Correction for the ordinary Mangler displacement thickness for slender cones
Mangler displacement thickness correction for slender cones
Bradley, R. H.↗
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Displacement thickness of the boundary layer with blowing
Displacement thickness for two-dimensional or axisymmetric compressible boundary layer with blowing
AXISYMMETRIC FLOW↗
Displacement thickness of the boundary layer with blowing.
Displacement thickness of boundary layer with blowing for arbitrary shaped bodies, noting stagnation flow
BOUNDARY LAYER SEPARATION↗
Nozzle boundary-layer displacement thickness at Mach numbers 30 to 70
Nozzle boundary layer displacement thickness at Mach 30-70 in helium using Langley hotshot tunnel tests
Miller, C. G.↗
Displacement thickness distributions in transonic flows about 3-D wings
The transonic 3-D inviscid small-perturbation solution of Bailey and Ballhaus is combined with a finite-difference solution for Prandtl's boundary-layer equations in order to include viscous effects. The inviscid-viscous interaction is modeled by means of the displacement surface, which can be thought of as the effective body surface seen by the inviscid flow. Displacement thickness, lift, and pressure distributions resulting from the combined solution are presented for transonic flows about the RAE 101 A wing and a Lockheed transport wing, both at small angles of attack. The influence of changing arbitrarily the start of transition on the displacement surface and lift is discussed for the RAE wing flow.
Kordulla, W.↗
Boundary-layer transition and displacement thickness effects on zero-lift drag of a series of power-law bodies at Mach 6
Wave and skin-friction drag have been numerically calculated for a series of power-law bodies at a Mach number of 6 and Reynolds numbers, based on body length, from 1.5 million to 9.5 million. Pressure distributions were computed on the nose by the inverse method and on the body by the method of characteristics. These pressure distributions and the measured locations of boundary-layer transition were used in a nonsimilar-boundary-layer program to determine viscous effects. A coupled iterative approach between the boundary-layer and pressure-distribution programs was used to account for boundary-layer displacement-thickness effects. The calculated-drag coefficients compared well with previously obtained experimental data.
Ashby, G. C., Jr.↗
Three dimensional compressible boundary-layer computations for a finite swept wing
Three-dimensional, compressible turbulent boundary-layer calculations have been performed for the finite supercritical wing of the NASA modified F8 transonic research airplane. Data on the boundary-layer thickness, displacement thickness, skin friction components, and integrated streamwise skin friction are presented for points along the streamwise stations of which the pressure measurements were previously made. Representative velocity profiles are shown, and boundary-layer-thickness contour plots and skin-friction vector plots are presented. Results are given for a Reynolds number of 1.5 million per foot, and for Mach numbers of 0.50 and 0.99.
Nash, J. F.↗
Additional three-dimensional boundary-layer computations for a finite swept wing
Calculations have been made of the three-dimensional, compressible, turbulent boundary layer on the finite supercritical wing of the NASA modified F-8 transonic research airplane. The calculations were based on the wing pressure distribution measured in flight at M = 0.90, instead of on wind tunnel data at M = 0.50 and 0.99. Data on the boundary-layer thickness, displacement thickness, skin-friction components, and integrated streamwise skin friction are presented for points along the streamwise stations at which pressure measurements were made.
Nash, J. F.↗
Computer simulation of transonic flow past airfoils with boundary layer correction
A computer program has been developed to solve the compressible flow equation for the velocity potential. The exterior of the airfoil is mapped onto the unit circle and the flow is computed on a grid in the circle plane. A relaxation method using backward differencing in the flow direction at supersonic points permits solutions for large supersonic areas. The pressure distribution resulting from the flow becomes the input to the von Karman momentum equation which when integrated gives the displacement thickness. This displacement thickness is smoothed and added to the airfoil to account for the turbulent boundary layer. The boundary layer correction is computed iteratively with the flow. Results from this program and test data agree well.
Bauer, F.↗
Turbulent-boundary-layer development on a moving ground belt of rough texture
The equations presented can be used to predict the shape factor and the ratio of the momentum thickness to the relative momentum thickness with reasonable accuracy for a moving ground belt provided that the stationary quantities are known and the two following basic approximations are valid: (1) Shape factor based upon velocity relative to the ground belt is nearly independent of the ratio of belt velocity to free-stream velocity. (2) The ratio of moving-belt momentum thickness to stationary-belt momentum thickness is independent of the coordinate measured in the streamwise direction. In addition, the integral quantities, momentum thickness and displacement thickness, can be predicted for the moving ground belt by using an empirically determined polynomial whose coefficients will change with different belt roughnesses.
Roper, A. T.↗
Laminar Boundary Layer Behind a Strong Shock Moving into Air
The laminar wall boundary layer behind a strong shock advancing into stationary air has been determined. Numerical results have been obtained for shock Mach numbers up to 14 using real gas values for density and viscosity and assuming Prandtl and Lewis numbers of 0.72 and 1, respectively. The numerical results for shear and heat transfer agree, within 4 percent, with a previously presented approximate analytical expression for these quantities. A slight modification of this expression results in agreement with the numerical data to within 2.5 percent. Analytical expressions for boundary-layer thickness and displacement thickness, correct to within 4 percent for the present data, have also been obtained.
Mirels, Harold↗
Calibration of Axisymmetric and Quasi-1D Solvers for High Enthalpy Nozzles
The proposed paper will present a numerical investigation of the flow characteristics and boundary layer development in the nozzles of high enthalpy shock tunnel facilities used for hypersonic propulsion testing. The computed flow will be validated against existing experimental data. Pitot pressure data obtained at the entrance of the test cabin will be used to validate the numerical simulations. It is necessary to accurately model the facility nozzles in order to characterize the test article flow conditions. Initially the axisymmetric nozzle flow will be computed using a Navier Stokes solver for a range of reservoir conditions. The calculated solutions will be compared and calibrated against available experimental data from the DLR HEG piston-driven shock tunnel and the 16-inch shock tunnel at NASA Ames Research Center. The Reynolds number is assumed to be high enough at the throat that the boundary layer flow is assumed turbulent at this point downstream. The real gas affects will be examined. In high Mach number facilities the boundary layer is thick. Attempts will be made to correlate the boundary layer displacement thickness. The displacement thickness correlation will be used to calibrate the quasi-1D codes NENZF and LSENS in order to provide fast and efficient tools of characterizing the facility nozzles. The calibrated quasi-1D codes will be implemented to study the effects of chemistry and the flow condition variations at the test section due to small variations in the driver gas conditions.
Papadopoulos, P. E.↗
Numerical simulation of steady transonic flow about airfoils
A computer code has been developed that couples a fast transonic full-potential AF2 solver with both an efficient integral boundary-layer method and a viscous wedge approximation of the shock/boundary-layer interaction. The efficiency of the coupled analysis methods and the method of coupling has resulted in a uniquely efficient analysis tool. The airfoil geometry is modified by the displacement thickness before the shock and the displacement thickness plus the viscous wedge thickness after the shock by considering the viscous effects as an equivalent transpiration boundary condition. The flow about conventional and supercritical airfoils under moderately strong shock situations has been calculated. Comparisons with experimental data indicate that this viscous correction method has improved the accuracy of the full-potential analysis. Furthermore, the computer time required to obtain a converged solution has been reduced.
Lee, S. C.↗
Assessment of computational models for thermoelectroelastic multilayered plates
A study is made of the accuracy of the steady-state (static) thermoelectroelastic response of multilayered hybrid composite plates predicted by five modeling approaches, based on two-dimensional plate theories. The plates consist of a combination of fiber-reinforced and piezothermoelastic layers. The standard of comparison is taken to be the exact three-dimensional thermoelectroelastic solutions, and the quantities compared include gross response characteristics (e.g., strain energy components, and average through-the-thickness displacements); detailed, through-the-thickness distributions of displacements and stresses; and sensitivity coefficients of the response quantities (derivatives of the response quantities with respect to material parameters of the plate). The modeling approaches considered include first-order theory; third-order theory; discrete-layer theory (with piecewise linear variation of the in-plane displacements, temperature and electric potential, in the thickness direction); and two predictor-corrector procedures.
Tang, Yvette T.↗
Effect of mean-velocity profile shapes on sound transmission through two-dimensional ducts
Acoustic propagation through a lined two-dimensional duct is examined in order to assess the influence of the shape of the mean-velocity profile on the attenuation rate. Five mean-velocity profiles are considered: linear, parabolic, Pohlhausen, 1/7th power law with a linear sub-layer, and linear with slip at the wall. It is shown that when the attenuation rate is tabulated as a function of the boundary-layer thickness, as is usually done, substantially different results are obtained from the several mean profiles. However, when the displacement thickness is used, a considerable collapse is achieved in the attenuation curves that are obtained from the various profiles. For downstream propagation, all profiles produce essentially the same results over a reasonable range of boundary-layer thickness. However, for many cases of upstream propagation, the results from the 'turbulent' boundary-layer profiles differ significantly from the results of the other profiles even when compared on the basis of displacement thickness.
Hayfeh, A. H.↗
A fast viscous correction method for full-potential transonic wing analysis
An analysis of the transonic flowfield around a three-dimensional wing is carried out using a strip method. Attention is given to the boundary layer growth in the streamwise direction. A viscous correction technique is defined for the TWING code for solving the full potential equations. A viscous ramp at the base of a shock is superimposed on the boundary layer displacement thickness generated by an integral boundary layer method. A relationship is then obtained between the effective displacement thickness and a vertical component of the surface velocity, a transpirational boundary condition. The viscous correction is found to be unnecessary in weak shock conditions but gives a better shock position and pressure distribution in a strong shock condition when compared with data from an ONERA M6 airfoil and the Hinson and Burdges (1980) Wing A.
Lee, S. C.↗
The prediction of two-dimensional airfoil stall progression
A generalized boundary condition potential flow calculation method was combined with a momentum integral boundary layer method and a base flow theory of separation to predict airfoil viscous-inviscid interference up to and beyond stall. The resultant program considers laminar and turbulent separation and is, therefore, applicable to thin or thick airfoil stall. The calculated flow field includes the airfoil and the separation bubble recombination region behind the airfoil. Calculated pressure distributions and equivalent airfoil shapes, including the displacement thickness of the viscous regions, are compared with flow field measurements for several airfoils. The measured displacement thicknesses and wake centerlines corroborate the calculated shape. The comparison also suggests the use of the analytical solution to evaluate the measurements.
Gross, L. W.↗
Numerical studies of transverse curvature effects on transonic flow stability
A numerical study of transverse curvature effects on compressible flow temporal stability for transonic to low supersonic Mach numbers is presented for axisymmetric modes. The mean flows studied include a similar boundary-layer profile and a nonsimilar axisymmetric boundary-layer solution. The effect of neglecting curvature in the mean flow produces only small quantitative changes in the disturbance growth rate. For transonic Mach numbers (1-1.4) and aerodynamically relevant Reynolds numbers (5000-10,000 based on displacement thickness), the maximum growth rate is found to increase with curvature - the maximum occurring at a nondimensional radius (based on displacement thickness) between 30 and 100.
Macaraeg, M. G.↗