# Effects of Surface Roughness on Shock-Wave/Turbulent Boundary-Layer Interaction at Mach 4 over a Hollow Cylinder Flare Model

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Program

#### 2.1. Wind Tunnel Facility

^{3}(8200 gal) of air down to 130 Pa (1 Torr). These conditions produce a freestream Mach number of 4 with a freestream unit Reynolds number range of 3.48–50.3 × 10

^{6}m

^{−1}(1.0–16.5 × 10

^{6}ft

^{−1}) and an average freestream velocity of 671 m/s (2201 ft/s). Optical windows with a viewing area of 280 × 432 mm (11 × 17 in) are located on the test section side walls to provide optical access for experiments [42]. A summary of wind tunnel conditions for this campaign can be found in Table 1. Given the nature of the Ludwieg tube operation using Mylar diaphragms, there is a roughly 15% uncertainty in target burst pressure prior to each test. For this reason, the burst pressures were slightly different between the smooth and rough surface test cases, leading to Reynolds numbers that differed by 12%. However, it is assumed in the present analysis that this change in the Reynolds number had a significantly smaller impact on the interaction when compared to the change in surface texture.

#### 2.2. Test Geometries

#### 2.3. Experimental Setup

#### 2.4. Schlieren Image Processing

^{®}script to correct the placement of images and determine the shock foot location, ${L}_{s}$, of the SWBLI [39]. To ensure accurate shock tracking, a reference point was established at the intersection of the HCF body and flare. However, the wind tunnel’s vertical and horizonal movement throughout the test run varied the position of the reference point. The wind tunnel motion was corrected and images were stabilized using a 2-D cross-correlation of the image stacks with a reference image using the predetermined reference point. The maximum peak correlation amplitudes in both axes were found and matched with the lag value. The lag values determined the required pixel shift needed to match the location of the refence image in the vertical and horizontal directions. Using the same algorithm previously verified by Combs et al. [39] by comparing image-based shock positions to surface-pressure data, the shock wave position was determined using a threshold-based algorithm that systematically identifies shock position in an image using measured intensity fluctuations in the interaction region. Although the algorithm has been described by Combs et al. [39], we will repeat the description here to make the details available in this open access forum.

_{1}, in an automated and accurate manner. This is a necessity when acquiring time-resolved data at 100 kHz, as tens of thousands of images are collected during each run. Furthermore, Cauchy edge detection and simple binary image schemes were found to be insufficient for the current experiments, likely owing to the relative complexity of the flowfield, high turbulent noise in the freestream, and low pixel resolution of the images acquired. The code identifies the location of shock structures through a 9-step process, outlined here:

- User-assisted definition of flowfield region of interest (ROI) where shock is likely to be located, through a graphical user interface.
- Rotate ROI image matrix by a user-defined estimated shock angle.
- Average rotated image matrix in vertical direction.
- Detect variation (s) in the line resulting from Step 3 to collect approximate location of shock structure center.
- Transform coordinates of shock center back to ROI image matrix.
- Based on the estimated shock angle, define a straight line passing through the shock center to serve as an initial estimate.
- For each shock structure and for each row i in the image matrix, interrogate along a line centered at the location of the initial estimate with bounds ±b, where b is a user-defined window size, and identify the position of each shock in row i by locating the center of the intensity variation along the line.
- Step 7 produces a shock location for each row in the image matrix. If fewer than five points are identified for a given shock feature, a not-a-number (NaN) result is returned for the image and an error is logged. Otherwise, a straight line is fit to the series of points. If the best-fit solution does not fit within a user-defined shock angle tolerance, a NaN result is returned for the image and an error is logged.
- Shock positions and angles are logged and (optionally) the result is displayed to the user in real time, and superimposed on the individual schlieren image. Shock location outliers that lie beyond user-defined bounds are also assigned a NaN value and result in an error being recorded.

^{®}pwelch command with a fast Fourier transform size of 7000 points and a Hamming window with 50% overlap and a frequency resolution, df, of 330 Hz.

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Radespiel, R.; Ali, S.R.C.; Muñoz, F.; Bowersox, R.; Leidy, A.; Tanno, H.; Kirk, L.C.; Reshotko, E. Experimental Investigation of Roughness Effects on Transition on Blunt Spherical Capsule Shapes. J. Spacecr. Rocket.
**2019**, 56, 405–420. [Google Scholar] [CrossRef] - Combs, C.S. Quantitative Measurements of Ablation-Products Transport in Supersonic Turbulent Flows Using Planar Laser-Induced Fluorescence. Ph.D. Dissertation, The University of Texas at Austin, Austin, TX, USA, 2015. [Google Scholar]
- Siddiqui, F.; Gragston, M.; Saric, W.S.; Bowersox, R.D.W. Mack-mode instabilities on a cooled flared cone with discrete roughness elements at Mach 6. Exp. Fluids
**2021**, 62, 213. [Google Scholar] [CrossRef] - Siddiqui, F.; Saric, W.S.; Bowersox, R.D. Interaction of Second-Mode Disturbances and 3-D Roughness on a Cooled Flared Cone at Mach 6. In Proceedings of the AIAA Scitech 2021 Forum, Virtual, 11–21 January 2021. [Google Scholar] [CrossRef]
- Stock, H.W.; Ginoux, J.J. Experimental results on crosshatched ablation patterns. AIAA J.
**1971**, 9, 971–973. [Google Scholar] [CrossRef] - Berg, D.E. Surface Roughness Effects on the Hypersonic Turbulent Boundary Layer. Ph.D. Dissertation, California Institute of Technology, Pasadena, CA, USA, 1977. [Google Scholar]
- Sietzen, F., Jr. From Mercury to CEV: Space Capsules Reemerge. Aerosp. Am.
**2005**, 43, 26–30. [Google Scholar] - Vignoles, G.L.; Lachaud, J.; Aspa, Y.; Goyhénèche, J.-M. Ablation of carbon-based materials: Multiscale roughness mod-elling. Compos. Sci. Technol.
**2009**, 69, 1470–1477. [Google Scholar] [CrossRef] - Chawla, K.K. Composite Materials Science and Engineering; Springer Science & Business Media: Berlin/Heidelberg, Germany, 1989. [Google Scholar] [CrossRef]
- Stern, E.C.; Poovathingal, S.; Nompelis, I.; Schwartzentruber, T.E.; Candler, G.V. Nonequilibrium flow through porous thermal protection materials, Part I: Numerical methods. J. Comput. Phys.
**2019**, 380, 408–426. [Google Scholar] [CrossRef] - Poovathingal, S.; Stern, E.C.; Nompelis, I.; Schwartzentruber, T.E.; Candler, G.V. Nonequilibrium flow through porous thermal protection materials, Part II: Oxidation and pyrolysis. J. Comput. Phys.
**2019**, 380, 427–441. [Google Scholar] [CrossRef] - Wu, Y.; Christensen, K.T. Outer-layer similarity in the presence of a practical rough-wall topography. Phys. Fluids
**2007**, 19, 085108. [Google Scholar] [CrossRef] - Wu, Y.; Christensen, K.T. Spatial structure of a turbulent boundary layer with irregular surface roughness. J. Fluid Mech.
**2010**, 655, 380–418. [Google Scholar] [CrossRef] - Mejia-Alvarez, R.; Christensen, K.T. Low-order representations of irregular surface roughness and their impact on a turbulent boundary layer. Phys. Fluids
**2010**, 22, 015106. [Google Scholar] [CrossRef] - Berry, S.A.; Auslender, A.H.; Dilley, A.D.; Calleja, J.F. Hypersonic Boundary-Layer Trip Development for Hyper-X. J. Spacecr. Rocket.
**2001**, 38, 853–864. [Google Scholar] [CrossRef][Green Version] - Jiang, N.; Webster, M.; Lempert, W.R.; Miller, J.D.; Meyer, T.R.; Ivey, C.B.; Danehy, P.M. MHz-rate nitric oxide planar laser-induced fluorescence imaging in a Mach 10 hypersonic wind tunnel. Appl. Opt.
**2010**, 50, A20–A28. [Google Scholar] [CrossRef] [PubMed][Green Version] - Dyakonov, A.; Danehy, P.; Garcia, A.; Borg, S.; Berry, S.; Inman, J.; Alderfer, D. Fluorescence Visualization of Hypersonic Flow Past Triangular and Rectangular Boundary-Layer Trips. In Proceedings of the 45th AIAA Aerospace Sciences Meeting, Reno, NV, USA, 8–11 January 2007. [Google Scholar] [CrossRef][Green Version]
- Danehy, P.; Bathel, B.; Ivey, C.; Inman, J.; Jones, S. NO PLIF Study of Hypersonic Transition over a Discrete Hemispherical Roughness Element. In Proceedings of the 47th AIAA Aerospace Sciences Meeting, Orlando, FL, USA, 5–8 January 2009. [Google Scholar] [CrossRef][Green Version]
- Bathel, B.; Danehy, P.; Inman, J.; Watkins, A.; Jones, S.; Lipford, W.; Goodman, K.; Ivey, C.; Goyne, C. Hypersonic Laminar Boundary Layer Velocimetry with Discrete Roughness on a Flat Plate. In Proceedings of the 40th Fluid Dynamics Conference and Exhibit, Chicago, IL, USA, 28 June–1 July 2010. [Google Scholar] [CrossRef][Green Version]
- Reda, D.; Wilder, M.; Bogdanoff, D.; Olejniczak, J. Aerothermodynamic Testing of Ablative Reentry Vehicle Nosetip Materials in Hypersonic Ballistic-Range Environments. In Proceedings of the USAF Developmental Test and Evaluation Summit, Woodland Hills, CA, USA, 16–18 November 2004. [Google Scholar] [CrossRef]
- Charwat, A.F. Exploratory Studies on the Sublimation of Slender Camphor and Naphthalene Models in a Supersonic Wind-Tunnel; Memorandum RM-5506-ARPA; Rand Corp: Santa Monica, CA, USA, 1968; Available online: https://apps.dtic.mil/sti/citations/AD0673531 (accessed on 28 July 2022).
- Latin, R.M.; Bowersox, R.D.W. Flow Properties of a Supersonic Turbulent Boundary Layer with Wall Roughness. AIAA J.
**2000**, 38, 1804–1821. [Google Scholar] [CrossRef] - Latin, R.M.; Bowersox, R.D.W. Temporal Turbulent Flow Structure for Supersonic Rough-Wall Boundary Layers. AIAA J.
**2002**, 40, 832–841. [Google Scholar] [CrossRef] - Peltier, S.J.; Humble, R.A.; Bowersox, R.D.W. Crosshatch roughness distortions on a hypersonic turbulent boundary layer. Phys. Fluids
**2016**, 28, 045105. [Google Scholar] [CrossRef] - Kocher, B.D.; Kreth, P.A.; Schmisseur, J.D.; LaLonde, E.J.; Combs, C.S. Characterizing Streamwise Development of Surface Roughness Effects on a Supersonic Boundary Layer. AIAA J.
**2022**, 1–14. [Google Scholar] [CrossRef] - Sahoo, D.; Smits, A.; Papageorge, M. PIV Experiments on a Rough Wall Hypersonic Turbulent Boundary Layer. In Proceedings of the 40th AIAA Fluid Dynamics Conference and Exhibit, Chicago, IL, USA, 28 June–1 July 2010. [Google Scholar] [CrossRef]
- Lindörfer, S.A.; Combs, C.S.; Kreth, P.A.; Bond, R.B.; Schmisseur, J.D. Scaling of cylinder-generated shock-wave/turbulent boundary-layer interactions. Shock Waves
**2020**, 30, 395–407. [Google Scholar] [CrossRef] - Bathel, B.F.; Jones, S.B.; Watkins, A.N.; Berry, S.; Goodman, K.; Combs, C.S.; Schmisseur, J.D.; Kreth, P.A.; Lash, E.L. Shockwave/Boundary-Layer Interaction Studies Performed in the NASA Langley 20-Inch Mach 6 Air Tunnel. In Proceedings of the AIAA Aviation 2019 Forum, Dallas, TX, USA, 17–21 June 2019. [Google Scholar]
- Gaitonde, D.V. Progress in shock wave/boundary layer interactions. Prog. Aerosp. Sci.
**2015**, 72, 80–99. [Google Scholar] [CrossRef] - Combs, C.S.; Clemens, N.T.; Danehy, P.M.; Bathel, B.; Parker, R.; Wadhams, T.; Holden, M.; Kirk, B. Fluorescence Imaging of Reaction Control Jets and Backshell Aeroheating of Orion Capsule. J. Spacecr. Rocket.
**2015**, 52, 243–252. [Google Scholar] [CrossRef] - Sansica, A.; Sandham, N.; Hu, Z. Forced response of a laminar shock-induced separation bubble. Phys. Fluids
**2014**, 26, 093601. [Google Scholar] [CrossRef] - Dolling, D.S. Fifty Years of Shock-Wave/Boundary-Layer Interaction Research: What Next? AIAA J.
**2001**, 39, 1517–1531. [Google Scholar] [CrossRef] - Hoffman, E.N.A.; Rodriguez, J.M.; Cottier, S.M.; Combs, C.S.; Bathel, B.F.; Weisberger, J.M.; Jones, S.B.; Schmisseur, J.D.; Kreth, P.A. Modal Analysis of Cylinder-Induced Transitional Shock-Wave/Boundary-Layer Interaction Unsteadiness. AIAA J.
**2022**, 60, 2730–2748. [Google Scholar] [CrossRef] - Estruch, D.; MacManus, D.G.; Richardson, D.P.; Lawson, N.J.; Garry, K.P.; Stollery, J.L. Experimental study of unsteadiness in supersonic shock-wave/turbulent boundary-layer interactions with separation. Aeronaut. J.
**2010**, 114, 299–308. [Google Scholar] [CrossRef] - Combs, C.S.; Lash, E.L.; Kreth, P.A.; Schmisseur, J.D. Investigating Unsteady Dynamics of Cylinder-Induced Shock-Wave/Transitional Boundary-Layer Interactions. AIAA J.
**2018**, 56, 1588–1599. [Google Scholar] [CrossRef] - Clemens, N.T.; Narayanaswamy, V. Low-Frequency Unsteadiness of Shock Wave/Turbulent Boundary Layer Interactions. Annu. Rev. Fluid Mech.
**2014**, 46, 469–492. [Google Scholar] [CrossRef][Green Version] - Murphree, Z.R.; Combs, C.S.; Yu, W.M.; Dolling, D.S.; Clemens, N.T. Physics of unsteady cylinder-induced shock-wave/transitional boundary-layer interactions. J. Fluid Mech.
**2021**, 918, A39. [Google Scholar] [CrossRef] - Combs, C.S.; Schmisseur, J.D.; Bathel, B.F.; Jones, S.B. Unsteady Analysis of Shock-Wave/Boundary-Layer Interaction Experiments at Mach 4.2. AIAA J.
**2019**, 57, 4715–4724. [Google Scholar] [CrossRef] - Combs, C.S.; Kreth, P.A.; Schmisseur, J.D.; Lash, E.L. Image-Based Analysis of Shock-Wave/Boundary-Layer Interaction Unsteadiness. AIAA J.
**2018**, 56, 1288–1293. [Google Scholar] [CrossRef] - Sun, Z.; Gan, T.; Wu, Y. Shock-Wave/Boundary-Layer Interactions at Compression Ramps Studied by High-Speed Schlieren. AIAA J.
**2020**, 58, 1681–1688. [Google Scholar] [CrossRef] - Dolling, D.S.; Or, C.T. Unsteadiness of the shock wave structure in attached and separated compression ramp flows. Exp. Fluids
**1985**, 3, 24–32. [Google Scholar] [CrossRef] - Kreth, P.A.; Gragston, M.; Davenport, K.; Schmisseur, J.D. Design and Initial Characterization of the UTSI Mach 4 Ludwieg Tube. In Proceedings of the AIAA Scitech 2021 Forum, Virtual, 11–21 January 2021. [Google Scholar] [CrossRef]
- Cobourn, J.W. Optical Measurements of Viscous Interactions on a Hollow-Cylinder/Flare in a Mach 4 Freestream. Master’s Thesis, The University of Tennessee, Knoxville, TN, USA, 2020. [Google Scholar]
- Settles, G.; Covert, E. Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transport Media; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2001. [Google Scholar] [CrossRef]
- Willert, C.E.; Mitchell, D.M.; Soria, J. An assessment of high-power light-emitting diodes for high frame rate schlieren imaging. Exp. Fluids
**2012**, 53, 413–421. [Google Scholar] [CrossRef]

**Figure 1.**Dimensional schematics of the hollow cylinder flare model, (

**a**) smooth surface, (

**b**) top view, and (

**c**) rough surface.

**Figure 3.**Representative schlieren images demonstrating computed shock positions of rough surface, (

**a**) instantaneous images, and (

**b**) corresponding shock tracking images.

**Figure 4.**Instantaneous (top) and mean (bottom) schlieren visualizations of SWBLI, (

**a**) smooth surface, and (

**b**) rough surface.

**Figure 6.**RMS fields for SWBLI, (

**a**) smooth surface, and (

**b**) rough surface. The white dashed lines indicate the mean shock position for each case.

**Figure 7.**(

**a**) Normalized shock foot location time series, and (

**b**) histogram normalized as a PDF of smooth and rough SWBLI mean shock foot location.

**Figure 8.**(

**a**) Intermittency of the rough and smooth surfaces’ ${L}_{s}$, and (

**b**) zero-crossing frequency of the shock foot location for smooth and rough surfaces.

**Figure 9.**(

**a**) Power spectral density of shock location versus frequency, (

**b**) coherence for rough and smooth surface, (

**c**) power spectral density of shock location versus Strouhal number (intermittent length scaling), (

**d**) power spectral density of shock location versus Strouhal number (boundary layer thickness scaling).

**Figure 10.**Plots of Strouhal number in the interactions region for representative (

**a**) smooth and (

**b**) rough interactions. The white dashed lines indicate the mean shock positions for each case.

**Figure 11.**Normalized power spectra of high-speed schlieren images, averaged over different frequency bands for smooth surface.

**Figure 12.**Normalized power spectra of high-speed schlieren images, averaged over different frequency bands for rough surface.

Case | Stagnation Pressure (kPa) | Static Pressure (kPa) | Stagnation Temperature (K) | Free Stream Velocity (m/s) | $\mathit{R}\mathit{e}/\mathit{x}\text{}\left({\mathbf{m}}^{-1}\right)$ |
---|---|---|---|---|---|

Smooth | 374 | 2.9 | 295 | 672 | 17.2 × 10^{6} |

Rough | 427 | 3.1 | 299 | 672 | 19.7 × 10^{6} |

Surface | Image Resolution | Acquisition Rate | Scale | Camera Lens |
---|---|---|---|---|

Smooth | 640 × 122 pixels | 200 kHz | 10.95 pixel/mm | 300 mm lens + 2x teleconverter |

Rough | 384 × 176 pixels | 200 kHz | 2.19 pixel/mm | 70–200 mm lens |

Surface | ${\mathit{R}}_{\mathit{a}}\text{}\left(\mathsf{\mu}\mathbf{m}\right)$ | δ (mm) | $\mathit{\theta}$ (deg) | ${\mathit{L}}_{\mathit{i}}\text{}\left(\mathbf{mm}\right)$ | ${\mathit{L}}_{\overline{\mathit{s}}}$$\text{}(\mathit{x}/\mathit{\delta})$ | σ | ${\mathit{\sigma}}^{2}$ | Kurtosis | Skewness |
---|---|---|---|---|---|---|---|---|---|

Smooth | 0.85 | 2.6 | 29 | 12 | −5 | 0.98 | 0.97 | 4.3 | −0.55 |

Rough | 9.22 | 11.4 | 20 | 71 | −10 | 1.49 | 2.23 | 3.4 | −0.77 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Garcia, M.; Hoffman, E.N.A.; LaLonde, E.J.; Combs, C.S.; Pohlman, M.; Smith, C.; Gragston, M.T.; Schmisseur, J.D. Effects of Surface Roughness on Shock-Wave/Turbulent Boundary-Layer Interaction at Mach 4 over a Hollow Cylinder Flare Model. *Fluids* **2022**, *7*, 286.
https://doi.org/10.3390/fluids7090286

**AMA Style**

Garcia M, Hoffman ENA, LaLonde EJ, Combs CS, Pohlman M, Smith C, Gragston MT, Schmisseur JD. Effects of Surface Roughness on Shock-Wave/Turbulent Boundary-Layer Interaction at Mach 4 over a Hollow Cylinder Flare Model. *Fluids*. 2022; 7(9):286.
https://doi.org/10.3390/fluids7090286

**Chicago/Turabian Style**

Garcia, Matt, Eugene N. A. Hoffman, Elijah J. LaLonde, Christopher S. Combs, Mason Pohlman, Cary Smith, Mark T. Gragston, and John D. Schmisseur. 2022. "Effects of Surface Roughness on Shock-Wave/Turbulent Boundary-Layer Interaction at Mach 4 over a Hollow Cylinder Flare Model" *Fluids* 7, no. 9: 286.
https://doi.org/10.3390/fluids7090286