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NASA NTRS1994

Long-wavelength asymptotics of unstable crossflow modes, including the effect of surface curvature

Stationary vortex instabilities with wavelengths significantly larger than the thickness of the underlying three-dimensional boundary layer are studied with asymptotic methods. The long-wavelength Rayleigh modes are locally neutral and are aligned with the direction of the local inviscid streamline. For a spanwise wave number Beta much less than 1, the spatial growth rate of these vortices is O(Beta(exp 3/2)). When Beta becomes O(R(exp -1/7)), the viscous correction associated with a thin sublayer near the surface modifies the inviscid growth rate to the leading order. As Beta is further decreased through this regime, viscous effects assume greater significance and dominate the growth-rate behavior. The spatial growth rate becomes comparable to the real part of the wave number when Beta = O(R(exp -1/4)). At this stage, the disturbance structure becomes fully viscous-inviscid interactive and is described by the triple-deck theory. For even smaller values of Beta, the vortex modes become nearly neutral again and align themselves with the direction of the wall-shear stress. Thus, the study explains the progression of the crossflow-vortex structure from the inflectional upper branch mode to nearly neutral long-wavelength modes that are aligned with the wall-shear direction.

Choudhari, Meelan↗

NASA NTRS1999

Simulation of Non-Linear Transonic Aeroelastic Behavior on the B-2

At high subsonic flight speeds, large flexible aircraft begin to encounter unsteady airloads which are not predicted by most currently available aerodynamic analysis and design methods. With increasing speed and the development of transonic flow and shocks, viscous effects quickly become very important, and flow separation can occur. The Northrop Grumman USAF B-2 Bomber encountered a nonlinear aeroelastic Residual Pitch Oscillation (RPO) under these conditions. Simulation studies were performed with the Computational Aeroelasticity Program-Transonic Small Disturbance, Viscous (CAPTSDv) computer program to evaluate its ability to predict these nonlinear aeroelastic responses. Open and closed loop simulations were performed to assess the participation of the flight control system. Control, system actuator hysteresis characteristics were modeled and found to be a significant participant in the RPO phenomenon. Simulations were also performed for varying Mach numbers and altitudes to establish the stability boundaries and compare with flight test data. These CAPTSDv simulations compared well with flight data and revealed many potential further modeling enhancements.

Residual pitch oscillation↗

NASA NTRS1994

Modeling near wall effects in second moment closures by elliptic relaxation

The elliptic relaxation model of Durbin (1993) for modeling near-wall turbulence using second moment closures (SMC) is compared to DNS data for a channel flow at Re(sub t) = 395. The agreement for second order statistics and even the terms in their balance equation is quite satisfactory, confirming that very little viscous effects (via Kolmogoroff scales) need to be added to the high Reynolds versions of SMC for near-wall-turbulence. The essential near-wall feature is thus the kinematic blocking effect that a solid wall exerts on the turbulence through the fluctuating pressure, which is best modeled by an elliptic operator. Above the transition layer, the effect of the original elliptic operator decays rapidly, and it is suggested that the log-layer is better reproduced by adding a non-homogeneous reduction of the return to isotropy, the gradient of the turbulent length scale being used as a measure of the inhomogeneity of the log-layer. The elliptic operator was quite easily applied to the non-linear Craft & Launder pressure-strain model yielding an improved distinction between the spanwise and wall normal stresses, although at higher Reynolds number (Re) and away from the wall, the streamwise component is severely underpredicted, as well as the transition in the mean velocity from the log to the wake profiles. In this area a significant change of behavior was observed in the DNS pressure-strain term, entirely ignored in the models.

Laurence, D.↗

NASA NTRS1988

The calculation of flow over iced airfoils

Progress toward the development of a method for predicting the flowfield of an iced airfoil is described and shown to offer the prospect of a priori calculations of the effects of ice accretion and roughness on airfoil performance. The approach is based on interaction of inviscid flow solutions obtained by a panel method and improved upon by a finite-difference boundary-layer method which, operating in an inverse mode, incorporates viscous effects including those associated with separated flows. Results are presented for smooth, rough and iced airfoils as a function of angle of attack. Those for smooth and rough airfoils confirm the accuracy of the method and its applicability to surfaces with roughness similar to that associated with insect deposition and some forms of ice. Two procedures have been developed to deal with large ice accretion and their performance is examined and shown to be appropriate to the engineering requirements.

Cebeci, Tuncer↗

NASA NTRS1992

Numerical Modeling of a Vortex Stabilized Arcjet

Arcjet thrusters are being actively considered for use in Earth orbit maneuvering applications. Experimental studies are currently the chief means of determining an optimal thruster configuration. Earlier numerical studies have failed to include all of the effects found in typical arcjets including complex geometries, viscosity, and swirling flow. Arcjet geometries are large area ratio converging nozzles with centerbodies in the subsonic portion of the nozzle. The nozzle walls serve as the anode while the centerbody functions as the cathode. Viscous effects are important because the Reynolds number, based on the throat radius, is typically less than 1,000. Experimental studies have shown that a swirl or circumferential velocity component stabilizes a constricted arc. This dissertation describes the equations governing flow through a constricted arcjet thruster. An assumption that the flowfield is in local thermodynamic equilibrium leads to a single fluid plasma temperature model. An order of magnitude analysis reveals the governing fluid mechanics equations are uncoupled from the electromagnetic field equations. A numerical method is developed to solve the governing fluid mechanics equations, the Thin Layer Navier-Stokes equations. A coordinate transformation is employed in deriving the governing equations to simplify the application of boundary conditions in complex geometries. An axisymmetric formulation is employed to include the swirl velocity component as well as the axial and radial velocity components. The numerical method is an implicit finite-volume technique and allows for large time steps to reach a converged steady-state solution. The inviscid fluxes are flux-split, and Gauss-Seidel line relaxation is used to accelerate convergence. Converging-diverging nozzles with exit-to-throat area ratios up to 100:1 and annular nozzles were examined. Quantities examined included Mach number and static wall pressure distributions, and oblique shock structures. As the level of swirl and viscosity in the flowfield increased the mass flow rate and thrust decreased. The technique was used to predict the flow through a typical arcjet thruster geometry. Results indicate swirl and viscosity play an important role in the complex geometry of an arcjet.

Pawlas, Gary E.↗

NASA NTRS1992

Effect of mean velocity shear on the dissipation rate of turbulent kinetic energy

The dissipation rate of turbulent kinetic energy in incompressible turbulence is investigated using a two-scale DIA. The dissipation rate is shown to consist of two parts; one corresponds to the dissipation rate used in the current turbulence models of eddy-viscosity type, and another comes from the viscous effect that is closely connected with mean velocity shear. This result can elucidate the physical meaning of the dissipation rate used in the current turbulence models and explain part of the discrepancy in the near-wall dissipation rates between the current turbulence models and direct numerical simulation of the Navier-Stokes equation.

Yoshizawa, Akira↗

NASA NTRS1983

Application of unsteady laminar triple-deck theory to viscous-inviscid interactions from an oscillating flap in supersonic and subsonic flow

Unsteady triple-deck theory is applied to analyze the local viscous-inviscid interaction of an idealized oscillating flap with a laminar boundary layer in either supersonic or subsonic external flow. For small flap amplitudes and small-to-moderate nondimensional frequencies, linearized analytical solutions by means of Fourier transformation are given for the pressure and shear distributions ahead of and behind the flap hinge. In the supersonic case, the predicted unsteady viscous effects reduce the pressure amplitude and spread it out upstream while causing it to lag the quasi-steady inviscid prediction (flap motion); this also results in an unsteady delay of incipient separation at the hinge to a higher flap amplitude. In contrast, the lowered unsteady viscous pressure distribution in purely subsonic flow slightly leads the flap motion, resulting in incipient separation at a smaller flap amplitude than the quasi-steady value. These trends are shown to be in qualitative agreement with available experimental data.

Inger, G. R.↗

NASA NTRS2003

Irreversible Entropy Production in Two-Phase Mixing Layers

This report presents a study of dissipation (irreversible production of entropy) in three-dimensional, temporal mixing layers laden with evaporating liquid drops. The purpose of the study is to examine the effects of evaporating drops on the development of turbulent features in flows. Direct numerical simulations were performed to analyze transitional states of three mixing layers: one without drops, and two that included drops at different initial mass loadings. Without drops, the dissipation is essentially due to viscous effects. It was found that in the presence of drops, the largest contribution to dissipation was made by heating and evaporation of the drops, and that at large length scales, this contribution is positive (signifying that the drops reduce turbulence), while at small scales, this contribution is negative (the drops increase turbulence). The second largest contribution to dissipation was found to be associated with the chemical potential, which leads to an increase in turbulence at large scales and a decrease in turbulence at small scales. The next smaller contribution was found to be that of viscosity. The fact that viscosity effects are only third in order of magnitude in the dissipation is in sharp contrast to the situation for the mixing layer without the drops. The next smaller contribution - that of the drag and momentum of the vapor from the drops - was found to be negative at lower mass loading but to become positive at higher mass loading.

Okongo, Nora↗

NASA NTRS1977

Influence of transverse surface waves on turbulent boundary layers

Wavy wall experiments using solid waves and progressive waves have been reported. For this paper, the major effects of waviness of the wall on the flow are identified as due to oscillatory curvature (convex-concavity) and oscillatory acceleration/deceleration of the flow, which imposes a highly nonequilibrium influence upon the turbulence structure. The theoretical analysis in this presentation takes into account proper turbulence modeling (including the nonequilibrium effects) for the wavy wall problem. The analysis proceeds in three stages: (1) inviscid solution for induced pressure due to the physical wall, (2) solution of a turbulent boundary layer with pressure gradients and curvature effects in the modeling from which the profile correction is computed, and (3) induced pressure computations for the corrected profile. The phase shift of pressure perturbations with respect to the physical wall can be predicted, and pressure drag and skin friction drag can be estimated, with nonlinear viscous effects included. Comparison of the theoretical estimates with experimental data are also presented.

Balasubramanian, R.↗

NASA NTRS1993

Effects of Buoyancy on Laminar, Transitional, and Turbulent Gas Jet Diffusion Flames

Gas jet diffusion flames have been a subject of research for many years. However, a better understanding of the physical and chemical phenomena occurring in these flames is still needed, and, while the effects of gravity on the burning process have been observed, the basic mechanisms responsible for these changes have yet to be determined. The fundamental mechanisms that control the combustion process are in general coupled and quite complicated. These include mixing, radiation, kinetics, soot formation and disposition, inertia, diffusion, and viscous effects. In order to understand the mechanisms controlling a fire, laboratory-scale laminar and turbulent gas-jet diffusion flames have been extensively studied, which have provided important information in relation to the physico-chemical processes occurring in flames. However, turbulent flames are not fully understood and their understanding requires more fundamental studies of laminar diffusion flames in which the interplay of transport phenomena and chemical kinetics is more tractable. But even this basic, relatively simple flame is not completely characterized in relation to soot formation, radiation, diffusion, and kinetics. Therefore, gaining an understanding of laminar flames is essential to the understanding of turbulent flames, and particularly fires, in which the same basic phenomena occur. In order to improve and verify the theoretical models essential to the interpretation of data, the complexity and degree of coupling of the controlling mechanisms must be reduced. If gravity is isolated, the complication of buoyancy-induced convection would be removed from the problem. In addition, buoyant convection in normal gravity masks the effects of other controlling parameters on the flame. Therefore, the combination of normal-gravity and microgravity data would provide the information, both theoretical and experimental, to improve our understanding of diffusion flames in general, and the effects of gravity on the burning process in particular.

Bahadori, M. Yousef↗

NASA NTRS2005

Sub-Grid Modeling of Electrokinetic Effects in Micro Flows

Advances in micro-fabrication processes have generated tremendous interests in miniaturizing chemical and biomedical analyses into integrated microsystems (Lab-on-Chip devices). To successfully design and operate the micro fluidics system, it is essential to understand the fundamental fluid flow phenomena when channel sizes are shrink to micron or even nano dimensions. One important phenomenon is the electro kinetic effect in micro/nano channels due to the existence of the electrical double layer (EDL) near a solid-liquid interface. Not only EDL is responsible for electro-osmosis pumping when an electric field parallel to the surface is imposed, EDL also causes extra flow resistance (the electro-viscous effect) and flow anomaly (such as early transition from laminar to turbulent flow) observed in pressure-driven microchannel flows. Modeling and simulation of electro-kinetic effects on micro flows poses significant numerical challenge due to the fact that the sizes of the double layer (10 nm up to microns) are very thin compared to channel width (can be up to 100 s of m). Since the typical thickness of the double layer is extremely small compared to the channel width, it would be computationally very costly to capture the velocity profile inside the double layer by placing sufficient number of grid cells in the layer to resolve the velocity changes, especially in complex, 3-d geometries. Existing approaches using "slip" wall velocity and augmented double layer are difficult to use when the flow geometry is complicated, e.g. flow in a T-junction, X-junction, etc. In order to overcome the difficulties arising from those two approaches, we have developed a sub-grid integration method to properly account for the physics of the double layer. The integration approach can be used on simple or complicated flow geometries. Resolution of the double layer is not needed in this approach, and the effects of the double layer can be accounted for at the same time. With this approach, the numeric grid size can be much larger than the thickness of double layer. Presented in this report are a description of the approach, methodology for implementation and several validation simulations for micro flows.

Chen, C. P.↗

NASA NTRS1981

Prediction of laminar and turbulent primary and secondary flows in strongly curved ducts

The analysis is based on a primary secondary velocity decomposition in a given coordinate system, and leads to approximate governing equations which correct an a priori inviscid solution for viscous effects, secondary flows, total pressure distortion, heat transfer, and internal flow blockage and losses. Solution of the correction equations is accomplished as an initial value problem in space using an implicit forward marching technique. The overall solution procedure requires significantly less computational effort than Navier-Stokes algorithms. The solution procedure is effective even with the extreme local mesh resolution which is necessary to solve near wall sublayer regions in turbulent flow calculations. Computed solutions for both laminar and turbulent flow compared very favorably with available analytical and experimental results. The overall method appears very promising as an economical procedure for making detailed predictions of viscous primary and secondary flows in highly curved passages.

Kreskovsky, J. P.↗

NASA NTRS1990

Extension of a three-dimensional viscous wing flow analysis user's manual: VISTA 3-D code

Three-dimensional unsteady viscous effects can significantly influence the performance of fixed and rotary wing aircraft. These effects are important in both flows about helicopter rotors in forward flight and flows about three-dimensional (swept and tapered) supercritical wings. A computational procedure for calculating such flow field was developed. The procedure is based upon an alternating direction technique employing the Linearized Block Implicit method for solving three-dimensional viscous flow problems. In order to demonstrate the viability of this method, two- and three-dimensional problems are computed. These include the flow over a two-dimensional NACA 0012 airfoil under steady and oscillating conditions, and the steady, skewed, three-dimensional flow on a flat plate. Although actual three-dimensional flows over wings were not obtained, the ground work was laid for considering such flows. In this report a description of the computer code is given.

Weinberg, Bernard C.↗

NASA NTRS1990

Comparison of several finite-difference methods

The present numerical study establishes that, with the MacCormack and 'two-four' methods, the solution accuracy obtainable in problems involving wave propagation, shock-wave and contact discontinuities, and viscous effects, will be strongly dependent on Courant number. The application of flux correction to the MacCormack and two-four methods is noted to significantly attenuate dispersion errors; the ensuing solutions capture the discontinuities in the shock-tube problem with improved accuracy and resolution, and are free of dispersion errors for the viscous Burgers' equation.

Biringen, S.↗

NASA NTRS1980

Unsteady effects of a control surface in two dimensional subsonic and transonic flow

The experimental results of steady and unsteady pressure measurements, carried out in subsonic and transonic flow on a 16 percent relative thickness supercritical aerofoil, equipped with a trailing edge flap involving 25 percent of the chord, in a sinusoidal motion are given. These experimental results are compared with those obtained by various methods of steady and unsteady inviscid flow calculations. Some calculation results in which viscous effects have been taken into account, for both steady and unsteady flows, are also presented.

Grenon, R.↗

NASA NTRS1953

Comparison of the Experimental and Theoretical Distribution of Lift on a Slender Inclined Body of Revolution at M = 2

Pressure distributions and force characteristics have been determined for a body of revolution consisting of a fineness ratio 5.75, circular-arc, ogival nose tangent to a cylindrical afterbody for an angle-of-attack range of 0 degrees to 35.5 degrees. The free-stream Mach number was 1.98 and the free-stream Reynolds number was approximately 0.5 x 10 sup 6, based on body diameter. Comparison of the theoretical and experimental pressure distributions shows that for zero lift, either slender-body theory or higher-order theories yield results which are in good agreement with experiment. For the lifting case, good agreement with theory is found only for low angles of attack and for the region in which the body cross-sectional area is increasing in the downstream direction. Because of the effects of cross-flow separation and the effects of compressibility due to the high cross-flow Mach numbers at large angles of attack, the experimental pressure distributions differ from those predicted by potential theory. Although the flow about the inclined body was, in general, similar to that assumed as the basis for Allen's method of estimating the forces resulting from viscous effects (NACA RM A91I26), the distribution of the forces was significantly different from that assumed. Nevertheless, the lift and pitching-moment characteristics were in fair agreement with the estimated value.

Perkins, Edward W↗

NASA NTRS1984

The effect of viscosity on impact cratering and possible application to the icy satellites of Saturn and Jupiter

Impact experiments in Newtonian fluids with a range of viscosities of 0.001 to 60 Pa s demonstrate that transient crater volume and shape depend on target viscosity as well as on gravity. Volume is reduced, and depth-to-diameter ratio is increased for cratering events in which viscosity plays a dominant role. In addition to being affected by target kinematic viscosity, viscous scaling is most strongly influenced by projectile diameter, less strongly by projectile velocity, and least strongly by gravity. In a planetary context, viscous effects can occur for craters formed by small or slow moving impacting bodies, low planetary surface densities, high surface viscosities, and low gravity values; conditions all likely for certain impacts into the icy satellites of Saturn and Jupiter, especially if liquid mantles were still present beneath solid crusts. Age dating based on crater counts and size-frequency distributions for these icy bodies may have to be modified to account for the possibility that viscosity-dominated craters were initially smaller and deeper than their gravity-controlled counterparts.

Fink, J.↗

NASA NTRS1992

Internal Shock Interactions in Propulsion/Airframe Integrated Three-Dimensional Sidewall Compression Scramjet Inlets

The advantages and design requirements of propulsion/airframe integration for high Mach number flight have led to extensive study of the three-dimensional sidewall compression scramjet inlet in recent years. Recent research publications have indicated testing over a broad range of Mach number (2 to 18) in a variety of test gases, such as air, helium, and tetrafluoromethane. Multiple experimental techniques have been employed to obtain detailed internal shock interaction data, performance data, and inlet starting limits. Computational fluid dynamics has been effectively used for preliminary parametric studies as well as in parallel with experiments to aid in the explanation of unusual or unexpected flow phenomena. Inlets of this genre afford a relatively simple, generic geometry while producing a highly complex, three-dimensional flow field dominated by shock/shock and shock/boundary layer interactions. While the importance of the viscous effects in high speed inlet interactions is recognized, the present work addresses in a parametric fashion the inviscid effects of leading edge sweep, sidewall compression, and inflow Mach number on the internal shock structure in terms of inlet compression and mass capture. In the process, the source of the of the Mach number invariance with leading edge sweep for a constant sidewall compression class of inlet is identified, and a previously undocumented spillage phenomenon in a constant effective wedge angle class of inlets is discussed.

Holland, Scott D.↗