Hypersonic Shock Wave-Boundary Layer Interaction and Leading Edge Slip

Nagamatsu, H. T.; Sheer, R. E.

doi:10.2514/8.5118

Cited by 19 publications

(19 citation statements)

References 14 publications

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“…Even under continuum flow conditions (kn<<1) the existence of slip near leading edge for very large Mach numbers was reported elsewhere (Nagamatsu, et al, 1961). According to the theory developed by those authors, the length of the slip region can be assumed as proportional to the free stream Mach number.…”

Section: Experimental Work A) T3 Shock Tunnel Facilitymentioning

confidence: 99%

“…While M ∞ is the free stream Mach number, μ is the dynamic viscosity ρ is the density and the subscript w relates to the wall and e to the edge of the boundary layer, respectively. The effects of the hypersonic viscous interactions on the pressure distribution over a flat plate as function of the parameter χ were presented in several works (Nagamatsu, et al, 1961;Hayes, et al, 1959;Minucci, 1991;Anderson, 1989). A common result is that the induced pressure change varies linearly with χ .Thus, one can write: Shock Wave Angle (degrees) Figure 14: Main characteristics of a separated flow over a compression ramp.…”

Section: Experimental Work A) T3 Shock Tunnel Facilitymentioning

confidence: 99%

“…Several works (Nagamatsu, et al, 1961;Nagamatsu, et al, 1960;Hayes, et al, 1959) have shown the existence of the three different flow field regions downstream the leading edge of a …”

Section: C) Airflow Visualizationmentioning

confidence: 99%

See 2 more Smart Citations

Experimental results of a Mach 10 conical-flow derived waverider to 14-X hypersonic airspace vehicle

Rolim¹,

Toro²,

Minucci³

et al. 2011

JATM

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Section: Experimental Work A) T3 Shock Tunnel Facilitymentioning

confidence: 99%

Section: Experimental Work A) T3 Shock Tunnel Facilitymentioning

confidence: 99%

See 1 more Smart Citation

Experimental results of a Mach 10 conical-flow derived waverider to 14-X hypersonic airspace vehicle

Rolim¹,

Toro²,

Minucci³

et al. 2011

JATM

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“…For the wedge surface parallel to the free stream direction, the flow deflection may be as large as 9 deg. This is due entirely to viscosity as determined from the shock wave experiments with a flat plate (9). A detailed discussion of these experiments along with the associated theory for the slip phenomena and the strong shock waveboundary layer interaction is presented in (9 and 10).…”

Section: Shock Wave Anglementioning

confidence: 99%

Oblique Shock Relations for Air at Mach 7.8 and 7200 R Stagnation Temperature

Nagamatsu

1960

ARS Journal

Self Cite

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Oblique shock relations for dissociated air in thermodynamic equilibrium have been calculated for a free stream flow Mach number of 7.8 in the test section with an equilibrium stagnation temperature of 7200 R in the reservoir. The results for the density, pressure and temperature ratios, and flow deflection across the shock wave are presented as functions of the shock wave angle. Complete equilibrium has been assumed in the calculations, utilizing the best available thermodynamic properties of air for the region considered. The real gas oblique shock relations have been experimentally verified by testing an adjustable two-dimensional wedge model in a hypersonic shock tunnel. Correlations of the calculated and experimental pressure ratios and shock wave angles are presented as functions of flow deflection angle. When allowance was made for the boundary layer displacement effect, the correlation was seen to be good. The reservoir conditions were selected to insure that the flow in the shock tunnel would be close to equilibrium.T HE ADVENT of missiles and space vehicles traveling at hypersonic flight speeds has recently stimulated much interest in the shock waves produced by such bodies. In particular, there has been considerable discussion of the "real gas effects" in the air immediately behind high Mach number shock waves. By "real gas effects" is meant the departure of the thermodynamic properties of the medium from a perfect gas with a constant specific heat ratio of 1.4. Although air departs from this perfect gas model at temperatures as low as 540 R, this concept has been used with considerable success in the past for analyzing low Mach number shock properties. However, at any flow condition even approaching that under consideration here, this model must be abandoned and, instead, the actual thermodynamic properties of air used.As soon as shock waves strong enough to excite vibration, dissociation or ionization and strong enough to produce chemical reactions are considered, the reaction rate question immediately comes to the forefront. In dealing with shock processes wherein a gas is required to absorb large quantities of kinetic energy as internal energy virtually instantaneously, one must be concerned not only with the final thermodynamic properties, but also with the time needed.to achieve thermodynamic equilibrium. A rigorous analytical method for treating the shock problem w r ould be to set up a careful kinetic theory model of the gas molecules with reaction rates, and then to analyze exactly what happens as the flow proceeds through the momentum and energy readjustments at the shock region. Unfortunately, there is insufficient knowledge of the properties and reaction rates of air at the present time to employ such a method. It is conceivable also that even if all of the rate constants and interaction parameters were known, the complexity of the calculation would prevent a practical solution.Recently (1,2) 5 shock relations for air under the assumption of instantaneous thermodynamic equilibrium downstrea...

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“…In region I, near the plate leading edge, there exists a delay in the formation of the shock layer and the boundary layer as a result of the slip phenomena in this region 3 . Close to the leading edge, the slip condition is stated and the flow is not a continuum, so that the Navier-Stokes equations are not valid 3 , and the first order kinetic flow theory should be applied 4 .…”

Section: Introductionmentioning

confidence: 99%

Self-similar compressible laminar boundary layers

Toro

Rusak

Nagamatsu

et al. 1997

35th Aerospace Sciences Meeting and Exhibit

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A new method of deriving a self-similar solution of the compressible laminar boundary layer equations is obtained for air as calorically or thermally perfect gas and where the viscosity is a power function of the temperature. Modified Levy-Mangier and Dorodnitsyn-Howarth transformations are introduced to solve the flow in a thin laminar boundary layer with no external pressure gradient and on a smooth flat plate. These transformations describe the similarity variable in terms of a power of the density that takes into account the viscosity-temperature power law relation. This results in an explicit relation between the stream function and the temperature fields described by a closed coupled system of nonlinear ordinary differential equations. Solutions are presented for boundary layer flows with Mach number of the external flow up to 4. The influence of the flow Prandtl number, wall to freestream temperature ratio, and power of the viscosity-temperature law is investigated. The present methodology also provides a simple way of comparing results according to various assumptions about the viscosity-temperature relations. (Author) ABSTRACTA new method of deriving a self-similar solution of the compressible laminar boundary layer equations is obtained for air as calorically or thermally perfect gas and where the viscosity is a power function of the temperature. Modified LevyMangier and Dorodnitsyn-Howarth transformations are introduced to solve the flow in a thin laminar boundary layer with no external pressure gradient and on a smooth flat plate. These transformations describe the similarity variable in terms of a power of the density that takes into account the viscositytemperature power law relation. This results in an explicit relation between the stream function and the temperature fields described by a closed coupled system of nonlinear ordinary differential equations. Solutions are presented for boundary layer flows with Mach number of the external flow up to 4. The influence of the flow Prandtl number, wall to freestream temperature ratio, and the power of the viscosity-temperature law are investigated. The present methodology also provides a simple way of comparing results according to various assumptions about the viscosity-temperature relations.

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Hypersonic Shock Wave-Boundary Layer Interaction and Leading Edge Slip

Cited by 19 publications

References 14 publications

Experimental results of a Mach 10 conical-flow derived waverider to 14-X hypersonic airspace vehicle

Experimental results of a Mach 10 conical-flow derived waverider to 14-X hypersonic airspace vehicle

Oblique Shock Relations for Air at Mach 7.8 and 7200 R Stagnation Temperature

Self-similar compressible laminar boundary layers

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