Numerical simulations of compressible and reacting temporal mixing layers and implications for modeling

Abstract

Numerical simulations of temporally evolving compressible inert and reacting mixing layers are performed. The results are examined in terms of modeling techniques for transport and reaction in compressible, turbulent mixing layers. In particular, the calculations are analyzed with respect to a recently proposed compressible algebraic stress turbulent transport model (ASM). This new model accounts for variations in the anisotropy of the normal stresses through modification of the pressure-suain terms of the Reynolds stress transport equations. Results from the simulations are consistent with recent detailed compressible mixing layer data and further support the compressibility modification to the pressure-strain of Goebel and Dutton2 and Elliott and Samimy4 provide the most detailed and useful data for numerical simulation evaluation. The following trends are clearly observed in the data of Goebel and Dutton2 or DuttOn et the shear stress and normalized growth rate decrease with increasing Mr, * normal stress anisotropy increases with increasing Mr, the correlation coefficient (Cuv) remains nearly constant within the mixing layer and at various conditions (i.e.. velocity ratios, density ratios, the compressibility effect is not dependent on the density gradient direction. and Mr),and modeling. It is shown that incompressible pressurestrain modeling overestimates the contribution of these terms under compressible conditions. Reacting mixing layer results are also uresented, consistent with Although conventional turbulent transport modeling can produce good results for incompressible mixing layers, shortcomings have been observed for ~~ ~ compressible mixing layers. Most notably, the decrease in normalized mixing layer growth rate (at the same velocity and density ratios) as the relative Mach number increases is not predicted by the basic incompressible models. Compressibility modifications have been proposed for various models. While some can duplicate the observed reduction in growth rate, they do not the physics Of the *Ow when previous simulations, the mixing layer structure is relatively unaffected by slow reactions. The growth rate, however, is slowed. As the reaction rate increases relative to the convective large-eddy roll-over time scale, the structure is changed considerably. In the slower reaction case, the heat release takes place in a more distributed fashion at the mixed vortex core and results in controlled exnansion of the eddv. For faster v parameters beyond the turbulent shear stress and mean growth rate are considered. Results from a modified one-equation algebraic stress model (ASM) that better predicts the compressible mixing layer behavior were presented by Bun and Dutton6 and Bun7. The authors r ~ ~ ~ ~ ~ --,. ---I--~ ~~ ~~~ reactions, a larger fraction of the reaction/heat release takcs place in the strained interface between the fuel and oxidizer layers within the vortices. This localized heat release greatly distorts the eddy structure. have also extended the model to a two-equation form using the compressible dissipation model of Sarkar and Balakrishnan* (see B d ) . Introduction and Background Many recent mixing layer investigations concern compressibility effects, as characterized by the relative ( M r ) or convective (Mc) Mach numbers. The convective Mach number can be interpreted as the Mach number of the freesaeams relative to a convective frame moving with the large scale structures; the relative Mach number is based on the velocity difference across the mixing layer. These Mach numbers have been effective for correlating the experimentally observed decrease in growth rate of compressible mixing layers (in combarison to incomuressible mixine lavers at the In the past, temporally evolving mixing layer simulations have provided a better understanding of the physical processes in incompressible mixing layers (e.g., Riley and Metcalfe9, Corcos and Shemanlo). Simulations have also improved the understanding of compressible mixin layers and their instability ( e . , Soetrisno ef d . l f Sandham and Reynolds* ). Compressible simulations have not, however, been exploited to improve compressible mixing layer i+ ~~, ~. ~. . ~ ~ . modeling. A major emphasis of this paper is to use temporal mixing layer simulations examine same freestream velocity and density r a~ ios ) l -~ . The recent laser Doppler velocimeter (LDV) measurements v * ** Graduate Research Assistant. Student Member AIAA. Associate Professor. Associate Fellow AIAA.