While FLOW-3D is known as the most accurate CFD tool in the world for modeling free-surface flows, many are unaware that it has a powerful compressible flow capability as well, which makes it well suited to simulate Laval nozzles.
A Laval nozzle is is a tube that is pinched in the middle, making an hourglass-shape. It is used as a way to accelerate the flow of a gas passing through the nozzle. Such nozzles are used in rocket and supersonic jet engines (as well as certain steam turbines).
In the example shown at left, helium flow through a rectangular convergent-divergent nozzle is simulated using FLOW-3D. Helium at room temperature is forced through the convergent section of the nozzle using an inlet pressure of 6.9E5 N/m2 while maintaining a low outlet pressure of 0.1N/m2. FLOW-3D‘s compressible flow solver captures the reflection and forward compression shock waves very well. As expected, flow chokes at the nozzle throat in about 1.5 milli-seconds as the flow becomes steady. The flow accelerates to a supersonic velocity of Mach 4 at the divergent outlet.
Cavitation in Laval Nozzles
Cavitation is a process that involves the formation, growth and collapse of vapor- or gas-filled cavities in a liquid. Cavitation constitutes an energy sink and may result in structural damage, fluid contamination and blockages. For this reason, designers typically try to avoid the occurrence of cavitation. However, controlled cavitation may be useful in some instances (e.g., in reducing skin friction drag on high speed torpedos or for inducing locally high pressures and temperatures for certain chemical reaction in liquid mixtures).
In the comparison shown on the left, a simulation with FLOW-3D was run to match experimental results for water flow through a planar-Laval nozzle.* In this example of 2D convergent-divergent flow, the water experiences a decrease in pressure in the nozzle that is below the vapor pressure of the water. Vapor cavities are seen to grow downstream of the nozzle, but then collapse once the exit pressure has had enough time to reverse the flow back toward the low-pressure, cavitating region. In the simulation, the cavitation pressure was set at 20 dynes/cm2 and the characteristic time to form cavitation bubbles was set at 0.001 seconds. The driving force for the fluid was obtained with a pressure boundary at the inlet and outlet of the nozzle corresponding to 150 and 50 dynes/cm2 respectively.
Helium flow through a rectangular convergent-divergent Laval nozzle is simulated using FLOW-3D. Helium at room temperature is forced through the convergent section of the nozzle using an inlet pressure of 6.9E5 N/m2 while maintaining a low outlet pressure of 0.1N/m2.