IMPLICIT MARCHING SOLUTION OF COMPRESSIBLE VISCOUS SUBSONIC FLOW IN PLANAR AND AXISYMMETRIC DUCTS
Abstract
A new streamwise marching procedure has been developed and coded for compressible viscous subsonic flow in planar or axisymmetric ducts with or without centerbodies. The continuity, streamwise momentum, cross-flow momentum, and energy equations are written in generalized orthogonal curvilinear coordinates. To allow the use of a marching procedure, second derivatives in the streamwise direction are neglected, and the pressure in the streamwise momentum equation is written as the sum of a known two-dimensional imposed pressure field and an unknown one-dimensional viscous correction. For turbulent flow, the Reynolds stress and turbulent heat flux terms are modeled using two different two-layer eddy viscosity turbulence models. Prior to each main marching step, a preliminary marching step is taken in which the integral mass flow rate equation and an uncoupled form of the streamwise momentum equation are solved simultaneously to obtain the viscous pressure correction. During the main marching step the four governing equations are solved simultaneously as a coupled system using an implicit finite-difference method, with the viscous pressure correction treated as a source term. The equations are linearized to second-order accuracy without using iteration by expanding each unknown term in a Taylor series in the streamwise direction. Results are presented for developing laminar flow in a circular pipe, laminar flow in a two-dimensional converging channel (Jeffery-Hamel flow), developing turbulent flow in a circular pipe, turbulent flow in a two-dimensional S-duct, and turbulent flow in a typical subsonic diffuser for a supersonic inlet. For all test cases, the results are compared with data and/or exact solutions. The computed results agree very well with the data and exact solutions for the laminar cases studied. The results for the turbulent cases also agree well with the data, although not quite as well as for laminar flow. The viscous pressure correction properly accounts for the effect of viscous blockage on the streamwise pressure gradient.
Degree
Ph.D.
Subject Area
Mechanical engineering
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