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

Abstract

Abstract:Results are presented for an innovative computational procedure that predicts time-dependent instabilities and deterministic ordered structures in three-dimensional steady-state laminar boundary-layer flows. The flow configuration considered is a corner flow with sidewall surface mass injection into a horizontal boundary-layer flow. The equations for the velocity fluctuations are cast into a spectral Lorenz-type format and incorporated into the overall computational procedure for the three-dimensional flow. The non-linear time-dependent solutions of the spectral equations predict deterministic spectral ordered structures within spiral structures. Spectral analysis of these fluctuating solutions yields the resulting entropy generation rates resulting from the dissipation of the ordered structures. The results for the entropy generation rates indicate the prediction of a strong burst of ordered structures within the range of injection velocities studied. This new computational method is applicable to only selected thermal design processes.

Entropy Generation through Non-Equilibrium Ordered Structures in Corner Flows with Sidewall Mass Injection

“…Entropy generation rates for corner flows with sidewall mass injection were reported by the author in a previous article [1]. These computations indicated the generation of non-equilibrium ordered structures at a normalized vertical station of approximately thirty-eight percent of the normalized laminar boundary layer thickness.…”

“…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 [1]. The choice of air at the given temperature and pressure yields an appropriate value for the kinematic viscosity.…”

“…42-45) points out, we must take into account that the nonlinear time series solutions obtained for the second and subsequent stations will be influenced by the fluctuations produced in the first and following stations. To accomplish this, we use the synchronization properties of the modified Lorenz set of equations describing the nonlinear solutions for the spectral components [1,14].…”

“…The fraction of dissipation kinetic energy within each empirical mode of the power spectral energy distribution is denoted as ξ j . Then the total rate of dissipation of the available fluctuating kinetic energy for the stream wise, normal and span wise velocity components is the summation, over the empirical modes, j, of the product of the kinetic energy fraction of each mode times the intermittency exponent for that mode, ζ j [1].…”

“…Combining these computational components into an overall computational procedure, we then compute the entropy generation rate for each of the ordered structures identified in the nonlinear time series solutions of the non-equilibrium spectral equations. The specific computational components are more fully described in Isaacson [1,14]. This article includes the following sections:…”