Fluids

What is Mixture Fraction Variance in Combustion Modelling?

• hardik2309
Subscriber
n non-premixed combustion, Mixture fraction and Mixture fraction variance conservation are used. what is the physical interpretation of mixture fraction variance? Why do the values of the scalers depend on it?nWhy does it conserve?nI have gone through the theory and guide and several other texts but could not find any simple explanation.nAny simple explanation of this term is requested.n
• wcao
Ansys Employee
Hi,nIn laminar flow, you can have phi = phi(Z). However, the non-premixed combustion model, or say flamelet model is for application in turbulent flow, where the reported variable should be averaged or filter phi_bar. To calculate Phi_bar, you will need to include the probability function P(Z). In Fluent, prescribed probability functions are used, the inputs of which include the Z^2_bar, this is why the values of the scalars such as the temperature or species will need to rely on the mixture fraction variance. Besides, if steady diffusive flamelet model is needed, the scalar dissipation rate Chi is also calculated from Z^2_bar. nThe physical meaning of Z'' is Z = Z- Z_bar while the Z^2_bar is more with statistical meaning instead of physical meaning. Its definition is close to turbulent kinetic energy k if you replace Z with the fluctuating velocity u.nThe mixture fraction variance is conservative because:nIts transport equation is derived from subtracting the transport equation of Z by the transport equation of ZnThe FVM scheme is conservative intrinsicly.nPlease check the link below:nArrayThis gives very detailed deduction for the mixture fraction variance equations. n