/************************************************************************************* * Program: t32c2t * * Purpose: Calculate CCT from TTT according to Scheil. * * * * Author: M J Peet * * Version: 0.21 * * Date: 09-July-08 * * Location: http://mathewpeet.org/thesis/programs/ * * License: GPL, Gnu Public License, you are free to modify and use this program * * if you distribute the program you must also distribute the code, along with any * * changes you make. Do not modify this header. * * * ************************************************************************************/ #include #include #define ARRAYSIZE 1600/* size of arrays used for globals - max temperature when using 1 K resolution for temperature*/ #undef HELLO /* control DEBUGGING CODE --- set to `define or undef' to test program structure */ #undef DEBUG /* control DEBUGGING CODE --- set to `define or undef' */ /* Globals */ int tempsK[ARRAYSIZE+1];/*!< maximum temp is (ARRAYSIZE) kelvin, the time spent at each temperature will be stored here. */ double starttK[ARRAYSIZE+1];/*!< corresponding time for when transformation is detectable at a temperature in TTT */ int main() { /** PSEUDO CODE * * Get input cooling (linear, ideal, data file?) * * Step through time, and record time spent at each temp * * Read in Time-temperature-transformation data (ttt) * * Calculate amounts of transformation at each temp during cooling * output temp and time when transformation is detectable * */ int transf_temp; /*!< temperature at which transformation is first detectable */ double startT,rate; initialise_global_starttK(); initialise_global_tempsK(); /*! initilise arrays for temp (0) and start time (large). */ /*test_ttt(); /* this should only need to be read once * should be adjusted to allow input from file / IO */ //test_globals(); read_ttt(); // calc_temp_erf(); /* calculate times spent at each temperature during cooling.*/ /*make cooling rate or section size a variable in calc_tempsK * include this in a loop to find when start_temp is non zero * this will allow to find critical cooling rate or section size * Also add analytical solution for cylinders */ startT=1273; //temperature in kelvin, you can use any as long as you use for input TTT also rate=0.00005; printf("cooling rate /K/s, temperature /K, time /s\n"); do { //printf("\nlinear cooling rate:"); printf("%lf, ",rate); initialise_global_tempsK(); calc_temp_lin(startT,rate); transf_temp = output_cct(); //printf("\nmain knows temperature was: %d\n", transf_temp); rate=rate*1.05; } while (transf_temp>0); /* call subroutine calc_temp_erf with different distances * and calculate cooling times in similar way * */ double surfaceT,diffusivity,depth,mindepth; surfaceT = 473; depth = 1; // in m mindepth = 0.000000001; // stop when we get this close to surface diffusivity = 0.00001175; // m^2/s // diffusivity 1.175e-5 m^2/s for 1C wt% steel (Holman), 5.44x10-2 cm^2/s for low alloy at 1000 K. startT=1273; printf("\n\nsemi infinite heat flow\n"); printf("Depth /m, temperature /K, time /s\n"); //ensure diffusivity is in appropriate units! do { //printf("\n Depth:"); printf("%lf, ",depth); initialise_global_tempsK(); calc_temp_erf(startT,surfaceT,diffusivity,depth); //show_globals(); transf_temp = output_cct(); // printf("\nmain knows temperature was: %d\n", transf_temp); depth=(depth/1.1); } while (transf_temp>0); /* there is also a solution of semi infinite heat flow * equation for shafts and cylinders * **/ /* could also calculate natural cooling curves for welding CCTs * */ /* QUESTION * is this only accurate if longer than * 1 unit of time is spent at each temperature? */ #ifdef DEBUG test_globals(); /* print contents of the two arrays */ printf ("\nGoodbye from program\n"); #endif /* DEBUG */ printf("\n"); return (0); } int test_globals() { int i; #ifdef HELLO printf("\nhello from test_globals subroutine\n"); #endif /* HELLO */ printf("\nContents of arrays as follows i, tempsK[i], starttK[i]\n"); for (i = ARRAYSIZE; i>=0; i--) if(tempsK[i]>0) printf("i = %#5d, tempsK[] = %#5d N, starttK[] =%4.4le s.\n",i,tempsK[i],starttK[i]); return (0); } int initialise_global_tempsK() { #ifdef HELLO printf("\nhello from initialise_global_tempsK subroutine\n"); #endif /* HELLO */ int i; for (i = ARRAYSIZE; i>=0; i--) { tempsK[i]=0; /*initialise */ } tempsK[0]=0; return (0); } int initialise_global_starttK() { #ifdef HELLO printf("\nhello from initialise_global_starttK subroutine\n"); #endif /* HELLO */ int i; for (i = ARRAYSIZE; i>0; --i) { starttK[i]=1.65e308; } starttK[0]=1.65e308; return (0); } int calc_temp_erf(double Ti, double Ts, double A, double X) { #ifdef HELLO printf("\nhello from calc_temps_erf subroutine\n"); printf("%lf %lf %lf %lf",Ts,Ti,A,X); #endif /* HELLO */ double time; double temp; int a; //double Ts, Ti, A, X; /* variables used in semi - infinite solution of heat flow */ /** Ti initial temperature, * Ts surface temperature, * A thermal diffusivity heat, * X distance - units depends upon units of A. * \f$\textrm{temp} = Ts + (Ti-Ts)\times \textrm{erf}\left(\frac{X}{2 \sqrt{A*\textrm{time}}} \right)\f$ **/ // printf("Ts: %lf Ti:%lf A:%lf X:%lf",Ts,Ti,A,X); time = 0.0; do { temp = Ts + (Ti-Ts)*(erf(X/(2.0*sqrt(A*time)))); /* 1 D heat flow /* temp = 1273 - (time*0.39); */ a = (int)temp; // printf("a = %#5d,temp = %4.4le K, time = %4.4le s.\n",a,temp,time); tempsK[a]++; time = time + 1.0; } while (temp > 0 && time < 10e7); //printf("\nCooled to %lf kelvin in %lf seconds.",temp, time); return (0); } int calc_temp_lin(double start_temp,double rate) { double time; double temp; //start_temp = 1273; //rate = 1.0; int a; #ifdef HELLO printf("\nhello from calc_temps_lin subroutine\n"); printf("I know start_temp %lf and rate is %lf",start_temp,rate); #endif /* HELLO */ time = 0.0; do { temp = start_temp - (time*rate); /* linear cooling */ a = (int)temp; #ifdef DEBUG printf("a = %#5d,temp = %4.4le K, time = %4.4le s.\n",a,temp,time); #endif /* DEBUG */ tempsK[a]++; time = time + 1.0; } while (temp > 0); #ifdef DEBUG printf("\nCooled to %lf Kelvin in %lf seconds.\n",temp, time); #endif /* DEBUG */ return (0); } int test_ttt() { printf("\nHello from test_ttt\n"); int i; for (i = 1000; i >= 600; i--) starttK[i] = 3000.0; return (0); } int read_ttt() { double tttT, tttt; int error_detect[ARRAYSIZE]; int i; for (i = ARRAYSIZE; i>=0; i--) error_detect[i]=0; #ifdef HELLO printf("\nhello from read_ttt\n"); #endif /* HELLO */ /* read numbers until you find a non number (eof or character) */ while((scanf("%lf %lf", &tttT, &tttt)) != EOF) { #ifdef DEBUG printf("%lf %lf \n",tttT,tttt); #endif /* DEBUG */ error_detect[(int)tttT]++; starttK[(int)tttT]=tttt; } return (0); } int show_globals() { printf("\nHello from show_globals\n"); int i; for (i = ARRAYSIZE; i >= 0; i--) printf("\n starttK[%d] %le, tempsK[%d] %d, tran: %le",i,starttK[i],i,tempsK[i],tempsK[i]*(1.0/starttK[i])); return (0); } int output_cct() /** this function returns the temperature at which transformation was first detected */ { #ifdef HELLO printf("\nhello from output_cct\n"); #endif /*HELLO*/ int b; int time; double amount = 0; /* volume fraction transformed as fraction of detectable amount */ // printf("Time for detectable transformation to occur during cooling."); //printf("Temperature, amount"); time =0; b = ARRAYSIZE; do { b--; amount += tempsK[b]*(1.0/starttK[b]); time += tempsK[b]; #ifdef DEBUG printf("b = %d amount = %le\n", b, amount); #endif /* DEBUG */ } while ((amount < 1.0) && b > 0 ); //printf("start detected at temperature of"); printf(" %d, %d\n",b,time); return b; }