CFD Studies on Flow Through Nozzles Using WIND at Low Mach Numbers

Abstract

This study documents a new WIND validation case for computing low Mach number flows through nozzles and investigates the relative thrust performance of circular and non-circular (elliptical) nozzles. Threedimensional, steady-state, CFD simulations of flow through one circular and two elliptic nozzles (aspect ratios of 2:1 and 3:1) with the same inlet and exit areas were performed for three exit jet velocities; Mach 0.05, 0.075 and 0.1. First order implicit time integration scheme and the second order physical space differencing with the turbulence SST (viscous, two-equation Shear Stress Transport) model were used for WIND simulations. In separate open water experiments, a Jet Ski Personal Watercraft (PWC) was outfitted with matching nozzle geometries (circular and 2:1 elliptical nozzles) and was tested at similar jet exit velocities. A minimal drop in the relative thrust performance of elliptical nozzles compared to the circular nozzle at all three exit jet flow conditions was observed. CFD results are in good agreement with PWC experiments. 1.0 Introduction The motivation for this study was twofold. First, to investigate the use of a compressible flow solver WIND for application to low Mach number flows, and second, to provide a validation case in the study of relative thrust performance of axisymmetric (circular) versus non-axisymmetric (elliptical) nozzles. It is well known that the performance of compressible Navier-Stokes (N-S) codes, in terms of the solution-accuracy, as well as the iterative convergence, degrades as the Mach number approaches zero. This is attributed to the existence of two very different time scales associated with the acoustics and fluid motion. The disparity between the acoustic wave speed, u+a, and the convective wave speed, u, leads to a large (infinite) ratio of the largest-tosmallest eigenvalue of the compressible equations, creating a stiff system. This has been identified as a stumbling block in the use of compressible N-S equations for low Mach number flows. To address this problem, a technique knows as local preconditioning, developed in recent years, is currently being investigated on several fronts. This technique provides a means to alter the eigenvalues towards a favorable condition number, which reduces the * Director. Aerodynamics Group. Member AIAA † Physicist. Member AIAA ‡ President. Associate Fellow AIAA American Institute of Aeronautics and Astronautics 1 42nd AIAA Aerospace Sciences Meeting and Exhibit 5 8 January 2004, Reno, Nevada AIAA 2004-531 Copyright © 2004 by Orbital Research, Inc. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. disparity in the wave speeds and also accelerates the convergence to steady state. The focus of this paper is not to develop or evaluate the performance of precond tioning techniques, but rather, to investigate the capabilities of a widely used Navier-Stokes compressible code WIND for low Mach number flow applications. A new validation case for WIND to study thrust performances of nozzles with low speed flows, i.e., exit jet velocities of Mach 0.05, 0.075 and 0.1, is presented. A good agreement between the CFD and experimental results is observed in the treatment of lowspeed incompressible flows; however, persistent problems encountered in reaching steady state convergence present an apparent need for improvements in the WIND code to address such flows. i This study also examines the relative thrust performances of circular versus elliptical nozzles (2:1 and 3:1 aspect ratio) using WIND. Results show that the thrust efficiency of both elliptical nozzles is minimally lower than the circular nozzle. The following sections present a brief description of the WIND code, design of the nozzles used in this validation study, computational grids, setting-up of the boundary conditions to simulate low Mach flow (medium: water) through nozzles, Jet Ski Personal Watercraft (PWC) experiments, and CFD results with experimental validation. 2.0 WIND Flow Solver WIND is a computational platform developed from the merger of three CFD codes: NASTD (the primary flow solver at McDonnell Douglas, now part of Boeing), NPARC (the original NPARC Alliance flow solver), and NXAIR (an AEDC code). It is a structured multi-zone flow solver with multiple turbulence models, and has been applied to a wide variety of complex configurations and flow regimes. An extensive validation effort is currently underway for the WIND code. This paper presents a new WIND validation case for applications to low Mach number flows. Thrust performance studies for three different nozzle designs with incompressible flow conditions at the nozzle exit are presented.