# Pressure Coefficient with a Minima of 0 on Compressor Airfoils in Cascade

I am a relatively recent BSME graduate working on reproducing the results of a technical paper to strengthen my ANSYS CFX skills. The paper is "Effect of Section Thickness and Trailing Edge Radius on the Performance of NACA-65 Series Compressor Blades in Cascades at Low Speeds" by Herrig, Emery, and Erwin. My goal is to reproduce pressure coefficient vs axial chord plots for one of the test cases using ANSYS CFX.

Problem Statement/Givens from Paper: The test was performed in a low-speed porous wall wind tunnel with an air average inlet speed of 95 ft/s. The particular airfoil geometry I am examining is an NACA 65-(12)12 (5 inch chord) at an angle of attack of 23.5 degrees with a solidity of 1.5. I made some assumptions not stated in the paper for my CFX model. I applied a free slip wall in place of the porous walls to capture the effect of boundary layer shedding. I also assumed the outlet static pressure was 1 atm and the inlet temperature is 15C. All other solid surfaces are applied as adiabatic walls with a no-slip condition. I am using the default k-epsilon turbulence model, isothermal heat transfer, and neglecting buoyancy effects. The pressure coefficient is to be determined along a mid-span plane on the surface of an airfoil far from the end walls (the third airfoil of the 5 I put in my cascade model).

The Problem: The provided results from the paper have a minimum pressure coefficient of 0. My results, however, have a minimum ~1.05. I noticed all the pressure coefficient figures in the paper have a minimum at 0 and no negative values.

My Attempt at a Solution: I created a polyline at the intersection of the center blade surface and the mid-span plane. I wrote expressions in CFX Post to determine the area-averaged density, inlet velocity (although this is redundant), and static pressure. Then, I created a new variable to calculate the pressure coefficient. The calculation being performed is (P_static_local-P_static_inlet)/(1/2*rho_static_inlet*velocity_inlet^2). I've attached the results from the paper and my produced results. My trend seems to be mostly correct (save the waviness from producing the airfoil profile myself), however, the problem of the y-axis scale still remains. . To complicate things further, the definition of the pressure coefficient they provide in the paper uses a local total pressure instead of a local static pressure, which changes the shape of the plot completely.

Does anyone know of a standard used to adjust the minimum pressure coefficient to 0? This is the only sort of logical explanation I can conjure at the moment. Of course, if anyone sees any glaring errors in my methodology please comment and let me know.

Thanks for your time

## 1 Answer

In the report $$P$$ is the total pressure and $$p$$ is the static pressure. See the page in the report before the one you attached in the OP.

With that definition, $$S$$ will be zero at the stagnation point near the leading edge of the airfoil, and $$S$$ will always be positive, as in their plots.

The "calculation being performed" that you give for the pressure coefficient in the OP using two static pressures is not the same as the paper's definition.

• Alephzero, thank you for your reply. The final figure I posted is the result using the equation given in the paper. As you can see, the shape is nowhere close to the paper and still has negative values. – mechcad Aug 8 '19 at 14:43
• Well, I can't understand how the equation in the paper can ever give you a negative value for S unless your boundary conditions are wrong and the flow doesn't look approximately like 2D flow past an airfoil. If it's not a modeling error or a bug in the code, we must be using different definitions of some of the quantities. – alephzero Aug 8 '19 at 22:48
• Alephzero, I believe I tried what you suggested. I probed the static pressure in the stagnation region and used that for my reference static pressure. It does do what you said; the pressure coefficient doesn't really dip below zero (it does slightly because of the accuracy of the probe). Looking at the static pressure contour, the solution does seem to match that of 2D flow past an airfoil. I completely agree that the real issue is determining which definitions are the correct ones for the calculation of the pressure coefficient. I think this is the solution to my problem. Thanks for your help – mechcad Aug 9 '19 at 14:44
• How does the static pressure you probed at the stagnation point compare with the total pressure (static + dynamic) at the inlet boundary conditions? That is probably what a pitot tube in the wind tunnel experiments was measuring as $P$. – alephzero Aug 9 '19 at 14:57
• I see what you are getting at. The static pressure at the stagnation point and the inlet total pressure are nearly the same, which is expected with little/ no pressure loss. I thought P was supposed to be the total pressure at the point on the airfoil surface where the coefficient was being calculated. But I definitely see why this is not the case now. Thank you again for your help! – mechcad Aug 9 '19 at 19:30