Week 2 - Converging diverging nozzle

OBJECTIVE:

Simulate flow across a Converging-Diverging Nozzle, Plot:

1. The pressure, velocity and temperature variations across the domain
2. The interpretation of Mach number across the field and at what distance from the inlet does the flow become supersonic.

THEORY:

A converging-diverging nozzle is an asymmetric hourglass-shaped device used to accelerate compressible fluids to supersonic speeds by converting thermal energy into mechanical energy.

Because the mass flow rate is constant, a subsonic gas flow will speed up if the pipe carrying it gets smaller. The gas flow through a nozzle is isentropic. The gas velocity locally reaches sonic (Mach number = 1.0) levels near the "throat," where the cross-sectional area is at its lowest, and this phenomenon is known as choked flow. When the cross-sectional area of the nozzle rises, the gas starts to expand, and the flow reaches supersonic velocities (Mach number > 1.0).

. As the gas exits the throat, the increased area allows it to undergo a Joule-Thompson expansion, in which the gas expands at supersonic speeds from high to low pressure, pushing the velocity of the mass flow beyond sonic speed.

GEOMETRY:

MESHING:

SETUP:

Fluid: Air with ideal gas law

Boundary Conditions:
Inlet: pressure inlet @ 101325 Pa
Outlet: pressure outlet @2735.775 Pa
Walls: Wall Boundary Condition
Axis of Nozzle: Symmetry Boundary Condition

Solver: Axisymmetric, Density-Based, Steady-State Solver

Turbulence Model: K-Epsilon Standard with Standard Wall Functions

RESULTS:

Pressure Contour:

Velocity Contour:

Temperature Contour:

Mach Number:

CONCLUSION:

• The flow becomes supersonic (M>1) beyond 0.55 mm from the inlet, i.e. after crossing the throat of the Nozzle, which is in line with the operation of a CD Nozzle.
• The temperature difference can be seen showing how thermal energy is converted to kinetic energy and achieve supersonic velocities.