**Abstract:**

For hypersonic simulations, unstructured flow solvers typically have problems predicting surface heat fluxes when strong shocks are present. This article outlines a workflow that applies best practices for structured and unstructured grids. In addition, unstructured grid generation can significantly reduce the time required to create quality grids for complex geometries. Several examples are computed using DPLR, a structured grid flow solver, and US3Dflow, an unstructured flow solver.

Results from the two codes are compared and they show excellent agreement. The unstructured grid workflow offers a viable and attractive alternative for hypersonic simulations.

## Introduction

It is desirable to run computational fl uid dynamic (CFD) simulations to predict the aerothermalenvironment of a spacecraft during atmospheric entry.

However, for complex geometries, the grid generation process for structured grids is often tedious and typically a bottleneck in the simulation workflow. During these times, unstructured grid generation offers a potential alternative by simplifying the grid generation process.

There are several instances when unstructured grid solvers have problems predicting surface heating, especially when strong shocks are present. These numerical issues can be mitigated by applying best practices developed for structured grids to unstructured grids. Proper shock alignment of unstructured grids can minimize numerical noise emanating from shocks, thereby reducing the spurious oscillations in computed surface quantities (such as pressure, temperature, and heat flux).

## Workflow for Structured Grids

As shown in Figure 1, the CFD workflow for structured grids starts with generating a surface grid around the spacecraft. For a simple shape, such as an idealized smooth Orion capsule, a structured surface grid can be easily constructed on the capsule’s surface.

Generated by extruding the surface grid outward using a hyperbolic PDE extrusion algorithm available in Cadence® Fidelity™ Pointwise® Mesh Generation. The surface grid, volume grid, and initial flow solution computed using DPLR—a structured grid, Navier-Stokes flow solver for reacting flows—are illustrated in Figure 2.

The next step in the workflow is to align the grid with the bow shock and adjust the wall spacing, so there is sufficient grid resolution to resolve the boundary layer in a viscous simulation properly. The tedious tasks of shock detection, shock smoothing, grid alignment, and updating the volume grid can all be handled automatically using the built-in grid adaption tool within DPLR. It usually takes approximately three to five CPU minutes to generate a new grid using the grid adaption subroutine.

## Workflow for Unstructured Grids

As an alternative to structured grids, a workflow using unstructured grids (see Figure 3) can simplify the grid generation process and produce faster turnaround times for hypersonic simulation.

**Initial grid**

To start the simulation, an initial grid needs to be generated. One option in Fidelity Pointwise is to utilize the T-Rex algorithm, an advancing front method. This technique is conceptually similar to the PDE-based hyperbolic method in that both involve extrusion of the volume grid from a surface grid. One key difference is that T-Rex tests each extrusion step for grid quality and potential collisions with other parts of the extrusion. If either test fails, the extrusion process is stopped locally for that point. The marching front continues for the remaining points until all tests fail, a specified maximum number of layers is reached, or the volume grid achieves isotropy.

When the marching front stops, the remaining volume is filled by a Delaunay-based isotropic grid algorithm. Once these parameters are set, the algorithm can be initialized to run without any user interactions.**Initial solution**

After the unstructured grid is generated, US3D—an unstructured grid, Navier-Stokes fl ow solver for reacting flows—simulates the flow on the initial grid. The computational domain is initialized using freestream conditions and an artificial boundary layer at the surface. A second-order implicit Euler-time integration and line relaxation method is selected to solve the governing equations. Line relaxation is active in the prismatic layers at the wall surface for a hybrid grid. Outside of this region, the solver switches to a point implicit method.**Shock detection and extraction**

4. Generate new surface and volume grids

Although the new iso-surface is smooth, it may contain triangles with very small areas, whichcould result in the generation of poor-quality volume cells. This problem can be resolved bycreating a new unstructured surface via the Fidelity Pointwise tool’s “On Database Entities”command. By selecting the “isotropic” option for unstructured domains, the new surface shouldbe quite uniform in cell size. If desired, the user can change the cell size distribution by addingsource terms. The plot of a new grid representing the bow shock surface is shown in Figure 5.

To test the unstructured workflow, the structured surface grids of the shuttle were used to create a hybrid volume grid. However, unlike the structured grid, the unstructured grid includes the exhaust nozzle details. Mesh generation for this case required one eight-hour workday, quite a reduction versus the structured grid. Further, comparing the heat flux shows excellent agreement between the two codes. Figure 8 illustrates the normalized heat flux contours on the wind side (left) and leeside (middle), and a plot of the centerline heat flux down the length of the vehicle (right). The peak centerline heat flux predicted by US3D is about 2% lower than the DPLR estimate. These results indicate that an unstructured flow solver can produce heating estimates comparable to a structured flow solver if best practices are applied.

**Conclusion**

A workflow using an unstructured grid has been developed and tested. As demonstrated by the Space Shuttle example, the new process can quickly produce accurate heating estimates for a complex geometry, proving to be a viable and promising alternative to traditional structured grid methods. In particular, the T-Rex meshing algorithm is shown to be fast, robust, and easy to implement. While an unstructured workflow does not off er a speed advantage over a structured workflow for simple geometries, the difference is significant for complex geometries.

Unstructured grid generation also offers great flexibility in modifying existing surface and volume grids because grid points can be easily added or deleted without the need to adhere to a particular grid topology. Overall, the current unstructured workflow offers a fast and straightforward process to model hypersonic flows for complex geometries.