OCR Text |
Show G,{s) over the computational surface is then used to construct the scalar field ~(x,r) throughout any region of interest. A class of profile shapes with k Independent parameters is used to represent the local scalar gradient profile along the layer-normal direction n. Tracking the first k Integral moments G,(s) via (4) then determines the local gradient profile. This allows the scalar gradient field V~(x,l) to be evaluated at each point on a grid chosen for the scalar field construction. The divergence V· V~(x ,r) of the resulting scalar gradient field Is then numerically evaluated on thiS grid, and then used as the (known) right hand side in the definition of the Laplacian. namely V2~ = V . V~(x,t) (8) The Poisson equation in (8) is then solved to give the conserved scalar field ~(x,r), which Is. then dUTerentlated to give the scalar energy dissipation rate field V~· V~(x,r). The Joint scalar and scalar diSSipation fields are then used to construct the chemical species field via the strained dissipation and reaction layer mapping approach (6.71. This mapping approach begins with the fact that each of the conserved scalar mixture fraction variables Si can be written as a linear sum over the chemical species and enthalpy fields Y,{x .r) as N ~,(x,t) = I,Qi.j lj(x,t) j=1 i = 1,2, ... ,m (9) where N-l Is the number of chemical species and m the number of elements Involved in the chemical system. Each of the conserved scalars ~i In (9) satisfies a locally one-dimensional advection-diffusion equation Similar to (2). Since scalar diSSipation layers In turbulent flows do .. ··· ......................... -..... --....... ..... Fig. 3. LIM model results for mLxtng and combustion In a planar turbulent Jet. showing at top the time-evolvtng computational surface on which the local Integral moment equations are solved. and at bottom the velocity vector field as obtained from the time-evolving vortiCity field. The tlme-evolv1ng moments at every point on this surface are computed from the LIM equations. with the strain rate 0 at every point determined from the defonnation of the surface by the vorticity field. These moments produce the conserved scalar field ~(x ,l) and the associated scalar energy dissipation rate field V~ . V~(x ,t) shown In Fig. 4. from which chemical species and reaction rate fields such as those In Fig. 5 are obtained using the strain dissipation and reaction layer mapping approach . |