“Bray–Moss–Libby model”的意思、由来-开放百科全书

In premixed turbulent combustion, Bray–Moss–Libby (BML) model is a closure model for a scalar field, built on the assumption that the reaction sheet is infinitely thin compared with the turbulent scales, so that the scalar can be found either at the state of burnt gas or unburnt gas. The model is named after Kenneth Bray, J. B. Moss and Paul A. Libby^[1]^[2].

Mathematical description^[3]^[4]

Let us define a non-dimensional scalar variable or progress variable

such that

at the unburnt mixture and

at the burnt gas side. For example, if

is the unburnt gas temperature and

is the burnt gas temperature, then the non-dimensional temperature can be defined as

The progress variable could be any scalar, i.e., we could have chosen the concentration of a reactant as a progress variable. Since the reaction sheet is infinitely thin, at any point in the flow field, we can find the value of

to be either unity or zero. The transition from zero to unity occurs instantaneously at the reaction sheet. Therefore, the probability density function (suppressing the time variable

) for the progress variable is given by

where

and

are the probability of finding unburnt and burnt mixture, respectively and

is the Dirac delta function. By definition, the normalization condition leads to

is nothing but the probability of finding burnt gas at location

. The density function is completely described by the mean progress variable.

Assuming constant pressure and constant molecular weight, ideal gas law can be shown to reduce to

where

is the heat release parameter. Using the above relation, the mean density can be calculated as follows

General density function

If reaction sheet is not assumed to be thin, then there is a chance that one can find a value for

in between zero and unity, although in reality, the reaction sheet is mostly thin compared to turbulent scales. Nevertheless, the general form the density function can be written as

where

is the probability of finding the progress variable which is undergoing reaction (where transition from zero to unity is effected). Here, we have

References

1. ^Bray, K. N. C., Libby, P. A., & Moss, J. B. (1985). Unified modeling approach for premixed turbulent combustion—Part I: General formulation. Combustion and flame, 61(1), 87–102.
2. ^Libby, P. A. (1985). Theory of normal premixed turbulent flames revisited. Progress in energy and combustion science, 11(1), 83–96.
3. ^Peters, N. (2000). Turbulent combustion. Cambridge university press.
4. ^Peters, N. (1992). Fifteen lectures on laminar and turbulent combustion. Ercoftac Summer School, 1428.

Mathematical description[3][4]

General density function

References

Mathematical description^[3]^[4]