Baseline Computational Fluid Dynamics Methodology For Longitudinal Mode Liquid Propellant Rocket Combustion Instability

A computational method for the analysis of longitudinal-mode liquid rocket combustion instability has been developed based on the unsteady, quasi-one-dimensional Euler equations where the combustion process source terms were introduced through the incorporation of a two-zone, linearized representation: (1) A two-parameter collapsed combustion zone at the injector face, and (2) a two-parameter distributed combustion zone based on a Lagrangian treatment of the propellant spray. The unsteady Euler equations in inhomogeneous form retain full hyperbolicity and are integrated implicitly in time using second-order, high-resolution, characteristic-based, flux-differencing spatial discretization with Roe-averaging of the Jacobian matrix. This method was initially validated against an analytical solution for nonreacting, isentropic duct acoustics with specified admittances at the inflow and outflow boundaries. For small amplitude perturbations, numerical predictions for the amplification coefficient and oscillation period were found to compare favorably with predictions from linearized small-disturbance theory as long as the grid exceeded a critical density (100 nodes/wavelength). The numerical methodology was then exercised on a generic combustor configuration using both collapsed and distributed combustion zone models with a short nozzle admittance approximation for the outflow boundary. In these cases, the response parameters were varied to determine stability limits defining resonant coupling onset.Litchford, R. J.Marshall Space Flight CenterCOMBUSTION STABILITY; COMPUTATIONAL FLUID DYNAMICS; LIQUID ROCKET PROPELLANTS; NUMERICAL ANALYSIS; LONGITUDINAL CONTROL; METHODOLOGY; LAGRANGIAN FUNCTION; FINITE DIFFERENCE THEORY; HIGH RESOLUTION; PROPELLANT SPRAYS; REACTION KINETICS; UNSTEADY FLOW; STABILITY; ACOUSTIC DUCTS; EULER EQUATIONS OF MOTION

First published in 1986 by Mashinostroenie, Moscow.

This monograph is intended as a concise and self-contained guide to practitioners and graduate students for applying approaches in computational fluid dynamics (CFD) to real-world problems that require a quantification of viscous incompressible flows. In various projects related to NASA missions, the authors have gained CFD expertise over many years by developing and utilizing tools especially related to viscous incompressible flows. They are looking at CFD from an engineering perspective, which is especially useful when working on real-world applications. From that point of view, CFD requires two major elements, namely methods/algorithm and engineering/physical modeling. As for the methods, CFD research has been performed with great successes. In terms of modeling/simulation, mission applications require a deeper understanding of CFD and flow physics, which has only been debated in technical conferences and to a limited scope. This monograph fills the gap by offering in-depth examples for students and engineers to get useful information on CFD for their activities. The procedural details are given with respect to particular tasks from the authors’ field of research, for example simulations of liquid propellant rocket engine subsystems, turbo-pumps and the blood circulations in the human brain as well as the design of artificial heart devices. However, those examples serve as illustrations of computational and physical challenges relevant to many other fields. Unlike other books on incompressible flow simulations, no abstract mathematics are used in this book. Assuming some basic CFD knowledge, readers can easily transfer the insights gained from specific CFD applications in engineering to their area of interest.

Volume 2 of this significant work presents previously unpublished cutting-edge lectures from the Third French-Russian Workshop on Fluid Dynamics held in Tashkent in April 1995. Reflecting the Workshop?s main themes, this book particularly focuses on: expermental investigation of unsteady separated flow, 3D configurations, laminar and transitional flows, turbulent shock, shock interaction in hypersonic flow, pressure pulsation in separated flows and jets and high enthalpy flows using wind tunnels. modeling of free surface flows, natural gas combustion, vortical gas flows and acoustic processes in complex channels, non-equilibrium hypersonic viscous flows, wall law for fluids and compressible fluid jets with vortex zones. theoretical predictions of aerodynamic performances with analyses of supersonic combustion, detonation, and sumulation of reactive mixing layer. solution methods for quasilinear parabolic equations and other calculations including incompressible Navier Stokes equations and parabolic equations by Monte-Carlo methods. numerical algorithms for the simulation of atmospheric gas dynamics, kinetic schemes for viscous gas dynamic flows and evolutionary algorithms for complex optimization problems. This book will be of particular interest to all engineers and research scientists in Fluid Dynamics, Aeronautics, Aerospace and Mechanical or Applied Mathematics.

Annotation Since the invention of the V-2 rocket during World War II, combustion instabilities have been recognized as one of the most difficult problems in the development of liquid propellant rocket engines. This book is the first published in the United States on the subject since NASA's Liquid Rocket Combustion Instability (NASA SP-194) in 1972. In this book, experts cover four major subject areas: engine phenomenology and case studies, fundamental mechanisms of combustion instability, combustion instability analysis, and engine and component testing. Especially noteworthy is the inclusion of technical information from Russia and China--a first.

Presented at the International Gas Turbine & Aeroengine Congress & Exhibition, Indianapolis, Indiana, June 7-10, 1999.

From the preface: Fluid dynamics is an excellent example of how recent advances in computational tools and techniques permit the rapid advance of basic and applied science. The development of computational fluid dynamics (CFD) has opened new areas of research and has significantly supplemented information available from experimental measurements. Scientific computing is directly responsible for such recent developments as the secondary instability theory of transition to turbulence, dynamical systems analyses of routes to chaos, ideas on the geometry of turbulence, direct simulations of turbulence, three-dimensional full-aircraft flow analyses, and so on. We believe that CFD has already achieved a status in the tool-kit of fluid mechanicians equal to that of the classical scientific techniques of mathematical analysis and laboratory experiment.