Experimental Investigation of Turbulent Boundary Layers in Hypersonic Flow

Lobb, R. Kenneth; Winkler, E. M.; Persh, Jerome

doi:10.2514/8.3262

Cited by 32 publications

(6 citation statements)

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“…expression ) has a Mach‐number dependence in addition to a Reynolds number dependence. Above Mach number of unity, the viscous drag coefficient decreases with increasing Mach number [e.g., Eckert , ; Lobb et al ., ; Hill , ]. The physical reasons for the Mach‐number dependence of the Navier‐Stokes drag coefficient are a combination of compressibility of the fluid, changes in the structure of the boundary layers, and thermal transport effects that change the fluid's kinematic viscosity.…”

Section: The Viscous Interactionmentioning

confidence: 99%

Physics‐based solar wind driver functions for the magnetosphere: Combining the reconnection‐coupled MHD generator with the viscous interaction

Borovsky

2013

JGR Space Physics

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[1] Driver functions for the Earth's magnetosphere-ionosphere system are derived from physical principles. Two processes act simultaneously: a reconnection-coupled MHD generator  and a viscous interaction.  accounts for the dayside reconnection rate, the length of the reconnection X line, and current saturation limits for the solar wind generator. Two viscous drivers are derived: Bohm viscosity ℬ and the freestream-turbulence effect  . A problematic proxy effect is uncovered wherein the viscous driver functions also describe the strength of reconnection. Two magnetospheric-driver functions written in terms of upstream solar wind parameters are constructed:  + ℬ and  +  . The driver functions are tested against seven geomagnetic indices. The reaction of the geomagnetic indices to  + ℬ and  +  is nonlinear: Nonlinear versions of the driver functions are supplied. Applying the driver functions at multiple time steps yields correlation coefficients of~85% with the AE and Kp indices; it is argued that multiple time stepping removes high-frequency uncorrelated signal from the drivers. Autocorrelation-function analysis shows strong 1 day and 1 year periodicities in the AE index, which are not in the solar wind driver functions; correspondingly, high-pass and low-pass filtering finds uncorrelated signal at 1 day and 1 year timescales. Residuals (unpredicted variance) between the geomagnetic indices and the driver functions are analyzed: The residuals are anticorrelated with the solar wind velocity, the solar F 10.7 radio flux, and the solar wind current saturation parameter. Removing diurnal, semiannual, and annual trends from the indices improves their correlation with the solar wind driver functions. Simplified versions of the driver functions are constructed: The simplified drivers perform approximately as well as the full drivers.

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Section: The Viscous Interactionmentioning

confidence: 99%

Physics‐based solar wind driver functions for the magnetosphere: Combining the reconnection‐coupled MHD generator with the viscous interaction

Borovsky

2013

JGR Space Physics

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“…It seems natural to ask whether any property like this may also hold for velocity profiles in the turbulent case. In an attempt to answer this question, a set of profiles measured by Lobb et al (1955) is examined in the present paper. These were obtained at Machnumbers between 5 and 8, and momentum-thickness…”

Section: Howarth's Transformationmentioning

confidence: 99%

“…6.1. Outer law Figure 6 shows a set of profiles of u/u, against y/6 measured by Lobb et al (1955) at Mach numbers between 4.93 and 8.18 and stagnation temperatures near 300 OK. The M = 8 profiles lie near a Bth power law, and those for M = 5 near a +th power law.…”

Section: Experimental Velocity Profilesmentioning

confidence: 99%

“…The object of this paper is to present a unified account of the distributions of velocity, shear stress and enthalpy in the compressible turbulent boundary layer on a flat plate. As a start, the set of velocity profiles measured over a range of heat-transfer conditions at Mach numbers between 5 and 8 by Lobb, Winkler & Persh (1955) is examined. It is found that by plotting in terms of the Howarth variable 7 = (p/p,)dy, the outer parts of the profiles for different Mach numbers are brought together on a single curve of the approximate form u/u, = (q/A)l/n, A being the transformed boundary-layer thickness.…”

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confidence: 99%

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Velocity and enthalpy distributions in the compressible turbulent boundary layer on a flat plate

Spence

1960

J. Fluid Mech.

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The object of this paper is to present a unified account of the distributions of velocity, shear stress and enthalpy in the compressible turbulent boundary layer on a flat plate. As a start, the set of velocity profiles measured over a range of heat-transfer conditions at Mach numbers between 5 and 8 by Lobb, Winkler & Persh (1955) is examined. It is found that by plotting in terms of the Howarth variable $\eta = \int ^y_0 (\rho|\rho_ 0)dy$, the outer parts of the profiles for different Mach numbers are brought together on a single curve of the approximate form u/u∞ = (η/Δ)1/n, Δ being the transformed boundary-layer thickness. By evaluating the reference density ρ0 and kinematic viscosity ν0 at the so-called ‘intermediate’ enthalpy (Eckert 1955) the innerparts of the profiles can also be collapsed, although less completely, to fit a ‘law of the wall’ u/uτ = A log (ηuτ/ν0 - c) + B. Here uτ = (τw/ρ0)½, and A, B and c are the same constants as in incompressible flow.These properties provide a physical starting point from which the remaining features of the mean flow can be calculated. By substitution of appropriate stream functions in the equation of motion the distribution of shear stress r in inner and outer regions is found; this approximates to the form $\tau |\tau_w = 1 - (u|u_\infty)^{(n+2)}$ over the whole layer. A relation between the distributions of enthalpy and shear stress is then found from the energy equation, using a turbulent Prandtl number a which is assumed constant across the layer to relate eddy conductivity to eddy viscosity. The final expression is similar in form to Crocco's integral for the laminar boundary layer with α taking the place of the laminar Prandtl number σ, but contains two extra terms proportional respectively to (α − σ)cf and (α − σ)c½j, which represent the effect of the inner viscous regions.The enthalpy integral is evaluated using the stated velocity-shear relation, and an expression which agrees well with the available experimental data is found for the heat-transfer coefficient as a function of recovery factor and skin-friction coefficient. It is also found that the usual quadratic enthalpy-velocity relation, exact for α = σ = 1, remains an acceptable approximation for Prandtl numbers considerably different from unity.

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“…5 He simply introduced wall properties for an insulated plate as functions of the free stream Mach Number in his formula for skin friction at low speeds, and evaluated the skin-friction coefficient as a function of the free stream Mach Number. This method receives some a posteriori justification from the results of Lobb, Winkler and Persh, 71 described above, in that they find the law of the wall valid up to high Mach Numbers provided that values of density and viscosity prevailing at the wall are used in the calculation of u* and y*.…”

Section: U*=u/u T =F(yu R /V)=f(y*) (1)mentioning

confidence: 99%

Some Features of Boundary Layers and Transition to Turbulent Flow

Kuethe

1956

Journal of the Aeronautical Sciences

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A brief review of the status of knowledge of laminar and turbulent boundary layers and of transition is given. Some new experimental results on transition in Poiseuille flow in a tube are reported. One set shows transition excited by the annular wake behind a ring airfoil. Another shows oscillograms of velocity fluctuations in the flow for several imposed disturbance amplitudes. These demonstrate successive stages in the breakdown of the flow.

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Experimental Investigation of Turbulent Boundary Layers in Hypersonic Flow

Cited by 32 publications

References 6 publications

Physics‐based solar wind driver functions for the magnetosphere: Combining the reconnection‐coupled MHD generator with the viscous interaction

Physics‐based solar wind driver functions for the magnetosphere: Combining the reconnection‐coupled MHD generator with the viscous interaction

Velocity and enthalpy distributions in the compressible turbulent boundary layer on a flat plate

Some Features of Boundary Layers and Transition to Turbulent Flow

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