GDTk

Eilmer Examples Catalogue

Supersonic flow over a convex corner

gdtk/examples/lmr/2D/convex-corner

Kyle A. Damm & Rowan J. Gollan 2023-07-04

This example is of supersonic flow over a convex corner: a Prandtl-Meyer expansion fan. It is test case B.1 "Prandtl-Meyer Expansion Fan" in the paper by Ghia et al. (2010). This particular example was set up by Kyle Damm with conditions to match the example in Ghia et al.:

\[M_{\infty} = 2.0; \quad \delta = -10.0^{\circ}; \quad \gamma = 1.4\]
mach field

Supersonic flow over a wedge

gdtk/examples/lmr/2D/wedge

Kyle A. Damm & Rowan J. Gollan 2023-07-05

This example is of supersonic flow over a wedge: essentially, flow through an oblique shock. It is test case B.2 "Steady-state Oblique Shock Wave" in the paper by Ghia et al. (2010). This particular example was set up by Kyle Damm with conditions to match the example in Ghia et al.:

\[M_{\infty} = 3.0; \delta = 15.0^{\circ}; \gamma = 1.4\]
Tip

This example shows some advanced grid manipulation:

  1. How to join StructuredGrid grids; and

  2. How to form an UnstructuredGrid from a StructuredGrid.
mach field

Supersonic flow through a Busemann diffuser

gdtk/examples/lmr/2D/diffuser-busemann

Rowan J. Gollan 2024-07-06

This example is of supersonic flow ithrough a Busemann diffuser. The particular example comes from the paper by Moelder (2003). The total pressure recovery is a measure of efficiency for the diffuser. Here, that value is: \(\Pi = p_{t3}/p_{t1} = 0.9582\). A Busemann diffuser can be characterised by the Mach numbers at: inflow (M1), just before the conical/terminating shock (M2), and just after this shock (M3). For this example, those values are:

\[M_1 = 5.77; \quad M_2 = 3.00; \quad M_3 = 2.48\]
Tip

This example:

  1. Uses the busemann.py module from the Python gdtk package to generate the diffuser contour.

  2. Has coarse-grid to fine-grid sequencing; it shows how to warm-start the fine-grid from coarse-grid solution.

  3. Shows the use of the ControlPointPatch with a "channel" guide patch.
mach and total p field

The simulation is axisymmetric so only top-half of images is used in simulation in domain. The white mesh overlay are the control points of the ControlPointPatch, not the grid. The grid is much much finer in resolution.

The top image shows how the diffuser acts to reduce Mach number. The bottom image, displaying total pressure, shows how most of the compression is isentropic until the terminating (conical) shock is encountered.

Supersonic turbulent flow over a flat plate

gdtk/examples/lmr/2D/turbulent-flat-plate

Nick N. Gibbons 2024-02-26

This example is a turbulent, supersonic flow over a flat plate at Mach 6.5, from Ye and Morgan (1994). In T4, the boundary layer at this condition is actually transitional, though here it is treated as fully turbulent from the leading edge. Both structured and unstructured variants are available, and the one equation "Edwards" variant of the Spalart-Allmaras turbulence model is used.

ParaView GL2PS Export Creator: GL2PS 1.4.2, (C) 1999-2020 C. Geuzaine For: VTK CreationDate: Tue Aug 20 15:25:04 2024 0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 3200 3300 3400 3500 3600 3700 3800 3900 4000 0 20 40 60 80 100 120 Y (mm) 0 50 100 150 200 250 300 350 400 450 500 550 600 X (mm) Turbulent Viscosity Pressure (Pa)
Figure 1. Pressure and turbulent viscosity color maps for the Mach 6.5 flat plate.

Steepening Wave Problem in 1D

gdtk/examples/lmr/2D/steepening-wave

Nick N. Gibbons and Lachlan Whyborn and Daryl Bond, 2024-12-18

This example is a so-called Simple Wave from "Fluid Mechanics", by L. D. Landau and E. M. Lifshitz. Essentially we begin with a velocity field in a sine wave, which steepens over time until the forward wave becomes a shock. Up until this point, an analytic solution is available to compare against.

We use this to exercise the Alpha-Split Flux implementation by Lachlan Whyborn, which is a compact high order, low dissiapation method, suitable for acoustics work and LES/DNS. The test script for this example checks the error compared to the analytic solution, and ensure its order of convergence is around 4.

Reacting premixed hydrogen over a 15 degree ramp

gdtk/examples/lmr/2D/reacting-ramp

Nick N. Gibbons & Kyle Damm 2024-04-08

This example is an inviscid, reacting, supersonic flow at Mach 3.4, consisting of a premixed hydrogen flow that impacts a 15 degree ramp. The subsequent shock compression causes the flow to ignite, a process which is modelled using the kinetic mechanism of Rogers and Schexnayder.

At present the ramp is solved first order, as I was mainly using it to tinker with the species equations in the JFNK, however it should solve second order with the correct limiter limiter settings.

Tightly-coupled conjugate heat transfer over a hollow cylinder

gdtk/examples/lmr/2D/cylinder-coupled-fluid-thermal

Saxon A. James, Rowan J. Gollan, Kyle A. Damm 2024-04-29

This examples simulates the induced heat transfer into a hollow cylinder placed in a supersonic flow, an experiment performed by Wieting (1987). This is an example of conjugate heat transfer (CHT) with a tightly coupled fluid and solid domain. A tightly-coupled approach means that both the fluid and solid are simulated in a transient manner. This example was first developed by Kyle Damm for use in Eilmer 4 and updated for Eilmer 5. More details on the development of the CHT solver can be found in the paper by Veeraragavan et al. (2016). and Damm et al. (2023).

Tip

This example shows how to configure fluid AND solid domains, and the use of grid arrays.

Verification via manufactured solutions (in 2D)

gdtk/examples/lmr/2D/manufactured-solutions

Rowan J. Gollan; Kyle A. Damm; Nick N. Gibbons; Peter A. Jacobs 2023-07-18

These examples form part of our verification suite using the Method of Manufactured Solutions. Specifically, we have manufactured solutions to test: Euler terms; Navier-Stokes terms; and Reynolds-averaged Navier-Stokes modelling with the \(k-\omega\) turbulence model. These manufactured solutions are steady so they serve to exercise the spatial discretisation.

This example is somewhat advanced: it makes heavy use of the user-defined customization points such as boundary conditions and source terms. It also shows how to provide a reference solution for use in post-processing.

Tip

This example contains:

  1. Scripted coordination (using Python) to run a series of simulations on grids of various refinement

  2. Use of user-defined boundary conditions and use of user-defined source terms

  3. Demonstration of the compute-norms command to find error norms through provision of a reference solution

Supersonic flow through a duct with triangular bumps

gdtk/examples/lmr/2D/supersonic-duct

Kyle A. Damm 2024-08-21

This example is of supersonic flow through a duct with triangular bumps. This test case has been taken from the paper by Nishikawa (2022). The duct has been discretised by a grid of unstructured triangular elements. The example was set up with the following conditions:

\[M_{\infty} = 2.0; \quad \rho_{\infty} = 1.0 ~~ kg\cdot m^{-3}; \quad T_{\infty} = 300.0 ~~ K; \quad \gamma = 1.4\]
density field

Supersonic flow over a ramp

gdtk/examples/lmr/2D/supersonic-ramp

Kyle A. Damm 2024-08-21

This example is of supersonic flow over a ramp. This test case has been taken from the paper by Marques et al. (2004). The ramp has been discretised by a grid of unstructured triangular elements. The example was set up with the following conditions:

\[M_{\infty} = 2.0; \quad \rho_{\infty} = 1.0 ~~ kg\cdot m^{-3}; \quad T_{\infty} = 300.0 ~~ K; \quad \gamma = 1.4\]
mach field

FIRE-II capsule simulation

gdtk/examples/lmr/2D/capsule-fire-II

Nick N. Gibbons; Rowan J. Gollan 2024-08-29

This is example is used to simulate the flow past the FIRE-II reentry capsule at the 1636s point on the trajectory, at an altitude of 71 km. The free stream conditions are:

\[u_{\infty} = 11.3 km/s; T_{\infty} = 210 K; \rho_{\infty} = 8.57e-5 kg/m^3\]
Tip

This example demonstrates how to:

  1. Setup a high-temperature gas model simulation (a two temperature, 11-species air model)

  2. Select a shock-fitting simulation

  3. Use a ControlPointPatch and manipulate some control points for fine-tuning of the grid

Verification via manufactured solutions (in 3D)

gdtk/examples/lmr/3D/manufactured-solutions

Rowan J. Gollan; Kyle A. Damm; Nick N. Gibbons; Peter A. Jacobs 2023-08-27

These examples form part of our verification suite using the Method of Manufactured Solutions. Specifically, we have manufactured solutions to test: Euler terms; Navier-Stokes terms; and Reynolds-averaged Navier-Stokes modelling with the \(k-\omega\) turbulence model. These manufactured solutions are steady so they serve to exercise the spatial discretisation. The set of cases here exercise the three spatial dimensions simulation capability.