The static pressure is shown as a static pressure coefficient, Cps, referenced to the inlet static pressure and normalized with the inlet dynamic pressure.
Blade Loading
The blade is highly loaded at all Reynolds numbers. In the first half of chord Cps on the pressure side is near the stagnation value of 1, while the suction side shows a fall to the minimum pressure.
Close to the leading edge, suction peaks, a fall then rise in pressure, can be seen on both sides of the blade. This is because the Langston blade has a circular arc leading edge with abrupt changes in curvature on both sides. The pressure side peak is close to the stagnation point and the same for all Reynolds numbers. The magnitude of the peak on the suction side (near x/c~0, Cps~-1.5) is largest at the highest Reynolds number, which has the thinnest boundary layer.
From around mid-chord, the pressure rises on the suction side. At Re=9000 and 44k this resulted in complete separation of the "laminar" boundary layer without reattachment before the trailing edge; this is reflected in the nearly constant pressure after x/c of 0.6 (Re=44k) or 0.7 (Re=9000).
At Re=66k the boundary layer is more turbulent and the constant rate of pressure recovery suggests no separation. A close look at the flow showed a very thin separation which closes before the trailing edge. The wobbles in the pressure recovery at Re=709k are due to the combination of a very thin boundary layer (displacement thickness ~ 0.002c) and small wobbles in the radius of curvature of the blade geometry as set up for the calculations.
Static Pressure and Separation
The interaction between the static pressure and the separation can be better seen in the plots below. The separation regions are outlined by two contours of U/Up, the magnitude of the velocity divided by the magnitude of the potential flow velocity at the local pressure.
At Re=9000 and 44k, the contours of U/Up=0.25 and 0.5 peel away from the blade but remain close together, indicating a very thin shear layer. (The wobbles in the 0.25 contour appear to be due to truncation errors, which can cause overshoots in the velocity as the separation region encounters the coarser grid away from the blade.) Inside the 0.25 contour there is low momentum fluid associated with the separation and a region of near uniform pressure until the separation is closed. At Re=9000 the separation is closed by the uniform pressure exit boundary condition at x/c=1.6 (end of plot), while at Re=44k the separation is closed mostly by turbulent mixing.
At the higher Reynolds numbers, as the shear layers on either side of the wake converge and mix out, there is a region of higher pressure as the flow realigns to a uniform direction.
Static Pressure and Mean Velocity
The pictures below show the same static pressure contours but with a selection of velocity vectors so that they can be individually seen. At Re=9000 and 44k the separations and wakes are well defined regions with very low mean velocity and no significant mean vortical structure.
back to High Turbulence Turbomachinery