Inconsistent calculation results of VSPAERO

[Eric Cheng]

Why does the cloud image result of my ΔCP look correct and reasonable, but why the lift coefficient and drag coefficient are ten times smaller than the normal value?

（ΔCP）

（AoA--CL）

（AoA--CDi）

(AoA--L/D）

The below is the *.vsp file for my test case with parameters of VSPAERO.

[Rob McDonald]

I notice that you set your Vref to a high value (137.16) compared to your freestream (27.84).

Vref is used in normalizing lift coefficients

CL = L / (0.5 * rho * Vref^2 * Sref)

When using rotating blades, we often use Vref equal to the tip speed of the blades so the Cp values on the blades are reasonable.

In order to get consistent Cp results comparing actuator disk to rotating blades (as the images show), the paper probably used the same Vref for everything.

However, in order to get CL and CD into numbers you are probably accustomed to, you need to scale by the ratio of (Vref/Vinf)^2.

Rob

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[Eric Cheng]

Rob, thank you very much! Your answer really helped me a lot, thank you again!

Below I post the calculation result of the lift coefficient after I modified the Vref (this result is obviously more correct than the previous one). 

Based on this, I have a new question, that is, why is the freestream velocity different from the value of the flying Mach number? Should I set Vref to 29.83564 or should I set it to 27.84 which is the same as the free flow speed? Which value can I choose to make CL and CD more accustomed and more accurate? (All my units are meters, and they are uniform)

By the way, what is the reason why the set freestream speed Vinf is inconsistent with the flying Mach number? Is it because the local sound propagation speed is different?

(The result of AoA--CL after I modified the Vref to 29.83546 m/s)

[Rob McDonald]

At its core, VSPAERO is a potential flow solver.  This means it is incompressible (M=0) and inviscid (Re=inf).

Think about elementary steady potential flow solutions you may be familiar with -- sources and sinks, thin airfoil theory, etc.

In these solutions, Velocity does not matter.  You can readily run with Vinf = 1.0 and get the right solution.

At its core, VSPAERO behaves somewhat like this.  However, as more complex models are added, things change a bit.

When you add a compressibility correction, you need to add a Mach number.  However, as a potential flow solver, there isn't really an energy equation, we just have a compressibility correction.  Something like sqrt(1-M^2) applied to the X-coordinate (VSPAERO has two options and they are more complex, but this gives the idea).  Consequently, the Mach number is a separate concept from Vinf -- it is just the number plugged into the compressibility correction.  We could have you input a speed of sound -- but Minf is what shows up in our equations and people think in terms of Mach -- so it makes sense to have Mach as the input.

Next, we may think about an unsteady flow.  Perhaps the wing is pitching in an oscillatory manner -- or there is a rotating blade.  Now Vinf matters -- we need to know how far the bulk flow moves in one period of oscillation.  This could be described by the Strouhal number, another important dimensionless number of flow.  However, people are relatively unfamiliar with Strouhal number -- so it makes more sense to specify the rotor speed in RPM and the freestream Velocity as Vinf.

Most codes use Vinf as Vref -- for airplane problems, this is usually the right choice.  However, what do you do for a helicopter in hover or a propeller in a static thrust condition?  In these cases, Vinf=0 -- so if you used it to nondimensionalize, you would get a divide by zero.  So, we allow the user to specify Vref if they need to.

For most problems, Vref=Vinf is the right choice.  However, in some situations you'll want to set Vref separately.

In the case of a fast helicopter rotor -- at a hover condition -- the rotor tips might be at M=0.95.  However, Minf=Vinf=0.  So, we have MachRef to go along with Vref.  That way, we can still apply the compressibility correction to rotating blades in an otherwise static flow.

So, Vinf and Mach should match --- and Vref and MachRef should match.

While you're at it, ReCref should match Vref and cref.

Rob

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[Eric Cheng]

Rob,

Thank you very much for your detailed and patient answers, which really solved my question.

Eric

[Minh Nguyen Ngoc]

Hi Rob, 

Thank you for your clarification above. As you mensioned, there were 2 methods, which I just found earlier by reading the paper: 

Evaluation of VSPAERO Analysis Capabilities for Conceptual Design of Aircraft with Propeller-Blown Wings - Carla N. D. Sheridan1, Dahlia D. V. Pham2

But I can't seems to find any official documents that mentions how can we change between Prandtl /   Karman-Tsien comressibility correction.

Or is it can only be change through scripting?

[Rob McDonald]

The Karman Tsien option has been removed from VSPAERO.  I don't know if it will come back.

Rob