Session: 10.1 - Boundary layer flows

Paper Number: 158470

158470 - On the Development of a Near Wall-Model for Ablating Solid Fuel Reacting Boundary Layers 

Abstract: 

The focus of this study is to develop a near-wall model for Large Eddy Simulations (LES) of full-scale hybrid rocket motors. The wide span in flow length scales ranging from the turbulent flow structures in the core of the engine to the reacting ablating boundary layer, necessitate the use of subgrid scale (SGS) wall models. Most existing wall models assume non-reacting flows with low or no surface blowing.  These models are not suitable for application to hybrid rocket motors.  The fundamental challenge in describing these boundary layers is the coupling of flow expansion, chemical reactions with conjugate heat and mass transfer with the fuel surface.  Local modeling formulations are therefore desirable. Early attempts at localized solutions include the work of Marxman and co-workers in the 1960s.  In their analysis, it is assumed the vertical mass flux from fuel blowing is constant through the boundary layer and the effects from volumetric expansion due to combustion are negligible.  Marxman theory provides the foundation of most current ballistic models for engineering analysis of hybrid rockets.   To explore the limits of Marxman theory, Direct Numerical Simulations of a slab burner configuration are conducted.  The DNS is based on a finite volume formulation for multi-component compressible flows employing AUSMUP+ flux vector splitting and high-order Runge-Kutta time integration.   The software is based on the use of PETSc library – allowing for detailed solutions with full chemistry through execution on massively parallel computing platforms at LLNL.   Analysis of these simulations reveal several of the approximations in Marxman theory are not correct.  The most significant of which is the role of volumetric expansion from combustion.  Further investigation of the DNS also revealed the existence of self-similar solutions using a new set of conservative variables.  Based on this knowledge, a similarity formulation is derived by assuming that vertical and streamwise mass flux, total enthalpy and mixture fraction are functions of the normalized boundary layer height. The chemical state is determined from the mixture fraction and total enthalpy using either equilibrium or flamelet chemistry modeling.  A conjugate mass and heat transfer boundary condition is used at the fuel surface coupling the net heat flow into the solid (conduction – surface radiation) to the vertical “blowing” mass flux. A solution to this system can be found as functions of the local edge mass flux, boundary layer height, and divergence of boundary layer height.  Boundary layer profiles using the theory are compared to DNS and experimental data for a a PMMA – GO2 system.  Results indicate overall good agreement over a wide range of flow and blowing conditions.  

Presenting Author: Kenneth Budzinski State University of New York at Buffalo

Presenting Author Biography: