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    SimScale DocumentationValidation CasesValidation Case: Sajben Diffuser Weak Shock

    Validation Case: Sajben Diffuser Weak Shock

    The aim of this validation is to compare the simulation results performed in SimScale using the compressible flow feature in its proprietary solver, Multi-purpose, with the simulation results in the study done by NASA titled, “Sajben Transonic Diffuser: Study #1\(^1\)”.

    The objective is to test the Multi-purpose solver’s ability to compute supersonic inviscid flows and in particular to capture normal shock waves.

    View Project

    Geometry

    The geometry replicates a flow domain of the Sajben Diffuser. The geometry is inspired from the schematic\(^1\) as shown in Figure 1:

    sajben diffuser geometry
    Figure 1: Schematic of Sajben Diffuser geometry\(^1\)

    This configuration has an entrance to throat area ratio of 1.4, and an exit to throat area ratio of 1.5. From the entrance, the throat is located at 4.04 times the throat height (\(h_{thr}\)) of 0.044 \(m\).

    The exact geometry profile was used to create a Sajben Difusser CAD model and imported into SimScale. It has a tiny thickness to represent a two-dimensional flow.

    simscale geometry wedge 15
    Figure 2: Geometry used in SimScale for validation

    Analysis Type and Mesh

    Analysis Type: Steady-state, Multi-purpose with k-epsilon and Compressible model

    Mesh and Element Types:

    The mesh was created with SimScale’s Multi-purpose mesh type, which is a body-fitted structured mesh. An automatic sizing definition was defined with two additional region refinements near the normal shock location.

    Mesh TypeFinenessTarget Cell Size (refinement 1) \(m\) Target Cell Size (refinement 2) \(m\)Number of cellsElement Type
    Automatic with region refinements55e-42.5e-430392453D Hexahedral
    Table 1: Mesh data for normal shock inside a diffuser validation case

    The resulting mesh is as observed below:

    cartesian mesh on normal shock flow
    Figure 3: Multi-purpose meshing performed on the Sajben diffuser. Two additional refinements were used near the normal shock.

    Simulation Setup

    Material

    Fluid:

    • Air
      • Dynamic viscosity \((\mu)\): 1.83e-5 \(kg/m.s\)
      • Molar mass \((M_m)\): 28.97 \(kg/kmol\)
      • Prandlt number \(Pr)\): 0.713
      • Specific heat \((C_p)\): 1004 \(J/kg.K\)

    Boundary Conditions

    Figure 4 shows the schematic of the boundary conditions applied:

    Figure 4: Boundary conditions applied on the Sajben Difusser CAD model
    Boundary ConditionValue
    Pressure inlet \([kPa]\)134.4478 (Absolute total pressure with 4.628 \(C\) total temperature)
    Pressure outlet \([kPa]\)110.66 (Fixed absolute static pressure)
    No slip wall (adiabatic)Top and bottom faces
    Slip wall (adiabatic)Front and back faces to replicate a 2D flow
    Table 2: Boundary conditions for the normal shock validation case

    Result Comparison

    The result output from the SimScale simulation is compared with the experimental and CFD results obtained from the NASA study\(^1\).

    Experimental Comparison

    SimScale results were compared against three plots from the NASA experimental study\(^1\): Pressure ratio along the top and bottom surface against the normalized x-coordinate of the profile, and the flow velocity profile at an axial location within the diffuser.

    The normalization in the x- and y-direction can be understood using the figure below:

    schematic nasa sajben diffuser normal shock
    Figure 5: Schematic of Sajben Diffuser Test Case\(^2\)

    The x-coordinate is normalized using the throat height \(h_{thr}\) (or \(H^+\)) and the y-coordinate is normalized using the height at any axial location.

    Pressure along the top surface

    Using the probe point feature in SimScale, the static pressure was measured at the top and bottom surface profile of the diffuser and compared against the study\(^1\). The static pressure values are normalized using the total absolute pressure at the inlet.

    Figure 6: Static Pressure at the top diffuser surface: SimScale vs NASA study\(^1\)

    Pressure along the bottom surface

    Figure 7: Static Pressure at the bottom diffuser surface: SimScale vs NASA study\(^1\)

    Figures 6 and 7 indicate that the shock location is precisely captured as the pressure drop and rise match for both sides of comparison.

    Velocity at an axial location

    The flow velocity profile was mapped at \(x\) = 0.1268 \(m\) or \(x/h_{thr}\) = 2.882 and compared against the study\(^1\).

    Figure 8: Flow velocity at an axial location \(x/h_{thr}\) = 2.882 in the Sajben Diffuser: SimScale vs NASA study\(^1\)

    The SimScale result tends to agree with the NASA experimental study and more accurately near the top and bottom boundary surfaces.

    Numerical Comparison with Mach Contours

    Additionally, Mach number contours for three codes WIND, NPARC, and NXAIR are computed in the study\(^1\). The WIND and NXAIR results show a well-defined normal shock than the NPARC results. The NXAIR shock position is slightly downstream of the position predicted by the other two codes. WIND and NPARC predict similar boundary layer growth downstream of the normal shock, while NXAIR predicts a thinner boundary layer.

    nasa normal shock study 1 mach
    Figure 9: Mach number contours as obtained from the CFD codes in the NASA study show a well-defined normal shock and boundary layer growth

    Mach number contours computed in SimScale show a similar behavior compared to the three codes. The normal shock is very well-defined at the same location as computed in the figure above as well as the plots. The sharp dip in pressures at the top and bottom surface is accurately reproduced as well.

    mach number contours for normal shock simscale sajben
    Figure 10: Mach number contours obtained using the Multi-purpose solver in SimScale agress explicitly with the codes in Figure 9 and show a distinct normal shock and similar boundary layer growth.

    References

    Note

    If you still encounter problems validating your simulation, then please post the issue on our forum or contact us.

    Last updated: March 14th, 2025

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