Doctoral Dissertations

Date of Award

5-2000

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Engineering Science

Major Professor

A. J. Baker

Committee Members

Joe Iannelli

Abstract

Computational simulation ofthe structure ofturbulent flow in a square duct can be analyzed using models derived from the mode elimination version of the renormalization group. A two-equation model developed elsewhere, coupled with a new nonlinear alge braic Reynolds stress model developed during the course of this dissertation research, are combined to address computation of anisotropic Reynolds stress distributions. The validation and veriflcation process for this new development is comprehensive as reported herein. First, model results are compared with several two-dimensional, homogeneous flows, producing good agreement with validation data. Next, comparisons are made with two-dimensional boundary layer and channel flows, and again results are quite good. Finally, the derived model is applied to prediction of square duct flow, with detailed comparisons made with measured mean velocity and Reynolds stress data. In the central 80% of the duct, results are within 20% of the measurements. Near the wallsand corners, the error can exceed 300%. For improvements, a new near-wall correction is proposed as the ratio of turbulence to mean flow time scales, hence, distance to the wall does not enter the formulation. The wall proximity correction for rapid straining is calibrated using direct numerical simulation results for a plane channel,and then applied to the square duct. The maximum error in normal stresses in the near-wall region decreases from 369% to 92%.

Based on this research, a new explanation is offered to explain the origin and evolution ofsecondary flows, from initial laminar boundary layers merging to fully developed duct flow. The essential role of instability is introduced, and the developed scenario is shown to be consistent with results from laminar calculations and measurements, linear stability theory, turbulent flow measurements, direct and large eddy simulations, and Reynolds averaged calculations.

A new difference formula is derived for the production terms in the K and e equations The new formula, obtained from a linear basis flnite element weak statement, produces a more stable and accurate computational implementation compared to conventional second-order central differences.

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