Heat and mass transfer in combustion chamber using a second-moment turbulence closure including an influence coefficient of the density fluctuation in film cooling conditions

The film cooling problem for chamber using calculation results are discussed. Results are obtained using original second moment closure model for turbulence Comparations between wellknown experimental data and prediction results are made for the verifica-tion.The difference between results obtained using members with density fluctuation and without them in second-moment turbulence closure are taken into account for discussing of the determination design solutions of the cooling.All predictions were made for chambers include calculations of film regenerative and radiation cooling. 1.Introduction________________ Obviosly,modern liquid-propelant rocet engines (LRE) development goes to the direction of increa sing of the pressure in the chamber LRE-Pk, and the problem of cooling of chambers becomes very important especially for the throat section square Fth. It creats many important designproblems for cooling of chambers LRE. It seems evidently to investigate cooling problems using calculation method for wide ranges pressure Pk to determine the main points of cooling problem and to compare prediction results to estimate the influence of using method on design solutions. We shall discuss the film cooling of the chamber with Pk=80 MPa. Copyright © 1998 by the American Institute of Aeronautics and Astronautics.Inc. All rirights reserved 2.The mathematical and physical model for momentum, heat and mass transfer. The problem of modeling of momentum, heat, mass transfer using second-order models for turbulence was discussed in original papers [1-7]. All these models do not include correlations with the density fluctuation mainly because of the small order of these correlations in flows with the low level of the pressure fluctuation and the temperature fluctuation. The problem of an estimation for the density fluctuation was discussed in [8-20]. There is a reason to discuss an influence of these correlations in particular for near-wall flows : heat transfer in the boundary layer with the high level of an external turbulence 20%-30% ; heat and mass transfer in near-wall jets in combustion chamber LRE. 2.1 Physical model It is well-known fact that in turbulent flows for the density we may write following general form: P p =( +p')= — (1) Usually [20], the form (1) is used approximately: P' T' p = (2) Then we have for the density fluctuation approximately: P T p « ((3) But this form gives good results when turbulent flows have small temperature fluctuations. We may see that for (P'/P)=0 and (T/T)=30%-50% the difference of results between (1) and (2) is 7%-16%. Obviosly, for the turbulent process with high level of an external density fluctuation in all main and transport equations, turbulence such result is not satisfactory. Why we shall try find another form for the density fluctuation. 2.2 Mathematical model levlev V.M. [18] have suggested following form for ——determination of the value density fluctuation using The general form for correlation u ' i u ' j is : hypothesis of Prandtl: __