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NASA NTRS1989

Time-dependent viscous incompressible Navier-Stokes equations - The finite difference Galerkin formulation and streamfunction algorithms

Numerical techniques are developed to solve the Navier-Stokes equations for unsteady incompressible flow. The extension of the finite-difference Galerkin (FDG) method of Stephens et al. (1984) to the continuous-time case in two or three space dimensions is explained, and the numerical implementation of the method is discussed with particular attention to the staggered-MAC-grid primitive-variable discretization, the application of discrete mass balance to avoid problems inherent in FDG schemes, the direct interpretation of the FDG expansion variables as a discrete streamfunction, and a mass-balance approach to two-dimensional problems with throughflow or obstacles. Numerical results are presented graphically for the evolution of asymptotic steady flow in a driven cavity at Reynolds number 400, 1000, or 3200; good agreement with published experimental data is demonstrated, with accurate predictions of secondary-vortex formation from wall bubble recirculations at Reynolds number 1000.

Goodrich, John W.↗

NASA NTRS1994

Computational Investigation of an F-18 Aircraft in the High-Alpha Regime

One of the goals of NASA's High Alpha Technology Program is to provide flight-validated design methods for the high-angle-of-attack regime. This is an integrated effort utilizing computational simulations, wind tunnel experiments, and flight tests using the F-18 High Alpha Research Vehicle (HARV). The dominant physics of the aircraft flows in the high alpha regime changes as the angle of attack is increased. At moderate angle of attack the flow is characterized by boundary layer separation and the formation of tight vortices. As the angle of attack is increased, these vortices break down producing unsteady wakes. With further increase in angle of attack, the, vortex breakdown moves progressively upstream until the entire flowfield becomes dominated by the unsteady wake. Previous computational work has demonstrated the ability to simulate flows about the F-18 HARV in the medium-to-high angle of attack range, where the flowfield is characterized by the vortex formation and subsequent breakdown. This paper extends the previous computations to include conditions of 45 degree angle of attack where the flowfield becomes dominated by the unsteady wake shed from the Leading Edge Extension (LEX), and regions of laminar and transitional flow appear on the fuselage forebody. A more complete surface geometry is utilized, which includes the features of the engine nacelle, inlet diffuser, and the boundary layer diverter duct. A volume grid sensitivity study was also performed to extend the accuracy of the results, most notably in the prediction of the LEX vortex breakdown position. This paper includes comparisons of computational results with both in-flight surface pressure measurements, and flow visualizations of the surface and off-surface particle trajectories.

Murman, Scott M.↗

NASA NTRS2009

Simulation of an Isolated Tiltrotor in Hover with an Unstructured Overset-Grid RANS Solver

An unstructured overset-grid Reynolds Averaged Navier-Stokes (RANS) solver, FUN3D, is used to simulate an isolated tiltrotor in hover. An overview of the computational method is presented as well as the details of the overset-grid systems. Steady-state computations within a noninertial reference frame define the performance trends of the rotor across a range of the experimental collective settings. Results are presented to show the effects of off-body grid refinement and blade grid refinement. The computed performance and blade loading trends show good agreement with experimental results and previously published structured overset-grid computations. Off-body flow features indicate a significant improvement in the resolution of the first perpendicular blade vortex interaction with background grid refinement across the collective range. Considering experimental data uncertainty and effects of transition, the prediction of figure of merit on the baseline and refined grid is reasonable at the higher collective range- within 3 percent of the measured values. At the lower collective settings, the computed figure of merit is approximately 6 percent lower than the experimental data. A comparison of steady and unsteady results show that with temporal refinement, the dynamic results closely match the steady-state noninertial results which gives confidence in the accuracy of the dynamic overset-grid approach.

Lee-Rausch, Elizabeth M.↗

NASA NTRS2016

Simultaneous Boundary-Layer Transition, Tip Vortex, and Blade Deformation Measurements of a Rotor in Hover

This paper describes simultaneous optical measurements of a sub-scale helicopter rotor in the U.S. Army Hover Chamber at NASA Ames Research Center. The measurements included thermal imaging of the rotor blades to detect boundary layer transition; retro-reflective background-oriented schlieren (RBOS) to visualize vortices; and stereo photogrammetry to measure displacements of the rotor blades, to compute spatial coordinates of the vortices from the RBOS data, and to map the thermal imaging data to a three-dimensional surface grid. The test also included an exploratory effort to measure flow near the rotor tip by tomographic particle image velocimetry (tomo PIV)an effort that yielded valuable experience but little data. The thermal imaging was accomplished using an image-derotation method that allowed long integration times without image blur. By mapping the thermal image data to a surface grid it was possible to accurately locate transition in spatial coordinates along the length of the rotor blade.

Rotorcraft↗

NASA NTRS1978

Experimental study of the laminar-turbulent transition of a concave wall in a parallel flow

The instability of the laminar boundary layer flow along a concave wall was studied. Observations of these three-dimensional boundary layer phenomena were made using the hydrogen-bubble visualization technique. With the application of stereo-photogrammetric methods in the air-water system it was possible to investigate the flow processes qualitatively and quantitatively. In the case of a concave wall of sufficient curvature, a primary instability occurs first in the form of Goertler vortices with wave lengths depending upon the boundary layer thickness and the wall curvature. At the onset the amplification rate is in agreement with the linear theory. Later, during the non-linear amplification stage, periodic spanwise vorticity concentrations develop in the low velocity region between the longitudinal vortices. Then a meandering motion of the longitudinal vortex streets subsequently ensues, leading to turbulence.

Bippes, H.↗

NASA NTRS1986

Vortex systems on slender rotating bodies and their effect on the aerodynamic coefficients

The turbulent flow of rotational bodies up to a length of 20 diameters with various head shapes and cylindrical tails was examined in the subsonic wind tunnel with the Mach number of M = 0.1. At angles of incidence lower than 30 degrees, a pair of symmetrical eddies rests stationary from head to tail on the trailing side, very close to the body. At angles between 30 and 60 degrees, the stationary eddies are asymmetrically pushed off. Between 60 and 90 degrees, the eddies detach themselves in an instationary manner. This includes, for example, the turbulent flow at the start-up of flying bodies in the presence of lateral winds. The results of measurments obtained by Mello at M = 2, an impulse method, and the cross flow theory according to Allen are used for comparison.

Fiechter, M.↗

NASA NTRS1987

Influence of disk leakage path on labyrinth seal inlet swirl ratio

The results of numerous investigators have shown the importance of labyrinth seal inlet swirl on the calculated dynamic stiffness of labyrinth seals. These results have not included any calculation of inlet leakage swirl as a function of geometry and sealing conditions of the given seal. This paper outlines a method of calculating the inlet swirl at a given seal by introducing a radial chamber to predict the gas swirl as it goes from the stage tip down to the seal location. For a centrifugal compressor, this amounts to including the flow path from the impeller discharge, down the back of the disk or front of the cover, then into the shaft seal or eye packing, respectively. The solution includes the friction factors of both the disk and stationary wall with account for mass flow rate and calculation of radial pressure gradients by a free vortex solution. The results of various configurations are discussed and comparisons made to other published results of disk swirl.

Kirk, R. Gordon↗

NASA NTRS1989

Advances in fluid dynamics

Various papers on advances in fluid dynamics are presented. Individual topics addressed include: nonunique solutions of the Euler equations; numerical solution of the biharmonic equation using a spectral multigrid method; finite-volume shape and placement for efficiency, accuracy, and physics; NND schemes and their application to numerical simulation of complex plume flow problems; symbolic analysis and computational algorithm construction; and velocity and mass flux distribution measurements of spherical glass beads in air flow in a 90-deg vertical-to-horizontal bend. Also discussed are: hyperbolic solution adaptive mesh generation; progress and future directions in CFD; numerical simulation of shock focusing; microbubble formation and splitting in a turbulent boundary layer for turbulence reduction; numerical study of spherical Taylor-Couette flow, trajectories of vortex lines beneath a free surface or above a plane; and a mathematical model for response of the coronary circulation to high sustained gravitational force fields.

Ballhaus, W. F., Jr.↗

NASA NTRS1950

The Boundary Layers in Fluids with Little Friction

The vortices forming in flowing water behind solid bodies are not represented correctly by the solution of the potential theory nor by Helmholtz's jets. Potential theory is unable to satisfy the condition that the water adheres at the wetted bodies, and its solutions of the fundamental hydrodynamic equations are at variance with the observation that the flow separates from the body at a certain point and sends forth a highly turbulent boundary layer into the free flow. Helmholtz's theory attempts to imitate the latter effect in such a way that it joins two potential flows, jet and still water, nonanalytical along a stream curve. The admissibility of this method is based on the fact that, at zero pressure, which is to prevail at the cited stream curve, the connection of the fluid, and with it the effect of adjacent parts on each other, is canceled. In reality, however, the pressure at these boundaries is definitely not zero, but can even be varied arbitrarily. Besides, Helmholtz's theory with its potential flows does not satisfy the condition of adherence nor explain the origin of the vortices, for in all of these problems, the friction must be taken into account on principle, according to the vortex theorem.

Blasius, H.↗

NASA NTRS2017

Computational Analysis of a Wing Designed for the X-57 Distributed Electric Propulsion Aircraft

A computational study of the wing for the distributed electric propulsion X-57 Maxwell airplane configuration at cruise and takeoff/landing conditions was completed. Two unstructured-mesh, Navier-Stokes computational fluid dynamics methods, FUN3D and USM3D, were used to predict the wing performance. The goal of the X-57 wing and distributed electric propulsion system design was to meet or exceed the required lift coefficient 3.95 for a stall speed of 58 knots, with a cruise speed of 150 knots at an altitude of 8,000 ft. The X-57 Maxwell airplane was designed with a small, high aspect ratio cruise wing that was designed for a high cruise lift coefficient (0.75) at angle of attack of 0deg. The cruise propulsors at the wingtip rotate counter to the wingtip vortex and reduce induced drag by 7.5 percent at an angle of attack of 0.6deg. The unblown maximum lift coefficient of the high-lift wing (with the 30deg flap setting) is 2.439. The stall speed goal performance metric was confirmed with a blown wing computed effective lift coefficient of 4.202. The lift augmentation from the high-lift, distributed electric propulsion system is 1.7. The predicted cruise wing drag coefficient of 0.02191 is 0.00076 above the drag allotted for the wing in the original estimate. However, the predicted drag overage for the wing would only use 10.1 percent of the original estimated drag margin, which is 0.00749.

Deere, Karen A.↗

NASA NTRS1999

Implicit and Multigrid Method for Ideal Multigrid Convergence: Direct Numerical Simulation of Separated Flow Around NACA 0012 Airfoil

Numerical investigation of flow separation over a NACA 0012 airfoil at large angles of attack has been carried out. The numerical calculation is performed by solving the full Navier-Stokes equations in generalized curvilinear coordinates. The second-order LU-SGS implicit scheme is applied for time integration. This scheme requires no tridiagonal inversion and is capable of being completely vectorized, provided the corresponding Jacobian matrices are properly selected. A fourth-order centered compact scheme is used for spatial derivatives. In order to reduce numerical oscillation, a sixth-order implicit filter is employed. Non-reflecting boundary conditions are imposed at the far-field and outlet boundaries to avoid possible non-physical wave reflection. Complex flow separation and vortex shedding phenomenon have been observed and discussed.

Liu, Chao-Qun↗

NASA NTRS1998

Low Dissipative High Order Shock-Capturing Methods using Characteristic-Based Filters

An approach which closely maintains the non-dissipative nature of classical fourth or higher- order spatial differencing away from shock waves and steep gradient regions while being capable of accurately capturing discontinuities, steep gradient and fine scale turbulent structures in a stable and efficient manner is described. The approach is a generalization of the method of Gustafsson and Olsson and the artificial compression method (ACM) of Harten. Spatially non-dissipative fourth or higher-order compact and non-compact spatial differencings are used as the base schemes. Instead of applying a scalar filter as in Gustafsson and Olsson, an ACM like term is used to signal the appropriate amount of second or third-order TVD or ENO types of characteristic based numerical dissipation. This term acts as a characteristic filter to minimize numerical dissipation for the overall scheme. For time-accurate computations, time discretizations with low dissipation are used. Numerical experiments on 2-D vortical flows, vortex-shock interactions and compressible spatially and temporally evolving mixing layers showed that the proposed schemes have the desired property with only a 10% increase in operations count over standard second-order TVD schemes. Aside from the ability to accurately capture shock-turbulence interaction flows, this approach is also capable of accurately preserving vortex convection. Higher accuracy is achieved with fewer grid points when compared to that of standard second-order TVD or ENO schemes. To demonstrate the applicability of these schemes in sustaining turbulence where shock waves are absent, a simulation of 3-D compressible turbulent channel flow in a small domain is conducted.

Yee, H. C.↗

NASA NTRS1998

Low Dissipative High Order Shock-Capturing Methods Using Characteristic-Based Filters

An approach which closely maintains the non-dissipative nature of classical fourth or higher- order spatial differencing away from shock waves and steep gradient regions while being capable of accurately capturing discontinuities, steep gradient and fine scale turbulent structures in a stable and efficient manner is described. The approach is a generalization of the method of Gustafsson and Oisson and the artificial compression method (ACM) of Harten. Spatially non-dissipative fourth or higher-order compact and non-compact spatial differencings are used as the base schemes. Instead of applying a scalar filter as in Gustafsson and Olsson, an ACM like term is used to signal the appropriate amount of second or third-order TVD or ENO types of characteristic based numerical dissipation. This term acts as a characteristic filter to minimize numerical dissipation for the overall scheme. For time-accurate computations, time discretizations with low dissipation are used. Numerical experiments on 2-D vortical flows, vortex-shock interactions and compressible spatially and temporally evolving mixing layers showed that the proposed schemes have the desired property with only a 10% increase in operations count over standard second-order TVD schemes. Aside from the ability to accurately capture shock-turbulence interaction flows, this approach is also capable of accurately preserving vortex convection. Higher accuracy is achieved with fewer grid points when compared to that of standard second-order TVD or ENO schemes. To demonstrate the applicability of these schemes in sustaining turbulence where shock waves are absent, a simulation of 3-D compressible turbulent channel flow in a small domain is conducted.

Yee, H. C.↗

NASA NTRS2022

Semispan Test Results of an Active Flow Control Enabled High-Lift Common Research Model in Landing Configuration

A 10%-scale semispan, Active Flow Control (AFC) enabled, simplified high-lift version of the Common Research Model (CRM-SHL-AFC) was tested in the 14- by 22-Foot Subsonic Tunnel at the NASA Langley Research Center. The main objective of the test was to develop an AFC system that can provide the necessary lift recovery on a simple-hinged flap high-lift system while minimizing its pneumatic power requirement. Three new types of AFC approaches were examined: Double-Row Sweeping Jets (DRSWJ), Alternating Pulsed Jets (APJ), and High Efficiency Low Power (HELP) actuators. The DRSWJ and the APJ actuators used two rows of unsteady jets, whereas the HELP actuators used an upstream row of sweeping jets combined with a downstream row of steady jets to overcome strong adverse pressure gradients. The test was conducted mostly at a freestream Mach number of 0.20. For exploration purposes, a limited number of runs were made at lower Mach numbers or using vortex generators (VGs). Minimal sensitivity to Mach number or VGs, for the cases evaluated, were observed. The AFC-induced lift coefficient increment was maintained over the AFC-off case for most flow-control cases examined. The CRM-SHL-AFC configuration equipped with HELP actuation was the only actuator configuration able to match or exceed the targeted lift performance of a reference conventional high-lift configuration. The presented aerodynamic data include lift, drag, and pitching moment coefficients as a function of angle of attack, with and without the Transonic Wall Interference Correction System (TWICS) method applied. Lift increments as a function of AFC pneumatic power usage (i.e., nozzle pressure ratio, mass flow, momentum coefficient, and power coefficient) are also presented at a lower angle of attack (α = 8.9°) and at maximum lift (α= 17.1°). At the two angles of attack, the surface pressure distributions and autospectral densities from the unsteady pressure transducers for the AFC-off case and the best HELP actuation case are compared.

high-lift↗

NASA NTRS1992

Hypersonic rarefied flow past spheres including wake structure

Results of a numerical study using the direct simulation Monte Carlo method are presented for hypersonic rarefied flow past spheres. The flow conditions considered are those corresponding to low density wind tunnel test conditions. The set of the experimental conditions for the calculations encompasses the transitional to near-continuum flow regimes. Comparison of the calculated drag with experimental results shows good agreement to well within the experimental error. Particular attention is focused on the wake structure. Calculations show that the wake is very rarefied with considerable thermal nonequilibrium for all the cases considered. No flow separation is observed in the wake for the near-continuum case where a vortex has been predicted by Navier-Stokes type calculations.

Dogra, Virendra K.↗

NASA NTRS1934

Effect of fuselage and engine nacelles on some aerodynamic properties of an airplane wing

With the aid of the method of J. Lotz, the writer undertook to solve theoretically the lift distribution along the span of an airplane wing, when the outline of the wing is uneven. This problem arises in the case of a mid-wing monoplane with embedded engine nacelles. The fuselage and the nacelles were considered as aerodynamically profiled, that is, as lift-producing parts. The task was therefore to determine not only the disturbance caused by the fuselage and nacelles, but also their share in the total lift of the wing. After the above-mentioned calculations, the induced velocity, due to the vortex system by which the wing was replaced, was also calculated and measured at the points corresponding, in an airplane, to the location of the horizontal tail surfaces.

Vladea, Joan↗

NASA NTRS1990

A numerical method for prediction of compressible turbulent flows with closure models

A new computer code to solve the time averaged Navier-Stokes equations is developed. Many of the state-of-the-art numerical techniques and algorithms have been tested and implemented in the program in order to achieve a better numerical accuracy and code efficiency. Various turbulence models are tested for a wide range of flows. The initial focus has been on two-equation eddy-viscosity models, which are the most advanced available in current compressible flow codes. The long term goal will be to test Reynolds-Stress models and to explore their performance in the high Mach number range. Although testing and improvement of turbulence models for supersonic and hypersonic flows is the primary objective of this research, part of the effort has been devoted to analyzing the vortex breakdown phenomena using new computer programs. Some preliminary results on the breakdown of a vortex flow in a tube are reported. Present calculations are restricted to two dimensional flow geometry.

Huang, P. G.↗

NASA NTRS1991

Numerical prediction of the unsteady flowfield around the F-18 aircraft at large incidence

This paper describes a numerical method capable of solving the steady and unsteady viscous flow around complete aircraft configurations at high angles of attack. This method is used to simulate the external flow around the F-18 aircraft, including deflected control surfaces. The current technique employs a generalized overset zonal grid scheme to decompose the computational space around the aircraft. The grid around various components of the aircraft are created numerically using a three-dimensional hyperbolic grid generation procedure. The Reynolds-averaged Navier-Stokes equations are integrated using a time-accurate, implicit procedure. Results for the turbulent flow around the F-18 aircraft at 30 degrees angle of attack show the details of the flowfield structure, including the unsteadiness created by the vortex burst and the resulting fluctuating airloads exerted on the vertical tail. The computed results agree fairly well with flight data for surface pressure, surface flow pattern, vortex burst location, and the dominant frequency for tail load fluctuations.

Rizk, Yehia M.↗