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NASA NTRS1971

An Analytical Investigation of an Oscillating Wedge in a Supersonic Perfect Gas Flow

Several aspects of the oscillating wedge are investigated to evaluate both the resulting trends for the wedge and methods of analyzing unsteady flows. An existing hypersonic small disturbance theory for an oscillating thin wedge is extended and applied. A perturbation method involving linearization about the known flow is then derived and discussed. Subsequently, a finite difference technique for calculating the complete unsteady flow field of the wedge in motion is presented and discussed in conjunction with some calculated quasi-static nonlinear trends.

Bennett, R. M.↗

NASA NTRS1972

Boundary layer stability on a yawed spinning body of revolution and its effect on the magnus force and moment

The parameters are established which are important to the stability of a boundary layer flow over a yawed spinning cylinder in a uniform stream. It is shown that transition occurs asymmetrically in general and this asymmetry can be important for the prediction of aerodynamic forces and moments (e.g., the Magnus effect). Instability of the steady-state boundary layer flow is determined using small disturbance theory. Although the approach is strictly valid only for the calculation of the conditions for stability in the small, experimental data indicate that in many problems, it provides a good estimate for the transition to turbulence.

Jacobson, I. D.↗

NASA NTRS1972

A finite-difference method for transonic airfoil design.

This paper describes an inverse method for designing transonic airfoil sections or for modifying existing profiles. Mixed finite-difference procedures are applied to the equations of transonic small disturbance theory to determine the airfoil shape corresponding to a given surface pressure distribution. The equations are solved for the velocity components in the physical domain and flows with embedded shock waves can be calculated. To facilitate airfoil design, the method allows alternating between inverse and direct calculations to obtain a profile shape that satisfies given geometric constraints. Examples are shown of the application of the technique to improve the performance of several lifting airfoil sections. The extension of the method to three dimensions for designing supercritical wings is also indicated.

Steger, J. L.↗

NASA NTRS1972

Sideslip of wing-body combinations

A small-disturbance theory is developed for predicting the aerodynamics of an airplane in sideslip. Second-order terms involving the interaction between sideslip angle and angle of attack, sideslip angle and wing camber, etc., are retained. It is found that the second-order terms can produce the dominant sideslip effects when the dihedral of the lifting surfaces is small. Numerical implementation of the theory requires a solution procedure capable of producing accurate velocity gradients in the first-order solution.

Rubbert, P. E.↗

NASA NTRS1975

Convergence acceleration and shock fitting for transonic aerodynamics computations

Two problems in computational fluid dynamics are studied in the context of transonic small-disturbance theory - namely, (1) how to speed up the convergence for currently available iterative procedures, and (2) how a shock-fitting method may be adapted to existing relaxation procedures with minimal alterations in computer programming and storage requirements. The paper contributes to a clarification of error analyses for sequence transformations based on the power method (including also the nonlinear transforms of Aitken, Shanks, and Wilkinson), and to developing a cyclic iterative procedure applying the transformations. Examples testing the procedure for a model Dirichlet problem and for a transonic airfoil problem show that savings in computer time by a factor of three to five are generally possible, depending on accuracy requirements and the particular iterative procedure used.-

Hafez, M. M.↗

NASA NTRS1977

Experimental studies of trailing-edge conditions on an oscillating airfoil at frequency parameters of up to one

This paper describes an investigation to find the range of reduced frequencies over which the classical Kutta-Joukowsky condition is valid and the nature of deviations beyond this range. An NACA 64A010 airfoil with a 15-cm chord is supported between the side walls of a 25-cm x 35-cm low-speed wind tunnel and oscillated over reduced frequencies ranging from 0.05 to 1.2. The experimentally determined loading near the trailing edge is measured and compared with unsteady incompressible small-disturbance theory. Experimental data are obtained both with and without a boundary-layer trip. It is observed that application of the Kutta-Joukowsky condition in the theoretical analysis is valid below a reduced frequency of about 0.6 in predicting the loading in the trailing-edge region. At reduced frequencies beyond 0.8, the predicted results underestimate the measured loading near the trailing edge, and the deviations increase further with reduced frequency. Similarly, the experimental phase angle of the loading in the trailing-edge region agrees reasonably with the linear theory up to k = 0.8 but lags the predicted value beyond k = 0.8.

Satyanarayana, B.↗

NASA NTRS1976

Analysis of transonic flow over lifting and oscillating airfoils

Finite element procedures are presented for the numerical solution of transonic flow over lifting and oscillating airfoils based on small disturbance theory. The algorithm is simple and effective in handling the mixed flow problem and, for airfoil in free air, treats the entire flow domain by making use of the far field asymptotic solution. Numerical results are presented and compared with experimental data and those obtained by finite difference relaxation techniques.

Chan, S. T. K.↗

NASA NTRS1979

Axisymmetric internal flows with shocks

Internal flow problems with supersonic entrance conditions and subsonic exit conditions are studied. The suitability of applying the transonic-small disturbance theory to internal flows is examined and found to be very limited. The full inviscid equations in nonconservative form are solved by relaxation. Jump conditions which conserve mass and normal momentum are applied explicitly at shock waves. This method is suitable for solving flows which include supersonic-subsonic shock waves nearly normal to the streamlines.

Rizk, M. H.↗

NASA NTRS1982

Transonic aerodynamics - History and statement of the problem

An historical account is given of the state of transonic aerodynamics research and theorization before 1940, and at selected points between that year and 1975, in order to provide a basis for the understanding and evaluation of the most recent developments in the field. Intensive development began during the Second World War, when fighter aircraft diving at speeds in excess of Mach 0.8 underwent buffeting and longitudinal trim shift effects. By 1960, transonic small disturbance theory had been established as a mathematical model for the prediction of the aerodynamic properties of airfoils, wings, and bodies throughout the Mach number range from zero to 1.5. In the years leading up to 1975, which saw the formulation of the transonic equivalence rule, improvements in the computational speed and memory capacity of computers became the most significant factor in the development of theory.

Spreiter, J. R.↗

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

Two recent extensions of the vortex method

The vortex method, coupled to an integral boundary-layer solver, is applied to the numerical simulation of high-Reynolds-number, separated flows in two new cases: a bluff body in a wind tunnel and flow in a cascade. In the bluff body case, the blockage effect of the tunnel walls is included approximately, assuming an inviscid boundary condition at the walls. The resulting increase in drag is computed, and compares well with a small-disturbance theory and with experiments. The results for flow in a cascade are compared with results from two finite-difference codes for a single-blade case, and good agreement is found. When a staggered cascade is treated with five independent blades, the simulation predicts rotating stall, depending on the angle of attack, and the essential features of the flow are correct. The sensitivity of this phenomenon to various parameters is studied and the stall boundary is found.

Spalart, P. R.↗

NASA NTRS1984

The effects of gusts on the fluctuating airloads of airfoils in transonic flow

Unsteady interactions of distributed and sharp-edged gusts with a stationary airfoil have been analyzed in two-dimensional transonic flow.A simple method of introducing such disturbances has been numerically implemented within the framework of unsteady, transonic small-disturbance theory. Representative solutions for various airfoils subjected to chordwise and transverse gusts show that the strength and unsteady motion of the shock wave on the airfoil significantly affect the flowfield development and, consequently, the dynamic airloads. Also a study was made of the reductions in the unsteady airloads that can be achieved by the proper active control motion of a trailing-edge flap, and a simple gust-alleviation strategy was developed. However, the chordwise pressure distributions associated with gusts are very different from those produced by trailing-edge flap oscillations. Consequently, the fluctuating lift and the unsteady pitching moments cannot both be eliminated simultaneously.

Mccroskey, W. J.↗

NASA NTRS1984

Transition and mixing in impulsively started jets and vortex rings

A new method is used to analyze transition in impulsively started jets and vortex rings. The method uses similarity variables to reduce the equations for unsteady particle paths to a quasi-autonomous system with the Reynolds number as a parameter. The flow pattern is represented in terms of the phase portrait of this system and the structure of the flow is defined by its critical points. Flow transition is examined in terms of bifurcations in the topology of the phase portrait which occur as the Reynolds number is increased. There is no assumption that the flow is parallel or that it is subjected to small disturbances. The method of analysis, through straightforward, is new and lies outside the usual small disturbance theory used to determine the stability of various profile shapes.

Cantwell, B. J.↗

NASA NTRS1986

Second-Order-Potential Analysis and Optimization

Optimum camber designed for supersonic and hypersonic vehicles. Second Order Potential Analysis and Optimization (SOPA) package set of computer programs used to predict aerodynamic characteristics and design optimum camber for both supersonic and hypersonic vehicles. Analysis program incorporates second-order-potential, small-disturbance theory for analysis of wing/body configurations. Optimization program uses analysis results to generate optimum camber, twist, or flap deflections by minimizing zero suction drag. SOPA written in FORTRAN V for batch execution.

Clever, W. C.↗

NASA NTRS1984

Supersonic second order analysis and optimization program user's manual

Approximate nonlinear inviscid theoretical techniques for predicting aerodynamic characteristics and surface pressures for relatively slender vehicles at supersonic and moderate hypersonic speeds were developed. Emphasis was placed on approaches that would be responsive to conceptual configuration design level of effort. Second order small disturbance theory was utilized to meet this objective. Numerical codes were developed for analysis and design of relatively general three dimensional geometries. Results from the computations indicate good agreement with experimental results for a variety of wing, body, and wing-body shapes. Case computational time of one minute on a CDC 176 are typical for practical aircraft arrangement.

Clever, W. C.↗

NASA NTRS1987

Unsteady transonic flow simulation on a full-span-wing-body configuration

The presence of a body influences both the aerodynamic and aeroelastic performance of wings. Such effects are more pronounced in the transonic regime. To accurately account for the effect of the body, particularly when the wings are experiencing asymmetric modal motions, it is necessary to model the full configuration in the nonlinear transonic regime. In this study, full-span-wing-body configurations are simulated for the first time by a theoretical method that uses the unsteady potential equations based on the small-disturbance theory. The body geometry is modeled exactly as the physical shape, instead of as a rectangular box, which has been done in the past. Steady pressure computations for wing-body configurations compare well with the available experimental data. Unsteady pressure computations when the wings are oscillating in asymmetric modes show significant influence of the body.

Guruswamy, Guru P.↗

NASA NTRS1989

Computational fluid dynamics research and applications at NASA Langley Research Center

Information on computational fluid dynamics (CFD) research and applications carried out at the NASA Langley Research Center is given in viewgraph form. The Langley CFD strategy, the five-year plan in CFD and flow physics, 3-block grid topology, the effect of a patching algorithm, F-18 surface flow, entropy and vorticity effects that improve accuracy of unsteady transonic small disturbance theory, and the effects of reduced frequency on first harmonic components of unsteady pressures due to airfoil pitching are among the topics covered.

South, Jerry C., Jr.↗

NASA NTRS1991

Computational analysis of hypersonic flows past elliptic-cone waveriders

A comprehensive study for the inviscid numerical calculation of the hypersonic flow past a class of elliptic-cone derived waveriders is presented. The theoretical background associated with hypersonic small-disturbance theory (HSDT) is reviewed. Several approximation formulas for the waverider compression surface are established. A CFD algorithm is used to calculate flow fields for the on-design case and a variety of off-design cases. The results are compared with HSDT, experiment, and other available CFD results. For the waverider shape used in previous investigations, the bow shock for the on-design condition stands off from the leading-edge tip of the waverider. It was found that this occurs because the tip was too thick according to the approximating shape formula that was used to describe the compression surface. When this was corrected, the bow shock became closer to attached as it should be. At Mach numbers greater than the design condition, a lambda-shock configuration develops near the tip of the compression surface. At negative angles of attack, other complicated shock patterns occur near the leading-edge tip. These heretofore unknown flow patterns show the power and utility of CFD for investigating novel hypersonic configurations such as waveriders.

Yoon, Bok-Hyun↗