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.
Highlights
In a recent article (Isaacson [1]), computational results for the entropy generation rates occurring in a three-dimensional boundary layer structure formed in a corner boundary-layer flow environment were reported
Further calculations indicate that the actual cross wind velocities produced by the formation of the sidewall boundary layer are insufficient to trigger the observed deterministic structures, and that the required values for the triggering velocities are twice that produced by the sidewall laminar boundary layer flow
We introduce a speculative method to connect the deterministic results for the entropic indices with the final phase of the dissipation of fluctuating kinetic energy into thermodynamic internal energy. We explore this computational connection through the concept of intermittency exponents and a relaxation process into the final thermodynamic entropy state
Summary
In a recent article (Isaacson [1]), computational results for the entropy generation rates occurring in a three-dimensional boundary layer structure formed in a corner boundary-layer flow environment were reported. The configuration to accomplish this analysis consists of a corner flow environment, with sidewall surface mass injection, with the mass injection uniform in the steam wise direction, along the sidewall at the intersection of the sidewall with the horizontal surface.
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