Dissipation in Skewed Boundary Layers

The entropy generation within a turbulent, collateral boundary layer is well understood and is characterized by a dissipation coefficient, $Cd$⁠. However, it is common for the transverse pressure gradients in turbomachines to create highly skewed boundary layers, where the velocity varies in direction as well as magnitude. A combined experimental and high-fidelity computational approach is used to quantify the effect of skew on the dissipation coefficient for the first time. At a nominal condition of 14 deg of skew and $Reθ$ of 1000, the increase in dissipation coefficient is 20% as determined from direct numerical simulation and 28% from experimental measurements, relative to the collateral boundary layer. Experimental data over a range of skew angles and $Reθ$ values show that $Cd$ increases approximately linearly with skew so that, at a skew of 25$∘$⁠, loss is 70% greater than in the collateral boundary layer. The implications for loss estimation are examined by evaluating boundary layer loss, in the Harrison turbine cascade, with and without the influence of skew on $Cd$⁠. By accounting for the skew in the boundary layer, a new proposed model has been used to calculate the loss coefficient in the Harrison cascade within 4% of the experimentally measured value.