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NASA NTRS1982

Computation of supersonic turbulent flow past a spinning cone

Computational results are presented for supersonic laminar and turbulent flow past a pointed cone at angle of attack obtained with a parabolic Navier-Stokes marching code. The code takes into account the asymmetries in the flowfield resulting from spinning motion and computes the asymmetric shock shape, crossflow and streamwise shear, heat transfer, crossflow separation, and vortex structure. The Magnus force and moments are also computed. Comparisons are made with other analyses based on boundary-layer equations. For certain laminar flow conditions, an anomaly is discovered in the displacement thickness contribution to the Magnus force when compared with boundary-layer results. For turbulent flow, at small angles of attack, good agreement is obtained with the experimental data and other theoretical results.

Agarwal, R. K.↗

NASA NTRS1982

Extraction of model performance from wall data in a 2-dimensional transonic flexible walled test section

Data obtained from the boundary of a test section provides information on the model contained within it. A method for extracting some of this data in two dimensional testing is described. Examples of model data are included on lift, pitching moment and wake displacement thickness. A FORTRAN listing is also described, having a form suitable for incorporation into the software package used in the running of such a test section.

Goodyer, M. J.↗

NASA NTRS1980

A study of optimum cowl shapes and flow port locations for minimum drag with effective engine cooling, volume 1

The contributions to the cruise drag of light aircraft arising from the shape of the engine cowl and the forward fuselage area and also that resulting from the cooling air mass flow through intake and exhaust sites on the nacelle were analyzed. The methods employed for the calculation of the potential flow about an arbitrary three dimensional body are described with modifications to include the effects of boundary layer displacement thickness, a nonuniform onset flow field (such as that due to a rotating propeller), and the presence of air intakes and exhausts. A simple, reliable, largely automated scheme to better define or change the shape of a body is also presented. A technique was developed which can yield physically acceptable skin friction and pressure drag coefficients for isolated light aircraft bodies. For test cases on a blunt nose Cessna 182 fuselage, the technique predicted drag reductions as much as 28.5% by body recontouring and proper placements and sizing of the cooling air intakes and exhausts.

Fox, S. R.↗

NASA NTRS1980

A study of optimum cowl shapes and flow port locations for minimum drag with effective engine cooling, volume 2

The listings, user's instructions, sample inputs, and sample outputs of two computer programs which are especially useful in obtaining an approximate solution of the viscous flow over an arbitrary nonlifting three dimensional body are provided. The first program performs a potential flow solution by a well known panel method and readjusts this initial solution to account for the effects of the boundary layer displacement thickness, a nonuniform but unidirectional onset flow field, and the presence of air intakes and exhausts. The second program is effectually a geometry package which allows the user to change or refine the shape of a body to satisfy particular needs without a significant amount of human intervention. An effort to reduce the cruise drag of light aircraft through an analytical study of the contributions to the drag arising from the engine cowl shape and the foward fuselage area and also that resulting from the cooling air mass flowing through intake and exhaust sites on the nacelle is presented. The programs may be effectively used to determine the appropriate body modifications or flow port locations to reduce the cruise drag as well as to provide sufficient air flow for cooling the engine.

Fox, S. R.↗

NASA NTRS1983

A method for modifying two-dimensional adaptive wind-tunnel walls including analytical and experimental verification

The theoretical development of a simple and consistent method for removing the interference in adaptive-wall wind tunnels is reported. A Cauchy integral formulation of the velocities in an imaginary infinite extension of the real wind-tunnel flow is obtained and evaluated on a closed contour dividing the real and imaginary flow. The contour consists of the upper and lower effective wind-tunnel walls (wall plus boundary-layer displacement thickness) and upstream and downstream boundaries perpendicular to the axial tunnel flow. The resulting integral expressions for the streamwise and normal perturbation velocities on the contour are integrated by assuming a linear variation of the velocities between data-measurement stations along the contour. In an iterative process, the velocity components calculated on the upper and lower boundaries are then used to correct the shape of the wall to remove the interference. Convergence of the technique is shown numerically for the cases of a circular cylinder and a lifting and nonlifting NACA 0012 airfoil in incompressible flow. Experimental convergence at a transonic Mach number is demonstrated by using an NACA 0012 airfoil at zero lift.

Everhart, J. L.↗

NASA NTRS1983

Effect of boundary layers on solid walls in three-dimensional subsonic wind tunnels

A linear method is developed which accounts for the effects of boundary layers on solid walls in subsonic three-dimensional wind tunnels. The streamwise gradient of the displacement thickness for a solid-wall boundary layer is expressed in terms of the von Karman momentum integral. The growth of the boundary layer due to the wall shearing stress is small compared to the variation caused by the model-induced pressure gradient. The viscous boundary condition can be expressed in terms of the edge velocity gradient and the gradient of the inviscid velocity potential function at the wall. Utilizing this analysis on the solid walls of several three-dimensional wind tunnel configurations shows that the most pronounced wall boundary-layer effect is on solid blockage for completely closed wind tunnels. For solid-wall tunnel configurations, the streamline curvature interference factor is reduced by a significant amount, while the lift interference factor at the model station does not depend on the boundary-layer parameter. For combination wall configurations, the slot effect of the horizontal walls dominates the viscous effect of the solid sidewalls.

Adcock, J. B.↗

NASA NTRS1983

A fast viscous correction method for unsteady transonic flow about airfoils

This study modified the inviscid, small-disturbances, unsteady, transonic code, LTRAN2, so that the viscous effect could be considered for the purpose of improving the code's accuracy without substantially increasing the computational time. By using a conventional integral boundary layer method to determine the displacement thickness and an empirical model of viscous wedge to simulate the suddenly thickened boundary layer behind a shock, it resulted in better agreement with experimental data for both the shock position and the pressure coefficient. Aerodynamic performances were calculated for two supercritical airfoils. When the unsteady procedure was used to obtain steady state results as the initial condition, the unsteady viscous solution for the RAE 2822 airfoil required 100.5% of the computational time of the inviscid solution. When an iterative scheme was used to obtain the steady state results as the initial condition, the unsteady viscous solution for the NLR 7301 airfoil required 88% of the computational time of the inviscid solution.

Lee, S. C.↗

NASA NTRS1983

Investigation of the effects of upstream sidewall boundary-layer removal on a supercritical airfoil

Sidewall boundary-layer effects have been investigated by applying partial upstream sidewall boundary-layer removal in the Langley 0.3-m Transonic Cryogenic Tunnel. Over the range of sidewall boundary-layer displacement thickness of these tests the influence on pressure distributions was found to be small for subcritical conditions; however, for supercritical conditions the shock position was affected by the sidewall boundary layer. For these tests, with and without boundary-layer removal, comparisons with predictions of the GRUMFOIL computer code indicated that Mach number corrections due to the sidewall boundary layer improves the agreement for both subcritical and supercritical conditions. The results show the necessity for accounting for sidewall effects even when the top and bottom wall effects are small.

Murthy, A. V.↗

NASA NTRS1982

The development of a two-dimensional wavepacket in a growing boundary layer

The evolution of a two-dimensional wavepacket in a growing boundary layer is discussed in terms of linear stability theory. The wavepacket is represented by an integral of periodic wavetrains, each of which is defined as a series in terms of the inverse of the local displacement thickness Reynolds number to the one half power. Comparisons are made between the waveforms computed directly from the integral, a steepest-descent expansion of the integral, and a global expansion about the peak of the wavepacket.

Gaster, M.↗

NASA NTRS1983

Hypersonic slender-wedge analysis with gradual change in angle of attack

The behavior of a narrow cross-section wedge wing moving at a high Mach number and subjected to an angle of attack changing exponentially with time is investigated. This type of wedge wing is commonly employed as a lifting surface in hypersonic vehicles. The time history of wall shear, heat transfer, displacement thickness, and viscous induced pressure are determined. Results show that for the same change in angle of attack, the flow attains the final steady state much faster when the change is exponential than when the change is made impulsively. In addition, the unsteady character of the flow is primarily confined to the initial stages of the change in the angle of attack.

Gupta, R. N.↗

NASA NTRS1983

Design of shock-free compressor cascades including viscous boundary layer effects

A computer code that generates shock-free transonic compressor cascade shapes while taking into account viscosity effects is developed. The mathematical model for the inviscid flow field is the full potential equation. The Kutta-Joukowski condition is satisfied by varying the free stream angle at downstream infinity. A boundary fitted computational grid of C-type is generated using a sequence of conformal mapping and nonorthogonal coordinate stretching and shearing transformations. The inviscid calculation is performed sequentially on up to four consecutively refined grids thereby accelerating the convergence of the solution process. The full potential equation is solved using a finite area technique and rotated, type-dependent finite differencing. Artificial viscosity of the first order is added in a fully conservative form. Shock-free cascade airfoil shapes are obtained using the fictitious gas concept of Sobieczky and the method of characteristics in the rheograph plane. Viscosity effects are incorporated via a boundary layer displacement thickness. The integral boundary layer code is based on Rotta's turbulence model and assumes transition region of zero length.

Dulikravich, G. S.↗

NASA NTRS1983

Numerical solution of three-dimensional unsteady transonic flow over wings including inviscid/viscous interactions

A numerical procedure is presented for computing the unsteady transonic flow field about three dimensional swept wings undergoing general time dependent motion. The outer inviscid portion of the flow is assumed to be governed by the modified unsteady transonic small disturbance potential equation which is integrated in the time domain by means of an efficient alternating direction implicit approximate factorization algorithm. Gross dominant effects of the shock boundary layer interaction are accounted for by a simple empirically defined model. Viscous flow regions adjacent to the wing surface and in the trailing wake are described by a set of integral equations appropriate for compressible turbulent shear layers. The two dimensional boundary layer equations are applied quasi-statically stripwise across the span. Coupling with the outer inviscid flow is implemented through use of the displacement thickness concept within the limitations of small disturbance theory. Validity of the assumptions underlying the method is established by comparison with experimental data for the flow about a high aspect ratio transport wing having an advanced airfoil section.

Rizzetta, D. P.↗

NASA NTRS1984

ALESEP: A computer program for the analysis of airfoil leading edge separation bubbles

The ALESEP program for the analysis of the inviscid/viscous interaction which occurs due to the presence of a closed laminar transitional separation bubble on an airflow is presented. The ALESEP code provides a iterative solution of the boundary layer equations expressed in an inverse formulation coupled to a Cauchy integral representation of the inviscid flow. This interaction analysis is treated as a local perturbation to a known solution obtained from a global airfoil analysis. Part of the required input to the ALESEP code are the reference displacement thickness and tangential velocity distributions. Special windward differencing may be used in the reversed flow regions of the separation bubble to accurately account for the flow direction in the discretization of the streamwise convection of momentum. The ALESEP code contains a forced transition model based on a streamwise intermittency function and a natural transition model based on a solution of the integral form of the turbulent kinetic energy equation. Instructions for the input/output, and program usage are presented.

Davis, R. L.↗

NASA NTRS1984

Effect of sidewall suction on flow in two-dimensional wind tunnels

A closed-form analysis of flow in a two-dimensional subsonic wind tunnel which uses sidewall suction around the model to reduce sidewall boundary-layer effects is presented. The model problem which is treated involves a flat plate airfoil in a tunnel with a suction window shaped to permit an analytic solution. This solution shows that the lift coefficient depends explicitly on the porosity parameter of the suction window and implicitly on the suction pressure differential. For a given sidewall displacement thickness, the lift coefficient increases as the suction-window porosity decreases.

Barnwell, R. W.↗

NASA NTRS1984

Investigation of sidewall boundary layer removal effects on two different chord airfoil models in the Langley 0.3-meter Transonic Cryogenic Tunnel

An investigation was carried out on two CAST 10-2 airfoil models with chords of 3 in. and 6 in. To evaluate the extent of sidewall influence on airfoil tests at transonic Mach numbers. The tests were conducted in the Langley 0.3-m Transonic Cryogenic Tunnel two-dimensional test section equipped with an upstream sidewall boundary layer removal system which reduces the boundary layer displacement thickness to about 1 percent of model halfspan from an initial 2 percent without boundary layer removal. Test results have shown the changes in the location of the shock on the upper surface of the airfoil to be about the same for both models with and without sidewall boundary layer removal. Even though large differences were noted in the high lift characteristics of the two models, the sidewall boundary layer removal had little effect on the differences. These tests also served to validate the boundary layer removal technique and the associated Mach number correction required with upstream boundary layer removal.

Murthy, A. V.↗

NASA NTRS1984

Integral boundary-layer models for turbulent separated flows

Two-dimensional, integral boundary-layer methods of the entrainment and dissipation type, with closure relationships which account for turbulent separated flows through the velocity and turbulence models, are developed. Kinematic shape factor relations used in the two methods are evaluated by comparison with recently obtained experimental data for separated flows. Prescribed-displacement-thickness computations are made with both methods and compared to experiment for a series of separated flows, including low speed and transonic shock-induced separation. Effects of upstream history on the turbulent shear stress development are shown to be important for the accurate prediction of the separated flows considered and the experimental trends are reasonably modeled by a rate equation derived from the turbulent kinetic energy equation.

Thomas, J. L.↗

NASA NTRS1984

An experimental study of a supercritical trailing-edge flow

An experimental study has been conducted of a transonic, turbulent, high-Reynolds-number blunt trailing-edge flow. The model shape and the surface pressure distribution are characteristics of a modern supercritical airfoil under shock-free conditions. Reynolds number and pressure gradient scaling of the boundary layer are relevant to airfoil applications. The data set is exceptionally accurate and consistent, with the momentum balance accounting for the flux of momentum to within 1 percent, except in the immediate vicinity of the blunt trailing edge. The experimental flow exhibits strong viscous-inviscid interaction and higher-order boundary-layer effects including strong adverse streamwise pressure gradient, significant normal pressure gradients associated with surface and streamline curvature, and significant wake curvature. Navier-Stokes calculations with a two-equation K-epsilon turbulence model predict the correct pressure distribution which demonstrates the utility of these engineering tools. The experiment approaches separation at the strailing edge. However, in comparison to the experiment, the calculations predict too high skin friction and insufficient displacement thickness growth. An analysis of the turbulent and mean flow fields reveals the turbulence model defects are likely in modeling the dissipation source and sink terms, and in the eddy viscosity relation.

Brown, J. L.↗

NASA NTRS1984

Effect of upstream sidewall boundary layer removal on an airfoil test

Sidewall boundary layer effects were investigated by applying partial upstream sidewall boundary layer removal in the Langley 0.3-m transonic cryogenic tunnel. Over the range of sidewall boundary layer displacement thickness of these tests the influence on pressure distribution was found to be small for subcritical conditions; however, for supercritical conditions the shock position was affected by the sidewall boundary layer. For these tests (with and without boundary layer remove) comparisons with predictions of the GRUMFOIL computer code indicated that Mach number corrections due to the sidewall boundary layer improve the agreement for both subcritical and supercritical conditions. The results also show that sidewall boundary layer removal reduces the magnitude of the sidewall correction; however, a suitable correction must still be made.

Johnson, C. B.↗