THE UNIVERSITY OF MICHIGAN DEPARTMENT OF MECHANICAL ENGINEERING CAVITATION AND MULTIPHASE FLOW LABORATORY WALTER E. LAY AUTOMOTIVE LABORATORY ANN ARBOR, MICHIGAN REPORT No. UMICH 014571-15-I COMPUTER ANALYSIS PROGRAMS COMPUTER GRAPHICS by Robert J. Niedzielski, Jr. Submitted to Prof. F. G. Hammitt for M.E. 490 Supported by NSF Grant No. ENG 75-2315 and University of Michigan Internal Funds (SEP and Work Study) April 20, 1978

ABSTRACT During the course of research in the Cavitation and Multiphase Flow Lab, it became necessary to write computer programs so that vast amounts of data could be simplified and correlated in a minimum amount of time. A total of five FORTRAN programs were written, one dealing with a cavitation project and the other four for wet steam tunnel research under the direction of a doctoral student, Mr. Wontaik Kim. In addition to these computer programs, machine plotting was done for the cavitation project using a canned plotting program known as the Adroit Display System (ADS). All of the computer work was done on the.Michigan Terminal System (MTS). This report contains the purpose of each computer program, explains what it does, and lists the equations that are used in it. Also included are program listings, lists of variables, user's guides, and flow charts.

TABLE OF CONTENTS Foreward and Acknowledgements 1 Acceleration Ratio Program 2 Break-up Time Analysis Program 5 Deformation of Droplet Program 8 Induced Velocity Program 10 Linefit Program 13 Computer Graphics 16 Appendices 18

FOREWARD AND ACKNOWLEDGEMENTS Except for the linefit program for the cavitation project, the other four computer programs are very closely related. Each program deals with wet steam flow across a simulated turbine blade, and more importantly, water droplet behavior after these drops leave the edge of the blade. Approximately forty high-speed movie films were analyzed and recordings were made for several hundred droplets. All of the data from these observations are stored in the computer and every program dealing with this subject matter makes use of this data file. Thus every program involving the steam tunnel research is similar in what it starts out with as a base but is different in what it calculates. The author would like to express his extreme appreciation of the help that was given to him by Mr. Michael Wegenka, a graduate student in Mechanical Engineering,who provided some much needed assistance, particularly with the plotting programs. -1

ACCELERATION RATIO PROGRAM One of the major investigations undertaken in the wet-steam tunnel research during the past year was to determine the acceleration of water droplets after they left the blade to see just how much velocity they could.obtain if they. hit another row of turbine blades. This was measured from the data obtained from the films at various steam velocities and liquid flow rates. But even though the actual drop's acceleration could be found, it was of extreme additional interest to see if the test results could be verified by analytical calculations. This computer program first determined the measured drop acceleration and then found the analytical acceleration, using three different equation to give three different definitions of analytical acceleration. The ratio of measured acceleration to analytical acceleration was also found, and displayed in the output. Program Calculations The measured acceleration was calculated from the relations Velocity = Distance/Time and Acceleration = Velocity/Time This was done for every observation and an average droplet acceleration was calculated for use in the rest of the program. There is one equation that is used to find the analytic acceleration. It is: Acceleration = (Drag Coefficient)( ) t)(teiam~el P Drop Diame ~^~ -

The reason why we have three different analytic accelerations is because we are using three ways to calculate the droplet drag coefficient. Each of these equations is different in the relations that they use. The three expressions have been proposed by Serafini, Abraham, and Churchill. The Serafini expression for the drag coefficient is: CD - ( 1+ 0.17 Re23) The Abraham expression for the drag coefficient is: DA 0.292 ( 1 96 )2 The Churchill expression for the drag coefficient is: Dc 24 +( R)5/9 9/5 All of these equations involve the droplet Reynolds number, or Re, which is found by: Re=(Drop Diameter) (Steam Velocity)/(Kinematic viscosity After all these drag coefficients were found, different analytic accelerations could be calculated and the ratio of measured acceleration was taken to each analytic acceleration. This was done in order to find the expression of analytic acceleration that was best suited to our experiment and gave reasonable predictions for every steam velocity and flow rate. After the computer calculated the various accelerations and ratios for a particular steam velocity and flow rate, it performed averaging routines tn find the mean values of measured

acceleration, drop diameter, Reynolds number, measured acceleration, analytic acceleration, and ratios. This allowed us to find the scatter around the mean value and how many of the points were far away from the norm. The standard method of taking averag was used: m Re =i Re/M n=l Once the averages were obtained and written out, the control and the counter were reset and the program resumed its calculations. This process continued for five steam velocities and many different flow rates until all the data was used and converted into the desired units. A fter this was done the output was examined and the best relation for analytic acceleration was choose

BREAK UP TIME ANALYSIS PROGRAM When one is studying water particle motion, a number of relationships become important and many different numbers can be calculated. Many of these numbers relate the droplet's speed and size in a dimensionless way. The purpose of this computer program was to find, for split particles only, the drop's initial and final dimensions, its velocity, the total time that observations were recorded, and the Weber number, Reynolds number, dimensionless break-up time, dynamic pressure ratio, and type of dimensionless time ratio. All of the calculations were carried out from the basic data file containing only the droplet's diameter, thickness, and position from the edge of the blade for each observation. It should be noted that there were very few particles that split up in our recordings at the lowest steam velocity, but as the steam velocity increases, the number of split particles increases until the higher steam velocities when almost every particle splits up. Program Calculations The real time is calculated by subtracting one from the total number of observations and multiplying this number by 0.001; the number of seconds between every observation. The 0.001 was found from a motion picture film speed of five thousand frames per second ar.d the fact that observations were recorded every five frames. Therefore there is one millisecond for every interval over which data was recorded.

Distance was found by subtracting the final position of the droplet from the initial position and converting it into metric dimensions. Velocity of the droplet is simply distance divided by time and the initial and final drop thicknesses and diameters were easily found. Next, the proper Mach number of the steam was determined. In order to find the Weber number, the following equation was used: We = ()(V(Do) (steam density)(steam velocity)2(drop diameter; We = surface tension Reynolds number can be found from Re - (V)(Do) Re = (steam velocity)(drop diameter) kinematic viscosity of steam Dimensionless break-up time is calculated according to the equation: Tb (DO) ) T (real time)(steam velocity) team density b ~ (drop diameter) * water density T~@ dynamic pressure ratio depends on the Mach number of the steam and follows from: Qm = 0.78 + [ f )(M'4 b4- Finally, the expression for dimensionless time times the square root of Qm or the dynamic pressure ratio was calculated. This was done to give some correlation between the actual dimensionless time and a time that it takes as the force moves around" -a.

the droplet. The results were printed out for every split droplet in one line across the page. Headings were written and the program continued for five different steam velocities until the data was exhaustd. ^

DEFORMATION OF DROPLET PROGRAM In the study of flUid mechanics and water droplet behavior, many important relations involve non-dimensional numbers. These dimensionless quantities do not have the same value as their actual counterparts, but can merely give a representation of what was happening and allow for some extra relationships to be developed. For this particular computer program, the water droplet observations were reduced into subsets and for every droplet observation, the ratio of the present drop diameter to the initial drop diameter was found, along with the mass ratio between present and initial droplets, dimensionless time and distance, and the ratio of droplet diameter divided by thickness. When particles split, the program calculated the dimensionless break-up time, Weber number, dynamic pressure, and a type of nondimensional "acceleration". This computer program is different from the other three dealing with the same experiment because it writes out results for every observation instead of just one line for every droplet with the average diameter being used for all the calculations. Program Calculations The area of the droplet was calculated from the relation A ='~/4 d2 and the volume of the droplet was found from the equation V = 16/3 At~where t is the thickness of the drop. The mass of the droplet is simply the volume times the density of the water.The real time is again calculated from the motion -8

picture film speed and the number of frames between each observation. Dimensionless time is calculated in the same way as it was in the Break-up Time Analysis Program except thatpis calculated at every observation and not just for split particles. Dimensionless distance is found by subtracting the droplet's initial position from its present position and dividing it by the initial diameter. These simple relationships were calculated for every observation and written out. If the particle split, some additional expressions were found. Initially, if the particle split up, dimensionless breakup time was defined as dimensionless time for the last observation. The Weber number was found as previously described and the dynamic pressure was found in two different units. Dynamic pressure is defined as p -1 iv2 d 2 and this number was calculated in both psia and newtons per meter squared. Finally,a dimensionless number was calculated that takes dimensionless distance and divides it by the dimensionless time squared. This type of dimensionless "acceleration" gives some relation between these two quantities and proved to be quite interesting.

INDUCED VELOCITY PROGRAM. After obtaining the data from the Acceleration Ratio prograr it was observed that for the higher steam velocities, the measured acceleration was consistently less than the analytical accelerations. In order to try to explain this phenomena, this computer program was written to find the induced velocity by the vortex, which affects the motion of the droplet, and also the vortex strength. Also included in this program is the work of Mr. Richard Tseng, who calculated a frequency of the droplet movement for the two lower steam velocities also called the periodicity of deceleration. Knowing this periodicity, we were able to calculate Strouhal numbers for the steam, liquid film, and the blade. All of this data, along with the average drop diameter, Reynolds number, measured acceleration, and acceleration ratio, was written out in a variety of formats. Program calculations The measured and analytic accelerations were calculated in the same way as in the previous programs. The definition of analytical acceleration that we used was the one by Serafini. The periodicity of deceleration data was stored in a file and read in so that the Strouhal number could be calculated as follow: s (D) v7I~T) Sv ('StamDrop diameter) v = (Steam velocity)(frequency) -iO

The Strouhal number for the film was calculated and film velocities were read into the program S. = v film T(V f) (i..(Drop diameter) v film = (film velocity)( frequency) The Strouhal number for the simulated turbine blade was found using the equation.4 v blade (V )(f) (blade width) v blade (steam velocity)(frequency) The induced velocity caused by the vortex involves first a calculation of the acceleration difference of analytical minus measured and then disregarding the calculational steps if the measured acceleration is greater than analytical acceleration. If this difference is positive, then the induced velocity is calculated by: Induced velocity =. a)(average diameter)(lQ( ) The vortex strength is found by the following equation: Vortex strength = (Induced velocityi ---- After all these numbers are calculated, a series of IF statements determine which format code to write on.The results

are written out and the program continues to calculate accelerations and ratios throughout but the StrQOhal numbers are only calculated for the first two steam velocities. -_-

LINIEFIT COMPUTER PROGRAM Introduction and Purpose During the course of cavitation damage research it became necessary to write a computer program to verify hand-drawn graphs and the observation that when a log plot of incubation period and MDPh was made, a straight line was obtained with a slope approximately equal to one. In order to confirm this observation, a linear regression analysis was carried out by the method of least squares. The logarithm base 10 was taken of each definition of incubation period( Tangent intercept and 0.1 Mil) and the logarithm base 10 was taken of the inverse of the maximum MDPR and these values were plotted on the x and y axes, respectively. Through regression analysis the slope of the best-fit line was found as well as the proportional constant for the best-fit line. Computer output verifies the fact that for each set of data, the slope of the line is approximately equal to one. It should also be noted that the original computer program was written by Michael Wegenka, who is now a graduate student in Mechanical Engineering at the University of Michigan, and who is responsible for a portion of the final computer program used in this report. Program Calculations The major relationship between the incubation period and MDPi can be found in the equation (Ip)m C/MDPR Taking the logarithm base 10 of each side of the equation we obtain m logo1 IP = loglo C - loglo l/MDPR Or, rearranging the equation loglo 1/MDP = m loglO IP - logio C This equation now has the same form as the basic equation for a line: y = mx+b where m is the slope of the line and b corresponds to the log of the proportional constant. In order to find m and C, the following equations

were used n n n xl iYi Xi ilYi/n i-1 i=2l i = - Yi - M( Xi)) /n i=l 1 C = 10 i=l i=l These two numbers are the ones that are most important in the MDF.P and incubation period analysis. In addition to a proportional constant for the best-fit line, a constant can be found for each pair of data points using the calculated slope according to the original equation C ( (xim)(yi) or C = (Incubation Period)m (MDPR) By finding the proportional constant for each pair of data points, an analysis can be made of all the proportional constants obtained for a set. The average proportional constant is calculated by I n C_ - Ci N ill The proportional constant mean deviation is found by 1 n MD - = IC - N i=l The proportional constant standard deviation is defined by C- Ci)2 SD / V ( N - 1) The proportional constant root mean square is calculated by RAjs - ) ci2 i=l -jq'

Output Results An inspection of the computer printout will show that underneath the title are two headings, one to describe the material tested and the other to detail which measure of incubation period was used. Then the raw data and their base 10 logarithms are listed as well as the proportional constant for each pair of data points. The slope of the line or exponent m in the original equation can then be found along with the proportional constant for the best fit line. Finally, there is a statistical analysis of the proportional constants from each pair of points and the average, mean and standard deviation, root mean square, and maximum and minimum proportional constants are listed for the set of data. All of these figures can be found for each material tested and the particular method of measuring incubation period that was used. I- \1-~

MACHINE PLOTTING Or CAVITATION DATA Once all of the data was collected for.the c'.aitationdamage research,'program, -:;' — i:'-r:.:\'.- and after a computer program was written to calculate the slope of the best-fit line and the corresponding proportional constant, the next logical thing to do was to make computer plots showing all of the data and the best fit line through them. This was accomplished by using the Adroit Display Subsystem(ADS) written by Professor Richard Phillii of the University of Michigan Aerospace Engineering Department. This plotting program can only be used on special graphics terminals and require that all data to be plotted be in a file and that some file is empty to store the graphs. A full,detailed description of ADS is in the possession of Michael Wegenka, the author, and Peter Felbeck, and this text is very necessary before any plots can be made. ADS is completely separate from the Plot Description System (PDS) that is on public file and is described in Volume 11 of the Mighigan Terminal System manuals. ADS can accomplish just about as much as the much more difficult MTS 11 plots. ADS has its own set of commands and produces CALCOMiP plots. If the person plotting desires to do as little work as possible, he can specify the type of axes and specify the data file and use the AUTO command to produce everything but the text. The basic procedure to making plots with ADS is relatively simple. First, specify the maximum and minimum x and y values. Next specify the axes(~ her rectar-ular, semi-log, or log-log) -I^

and then tell the computer where to put the tick marks. Once you have the tick marks you can label the tick marks and the axes. ADS has a separate TEXT subroutine mode, using it you can put any text in the graph as large or as small as you want it wherever you want it. HORZ or VERT specifies the orientation of the text in the graph and SCAT controls the size of the text. The GO command allcws you to enter text and position it wherever you want, using cross-hairs that appear on the screen of the graphics terminal. The ADD command allows you to enter data into the graph structure and the DATA command plots the data(using the default character +) on the screen. Of particular importance to Aerojet graphs was the CRVF command. CRVF (for curvefit) calculated the best fit straight line (in our case) and draws it on the screen. There is a variety of other very useful commands, all of which can be found in the ADS description. There are a few more very important ADS commands that save a lot of time and make plotting easier. The SAVE command will place whatever is on the screen into a file, which can be called back by the REST (restore) command. This eliminates having to always having to specify general text and axes labels and tick marks. Finally the CALC command produces the necessary commands to produce a CALCOMP plot and stores this in a file. Actual plots cannot be made until the $RUN *CCQUEUE command is used.

TABLE OF APPENDICES Appendix 1 User's Guide 19 Appendix 2 List of Files 22 Appendix 3 Acceleration Ratio Flow Chart 23 Appendix 4 Acceleration Ratio Program Listing 25 Appendix 5 Acceleration Ratio List of Variables 27 Appendix 6 Break up Time Analysis Flow Chart 30 Appendix 7 Break up Time Analysis Program Listing 31 Appendix 8 Break up Time List of Variables 32 Appendix 9 Deformation of Droplet Flow Chart 33 Appendix 10 Deformation cf Droplet Program Listing 34 Appendix 11 Deformation List of Variables 36 Appendix 12 Induced Velocity Flow Chart 38 Appendix 13 Induced Velocity Program Listing 40 Appendix 14 Induced Velocity List of Variables 43 Appendix 15 Linefit Program Flow Chart 45 Appendix 16 Linefit Program Listing 46 Appendix 17 Linefit Program List of Variables 48 Appendix 18 Sample ADS Commands 49 Appendix 19 Sample Computer Plots of Cavitation 51 5-19

USER'S GUIDE In order to run the computer programs that are described in this report, some basic knowledge of the Michigan Terminal System is required. The actual commands that are used will be provided for each program, and can also be found in the program listings themselves. All of the programs are on punched cards except for the linefit program, which is on file in the computing center. All of the data, however, is on file, and in order to run the programs smoothly and change things when needed, one really needs to know about how to operate terminals and how to edit files. All of the programs were written in FORTRAN, and one should know exactly what each program does before he attempts to change it. Keeping all of this in mind, it should be noted that the detailed explanation of the requirements for putting data into a file can be found in Michael Wegenka's December, 1977 report number UTnICH 014571-11-I and will not be repeated here. The programmer should have no problem with his data files, however, as long as he keeps two things in mind:first, make the formats large enough to accomadate a large range of data with a lot of decimal places; and, second, when entering data into a file, be sure to always include a decimal point and a comma between each number. The basic commands to run a MTS job from the card reader are as follows: $SIGNCN ODLU T=3 P=20 PASSWORD $RUT *FTN These three cornands sign you on the computer and allow ^T-`

you to identify yourself as aparticular user with a signon ID. The password is your control to prevent other people from using your account. The first parameter after the signron ID is a time limit of the use of thetain unit of the computer in seconds and the second parameter is the page limit. These two parameters should always be used so that if something is wrong with your program, it will not go on continously and use all of your money. Additionally, if you want to specify a higher-quality printer, the command PRINT=TN on the signon card will assure that this happens. The $RUN card tells the computer that it should use the Fortran compiler for your program. These three cards must always appear at the beginning of every program. After all of the program cards appear, some additional MTS commands are necessary: $RUN -LOAD 1=T3DATA 2=FDATA 5=WDATA(1,1873) $ENDFILE $SIGNOFF The $RUN -LOAD card is probably the most important because it specifies which files are to be used in the input/output statements. Whenever you use a read or write statement, a particular unit is specified. Usually, by default, Unit 5 is attache to a card reader and unit 6 is attached to a line printer. For our purposes, however, unit 5 must be attached to a data file and other units( for example, units one and two in the induced velocity program) can be attached to other files with other necessary data. Things can also be written into a file in additic to getting output on a printer. Thip. can be done by using, for example, Unit 7 as a place to store data in a file ( as it was -^-

in the linefit program). In order to run the linefit program off a terminal ( using the compiled program LF) the following MTS command card is necessary: $RUN LF 5=MDPRDATA 6=*PRINT* 7=-A ROUTE=CNTR This tells the computer to use the compiled program, read the data from the file MDPRDATA, print the results on a line printer, and store some of the calculations in the temporary file -A. The ROUTE=CNTR is not necessary because the Computing Center on North Campus is the default route but if you want to pick up your output at NUBS, you must specify ROUTB=NUBS on this line. If you use punched cards, the ROUTE= and 6= can be omitted because you are automatically defaulted to a line printer at wherever you are originating your job. -0^h

CURRENT LINE FILES FDATA Contains values of liquid film velocity LF Compiled linefit program LINEFIT Program listing of the best straight line-fit prograi MDPRDATA Data file with incubation periods and MDPR values PFILE Plot file with data in the proper form to be used the ADS plot routine T3DATA Contains periodicity of deceleration data based on.3 peak T5DATA Contains periodicity of deceleration data based on.5 peak WATERDROP Original acceleration program listing WD Compiled acceleration program WGABAR Listing of measured acceleration and ratio for every droplet WGAVG Listing of measured acceleration and ratio for a given steam velocity and flow rate WDA TA Complete data. file containing ah.L of the data for all the observations and the distance away from the edge of the blade, drop diameter, and drop thickness - ^-~

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$SIG ODLU T=3 P=20 $R *FTN 5=WCATA C ***************** ACCELERATICN RATIC EFOGBRA ********t ****** C THIS PROGRAM CALCULATES THE MEASURED ACCELERATION AND THREE C ANALYTIC ACCELERATIONS:SERAFINI, CEURCHILI, AND ABRAHAM. C IT ALSO FINDS THE ACCELERATION RATICS AND DETERMINES AVERAGE C VALUES FOR EACH STEAM VELOCITY AND FLCW RATE. DIMENSION ACEL(20),FN(20),DIA(20),T(20),X(20),TD(20),DELX(20), 1 VEL(20),DELV(20),ABAR(25),DRPU(25),RE(25),CDS(25),AS(25),RS(25), 2 CDA(25) 25)RA(25)5),CDC(25),AC(25),RC(25)R 5) WRITE(6,199) TOTHRD=2./3. ANIN=9./5. FIVNIN=5./9. CON=30. 48 READ(5,101) FILMV,RHCW,CONFAC,VCHECK,QCHECK M=.0 O 1 ASUM=0.0 TTOL=0.0 DPSUM=O.0 C ***** READ THE DATA EOR EACH OBSERVATICN **** DO 110 I=1,20 READ(5,101) FN(I),DIA (),T(I),X(I) DPSUM=DPSUM+DIA (I) IF(T(I).LT. 0.0) GO TO 120 IF(X(I) LT. 0.0) GO TO 130 110 CONTINUE 120 T (1)=ABS(T(I)) 130 X(I)=ABS(X (I)) READ(5,101) V,Q IF(I.EQ. 2) GO TO t C **** CHECK TC SEE IF THERE RE E NEW CCNDITIONS ***t IF(V.NE. VCHECK.OR.Q.NE.QCHECK) GO TO 160 100 M=M+1 DRPU (M)=DPSUM/I*. 45 C ***** CALCULATE THE MEASURED ACCELERATICN **** DO 150 J=2,I TD (J-1)=0.001 TTOL=TIOL+TD (J-1) DELX (J-1)= (X(J)-X (J-1) )*0.45 VEL (J-1)=DELX (J-1)/TD (J-1) IF(J.EQ.2) GO TO 150 DTAVG= (TD (J-1) +TD (J-2) ) /2.0 DELV (J-2)=VEL (J-1)-VEL (J-2) ACEL (J-2) =DELV (J-2) /2./DTAVG ASUM=ACEL (J-2) +ASUM 150 CONTINUE IM2=I-2 ABAR (M)=ASUM/IM2 SVEL=V *CON C ***** CALCULATE THE ANALYTIC ACCELERATICNS **** RE(M) =V*DRPU(N) *32.61 CDS () =24./RE (M)*(1.+0. 17*RE-(M) **TCTHED) AS(M)= (CDS (M) *0.75) *.0001135/DREgU () *SVEI**2 RS (M)=AEBA () /AS (M) CDA () =.292* ( (1.+ (9.06/ (2*RE () ) **.5) ) **2) AA (M)= (CDA (M) *0,75) *.0001135/DREU (a) *SVEL**2 RA (M) =ABAR (M)/AA () CDC (M) =24./RE (M) ( (1. + (RE (~1) /60) **FIVNIN) **ANIN)

AC (M)= (CDC (M). 75) *. CO001135/DEP (M) *SVEL**2 RC (M)=ABAR (M)/AC () WRITE(6,200) V,Q, DSPU (),RE(M),ABAR (M),AS (M),RS (M),AA(.M),RA(M) 1 AC (),RC(M) GO TO 1 C ***** DETERMINE AVERAGES ****~ 160 DPS=O0.O RESUM=0O0 ACCSM= 0.0 SESU = O.O RSUM=0.0 AASm=0.0 RASM=0. 0 ACSM=0.0 RCSM=0.0 DO 170 N=1,M DPSM=DPSM+DBPU (N) RESUM=RESUM+RE (N) ACCSM=ACCSM+ABAR (N) SESUM=SESUM+AS (N) RSUM=RS UM + (N) AAS MA ASM+ AA (N) RASM-RASM+RA (N) ACSMACSM+AC (N) RCSM=RCSM+RC (N) 170 CONTINUE DPBAR=DPSM/M REBAR=RES UM/M ASBAR=ACCSM/M SEBAR SESUM/M RBARR SUM/M AABAR= AAS/M RABAR=RAS/M, ACBAR= AC3SM/M RCBAR=RCSM/M WRITE (6, 201) QCHECK,DPBAR,REBAR,ASBAi,SEER, REAR, AAEAR, 1 RABAR,ACBAR,CEBAR M=0 0 VCHECK=V QCHECK=Q IF(I.EQ.1) CALL EXIT GO TO 100 101 FORMAT(6(F10.5)) 199 FORMAT ('1','STEAM' 4X'FLOW,3X' DROP' 4X,'REYNOLDS',3X, 1' EASURED' 5X'SERAFINI SERAFINI AB AHAM ABRAHA',3X, 2'CHURCHILL', 2X,'CHURCHILL'/' VELOCITY',2X, RATE DIAMETER' 3 3X,'NUMBER,2X'ACCELERATION ACCELERATICN,2X,'RATIO',3X, 4'ACCELERATION RATIO ACCELERATICN',3X,'ATIO'/ (FEET/S)', 5 1X, (CC/M) (CM) I, 13X, (CM/SEC**2) (CM/SEC**2), 6 11X, (CM/SEC**2), 11X'(C /SEC**2)') 200 FORMAT ('0' 1 X, F6. 1,3X f4 1,2X, 6. q 4, X, F8.3 3, X,F 11. 3 3X, 1 F10.3,3X,F6.3,3XJ,F 10.3,3X,F6.3,2X,F10.2, 4X,F6.3) 201 FORMAT ('O','*AVG FCR Q=,F3.0,1X,F6.4,3XF8.3, 1XFll3,3X, 1 F10.3,3X,F6.3,3X, F10.33X, F6.3,2X, F10.2,4X,F6.3) END $ENDFILE $R -LOAD 5=WDATA $EN -F ILE $SIG U _ -^

^A ct-(e(@ n R L;t PC e e r AA(M) Analytical acceleration as calculated by Abraham AABAR Average of all Abraham accelerations for a particular steam velocity and flow fate AASM Sum of all Abraham accelerations for a particular steam velocity and flow rate ABAR(M) Average of the measured acceleration for one droplet AC(M) Analytical acceleration as calculated by Churchill ACBAR Average of all Churchill accelerations for a particular steam velocity and flow rate ACCSM Sum of all the measured accelerations for a particular steam velocity and flow rate ACEL(J) Measured acceleration of one droplet for three successive film readings ACSM Sum of all the Churchill accelerations for a particular steam velocity and flow rate ANIN A constant, five-ninths AS(M) Analytical acceleration as calculated by Serafini ASBAR Average of all measured accelerations for a particular steam velocity and flow rate ASUMJ Sum of all the measured accelerations for one droplet CDA(M) Abraham's experssion for the drag coefficient CDC(M) Churchill's expression for the drag coefficient CDS(M) Serafini's expression for the drag coefficient CON A constant conversion factor, 30.48, the number of cm/ sec in one foot/sec CONFAC A constant conversion factor,.45, the number of centimeters in one measured screen unit DELV(J) The difference between two consecutively measured velocities DELX(J) The difference between two consecutively measured distances DIA(J) The diameter of the water droplet for a particular observation DPBAR The average of all the diameters for a particular steam velocity and flow rate -^lc -

DPSM The sum of all the diameters for a particular steam velocity and flow rate DPSUM The sum of all the diameters observed for a particular droplet DRPU(M) The average of all diameters observed for a particular droplet DTAVG The average time between each successive observation FILMV The film speed at which the pictures were taken FIVNIN A constant, five-ninths FN(I) Number of frames between each successive observation IM2 The number of observations in a set minus two M A counter which teels how many different cases were obser for each steam velocity and flow rate Q Flow rate of water entering the test section QCHECK A control that is used to see if the flow rate has change RA(M) The ratio of measured acceleration to Abraham acceleratic for a particular water droplet RABAR The average of all measured/Abraham acceleration ratios for a particular steam velocity and flow rate RASM The sum of all measured/Abraham acceleration ratios for a particular steam velocity and flow rate RBAR The average of all measured/Serafini acceleration ratios for a particular steam velocity and flow rate RC(M) The ratio of measured acceleration to Churchill acceleration for a particular water droplet RCBAR The average of all measured/Churchill acceleration ratios for a particular steam velocity and flow rate RCSM The sum of all measured/Churchill acceleration ratios foi a particular steam velocity and flow-rate RE(M) Reynolds number for a particular water droplet REBAR The average of all Reynolds numbers for a particular steam velocity and flow rate RESUYI The sum of all Reynolds numbers for a particular steam velocity and flow rate RHOW Density of water 38

RS(M) The ratio of measured acceleration to Serafini acceleration for a particular water droplet RSUM The sum of all measured/Serafini acceleration ratios for a particular steam velocity and flow rate SEBAR Average of all Serafini accelerations for a particular steam velocity and flow rate SESTME Sum of all Serafini accelerations for a particular steam velocity and flow rate SVEL Steam velocity in cm/sec T(I) Thickness of the water droplet for a particular observation TD(J) Elapsed time between observations TOTHRD A constant, two-thirds TTOL Total time that observations on a particalar drop were made V Steam velocity VCHECK A control that is used to see if the steam velocity has changed VEL(J) Measured velocity of one droplet for two successive film readings X(I) Distance an individual particle was away from the edge of the blade

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$SIG ODLU T=3 P=20 $R *FTN 5=WDATA(2,1873) C ************ BREAK-UP TIME ANALYSIS BPOGRAM *********** C THIS PROGRAM CALCULAIES THE INITIAL AND EINAL C DIMENSIONS OF A DROP AND ITS VELOCITY FOR SPLIT CASES ONLY. C IT ALSO FINDS WEBER NUMBER, REYNCLDS NUMBEE, DIMENSIONLESS C BREAK-UP TIME, AND THE DYNAMIC PRESSURE RATIO. DIMENSION FN(20), DIA (20), T (20), X(20) WRITE(6,199) C ***** BEAD THE DATA FOR EACH CBSERVATICN **** 1 DO 110 I=1,20 READ (5,101) FN(I), DIA(I), T(I), X(I) IF (T(I).LT.0.0) GO TO 130 IF (X(I).LT.0.0) GO TO 140 110 CONTINUE 130 IF (I.EQ. 2) GO TO 140 TIHE= (I-1.0) *0.001 DIST (X (I) -X (1) ) 0.45 VEL=DIST/TIME C ***** FIND THE INITIAL AND FINAL DROP DIMENSIONS ***** DRPI=DIA (1) *0.45 DRPF=DIA (I) 0.45 THKI=T (1) *0.45 THKF=ABS (T (I)) 0. 45 READ(5,101) V,Q C ***** DETERMINE THE STEA M MACH NUMBER **** IF (V.EQ.305.0) SMACH=0.23 IF(V.EQ.520.0) SMACH=0.38 IF (V. EQ.825.0) SMACH=0.61 IF (VV.EQ.975.0) SMACH=0.72 IF(V EQ. 1100.0) SMACB=0.81 WE= (V**2) *DRPI*1.435E-3 RE=V*DRPI*32.6 1 TB= (TIME*V) /DRP*0. 323 QM0. 78+1. 47/(1.+2. 1*S ACH**3.4) QMTB=SQRT (CM) *TE WRITE (6,200) V,Q,DRPI,THKI,DRPF,THF,VEL,TIME,SMACH,WE,RE,TB, 1 QM, QTB GO TO 1 140 READ (5, 101) V,Q GO TO 1 101 FORMAT (6(F10.5)) 199 FORMAT (' 1 2X'STEA,4X, FLC', 2X,'INITIAL', 3X, 1'INITIAL' 4X, FINAL' 6X,'FINAL' 6X,'DROP,5X, 2'TOTAL MACH',5X,'WE',6X,'RE'6X,'TB',5X,'M', 4X,'QM.5TB'/ 3 2X,'VELOCITY RATE DIAMETEi THICKNESS rIAMETER THICKNESS', 4 2X,'VELOCITY TIME NUMBER (RS*V**2 (V*DO/', 5 1X,' (T*V/DC PRESS'/2,' (FEET/S) (CC/M) (CM), 6X 6' (CM), 6X' (CM),6X' (C) 5X,' (Ca/S)' 4X,' (SEC)' 8X, 7'*DO/SIG) KVIS) *RS*.5) RATIO') 200 FORMAT ('0',F8 3,2XF4. 12X F8. 5, 1XF9.5,2X, 1 F8. 5,2XF9. 5, 2X, F8 3, 3X F4 3,2X F F 4 2, X 6 2, 2XF6. 1 2 2X,F6.3,2X,F5.3,2X,F5.2) END $ENDFILE $R -LOAD 5=WDATA (2, 1873) $EN FILE $SIG ~Lj J L L~~ L4 L ~, ~J C L ~ ~-J LJ1J ~ I J LC 1 J L r~~i IJr~~L~l~Ir 1L~~~ k~t~4~i I~ ~~k~~~i k^ r^ ~ ~ kr~ r~ t

a3renk Up Tmrne Ar4^kjis Progcrm DIA(I) Diameter of an individual droplet at a particular observe DIST The distance that the particle travelled since the last observation DRPF Final observed diameter of a particular droplet DRPI Initial observed diameter of a particular droplet FN(I) Number of frames between each successive observation Q Flow rate of water in the test section QM Ratio of dynamic pressure QMTB Square -root of the dynamic pressure ratio times dimensic less break-up time RE Reynolds number for a particular particle SMACH Mach number of the steam through the test section T(I) Thickness of an individual droplet at a particular observation TB Dimensionless break-up time THKF Final observed thickness of a particular droplet THKI Initial observed thickness of a particular droplet TIMrE Real time measured between observations V Steam velocity in the system VEL Droplet velocity across the test section WE Weber number for a particular particle X(I) Distance of an individual droplet from the edge of the blade at a particular observation

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$SIG ODLU T=4 P=75 $R *FTN 5=WDATA(2,1873) C *%% DEFORMATION CF DRCPLET PFOGRAM ************* C THIS PROGRAM CALCULATES A MASS RATIO, DIESNSIONlESS DISTANCE C AND DIMENSIONLESS TIME. IT ALSO FINDS THE WEBER NUMBER AND C DYNAMIC PRESSURE FOR SPLIT PARTICLES. DIMENSION FN(20),DIA (20),T(20),X(20),DR (20),R (20),DT(20), 1 XBAR(20),AREA(20),VCL (20),AMASS(20),DCVT (20) WRITE (6,500) M=0 RHOW 1.0 1 KI=0 DPSUM=0.0 C ***** READ THE DATA FOR EACH CBSERVATICN ***** DO 10 I=1,20 READ(5,101) FN(I),DIA (),T (),X (I) DIA (I) DIA (I) *0.45 T (I)=T (I) 0.45 X(I)= (I) *0.45 DPSUM=DPSUM+DIA (I) IF (T(I).LT.0.0) GO TO 30 IF (X(I).LT.0.0) GO TO 40 10 CONTINUE 30 K11=1 T (I) =ABS (T ()) 40 x (I)=AES(X(I)) READ(5,101) V,Q IF(I.EQ.2) GO TO 1 M=, + 1 DRPU=DPSUM/I TSUM=0O.O AMASS (1)- (3. 141593/4*DIA (1) **2) *1 (1) *1E./3. C ***** ITERATIVE CALCULATING CPEHATICNS **** DO 100 J=2,I DOVT (J)=DIA (J)/T (J) DR (J) DIA (J) /DIA (1) AREA(J) =3. 141593/4*DIA (J) **2 VOL (J)=AREA (J) *T (J) *16./3 AMASS (J) =VCL (J) *RHCW RM (J) =AMASS (J) /AMASS (1) TSU =TSUM+0.001 DT (J)= (TSUM*V)/DIA (1) *0.323 XBAR(J)= (X (J)-X (1)) /IA (1) WRITE(6,600) M,V,Q,DE (J),RM(J),DT(J),XEAR (J),DOVT (J) 100 CONTINUE C ***** SEE IF THE PARTICLE SPLIT *'*** IF(K1.EQ. 1) GO TO 50 GO TO 1 50 TB=DT(J) WE= (V* *2) * D PU1. 435E-3 PD=7.7E-7*V**2 PD2=PD* 6. 89E3 DD=XBAR (J) /TB**2 WRITE (6,610) TE,WE,PE,PD2,TSUM, DD GO TO 1 101 FORMAT (6 (F10.5)) 500 FORMAT (' 1' 2X'SET',X STEAM' 4X,'FLOW DIA.ETER',3X, 1'MASS DIMENSIONLESS CIMENSIONLESS ~IAMETEB/',/ NUMB3E,2X, 2'VELOCITY',2X,'RATE',4X,'RATIO',4X,'RAIC',5X,'TIIE'',9X, -3 L

3'DISTANCE',4X,'THICKNESS'/8X,' (FEET/S) (CC/!) (D/DO)',3X, 4' (/MO)',7X,'T',11X,' (X/DO)') 600 FORMAT ('01l,X,I4,4X,F5.014X,F4. 1,3X,F6.2,3X,F6.2, 1 2X,9. 4, 6X,F9.4, 5X,F6.3) 610 FORMAT ('0','PABTICLE EROKE UJP', 2X'T= F6.3,2X,'WE=, 1 F6.2,2X,'PD=',F8.5,'PSIA' F9.2,'N/M**2',2X, TIME=',F5.3,2X 2'X/TB**2=,F10.6) END $R -LOAD 5=WDATA(2,1873) $EN DF ILE $SIG

De frm aT)Qn er ropier Pr atrv) AMASS(J) Mass of an individual droplet AREA(J) Surface area of an individual droplet DD Dimensionless distance divided by break-up time DIA(I) Diameter of an individual droplet at a particular observation DOVT(J) The ratio of diameter to thickness for a particular drop DPSUM The sum of all the diameters observed for a particular droplet DR(J) The ratio of each diameter to the initial diameter for a particular droplet DRPU The average diameter of a particular droplet DT(J) Dimensionless time FN(I) Number of frames between each successive observation K1 A control to see if the particle split M A counter which tells the total number of droplets obser and assigns them a set number PD Dynamic pressure for a split droplet in psia PD2 Dynamic pressure for a split droplet in Newtons/meter2 Q Flow rate of water in the test section RHOW Density of water RM(J) The ratio of each droplet mass to the initial mass for a particular droplet T(i) Thickness of an individual droplet at a particular observation TB Dimensionless break-up time in which the droplet splits TSUI The sum of the time over which observations of a particu droplet were measured V Steam velocity in the system VOL(J) Volume of an individual droplet WE Weber number for a split droplet X(I) Distance an individual particle was away from the edge o the blade - 3L -

XBAR(J) Dimensionless distance, distance away from the blade divided by drop diameter -3 -

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tSIG ODLU T=3 P=20 $R *FTN 5=WDATA C *:** ******** T* INDUCED VELOCITY PROGRAM **.*************** C THIS PROGRAM CALCULATES THE MEASUPEC AND ANALYTIC C ACCELERATION AND THE INDUCED VORTEX VELOCITY AND VORTEX C STRENGTH. I ALSO FINDS STEAMtFILIAND BLADE STROUHAL NUMBERS DIMENSION ACEL(? 0), FN0( ) A(20) 20),X(20) T20 T(20 X(20)T 20 DELX(20) 1 VEL(20),DF LV(20), AAR(25),R PU(25) t RE ( 25 ) CS (25) AS(25) 2 VELIN(25),VORST(25f ),ADIFF({5),RS(25) TOT HP D= 2./3. CON=30*4 8 C ***** EAD SOME PPELIMINARY DATA ***** READ(5,101) F It MV, RHCW, CON FAC,VC CHECKCHECK READ( 2,102) STETA, WATER, FLMVEL,STFNUM WR ITE(6 90) M=0.0 1 A SJM=O. O K 1=0 KI=O TTOL=0.O DPSUM=O.O C **^** R EAD THE DATA FOP EACH CBSERVATION ***** DO 110 I=1,?0 READ 5, 101) FN(I)DIA(l)T(l), ),X(I) DSUM=DP SJM+OI ( I ) IF(T(I).LT. 0.0) GO TO 120 IF(X(I).LT. 0.0) GO TO 130 110 CONTINUE 120 T(I)=ABS(T(I)) 130 X(IT=ABS(X(I)) READ(5,101) V,0 T-(I *.E. 2) GO TO 1 C. **~* CHECK TC SEE IF THERE ARE NEW CONDITICNS ***** IF(V.NE.VCHECK.OR.Q.NE.OCFCK) GO TO 160 100 M=M+ 1 DRPU ( M )=OPSUM/I *45 C_ ***-** CALCULATF THE MEASUJRED ACCELERATION ***** DO 150 J=,2t TOt(J- )=0.001 TTOL=TTOL+TD ( J-1) L x L J- X ( J- )X(J)-X(J- 1 ) *045 VEL ( J-1 ) =DELX(J-)/T(J-l) IF(J.EQ.2} GO T0 150 DTAVG=(TD(J-1)+TD(J-2) )/2.0 ELV( J-2)=VFL(J-I )-VEL (J-2) ACEL ( J-2 )=OELV( J-2 )/2./CTAVG ASUM=ACEL (J-2) +ASUM 150 CONTINUE TF(VCHECK.GT.520) GO TO 105 IT1(J.LT.6 ) CO Tn 105 C ***** READ PERIODICITY OF CECELERATION DATA m**'* EAD(1,?9 ) DELT S T NU=DR PU ( ) / V/CON/ODELT* 1000. STFNfM=,Dl PU ( -" ) /: L^-,AV E L /DE LT* O. STNiM=L&OO /DELT / /rr f k1=1 105 TM2iI-2 -,tn.. (?.i ~:..)a S tJ.~t? / i', 2 SVL=V*CO.N 100. OFLOW=O /f0.

C **:*-* CALCULATE THE SEPAFINI ANALYTIC ACCELERATION *t*** P ( M) =V*ORPU (M )32.6 COS (M)=?4. / E M )*( 1. +0.17*R (I ) *TOTHRD) AS (M) (CDS (4) *0.75)*.0001135/ORPU(M)*SVS:L**2*10000. $ S ( M) ABAAP l M)/ AS( Sh ) OI F ( M)=AS (M)-AB P (M IF(ADIFF(),.LT.O.O) GO TO 155 C **' p FIND INDUCED VELOCITY AND VCRTEX STRENGTH *C** VIL IN () =S O RT ( A dI: (M) *CRPU(M )*1.333)*100. VOqST (M) =V L IN ( M)*0. 168*100 1=55 IF(VCHeCK rT 520 ) GO TO 1I1 C **c*.c DETERMINE WH'ICH WRITE STATEMENT TO USE **** I (K1. E.1.AND. ADIFF(M).GT.O.0) GO TO 156 If(KI.EO I.ANO.ADIF F(M).LT..0) GO TO 157 1F (K1. ECO.0.C.AOFF(F). GT..0) GO TO 153 F(KI.EO.O.AND. ADIFF(M).LT.O,0) GO TO 159 156 WRITE(6 600) SVEL,QFLCW,PRPU(W),RE(M) ABAR(M),RS(M),VELIN(M), 1 VORST(M),DELTSTNUMFLMVELSTFNM,S'TPNM GO TO 1 157 WRITF(6,610) SVEL.OFLCW,DRPU(M), RE(M),ARBA(M),RS(M),DELT,STNUM, 1 FLMVELSTFNMSTSNM GO TO 1 158 WRITE(6,620) SVELtFLOWDRPU M) tRE(M),A8AR(M),RS(M),VELIN(M), 1 VOPST M) FLMVEL GO TO I 159 WRITE(6,630) SVELQFLCWORUt(M),RE(M) ABAR(M),PRS(M),FLMVEL GO TO 1 161 IF (ADIFF(M) LT.0.0) GO TC 162 WRITE(6,64S0) SVEL,FLCW,DPU(M),RE(M),ABAR(M),RS(M),VELIN(M), I VORST(M) GO TC 1 162 WRITF (6,650) SVEL, FLCWnDPU(M),PE( r ), A 43AR (),RS(M) GO TO 1 C ***** RESET THE COUNTER ***** 160 M=0 VCHECK=V oCHECK=O IF(VCHECK.GT.520 ) GO TO 170 READ(2,102) STEAM,WATER,FL VEL,STFNUM 170 IF(I.EO.I) CALL EXIT GO TO 100 90 FORMAT ( 1',X, STEAM FLOW',6X,'RCP REYNOLDS MEASURED' 1 3X,'ACCELER- INDUCED VORTEX PE ICOICITY OF STROUHAL',2X, 2'FILM STROUHAL STROUHAL'/ VELOCITY RATE DIAMETER',3X, 3'NUMBER ACCELERATION ATION VELOCITY STRENGTH DECELERATIONt, 4 4X,'NUMBER VELOCITY N R NUMBER U ER'/ M/ SEC) (CM**2/S),3X, 5'(CM)',14X,'(CM/S:C**2) RATIO (CM/SEC) (CM**2/S)',2X, 6'(10Q**3 SEC)', 5X,'STEAM (CM/SEC) FILM, 5X,'BLADE') 9c FORMAT ( 5.?) 101 FORMAT(6 F10.5) 102 FORMAT(4FE. L ) 600 FORMAT ('' lX, 5.1,3X,F6.4,4X,F6.4,3X,F7.2, 3XF10.2,2X,F6.3,3X, 1 FB2,I XF9.2, XXX,F5.2,7XF8.6,2X, F6E3,3X,F6.4,9X,F7.5) 610 FOPMAT ('0',I1X, 513XF6 4, X, o6,3XF7.2 3XF10.2,2X,F6.3,25X, 1 F. 2,7X,FE6, 2X,F. 3,3X, FE.4,4X,F7.5) 620 FORMAT ( 0', 1X,F5.1,3X,F6.4,4X,F6.4,3X,F7.2, 3X,F10. 2,2X,F6.3,3X, I m8.2, X,FC.2,225X,6.3) 630 FOQMAT ('0', 1X,5, 1,3X, F.4,4zX,F6. 4,3X,F7.2,3X,FO. 2,2X,F6.3, I 47X,:6.3) 640 FORMAT ('0', X,F5.1,3X,F6.4,4X,F6.4,3X,F7.2,3X,FIO.2,2X,F6.3,3X,

I P8.2,1XF9.2) 650 FORMAT ( t' lX', FX, 5.1, 3X,F6.4,4X,F6.,43X,F7.2,3X,FIO.2,2XF6.3) -END $R -LOAD =-T.3ATA 2=FCATA 5=WDATA 4EN N O IL $SIG -S IS

nduvc^ V\elochy P' rgt ABAR(M) Average of the measured acceleration for one droplet ACEL(J) Measured acceleration of one droplet for three successive film readings ADIFF(M) The difference between berafini and measured acceleration AS(M) Analytical acceleration as calculated by Serafini ASUM Sum of all the measured accelerations for one droplet CDS(M) Serafini's expression for the drag coefficient CON A constant conversion factor, 30.48, the number of centimeters in one foot CONFAC A constant conversion factor,.45, the number of centimeters in one measured screen unit DELT The periodicity of deceleration of one given droplet DELV(J) The difference between two consecutively measured velocities DELX(J) The difference between two consecutively measured distances DIA(i) Diameter of the water droplet for a particular observation DPSUM The sum of all diameters observed for a particular droplet DRPU(M) The average of all diameters observed for a particular droplet DTAVG The average time between each successive observation FILMV The film speed at which the pictures were taken FLNMVEL liquid film velocity on the blade FN(I) Number of frames between each successive observation IM2 The number of observations in a set minus two K1 A control which tells if the particle has a periodicity of deceleration associated with it M. A counter which tells how many different cases were observed for each steam velocity and flow rate Q Flow rate of water entering the test section QCHECK A control that is used to see if the flow rate has changed QFLOW Specific water flow rate in centimeters squared per second

RE(M) Reynolds number for a particular droplet RHOW Density of water RS(M) The ratio of measured acceleration to Serafini acceleratic for a particular droplet STBNM Strouhal number calculated from the blade width STEAM Steam velocity STFNM Strouhal number calculated from the film velocity STFNUM Average values of film Strouhal number for a particular steam velocity and flow rate STNJu.i Strouhal number calculated from the steam velocity SVEL Steam velocity in meters per second T(I) Thickness of the water droplet for a particular observati TD(I) Elapsed time between observations TOTiRD A constant, two-thirds TTOL Total time that observations on a particular drop are being made V Steam velocity VCHECK A control to see if the steam velocity has changed VEL(J) Measured velocity of one droplet for two successive film readings VELIN(M) Induced velocity caused by the vortex shedding VORST(M) Vortex strength WATER Flow rate of water entering the test section X(I) Distance an individual particle was away frcm the edge of the blade,L^-

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CO PUT PtO A 0 el A $SIG ODLU T=l P=10 PRINT=T FCUTE=CT'IE BATCE, NORMAL, UNIV **LAST SIGNON WAS: 15:34:39 USER "0DLU" SIGNED ON.T 15:39: 16 ON FRI MAR 21/78 $L LINEFIT 1 C ******** STRAIGHT LINE FIT E.CGR.A *~* * 2 C ** THIS PROGRAM CALCULATES TEE BEST LINE FIT TO A 3 C ** CF LCGARITHMIC C~ETA EY THE METHOD OF LEAST SQUAl 14 DIMENSION X (99), XCLG (99), Y (99), YLOG (99), C(99) 5 C *** READ NUMBER OF DATA PCINTS FCE THE SET * 6 1 READ(5,80C) AN,TYPE,SOLN 7 XSU = 0.0 8 YSUm = 0.0 9 XYSU = 0.0 10 X2SM T 0.0 11 CSU. = 0.0 12 SU:MD = 0.0 13 CSUM2 = 0.0 14 N = AN 15 DO 850 I=1,N 16 READ (5,800) Y(I), X(I) 17 XLOG(I)= ALCG10(X(I)) 18 YLOG (I) = ALCG10 (1/Y (I)) 19 XSUm= XICG(I)+XSUiq 20 YSUM=YLOG (I) +YSU 21 XYSUM= XLCGJ () *YLOG (I) +XYS U 22 850 X2SUM= XLCG(I)**2 +X2SUM 23 EX = (XYSUI - XSUJ*YSU'/AA) / (X2SUJ - XSU~**2/. 24 CT 10.** ((ABS (YSUI) +EX*XSUM ) / AN ) 25 WRITE(6, 200) 26 IF(TYPE.EQ. 1.0) WRITE (6,201) 27 IF (TYPE. EQ.2.0) WRITE(6,202) 28 IF(TYPE.EQ.3.0) WRITE (6,203) 29 IF (TYPE.EQ.4.0) WRITE (6,204) 30 IF (TYPE.EQ.5.0) WRITE (6,205) 31 IF(SCLN.EC. 1.0) WRITE (6,211) 32 IF(SOLN.EQ.2.0) WRITE(6,212) 33 WRITE(6,220) 34 DO 875 1-1,N 35 C (I) = Y (I)*X (:) ** (ABS (EX)) 36 WRITE(6,820) X(I), XICG (I), Y(I), YLOG (I), C (I) 37 875 CSUI = C () + CSUw 38 CAVG = CSUM/AN 39 WRITE (7,840) CT, EX 40 CMAX = C(1) 41 C MIN = C(1) 42 DO 885 I=1,N 43 IF ( CMAX LTZ. C (I) ) CMAX - C (I) 44 IF( CMIN.GI. C (I) ) CMIN = C (I) 45 SUMDIF = A~S (C(I) - CAVG) 46 SUMOMD = SUMDIF + SUI MD 47 SU1MD2 = SUM13DIF**2 + SUMD2 48 885 CSUM2: C(I)**2 + CS U2 49 DV~EAN = SUMMD / AN 50 STNDV = SQRT( SUMD2 / (AN-1) ) 51 RYS = SQRT( CSU!.2 / AN ) 52 C *** PRINT STATISTICS CF PROPCRT'IC.K.AL CCNSTANTS -*'* 53 WRITE(6,830) S X, CT, CAVG,CV^EAN,STNDV,R4^S, 54 1 C1AX, CMIN 55 GO TO I - L o —

56 800 FORMAT (3F103) 57 200 FORMAT (1', 15X,'MDER AND INCUEATION DATA ANALYSIS') 58 201 FORMAT ('0', 24X, ALUI NUM 1100-0') 59 202 FORMAT ('' 20X,'STAINLESS STEEL 17-4 PH') 60 203 FORM.AT ('0' 24X,'TITANIUM GAL-4V') 61 204 FORMAT ('0',17XfSTAINLESS STEEI 17-4 PH (CAST)') 62 205 FORMAT ('0',15X, STAIILESS STEEI 17-4 PH (WROUGHT)') 63 211 FORMAT ('',23X,'TANGENT INTEFCEPT') 64 212 FORMAT ('',28X,'0.1 MIL') 65 220 FORMAT ('0' 4X,'INCUBATICN DAT',8X,'r DPR DATA' 7X, 66 1'PROPORTION AL' /5X, ICBT'2X IOG (INC TN)' 3X,'M DPR',2X 67 2'LOG(MDPR)',5X,'CCNSTANT'/) 68 820 FORMAT (2 ( 10.3,F10.6),F15.3) 69 830 FORMAT(//12,'SLOPE OF LINE(EXPCNENT,N) =',T35, F1.7// 70 3T2,'BEST PROPORTICNALITY CCNSTANT =', T34,F11.3//// 71 4' STATISTICAL ANALYSIS CF PFOPCRTIONAL CONSTANT'/// 72 5T2,'ARITHMATIC MEAN',T34,F12 3// 73 6T2,'MEAN DEVIATICN =,T34,F12 3// 74 7T2,'STANCARD DEVIATION =',T34,F12,3// 75 9T2,'ROCT MEAN SQUAtE =',T34,F12.3// 76 1T2,'MAXIMUM PRCPOQTICN AI CCNSTANT =,T34,F12 3// 77 2T2,'MINIUM PREPCETICNAL CCNSTANT =,T34,F12.3// 78 3 28('* t)) 79 840 FORMAT (F20. 10,',1,F 2. 10,', ) 80 END END OF FILE $ SI G _9>

LIST OF VARIABLES AN Number of data points through which the line is to be drawn C(I) Proportionality constant for each pair of data points CAVG Average of all proportional constants for each set CMAX Maximum proportional constant in a set CMIN Minimum proportional constant in a set CSUMi Sum of all proportional constants for each set CSUM2 Sum of all the squares of the proportional constants for each set CT Best proportional constant as measured from the calculated slope of the line DVMEAN Mean deviation of all proportional constants in a set EX Exponent of the best fit line N Number of data points in a set RMS Root mean square of all proportional constants in a set SOLN Method by which incubation period is measured SUIDIF Absolute value of the difference between the average and individual proportional constants SUMMD Sum of all the SUMDIF values SUMMD2 Sum of all the squares of the SUMDIF values STNDV Standard deviation of all proportional constants in a set TYPE The particular material that was tested X(I) Abscissa input data point XLOG(I) Log base 10 of the point X(I) XSUM1 Sum of all the XLOG(I) points for a set X2SUM Sum of all the squares of XLOG(I) points for a set XYSUI Sum of all the XLOG(I) and YLOG(I) points for a set Y(I) Crdinate input data point YLOG(I) Log base 10 of the inverse of the point Y(I) YSUM Sum of the YLOG(I) points for a set -cs

SARPLE ADS COMMvANDS (TITANIUM) $SIGNON ODLU $RUN AERO:GRAF C: YMIN=. 0001 C: Y1AX = 1. C: XMIN=l. C: XMAX=10000. C: LLOG C: TICY=.OOO1,9 C: TICX=1,9 C: LBLY=F6.4,1,1 C: LBLX=I6,1, 1 C: ADD FILE PFILE(1,16) C: DATA C: CRVF=1,14 C: TEXT T: HORZ T: SCAT=1 T: GO INCUBATION PERIOD (MIN)@ T: VERT T: GO 1/MDPR (MILS/1000 E.RS)@ T: HORZ T: SCAT. 75 T: GO ~c-L^

TITANIUM 6AL-4Vi T: GO (TAN INTERCEPT)@ T: GO N=.918@ T: GO C=4721@ T: END C: AUTO C: CALC=1.25 C: MTS #RUN *CCQUELrE PAR=PLOTI #SIGNOFF _T O

0. 001 0o U)| NALUMINUM 1100-0 Or: CTAN INTERCEPT) o | N=.999 co C=4721., +< \ /+ 0n 0001 C] CL Q-, i 0. 00001-. 1 10 100 INCUBATION PERIOD CMIND

0. 100 (f) STAINLESS STEEL 17-4 PH Or: CO. I1 MIL) Tz o N=1. 24 o CC=-61944 C 0,01000 + co -J LOa 001 I~ 1, Oa0001 1 10 100 1000 INCUBATION PERIOD (MIND

1. 000)C TITANIUM 6AL-4V ^I| C0.1 MILD ) 0D0.100 N=1.09 CD o C=17553 0. 0100 L0.0010 0 / z, 0. 0001- ~... -1 1 10 100 1000 10000 INCUBATION PERIOD CMIN)