Validation Case: Compressible Flow In a de Laval Nozzle

This validation case belongs to fluid dynamics. The aim of this test is to validate the following parameters for a compressible, steady-state turbulent flow through a de Laval Nozzle:

Mach number across the nozzle.

Pressure across the nozzle.

The simulation results from SimScale were compared to analytical results obtained from methods presented in [1].

A typical configuration of the de Laval nozzle with a non-smooth throat that was chosen as the geometry can be seen below:

The nozzle is axisymmetric and an angular slice of the complete geometry with a wedge angle of 18\(°\) was used. The following table contains the coordinates of the reference points:

The hexahedral mesh was created externally, and then was imported on to the SimScale platform, with an inflation of \(y^+\) = 30 near the walls, as the ‘wall functions’ model was chosen. In order to keep the flow two-dimensional, the mesh was designed to have only one layer in the \(y\) direction.

\(P_{stag}\) : the stagnation pressure, assumed to be 0.1301 \(MPa\)

\(\rho\) : the density of the fluid

Result Comparison

A comparison of the Mach number and pressure variation in the nozzle obtained with SimScale with analytical results is given below:

A source of deviation between the calculated and analytical results exists because the latter is calculated with a one-dimensional hypothesis. This means that all parameters are assumed to be uniform in the radial direction, while in the following figures, it seems that there exists radial variation too in the flow variables.

One can observe the radial variation causing results to slightly deviate:

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