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At least 1,099 records · Page 61

Application of the laser velocimeter to airfoil research

A laser velocimeter (LV) was installed in the Langley V/STOL tunnel to measure the velocity field about a wing with a NACA 0012 airfoil section. These measurements were compared at low angle of attack with a two dimensional, viscous flow prediction program. The velocity field over the wing in a fully stalled condition was also measured by the LV. The unique ability of the LV to measure absolute flow magnitude and direction without prior knowledge of general flow direction was demonstrated in the complex separated reverse flows near the wing upper surface at the high angle of attack. The general characteristics of the flow field over the stalled wing were substantiated by a vapor screen flow visualization technique.

Hoad, D. R.↗

Topology of two-dimensional and three-dimensional separated flows

It is shown that topology rules can define a small number of singular points on an aerodynamic surface and in the flow which can be combined in various ways to create the structures and characterize the physical mechanisms of three-dimensional separated flows. This topological development is based on the hypothesis that vector fields of skin-friction lines and external streamlines remain continuous. Among examples treated are the lee-side separated flows about slender bodies at angle of attack with symmetric or asymmetric wake structures; about a protuberance normal to a wall; and over a rearward-facing axisymmetric step.

Tobak, M.↗

General Potential Theory of Arbitrary Wing Sections

The problem of determining the two dimensional potential flow around wing sections of any shape is examined. The problem is condensed into the compact form of an integral equation capable of yielding numerical solutions by a direct process. An attempt is made to analyze and coordinate the results of earlier studies relating to properties of wing sections. The existing approximate theory of thin wing sections and the Joukowski theory with its numerous generalizations are reduced to special cases of the general theory of arbitrary sections, permitting a clearer perspective of the entire field. The method which permits the determination of the velocity at any point of an arbitrary section and the associated lift and moments is described. The method is also discussed in terms for developing new shapes of preassigned aerodynamical properties.

Theodorsen, T.↗

Drag reduction effects in turbulent boundary layers over wavy walls

Two dimensional incompressible flow over wavy surfaces are analyzed numerically by spectral methods. Algorithms for periodic flows (Fourier modes in the periodic flow direction and Chebycheff modes in the normal direction), and inflow-outflow boundary conditions (Chebycheff modes used in both directions) are described. Results obtained using both codes are reported for laminar flows. Comparisons with known theoretical and experimental results are made.

Balasubramanian, R.↗

Steady state spurious errors in shock-capturing numerical schemes

The behavior of the steady state spurious error modes of the MacCormack scheme and the upwind scheme of Warming and Beam was obtained from a linearized difference equation for the steady state error. It was shown that the spurious errors can exist either as an eigensolution of the homogeneous part of this difference equation or because of excitation from large discretization errors near oblique shocks. It was found that the upwind scheme does not permit spurious oscillations on the upstream side of shocks. Examples are given for the inviscid Burgers' equation and for one and two dimensional gasdynamic flows.

Karlsen, L. K.↗

A two dimensional model of viscous slot flow

The effects of viscosity on flows through slots are investigated. Using Briley's formulation of the Alternating Direction Implicit method together with the Thompson transformation, numerical solution of viscous incompressible flow through a slot is simulated, for Reynolds number 1000 and openness ratio one tenth. The problem is formulated in terms of stream function and vorticity. A wall iteration of Israeli type is employed to iteratively induce the no slip condition on velocity.

Cooke, C. H.↗

A diagonal form of an implicit approximate-factorization algorithm

A modification of an implicit approximate-factorization finite-difference algorithm applied to partial differential equations is presented. This algorithm is applied to the two- and three-dimensional Euler equations in general curvilinear coordinates. The modification transforms the coupled system of equations into an uncoupled diagonal form that requires less computational work. For steady-state applications, the resulting diagonal algorithm retains the stability and accuracy characteristics of the original algorithm. The diagonal algorithm reduces the storage requirement of the implicit solution process and therefore has an important effect on the application of implicit finite-difference schemes to vector processors. Results are presented for realistic two-dimensional transonic flow fields about airfoils. Computation costs are reduced to 24-34%.

Pulliam, T. H.↗

Low Reynolds number airfoil survey, volume 1

The differences in flow behavior two dimensional airfoils in the critical chordlength Reynolds number compared with lower and higher Reynolds number are discussed. The large laminar separation bubble is discussed in view of its important influence on critical Reynolds number airfoil behavior. The shortcomings of application of theoretical boundary layer computations which are successful at higher Reynolds numbers to the critical regime are discussed. The large variation in experimental aerodynamic characteristic measurement due to small changes in ambient turbulence, vibration, and sound level is illustrated. The difficulties in obtaining accurate detailed measurements in free flight and dramatic performance improvements at critical Reynolds number, achieved with various types of boundary layer tripping devices are discussed.

Carmichael, B. H.↗

Numerical studies of laminar and turbulent drag reduction

Two-dimensional incompressible flow over wavy surfaces is studied numerically by spectral methods. Turbulence effects are modeled. Results for symmetric and asymmetric wave forms are presented. Effect of propagating surface waves on drag reduction is studied. Comparisons between computer simulations and experimental results are made.

Balasubramanian, R.↗

A flight investigation of blade-section aerodynamics for a helicopter main rotor having RC-SC2 airfoil sections

Pressure data at 90 percent blade radius for a helicopter main rotor with RC-SC2 blade sections was obtained. Concurrent measurements were made of vehicle flight state, performance and some rotor loads. The test envelope included hover, level flight from about 65 to 144 knots, climb and descent, and collective fixed maneuvers. Airfoil pressure distributions obtained in flight agree with those theoretical calculations for two dimensional, steady flow.

Morris, C. E. K., Jr.↗

Unsteady boundary-layer injection

The boundary-layer equations for two-dimensional incompressible flow are integrated numerically for the flow over a flat plate and a Howarth body. Injection is introduced either impulsively or periodically along a narrow strip. Results indicate that injection perpendicular to the wall is transmitted instantly across the boundary layer and has little effect on the velocity profile parallel to the wall. The effect is a little more noticeable for flows with adverse pressure gradients. Injection parallel to the wall results in fuller velocity profiles. Parallel and oscillatory injection appears to influence the mean. The amplitude of oscillation decreases with distance from the injection strip but further downstream it increases again in a manner reminiscent of an unstable process.

Telionis, D. P.↗

Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme.

Yee, H. C.↗

Application of second-order-accurate Total Variation Diminishing (TVD) schemes to the Euler equations in general geometries

A one-parameter family of explicit and implicit second-order-accurate, entropy satisfying, total variation diminishing (TVD) schemes was developed by Harten. These TVD schemes were the property of not generating spurious oscillations for one-dimensional nonlinear scalar hyperbolic conservation laws and constant coefficient hyperbolic systems. Application of these methods to one- and two-dimensional fluid flows containing shocks (in Cartesian coordinates) yields highly accurate nonoscillatory numerical solutions. The goal of this work is to expand these methods to the multidimensional Euler equations in generalized coordinate systems. Some numerical results of shock waves impinging on cylindrical bodies are compared with MacCormack's method.

Yee, H. C.↗

Marching grid generation using parabolic partial differential equations

The feasibility of using parabolic partial differential equations for grid generation is examined. Source terms in the form of a linear interpolation between the current grid and the outer boundary are used in generating a grid for a two-dimensional airfoil flow. Grid generation equations are derived by assuming that grid spacings are locally nonuniform on the computational domain. The grid spacing control method is described in detail, and the local orthogonality of the grid lines is discussed. An O-mesh and an H-mesh generated by the described method are shown.

Nakamura, S.↗

Implicit total variation diminishing (TVD) schemes for steady-state calculations

The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme. Previously announced in STAR as N83-23085

Yee, H. C.↗