A computer aided mapping for electrochemical engineering analysis has been developed using a microcomputer

system. Softwares for linear interpolation, sorting, serialising and plotting have been developed

and reported with flow charts, program listing and plotted result

Birlasekaran, S.

Kalidoss, R.

Thirumalai, A.

IR@CECRI

Bulletin of Electrochemistry 1 (6) Nov.-Dec. 1985. pp. 591-600 CONTOUR POTENTIAL MAPPING A THIRUMALAI, S BIRLASEKARAN and R KALIDOSS Central Electrochemical Research Institute. Karaikudi - 623 006 ABSTRACT A computer aided mapping for eledrochemical engineering analysis has been developed using a micm- computer system. Softwares for linear interpolation, sorting, serialising and plotting have been developed and reported with flow charts, program listing and plotted results. Key words : Mlcro computer system, equlpotential mapping, electrochemical englnwrlng. INTRODUCTION A utomatic equipotential mapping is an important d y s i n g  eofhvare necessary for electrochemical engineering deaips. It is widely used to plot the equipotential contours in the following electrochemical studies: (a) Surface potential measurement of a corroding structure like bridge, house construction etc (b) current distribution study in electrochemical impressed cumnt protection system (c) cumnt distribution rtudy in electrolysis cells, metal finishing tanks, battery grids and metal anoda and (d) temperature distribution study in molten b&s and furnaces. Potential, current or temperature is determined by some techniques at various nodal points of the system being analysed. Normally collected dataueanalysed by manual method or by computer [I -3, 51. Mmual method8 are more laborious and less precise in output. Many big computer systems [2] have their own developed programs and it is costly to use with less manipulation. In this laboratory, we have developed softwares to be used with 8 bit micro- computer. Very interesting results as desired have been obtained. Brief details on the logic followed, flow charts and listing of the programs are pnsented below. Statement of the problem A two-dimensional area can be divided into a convenient linear way whereby we get a definite number of nodal poinb. Functional value at there nodal points arc obtained by mathematical analysis 13, 41 or by experimental methods [I]. Desired equipotential contour h u  to be drawn by locating the points having the same potential valua. Linear interpolation method is used to fix the point of equipotential lying in betwan the nodal poinb. These points have to be connected requentially without cutting the other contour lines. Desired number of equipoteetinl l i na  h u  to bedrawn to estimate the gradient and other panunetem. Method of approach For our analysis, we have taken the computed results of reference [3]. Battery grid structure potentials are d y s e d  and potential distributions are plotted in figures 1 and 2. Uaing mathematical equations [4], the potential values are generated and equipotential liues are plotted in figures 3 and 4. Basically the involved steps are : a) Recording of potentials are nodal points either by experiqental or by mathematical analysis b) Determine the maximum and minimum extreme potential values and divide the interval into the required number. c) Determine the poi& having the same required potential values using interpoletien and store thrm in a file Fig. 1 : Potential distribution in a banery grid strudure without a slot cut d) Sort out the data in the file so that the points can be sequentially connected without intercepting other contour lines. Store them in the plot file. e) Plot the data taking the rlected file one by one. Program listing 1 briefs the mathematical computation of potential between two equally charged lines 141. The computed values are stored in the file PH11.DAT. While in analysis on battery grid current distribution, the numerical values at nodal points are determined by a method reported earlier [3]. Program listing 2 does the job of interpolation along rowire,  columnwine and diagonalwise at the appropriate nodal points. The estimated values are stores in the file B13T. It is sorted and loaded into HKDAT file. Program listing 3 serialises the points to be connected sequentially. Thirumalai et al- Contour potential mapping Fig. 2 :  Potential distribution in a banely grid structure with a slot cut Fig. 3 :  Potential d~stribution across two spherical electrodes kept at positive and negatlve potent~ats DESCRIPTION Program lirting - 1 This is a simple routine to demonstrate the data generation. The formula used is where r l  and r2 are the distances from the charge centres to the point (IJ). V(I,J) values are stored in PHl1.DAT file. In fig. 5, the flow chart of program listing 2 is presented. Opening the above data files, extreme limits of V(I,J) are determined as MAX and MIN. Fig. 4 : Potentla1 d~stribution across two spherical electrodes kept at positive potentials Fig. 5: Flow chart for program listing 2 Counter ND is used to count the number of points having same potential and initially it ie set to zero. Required equipotential value is selected as H. The interval between consecutive nodal points are subdivided into 10 or any desired precision. The value of H is searched at all the nodal points. If it is found, they are recorded in B13T.DAT file and the counter ND is corres- pondingly incremented. If it lies within the nodal points, linear interpolation is done is rowwise, columnwise and diagonalwise and the counter is incremented. The located data points for a particular H value is loaded in Bl3T.DAT file and the number ND having H value is printed out for reference. If another H value is required similar procedure is followed and the final data is stored in another data file. They me sorted in descending order using SORT routine and sorted in HK.DAT file. 592 Bulletin of Electrochemistry 1 (6) Nov.-Dec. 1985 Thi~malei et al- Contour potential mapping LO REM PROGRAM FOR POTENTIAL BETWEEN TWO 20 DIM POT(50,50) 30 K=01 40 OPEN "O",#I,"PHIl.DAT" 50 E=ll 60 FOR 1=0 T O  10 70 FOR J=0 T O  10 80 I F  1=0 AND J = C  GOT0 90 ELSE 110 90 POT(I,J)=201 b 100 GOT0 la0 :10 IF !=I0 AND J=0 GOT0 120 ELSE 140 120 POT( I ,  J,=20' 130 GOT0 180 140 R1=SQR(I'Z+Ja2) 150 K=K-rl 160 R2=SQR!IlO-I)'2+J'2) P O ' T ( I , J ~ = ! - 2 * E * L O G ( R l ) - 2 * E * L O G ( R 2 ) ) + 2 0 !  PRINT POT(I,J),J,I PRINT +L.POT(I,Jj NEX'f J NEXT I CLOSE #1  SrCiI! END Table I1 I P r o m  Limting 2 110 REM PROGRAM FOR INTERPOLATiON TO COLLECT EOUIPOTENTIAL POINTS 20 OPTION BASE 0 30 DIM X ( 2 1 0 , 1 5 ~ , W S ( 1 0 0 ~ , Y P ~ 2 O O ~ , X P ~ Z O O )  40 OPEN "I",#l,"PHIl DAT" 50 FOR I=l. TO 10 60 FOR J=1 T O  10 70 INPUT C1, X(1,J) 80 PRINT X(I,J) ,I;J 9 0  NEXT J 1 r ) O  PRINT 1 1 0 NEXT 1 1 2 0  PRINT I 30 CLOSE #1 ! 4 C  GOT0 1830 150 INPUT H 140 LET ND=Ol 170 OPEN "O",#l,"R13T.DAT" 180 PRINT "H= "H :90 GOSUB 530 200 GOSUB 720 210 GOSUB 1110 220 CLOSE #1 230 RESET Bulletin of Eledrochemistry 1 (6) Nov.- Dec 1985. 593 Thi~majai et el- Contour potentla1 mappng 2q0 PRINT "ND= "ND 250 END 260 IF (L=l0 AND KtlO) AND (X(I,J)=H AND X(I,K)=H) G O T 0  430 270 IF X('I,J)=H G O T 0  460 280 IF X(I,K)=H G O T 0  430 290 P=(X(I,J)-X(1,K))llO 300 IF X(I,J)<X(I,K) G O T 0  370 310 S=X(I,J)-P 320 YP(ND)=J+. 1 330 XP(ND)=I 340 S=S-P 350 YP(ND)=YP(ND)+.l 360 IF S < = H  G O T 0  490 ELSE 340 370 S=X( I ,K)+P 380 YP(ND)=K-.1 390 XP(ND)rI 400 S = S + P  410 YS(ND)=YP(ND)-. 1 420 IF S < = H  G O T 0  490 ELSE 400 430 XP(ND)=I 440 YP(ND)=K 450 COTO 4.90 460 XP(ND)=I 470 YP(ND)=J 480 G O T 0  490 490 X P ( N D ) = X P ( N D ) ~ ~ O  500 YP(ND)=YP(ND)*lO 510 PRINT #l,USING "tltlt It1';YP(ND);XP(FlD) 520 RETURN 530 FOR Irl T O  10 540 FOR Jnl T O  9 550 KtJ+1 560 IF X(I,J)=H XOR X(I,K)=H G O T 0  660 570 IF X(I,J)=H AND X(I,K)=H G O T 0  600 580 IF X ( I , J ) < H  XOR X ( I , K ) < H  T H E N  660 590 COTO 680 600 IF J = 9  AND X(I,K)=H G O T 0  620 610 C O T 3  660 620 YP(ND)=K*lO 630 XP(ND)=I*10 64.0 PRINT #l,USING "#lt#.#";YF(ND);XP(ND) 650 GOTO 680 660 ND=ND+l 670 COSUB 260 680 N E X T  J 690 PRINT 700 N E X T  I 710 RETURN 720 FOR 1 1 1  T O  9 730 FOR J=l T O  10 740 LrIbI 750 IF X(I,J)=H XOR X(L,J)=H COTO 790 594 Bulletin of Eledrochemistw 1 (6) Nov. -Dee 1985 Thirumalai et al- Contour potential mapping 740 IF X(I,J)=H AND X(L,J)=H GOT0 790 770 IF X(I,J)<H XOR X(L,J_)<H THEN 790 780 GOT0 820 790 ND=ND+l 800 COSUB 060 810 PRINT C1,USING "###.#";YP(ND);XP(ND) 820 NEXT J 830 PRINT 840 NEXT I 850 RETURN 860 IF (I=9 AND J-10) AND (X(I,J)=H AND X(L,J)=H) GOT0 1060 870 IF X(I,J)=H GOT0 1030 880 IF X(L,J)=H GOT0 1060 890 P=(X(I,J)-X(L,J))/lO 900 IF X(I,J)(X(L,J) GOT0 970 910 S=X(I,J)-P 920 XP(ND)=I+ 1 930 YP(ND)=J 940 S=S-P 3 5 0  XP(ND)=XP(ND)+.l 960 IF S < = H  GOT0 1080 ELSE 940 970 S=X(L,J'+P 980 XP(ND)=L- 1 990 YP(ND)-J 1000 S=S+P 1010 XP(ND)=XP(ND)- 1 1020 IF S < = H  GOT0 1080 ELSE 1000 1030 XP(ND)=I 1040 YP(ND)=J 1050 GOT0 1080 1060 XP(ND)=L 1070 YP(ND)=J 1080 YP(ND)=YP(ND)*10 1090 XP(ND)=XP(ND)*lO 1100 RETURN 1110 FOR I t 1  T O  9 1120 FOR J=l T O  9 1130 K=J+l 1140 L=I+l 1150 IF X(1,J)rH XOR X(L,K)=H GOTO 1250 1160 IF X(1,J)sH AND X(L,X)=H GOT0 1250 1170 IF X(I,J)<H XOR X ( L I K ) < H  GOT0 1250 1180 IF X(L,J)tH XOR X(I,K)=H GOT0 1540 1190 IF X(L,J)<H XOR X(I,K)'<H GOT0 1540 1200 IF X(L,J)=H AND X(1,K)rH GOTO 1540 1210 NEXT J 1220 PRINT 1230 NEXT I 1240 RETURN 1250 ND=ND+l 1260 IF (K110 AND Ls10) AND (X(I,J)=H AND X.(L,K)=H) GOT0 1480 1270 IF X(I,J)=H GOTO 1450 Bulletin of Eledrochem~stiy 1 (6) Nov.-Dec 1985 595 Thirumalai et al- Contour potential mapping IF X(L,K)=H GOT0 1480 P~(x(I,J)-X(L,K))/~O IF X(I,J)<X(L,K) GOT0 1380 S=X(I,J)-P YP(ND)=J+.l XP(ND)=I+.l S=S-P YP(ND)=YP(ND)+.l XP(ND)=XP(ND)+.l IF S < = H  COTO 1500 ELSE 1340 S=X(L,K)+P YP(ND)eK-.I XP(ND)=L-. 1 S=S+P YP(ND)=YP(ND)-.I XP(ND)=XP(ND)-.I IF Si=H COTO 1500 ELSE 1410 XP(ND)=I YPiND)=J GOT0 1500 XP<ND)=L YP(ND)=K XP(ND)=XP(ND)*lO YP(ND)=YP(ND)*lO PRINT #l,USINC " # # #  #";YP(ND);XP(ND) COTO 1 18 0 ND=ND+ 1 I F  (K=10 AND L=10) AND (X(I,K)=H AND X(L,J)=H) GOT0 1770 IF  X(I,Ki=H GOT0 1770 IF  X(L,J)=H GOTO 1740 P=(X(I,K)-X(L,J))IIO IF X!I,Kj<X!LIJ) COT0 1670 S=XiI,K)-F YP<NDj=K-.1 XP(ND)=I+. 1 .- .- :: = .-, - F %PiNDj=YE'(ND!- 1 XP!NCj=XP(ND)+ I T F  S(=H COT0 1790 ELSE 1630 S=XIL, J)+P ' 'Y'P(I.ID) =J+ 1 XP(NDj=L- 1 S=S+F YP(ND~=YF~:ND)+ 1 .XP(NOi=XF(NG)-. I. IF .S,C=H GOT(] 1790 ELSE 1700 SF:N?J)=.L 'fP(ND)=J :;!3T'13 : 7 C O  :-: P ' ND 1 = i " F! '.!3 i =Y: :' P . ,', tiI3='~.fP("lr!,*.l.o 596 Bulletin of Electrochemistry 1 (6) Nov.-Dec. 1985 Thrrumala~ et al- Contour Potentla1 mapping 1000 XP(ND)=XP(ND)*lO 1810 PRINT #l,USlNG "###.#";YP(ND) XF(ND) 1820 GOT0 1210 1830 LET MAX=X(O,O) 1840 MIN=X(O,O) 1850 FOR 1=0 TO 10 1860 FOR J=0 T O  10 1870 IF MAX(X(1,J) THEN MAX=X(I,J) 1880 IF MIN)X(I,J, THEN MIN=k(l,J) 1890 NEXT J 1900 NEXT I 1910 PRJNT MAX,MLN 1920 GOT0 1 5 0  Table 111 I Program Limting 3 1 G REM PR0GFiAr.I FOR SljR'r1I.11-9 hi\ii  S E F  TALISING 20 DIM ~(20d),B(200;,AY(100) 30 DIM X ( 2 0 0 ) . C ~ 1 0 0 ~ , Y ( 2 0 0 ) . A 1 ( 5 0 ) , A 2 ( 5 0 ) ; Y P ( 1 0 0 ~ , X P ~ l O O ~  40 DIM R X ( 1 0 0 ~ , R Y ~ 1 0 0 ~ , X X ( 1 0 0 ~ , Y Y ~ 1 0 0 ~ , A X ~ 1 0 0 3  50 LET L=O' 60 OPEN "I",#l,"HK DAT" 70 IF EOF(1) GOTO 110 80 L=L+1 3 0  INPUT #l,YPtL),XP(L, 100 GOT0 70 110 PRJNT " L =  "I. 120 FOR I = l  TO I. 130 X X (  J)=YP(I) 140 YY(I)=XP(I) 1 5 1 3  PRINT XX(I),YY(I) 160 NEXT I ;70 PRINT 180 CLOSE # 1  ;30 J=O' 200 FOR I = l  T O  L 210 IF XX(I)=XX(I+l) 9ND fY(I)=YY(I+l) COTC 250 220 J=J+l 230 X(J)=RX(I) 240 Y(J)=YY(I) 250 NEXT I %60 PRINT "J= "J 270 LET JK=J 280 K=0' 290 FOR I = l  T O  JK 300 IF XX(I)<)XX(I+l) GOT0 330 31 0 K=K+1 320 GOTO 370 3.30 IF K=O GOT0 370 340 K=K+l 350 C(I)=K 3t0 K=O! Bulletin of Electrochemistry 1 (6) Nov. - Dec. 1985 597 Thi~malai et at- Contour potential mapping 370 NLXT I 3 8 0  MkX=t(i) 390 FOR 1 - 1  T O  JK 400 'IF MAX(C(1) THE,N MAX=C(I) 410 NEXT I 420 PRINT "SS= "MAX 430 SSrMAX+l 440 FOR 1=l T O  JK 450 PRINT X(I),Y(I) 460 N E X T  I 470 XI-O! 480 D=SQR( 10'2+10'2) 490 FOR 1=1 T O  JK 500 A(I)rO 510 B(I)=O 520 NEXT I 530 XrX( 1 )  540 YeY(1). 550 1x11 560 N=01 570 P=01 580 M = O '  5 9 0  K=Oi 600 L E T  I=I+l 610 IT X=X(I) AND Y=Y(I) COTO 600 620 Dl=SQR{(X-X(I))^2+(Y-Y(1))*2) 630 DZ=SQR((X-X(I+1))'2+(Y-Y(I+l))-Z) 640 PRlNT D i , X ; Y , X ( I ) , Y ( I ) , D 2 ; X ( I + l ) ; Y ( I + l )  650 IF D1(=D AND DZ(=D GOT0 700 660 I F  D1(=D COTO 890 6 ; 0  IF DZZ=D GOTO 950 A80 IF (X(?)=O AND Y < I ) = O )  AND I)M COTO 1210 690 COTO 1070 700 IF D l < D 2  GOT0 820 7'10 N=N+l 7%0 A(N)=X 730 B(N)=Y 740 N=N+l - c rdO A(N)=X(I+l) '760 B(N)=Y(I+l) 770 x=x('I) 780 Y=Y(I) 790 I=I+1 800 PRINT A(NJ, B(N) 910 COT0 600 820 N=N+ 1 9 3 0  A(N)=X 340 B(N)=Y ??!I X=X(I) !360 Y = Y (  I )  670 PRINT A(Kb,B(N) 8 f l O  T?T..> j C ! O  598 Bulletin of El&rochemistry 1 (6) Nov. - Dec 1985 Th~rumala~ et al- Contour potent~al mappmg 5980 N = N t  1 ? O D  A!N!=X 9 1 0  B < N ! = Y  9 2 0  X=X(I! Y 3 0  Y = Y ( I )  940 COTO 1060 950 N = N + 1  P60 A(N)=X 970 B(N)=Y 980 X=X(I+l) 990 Y = Y ( I + l )  1000 K=K+1 1010 IF K=l G O T 0  1020 ELSE 1040 1020 P=(JK-I) 1030 M = ( J K + P )  1040 X(M-K)=X(I) 1050 Y(M-K)=Y(I) 1060 G O T 0  600 1070 K=K+1 1080 !F K=l C O T O  I090 ELSE 1110 lo49 6 P =  (JK- I ) l t O O  M = ~ J K + P )  1110 X(M-K)=X(I) 1120 Y4M-K)=Y(I) :I30 IC=K+l 1 ? 4 0  IF Knl G O T 0  1150 ELSE 1170 1150 P=(JK-I) I160 M=(JK+P) 1170 T=I.+l 1180 X(wrk)=X(I) 1190 Y(M-K)=Y(I) I200 G O T 0  6 0 0  1210 FOR 1=1 T O  ( J K + K )  1220 PRINT X ( I ) , Y ( I ) , M , P  1230 N E X T  I 1240 N=N+I 1250 A(N)=X 1260 B(N)=Y I270 K = O !  1280 FOR 1=1 T O  N 1290 IF A(I)=A(I+l) AND B ( I ) = B [ I + l )  COTO 1 3 3 0  1300 K=K+l 1310 RX(K)=A(I) I320 RY(K)=B(I) 3330 N E X T  I I340 FOR I=l T O  K 1 ? 5 0  PRINT A X ( I ) ; R Y ( I )  1360 N E X T  I i3'70 PRINT 1380 Xl=X1+1 1 3 9 0  P R I N T  "No OF LOOPS= "Xi 1 4 0 Q  IF Xl=SS COTO 1460 Bulletin of Electrochemistry 1 (6) Nov. -Dec. 1985 599 Th~rumalar et al- Contour potentlal mappmg 1410 FOR 1=1 TO K 1420 X(I)=RX(I) 2430 Y(Ii=RY(I) 1440 N E X T  I 1 4 5 0  G O T 0  480 1460 O P E N  "O",#l,"HlK.DAT'! 1470 FOR 1=1 T O  K 1480 P R I N T  # 1 , U S I N G  " # # # . W H ; R X ( 1 ) ; R Y ( I )  1490 N E X T  I 1500 CLOSE # 1  1510 PRI.NT "N="N,"K= "K 1520 S T O P  1530 E N D  Program limting - S In fig. 6, the flow-chart of program listing 3 is shown. Fig. 6 : Flow chart for program listing 3 Conditioning of the HK.DAT file is done by removing repetitively occuring points. Taking X-axis an refermce, the number of Y ordinates d a t e d  with each X coordinate is determined. This data han been estimated to determine the Y ordinate for a particular X coordinate to be connected sequentially in cane of multi Y ordinates for a x  coordinate. A search window technique has been developed. A square window of diagonal length-D is located at one extreme end of grid [say X - x(1) and Y - y (l)] .  The distance Dl and D2 of two consecutive points from (X,Y) in the array are determined. If Dl and D2 lie within the window, Dl and D2 are compared and the closest points are stored in A (N) and B(N) and the reference points X and Yare approximately shifted. Similar logical steps are followed if Dl and D2 alone lie within D. If both points lie outside the window, these points are moved to stack points outbide this array of points sequentially. By these methods, the equipotential points are arranged in RX(N) and RY(N) sequmtidy and are stored in H1K.DAT. Using semigraph routines avail- able in the microcomputer unit, these files are called and plotted o w  by one. The loftwuc hating of the above programs are shown in Tables I to 111. RESULTS Figum 1 to 4 dirplay the plotr of malysed results. Figure 1 shows the equi- potential contoun drawn on a battery grid structure with current feeding point at the right hand corner. Concmtrntion of gradient could be viaualised near the feeding end. Figure 2 shows the equipotential contoun drawn on a battery grid structure with a slot-cut and with cumnt feeding point at the right hand corner. Improved distribution of grculimt on the right hand side of the grid m d  increased voltage drop on the electrode could be seen. Figure 3 shows the potential diatribution across two line electrodes kept at positive and negative potentials. S t a p  g d i e n t  could be seen near the electrode mds. Figure 4 shows the potmtial distribution between two line electrodes kept at positive potentials. The caving-in of the potential lines could be seen near the electrodes. Manually plotted reaultr of the m e  could be seen in references (31 and (41 for comparilon. CONCLUSION From the reaultr, it could be seen that such sofhwecl developed in microcomputer system could be used more effectively for contour potmtial mapping. More resolution could be obtained by having more memory apace and applying various types of interpolation techniques. The developed pro- is very flexible for use: REFERENCES 1. Steel in concrete -Electrochenir&y # C m i o n  Newslet&r, No. 7, January ABl -No: ISSN 0106 2239. Danish Comsion Centre, Denmark 2. EA Erdelyi, E F  Fuchs and D H Binkley, IEEE Trans on Power Apparahu and Sytum, 8s - 7 (1970) 1565 3. LE V d u ;  EW Brooman and HA Cuggiti-J. A@ Electrochem 14 (1982) 721 4. WR Smyth-Static and dynamic electricity, McGraw Hill Book Co., Inc., New York, 1950 5. DE Hall, EJ Taylor and DJ Kentanski, Plating d Surf Finish 72 - 3  (1985) 60 # I I 600 Bulletin of Electrochemistry 1 (6) Nov.-Dec. 1985 

Contour potential mapping

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