Dear anyone who can help me. i'm a student in last year, i have a hard subject to do , and if you permit i need your help, that is the problem : I have to study the " Fire induced air flow in a tunnel using the low reynolds k, epsilon model". So i have take the Navier- stokes equations ( continuity equation +3 motion equations ( 3 D ) and applied to them the reynolds decomposition ( function = mean of the fuction + fluctuation of the function ) so i have done that for velocities u, v, w and the pressure ; after simplifing i obtain four equations of course , so i must apply the low reynolds number k, epsilon model , and i must close the system equations by another additional equations , so what are these equations , please can you write the system for me , i have already write the first four equations ( continuitu + 3 motion ). Please ,i need your help to begin my work ,i had to dicretize equations and apply a numerical methods ( finite method elements and finite difference method to solve the system. Thank you very much. nb : low reynolds number constants can be found here :http://cfd.me.umist.ac.uk/tmcfd/models/lrnke.html and here : http://cfd.me.umist.ac.uk/tmcfd/models/hrnke.html ps: what i need exactly is the "final system to solve , " JUST THE SYSTEM OF EQUATIONS ", ( i will solve it numerically ) , you can simplify boundary conditions if it's needed or take the simpliest case. Please sir i really need your help , i'm really desperate. Best regards.

I am not quite sure about your problem: you have Reynolds-averaged N-S equation which can be closed by applying k-e model. So you have: 6 equations (mass, 3 momentums, k and e). The purpose of solving k-e equations is to provide turbulent viscosity which is the only additional requirement in the momentum equation. The turbulent viscosity is linked to k-e through Mu_t = Fmu *Cmu *density * k^2/e where Fmu is the low Reynolds Number influence.

Thank you very much for your answer , but i have forget to tell you about a missing equation which contain probably the temperature of the air as a variable, so an additionnal equation -> addtionnal variables, what is your opinion sir , can you help me . Best regards.

Well, you can solve an enthalpy equation (in the form of static enthalpy or total enthalpy) for temperature: the turbulent heat flux overbar(density*v'*h') is linked to Mu_t/Prandtle_Number*grad(h) where h is mean enthalpy - should be able to find it in any turbulence modelling book.

thank you very much for your answer, i'll follow your advice. Best regards.

please Mr John. L can you give me your email , i need it in order to send you my work , i need your opinion, we have talked about my work , do you remember ( heated air flow in a ventilated tunnel ) Thank you very much