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Program determines direct surface loadings, using pressure terms that correctly represent known singularity functions around boundaries or wing with control surface. Program provides numerical prediction of unsteady loadings caused by control-surface motions.
A theoretical analysis and computer program was developed for the prediction of unsteady lifting surface loadings caused by motions of leading edge and trailing edge control surfaces having sealed gaps. The final form of the downwash integral equation was formulated by isolating the singularities from the nonsingular terms and using a preferred solution process to remove and evaluate the downwash discontinuities in a systematic manner. Comparisons of theoretical and experimental pressure data are made for several control surface configurations. The comparisons indicate that reasonably accurate theoretical pressure distributions and generalized forces may be obtained for a wide variety of control surface configurations. Spanwise symmetry or antisymmetry of motion, and up to six control surfaces on each half span can be accommodated.
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An approximate analysis is presented which is applicable to nonorthogonal coordinate systems having a curved centerline and planar transverse coordinate surfaces normal to the centerline. The primary flow direction is taken to coincide with the local direction of the duct centerline and is hence normal to transverse coordinate planes. The formulation utilizes vector components (velocity, vorticity, transport equations) defined in terms of local Cartesian directions aligned with the centerline tangent, although the governing equations themselves are expressed in general nonorthogonal coordinates. For curved centerlines, these vector quantities are redefined in new local Cartesian directions at each streamwise location. The use of local Cartesian variables and fluxes leads to governing equations which require only first derivatives of the coordinate transformation, and this provides for the aforementioned ease in using constructed coordinates.
A numerical procedure to calculate the flow fields resulting from the viscous inviscid interactions that occur when a strong jet exhaust and aircraft flow field coupling exists was developed. The approach divides the interaction region into zones which are either predominantly viscous or inviscid. The flow in the inviscid zone, which surrounds most of the aircraft, is calculated using an existing potential flow code. The viscous flow zone, which encompasses the jet plume, is modeled using a parabolized Navier-Stokes code. The procedure features the coupling of the zonal solutions such that sufficient information is transferred between the zones to preserve the effects of the interactions. The zonal boundaries overlap and the boundary conditions are the information link between zones. An iteration scheme iterates the coupled analysis until convergence has been obtained.
A new boundary-layer relaxation procedure is presented. In the spirit of the theory of matched asymptotic expansions, a multiplicative composite of the appropriate velocity representations for the inviscid and viscous regions is prescribed. The resulting equations are structured so that far from the surface of the body the momentum equations lead to the Bernoulli relation for the pressure, while the continuity equation reduces to the familiar compressible potential equation. Close to the body surface, the governing equations and solution techniques are characteristic of those describing interacting boundary-layers; although, the full Navier-Stokes equations are considered here. Laminar flow calculations for the subsonic flow over an axisymmetric boattail simulator geometry are presented for a variety of Reynolds and Mach numbers. A strongly implicit solution method is applied for the coupled velocity components.
A nonlinear vortex-lattice method is utilized for the calculation of separated vortex flows over slender bodies at high incidence. Symmetric and asymmetric vortex flow cases are calculated showing good agreement with recently obtained experimental data for an ogive-cyclinder body at high Reynolds numbers. The only input needed for these calculations is the positions of the separation lines on the body. Studies of some of the numerical aspects of this method are described and conclusions are implemented to improve the calculations.
Mean flow measurements have been made in a supersonic turbulent boundary layer experiencing a short region of concave curvature and an adverse pressure gradient. The incoming boundary layer had a Mach number of 2.87 and a unit Reynolds number of 6.3 x 10 to the 7th/m. Flow over constant radii curvatures of delta (0)/R = 0.10 and 0.02 with a fixed turning angle of 8 deg were investigated. Results indicate that both flows remain two-dimensional; length scales increase over their equilibrium values; the mean flow behaves similarly to subsonic flows experiencing concave curvature and lateral divergence; and boundary layer behavior is strongly similar to a corresponding 8 deg ramp flow.
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The effectiveness of a trailing disk, or trapped vortex concept, in reducing the base drag of a large body of revolution was studied from measurements made both in flight and in a wind tunnel. Pressure data obtained for the flight experiment, and both pressure and force balance data were obtained for the wind tunnel experiment. The flight test also included data obtained from a hemispherical base. The experiment demonstrated the significant base drag reduction capability of the trailing disk to Mach 0.93 and to Reynolds numbers up to 80 times greater than for earlier studies. For the trailing disk data from the flight experiment, the maximum decrease in base drag ranged form 0.08 to 0.07 as Mach number increased from 0.70 to 0.93. Aircraft angles of attack ranged from 3.9 to 6.6 deg for the flight data. For the trailing disk data from the wind tunnel experiment, the maximum decrease in base and total drag ranged from 0.08 to 0.05 for the approximately 0 deg angle of attack data as Mach number increased from 0.30 to 0.82.
The heat transfer in heated wires was measured using a constant temperature anemometer over a Mach number range from 0.05 to 0.4 and pressures from 0.5 to 8.0 atmospheres. The total temperature ranged from 80 to 120 F and the wire diameters were 0.00015, 0.00032, and 0.00050 inch. The heat transfer data is presented in the form of a corrected Nusselt number. Based on suggested criteria, much of the data was obtained in the slip flow regime. Therefore, the data is compared with data having comparable flow conditions. The possible application of the heat transfer data to hot wire anemometry is discussed. To this end, the sensitivity of the wires to velocity, density, and total temperature is computed and compared using two different types of correlations.
We have developed a Schwarz type domain decomposition method for a pressure base, two- and three-dimensional Navier-Stokes solver. This technique allows one to partition a flow path, which can be characterized by complex geometry and/or complicated flow physics, into smaller sub-domains according to the local geometric simplicity or estimated flow scales. We can, then, sweep the sub-domains in some order and solve the Navier-Stokes equations using as boundary conditions, along the domain interfaces, the Dirichlet conditions which are taken from the most recent update of the solution in the adjacent neighboring domains. With this technique, one can minimize the adverse effects caused by grid skewness and the stiffness problem caused by disparate flow scales. Here, we report the results of a few fundamental flow cases to demonstrate that a judicious use of the multi-domain method can offer a significant convergence acceleration over the traditional one-domain method. This method can be extended to exploit the architecture of a parallel computer to further improve the speed.
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A frequency domain linearized unsteady aerodynamic analysis is presented for three-dimensional unsteady vortical flows around a cascade of loaded airfoils. The analysis fully accounts for the distortion of the impinging vortical disturbances by the mean flow. The entire unsteady flow field is calculated in response to upstream three-dimensional harmonic disturbances. Numerical results are presented for two standard cascade configurations representing turbine and compressor bladings for a reduced frequency range from 0.1 to 5. Results show that the upstream gust conditions and blade sweep strongly affect the unsteady blade response.
This paper presents an overview of wind-tunnel investigations and flight research activities in the United States and Europe devoted to advancing the state-of-the-art and reducing the risk associated with the application of laminar flow control (LFC) technology. The paper highlights LFC research conducted within the last five years.
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A general method for studying the flow of a compressible fluid around a closed body was discussed in Part I of this report. Here, application is made to the specific case in which the linearized equation of state is used. For a given incompressible flow around a specific profile, a corresponding compressible flow is found. The flow at infinity remains unchanged. Detailed studies are made of the flow with circulation around a unit circle, and velocity distributions are found for a wide range of Mach number and angle of attack. Comparisons are made with other methods.
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