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All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Simulations of curved turbulent boundary layers

The objective of this work is to develop a space-time accurate numerical method for the solution of incompressible Navier-Stokes equations in generalized coordinates. The resulting code is to be used for direct and large-eddy simulation of turbulence in complex geometries. In a previous paper, the system of Navier-Stokes equations in general curvilinear coordinates was solved by a second-order accurate finite-difference scheme. Satisfactory results were obtained for several flows in two and three dimensions. The system of Navier-Stokes for the fluxes are given in Orlandi (1989). The main deficiency of the numerical scheme was the large CPU time required for the solution of the Poisson equation for the 'pressure' field. The point SOR relaxation, in conjunction with a multigrid scheme, was used for the Poisson equation. In some cases, particularly with very fine grids, it was impossible to obtain a divergent-free flow. A preliminary attempt is made to compute the spatially evolving flow of Swearingen & Blackwelder. To reduce the streamwise distance, the inflow was at a distance x = 60 cm from the leading edge.

Orlandi, Paolo↗
NASA NTRS1953

Theoretical pressure distribution and wave drags for conical boattails

Afterbody pressure distributions and wave drag were calculated using a second-order theory for a variety of conical boattails at zero angle of attack. Results are presented for Mach numbers from 1.5 to 4.5, area ratios from 0.200 to 0.800, and boattail angle from 3 degrees to 11 degrees. The results indicate that for a given boattail angle, the wave drag decreases with increasing Mach number and area ratio. The wave drag, for a constant area ratio, increases with increasing boattail angle. For a specific Mach number, area ratio, and fineness ratio, a comparison of the wave-drag coefficients for conical, tangent-parabolic, and secant-parabolic boattails showed the conical boattail to have the smallest wave drag.

Jack, John R↗
NASA NTRS1954

Aerodynamics of Slender Bodies at Mach Number of 3.12 and Reynolds Numbers from 2 x 10(exp 6) to 15 x 10(exp 6) IV : Aerodynamic Characteristics of Series of Four Bodies Having Near-parabolic Noses and Cylindrical Afterbodies

Pressure distributions and forces for a series of four bodies of revolution having nose-fineness ratios varying from 4 to 10 have been obtained and compared with theory for a Mach number of 3.12, a Reynolds number range of 2x10(sup)6 to 14x10(sup)6, and angles of attack from zero to 9 degrees. In general, a comparison of the experimental data with a second-order theory showed good agreement for the range of variables investigated.

BODIES - FITNESS RATIO↗
NASA NTRS1954

Aerodynamics of Slender Bodies at Mach Number of 3.12 and Reynolds Numbers from 2 x 10(exp 6) to 15 x 10(exp 6) V : Aerodynamic Load Distributions for a Series of Four Boattailed Bodies

Pressure distributions for a series of four boattailed bodies of revolution were obtained and compared with theory for a Mach number of 3.12, a Reynolds number range of 2 x 10 to 6th power to 14 x 10 to the 6th power, and angles of attack from zero to 9 degrees. Second-order theory adequately predicted the pressure distribution for regions free of the effects of cross-flow separation.

Moskowitz, Barry↗
NASA NTRS1956

An analog study of a shock-position diffuser control on a supersonic turbojet engine

Shock position was assumed to be controlled by air bleed through a diffuser-exit bypass door operated by a second-order servomotor. Pressure disturbance resulting from changes in bypass-door position had whereas a disturbance in engine speed had a large effect on diffuser pressure and could impose severe requirements on diffuser control response. The controlled diffuser response improved with faster servomotor response and smaller diffuser dead time and lag. The effect of diffuser dead time on diffuser response was greater than the effect of diffuser lag.

Novik, David↗
NASA NTRS1958

Investigation of a Nonlinear Control System

A discontinuous variation of coefficients of the differential equation describing the linear control system before nonlinear elements are added is studied in detail. The nonlinear feedback is applied to a second-order system. Simulation techniques are used to study performance of the nonlinear control system and to compare it with the linear system for a wide variety of inputs. A detailed quantitative study of the influence of relay delays and of a transport delay is presented.

Flugge-Lotz, I↗
NASA NTRS1942

On the use of residue theory for treating the subsonic flow of a compressible fluid

A new mathematical technique, due to Milne-Thomson, is used to obtain an improved form of the method of Poggi for calculating the effect of compressibility on the subsonic flow past an obstacle. By means of this new method, the difficult surface integrals of the original Poggi method can be replaced by line integrals. These line integrals are then solved by the use of residue theory. In this way an equation is obtained giving the second-order effect of compressibility on the velocity of the fluid. The method is practicable for obtaining the higher-order effects of compressibility on the velocity field. As an illustration of the general result, the flow past an elliptic cylinder is discussed.

Kaplan, Carl↗
NASA NTRS1950

Frequency response of linear systems from transient data

Methods are presented that use general correlative time-response input and output data for a linear system to determine the frequency-response function of that system. These methods give an exact description of any linear system for which such transient data are available. Examples are shown of application of a method to both an underdamped and a critically damped exact second-order system, and to an exact first-order system with and without dead time. Experimental data for a turbine-propeller engine showing the response of engine speed to change in propeller-blade angle are presented and analyzed.

Laverne, Melvin E↗
NASA NTRS1951

On the particular integrals of the Prandtl-Busemann iteration equations for the flow of a compressible fluid

The particular integrals of the second-order and third-order Prandtl-Busemann iteration equations for the flow of a compressible fluid are obtained by means of the method in which the complex conjugate variables are utilized as the independent variables of the analysis. The assumption is made that the Prandtl-Glauert solution of the linearized or first-order iteration equation for the two-dimensional flow of a compressible fluid is known. The forms of the particular integrals, derived for subsonic flow, are readily adapted to supersonic flows with only a change in sign of one of the parameters of the problem.

Kaplan, Carl↗
NASA NTRS1957

Comparison of several methods for obtaining the time response of linear systems to either a unit impulse or arbitrary input from frequency-response data

Several methods of obtaining the time response of Linear systems to either a unit impulse or an arbitrary input from frequency-response data are described and compared. Comparisons indicate that all the methods give good accuracy when applied to a second-order system; the main difference is the required computing time. The methods generally classified as inverse Laplace transform methods were found to be most effective in determining the response to a unit impulse from frequency-response data of higher order systems. Some discussion and examples are given of the use of such methods as flight-data-analysis techniques in predicting loads and motions of a flexible aircraft on the basis of simple calculations when the aircraft frequency response is known.

Donegan, James J↗
NASA NTRS1989

CSI compensation for reduced-order model based control of a flexible robot manipulator

In controller design for flexible structures, certain system modes are extremely important for the overall performance of the structure. A reduced-order model (ROM) based control focuses on these modes, providing a viable, active control algorithm for large systems. Unfortunately, unmodeled structure dynamics can interact with the ROM controller (CSI) and cause crippling deterioration of system performance, possibly to the point that system stability is lost. A residual model filter (RMF) eliminates one channel of control structure interaction (CSI), while adding only a simple, second-order filter to the control loop. Thus, the ROM controller can be designed independently, based strictly on performance criteria, and residual mode filters can then be selected to compensate for CSI. A flexible robot manipulator is used for preliminary experimentation with the ROM/RMF design methodology. Since the controller was to be implemented both with, and without compensation for CSI, the ROM control gains are carefully chosen such that closed loop stability is never compromised. In this way, RMF effectiveness is easily evaluated in terms of the improvement in system performance resulting from CSI compensation.

Reisenauer, Brian T.↗
NASA NTRS1990

Computation of three-dimensional compressible boundary layers to fourth-order accuracy on wings and fuselages

A solution method, fourth-order accurate in the body-normal direction and second-order accurate in the stream surface directions, to solve the compressible 3-D boundary layer equations is presented. The transformation used, the discretization details, and the solution procedure are described. Ten validation cases of varying complexity are presented and results of calculation given. The results range from subsonic flow to supersonic flow and involve 2-D or 3-D geometries. Applications to laminar flow past wing and fuselage-type bodies are discussed. An interface procedure is used to solve the surface Euler equations with the inviscid flow pressure field as the input to assure accurate boundary conditions at the boundary layer edge. Complete details of the computer program used and information necessary to run each of the test cases are given in the Appendix.

Iyer, Venkit↗
NASA NTRS1995

Effect of turbulence models on criticality conditions in swirling flows

The critical state of vortex cores downstream of vortex breakdown has been studied. Base vortical flows were computed using the Reynolds-averaged, axisymmetric Navier-Stokes equations. Standard K - epsilon, RNG and second-order Reynolds stress models were employed. Results indicate that the return to supercriticality is highly dependent on the turbulence model. The K - epsilon model predicted a rapid return of the vortex to supercritical conditions, the location of which showed little sensitivity to changes in the swirl ratio. The Reynolds stress model predicted that the vortex remains subcritical to the end of the domain for each of the swirl ratios employed, and provided results in qualitative agreement with experimental work. The RNG model produced intermediate results, with a downstream movement in the critical location with increasing swirl. Calculations for which area reductions were introduced at the exit in a subcritical flow were also performed using the Reynolds stress model. The structure of the resulting recirculation zone was altered significantly. However, when area reductions were employed within supercritical flows as predicted using the two-equation models, no significant influence on the recirculation zone was noted.

Gatski, Thomas B.↗
NASA NTRS1991

First-order inflation

In the original proposal, inflation occurred in the process of a strongly first-order phase transition. This model was soon demonstrated to be fatally flawed. Subsequent models for inflation involved phase transitions that were second-order, or perhaps weakly first-order; some even involved no phase transition at all. Recently the possibility of inflation during a strongly first-order phase transition has been revived. In this talk I will discuss some models for first-order inflation, and emphasize unique signatures that result if inflation is realized in a first-order transition. Before discussing first-order inflation, I will briefly review some of the history of inflation to demonstrate how first-order inflation differs from other models.

Kolb, Edward W.↗
NASA NTRS1976

Numerical Solutions of Supersonic and Hypersonic Laminar Compression Corner Flows

An efficient time-splitting, second-order accurate, numerical scheme is used to solve the complete Navier-Stokes equations for supersonic and hypersonic laminar flow over a two-dimensional compression corner. A fine, exponentially stretched mesh spacing is used in the region near the wall for resolving the viscous layer. Good agreement is obtained between the present computed results and experimental measurement for a Mach number of 14.1 and a Reynolds number of 1.04 x 10(exp 5) with wedge angles of 15 deg, 18 deg, and 24 deg. The details of the pressure variation across the boundary layer are given, and a correlation between the leading edge shock and the peaks in surface pressure and heat transfer is observed.

Hung, C. M.↗
NASA NTRS1961

Aerodynamic Effects of Some Configuration Variables on the Aeroelastic Characteristics of Lifting Surfaces at Mach Numbers from 0.7 to 6.86

Results of flutter tests on some simple all-movable-control-type models are given. One set of models, which had a square planform with double-wedge airfoils with four different values of leading- and trailing-edge radii from 0 to 6 percent chord and airfoil thicknesses of 9, 11, 14, and 20 percent chord, was tested at Mach numbers from 0.7 to 6.86. The bending-to-torsion frequency ratio was about 0.33. The other set of models, which had a tapered planform with single-wedge and double-wedge airfoils with thicknesses of 3, 6, 9, and 12 percent chord, was tested at Mach numbers from 0.7 to 3.98 and a frequency ratio of about 0.42. The tests indicate that, in general, increasing thickness has a destabilizing effect at the higher Mach numbers but is stabilizing at subsonic and transonic Mach numbers. Double-wedge airfoils are more prone to flutter than single-wedge airfoils at comparable stiffness levels. Increasing airfoil bluntness has a stabilizing effect on the flutter boundary at supersonic speeds but has a negligible effect at subsonic speeds. However, increasing bluntness may also lead to divergence at supersonic speeds. Results of calculations using second-order piston-theory aerodynamics in conjunction with a coupled-mode analysis and an uncoupled-mode analysis are compared with the experimental results for the sharp-edge airfoils at supersonic speeds. The uncoupled-mode analysis more accurately predicted the flutter characteristics of the tapered-planform models, whereas the coupled-mode analysis was somewhat better for the square-planform models. For both the uncoupled- and coupled-mode analyses, agreement with the experimental results improved with increasing Mach number. In general, both methods of analysis gave unconservative results with respect to the experimental flutter boundaries.

Hanson, Perry W.↗
NASA NTRS1982

A Numerical Method for Solving the Equations of Compressible Viscous Flow

Although much progress has already been made In solving problems in aerodynamic design, many new developments are still needed before the equations for unsteady compressible viscous flow can be solved routinely. This paper describes one such development. A new method for solving these equations has been devised that 1) is second-order accurate in space and time, 2) is unconditionally stable, 3) preserves conservation form, 4) requires no block or scalar tridiagonal inversions, 5) is simple and straightforward to program (estimated 10% modification for the update of many existing programs), 6) is more efficient than present methods, and 7) should easily adapt to current and future computer architectures. Computational results for laminar and turbulent flows at Reynolds numbers from 3 x 10(exp 5) to 3 x 10(exp 7) and at CFL numbers as high as 10(exp 3) are compared with theory and experiment.

MacCormack, R. W.↗
NASA NTRS1981

Numerical Simulation of Three-Dimensional Boattail Afterbody Flowfields

The thin shear-layer approximations of the three-dimensional, compressible Navier-Stokes equations are solved for subsonic, transonic, and supersonic now over axisymmetric boattail bodies at moderate angles of attack. The plume is simulated by a solid body configuration identical to those used In experimental tests. An implicit algorithm of second-order accuracy is used to solve the equations on the ILLIAC 4 computer. The turbulence is expressed by an algebraic model applicable to three-dimensional flowfields with moderate separation. The formulation used is attractive in its independence of boundary-layer parameters. Such a simple model, however, is incapable of supporting detailed quantitative descriptions of complex shear flows. Never-the-less, good qualitative comparisons are found with three different sets of experimental date. Quantitative improvement will depend on improved turbulence transport descriptions.

Deiwert, G. S.↗