Abstract
This paper presents the results of a study of the prediction of the entropy growth within an internal free shear layer of an ideal gas flow downstream of a sudden expansion of the flow area. The objective of the study is exploratory in nature by invoking concepts from information theory to connect the deterministic prediction of the spectral entropy growth within the shear layer to the experimentally inferred increase in entropy across the flow region. The deterministic prediction of the spectral entropy increase along the shear layer is brought into agreement with the experimentally inferred increase in entropy through the ad hoc inclusion of the activation spectral entropy. The values for this activation spectral entropy are directly related to the area ratios across the expansion region and have a specific numerical value for each area ratio.
Highlights
The engineering evaluation of the flow of an ideal gas downstream of a sudden expansion or backward-facing step is a highly developed field in computational fluid dynamics (Gosman et al [1], Patankar [2,3], Hirsch [4])
We find that the activation spectral entropy must be introduced to allow the numerical value of the predicted spectral entropy increase to match the experimental value
These results show the periodic behavior for the forcing function
Summary
The engineering evaluation of the flow of an ideal gas downstream of a sudden expansion or backward-facing step is a highly developed field in computational fluid dynamics (Gosman et al [1], Patankar [2,3], Hirsch [4]). Our objective here is to use this well-studied environment as a tool to test the hypothesis arising from information theory that the spectral entropy predicted from the solution of the time-dependent fluctuation form of the shear layer equations may be connected to the actual entropy increase observed across the flow region downstream of a sudden expansion. We consider the internal free shear layer following the separation of the flow from the edge of the sudden expansion into the expansion volume. We model the three continuity equations and the three equations of motion for the fluctuating velocity components along the shear flow. We include the physics appropriate for an internal free shear layer, including the nonlinear coupling terms between the velocity components within the equations of motion
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