Analysis of Film Cooling in Rocket Progress Report

This report summarizes the progress to date on the NASA contract #NAGS-212, Task No. 3. The overall project consists of three tasks, and Task 1 and Task 2 are now complete. Task 1 involved the modification of the wall functions in the code FDNS to use a Reynolds Analogy-based method. This task was completed in August, 1992. Task 2 involved the verification of the code against experimentally a_-ailable data. The data chosen for comparision was from an experiment involving the injection of helium from a wall jet. Results obtained in completing this task also show the sensitivity of the FDNS code to unknown conditions at the injection slot. This task was completed in September, 1992. Background. Analysis of film cooling in rocket nozzles by computational fluid , dynamics (CFD) computer codes is desirable for two reasons. First, it allows pre: diction of resulting flow fields within the rocket nozzle, in particular the interaction of the coolant boundary layer with the main flow. This facilitates evaluation of :potential cooling configurations with regard to total thrust, etc., before construction and testing of any prototype. Secondly, CFD simulation of film cooling allows for assessment of the effectiveness of the proposed cooling in limiting nozzle wall temperature rises. This latter objective is the focus of the current work. A NASA code is available for the analysis of CFD processes. The FDNS (Finite Difference Navier Stokes) code was commissioned by MSFC and was authored by SECA, Inc. in 1990. Briefly, the FDNS code uses a central differencing scheme, coupled with artificial damping to capture shock waves, to solve for the heat, mass, and momentum conservation within an arbitrary geometrical domain. The code uses either a "standard" or "extended" k-e turbulence model with an implementation of Launder and Spalding-like [1]wall functions for modelling of solid wall boundaries. Furthermore, the code allows for either equilibrium or finite-rate chemical reactions. A major re-write of the code was performed over 1991-92 by Dr. Y. S. Chen, now of Engineering Sciences Incorporated (ESI). The resulting code is streamlined, has 3-D capability, but is limited to finite-rate chemical reactions. This code also has three turbulence models: standard k-e, "extended" k-e, and a low Reynolds number k-_. During the summer of 1991, Keith Woodbury of The University of Alabama performed computations using the NASA code FDNS for high-speed flow of air over an isothermal flat plate. The focus of his analysis was on the computed heat flux from the wall. The results showed that the FDNS code predicted heat fluxes about an order of magnitude lower than those measured under similar conditions in a shock tunnel . The explanation for the discrepancy is two-fold. First, the k-_ turbulence model used in FDNS does not account for the retarded velocity of the fluid in the near-wall region. Secondly, the particular form of the wall function used as a boundary condition for the energy equation does not adequately account for the effect of viscous heating in the near-wall region. Project Plan. The desired objective is to use the FDNS code to predict wall heat fluxes or wall temperatures in rocket nozzles. As prior work [2] has revealed that the FDNS code is deficient in the thermal modeling of boundary conditions, the first step is to correct these deficiencies in the FDNS code. Next, these changes must be tested against available data. Finally, the code will be used to model film cooling of a particular rocket nozzle. Table 1 summarizes the tasks to be completed under this project. The modifications to the FDNS code will be in the handling of the thermal boundary condition at the solid wall. The goal is to introduce as few changes as possibh: il_to tile FDNS code, but enough to bring predictions from FDNS in line with available data. Previous work [2] demonstated that a simplistic Reynolds' Analog3' brought the FDNS code predictions for wall heat flux into reasonable