSI psi TIN TIN ~F PVAP PVAP psi TVAP TVAP ~F HVAP HVAP Btu/lbm TMV TMV mv Thermocouple T acutal TA ~F calibration YA YA in. TB YB in./volt TCAL mv/v Duct width XW in. Duct Depth YD in. Exit vapor enthalpy HV OUT Btu/lbm 58

RFAIL I OSS I MF lS I nN PR (1 6 ) Y \ (16) T\/ (16) T ( ) Y (16 ), \!(16) P\ AP(1 0) 1 H AP( 10 ),TM\/( 10),TACT( 10),H!T( 16), X(4),T AP( 10) 2HFI.IIX ( 16 ) ARFA (4 ) NAM FLIST/FXP)DAT/Y\/T\/V,PR,WR, OR, BARl, AMPS.\/rOTS,PSE, PS I,TC AL,YA,YR DATA P\/AP, T\/AP.H\/AP TMVI,TACT,Y), X!, X/.3629?2,. 949?24 t? 2230, 4.7414, C9.340,. 1 7186. 9.840,49.200,77.693, 117.992, 70., 100,130. I160., 190., C?20.,n50.,?80.. 0.. 340., 109.1, 1105.1., 117.,1130.2,).142.11153. C 4, 1164.0, 1,173.8, ]1 8. 5, 1190., 1.07, 1.94, 2.?,. 71,4 61, 5. 51,6.4, 7 C.33,8.2 5 9. 1 7,70., 1(00., 130., 160., 190. * 2?0., 50.,?80.,310.,340., 4. C4.2.5,.5.1.0, 1.5,?.0/ IlR. I TF (6, 33) 33 FORMAT('OSTFAM TARI FS. TFMPS,PRFSSRIJF, FNTHALPY') R T TF (6,30 ) ( TVAP( I ), =1, 0 ) WR I TF (, 30) (P\ AP ( I ), T =1 1 ) R I TF (6. 30 ) (HVAP ),=1.10) WR I TF (6h 34) 34 FFRMAT(.OTHFRMOCnlIPLF DATA, nFG MTI LI/fOLTS') WRITF(6,30) (TACT( I), 1=1.,10) WIR T T F ( 6, 30 ) ( T A /T ( I ), T = 1., 1 0 )!,WRTTF(6, T VnT) T=].,].f) WR ITF (6 3 ) ( X ( T ), =1 4) n3 FnRMAT( 10 F1 o03 / ) 5 PRFAD (5, XPnAT) WtR T TF ( 6, 35) 35 FnRMAT('ORAWI DATA, YPSnITIf-}N, THEFR NMDOt i PLF, PRFSSIkRE') WRITF (6,20) ((IYV( T),T\!(I) PRP( T ) ).I=l.1 ) WRITE (636)? FFRMAT ( [4,2Fl)3, Fl( n4/)!.,R T TE (h 6 ~h ) 36 FnRMAT('OWFT RtiLR, nRYRI JL, RARNMF TF-R ClRR FIT, \/nv TAG(F, IN AND!" FXIT S ITATIC PRFSSIJRF, TCAL, P1S IT CAI. YA.YR ) W, RIT (6.1 ) WR, R, RARn. AMP.S, VOfI TS,PS I,PSF., TCAL, YA YR 21 F RMAT ( 1 F10.3/ ) C TFMP CnN MV TO nFCG F nn 50 1=1,16 TFMP=T\/( T )':TCAt1 DN 49 J=1 l9 F ( TFMP. T. TM\ (,J ).OR.TFMP. GT. TM\/(+ )) ),n Tn 49 T( I ) =TACT ( )+ ( TA(T ( +1 )-TAC,T ( ) ) / ( TM (J+1 )-TM\/( J ) ) ( TFMP-TM V ( ) ) 49 CONT(ITI\IUF 50 nT N rTIN F C Y POSITIrN AND \IElCITY CONiV nn ho I=,.16 Y ( I )=YA+YR YV\/( I ) 60 \V( )=SORT( 3440.' P R( I ),(46h +T( I ) ( AR,: nO.z 491+PS ) ) \A \ =., nn 22 1=1,16 TAV=TA\+T( I) 22 VAV=VA\/+\/(I TAV=TA \/16. \/ A/=VA \/ /16. Wl, I TF(6,23) TAVV/AV\ 23 FORMAT( 2F12.3/) IR I TF ( 6, 37 ) 37 FORMAT('ICORRECTFn DATA, POs ITI NV\/FLFOCITY,TFMP ).IR I TF(6.31 ) ((I,Y( ),V( I ),T( I ) ) T =1., 16) 31 FORIAT ( I4,2Flo0.3, F1n. 3/) C SARATIRATION PRFSSIJRF VIA WlR nn 70 1=1,9 IF(lWR.IT.TVAP( I ). n.OR lR.GT.TVTAP( 1+1)) C.Or TO 70 59

P\/=P\/ AP (I )+ (PVAP ( +1 )-P\/AP ( I) ) /( T \/AP( 1+1 )-TVAP( I ) )*( W-T\/AP( I ) ) 70 C n\lTI NINUF C SPECIFIC HUMIDITY P A R=R AR N: 4. 69. / 29 92+P SF W=O.622*PV/(PAIR-PV) C INLFT VAPlOR ENTHALPY nn 71 1=1,9 IF(-DR.LT.T\/AP(I ) nR.DP.T.T\AP( I+1 )) Gn Tn 71 H\/APIN=HVAP (I)+(H\/AP(I+1 )-HVAP( I )) /(T\/AP( +1)-TVAP(I)) 1/(DP-TVAP( ) ) 71 CONT I NJUE WR I TE (6 38 ) 38 FnRMAT( OVAPOR PRESSIJRF,A I PRESSSPFC. HIJMID,INLET VAPOR ENTH.') WRITF (6,26) PVPAIRW,HV\APIN 26 FnRMAT(4F12.4/) C niOTLFT VAPOR ENTHALPY nn 7? =1.l, 16 nn 73 1=1,9 TF(T(,J),IT.TV\AP(I).OR.T(J).GT.TV\AP( +1)) GO Tn 73 HVnUT( J )=HVAP( I )+(H\/AP( 1+1 )-H\AP( I) )/( TVAP ( I+1 )-TVAP( I ))( T( J)1TVAP( ) ) 73 Cr, nTI hNIF 72 C NTINUJF C nljTLFT FNITHALPY FLUX —LOCAL nn aO 1=1.,16 sn HFLIJX(I)=144./53.3 (PAIR-P\I)/(46h.+T(I))'\/( I ).(0.24*,(T(I)-DR) I + w^ ( H\/ntT ( I )-H\!AP I n ) WR I TE (h 6 39 ) 39 FnRMAT('OEXIT VAPOR FNTH, FNTHALPY FLUtX') WRITE (, 32 ) ((,H\/nl T ( I),HF I IX ( I)) I= 1 16 ) 32 FnRMAT(I4,2F10,3/) C nIITL FT ENTHALPY FLUIX AT EACH X STATION nn 5 J1=1,4 T=1+4^*(J-1) 85 ARFA(,I )=(YD-Y ( ) )HFl..lX( I )/2. 1+(Y( I+0)-Y( I+1 ) )'(HFLIIX( 1+1 )+HFIJX( (I+O) )/?. 2 + ( Y ( I + ] )-Y ( I +2 ) )'* (H F LIt JX ( I + 2 )+HF LI I X ( + 1 ) ) / 2. 2+(Y( I+1 )-Y( I+2 ) )* (HELIJX ( I+?)+HELIX( I+1 ) )/2. 3+(Y( I+2)-Y( 1+3 ) ) (HFLIIX( T+3)+HFIIX ( I+?) )/2. 4+Y ( 1+3 )HFLIJX (+3 )/2. WRIR I TE (6,40 ) 40 FnRMAT('OENTHALPY FLIX/WlIDTH AT FOUR X STAS. ) WRITE(6.2f8) (ARFA(I),1=] 1,4) 28 FnRMAT(4F10.4/) C nITLFT ENITHALPY FLUX 7FTA=AREA(1. )X (1)/2. I+(X(2)-X(1))*(ARFA(2)+ARFA(1 ))/. 2+(X(3)-X(2))'- (ARFA(3)+ARFA(2))/2. 3+( X ( 4 )-X ( 3 ) )* ( ARFA ( 4 )+AREA ( 3 ))/2. 4+(XW-X(4) )*ARFA(4)/?. 7FTA=7FTA/1 44. F)rlT=AMPS.: \/Vl)lTS 3. 4 13/36n0. I SS= FDI T-7 F'A FF=ZETA/EOn)T WRITE(,41) 41. FnRMAT('O!,!ATTS IJN.l.nSS EFFF., NFT HFAT F..LX') W.PRITFE(h2P) FDOT, n. nSS.,FFF,7FTA Gn Tn 5 FND 60

UNIVERSITY OF MICHIGAN I I9015 03026 6129ll 3 9015 03026 6129