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Compressible subsonic flow

High speed train

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Introduction

intro

High-speed trains run in the subsonic compressible flow regime with Mach numbers in the range of 0.3 to 0.4. In CFD, the pressure-based solver of SIMPLE algorithm is often used for low-speed flows and the density-based solver for high-speed flows. This challenge aims to validate the stability of Baram's incompressible solver, buoyantSimpleNFoam, in the subsonic compressible flow regime.

We use a high-speed train model with simplified vehicle connections, bogies(wheels), and pantographs, and the train speed is 400 km/h.

With a mesh of about 2 millions, the convergence was achieved in about 300 iterations(about 20 minutes on an 8-core CPU). The convergence is much better compared to the results obtained using OpenFOAM's standard solvers buoyantSimpleFoam and rhoSimpleFoam.

The computational conditions are as follows

  • solver : buoyantSimpleNFoam
  • turbulence model : \(SST\) \(k-\omega\) model
  • density : Perfect Gas
  • viscosity : 1.79e-5 \(kg/ms\)
  • flow condition : 400 \(km/h\)(111.11 \(m/s\)) at inlet

Start BaramFlow and load mesh

Run the program and select [New Case] from the launcher. In the launcher, select [Pressure-based] for [Solver Type] and [None] for [Multiphase Model].

Use the given polyMesh folder. In the top tab, click [File]-[Load Mesh]-[OpenFOAM] in that order and select the polyMesh folder.


General

For this example, we'll use default conditions.

Models

For this example, we'll use \(SST\) \(k-\omega\) model for turbulence.

Include Energy.


Materials

Material properties of air is as follows

  • Density : Perfect Gas
  • Specific heat : 1006
  • Viscosity : 1.79e-05
  • Thermal Conductivity : 0.0245
  • Molecular Weight : 28.966


Boundary Conditions

Set the boundary type and values as shown below.

  • Hex6_1_xMin : Velocity Inlet
    • Velocity Specification Method : Magnitude, Normal to Boundary
    • Velocity Magnitude : 111.11
    • Turbulence Specification Method : Intensity and Viscosity Ratio
    • Turbulent Intensity : 1
    • Viscosity ratio : 100
    • Temperature : 300

  • Hex6_1_xMax : Pressure Outlet
    • Pressure : 0

  • Hex6_1_zMin : Wall
    • Velocity Condition : Translational Moving Wall
    • Velocity : (111.11 0 0)

  • train_surface_0 : Wall

  • Hex6_1_yMin, Hex6_1_yMax, Hex6_1_zMax : Symmetry

Reference Values

The Reference Value is used to calculate the aerodynamic coefficient. Since this is not a problem with experimental data, you do not need to enter an exact value and set the velocity to 111.11.

Numerical Conditions

In this example, we'll change the settings as shown below.

  • Pressure-Velocity Coupling : SIMPLEC

  • Discretization Schemes

    • Pressure : Momentum Weighted Reconstruct
    • Momentum, Energy, Turbulence :Second Order Wpwind

  • Under-Relaxation Factors

    • Pressure : 0.8
    • Momentum, Energy, Turbulence : 0.9
    • Density : 1.0

  • Convergence Criteria

    • Pressure, Momentum, Turbulence : 1e-4
    • Energy : 1e-6

Monitor

Monitor the force coefficients of train.

Select [Monitors]-[Add]-[Forces] and select train_surface_0 at [Boundaries].


Initialization

Enter the value and click the Initialize button at the bottom. Then click the [File]-[Save] menu to save the case file.

  • Velocity : (111.11 0 0)
  • Pressure : 0
  • Temperature : 300
  • Scale of velocity : 111.11
  • Turbulent Intensity : 1
  • Turbulent Viscosity Ratio : 10

Run

Selct [Parallel]-[Environment] in menu. Set Number of Cores as you want and select [Local Machine] for [Parallel Type].

Change the values as shown below, and click [Start Calculation] button.

  • Number of Iterations : 1000
  • Save Interval : 1000


When the calculation is started, you can see the graphs of Residuals and Force monitor as shown below.

intro

intro

Post-processing

Click the parview button in [External tools] to open the paraview.

Change the [Case Type] to [Decomposed Case].

To draw the pressure distribution around the vehicle, select train_surface_0, ground, symmetry from Mesh Regions and Coloring as p_rgh.


Hot subsonic jet

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Link to youtube video

Introduction

intro

intro

This is an example flow simulation of a high-temperature subsonic nozzle with a temperature of 260\(^o C\) and a Mach number of 0.376 at the nozzle throat.

The geometry and experimental conditions are provided by NASA Langley Research Center.

https://turbmodels.larc.nasa.gov/jetsubsonichot_val.html

Experimental results from NASA ARN2 (Acoustic Research Nozzle 2) with the following geometry and conditions

  • Radius of the nozzle neck: 1 inch
  • Pressure ratio, \(p/p{ref}\) = 1.10203, \(p{ref}\) = 14.3 psi
  • Temperature ratio, \(T/T{ref}\) = 1.81388, \(T{ref}\) = 530 R
  • Nozzle exit Mach number: 0.376

Along with the experimental results, we provide calculations from the \(SST\) k-\(omega\) model and the Spalart-Allmaras model from the NASA WIND code.

  • solver : buoyantSimpleNFoam
  • turbulence model : \(standard\) \(k-\epsilon\)
  • density : Perfect Gas
  • viscosity and thermal conductivity : Sutherland law
  • nozzle inlet condition : 10059.65 Pa, 534.086 K

Start BaramFlow and load mesh

Run the program and select [New Case] from the launcher. In the launcher, select [Pressure-based] for [Solver Type] and [None] for [Multiphase Model].

Use the given polyMesh folder. In the top tab, click [File]-[Load Mesh]-[OpenFOAM] in that order and select the polyMesh folder.


General

Set Time as Steady, Gravity as (0 0 0).

Set Operating Pressure as 98595.03.


Models

For this example, we'll use \(Standard\) \(k-\epsilon\) model for turbulence.

Include Energy.

Materials

Material properties of air is as follows

  • Density : Perfect Gas
  • Specific heat : 1006
  • Viscosity : Sutherland, As = 1.46e-6, Ts = 110.4
  • Molecular Weight : 28.966


Boundary Conditions

Set the boundary type and values as shown below.

  • inlet : Pressure Inlet
    • Total Pressure : 10059.65
    • Turbulence Specification Method : Intensity and Viscosity Ratio
    • Turbulent Intensity : 1
    • Viscosity ratio : 10
    • Temperature : 534.086

  • outlet : Pressure Outlet
    • Pressure : 0
    • Specify Backflow Properties : on
      • Backflow Total Temperature : 294.4444
      • Turbulence Specification Method : Intensity and Viscosity Ratio
      • Turbulent Intensity : 1
      • Viscosity ratio : 10

  • farfield : Velocity Inlet
    • Velocity Specification Method : Component (3.44 0 0)
    • Turbulence Specification Method : Intensity and Viscosity Ratio
    • Turbulent Intensity : 1
    • Viscosity ratio : 10
    • Temperature : 294.4444

  • nozzle : Wall

    • Velocity : No Slip
    • Temperature : Adiabatic

  • frontAndBackPlanes_pos, frontAndBackPlanes_neg : Wedge

Numerical Conditions

In this example, we'll change the settings as shown below.

  • Pressure-Velocity Coupling : SIMPLE

  • Discretization Schemes

    • Pressure : Momentum Weighted Reconstruct
    • Momentum, Energy, Turbulence :Second Order Wpwind

  • Under-Relaxation Factors

    • Pressure : 0.1
    • Momentum : 0.3
    • Energy : 0.9
    • Turbulence : 0.2

  • Convergence Criteria

    • Pressure : 0
    • Momentum, Energy, Turbulence : 0.001

  • Advanced

    • Minimum Static Temperature : 100
    • Maximum Static Temperature : 1000
    • Turn on Include Viscous Dissipation Terms

Monitor

In this example, we will monitor the axial velocity of a point with x/D of 20 on the axis. Select [Add]-[Points].

Enter X-Velocity for Field and (1.016 0 0) for Coordinate.


Initialization

Enter the value and click the Initialize button at the bottom. Then click the [File]-[Save] menu to save the case file.

  • Velocity : (3.44 0 0)
  • Pressure : 0
  • Temperature : 294.4444
  • Scale of velocity : 100
  • Turbulent Intensity : 1
  • Turbulent Viscosity Ratio : 10

Run

Selct [Parallel]-[Environment] in menu. Set Number of Cores as you want and select [Local Machine] for [Parallel Type].

Change the values as shown below, and click [Start Calculation] button.

  • Number of Iterations : 20000
  • Save Interval : 1000


When the calculation is started, you can see the graphs of Residuals and point monitor as shown below.

intro

intro

Post-processing

Click the parview button in [External tools] to open the paraview.

Change the [Case Type] to [Decomposed Case].

Change [Coloring] to U.


Subsonic cavity flow

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Introduction

include surface's own gap

This example computes subsonic two-dimensional cavity flow.

The geometry and flow conditions are as follows

  • L/D = 2 (the ratio of the length and height of the cavity)
  • Mach Number = 0.6
  • Reynolds Number = 2.75e+5
  • Prandtl Number = 0.7

The mesh was converted from a plot3d format created in matlab.

The solver is buoyantPimpleNFoam, a pressure-based thermal flow solver developed by NEXTfoam.

The boundary conditions at the outlet and the top surface are waveTransmissive (non-reflecting) with no reflection of pressure waves.

The computational conditions are as follows

  • solver : buoyantPimpleNFoam
  • turbulence model : \(SST\) \(k-\omega\)
  • density : Perfect Gas
  • inlet temperature : 300 K
  • inlet pressure : 101325 Pa

Start BaramFlow and load mesh

Run the program and select [New Case] from the launcher. In the launcher, select [Pressure-based] for [Solver Type] and [None] for [Multiphase Model].

Use the given polyMesh folder. In the top tab, click [File]-[Load Mesh]-[OpenFOAM] in that order and select the polyMesh folder.


include surface's own gap

General

Change Time to Transient.


Models

For this example, we'll use \(SST\) \(k-\omega\) model for turbulence.

Include Energy.

Materials

Material properties of air is as follows

  • Density : Perfect Gas
  • Specific heat : 1006
  • Viscosity : 0.00178 (value for the Reynolds number)
  • Thermal Conductivity : 2.562 (value for the Prandtl number)
  • Molecular Weight : 28.966


Boundary Conditions

Set the boundary type and values as shown below.

  • inlet : Velocity Inlet
    • Velocity Specification Method : Magnitude, Normal to Boundary
    • Velocity Magnitude : 208.31
    • Turbulence Specification Method : Intensity and Viscosity Ratio
    • Turbulent Intensity : 1
    • Turbulent Viscosity Ratio : 10
    • Temperature : 300

  • outlet, top : Pressure Outlet
    • Pressure : 0
    • with Non-Reflecting Boundary option

  • cavityFront, cavityBottom, cavityRear, frontBottom, rearBottom : Wall

    • Velocity Condition : No Slip

  • frontPlane, backPlane : Empty

Numerical Conditions

In this example, we'll change the settings as shown below.

  • Pressure-Velocity Coupling : SIMPLE

  • Discretization Schemes

    • Time : Second Order Implicit
    • Pressure : Momentum Weighted Reconstruct
    • Momentum, Energy, Turbulence : Second Order Wpwind

  • Max Iteration per Time Step : 20

  • Number of Correctors : 2

  • Under-Relaxation Factors

    • Pressure : 0.3 / 1
    • Momentum, Turbulence : 0.7 / 1
    • Energy, Density : 1 / 1

Monitor

Monitor pressure at cavity center point. Click [Add]-[Point].

Set coordinate as (0 -0.5 0.25).


Initialization

Set values as follows

  • Velocity : (208.31 0 0)
  • Pressure : 0
  • Temperature : 300
  • Scale of velocity : 208.31
  • Turbulent Intensity : 1
  • Turbulent Viscosity Ratio : 10

Initialize the velocity inside the cavity to zero. Under [Advanced]-[Sections], select [Create]-[Hex] and enter the Min/Max coordinates as (-1 -1 -1), (1 0 1). Select Velcity and give it a value of (0 0 0).


Enter the value and click the Initialize button at the bottom. Then click the [File]-[Save] menu to save the case file.

Run

Selct [Parallel]-[Environment] in menu. Set Number of Cores as you want and select [Local Machine] for [Parallel Type].

Change the values as shown below, and click [Start Calculation] button.

  • Time Stepping Method : Fixed
  • Time Step Size : 1e-5
  • End Time : 0.5
  • Save Interval : Every 0.002 sec


Post-processing

Click the parview button in [External tools] to open the paraview.

Change the [Case Type] to [Decomposed Case].

Change [Coloring] to U.