Quote from lullaby98 on 22. August 2026, 10:08

Hi Everyone,

I’m a PhD Student working on modeling a small VAWT for micro-generation (NACA0021, chors = 0.085, H = 1.5, R= 0.515), for which some experimental data is available, and I’m trying to set up a QBlade model of it (currently running 2.0.9.7 CE on Windows). While trying to understand the DMS solver better, I looked through the last publicly available source code (2.0.4a) and ran into two things I don’t quite understand.

While working through the classical DMST closure (Paraschivoiu 2002 with the Glauert correction) by hand for some streamtubes at higher TSR (from 3 to 5), I found cases where the aerodynamic CX(a) curve and the momentum CX(a) curve don’t seem to intersect anywhere in [0,1] – meaning no equilibrium would exist for that streamtube under the classical theory. I’m not sure yet whether that’s a mistake on my end or a genuine feature of the model in that regime, so I went to look at how QBlade’s DMS module (variable induction mode) handles this internally, using the last publicly available source code (2.0.4a). While there, I ran into two things I don’t quite understand.

— 1. Fx formula (2.0.4a source, DData.cpp) —

In the variable-induction branch (m_bVariable = true), the upwind Fx term (~line 650) is:

Fx = blades*m_c_local.at(i)/8/PI_/m_radius_local.at(i)
*pow(W/m_velocity_inf.at(i),2)
*((Cn*cos(theta)+Ct*sin(theta)/cos(delta)));

From what I understand of the classical DMST formulation, I would have expected an extra 1/|cos(theta)| factor in there. I don’t see it here, and I don’t see it in the downwind equivalent either (~line 891). Am I missing where it comes in, or misunderstanding the formulation?

— 2. Upwind vs downwind (2.0.4a source, DData.cpp) —

Still in the same branch, the upwind update (~line 650-666) is:

u_old = u;
u = pow(u,2)+Fx;

double CTT;
CTT = 4*u*(1-u);

if (CTT>0.96*F)
{
u = (18*F-20-3*pow(fabs(CTT*(50-36*F)+12*F*(3*F-4)),0.5))/(36*F-50);
}

if (u<=0) u=0.01;
if (u>=1) u=0.99;

while the downwind update (~line 891-897) is:

Fx = blades*m_c_local.at(i)/8/PI_/m_radius_local.at(i)
*pow(W/m_velocity_equil.at(i),2)
*((Cn*cos(theta)+Ct*sin(theta)/cos(delta)));

u2_old = u2;
u2 = pow(u2,2)+Fx;

if (u2>=1) u2 = 0.99;
if (u2<=0) u2 = 0.01;

The downwind branch doesn’t check CTT against the 0.96*F threshold and never goes through the closed-form correction – just the clamp to [0.01, 0.99]. I don’t understand why the two branches differ here.

Thanks for the time and for any help.