Assessment of Pseudoshock Models Against Experiment in a Low-Aspect-Ratio Isolator
Abstract
A highly confined shock train is investigated in a direct-connect isolator facility with a Mach 2 inflow and a constant-area low-aspect-ratio rectangular test section. High-speed schlieren imaging, wall static pressure measurements, surface oil-flow visualization, and particle image velocimetry from this isolator are synthesized into a three-dimensional schematic of the shock train structure. Against this, the prevailing pseudoshock models in the literature are assessed to evaluate the validity of their underlying assumptions. None of the prevailing pseudoshock models are found to simultaneously model the pressure and Mach number profiles, indicating a gap in the model formation and underlying assumptions when applied to the experimental isolator of interest. The presence of distortion in the isolator flowfield, such as a wall-bounded vortex, is found to skew the structure of the shock train, altering the strength and distribution of the compressive pressure gradient. It is further observed that the separated flow morphology surrounding the shock train is not monolithic, as is typically assumed, adjusting the balance of compressive forces within the shock cells. These findings lead to the conclusion that existing flux-conserved modeling approaches require modification to be effective in distorted and highly confined cases, including closure models that capture the three-dimensional distorted structure of the approach flow and its evolution along the shock train.
References
[1] , “Shock Train and Pseudo-Shock Phenomena in Internal Gas Flows,” Progress in Aerospace Sciences, Vol. 35, No. 1, 1999, pp. 33–100. https://doi.org/10.1016/S0376-0421(98)00011-6
[2] , “Pseudo-Shock Waves and their Interactions in High-Speed Intakes,” Progress in Aerospace Sciences, Vol. 82, April 2016, pp. 36–56. https://doi.org/10.1016/j.paerosci.2016.02.001
[3] , “Unstart Phenomena Induced by Flow Choking in Scramjet Inlet-Isolators,” Progress in Aerospace Sciences, Vol. 97, Feb. 2018, pp. 1–21. https://doi.org/10.1016/j.paerosci.2017.12.001
[4] , “Scaling of Pseudoshock Length and Pressure Rise,” 2018 AIAA Aerospace Sciences Meeting, AIAA Paper 2018-1617, 2018. https://doi.org/10.2514/6.2018-1617
[5] , “Locations and Oscillation Phenomena of Pseudo-Shock Waves in a Straight Rectangular Duct,” Japan Society of Mechanical Engineers International Journal, Series 2: Fluids Engineering, Heat Transfer, Power, Combustion, Thermophysical Properties, Vol. 31, No. 1, 1988, pp. 9–15. https://doi.org/10.1299/jsmeb1988.31.1_9
[6] , “On the Origin and Propagation of Perturbations that Cause Shock Train Inherent Unsteadiness,” Journal of Fluid Mechanics, Vol. 861, Feb. 2019, pp. 815–859. https://doi.org/10.1017/jfm.2018.927
[7] , “Experimental Results of Shock Trains in Rectangular Ducts,” 4th Symposium on Multidisciplinary Analysis and Optimization, AIAA Paper 1992-5103, 1992. https://doi.org/10.2514/6.1992-5103
[8] , “Characteristics of Multiple Shock Wave/Turbulent Boundary Layer Interactions in Rectangular Ducts,” 1st National Fluid Dynamics Conference, AIAA Paper 1988-3803, 1988. https://doi.org/10.2514/6.1988-3803
[9] , “Large-Eddy Simulations of a Normal Shock Train in a Constant-Area Isolator,” AIAA Journal, Vol. 52, No. 3, 2014, pp. 539–558. https://doi.org/10.2514/1.J052348
[10] , “Numerical Investigation of Shock-Train Response to Inflow Boundary-Layer Variations,” AIAA Journal, Vol. 55, No. 9, 2017, pp. 2888–2901. https://doi.org/10.2514/1.J055333
[11] , “Corner flow Separation from Shock Train/Turbulent Boundary-Layer Interactions in Rectangular Isolators,” 20th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, AIAA Paper 2015-3546, 2015. https://doi.org/10.2514/6.2015-3546
[12] , “Shock Train Unsteadiness Characteristics, Oblique-to-Normal Transition, and Three-Dimensional Leading Shock Structure,” AIAA Journal, Vol. 56, No. 4, 2018, pp. 1569–1587. https://doi.org/10.2514/1.J056344
[13] , “Structure of Shock Waves in Cylindrical Ducts,” AIAA Journal, Vol. 11, No. 10, 1973, pp. 1404–1408. https://doi.org/10.2514/3.50600
[14] , “Research on Supersonic Combustion,” Journal of Propulsion and Power, Vol. 9, No. 4, 1993, pp. 499–514. https://doi.org/10.2514/3.23652
[15] , “Flow Modeling of Pseudoshocks in Backpressured Ducts,” AIAA Journal, Vol. 53, No. 12, 2015, pp. 3577–3588. https://doi.org/10.2514/1.J054021
[16] , “Simple Physics-Based Model for the Prediction of Shock-Train Location,” Journal of Propulsion and Power, Vol. 34, No. 6, 2018, pp. 1428–1441. https://doi.org/10.2514/1.B37031
[17] , “Data-Driven One-Dimensional Modeling of Pseudoshocks,” Journal of Propulsion and Power, Vol. 35, No. 2, 2019, pp. 313–327. https://doi.org/10.2514/1.B37175
[18] , “Rigid Body Response of a Mach 2 Shock Train to Downstream Forcing,” 2018 Fluid Dynamics Conference, AIAA Paper 2018-3542, 2018. https://doi.org/10.2514/6.2018-3542
[19] , “Theoretical Pressure Recovery Through a Normal Shock in a Duct with Initial Boundary Layer,” Journal of the Aeronautical Sciences, Vol. 20, No. 3, 1953, pp. 169–174. https://doi.org/10.2514/8.2582
[20] , “One-Dimensional Treatment of Compressible Flow Through a Duct,” Transactions of the Japan Society of Mechanical Engineers, Series B, Vol. 58, No. 549, 1992, pp. 1650–1653. https://doi.org/10.1299/kikaib.58.1650
[21] , “Mass-Averaging Pseudo-Shock Model in a Straight Flow Passage,” Proceedings of the Institution of Mechanical Engineers: Journal of Aerospace Engineering, Part G, Vol. 213, No. 6, 1999, Paper 365. https://doi.org/10.1243/0954410991533089
[22] , “One-Dimensional Treatment of Steady Gas Dynamics,” Fundamentals of Gas Dynamics: High Speed Aerodynamics and Jet Propulsion, Princeton Legacy Library, 1st ed., edited by Emmons H. W., Vol. 3, Princeton Univ. Press, Princeton, NJ, 1958, pp. 64–349.
[23] , “Scramjet Flowpath Integration,” Scramjet Propulsion, 1st ed., edited by Murthy S. and Curran E., Vol. 189,
Progress in Astronautics and Aeronautics , AIAA, Reston, VA, 2000, pp. 1105–1293.[24] , “Motion of Particles with Inertia in a Compressible Free Shear Layer,” Physics of Fluids A: Fluid Dynamics, Vol. 3, No. 8, 1991, pp. 1915–1923. https://doi.org/10.1063/1.857921
[25] , Dynamic and Thermodynamics of Compressible Flow, 1st ed., Vol. 1, Ronald, New York, 1953, pp. 78–82.
[26] , “PIV Uncertainty Quantification from Correlation Statistics,” Measurement Science and Technology, Vol. 26, No. 7, 2015, Paper 074002. https://doi.org/10.1088/0957-0233/26/7/074002
[27] , “Collaborative Framework for PIV Uncertainty Quantification: Comparative Assessment of Methods,” Measurement Science and Technology, Vol. 26, No. 7, 2015, Paper 74004. https://doi.org/10.1088/0957-0233/26/7/074004.
[28] , “PIV Uncertainty Propagation,” Measurement Science and Technology, Vol. 27, No. 8, 2016, Paper 084006. https://doi.org/10.1088/0957-0233/27/8/084006.
[29] , “Effect of Turbulence Model Uncertainty on Scramjet Isolator Flowfield Analysis,” Journal of Propulsion and Power, Vol. 36, No. 1, 2020, pp. 109–122. https://doi.org/10.2514/1.B37597
[30] , “Effect of Vibrational Nonequilibrium on Isolator Shock Structure,” Journal of Propulsion and Power, Vol. 34, No. 5, 2018, pp. 1334–1344. https://doi.org/10.2514/1.B37108
[31] , “Corner Separation Effects for Normal Shock Wave/Turbulent Boundary Layer Interactions in Rectangular Channels,” Journal of Fluid Mechanics, Vol. 707, Sept. 2012, pp. 287–306. https://doi.org/10.1017/jfm.2012.279
[32] , “Three-Dimensional Nature of Shock Trains in Rectangular Scramjet Isolators,” 54th AIAA Aerospace Sciences Meeting, AIAA Paper 2016-1164, 2016. https://doi.org/10.2514/6.2016-1164
[33] , “Relationship between Intermittent Separation and Vortex Structure in a Three-Dimensional Shock/Boundary-Layer Interaction,” AIAA Journal, Vol. 54, No. 6, 2016, pp. 1862–1880. https://doi.org/10.2514/1.J053905
[34] , Shock Wave-Boundary-Layer Interactions, 1st ed., Cambridge Univ. Press, Cambridge, England, U.K., 2011, pp. 202–258, Chap. 5. https://doi.org/10.1017/CBO9780511842757