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

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.

Entropy Generation through Deterministic Spiral Structures in Corner Flows with Sidewall Surface Mass Injection

“…At the final equilibrium state, the stream wise velocity of the dissipated structure vanishes. The entropy generation rates through the deterministic ordered structures may then be determined from Equation (7) [1]. Equation (7) has the form found experimentally by Mazellier and Vassilicos [29] for the dissipation of turbulence energy in fractal grid-generated wind tunnel flows.…”

“…It has previously been found that a crosswind velocity in a corner boundary layer flow could trigger instabilities in the three-dimensional laminar boundary layer along the horizontal surface [1]. This crosswind velocity had been attributed to the developing boundary layer along the sidewall surface.…”

“…The solution of the steady-state boundary-layer equations that provides these control parameters is dependent on the particular value of the kinematic viscosity applied in the calculations. We have found that only a narrow range of kinematic viscosities yields the prediction of ordered structures from the computational procedure (see e.g., [1][2][3][4][5]). The range of appropriate values of kinematic viscosities has not been delineated and remains as work to be done.…”

“…The local boundary layer steady state velocity may be written as u = u e f', where f' 1 is the derivative of the Falkner-Skan stream function f with respect to the normalized distance η. The expression for the entropy generation rate through the deterministic ordered structures may then be written as [1]:…”