When I calculate a thermochemical nonequilibrium flow past a blunt cone at high Mach number by N-S equations,I find the reaction rate coefficients is so large that they exceed the range of single precision real,which in turn results in the blow-up of my program.Although I scan my program again by again,I find no problems on my formulae,which are all taken from C.Park's "nonequilibrium hypersonic aerodynamics".

Peter A.Gnoffo shows a limit should be imposed on the temperature used to compute the reaction rate coefficients on NASA TM 4674,but I don't know how to implement his method.

All recommendations are welcomed!

Thanks in advance.

One method may be to calculate the adiabatic temperature rise. You can get this temperature if the whole amount of all your components you have react. Depending on your chemical equations and your system it might be difficult to find this temperature. You have to write down a proper formulation of the adiabatic temperature rise and solve the non linear equation (by newton) which results: because your temperature arises you have a change in your heat capacity which changes the "amount of heat" absorbed by your system, which changes your temperature. You may find the formula for the adiabatic temperature rise in many books for chemical engineering.

Anyway since you have found the maximal temperature that your system might achieve depending on chemical equations (and you konw how many grad your temperature rises because of your flow) you may add maximal 100 Grad. This temperature should be the maximal temperatur aloud in your System. Anyway from time to time you do have such problems. The temperature rises and you get problems with almost everything (density, heat capacity ...) but after some iterations your systems cools down.

Jannis

Thank Dotsikas for your recomendations. I want to further explain my situation.I use two-temperature model in computation.As you said,I solve the translational temperature by explicit formula and the vibrational temperature by Newton iteration.The heat capacity is the function of temperature.The blunt cone is the experimental model of RAMC-3 at 76.3 Km altitude with the velocity 7.65km/s.The reactions, their rate coefficient and the equilibrium constant are those of Park's model from "nonequilibrium hypersonic aerothermodynamics".The initial flow field are free stream.I use LU-SGS and MUSCL TVD scheme.

From the beginning of computation,I found the very high abnormal reaction rate coefficient even the translational temperaure is not very high.After several iterations,The program blow up on account of float overflow even at very low CFL number.

However,I succeeded in yielding a good result by Dunn-Kang's model.I don't know the reasons.

What happens with your reaction rates if you calculate everything at ONE KONSTANT temperatur? If you get the results try to increase your Temperature by some grad and see how your reaction rates change during your calculation until you get a converged solution for this temperatur field. If they arise and then fall down, it´s good.

An other way: Try to solve your Problem and obtain your flow field without the chemical reaction. After having done it use the data from your flow simulation to solve ONLY the chemical equilibrium problem, while keeping the temperature and everything else konstant. If it doesn´t work set back your temperature and then try to rise it with very small slopes. ***the solution is not the solution you are looking for***

Target: Is it possible to obtain reasonable results for your rate coefficients and equilibrium constants with your method? How many reactions do you have?

best regards

Jannis Dotsikas

Jannis Dotsikas:

I'm very apperciative to your comments.

I'v found the reason.It's necessary to limit the control temperature,which is used to calculate the reaction rate coefficients,in order to ensure the running of program.As for nonequilibrium hypersonic flow at high altitude,the temperature is so low as not to ignite the dissociation reactions.However,the reaction rate coefficients and the equilibrium coefficients are yielded at the temeprature far beyond the temperature of free stream,so it will lead to float overflow to calculate the reaction rate coefficients at such low temeprature.After I impose a lower limit temperature 1000K as Gnoffo used,I obtain a satisfactory result.

Thanks a lot for your precious suggestions again.