Numerical study of bluntness effects on laminar leading edge separation in hypersonic flow.

*(English)*Zbl 1430.76352Summary: Bluntness effects on laminar hypersonic leading edge separation are investigated numerically at Mach number \(M\approx 10\), unit Reynolds number \(Re=1.3\times 10^6\text{m}^{-1} \), specific enthalpy \(h_o=3.1\text{MJ}\,\text{kg}^{-1}\) and wall-to-stagnation temperature ratio \(T_w/T_o=0.1\). Such effects are important from an experimental point of view and because bluntness can affect a separated flow favourably or adversely. In this study, two blunt leading edge cases of small radius \((15\mu\text{m})\) and large radius \((100\mu\text{m})\) are investigated. A comparison with the idealised sharp leading edge case is also given. General flow features and surface parameters such as the shear stress, pressure and heat flux are presented and analysed. The results have also been interpreted in terms of Cheng’s displacement-bluntness similitude parameter affecting the size of separation. Previous experiments by Holden delineated small and large bluntness effects based on Cheng’s parameter and considering small to moderate separated regions. In this study, leading edge separation was found to suppress the favourable effect of bluntness in delaying separation. Bluntness, furthermore, seemed to promote the appearance of secondary vortices within a main separated region. Analysis of reverse flow boundary layer profiles such as velocity, pressure and temperature is also given. It is shown that bluntness accentuates large transverse gradients. This in turn adversely effects the reverse flow boundary layer leading to the appearance of secondary vortices.

##### MSC:

76K05 | Hypersonic flows |

76N20 | Boundary-layer theory for compressible fluids and gas dynamics |

76M99 | Basic methods in fluid mechanics |

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##### References:

[1] | ,, Viscous and leading-ddge thickness effects on the pressures on the surface of a flat plate in hypersonic flow, J. Aero. Sci., 21, 6, 430-431, (1954) |

[2] | , & , 1958 Effects of boundary-layer displacement and leading-edge bluntness on pressure distribution, skin friction, and heat transfer of bodies at hypersonic speeds. NACA Tech. Note 4301. |

[3] | ,; ,; ,; ,; ,, Leading edge bluntness effect on the flow in a model air-inlet, Fluid Dyn., 49, 4, 454-467, (2014) · Zbl 1301.76003 |

[4] | ,; ,; ,, On the existence of a threshold value of the plate bluntness in the interference of an oblique shock with boundary and entropy layers, Fluid Dyn., 43, 3, 369-379, (2008) |

[5] | , 1956 Effect of leading-edge geometry on boundary-layer transition at mach 3.1. NACA Tech. Note 3659. |

[6] | ,; ,; ,, Inviscid-viscous interaction on triple-deck scales in a hypersonic flow with strong wall cooling, J. Fluid Mech., 220, 309-337, (1990) · Zbl 0711.76055 |

[7] | ,; ,, Laminar separation, Annu. Rev. Fluid Mech., 1, 1, 45-72, (1969) |

[8] | ,; ,; ,; ,, Effect of Reynolds number on laminar separation of a supersonic stream, AIAA J., 17, 4, 336-343, (1979) · Zbl 0396.76040 |

[9] | , , , , , , , , , & , 2015 Development of the us3d code for advanced compressible and reacting flow simulations. In 53rd AIAA Aerospace Sciences Meeting, AIAA Paper 2015-1893. |

[10] | ,; ,; ,, Advances in computational fluid dynamics methods for hypersonic flows, J. Spacecr. Rockets, 52, 1, 17-28, (2014) |

[11] | ,; ,; ,, An instability in supersonic boundary-layer flow over a compression ramp, J. Fluid Mech., 300, 265-285, (1995) · Zbl 0848.76020 |

[12] | ,; ,; ,, The influence of wall cooling on hypersonic boundary-layer separation and stability, J. Fluid Mech., 321, 189-216, (1996) · Zbl 0890.76073 |

[13] | ,; ,, The integration of the two-dimensional laminar boundary-layer equations past the point of vanishing skin friction, J. Fluid Mech., 26, 1, 163-182, (1966) |

[14] | , , , & , 1958 Investigation of separated flows in supersonic and subsonic streams with emphasis on the effect of transition. NACA Tech. Rep. 1356. |

[15] | ,; ,; ,; ,, Boundary-layer displacement and leading-edge bluntness effects in high-temperature hypersonic flow, J. Aero. Sci., 28, 5, 353-381, (1961) · Zbl 0098.40101 |

[16] | ,; ,, Inviscid leading-edge effect in hypersonic flow, J. Aero. Sci., 23, 7, 700-702, (1956) |

[17] | , 1999Quasi-simultaneous coupling for wing and airfoil flow. In Domain Decomposition Methods in Science and Engineering, pp. 197-205. Domain Decomposition Press. |

[18] | , 1959 The effect of leading-edge sweep and surface inclination on the hypersonic flow field over a blunt flat plate. NASA-MEMO-12-26-58A. |

[19] | , & , 1997Numerical investigation of boundary-layer instabilities over a blunt flat plate at angle of attack in supersonic flow. In New Results in Numerical and Experimental Fluid Mechanics, pp. 103-110. Springer. |

[20] | , , , & , 2006Numerical simulation of the AEDC waverider at Mach 8. In 25th AIAA Aerodynamic Measurement Technology and Ground Testing Conference, AIAA 2006-2816. |

[21] | ,, Effects of shock impingement on the heat transfer around blunt bodies, AIAA J., 6, 1, 15-21, (1968) |

[22] | , & , 1968 Low-density, leading-edge bluntness, and ablation effects on wedge-induced laminar boundary layer separation at moderate enthalpies in hypersonic flow. NASA Tech. Note D-4829. |

[23] | ,, An experimental investigation of heat transfer effects on boundary layer separation in supersonic flow, J. Fluid Mech., 2, 2, 105-122, (1957) |

[24] | ,, On laminar boundary-layer flow near a position of separation, Q. J. Mech. Appl. Maths, 1, 1, 43-69, (1948) · Zbl 0033.31701 |

[25] | , & , 1972 Effects of wall cooling and leading-edge blunting on ramp-induced, laminar flow separations at Mach numbers from 3 through 6. Tech. Rep. Arnold Engineering Development Center. AEDC-TR-71-274. |

[26] | ,, Experimental studies on the lip shock, AIAA J., 6, 2, 212-219, (1968) |

[27] | ,, Viscous hypersonic similitude, J. Aero. Sci., 26, 12, 815-824, (1959) · Zbl 0093.18804 |

[28] | ,; ,, Hypersonic Flow Theory, (1959), Elsevier |

[29] | ,, Basics of Aerothermodynamics, (2005), Springer |

[30] | ,, Experimental studies of separated flows at hypersonic speeds. II - Two-dimensional wedge separated flow studies, AIAA J., 4, 5, 790-799, (1966) |

[31] | ,, Boundary-layer displacement and leading-edge bluntness effects on attached and separated laminar boundary layers in a compression corner. II - Experimental study, AIAA J., 9, 1, 84-93, (1971) |

[32] | , , , , , & , 2013 Measurements of real gas effects on regions of laminar shock wave/boundary layer interaction in hypervelocity flows for blindcode validation studies. In 21st AIAA Computational Fluid Dynamics Conference, 24-27 June, San Diego, California, USA, AIAA-2013-2837, p. 2837. |

[33] | , , , & , 1965 An Investigation of Heat Transfer within Regions of Separated Flow at a Mach Number of 6.0. NASA Tech. Note TN D-3074. |

[34] | ,, Optical Studies and Simulations of Hypervelocity Flow Fields Around Blunt Bodies, (2010), Citeseer |

[35] | ,; ,, Effect of leading edge bluntness on the interaction of ramp induced shock wave with laminar boundary layer at hypersonic speed, Comput. Fluids, 96, 177-190, (2014) · Zbl 1391.76280 |

[36] | ,, Hypersonic viscous interaction on sharp and blunt inclined plates, AIAA J., 7, 7, 1280-1289, (1969) |

[37] | ,; ,; ,, Hypersonic boundary-layer separation on a cold wall, J. Fluid Mech., 274, 163-195, (1994) · Zbl 0837.76019 |

[38] | ,; ,, Hypersonic aerodynamics on thin bodies with interaction and upstream influence, J. Fluid Mech., 277, 85-108, (1994) · Zbl 0865.76034 |

[39] | , 2018 Laminar hypersonic leading edge separation. PhD thesis, University of New South Wales. |

[40] | , , , , , & , 2014Hypersonic leading edge separation. In 19th Australasian Fluid Mechanics Conference, vol. 1, pp. 268-271. Australasian Fluid Mechanics Society. |

[41] | ,; ,; ,; ,, Laminar hypersonic leading edge separation – a numerical study, J. Fluid Mech., 821, 624-646, (2017) · Zbl 1383.76317 |

[42] | , , , & , 2015 Numerical investigation of bluntness effects on hypersonic leading edge separation. In 53rd AIAA Aerospace Sciences Meeting, Kissimmee, Florida, AIAA-2015-0984. |

[43] | ,, Viscous-inviscid flow matching: Analysis of the problem including separation and shock waves, La Rech. Aerospatialele, 1977‐6, 349-358, (1977) |

[44] | ,, Viscous-inviscid flow matching: Numerical method and applications to two-dimensional, transonic and supersonic flows, La Rech. Aerospatiale, Bull. Bimestriel, (Paris), 183, 65-76, (1978) |

[45] | , , , , , & , 2019Rotational temperature imaging of a leading-edge separation in hypervelocity flow. In 31st International Symposium on Rarefied Gas Dynamics, . 110001. |

[46] | , & , 1952Hypersonic viscous flow over a flat plate. In Physical Review, vol. 86, pp. 600-600. · Zbl 0637.60004 |

[47] | , 1953 On boundary layers and upstream influence. II. Supersonic flows without separation. 217 (1131), 478-507. · Zbl 0053.14702 |

[48] | ,; ,; ,, High-enthalpy, hypersonic compression corner flow, AIAA J., 34, 6, 1130-1137, (1996) |

[49] | , 1998 Effects of flow and geometry parameters on shock-wave boundary-layer interaction phenomena. In 8th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, Norfolk, VA, USA, AIAA-98-1570. |

[50] | ,; ,, Aerodynamically blunt and sharp bodies, J. Spacecr. Rockets, 31, 3, 378-382, (1994) |

[51] | ,, Boundary-layer flow near the trailing edge of a flat plate, SIAM J. Appl. Maths, 18, 1, 241-257, (1970) · Zbl 0195.27701 |

[52] | , 1957 Some effects of bluntness on boundary-layer transition and heat transfer at supersonic speeds. NACA Tech. Rep. TR-1312. |

[53] | ,; ,; ,, Roughness, bluntness, and angle-of-attack effects on hypersonic boundary-layer transition, J. Fluid Mech., 24, 1, 1-31, (1966) |

[54] | ,, Theory of laminar boundary layer separation in supersonic flow, Fluid Dyn., 4, 4, 33-35, (1969) · Zbl 0256.76041 |

[55] | ,, Asymptotic theory of plane steady supersonic flows with separation zones, Fluid Dyn., 5, 3, 372-381, (1970) |

[56] | , 1973Special features of boundary-layer separation on a cooled body and its interaction with a hypersonic flow. Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza6, 99-109 (translation in Fluid Dyn.8 (6), 931-939). |

[57] | , , , & , 2009Temperature factor effect on separated flow features in supersonic gas flow. In BAIL 2008-Boundary and Interior Layers, pp. 39-54. Springer. · Zbl 1179.35222 |

[58] | , & , 2014 US3D predictions of double-cone and hollow cylinder-flare flows at high enthalpy. In 44th AIAA Fluid Dynamics Conference, Atlanta, GA, USA, AIAA 2014-3366. |

[59] | , 1957The conditions for the separation of boundary layers. In Contributions to the Development of Gasdynamics, pp. 6-18. Springer. |

[60] | , 1977 Dominance of radiated aerodynamic noise on boundary-layer transition in supersonic-hypersonic wind tunnels: theory and application. PhD thesis, University of Tennessee, Knoxville, TN. |

[61] | ,, On fluid motions with very small friction, Verhldg, 3, 484-491, (1904) |

[62] | ,, Grid convergence error analysis for mixed-order numerical schemes, AIAA J., 41, 4, 595-604, (2003) |

[63] | ,, Leading-edge bluntness effects on aerodynamic heating and drag of power law body in low-density hypersonic flow, J. Braz. Soc. Mech. Sci. Engng, 27, 3, 236-242, (2005) |

[64] | ,; ,; ,, Surface-cooling effects on compressible boundary-layer instability, Eur. J. Mech. (B/Fluids), 10, 2, 117-145, (1991) · Zbl 0725.76043 |

[65] | ,, About the secondary separation at supersonic flow over a compression ramp, TsAGI Sci. J., 40, 5, 587-607, (2009) |

[66] | ,, Steady and unsteady boundary-layer separation, Annu. Rev. Fluid Mech., 18, 1, 197-220, (1986) |

[67] | ,, A reversed flow singularity in interacting boundary layers, Proc. R. Soc. Lond. A, A420, 21-52, (1988) · Zbl 0655.76030 |

[68] | , 1969Boundary layer transition on hypersonic blunt, slender cones. In 2nd Fluid and Plasma Dynamics Conference, San Francisco, CA, USA, AIAA 1969-705. |

[69] | , 1978 Effect of bluntness and angle of attack on boundary layer transition on cones and biconic configurations. In Proceedings of 17th Aerospace Sciences Meeting, New Orleans, LA, USA, AIAA-1979-269. |

[70] | , 1964The Theory of Laminar Boundary Layers in Compressible Fluids, vol. 3. Clarendon Press. · Zbl 0114.18705 |

[71] | ,, On laminar boundary layers near corners, Q. J. Mech. Appl. Maths, 23, 2, 137-152, (1970) · Zbl 0201.29601 |

[72] | ,, Multistructured boundary layers on flatplates and related bodies, Adv. Appl. Mech., 14, 145-239, (1974) |

[73] | ,; ,, Self-induced separation, Proc. R. Soc. Lond. A, 312, 1509, 181-206, (1969) · Zbl 0184.52903 |

[74] | , 1972Viscous interaction effects on re-entry aerothermodynamics: theory and experimental results. AGARD Lecture Series42, 10-1-10-28. |

[75] | ,, Laminar separation, Fluid Dyn., 7, 3, 407-417, (1972) · Zbl 0313.76017 |

[76] | ,, The formation of a blast wave by a very intense explosion. I. Theoretical discussion, Proc. R. Soc. Lond. A, 201, 1065, 159-174, (1950) · Zbl 0036.26404 |

[77] | , 1966 Effects of leading-edge bluntness and ramp deflection angle on laminar boundary-layer separation in hypersonic flow. NASA Tech. Note D-3290. |

[78] | ,, Similarity laws of hypersonic flows, Stud. Appl. Maths, 25, 1-4, 247-251, (1946) · Zbl 0063.07867 |

[79] | ,; ,; ,, Investigation of unsteady, hypersonic, laminar separated flows over a double cone geometry using a kinetic approach, Phys. Fluids, 30, 4, (2018) |

[80] | ,, Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method, J. Comput. Phys., 32, 1, 101-136, (1979) · Zbl 1364.65223 |

[81] | , 1979 A numerical method for the calculation of laminar, incompressible boundary layers with strong viscous-inviscid interaction. Tech. Rep. NLR TR 79023. National Aerospace Laboratory. |

[82] | , 1980Boundary layers with strong interaction: from asymptotic theory to calculation method. In BAIL 1 Conf. on Boundary and Interior Layers - Computation and Asymptotic Methods, pp. 149-163. Boole Press. |

[83] | ,; ,, New method for supersonic boundary-layer separations, AIAA J., 12, 11, 1491-1497, (1974) · Zbl 0298.76039 |

[84] | ,; ,; ,, Data parallel line relaxation method for the Navier-Stokes equations, AIAA J., 36, 9, 1603-1609, (1998) |

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