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  1. clearvars
  2. tf = 2*60;
  3. nt = 10000;
  4. deltat=tf/nt;
  5. xf = 72E-3;
  6. nx = 14;
  7. deltax = xf/nx;
  8. yf = 72E-3;
  9. ny = 14;
  10. deltay = yf/ny;
  11. p = 6200 ;
  12. T0 = 293;
  13. pa0 = 0;%40;
  14. pw0 = 0;%1350 ;
  15. pb0 = p-pa0-pw0;%4801;
  16. Mw = 18.01528E-3;
  17. Mb = 28.97E-3;
  18. Ma = 44.01E-3;
  19. b0 = 0.225;
  20. lambdaa0 = 60000;
  21. theta0 = 0.422;
  22. alpha = 0.949;
  23. etas0 = 1.97*Ma;
  24. chi = 2.37;
  25. cg0 = 6.86;
  26. lambdac = -4120;
  27. ka0 = 2.27;
  28. lambdak = -2530;
  29. cm0 = 0.0208*Mw;
  30. beta = 1540;
  31. aant = 4.6543;
  32. bant = 1435.264;
  33. cant = -64.848;
  34. vs = 629E-6;
  35. vsa = 1000E-6;
  36. vsw = 1000E-6;
  37. rhos = 55.4;
  38. cps0 = 2.07E3;
  39. cpsa = 2E3;
  40. cpsw = 4.19E3;
  41. cpga = 0.86E3;
  42. cpgw = 1.9E3;
  43. cpgb = 1.006E3;
  44. keff = 44.5E-3;
  45. D0 = 2.2E-5;
  46. lambdasa = 60E3;
  47. lambdasw = 49E3;
  48.  
  49. l = 299E-3;
  50. vg0 = (1 - vs*rhos)*(deltay*deltax*l);
  51. R = 8.314;
  52.  
  53. for i = 1:(nx+1)
  54. for j = 1:(ny+1)
  55. T(i,j,1) = T0;
  56. rhoa(i,j,1) = Ma*pa0*vg0/(R*T0);
  57. rhow(i,j,1) = Mw*pw0*vg0/(R*T0);
  58. rhob(i,j,1) = Mb*pb0*vg0/(R*T0);
  59. vg(i,j,1) = vg0;
  60. end
  61. end
  62.  
  63. n=1;
  64.  
  65. for i=2:(nx)
  66. for j=2:(ny)
  67.  
  68. t(n) = (n-1)*deltat;
  69. t = t(n);
  70.  
  71. pa = (rhoa(i,j,n)/Ma)*R*T(i,j,n)/vg(i,j,n);
  72. vga = vg(i,j,n)/rhoa(i,j,n);
  73. vgpa = R*T(i,j,n)/(Ma*p);
  74.  
  75. pw = (rhow(i,j,n)/Mw)*R*T(i,j,n)/vg(i,j,n);
  76. vgw = vg(i,j,n)/rhow(i,j,n);
  77. vgpw = R*T(i,j,n)/(Mw*p);
  78.  
  79. pb = (rhob(i,j,n)/Mb)*R*T(i,j,n)/vg(i,j,n);
  80. vgb = vg(i,j,n)/rhob(i,j,n);
  81. vgpb = R*T(i,j,n)/(Mb*p);
  82.  
  83.  
  84. D = D0*(101300/p)*(T(i,j,n)/310)^1.5;
  85.  
  86. cg = cg0*exp(lambdac/(R*T(i,j,n))) ;
  87. ka = ka0*exp(lambdak/(R*T(i,j,n)));
  88. cm = cm0*exp(beta/T(i,j,n));
  89. psat = 100000*10^(aant - bant/(T(i,j,n)+cant));
  90.  
  91. sw = cg*cm*ka*pw/psat;
  92. uw = 1 - ka*pw/psat;
  93. vw = 1 + (cg -1)*ka*(pw/psat);
  94.  
  95. dswdpw = cm*cg*ka/psat;
  96. duwdpw = -ka/psat;
  97. dvwdpw = (cg-1)*ka/psat;
  98.  
  99.  
  100. dqwdsw = 1/(uw*vw);
  101. dqwduw = -sw/(uw^2*vw);
  102. dqwdvw = -sw/(uw*vw^2);
  103.  
  104. qw(i,j,n) = sw/(uw*vw);
  105.  
  106. b = b0*exp( (lambdaa0/(R*T0))*((T0/T(i,j,n))-1));
  107. theta = theta0 + alpha*(1-(T0/T(i,j,n)));
  108. etas = etas0*exp(chi*(1-(T0/T(i,j,n))));
  109.  
  110. dqadpa = b*etas*((b*pa)^theta+1)^(-(theta+1)/theta);
  111.  
  112. qa(i,j,n) = etas*b*pa/(1+(b*pa)^theta)^(1/theta);
  113.  
  114. dTdx = ( T(i+1,j,n) - T(i-1,j,n) ) / (2*deltax);
  115. dTdy = ( T(i,j+1,n) - T(i,j-1,n) ) / (2*deltay);
  116. d2Tdx2 = ( T(i+1,j,n) - 2*T(i,j,n) + T(i-1,j,n) ) / deltax^2;
  117. d2Tdy2 = ( T(i,j+1,n) - 2*T(i,j,n) + T(i,j-1,n) ) / deltay^2;
  118.  
  119. drhodxa = ( rhoa(i+1,j,n) - rhoa(i-1,j,n) ) / (2*deltax);
  120. drhodya = ( rhoa(i,j+1,n) - rhoa(i,j-1,n) ) / (2*deltay);
  121. d2rhodx2a = ( rhoa(i+1,j,n) - 2*rhoa(i,j,n) + rhoa(i-1,j,n) ) / deltax^2;
  122. d2rhody2a = ( rhoa(i,j+1,n) - 2*rhoa(i,j,n) + rhoa(i,j-1,n) ) / deltay^2;
  123.  
  124. drhodxw = ( rhow(i+1,j,n) - rhow(i-1,j,n) ) / (2*deltax);
  125. drhodyw = ( rhow(i,j+1,n) - rhow(i,j-1,n) ) / (2*deltay);
  126. d2rhodx2w = ( rhow(i+1,j,n) - 2*rhow(i,j,n) + rhow(i-1,j,n) ) / deltax^2;
  127. d2rhody2w = ( rhow(i,j+1,n) - 2*rhow(i,j,n) + rhow(i,j-1,n) ) / deltay^2;
  128.  
  129. drhodxb = ( rhob(i+1,j,n) - rhob(i-1,j,n) ) / (2*deltax);
  130. drhodyb = ( rhob(i,j+1,n) - rhob(i,j-1,n) ) / (2*deltay);
  131. d2rhodx2b = ( rhob(i+1,j,n) - 2*rhob(i,j,n) + rhob(i-1,j,n) ) / deltax^2;
  132. d2rhody2b = ( rhob(i,j+1,n) - 2*rhob(i,j,n) + rhob(i,j-1,n) ) / deltay^2;
  133.  
  134. Vnet = 0;
  135. Aa = rhos*(dqadpa*(R/Ma)*(T(i,j,n)/vg(i,j,n)));
  136. Aw = rhos*((dqwdsw*dswdpw)+(dqwduw*duwdpw)+(dqwdvw*dvwdpw))*(R/Mw)*T(i,j,n)/vg(i,j,n);
  137.  
  138. rhoa(i,j,n+1) = rhoa(i,j,n) + ((D*(d2rhodx2a+d2rhody2a)-(1/vga)*Vnet)/(Aa+1))*deltat;
  139. rhow(i,j,n+1) = rhow(i,j,n) + ((D*(d2rhodx2w+d2rhody2w)-(1/vgw)*Vnet)/(Aw+1))*deltat;
  140. rhob(i,j,n+1) = rhob(i,j,n) + ((D*(d2rhodx2b+d2rhody2b)-(1/vgb)*Vnet))*deltat;
  141.  
  142. sumrhocp = rhos*cps0+ rhoa(i,j,n)*cpga+ rhob(i,j,n)*cpgb +rhow(i,j,n)*cpgw+ rhos*cpsw*qw(i,j,n) + rhos*cpsa*qa(i,j,n) ;
  143.  
  144. T(i,j,n+1) = T(i,j,n) +(deltat/sumrhocp)*( D*(cpga*(drhodxa*dTdx+drhodya*dTdy)+cpgw*(drhodxw*dTdx+drhodyw*dTdy)+cpgb*(drhodxb*dTdx+drhodyb*dTdy)) +...
  145. keff*(d2Tdx2 + d2Tdy2) );
  146.  
  147. % sumrhocp = rhos*cps0+ rhoa(i,j,n)*cpga+ rhob(i,j,n)*cpgb +rhow(i,j,n)*cpgw+ rhos*cpsw*qw(i,j,n) + rhos*cpsa*qa(i,j,n) ;
  148. % T(i,j,n+1) = T(i,j,n) +deltat*(keff*(d2Tdx2 + d2Tdy2) )/sumrhocp ;
  149.  
  150. vg(i,j,n+1) = vg(i,j,n);
  151. end
  152. end
  153. for j = 2:(ny)
  154.  
  155. rhoa(1,j,n+1)=rhoa(2,j,n+1);
  156. rhoa(nx+1,j,n+1)=rhoa(nx,j,n+1);
  157.  
  158. rhow(1,j,n+1)=rhow(2,j,n+1);
  159. rhow(nx+1,j,n+1)=rhow(nx,j,n+1);
  160.  
  161. rhob(1,j,n+1)=rhob(2,j,n+1);
  162. rhob(nx+1,j,n+1)=rhob(nx,j,n+1);
  163.  
  164. end
  165.  
  166. for i = 2:(nx)
  167. rhoa(i,1,n+1)=rhoa(i,2,n+1);
  168. rhow(i,1,n+1)=rhow(i,2,n+1);
  169. rhob(i,1,n+1)=rhob(i,2,n+1);
  170. rhoa(i,ny+1,n+1)=rhoa(i,ny,n+1);
  171. rhow(i,ny+1,n+1)=rhow(i,ny,n+1);
  172. rhob(i,ny+1,n+1)=rhob(i,ny,n+1);
  173.  
  174. end
  175.  
  176. % rhoa(1,1,n+1) = ( rhoa(2,1,n+1) + rhoa(1,2,n+1) + rhoa(2,2,n+1) ) / 3 ;
  177. % rhow(1,1,n+1) = ( rhow(2,1,n+1) + rhow(1,2,n+1) + rhow(2,2,n+1) ) / 3;
  178. % rhob(1,1,n+1) = ( rhob(2,1,n+1) + rhob(1,2,n+1) + rhob(2,2,n+1) ) / 3;
  179.  
  180. % rhoa(nx+1,1,n+1) = ( rhoa(nx+1,2,n+1) + rhoa(nx,1,n+1) + rhoa(nx,2,n+1) ) / 3;
  181. % rhow(nx+1,1,n+1) = ( rhow(nx+1,2,n+1) + rhow(nx,1,n+1) + rhow(nx,2,n+1) ) / 3;
  182. % rhob(nx+1,1,n+1) = ( rhob(nx+1,2,n+1) + rhob(nx,1,n+1) + rhob(nx,2,n+1) ) / 3;
  183.  
  184. % rhoa(1,ny+1,n) = ( rhoa(2,ny+1,n+1) + rhoa(1,ny,n+1) + rhoa(2,ny,n+1) ) / 3;
  185. % rhow(1,ny+1,n) = ( rhow(2,ny+1,n+1) + rhow(1,ny,n+1) + rhow(2,ny,n+1) ) / 3;
  186. % rhob(1,ny+1,n) = ( rhob(2,ny+1,n+1) + rhob(1,ny,n+1) + rhob(2,ny,n+1) ) / 3;
  187.  
  188. % rhoa(nx+1,ny+1,n) = ( rhoa(nx+1,ny,n+1) + rhoa(nx,ny+1,n+1) + rhoa(nx,ny,n+1) ) / 3;
  189. % rhow(nx+1,ny+1,n) = ( rhow(nx+1,ny,n+1) + rhow(nx,ny+1,n+1) + rhow(nx,ny,n+1) ) / 3;
  190. % rhob(nx+1,ny+1,n) = ( rhob(nx+1,ny,n+1) + rhob(nx,ny+1,n+1) + rhob(nx,ny,n+1) ) / 3;
  191.  
  192. for i = 1:(nx+1)
  193. if t <= 20*60
  194. T(i,1,n+1) = -0.0175005443*(t/60)^3+0.5250113819*(t/60)^2-0.000000367*(t/60)+20.000108611+273;
  195. T(i,ny+1,n+1) = T(i,1,n+1);
  196. else
  197.  
  198. T(i,1,n+1) = 363;
  199. T(i,ny+1,n+1) = 363;
  200. end
  201.  
  202.  
  203.  
  204. end
  205.  
  206. for j = 1:(ny+1)
  207. if t <= 20*60
  208.  
  209. T(1,j,n+1) = -0.175*(t/60)^2 + 7*(t/60) + 293;
  210. T(nx+1,j,n+1) = T(1,j,n+1);
  211. else
  212.  
  213. T(1,j,n+1) = 363;
  214. T(nx+1,j,n+1) = 363;
  215. end
  216. end
  217.  
  218.  
  219. for n = 2:nt
  220. for i=2:(nx)
  221. for j=2:(ny)
  222.  
  223. t(n) = (n-1)*deltat;
  224. t = t(n);
  225.  
  226. pa = (rhoa(i,j,n)/Ma)*R*T(i,j,n)/vg(i,j,n);
  227. vga = vg(i,j,n)/rhoa(i,j,n);
  228. vgpa = R*T(i,j,n)/(Ma*p);
  229.  
  230. pw = (rhow(i,j,n)/Mw)*R*T(i,j,n)/vg(i,j,n);
  231. vgw = vg(i,j,n)/rhow(i,j,n);
  232. vgpw = R*T(i,j,n)/(Mw*p);
  233.  
  234. pb = (rhob(i,j,n)/Mb)*R*T(i,j,n)/vg(i,j,n);
  235. vgb = vg(i,j,n)/rhob(i,j,n);
  236. vgpb = R*T(i,j,n)/(Mb*p);
  237.  
  238.  
  239. D = D0*(101300/p)*(T(i,j,n)/310)^1.5;
  240.  
  241.  
  242. cg = cg0*exp(lambdac/(R*T(i,j,n))) ;
  243. ka = ka0*exp(lambdak/(R*T(i,j,n)));
  244. cm = cm0*exp(beta/T(i,j,n));
  245. psat = 100000*10^(aant - bant/(T(i,j,n)+cant));
  246.  
  247. sw = cg*cm*ka*pw/psat;
  248. uw = 1 - ka*pw/psat;
  249. vw = 1 + (cg -1)*ka*(pw/psat);
  250.  
  251. dswdpw = cm*cg*ka/psat;
  252. duwdpw = -ka/psat;
  253. dvwdpw = (cg-1)*ka/psat;
  254.  
  255. dqwdsw = 1/(uw*vw);
  256. dqwduw = -sw/(uw^2*vw);
  257. dqwdvw = -sw/(uw*vw^2);
  258.  
  259. qw(i,j,n) = sw/(uw*vw);
  260.  
  261. b = b0*exp( (lambdaa0/(R*T0))*((T0/T(i,j,n))-1));
  262. theta = theta0 + alpha*(1-(T0/T(i,j,n)));
  263. etas = etas0*exp(chi*(1-(T0/T(i,j,n))));
  264.  
  265. dqadpa = b*etas*((b*pa)^theta+1)^(-(theta+1)/theta);
  266.  
  267. qa(i,j,n) = etas*b*pa/(1+(b*pa)^theta)^(1/theta);
  268.  
  269. dTdx = ( T(i+1,j,n) - T(i-1,j,n) ) / (2*deltax);
  270. dTdy = ( T(i,j+1,n) - T(i,j-1,n) ) / (2*deltay);
  271. d2Tdx2 = ( T(i+1,j,n) - 2*T(i,j,n) + T(i-1,j,n) ) / deltax^2;
  272. d2Tdy2 = ( T(i,j+1,n) - 2*T(i,j,n) + T(i,j-1,n) ) / deltay^2;
  273.  
  274. drhodxa = ( rhoa(i+1,j,n) - rhoa(i-1,j,n) ) / (2*deltax);
  275. drhodya = ( rhoa(i,j+1,n) - rhoa(i,j-1,n) ) / (2*deltay);
  276. d2rhodx2a = ( rhoa(i+1,j,n) - 2*rhoa(i,j,n) + rhoa(i-1,j,n) ) / deltax^2;
  277. d2rhody2a = ( rhoa(i,j+1,n) - 2*rhoa(i,j,n) + rhoa(i,j-1,n) ) / deltay^2;
  278.  
  279. drhodxw = ( rhow(i+1,j,n) - rhow(i-1,j,n) ) / (2*deltax);
  280. drhodyw = ( rhow(i,j+1,n) - rhow(i,j-1,n) ) / (2*deltay);
  281. d2rhodx2w = ( rhow(i+1,j,n) - 2*rhow(i,j,n) + rhow(i-1,j,n) ) / deltax^2;
  282. d2rhody2w = ( rhow(i,j+1,n) - 2*rhow(i,j,n) + rhow(i,j-1,n) ) / deltay^2;
  283.  
  284. drhodxb = ( rhob(i+1,j,n) - rhob(i-1,j,n) ) / (2*deltax);
  285. drhodyb = ( rhob(i,j+1,n) - rhob(i,j-1,n) ) / (2*deltay);
  286. d2rhodx2b = ( rhob(i+1,j,n) - 2*rhob(i,j,n) + rhob(i-1,j,n) ) / deltax^2;
  287. d2rhody2b = ( rhob(i,j+1,n) - 2*rhob(i,j,n) + rhob(i,j-1,n) ) / deltay^2;
  288.  
  289.  
  290. sumrhocp = rhos*cps0+ rhoa(i,j,n)*cpga+ rhob(i,j,n)*cpgb +rhow(i,j,n)*cpgw+ rhos*cpsw*qw(i,j,n) + rhos*cpsa*qa(i,j,n) ;
  291.  
  292. T(i,j,n+1) = T(i,j,n) +(deltat/sumrhocp)*( D*(cpga*(drhodxa*dTdx+drhodya*dTdy)+cpgw*(drhodxw*dTdx+drhodyw*dTdy)+cpgb*(drhodxb*dTdx+drhodyb*dTdy)) +...
  293. keff*(d2Tdx2 + d2Tdy2) );
  294.  
  295. % sumrhocp = rhos*cps0+ rhoa(i,j,n)*cpga+ rhob(i,j,n)*cpgb +rhow(i,j,n)*cpgw+ rhos*cpsw*qw(i,j,n) + rhos*cpsa*qa(i,j,n) ;
  296. % T(i,j,n+1) = T(i,j,n) +deltat*(keff*(d2Tdx2 + d2Tdy2) )/sumrhocp ;
  297.  
  298.  
  299. Vnet = rhos*((qa(i,j,n)-qa(i,j,n-1))/deltat)*(vsa-vgpa)+rhos*((qw(i,j,n)-qw(i,j,n-1))/deltat)*(vsw-vgpw)+((T(i,j,n+1)-T(i,j,n))/deltat)*vg(i,j,n)/T(i,j,n+1) + D*(d2rhodx2a+d2rhody2a)*vgpa+D*(d2rhodx2w+d2rhody2w)*vgpw+D*(d2rhodx2b+d2rhody2b)*vgpb;
  300. Aa = rhos*(dqadpa*(R/Ma)*(T(i,j,n)/vg(i,j,n)));
  301. Aw = rhos*((dqwdsw*dswdpw)+(dqwduw*duwdpw)+(dqwdvw*dvwdpw))*(R/Mw)*T(i,j,n)/vg(i,j,n);
  302.  
  303.  
  304. rhoa(i,j,n+1) = rhoa(i,j,n) + ((D*(d2rhodx2a+d2rhody2a)-(1/vga)*Vnet)/(Aa+1))*deltat;
  305. rhow(i,j,n+1) = rhow(i,j,n) + ((D*(d2rhodx2w+d2rhody2w)-(1/vgw)*Vnet)/(Aw+1))*deltat;
  306. rhob(i,j,n+1) = rhob(i,j,n) + ((D*(d2rhodx2b+d2rhody2b)-(1/vgb)*Vnet))*deltat;
  307.  
  308. vg(i,j,n+1) = vg(i,j,n) + deltat*( -rhos*( vsa*((qa(i,j,n)-qa(i,j,n-1))/deltat)+ vsw*( qw(i,j,n)-qw(i,j,n-1) )/deltat ) )*deltat;
  309. end
  310. end
  311.  
  312. for j = 2:(ny)
  313.  
  314. rhoa(1,j,n+1)=rhoa(2,j,n+1);
  315. rhoa(nx+1,j,n+1)=rhoa(nx,j,n+1);
  316.  
  317. rhow(1,j,n+1)=rhow(2,j,n+1);
  318. rhow(nx+1,j,n+1)=rhow(nx,j,n+1);
  319.  
  320. rhob(1,j,n+1)=rhob(2,j,n+1);
  321. rhob(nx+1,j,n+1)=rhob(nx,j,n+1);
  322.  
  323. end
  324.  
  325. for i = 2:(nx)
  326. rhoa(i,1,n+1)=rhoa(i,2,n+1);
  327. rhow(i,1,n+1)=rhow(i,2,n+1);
  328. rhob(i,1,n+1)=rhob(i,2,n+1);
  329. rhoa(i,ny+1,n+1)=rhoa(i,ny,n+1);
  330. rhow(i,ny+1,n+1)=rhow(i,ny,n+1);
  331. rhob(i,ny+1,n+1)=rhob(i,ny,n+1);
  332.  
  333. end
  334.  
  335. % rhoa(1,1,n+1) = ( rhoa(2,1,n+1) + rhoa(1,2,n+1) + rhoa(2,2,n+1) ) / 3 ;
  336. % rhow(1,1,n+1) = ( rhow(2,1,n+1) + rhow(1,2,n+1) + rhow(2,2,n+1) ) / 3;
  337. % rhob(1,1,n+1) = ( rhob(2,1,n+1) + rhob(1,2,n+1) + rhob(2,2,n+1) ) / 3;
  338.  
  339. % rhoa(nx+1,1,n+1) = ( rhoa(nx+1,2,n+1) + rhoa(nx,1,n+1) + rhoa(nx,2,n+1) ) / 3;
  340. % rhow(nx+1,1,n+1) = ( rhow(nx+1,2,n+1) + rhow(nx,1,n+1) + rhow(nx,2,n+1) ) / 3;
  341. % rhob(nx+1,1,n+1) = ( rhob(nx+1,2,n+1) + rhob(nx,1,n+1) + rhob(nx,2,n+1) ) / 3;
  342.  
  343. % rhoa(1,ny+1,n) = ( rhoa(2,ny+1,n+1) + rhoa(1,ny,n+1) + rhoa(2,ny,n+1) ) / 3;
  344. % rhow(1,ny+1,n) = ( rhow(2,ny+1,n+1) + rhow(1,ny,n+1) + rhow(2,ny,n+1) ) / 3;
  345. % rhob(1,ny+1,n) = ( rhob(2,ny+1,n+1) + rhob(1,ny,n+1) + rhob(2,ny,n+1) ) / 3;
  346.  
  347. % rhoa(nx+1,ny+1,n) = ( rhoa(nx+1,ny,n+1) + rhoa(nx,ny+1,n+1) + rhoa(nx,ny,n+1) ) / 3;
  348. % rhow(nx+1,ny+1,n) = ( rhow(nx+1,ny,n+1) + rhow(nx,ny+1,n+1) + rhow(nx,ny,n+1) ) / 3;
  349. % rhob(nx+1,ny+1,n) = ( rhob(nx+1,ny,n+1) + rhob(nx,ny+1,n+1) + rhob(nx,ny,n+1) ) / 3;
  350.  
  351. for j = 1:(ny+1)
  352. if t <= 20*60
  353.  
  354. T(1,j,n+1) = -0.175*(t/60)^2 + 7*(t/60) + 293;
  355. T(nx+1,j,n+1) = T(1,j,n+1);
  356. else
  357.  
  358. T(1,j,n+1) = 363;
  359. T(nx+1,j,n+1) = 363;
  360. end
  361. end
  362.  
  363.  
  364. for i = 1:(nx+1)
  365. if t <= 20*60
  366.  
  367. T(i,1,n+1) = -0.0175005443*(t/60)^3+0.5250113819*(t/60)^2-0.000000367*(t/60)+20.000108611+273;
  368. T(i,ny+1,n+1) = T(i,1,n+1);
  369. else
  370.  
  371. T(i,1,n+1) = 363;
  372. T(i,ny+1,n+1) = 363;
  373. end
  374.  
  375.  
  376.  
  377. end
  378.  
  379.  
  380. end
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