Students at Texas A&M University used Pointwise in conjunction with NASA’s DPLR CFD code to investigate hypersonic boundary layer stability on the HIFiRE-5 benchmark case.

authors:

### Alexander Moyes, Travis Kocian, Daniel Mullen, and Helen Reed

Aerospace Engineering, Texas A&M University

## I. Introduction

The aerospace community has recently focused a great deal of attention toward hypersonic vehicle development. Hypersonic vehicles and the obstacles of designing them are not new concepts, but recent technological breakthroughs have made it possible to understand these difficulties and address them. One of the most important difficulties that needs to be overcome is aerodynamic heating. At hypersonic speeds, this heating can lead to extremely high temperatures that can cause materials to disintegrate, control surfaces to become ineffective, and communications to be lost. Solving the aerodynamic heating problem could be the catalyst for accelerating the development of hypersonic vehicles and extending their usability. It does not mean all flows need to be laminar for the full extent of a vehicle, but rather it means accurately predicting and/or controlling where the flow is laminar, turbulent, or transitioning. The laminar-turbulent transition process can be modified by vehicle configuration, flow conditions, and chemical reactions, and it is important to understand the various mechanisms that lead to transition and their receptivity process.

## II. Boundary-Layer Stability on HIFiRE-5 Elliptic Cone in Hypersonic Flow

The Hypersonic International Flight Research Experimentation (HIFiRE) program was initiated with two experiments focused on studying boundary layer stability at hypersonic speeds (HIFiRE-1 and HIFiRE-5). One of the experiments, HIFiRE-5, was focused on leading edge transition and three-dimensional instabilities on non-axisymmetric configurations. The final chosen configuration for HIFiRE-5 was a 2:1 elliptic cone. Two flights were completed, with the second obtaining hypersonic transition data. HIFiRE-5a was tested in April 2012 and achieved supersonic speeds (Kimmel et al. (2013)), and HIFiRE-5b was tested in May 2016 and reached hypersonic speeds (Kimmel et al. (2017)). Elliptic cone geometries with a 2:1 cross-section at hypersonic speeds were first studied by Kimmel et al. (1997) using linear stability theory and crossflow correlations in order to study the crossflow instability. Wind-tunnel tests using Schlieren photography and surface oil-flow followed shortly after (Kimmel et al. (1999)), along with hot-film probe measurements (Poggie et al. (2000)). Traveling and stationary crossflow were present away from the planes of symmetry, and the centerline was found to be transitional.

While the flight model was being built and tested, a 38.1% scale model was designed for ground tests. This wind tunnel geometry has been analyzed in the Boeing/AFOSR Mach 6 Quiet Tunnel at Purdue University and the Texas A&M University Mach 6 Quiet Tunnel and Actively Controlled Expansion Wind Tunnel. Concurrently, detailed linear and nonlinear computational analysis was being completed.

## A. Basic-State Calculation

The geometry considered in the present study is the HIFiRE-5b flight geometry. The geometry has a nose radius of 2.5 millimeters along the semi-minor axis and 5 millimeters along the semi-major axis. The total length of the geometry is 0.86 meters with a base diameter of 0.216 meters and 0.432 meters along the semi-minor and semi-major axis, respectively. This geometry maintains a 2:1 relationship along its entire length. The half-angle of the geometry is 7 degrees along the semi-minor axis. The flight test remained within the bounds of ±2 deg. angle of attack (AoA) and ±2 deg. yaw angle with some spin (private communication with Roger Kimmel). Sensors were distributed over half of the flight geometry and that half will be assumed the “top view” for this analysis.

The CFD software being used is the Data Parallel Relaxation (DPLR) NASA flow solver. The shock location is established by iteratively clustering grid cells closer to the shock and running DPLR. A structured rectangular domain is projected onto the nose of the cone to create a domain on the surface. Figure 1 and Fig. 2 shows the mesh used in the current study. The mesh is a multi-domain structured grid, created in Pointwise. The grid consists of 700 points in the axial direction, 569 in the wall normal direction, and 505 around the azimuth. Symmetry allows the basic state to be calculated as a half-cone solution. The grid totals approximately 200 million grid cells.

Once the mesh was created with Pointwise, it was imported into DPLR and the basic state was computed at the following conditions: freestream Mach number M_{∞} = 7.793, 1 deg. angle of attack (AoA), freestream temperature T_{∞} = 216 K, and freestream pressure P_{∞} = 3380 Pa abs., resulting in a unit Reynolds number Re′ = 8.83×10^{6} per meter. An isothermal, constant wall-temperature condition, T_{wall} = 373 K, was imposed.

Figure 3 shows the basic-state Mach contour solution obtained in DPLR. The flowfield is quite complicated with a strong azimuthal velocity created by the geometry leading to a mushroom structure. The formation of these complex flow structures is a product of the steady, undisturbed, laminar flow basic-state solution, and no intentional disturbances or excitations are input to cause their manifestation. It is important to capture these details for boundary-layer stability. Basic-state solutions produced by DPLR were post-processed and followed by a stability analysis performed with EPIC, a code developed at Texas A&M University (Oliviero et al. (2015)). EPIC has the ability to do linear stability theory (LST), parabolized stability equations (PSE) – both linear and nonlinear. Results from PSE calculations for the HIFiRE-5b were presented originally in Moyes et al. (2017) and are summarized here.

## B. Boundary-Layer Stability Results

Linear PSE (LPSE) provides N-factors (or amplification) of a disturbance along a specified direction, such as a streamline. Stationary crossflow was analyzed on this geometry, which most closely follows a vortex path, described in detail by Oliviero et al. (2015). Figure 4 is a top view contour of the HIFiRE-5b geometry, where z = 0 represents the geometric ray along the semi-minor axis, and the negative ‘z’ corresponds to reflected results from the positive ‘z’. The dashed-black lines represent the mushroom structure where an instability mechanism, different from stationary crossflow, may exist. The values shown represent the largest LPSE N-factor at each location. The dots are flight test sensors and are colored according to whether they are laminar or at least transitional (private communication with Roger Kimmel). Blue dots represent laminar flow, red dots indicate enough mean-flow distortion to register in the heat transfer, and transition onset is based on the first departure from laminar heating. Comparing the stationary crossflow amplification front from the LPSE calculations to the flight test sensor colors, the fronts are very similar.

The stationary crossflow instability can display nonlinear affects early on. Therefore, it is necessary to provide an initial disturbance amplitude and model the instability with NPSE. The very nature of the vortex structures significantly distorts the mean flow. An iterative technique was used in order to calculate the initial amplitude of the stationary crossflow disturbance. This involved correlating the nonlinear development of the stationary crossflow with the transitional flight sensors along each path. One of the vortex path’s nonlinear stationary crossflow development is shown below.

Modified basic states downstream of transition onset are reconstructed using the NPSE disturbance wave added to the laminar basic state. The modified basic states are assumed to span an azimuthal interval of one wavelength. The ρu mass flux modified basic states from 0.45 to 0.70 meters can be seen in Fig. 5. The nonlinear effects and disturbance amplitudes become substantial at further downstream axial locations.

## References

- Kimmel, R., Adamczak, D., Juliano, T., and DSTO AVD Brisbane Team, “HIFiRE-5 Flight Test Preliminary Results,” AIAA Paper 2013-0377, 2013.
- Kimmel, R., Adamczak, D., and DSTG AVD Brisbane Team, “HIFiRE-5b Flight Overview,” AIAA Paper 2017-3131, 2017.
- Kimmel, R., Klein, M., and Schwoerke, S., “Three-Dimensional Hypersonic Laminar Boundary-Layer Computations for Transition Experiment Design,”
*Journal of Spacecraft and Rockets*, Vol. 34, No. 4, 1997. - Kimmel, R., Poggie, J., and Schwoerke, S., “Laminar-Turbulent Transition in a Mach 8 Elliptic Cone Flow,”
*AIAA Journal*, Vol. 37, No. 9, 1999. - Poggie, J., Kimmel, R., and Schwoerke, S., “Traveling Instability Waves in a Mach 8 Flow Over an Elliptic Cone,”
*AIAA Journal*, Vol. 38, No. 2, 2000. - Oliviero, N., Kocian, T., Moyes, A., and Reed, H.,“EPIC: NPSE Analysis of Hypersonic Crossflow Instability on Yawed Straight Circular Cone,” AIAA Paper 2015-2772, 2015.
- Moyes, A., Kocian, T., Mullen, D., and Reed,H., “Boundary Layer Stability Analysis of HIFiRE-5b Flight Geometry,” AIAA Paper 2017-4301, 2017.

[*Editor’s note: Any and all typographical errors in this article are the fault of the translation of the original article into blog format. They are not the fault of the authors.*]

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