A little while ago I was ruminating on the subject of needing to know the thermodynamic properties of materials before you could do simulations of those materials. I therefore figured I’d spend the week dusting off some old functions I’d written for the saturated thermodynamic properties of steam and implementing them as a web page using Javascript and jQuery. That work is proceeding but let me describe how I produced the functions themselves.
I started by using a curve fit program I’d written to develop functions of the thermodynamic properties of saturated water in its liquid and gaseous forms. The fit program could also generate functions for the first three derivatives of the originally fit functions in many cases, although it was rare to ever employ more than the first derivative. In order to make reasonable curves I had to do the fits piece-wise over the applicable range of temperatures and pressures. The resulting functions looked something like this:
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function TFind_P(T) { var temp = 0.0; if (T < -40.0) { temp = 0.0; } else if (T < 32.018) { T = T + 4.00000000000000E+0001 + 2; temp = -5.82750190795537E-0004; temp += ( 3.10138202245116E-0004 * T); temp += (-9.96845835382852E-0006 * T * T); temp += ( 2.93452465077397E-0007 * T * T * T); temp += 1.90000000000000E-0003; } else if (T <= 95) { temp = 1.02291643993728E-0001 * T; temp += (-1.56461430882940E+0001 / T); temp += (-7.77500161911500E-0001 * Math.sqrt(T)); temp += (-5.68581901662451E-0001 * Math.log(T)); temp += (-5.57135053654371E-0004 * T * T); temp += ( 2.68643222990479E-0006 * T * T * T); // temp += 4.06678025391659E+0000 + 8.86600000000000E-0002;} temp += 4.15544025391659E+0000; } else if (T <= 281.03) { temp = 3.92079417112400E+0001 * T; temp += ( 4.01213788918853E+0004 / T); temp += (-1.28706905409880E+0003 * Math.sqrt(T)); temp += ( 3.50936122348532E+0003 * Math.log(T)); temp += (-3.40581930733492E-0002 * T * T); temp += ( 3.01211718278793E-0005 * T * T * T); temp += -7.30111133292317E+0003; temp += 0.00000000000000E+0000; } else if (T <= 373.13) { temp = -4.46073180369288E+0003 * T; temp += (-2.91401612241211E+0007 / T); temp += ( 2.35876174171448E+0005 * Math.sqrt(T)); temp += (-1.02466834830570E+0006 * Math.log(T)); temp += ( 1.41416476892482E+0000 * T * T); temp += (-3.85708716196032E-0004 * T * T * T); temp += 3.07749988717651E+0006; temp += 5.00000000000000E+0001; } else if (T <= 621.21) { temp = 6.08822615030408E+0003 * T; temp += ( 6.96757841217041E+0007 / T); temp += (-3.68132442183495E+0005 * Math.sqrt(T)); temp += ( 1.83794467631912E+0006 * Math.log(T)); temp += (-1.51896496594964E+0000 * T * T); temp += ( 3.61841945230257E-0004 * T * T * T); temp += -6.03886787577057E+0006; temp += 1.80000000000000E+0002; } else { temp = 0.0; } return temp; } |
The functions can be written more efficiently but this is the closest translation from the original Pascal. If I chose to continue using these tools I would make them far more efficient.