Solving Equations

[HotSteam]

I know some solving methods. But so far have been unable to write a fast converging algotithm for the problem.

I am working in steam properties IAPWS-95 and 97 plugin for MathCad and Vissim. The problem is solving two equations of two unknowns. I.E. pressure = p(t,d) and entropy = s(t.d) given pressure and entropy I have to search for t and d. The function p(t,d) is a 64 term equation and quite a few terms have factors of a*e^f(t,d)

Any sugestions on a fast converging algorithm?

 

[IRstuff]

What's wrong with using the Given-Find solver?

TTFN

 

[HotSteam]

Sorry. The plugin is in C++ I need an algorithm I can implement in C/C++. There is the added problem that if the density temperature lies to far inside saturated water/steam mixture region the formula cause floating point exceptions. So while solving I must also keep in the vapoer or liquid regions or switch and find a saturation state including quality. With the IAPWS-95 formula you must solve for vapor and liquid densities that satisfy an equalibrum formula at the saturation temperature. I cheat on that by using the IFC-97 formulation as a close aproxamation of the saturation line unless my variables are outside by more then 0.05%.

The code can made to work with most any programe that alows plugins to be writen in C or C++.

 

[ijl]

Solving sets of nonlinear equations is tough, mostly. Better to see what the others have done. Try Google. Suitable search-terms are

"steam tables", "backward equations", "p(v,s)", entropy, for example.

Here is one link from a quick search

http://www.iapws.org/release.htm

rvsvp

 

[25362]

There is an article in the ChE issue of May 12, 1986 by Gonz[á]lez-Pozo, titled Formulas to estimate properties for dry, saturated steam, under the Plant Notebbok heading. The formulas contain seven coefficients, and are claimed to have very low % errors.