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NASA NTRS2020

Verification of Anisotropic Mesh Adaptation for Turbulent Simulations over ONERA M6 Wing

Unstructured anisotropic mesh adaptation is known to be an efficient way to control discretization errors in Computational Fluid Dynamics (CFD) simulations. Method verification is required to provide the confidence for routine use in production analysis. The current work aims at verification of anisotropic mesh adaptation for RANS simulations over the ONERA M6 wing. The present verification study is performed using four different flow solvers, three different implementations of the metric field, and three mesh mechanics packages. Two of the flow solvers use stabilized finite-element discretizations (FUN3D-SFE and GGNS), one uses finite-volume discretization (FUN3D-FV), and the last one uses mixed finite-volume and finite element discretizations (Wolf). The mesh adaptation is based on an error estimator that aims to control the quadratic error term in the linear interpolation of Mach number. Two sets of adaptations were performed; the first one controls the interpolation error in L2 norm and the second one controls the interpolation error in L4 norm. Convergence studies were performed on the forces and the pitching moment using all four solvers, and the results are compared with previously verified convergence studies on fixed (nonadapted) meshes. Both forces and pitching moment on adapted meshes are found to be converging to the fine mesh values faster than those on fixed meshes. In addition to forces and moments, convergence of surface pressure and skin friction coefficients at various measurement locations on the wing are also presented. Adapted-mesh surface pressure distributions agree with the fine fixed mesh pressure distributions. Adapted-mesh skin friction distributions contain high frequency noise with mean values approaching the fixed mesh pressure skin friction distributions.

Aravind Balan↗
NASA NTRS1943

Determination of general relations for the behavior of turbulent boundary layers

An analysis has been made of a considerable amount of data for turbulent boundary layers along wings and bodies of various shapes in order to determine the fundamental variables that control the development of turbulent boundary layers. It was found that the type of velocity distribution in the boundary layer could be expressed in terms of a single parameter. This parameter was chosen as the ratio of the displacement thickness to the momentum thickness of the boundary layer. The variables that control the development of the turbulent boundary layer apparently are: (1) the ratio of the nondimensional pressure gradient, expressed in terms of the local dynamic pressure outside the boundary layer and boundary-layer thickness, to the local skin-friction coefficient and (2) the shape of the boundary layer. An empirical equation has been developed in terms of these variables that, when used with the momentum equation and the skin-friction relation, makes it possible to trace the development of the turbulent boundary layer to the separation point.

Von Doenhoff, Albert E↗
NASA NTRS1950

Approximate Turbulent Boundary-Layer Development in Plane Compressible Flow Along Thermally Insulated Surfaces with Application to Supersonic-Tunnel Contour Correction

Numerical solutions of the differential equation obtained from the momentum theorem for the development of a turbulent boundary layer along a thermally insulated surface in two-dimensional and in radial shock-free flow are presented in tabular form for a range of Mach numbers from 0.100 to 10. The solution can be used in a step-wise procedure with any given distribution of favorable pressure gradients and for zero pressure gradients. Solutions are also given for use with moderate adverse pressure gradients. The mean velocity in the boundary layer is approximated by a power-law profile. In view of the stepwise integration methods to be used, the exponent designated the profile shape can be varied along the surface between the integral fraction limits 1/5 and 1/11 through interpolation. Agreement obtained between theoretical and experimental boundary-layer development in a supersonic nozzle at a nominal Mach number of 2 indicates the general validity of the approximations used in the analysis - in particular, the method of extrapolating low-speed skin-friction relations to high Mach number flows. The extrapolation method used assumes that the skin-friction coefficient depend primarily on Reynolds number, provided that the density and the kinematic viscosity are evaluated at surface conditions.

BOUNDARY LAYER - WIND TUNNEL WALLS↗
NASA NTRS1993

Laser Interferometer Skin-Friction measurements of crossing-shock wave/turbulent boundary-layer interactions

Wall shear stress measurements beneath crossingshock wave/turbulent boundary-layer interactions have been made for three interactions of different strengths. The interactions are generated by two sharp fins at symmetric angles of attack mounted on a flat plate. The shear stress measurements were made for fin angles of 7 and 11 degrees at Mach 3 and 15 degrees at Mach 4. The measurements were made using a Laser Interferometer Skin Friction (LISF) meter; a device which determines the wail shear by optically measuring the time rate of thinning of an oil film placed on the test model surface. Results of the measurements reveal high skin friction coefficients in the vicinity of the fin/plate junction and the presence of quasi-two-dimensional flow separation on the interaction centerline. Additionally, two Navier-Stokes computations, one using a Baldwin-Lomax turbulence model and one using a k-~ model, are compared to the experimental results for the Mach 4, 15 degree interaction case. While the k-~ model did a reasonable job of predicting the overall trend in portions of the skin friction distribution, neither computation fully captured the physics of the near surface flow in this complex interaction.

Garrison, T. J.↗
NASA NTRS1994

Laser interferometer skin-friction measurements of crossing-shock-wave/turbulent-boundary-layer interactions

Wall shear stress measurements beneath crossing-shock-wave/turbulent boundary-layer interactions have been made for three interactions of different strengths. The interactions are generated by two sharp fins at symetric angles of attack mounted on a flat plate. The shear stress measurements were made for fin angles of 7 and 11 deg at Mach 3 and 15 deg at Mach 3.85. The measurements were made using a laser interferometer skin-friction meter, a device that determines the wall shear by optically measuring the time rate of thinning of an oil film placed on the test model surface. Results of the measurements reveal high skin-friction coefficients in the vicinity of the fin/plate junction and the presence of quasi-two-dimensional flow separation on the interaction center line. Additionally, two Navier-Stokes computations, one using a Baldwin-Lomax turbulence model and one using a k-epsilon model, are compared with the experimental results for the Mach 3.85, 15-deg interaction case. Although the k-epsilon model did a reasonable job of predicting the overall trend in portions of the skin-friction distribution, neither computation fully captured the physics of the near-surface flow in this complex interaction.

Garrison, T. J.↗
NASA NTRS1998

Transition in Turbine Flows

We have further developed our capabilities to analyze transition in turbine boundary layers from first principles by integrating the nonlinear parabolized stability equations (PSE) with improved initial and boundary conditions. With modified iteration schemes, we are able to proceed deeper into the transition region where skin friction coefficient and heat transfer coefficient significantly increase. Initial and boundary conditions at elevated turbulence levels can be derived by receptivity analysis. Test runs for ERCOFTAC test case T3A at 2.4\% turbulence level provide results in good agreement with the experimental data. The sharper minimum of the skin coefficient also shown by DNS results is likely due to the missing intermittency. The method has been applied to various experimentally studied turbine blades (UTRC, VKI, Zierke, Langston, Hippensteele, and others). The PSE results, though physically reasonable, do not agree as well as expected with the experimental findings. We have, therefore, performed an extensive search for the reasons of the seemingly systematic deviations. A first source of uncertainty has been found in the often insufficient documentation of the experiments (e.g. on blockage by end-wall boundary layers). However, variation of the relevant parameters does not lead to more satisfactory agreement. A second reason has been found in the "standard procedure" which considers a 2D flow at midspan and uses a panel code and subsequent boundary-layer code to obtain the laminar basic flow for the transition analysis. Comparison with the pressure distribution obtained with a 3D design code (RVC3D) shows significant three-dimensionality of the flow (e.g. in the UTRC experiments). The spanwise variation has been neglected in our original PSE code. To overcome this problem, we have developed the PSE/3D for fully 3D boundary layers to account for streamwise and spanwise variations. Since the design code does not provide the boundary-layer flow with sufficient resolution, we have generated the Euler solution and employed a 3D boundary-layer code to obtain the viscous basic flow. Although only the linear stability level of PSE/3D has been implemented so far, the discrepancies with the experiments change but do not disappear. We still find deviations between the computed and experimental variations of C(sub f), and St along the blade for laminar flow. The main reason can be seen by comparing the solution of the boundary-layer code with the viscous results of the design code. The conventional boundary-layer solution exhibits an asymptotic behavior appropriate in external aerodynamics but does not match the steep gradients of the inviscid flow through the passage and consequently provides biased results for C(sub f), and St. An attempt is currently being made to correct this deficiency. Before attempting to perform the transition analysis for the viscous flow provided by the design code, we have analyzed the implementation and "best possible" results. Code and results exhibit flaws that may negatively affect the design and are intolerable for transition analysis. Therefore, we have decided to develop a new code to obtain a reliable basis for stability and transition studies. We expect to report improved results by the time of the meeting.

Herbert, Thorwald↗
NASA NTRS1996

Uncertainty Analysis for Oil-Film Interferometry Skin-Friction Measurement Techniques

Over the past 20 years, the use of oil-film interferometry to measure the skin friction coefficient (C(sub f) = tau/q where tau is the surface shear stress and q is the dynamic pressure) has increased. Different forms of this oil-film technique with various levels of accuracy and ease of use have been successfully applied in a wide range of flows. The method's popularity is growing due to its relative ease of implementation and minimal intrusiveness as well as an increased demand for C(sub f) measurements. Nonetheless, the accuracy of these methods has not been rigorously addressed to date. Most researchers have simply shown that the skin-friction measurements made using these techniques compare favorably with other measurements and theory, most of which are only accurate to within 5-20%. The use of skin-friction data in the design of commercial aircraft, whose drag at cruise is 50% skin-friction drag, and in the validation of computational fluid dynamics programs warrants better uncertainty estimates. Additional information is contained in the original extended abstract.

Naughton, Jonathan W.↗
NASA NTRS1984

Correlation of transonic-cone preston-tube data and skin friction

Preston-tube measurements obtained on the Arnold Engineering Development Center (AEDC) Transition Cone have been correlated with theoretical skin friction coefficients in transitional and turbulent flow. This has been done for the NASA Ames 11-Ft Transonic Wind Tunnel (11 TWT) and flight tests. The developed semi-empirical correlations of Preston-tube data have been used to derive a calibration procedure for the 11 TWT flow quality. This procedure has been applied to the corrected laminar data, and an effective freestream unit Reynolds number is defined by requiring a matching of the average Preston-tube pressure in flight and in the tunnel. This study finds that the operating Reynolds number is below the effective value required for a match in laminar Preston-tube data. The distribution of this effective Reynolds number with Mach number correlates well with the freestream noise level in this tunnel. Analyses of transitional and turbulent data, however, did not result in effective Reynolds numbers that can be correlated with background noise. This is a result of the fact that vorticity fluctuations present in transitional and turbulent boundary layers dominate Preston-tube pressure fluctuations and, therefore, mask the tunnel noise eff ects. So, in order to calibrate the effects of noise on transonic wind tunnel tests only laminar data should be used, preferably at flow conditions similar to those in flight tests. To calibrate the effects of transonic wind-tunnel noise on drag measurements, however, the Preston-tube data must be supplemented with direct measurements of skin friction.

Abu-Mostafa, A. S.↗
NASA NTRS1968

Survey of the Relationship Between Theory and Experiment for Convective Heat Transfer From Rocket Combustion Gases

The problem of predicting the distribution of heat flux in a rocket engine is complicated by a flow field and thermodynamics so perturbed by as yet indescribable combustion effects that it continues to be necessary to utilize a simplified theoretical model against which to compare experimental results in order to gain insight. The most successful model applied to this problem is that of a compressible, turbulent, accelerating boundary layer flow with an arbitrary point of origin, and chemical reaction restricted to equilibrium recombination or diffusion-limited recombination on a catalytic wall. Analysis of this model was not possible without making several assumptions about the nature of the skin friction coefficient relationship and Reynold's analogy in an accelerating boundary layer flow. The paper summarizes the analysis of this model (together with detailed treatment of the special problems of variable properties, chemical reaction, and sources of transport properties), and describes several closed-form equations that have also been developed and applied to the problem. Described are results of several experiments with hot air flow made for the purpose of checking the validity of the assumptions in the boundary layer analysis. Most significant, however, are presentations of sample distributions of local heat flux measured in rocket engines operating with a wide range of conditions, propellants, injectors and sizes. When compared with predictions, these data show the significant range of deviation in heat flux that results from the combustion effects and which precludes a generally accurate prediction theory or correlation equation until the combustion process itself is correlated.

D R Bartz↗
NASA NTRS1972

An analysis of the relaxation of laminar boundary layer on a flat plate after passage of an interface with application to expansion-tube flows

The relaxation of the accelerating-gas boundary layer to the test-gas boundary layer over a flat plate in an expansion tube is analyzed. Several combinations of test gas and acceleration gas are considered. The problem is treated in two conically similar limits: (1) when the time lag between the arrival of the shock and the interface at the leading edge of the plate is very large, and (2) when this lag is negligible. The time-dependent laminar-boundary-layer equations of a binary mixture of perfect gases are taken as the flow-governing equations. This coupled set of differential equations, written in terms of the Lam-Crocco variables, has been solved by a line-relaxation finite-difference techniques. The results presented include the Stanton number and the local skin-friction coefficient as functions of shock Mach number and the nondimensional distance-time variable. The results indicate that more than 95 percent of the test-gas boundary layer exists over a length, measured from the leading edge of the plate, equal to about three-tenths of the distance traversed by the interface in the free stream.

Gupta, R. N.↗
NASA NTRS1973

Comparison of predicted and measured low-speed performance of two 51 centimeter-diameter inlets at incidence angle

Theoretical and experimental internal flow characteristics of two 51-cm-diameter inlets are compared. Theoretical flow characteristics along the inlet surface were obtained from an axisymmetric potential flow and boundary layer analysis. The experimental data were obtained from low-speed tests of a high-bypass-ratio turbofan engine simulator. Comparisons between calculated internal surface pressure distributions and experimental data are presented for a free-system velocity of 45 m/sec and for incidence angles from 0 deg to 50 deg. Analysis of boundary layer separation on the inlet lip at incidence angle is the major emphasis of this report. Theoretical boundary layer shape factors, skin friction coefficients, and velocity profiles in the boundary layer are presented, along with the location of the transition region. Theoretical and experimental separation locations are also discussed.

Albers, J. A.↗
NASA NTRS1974

Comparison of theoretical and experimental boundary-layer development in a Mach 2.5 mixed-compression inlet

An analytical investigation was made of the boundary layer flow in an axisymmetric Mach 2.5 mixed compression inlet, and the results were compared with experimental measurements. The inlet tests were conducted in the Lewis 10- by 10-foot supersonic wind tunnel at a unit Reynolds number of 8.2 million/m. The inlet incorporated porous bleed regions for boundary layer control, and the effect of this bleed was taken into account in the analysis. The experimental boundary layer data were analyzed by using similarity laws from which the skin friction coefficient was obtained. The boundary layer analysis included predictions of laminar and turbulent boundary layer growth, transition, and the effects of the shock boundary layer interactions. In addition, the surface static pressures were compared with those obtained from an inviscid characteristics program. The results of investigation showed that the analytical techniques gave satisfactory predictions of the boundary layer flow except in regions that were badly distorted by the terminal shock.

Hingst, W. R.↗
NASA NTRS1974

Computer program for calculation of real gas turbulent boundary layers with variable edge entropy

A user's manual for a computer program which calculates real gas turbulent boundary layers with variable edge entropy on a blunt cone or flat plate at zero angle of attack is presented. An integral method is used. The method includes the effect of real gas in thermodynamic equilibrium and variable edge entropy. A modified Crocco enthalpy velocity relationship is used for the enthalpy profiles and an empirical correlation of the N-power law profile is used for the velocity profile. The skin-friction-coefficient expressions of Spalding and Chi and Van Driest are used in the solution of the momentum equation and in the heat-transfer predictions that use several modified forms of Reynolds analogy.

Boney, L. R.↗
NASA NTRS1976

Turbulent boundary layers over nonstationary plane boundaries

Methods of predicting integral parameters and skin-friction coefficients of turbulent boundary layers developing over moving-ground-planes are evaluated using test information from three different wind tunnel facilities at the NASA Langley Research Center. These data include test information from the VSTOL tunnel which is presented for the first time. The three methods evaluated were: (1) relative integral parameter method, (2) relative power law method, and (3) modified law of the wall method. Methods (1) and (2) can be used to predict moving-ground-plane shape factors with an expected accuracy of + or - 10%. They may also be used to predict moving-ground-plane displacement and momentum thicknesses with lower expected accuracy. This decrease in accuracy can be traced to the failure of approximations upon which these methods are based to prove universal when compared with VSTOL tunnel test results.

Roper, A. T.↗
NASA NTRS1976

Wall-wake velocity profile for compressible nonadiabatic flows

The paper suggests a new form of the wall-wake profile which is applicable to flows with heat transfer, and for which the velocity gradient at the boundary-layer edge is zero. The modified profile - which takes into account the effect of turbulent Prandtl number - is found to provide a good representation of experimental data for a wide range of Mach numbers and heat transfer. The skin friction coefficient values determined by a least squares fit of the profile to the data are in good agreement with values measured by the floating element technique. The values of boundary-layer thickness determined by the fit correspond more closely to the outer edge of the viscous flow region than those obtained with earlier versions of the wall-wake profile.

Sun, C.-C.↗
NASA NTRS1978

Turbulent boundary layers over nonstationary plane boundaries

Methods of predicting integral parameters and skin friction coefficients of turbulent boundary layers developing over moving ground planes were evaluated. The three methods evaluated were: relative integral parameter method; relative power law method; and modified law of the wall method.

Roper, A. T.↗
NASA NTRS1978

A critical evaluation of the predictions of the NASA-Lockheed multielement airfoil computer program

Theoretical predictions of several versions of the multielement airfoil computer program are evaluated. The computed results are compared with experimental high lift data of general aviation airfoils with a single trailing edge flap, and of airfoils with a leading edge flap and double slotted trailing edge flaps. Theoretical and experimental data include lift, pitching moment, profile drag and surface pressure distributions, boundary layer integral parameters, skin friction coefficients, and velocity profiles.

Brune, G. W.↗