Similarity transformation for equilibrium flows, including effects of blowing and suction

TL;DR

This paper develops a similarity transformation for turbulent boundary layer flows with blowing and suction, enabling universal profile mapping and accurate predictions of mean velocities and stresses using symmetry analysis.

Contribution

It introduces a new similarity transformation based on symmetry analysis that accounts for blowing and suction effects in turbulent boundary layers, unifying different flow conditions.

Findings

Transformation accurately maps velocity profiles under various blowing/suction conditions.

Predictions of mean velocities and Reynolds stresses agree well with DNS data.

Transformation is a group invariant, ensuring consistency across different flow scenarios.

Abstract

A similarity transformation for the mean velocity profiles is obtained in sink flow turbulent boundary layers (TBL), including effects of blowing and suction. It is based on symmetry analysis which transforms the governing partial differential equations (for mean mass and momentum) into an ordinary differential equation and yields a new result including an exact, linear relation between the mean normal ($V$) and streamwise ($U$) velocities. A characteristic length is further introduced which, under a first order expansion in wall blowing/suction velocity, leads to the similarity transformation for $U$. This transformation is shown to be a group invariant under a generalized symmetry analysis and maps different $U$ profiles under different blowing/suction conditions into a (universal) profile under no blowing/suction. Its inverse transformation enables predictions of all mean quantities in the mean mass and momentum equations - $U$, $V$ and the Reynolds shear stress - in good agreement with direct numerical simulation (DNS) data.