Entropy Generation through Deterministic Spiral Structures in a Corner Boundary-Layer Flow

Lavar Isaacson

doi:10.3390/e17085304

Abstract

It is shown that nonlinear interactions between boundary layers on adjacent corner surfaces produce deterministic stream wise spiral structures. The synchronization properties of nonlinear spectral velocity equations of Lorenz form yield clearly defined deterministic spiral structures at several downstream stations. The computational procedure includes Burg’s method to obtain power spectral densities, yielding the available kinetic energy dissipation rates within the spiral structures. The singular value decomposition method is applied to the nonlinear time series solutions yielding empirical entropies, from which empirical entropic indices are then extracted. The intermittency exponents obtained from the entropic indices allow the computation of the entropy generation through the spiral structures to the final dissipation of the fluctuating kinetic energy into background thermal energy, resulting in an increase in the entropy. The entropy generation rates through the spiral structures are compared with the entropy generation rates within an empirical turbulent boundary layer at several stream wise stations.

Highlights

Corner boundary layer flows are found everywhere in our mechanical world
The application of an exploratory computational procedure to the three-dimensional flow in a corner laminar boundary-layer environment predicts the development of deterministic spiral structures within the boundary-layer flow
It has been found that the initial boundary layer along the vertical surface of the right-angle corner provides a triggering crosswind velocity for the generation of fluctuating spiral structures in the horizontal boundary layer flow

Summary

Introduction

Corner boundary layer flows are found everywhere in our mechanical world These types of flows occur in applications as different as square ducts in heating-cooling ventilation systems to the connections of aircraft wings to aircraft bodies. We report the results of the application of a computational procedure to calculate the three-dimensional boundary layer flow in a right-angle corner flow environment. The development of the computational procedure begins with the observation that the stream wise velocity will form laminar boundary layers in the stream wise direction along both the horizontal surface and the vertical surface of the corner configuration. As the boundary layer forms along the vertical surface in the stream wise direction, it will produce a velocity normal to the vertical surface in the direction of the z-axis. We have found that this cross flow velocity and resulting velocity profile are key elements in the triggering of deterministic spiral structures in the corner boundary layer flow

Results

Discussion

Conclusion