LARGE EDDY INTERACTIONS IN CURVED WALL BOUNDARY LAYERS--MODEL AND IMPLICATIONS

SEUNG KYU HONG, Purdue University

Abstract

An analytical framework, called the Large Eddy Interaction Model (LEIM), has been developed based on the identification of large eddies that undergo changes in a flow on account of interaction with the mean flow and the spectrum of eddies present in the turbulence. The mean flow may, in general, involve inhomogeneous shear, such as in a boundary layer flow. The eddy-eddy interactions give rise to transport process, which may be modelled on the basis of simple gradient-diffusion or alternatively, the hypothesis of a velocity scale for the evolution of the turbulence field. The structure of a large eddy can then be utilized to determine various aspects of the structure of turbulence under given initial and boundary conditions. Curved wall boundary layers present an important case of complex turbulent flows. Considering four sets of experimental data available on variously curved wall flows, the applicability of LEIM has been tested. In each case the objective has been to obtain turbulent stress distributions, stress ratios and anisotropy as well as the deformation of the eddy in terms of wave number and orientation. In each case also the extent of adjustment of transport process required for given shear and wall curvature is determined and compared with the value for the flat plate zero-pressure gradient case. In order to determine the influence of wall curvature on different parts of the boundary layer, a three-layer boundary layer model (based on an asymptotic expansion procedure) is considered in conjunction with the LEIM. It is found that the outer part of the boundary layer becomes progressively more affected as (VBAR)(delta)/R(VBAR) increases in the range 0.01 to 0.1. Other phenomenological aspects pertain to the manner in which anisotropy can arise and change in a given flow and the manner in which turbulent transport is affected by reversal or removal of an additional strain in a complex flow. The LEIM developed is suitable for obtaining the local turbulence structure in a time-averaged sense in any shear flow so long as the mean flow development and the initial conditions of flow are known. Although the eddy-eddy interactions are nonlinear in nature, it is found that linear models for transport are adequate and the solution is not strongly dependent upon the nonlinearity itself. The LEIM thus provides a simple and direct method of determining the changes in turbulence structure and for assessing various turbulent processes in complex flows.

Degree

Ph.D.

Subject Area

Fluid dynamics|Gases

COinS