An investigation of the high speed turbulent boundary layer with heat transfer and arbitrary pressure gradient. Part 1 - Summary report
Behavior of high speed turbulent boundary layer with heat transfer and streamwise pressure gradient
Boccio, J.↗
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Calculation of compressible adverse pressure gradient turbulent boundary layers.
Difficulties encountered in computing profile shapes in supersonic turbulent boundary layers with large pressure gradients, which result from a disagreement between data and theory, are investigated. Possible reasons given by various authors for this disagreement are discussed. Initial results seem to indicate that conventional reasons do not account for the observed difficulties. However, inclusion of the effect of curvature upon turbulent mixing has brought an improvement in calculations. Possible three-dimensional effects are also examined.
Bushnell, D. M.↗
Experimental investigation of a three dimensional turbulent boundary layer with a non disappearing pressure gradient
The results of measuring profiles of temporally determined velocities and Reynolds tension, wall shear stresses and pressure distribution in a three dimensional, turbulent boundary layer with pressure gradients in both tangential directions are reported. For determining the velocities X wire probes were used whose cooling was gauged according to magnitude and direction of the flow and was described with an effective cooling speed. In the evaluation consideration is given to the directional sensitivity of the hot wire. The ratio of the turbulence viscosities is calculated for both tangential directions and is found to be approximately N equals 1.2. Further, the profiles of the mixing path lengths for the flow direction are found to vary only slightly with increasing X-coordinates, while the boundary layer thickness increases substantially. The relationships of turbulent shear stress to turbulent, kinetic fluctuation energy is approximately constant over a large part of the boundary layer.
Mueller, U.↗
Effect of randomly fluctuating pressure gradients, with arbitrarily specified power spectrum and probability density, on flow in channels
Randomly fluctuating, non-Gaussian pressure gradient effect on steady, incompressible channel flow
Perlmutter, M.↗
An experimental investigation of the turbulent boundary layer undergoing both adverse pressure gradient and cross flow along a plane of symmetry
Hypervelocity wind tunnel investigation of turbulent boundary undergoing adverse pressure gradient and cross flow along plane of symmetry
Zakkay, Victor↗
Transitional Boundary Layers Under the Influence of High Free Stream Turbulence, Intensive Wall Cooling and High Pressure Gradients in Hot Gas Circulation
The requirements for fundamental experimental studies of the influence of free stream turbulence, pressure gradients and wall cooling are discussed. Under turbine-like free stream conditions, comprehensive tests of transitional boundary layers with laminar, reversing and turbulent flow increments were performed to decouple the effects of the parameters and to determine the effects during mutual interaction.
Rued, Klaus↗
An experimental investigation of boundary layer transition in an adverse pressure gradient
The evolution of a small perturbation introduced periodically into a boundary layer with a moderately strong adverse pressure gradient (APG) was investigated experimentally using the hot-wire method. The magnitude of the disturbance is found to decay with the streamwise distance in the APG before undergoing rapid growth and triggering transition in a very repetitive manner. The evidence suggests that the laminar layer separates and that the transition mechanism is an inviscid shear-layer type of instability. Contours of spanwise vorticity in the plane of the disturbance show the formation of roll-ups in the initial stages. Subsequent interaction with the wall leads to the formation of large-scale vortex loops which merge into a single vortex loop further downstream.
Watmuff, Jonathan H.↗
The Compressible Laminar Boundary Layer with Heat Transfer and Arbitrary Pressure Gradient
An approximate method for the calculation of the compressible laminar boundary layer with heat transfer and arbitrary pressure gradient, based on Thwaites' correlation concept, is presented. With the definition of dimensionless shear and heat-transfer parameters and an assumed correlation of these parameters in terms of a momentum parameter, a complete system of relations for calculating skin friction and heat transfer results. Knowledge of velocity or temperature profiles is not necessary in using this calculation method. When the method is applied to a convergent-divergent, axially symmetric rocket nozzle, it shows that high rates of heat transfer are obtained at the initial stagnation point and at the throat of the nozzle. Also indicated are negative displacement thicknesses in the convergent portion of the nozzle; these occur because of the high density within the lower portions of the cooled boundary layer. (author)
Cohen, Clarence B↗
Convective heat transfer studies at high temperatures with pressure gradient for inlet flow Mach number of 0.45
Heat transfer measurements were determined for a flat plate with and without pressure gradient for various free stream temperatures, wall temperature ratios, and Reynolds numbers for an inlet flow Mach number of 0.45, which is a representative inlet Mach number for gas turbine rotor blades. A shock tube generated the high temperature and pressure air flow, and a variable geometry test section was used to produce inlet flow Mach number of 0.45 and accelerate the flow over the plate to sonic velocity. Thin-film platinum heat gages recorded the local heat flux for laminar, transition, and turbulent boundary layers. The free stream temperatures varied from 611 R (339 K) to 3840 R (2133 K) for a T(w)/T(r,g) temperature ratio of 0.87 to 0.14. The Reynolds number over the heat gages varied from 3000 to 690,000. The experimental heat transfer data were correlated with laminar and turbulent boundary layer theories for the range of temperatures and Reynolds numbers and the transition phenomenon was examined.
Pedrosa, A. C. F.↗
A new turbulence closure model for boundary layer flows with strong adverse pressure gradients and separation
A new turbulence closure model designed specifically to treat two-dimensional, turbulent boundary layers with strong adverse pressure gradients and attendant separation, is presented. The influence of history effects are modeled by using an ordinary differential equation (ODE) derived from the turbulence kinetic-energy equation, to describe the streamwise development of the maximum Reynolds shear stress in conjunction with an assumed eddy-viscosity distribution which has as its velocity scale the maximum Reynolds shear stress. In the outer part of the boundary layer, the eddy viscosity is treated as a free parameter which is adjusted in order to satisfy the ODE for the maximum shear stress. Because of this, the model s not simply an eddy-viscosity model, but contains features of a Reynolds-stress model. Comparisons with experiments are presented which clearly show the proposed model to be superior to the Cebeci-Smith model in treating strongly retarded and separated flows. In contrast to two-equation, eddy-viscosity models, it requires only slightly more computational effort than simple models like the Cebeci-Smith model.
Johnson, D. A.↗
An investigation of the high speed turbulent boundary layer with heat transfer and arbitrary pressure gradient. Part 3 - Computer program manual
Computer program for determining properties of high speed turbulent boundary layer with heat transfer and arbitrary pressure gradient
Boccio, J.↗
Pressure-gradient effects on hypersonic turbulent skin friction and boundary-layer profiles.
Local skin friction, total-temperature profiles, and pitot-pressure profiles were measured on the wall of a Mach-7.4 wind tunnel. The wall to adiabatic wall temperature ratio was varied from 0.3 to 0.5. Boundary-layer characteristics were compared with those predicted by a finite-difference method. Local skin friction was predicted to within 15%. Pressure-gradient effects on the temperature and Mach number distributions and the shape factor (displacement thickness/momentum thickness) were underpredicted, but the velocity distributions were closely predicted.
Hopkins, E. J.↗
Correlation of boundary layer quantities for hypersonic laminar flows with zero pressure gradient for several gases
The laminar boundary layer has been theoretically studied for six gases for flows over cold walls with zero pressure gradient at Mach numbers between 5.5 and 12.5 to correlate boundary layer quantities for the various gases. The flow conditions considered correspond to those that can be generated in test facilities such as the shock tunnel and the expansion tube. Computed results obtained using real gas properties indicate that the Eckert number based on edge conditions serves to correlate the results in terms of the wall shear stress and enthalpy gradient, the Stanton number, and the momentum thickness for the various gases within plus or minus 10 per cent for Te = Tw and Te approximately 3Tw. Computed Reynolds analogy factors exhibit very good agreement with those predicted by the Colburn analogy. Velocity and displacement thicknesses correlate well with Eckert number for Te = Tw, but fail to correlate for Te approximately 3Tw. Differences in results are traced to property variations. Results show that the Eckert number is a significant correlating variable for the flows considered.
Cook, W. J.↗
A Method for Computing Turbulent Heat Transfer in the Presence of a Streamwise Pressure Gradient for Bodies in High-Speed Flow
A modified Reynolds analogy between skin friction and heat transfer which depends upon local pressure gradient is derived. Exact and approximate solutions are derived from the differential equations; the exact solution is applicable for arbitrary initial (transition) conditions and the approximate solution requires fully developed turbulent flow from stagnation point or leading edge. The exact solution (restricted to stagnation initial conditions) and the approximate solutions are shown to agree with one another within 5 percent when applied to several blunt shapes. The present solutions generally predict the measured heating rates on these bodies within the accuracy of the measurements provided transition began upstream of the peak heating region. The present solutions appear to be sufficiently accurate for design purposes.
Cohen, Nathaniel B.↗
An investigation of the high speed turbulent boundary layer with heat transfer and arbitrary pressure gradient. Part 2 - The compressibility transformation - General considerations
Compressibility transformation properties and high speed turbulent boundary layer flow with mass transfer and arbitrary pressure gradient
Economos, C.↗
Survey and bibliography on attainment of laminar flow control in air using pressure gradient and suction, volume 1
A survey was conducted and a bibliography compiled on attainment of laminar flow in air through the use of favorable pressure gradient and suction. This report contains the survey, summaries of data for both ground and flight experiments, and abstracts of referenced reports. Much early information is also included which may be of some immediate use as background material for LFC applications.
Bushnell, D. M.↗
Roll-up of vorticity in adverse-pressure-gradient boundary layers
It is shown how the unsteady, nonlinear critical-layer equation determines the evolution of instability waves in a weak adverse-pressure-gradient boundary layer. Numerical solutions show that the nonlinearity halts the growth of these inviscidly unstable waves. The stabilizing effect of nonlinearity, in the present case, can be described as a consequence of either the increase (toward zero) of the phase jump across the critical layer or the roll-up of the critical-layer disturbance vorticity.
Goldstein, M. E.↗
A theoretical and experimental investigation of the hypersonic turbulent boundary layer subject to normal and longitudinal pressure gradients and cross flow along a windward plane of symmetry.
A theoretical and experimental investigation for the hypersonic turbulent boundary layer undergoing both normal and longitudinal pressure gradients and cross flow along the plane of symmetry on the windward side of a body of revolution is presented. The purpose of this investigation is to provide a method for calculating boundary layers that occur on the centerline of symmetry of an inlet. The three-dimensional compressible integral equations are written along the symmetry plane and integrated numerically, and the effect of the cross flow on the behavior of the boundary layer is also studied. The experiments were performed at Mach number 6 and Reynolds number of 44,000,000/ft for the axisymmetric case and for the case with cross flow. The velocity profiles and the boundary layer parameters agree relatively well with theoretical values with and without cross flow effects. The presence of the cross flow alters significantly the value of the profiles. Total temperature-velocity correlations deviate from the linear Crocco distribution. Heat transfer rates agree with theoretical values and values obtained by the flat plate reference enthalpy method. Cross flow influence on the heat transfer rates is of minor relevance.
Zakkay, V.↗