Compressible Flow in a Converging-Diverging Nozzle

Analysis Characteristics

• Steady-state
• axisymmetric
• 2D internal
• Turbulent
• Compressible
• Adiabatic

Reference

White, F.M., Fluid Mechanics, McGraw-Hill, New York, 1979

Problem Description

Compressible flow through a converging-diverging nozzle is a classic fluid mechanics problem. For ideal flow (no friction), shockless and choked conditions, there are analytical expressions for determining the exit Mach number, pressure and temperature.

For this verification analysis, the inlet conditions are set so that the flow is choked and the Mach number at the throat is 1.0 for ideal flow conditions. Friction is included in the analysis, so the interaction between the boundary layer and the supersonic flow in the diverging portion is apparent.

Outlet conditions predicted by Autodesk® CFD are compared to values predicted using ideal flow theory.

Geometry and Boundary Conditions

• Outlet Area to Throat Area Ratio = 2.64
• Inlet Area to Throat Area Ratio = 2.40
• Inlet Conditions: u = 111.5 m/s, p= 90.183 kPa - gage (Ma = 0.25)
• Stagnation temperature = 500 K
• Outlet Conditions: unknown

Results

Comparison of exit conditions:

	Benchmark	2018: Build 20170308	% Error	2019: Build 20180130	% Error
Exit Mach Number	2.5	2.483	0.642	2.475	0.995
Exit Velocity	747 m/s	744.95	0.274	743.77	0.274
	0.061	0.0748	22.73	0.0822	34.73