CFD Online URL
[Sponsors]
Home > Wiki > Ringleb flow

Ringleb flow

From CFD-Wiki

Jump to: navigation, search
  • q = magnitude of velocity
  • \theta = angle between velocity and x-axis
  • \psi = stream function

\psi = \frac{1}{q} \sin\theta

Take


k = \frac{1}{\psi}

to be constant as a streamline.

Streamline equations:


x(q) = \frac{1}{2 \rho(q) } \left( \frac{1}{q^2} - \frac{2}{k^2} \right) +
\frac{1}{2} J(q)

y(q) = \pm \frac{1}{kq\rho(q)} \sqrt{ 1 - \frac{q^2}{k^2} }

where


J(q) = \frac{1}{c} + \frac{1}{3c^3} + \frac{1}{5c^5} - \frac{1}{2}
\log\left( \frac{1 + c}{1 - c} \right)

c(q) = \sqrt{ 1 - \frac{\gamma-1}{2} q^2 }

\rho(q) = c^{2/(\gamma-1)}

References

  • Shapiro ({{{year}}}), Mechanics and Thermodynamics of Compressible flows, {{{rest}}}.
My wiki