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A boundary-layer integral approach is combined with a finite-difference relaxation method to calculate viscous interactions between separated flows at subsonic and transonic velocities. Results are obtained for separated laminar flows on circular-arc airfoils at zero angle of attack and are compared with data of Collins (1972). Inviscid and viscous flows are covered.
Flow field measurements of three subsonic rectangular cold air jets are presented. The three cases had aspect ratios of 1x2, 1x4 at a Mach number of 0.09 and an aspect ratio of 1x2 at a Mach number of 0.9. All measurements were made using a 3-D laser Doppler anemometer system. The data includes the mean velocity vector, all Reynolds stress tensor components, turbulent kinetic energy and velocity correlation coefficients. The data are presented in tabular and graphical form. No analysis of the measured data or comparison to other published data is made.
In gasdynamic systems, information travels in one direction for supersonic flow and in both directions for subsonic flow. A shock occurs at the transition from supersonic to subsonic flow. Thus, to simulate these systems, any simulation method implemented for the quasi-one-dimensional Euler equations must have the ability to capture the shock. In this paper, a technique combining both backward and central differencing is presented. The equations are subsequently linearized about an operating point and formulated into a linear state space model. After proper implementation of the boundary conditions, the model order is reduced from 123 to less than 10 using the Schur method of balancing. Simulations comparing frequency and step response of the reduced order model and the original system models are presented.
This report is devoted to the study of two-dimensional steady motion of a compressible fluid. It is shown that the complete flow pattern around a closed obstacle cannot be obtained by the method of Chaplygin. In order to overcome this difficulty, a formula for the stream-function of a two-dimensional subsonic flow is derived. The formula involves an arbitrary function of a complex variable and yields all possible subsonic flow patterns of certain types. Conditions are given so that the flow pattern in the physical plane will represent a flow around a closed curve. The formula obtained can be employed for the approximate determination of a subsonic flow around an obstacle. The method can be extended to partially supersonic flows.
A new finite-difference scheme has been developed to solve efficiently the unsteady Euler equations for three-dimensional inviscid supersonic flows with subsonic pockets. The technique utilizes planar Gauss-Seidel relaxation in the marching direction and approximate factorization n the crossflow plane. An 'infinitely large' time step is used in parts of the flowfield where the component of velocity in the marching direction is supersonic - here the Gauss-Seidel sweeps are restricted to the forward direction only, and the procedure reduces to simple space-marching; a finite time step is used in parts of the flowfield where the marching component of velocity is subsonic - here, backward and forward Gauss-Seidel sweeps are employed to allow for upstream and downstream propagation of signals, and a time-asymptotic steady state is obtained. The discretization formulas are based on finite-volume implementation of high accuracy (up to third-order) total variation diminishing formulations. Numerical solutions are obtained for an analytically defined forebody, a realistic fighter configuration, and the Space Shuttle. The results are in very good agreement with available experimental data and numerical solutions of the full-potential equation.
This paper summarizes solutions submitted for the Reynolds-averaged Navier-Stokes (RANS) test suite of the High-Fidelity CFD Verification Workshop. The goal of the workshop is to establish standards for verification of computational fluid dynamics (CFD) approaches to simulations of steady and unsteady turbulent flows. The RANS verification studies focus on a one-equation Spalart-Allmaras model with quadratic constitutive relation and rotation correction, SA-neg-QCR2000-R. The verification test cases are a two-dimensional subsonic flow around a Joukowski airfoil, a three-dimensional subsonic flow around an extruded NACA 0012 wing in a tunnel, and a subsonic flow around a wing-body configuration developed for verification of solvers participating in the 5 𝑡 ℎ High-Lift Prediction Workshop. The turbulencemodel formulation, geometry, flow conditions, grids, and reference solutions are described in detail. Solutions for the test cases are computed by seven established CFD solvers on adaptedand fixed-grid families using different discretization approaches. While some noticeable differences between solutions remain, the results achieved by contributing solvers show that different solutions computed for the same RANS model on different grid families can converge to a common limit with grid refinement. The apparent requirements for grid convergence are a well designed family of grids that provide sufficient resolution in important areas and a strong solver capable of deep iterative convergence on each grid. For each test case in the study, the variation between aerodynamic forces computed by different solvers on the finest grids of different families is less than 2%.
This report presents a theoretical and experimental investigation of the effect of wind-tunnel walls on the air forces on an oscillating wing in two-dimensional subsonic compressible flow. A method of solving an integral equation which relates the downwash on a wing to the unknown loading is given, and some comparisons are made between the theoretical results and the experimental results. A resonance condition, which was predicted by theory in a previous report (NACA report 1150), is shown experimentally to exist. In addition, application of the analysis is made to a number of examples in order to illustrate the influence of walls due to variations in frequency of oscillation, Mach number , and ratio of tunnel height to wing semichord.
Routine determination of inviscid subsonic flow fields about wing-body-tail configurations employing a Green's function approach for numerical solution of the perturbation velocity potential equation is successfully extended into the high subsonic subcritical flow regime and into the shock-free supersonic flow regime. A modified Green's function formulation, valid throughout a range of Mach numbers including transonic, that takes an explicit accounting of the intrinsic nonlinearity in the parent governing partial differential equations is developed. Some considerations pertinent to flow field predictions in the transonic flow regime are discussed.
The present paper describes the verification and validation of a quasi one-dimensional pressure based finite volume algorithm, implemented in Generalized Fluid System Simulation Program (GFSSP), for predicting compressible flow with friction, heat transfer and area change. The numerical predictions were compared with two classical solutions of compressible flow, i.e. Fanno and Rayleigh flow. Fanno flow provides an analytical solution of compressible flow in a long slender pipe where incoming subsonic flow can be choked due to friction. On the other hand, Raleigh flow provides analytical solution of frictionless compressible flow with heat transfer where incoming subsonic flow can be choked at the outlet boundary with heat addition to the control volume. Nonuniform grid distribution improves the accuracy of numerical prediction. A benchmark numerical solution of compressible flow in a converging-diverging nozzle with friction and heat transfer has been developed to verify GFSSP's numerical predictions. The numerical predictions compare favorably in all cases.
Analyses and numerical procedures are presented to investigate the radiative interactions of gray and nongray absorbing-emitting species between two parallel plates and in a circular tube. Laminar fully developed incompressible as well as entrance region subsonic flows are considered. The participating species considered are OH, CO, CO2, CH4, and H2O. Results obtained for different flow conditions indicate that the radiative interactions can be quite significant in fully developed incompressible flows. For subsonic flows, however, the flowfield is not changed significantly due to radiative interactions.
This report represents a general theory applicable to axial, radial, and mixed flow turbomachines operating at subsonic and supersonic speeds with a finite number of blades of finite thickness. References reflect the evolution of computational methods used, from the inception of the theory in the 50's to the high-speed computer era of the 90's. Two kinds of relative stream surfaces, S(sub 1) and S(sub 2), are introduced for the purpose of obtaining a three-dimensional flow solution through the combination of two-dimensional flow solutions. Nonorthogonal curvilinear coordinates are used for the governing equations. Methods of computing transonic flow along S(sub 1) and S(sub 2) stream surfaces are given for special cases as well as for fully three-dimensional transonic flows. Procedures pertaining to the direct solutions and inverse solutions are presented. Information on shock wave locations and shapes needed for computations are discussed. Experimental data from a Deutsche Forschungs- und Versuchsanstalt fur Luft- und Raumfahrt e.V. (DFVLR) rotor and from a Chinese Academy of Sciences (CAS) transonic compressor rotor are compared with the computed flow properties.
Prandtl (1946) has concluded that for yawed laminar incompressible flows the streamwise flow is independent of the spanwise flow. However, Ashkenas and Riddell (1955) have reported that for turbulent flow the 'independence principle' does not apply to yawed flat plates. On the other hand, it was also found that this principle may be applicable to many turbulent flows. As the sweep angle is increased, a sweep angle is reached which defines the interval over which the 'independence principle' is valid. The results obtained in the present investigation indicate the magnitude of the critical angle for subsonic turbulent flow over a swept rearward-facing step.
Flow field measurements are presented of 3 subsonic rectangular cold air jets. The 3 cases presented had aspect ratios of 1 x 2, 1 x 4 at a Mach number of 0.09 and an aspect ratio of 1 x 2 at a Mach number of 0.9. All measurements were made using a 3-D laser Doppler anemoneter system. The presented data includes the mean velocity vector, all Reynolds stress tensor components, turbulent kinetic energy and velocity correlation coefficients. The data is presented in tabular and graphical form. No analysis of the measured data or comparison to other published data is made. All tabular data are available in ASCII format on MS-DOS compatible disks.
A wind tunnel experiment was conducted in the NASA Langley Research Center (LaRC) 8-foot Transonic Pressure Tunnel (TPT) to determine the effects of passive surface porosity on vortex flow interactions about a general research fighter configuration at subsonic and transonic speeds. Flow- through porosity was applied to a wind leading-edge extension (LEX) mounted to a 65 deg cropped delta wind model to promote large nose-down pitching moment increments at high angles of attack. Porosity decreased the vorticity shed from the LEX, which weakened the LEX vortex and altered the global interactions of the LEX and wing vortices at high angles of attack. Six-component forces and moments and wing upper surface static pressure distributions were obtained at free- stream Mach numbers of 0.50, 0.85, and 1.20, Reynolds number of 2.5(10(exp-6) per foot, angles of attack up to 30 deg and angles of sideslip to plus or minus 8 deg. The off-surface flow field was visualized in selected cross-planes using a laser vapor screen flow visualization technique. Test data were obtained with a centerline vertical tail and with alternate twin, wing-mounted vertical fins having 0 deg and 30 deg cant angles. In addition, the porosity of the LEX was compartmentalized to determine the sensitivity of the vortex- dominated aerodynamics to the location and level of porosity applied to the LEX.
A numerical approach is presented for the computation of flows in which the component of velocity in the selected marching direction is subsonic although the total velocity is supersonic. A local coordinate rotation procedure is employed together with an implicit differencing scheme. Complex coordinate transformations and time-consuming iterations are avoided. The implementation of the described approach is illustrated with the aid of a two-dimensional problem. An application in the case of three-dimensional flows is also discussed.
A wind tunnel experiment was conducted in the NASA Langley Research Center (LaRC) 8-Foot Transonic Pressure Tunnel (TPT) to determine the effects of passive surface porosity on vortex flow interactions about a general research fighter configuration at subsonic and transonic speeds. Flow-through porosity was applied to a wing leading-edge extension (LEX) mounted to a 65 deg cropped delta wing model to promote large nose-down pitching moment increments at high angles of attack. Porosity decreased the vorticity shed from the LEX, which weakened the LEX vortex and altered the global interactions of the LEX and wing vortices at high angles of attack. Six-component forces and moments and wing upper surface static pressure distributions were obtained at free-stream Mach numbers of 0.50, 0.85, and 1.20, Reynolds number of 2.5(10(exp 6)) per foot, angles of attack up to 30 deg, and angles of sideslip to +/- 8 deg. The off-surface flow field was visualized in selected cross-planes using a laser vapor screen flow visualization technique. Test data were obtained with a centerline vertical tail and with alternate twin, wing-mounted vertical fins having 0 deg and 30 deg cant angles. In addition, the porosity of the LEX was compartmentalized to determine the sensitivity of the vortex-dominated aerodynamics to the location and level of porosity applied to the LEX.
A study was conducted to evaluate the technical and economic feasibility of applying laminar flow control (LFC) to the wings and empennage of long-range subsonic transport aircraft for initial operation in 1985. For a design mission range of 5500 n mi, advanced technology LFC and turbulent-flow aircraft were developed for a 200-passenger payload, and compared on the basis of production costs, direct operating costs, and fuel efficiency. Parametric analyses were conducted to establish optimum geometry, advanced system concepts were evaluated, and configuration variations maximizing the effectiveness of LFC were developed. The final comparisons include consideation of maintenance costs and procedures, manufacturing costs and procedures, and operational considerations peculiar to LFC aircraft.
This is an invited paper for the SciTech 2023 special session, High-Fidelity CFD Verification Pre-Workshop. The paper presents three benchmark cases for verification of Reynolds-averaged Navier-Stokes solvers. The verification studies focus on a one-equation Spalart-Allmaras model, SA-neg-QCR2000-R. The benchmark cases are a two-dimensional subsonic flow around a Joukowski airfoil, a subsonic three-dimensional flow around an extruded NACA0012 wing in a tunnel, and a subsonic flow around a wing-body configuration developed by Boeing for verification of solvers participating in the High-Lift Prediction Workshop. The turbulence-model formulation, geometry, flow conditions, grids, and the desired submission data are described in detail. Reference solutions computed by established codes are shown.