Example 1: Cavity Flow

This example shows the necessary steps for studying the flow pattern that appears in a lateral, cavity of a by-flowing fluid - one side of the cavity being swept by the outer flow.

The flow pattern will be calculated using the incompressible Navier-Stokes equations for a Reynolds number of 1 (in order to capture turbulence effects that appear at higher Reynolds numbers, a finer mesh would be necessary).

The geometry simply consists of a square, representing a cavity, its top face being swept by the passing fluid. This problem is a two-dimensional case solved to illustrate the basic capabilities of Tdyn.

Incompressible flow

Viscous, non-turbulent case

Reynolds number equal to 1

The Reynolds number is defined as Re = r ν L / m In this equation, L represents the characteristic length of the problem, which in this case is the edge length of the cavity, r and m are the density and the viscosity of the fluid respectively, and v is the velocity of the flow on the swept line.

For the example to be solved, we can choose arbitrarily:

L = 1 m

v = 1 m/s

r = 1 kg/m3

m = 1 kg/ms

By substituting the variables for their value in the equation above we obtain the Reynolds number:

Re = 1