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All sourcesNASA NTRSDOE OSTI
NASA NTRS2016

Changes in Flat Plate Wake Characteristics Obtained With Decreasing Plate Thickness

The near and very near wake of a flat plate with a circular trailing edge is investigated with data from direct numerical simulations. Computations were performed for four different Reynolds numbers based on plate thickness (D) and at constant plate length. The value of θ/D varies by a factor of approximately 20 in the computations (θ being the boundary layer momentum thickness at the trailing edge). The separating boundary layers are turbulent in all the cases. One objective of the study is to understand the changes in wake characteristics as the plate thickness is reduced (increasing θ/D). Vortex shedding is vigorous in the low θ/D cases with a substantial decrease in shedding intensity in the largest θ/D case (for all practical purposes shedding becomes almost intermittent). Other characteristics that are significantly altered with increasing θ/D are the roll-up of the detached shear layers and the magnitude of fluctuations in shedding period. These effects are explored in depth. The effects of changing θ/D on the distributions of the time-averaged, near-wake velocity statistics are discussed.

Wakes↗
NASA NTRS1995

Forced Convection and Sedimentation Past a Flat Plate

The steady laminar flow of a well-mixed suspension of monodisperse solid spheres, convected steadily past a horizontal flat plate and sedimenting under the action of gravity, is examined. It is shown that, in the limit as Re approaches infinity and epsilon approaches 0, where Re is the bulk Reynolds number and epsilon is the ratio of the particle radius a to the characteristic length scale L, the analysis for determining the particle concentration profile has several aspects in common with that of obtaining the temperature profile in forced-convection heat transfer from a wall to a fluid stream moving at high Reynolds and Prandtl numbers. Specifically, it is found that the particle concentration remains uniform throughout the O(Re(exp -1/2)) thick Blasius boundary layer except for two O(epsilon(exp 2/3)) thin regions on either side of the plate, where the concentration profile becomes non-uniform owing to the presence of shear-induced particle diffusion which balances the particle flux due to convection and sedimentation. The system of equations within this concentration boundary layer admits a similarity solution near the leading edge of the plate, according to which the particle concentration along the top surface of the plate increases from its value in the free stream by an amount proportional to X(exp 5/6), with X measuring the distance along the plate, and decreases in a similar fashion along the underside. But, unlike the case of gravity settling on an inclined plate in the absence of a bulk flow at infinity considered earlier, here the concentration profile remains continuous everywhere. For values of X beyond the region near the leading edge, the particle concentration profile is obtained through the numerical solution of the relevant equations. It is found that, as predicted from the similarity solution, there exists a value of X at which the particle concentration along the top side of the plate attains its maximum value phi(sub m) and that, beyond this point, a stagnant sediment layer will form that grows steadily in time. This critical value of X is computed as a function of phi(sub s), the particle volume fraction in the free stream. In contrast, but again in conformity with the similarity solution, for values of X sufficiently far removed from the leading edge along the underside of the plate, a particle-free region is predicted to form adjacent to the plate. This model, with minor modifications, can be used to describe particle migration in other shear flows, as, for example, in the case of crossflow microfiltration.

Pelekasis, Nikolaos A.↗
NASA NTRS1995

The Physics of Turbulence in the Boundary Layer

The geometry of the velocity field in a numerically simulated incompressible turbulent boundary layer over a flat plate at Re theta=670 has been studied using the invariants of the velocity gradient tensor. These invariants are computed at every grid point in the flow and used to form the discriminant. Of primary interest are those regions in the flow where the discriminant is positive; regions where, according to the characteristic equation, the eigenvalues of the velocity gradient tensor are complex. An observer moving with a frame of reference which is attached to a fluid particle lying within such a region would see a local flow pattern of the type stable-focus-stretching or unstable-focus-compressing. When the flow is visualized this way, continuous, connected, large-scale structures are revealed that extend from the point just below the buffer layer out to the beginning of the wake region. These structures are aligned with the mean shear close to the wall and arch in the cross-stream direction away from the wall. In some cases the structures observed are very similar to to the hairpin eddy vision of boundary layer structure proposed by Theodorsen. That the structure of the flow is revealed more effectively by the discriminant rather than by the vorticity is important and adds support to recent observations of the discriminant in a channel flow simulation. Of particular importance is the fact that the procedure does not require the use of an arbitrary threshold in the discriminant. Further analysis using computer flow visualization shows a high degree of spatial correlation between regions of positive discriminant, extreme negative pressure fluctuations and large instantaneous values of Reynolds shear stress.

Kline, Stephen↗
NASA NTRS2000

Measurements in Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions

Detailed velocity measurements were made along a flat plate subject to the same dimensionless pressure gradient as the suction side of a modern low-pressure turbine airfoil. Reynolds numbers based on wetted plate length and nominal exit velocity were varied from 50,000 to 300,000, covering cruise to takeoff conditions. Low and high inlet free-stream turbulence intensities (0.2% and 7%) were set using passive grids. The location of boundary-layer separation does not depend strongly on the free-stream turbulence level or Reynolds number, as long as the boundary layer remains non-turbulent prior to separation. Strong acceleration prevents transition on the upstream part of the plate in all cases. Both free-stream turbulence and Reynolds number have strong effects on transition in the adverse pressure gradient region. Under low free-stream turbulence conditions transition is induced by instability waves in the shear layer of the separation bubble. Reattachment generally occurs at the transition start. At Re = 50,000 the separation bubble does not close before the trailing edge of the modeled airfoil. At higher Re, transition moves upstream, and the boundary layer reattaches. With high free-stream turbulence levels, transition appears to occur in a bypass mode, similar to that in attached boundary layers. Transition moves upstream, resulting in shorter separation regions. At Re above 200,000, transition begins before separation. Mean velocity, turbulence and intermittency profiles are presented.

Volino, Ralph J.↗
NASA NTRS1974

Surface pressure fluctuations in hypersonic turbulent boundary layers

The surface pressure fluctuations on a flat plate model at hypersonic Mach numbers of 5.2, 7.4 and 10.4 with an attached turbulent boundary layer were measured using flush mounted small piezoelectric sensors. A high frequency resolution of the pressure field was achieved using specially designed small piezoelectric sensors that had a good frequency response well above 300 KHz. The RMS pressures and non-dimensional energy spectra for all above Mach numbers are presented. The convective velocities, obtained from space time correlation considerations are equal to 0.7 U sub infinity. The results indicate the RMS pressures vary from 5 to 25 percent of the mean static pressures. The ratios of RMS pressure to dynamic pressure are less than the universally accepted subsonic value of 6 x 10/3. The ratio decreases in value as the Mach number or the dynamic pressure is increased. The ratio of RMS pressure to wall shear for Mach number 7.4 satisfies one smaller than or equal to p/tau sub w smaller than or equal to three.

Raman, K. R.↗
NASA NTRS1996

Computational Methods for Frictional Contact With Applications to the Space Shuttle Orbiter Nose-Gear Tire

A computational procedure is presented for the solution of frictional contact problems for aircraft tires. A Space Shuttle nose-gear tire is modeled using a two-dimensional laminated anisotropic shell theory which includes the effects of variations in material and geometric parameters, transverse-shear deformation, and geometric nonlinearities. Contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the stress resultants, the generalized displacements, and the Lagrange multipliers associated with both contact and friction conditions. The contact-friction algorithm is based on a modified Coulomb friction law. A modified two-field, mixed-variational principle is used to obtain elemental arrays. This modification consists of augmenting the functional of that principle by two terms: the Lagrange multiplier vector associated with normal and tangential node contact-load intensities and a regularization term that is quadratic in the Lagrange multiplier vector. These capabilities and computational features are incorporated into an in-house computer code. Experimental measurements were taken to define the response of the Space Shuttle nose-gear tire to inflation-pressure loads and to inflation-pressure loads combined with normal static loads against a rigid flat plate. These experimental results describe the meridional growth of the tire cross section caused by inflation loading, the static load-deflection characteristics of the tire, the geometry of the tire footprint under static loading conditions, and the normal and tangential load-intensity distributions in the tire footprint for the various static vertical loading conditions. Numerical results were obtained for the Space Shuttle nose-gear tire subjected to inflation pressure loads and combined inflation pressure and contact loads against a rigid flat plate. The experimental measurements and the numerical results are compared.

Tanner, John A.↗
NASA NTRS1996

Computational methods for frictional contact with applications to the Space Shuttle orbiter nose-gear tire: Comparisons of experimental measurements and analytical predictions

A computational procedure is presented for the solution of frictional contact problems for aircraft tires. A Space Shuttle nose-gear tire is modeled using a two-dimensional laminated anisotropic shell theory which includes the effects of variations in material and geometric parameters, transverse-shear deformation, and geometric nonlinearities. Contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the stress resultants, the generalized displacements, and the Lagrange multipliers associated with both contact and friction conditions. The contact-friction algorithm is based on a modified Coulomb friction law. A modified two-field, mixed-variational principle is used to obtain elemental arrays. This modification consists of augmenting the functional of that principle by two terms: the Lagrange multiplier vector associated with normal and tangential node contact-load intensities and a regularization term that is quadratic in the Lagrange multiplier vector. These capabilities and computational features are incorporated into an in-house computer code. Experimental measurements were taken to define the response of the Space Shuttle nose-gear tire to inflation-pressure loads and to inflation-pressure loads combined with normal static loads against a rigid flat plate. These experimental results describe the meridional growth of the tire cross section caused by inflation loading, the static load-deflection characteristics of the tire, the geometry of the tire footprint under static loading conditions, and the normal and tangential load-intensity distributions in the tire footprint for the various static vertical-loading conditions. Numerical results were obtained for the Space Shuttle nose-gear tire subjected to inflation pressure loads and combined inflation pressure and contact loads against a rigid flat plate. The experimental measurements and the numerical results are compared.

Tanner, John A.↗
NASA NTRS2020

Transition induced by Streamwise Arrays of Roughness Elements on a Flat Plate in Mach 3.5 Flow

The flow behind streamwise arrays of roughness elements was examined with a hot-wire probe. The roughness elements had heights of approximately 20% and 40% of the boundary layer thickness and different spacings and orientations of these roughness elements were tested. The circular roughness elements were spaced two diameters apart or four diameters apart from center to center. Transition moved upstream only when the roughness elements were spaced four diameters apart. The rectangular roughness elements were oriented so that they were at a 45-degree angle relative to the leading edge of the plate. Tandem rectangular elements either had the same orientation or opposing orientation. Mean mass-flux and total-temperature profiles of the flow field downstream of the roughness elements were examined for mean-flow distortion. Mass-flux fluctuation profiles showed that a 45-kHz odd-mode disturbance was present downstream of the shorter circular roughness elements. The dominant instability downstream of the taller circular roughness elements was a 65–85 kHz even-mode disturbance. Mass-flux fluctuation profiles showed that the dominant mode downstream of the tandem rectangular roughness elements with the same orientation was similar to that of a single roughness element and centered at a frequency of approximately 55 kHz. The 55-kHz instability appeared to correspond to increased spanwise shear, and thus was determined to be an odd-like mode. The dominant instability downstream of the tandem roughness elements with opposing orientation was centered at a frequency of 65 kHz and did not transition in the measurement region.

Amanda Chou↗
NASA NTRS1953

An analysis of laminar free-convection flow and heat transfer about a flat plate paralled to the direction of the generating body force

The free-convection flow and heat transfer (generated by a body force) about a flat plate parallel to the direction of the body force are formally analyzed and the type of flow is found to be dependent on the Grashof number alone. For large Grashof numbers (which are of interest in aeronautics), the flow is of the boundary-layer type and the problem is reduced in a formal manner, which is analogous to Prandtl's forced-flow boundary-layer theory, to the simultaneous solution of two ordinary differential equations subject to the proper boundary conditions. Velocity and temperature distributions for Prandtl numbers of 0.01, 0.72, 0.733, 1, 1, 10, 100, and 1000 are computed, and it is shown that velocities and Nusselt numbers of the order of magnitude of those encountered in forced-convection flows may be obtained in free-convection flows. The theoretical and experimental velocity and temperature distributions are in good agreement. A flow and a heat-transfer parameter, from which the important physical quantities such as shear stress and heat-transfer rate can be computed, are derived as functions of Prandtl number alone.

Ostrach, Simon↗
NASA NTRS2002

Experimental Investigation of Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions

Modern low-pressure turbine airfoils are subject to increasingly stronger pressure gradients as designers impose higher loading in an effort to improve efficiency and to reduce part count. The adverse pressure gradients on the suction side of these airfoils can lead to boundary-layer separation, particularly under cruise conditions. Separation bubbles, notably those which fail to reattach, can result in a significant degradation of engine efficiency. Accurate prediction of separation and reattachment is hence crucial to improved turbine design. This requires an improved understanding of the transition flow physics. Transition may begin before or after separation, depending on the Reynolds number and other flow conditions, has a strong influence on subsequent reattachment, and may even eliminate separation. Further complicating the problem are the high free-stream turbulence levels in a real engine environment, the strong pressure gradients along the airfoils, the curvature of the airfoils, and the unsteadiness associated with wake passing from upstream stages. Because of the complicated flow situation, transition in these devices can take many paths that can coexist, vary in importance, and possibly also interact, at different locations and instances in time. The present work was carried out in an attempt to systematically sort out some of these issues. Detailed velocity measurements were made along a flat plate subject to the same nominal dimensionless pressure gradient as the suction side of a modern low-pressure turbine airfoil ('Pak-B'). The Reynolds number based on wetted plate length and nominal exit velocity, Re, was varied from 50;000 to 300; 000, covering cruise to takeoff conditions. Low, 0.2%, and high, 7%, inlet free-stream turbulence intensities were set using passive grids. These turbulence levels correspond to about 0.2% and 2.5% turbulence intensity in the test section when normalized with the exit velocity. The Reynolds number and free-stream turbulence level do not have a significant effect on the location of boundary-layer separation unless they are high enough to induce transition upstream of separation. The location and extent of the transition zone, in contrast, depend strongly on Re and TI. The beginning of reattachment closely follows the onset of transition. Under low free-stream turbulence conditions the boundary layer is laminar at separation and then begins to exhibit fluctuations in a finite frequency band in the shear layer over the separation bubble. These fluctuations are due to instability waves. The fluctuations grow in magnitude, higher harmonics are generated, and finally lead to a breakdown to turbulence. Transition begins in the shear layer, but quickly spreads to the near wall region and causes the boundary layer to reattach. The transition is rapid and the resulting turbulence contains a full range of high and low frequencies. Under high free-stream turbulence conditions, slowly growing low-frequency fluctuations are induced in the pretransitional boundary layer by the free-stream. The separation bubbles are considerably thinner than in the low TI cases, resulting in thinner boundary layers at the end of the test wall. At Re=50,000 and 100,000, the pre-transitional boundary layer separates at about the same location as in the low TI cases. Transition occurs through a bypass mode, begins upstream of the corresponding low-TI location, and proceeds in a manner similar to that of an attached boundary layer. Under high TI at Re=200,000 and 300,000, transition begins before separation. The boundary layer may separate, but if it does the separation bubble is very short and does not significantly affect the downstream development of the boundary layer. A comparison is made to previous work in a simulated cascade.

Hultgren, Lennart S.↗
NASA NTRSDate not supplied

Toward Verification of the γ-Reθt Transition Model in OVERFLOW and FUN3D

The results of an ongoing assessment of the transition modeling capability in NASA's OVERFLOW and FUN3D programs are presented, with a focus on the Langtry-Menter γ-Reθt transition model in combination with the shear-stress transport (SST) turbulence model. While the effect of numerics and boundary conditions on the accuracy and iterative convergence of RANS solutions for fully turbulent flows has been well documented, especially in the context of canonical flow configurations, the same cannot be said for transport-equation-based transition models coupled with RANS-based turbulence models. Given the criticality of transition modeling for new aircraft design and optimization, there has been a renewed focus on the accuracy of such transition models and their inconsistent implementation across different flow solvers as seen from the AIAA and NATO-AVT workshops. In this work, we aim to establish the verification of such models via these two well established CFD codes with different numerics. The goal is to produce high-quality data, such as grids, solutions, and other auxiliary data, that may be utilized for code verification by others in the CFD community. As a first step, the work reported here is focused on the Langtry-Menter transition model as applied to two simple 2D configurations, namely the flat plate, and the NLF-0416, respectively. The paper also highlights how the boundary conditions and baseline turbulence model can affect the solutions from the SST-based Langtry-Menter transition model. A preliminary evaluation of the automatic mesh adaption capabilities of these solvers and potential benefits for flow configurations involving a mix of laminar, transitional, and fully turbulent flows is also reported.

CFD Modeling↗
NASA NTRS2011

Underexpanded Supersonic Plume Surface Interactions: Applications for Spacecraft Landings on Planetary Bodies

Numerical and experimental investigations of both far-field and near-field supersonic steady jet interactions with a flat surface at various atmospheric pressures are presented in this paper. These studies were done in assessing the landing hazards of both the NASA Mars Science Laboratory and Phoenix Mars spacecrafts. Temporal and spatial ground pressure measurements in conjunction with numerical solutions at altitudes of approx.35 nozzle exit diameters and jet expansion ratios (e) between 0.02 and 100 are used. Data from steady nitrogen jets are compared to both pulsed jets and rocket exhaust plumes at Mach approx.5. Due to engine cycling, overpressures and the plate shock dynamics are different between pulsed and steady supersonic impinging jets. In contrast to highly over-expanded (e <1) and underexpanded exhaust plumes, results show that there is a relative ground pressure load maximum for moderately underexpanded (e approx.2-5) jets which demonstrate a long collimated plume shock structure. For plumes with e much >5 (lunar atmospheric regime), the ground pressure is minimal due to the development of a highly expansive shock structure. We show this is dependent on the stability of the plate shock, the length of the supersonic core and plume decay due to shear layer instability which are all a function of the jet expansion ratio. Asymmetry and large gradients in the spatial ground pressure profile and large transient overpressures are predominantly linked to the dynamics of the plate shock. More importantly, this study shows that thruster plumes exhausting into martian environments possess the largest surface pressure loads and can occur at high spacecraft altitudes in contrast to the jet interactions at terrestrial and lunar atmospheres. Theoretical and analytical results also show that subscale supersonic cold gas jets adequately simulate the flow field and loads due to rocket plume impingement provided important scaling parameters are in agreement. These studies indicate the critical importance of testing and modeling plume-surface interactions for descent and ascent of spacecraft and launch vehicles.

Mehta, M.↗
NASA NTRS2023

Microstructural Changes and Pb Mobility During the Zircon to Reidite Transformation: Implications for Planetary Impact Chronology

Impact events modify and leave behind a complex history of rock metamorphism on terrestrial planets. Evidence for an impact event may be recorded in physical changes to minerals, such as mineral deformation and formation of high P-T polymorphs, but also in the form of chemical fingerprints, such as enhanced elemental diffusion and isotopic mixing. Here we explore laboratory shock-induced physical and chemical changes to zircon and feldspar, the former of which is of interest because its trace elements abundances and isotope ratios are used extensively in geochemistry and geochronology. To this end, a granular mixture of Bishop Tuff sanidine and Kuehl Lake zircon, both with well characterized Pb isotope compositions, was prepared and then shocked via a flat plate accelerator. The peak pressure of the experiment, as calculated by the impedance matching method, was ~24 GPa although a broader range of P-T conditions is anticipated due to starting sample porosity. Unshocked and shocked materials were characterized via scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), and Raman spectroscopy. These methods show that the starting zircon material had abundant metamict regions, and the conversion of the feldspar to glass in the post-shock material. Analyses of the shocked product also yielded multiple occurrences of the high-pressure ZrSiO 4 polymorph reidite, with some domains up to 300 μm across. The possibility of U-Pb system disturbance was evaluated via laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS) and secondary ion mass spectrometry (SIMS). The isotopic data reveal that disturbance of the U-Pb geochronometer in the reidite was minimal (<2% for the main U-Pb geochronometers). To better constrain the P-T conditions during the shock experiment, we complement impedance matching pressure calculations with iSALE2D impact simulations. The simulated results yield a range of P-T conditions experienced during the experiment and show that much of the sample may have reached >30 GPa, which is consistent with formation of reidite. In the recovered shocked material, we identified lamellae of reidite, some of which interlock with zircon lamellae. Reidite {112} twins were identified, which we interpret to have formed to reduce stress between the crystal structure of the host zircon and reidite. These two findings support the interpretation that shear transformation enabled the transition of zircon to reidite. The size and presence of reidite found here indicate that this phase is probably common in impact-shocked crustal rocks that experienced ~25 to ~35 GPa, especially when the target material has porosity. Additionally, shock loading of the zircon and transformation to reidite at these pressures in porous materials is unlikely to significantly disturb the U-Pb system in zircon and that the reidite inherits the primary U and Pb elemental and isotopic ratios from the zircon.

Bishop Tuff↗
NASA NTRS1959

Some Basic Aspects of Magnetohydrodynamic Boundary-Layer Flows

An appraisal is made of existing solutions of magnetohydrodynamic boundary-layer equations for stagnation flow and flat-plate flow, and some new solutions are given. Since an exact solution of the equations of magnetohydrodynamics requires complicated simultaneous treatment of the equations of fluid flow and of electromagnetism, certain simplifying assumptions are generally introduced. The full implications of these assumptions have not been brought out properly in several recent papers. It is shown in the present report that for the particular law of deformation which the magnetic lines are assumed to follow in these papers a magnet situated inside the missile nose would not be able to take up any drag forces; to do so it would have to be placed in the flow away from the nose. It is also shown that for the assumption that potential flow is maintained outside the boundary layer, the deformation of the magnetic lines is restricted to small values. The literature contains serious disagreements with regard to reductions in heat-transfer rates due to magnetic action at the nose of a missile, and these disagreements are shown to be mainly due to different interpretations of reentry conditions rather than more complicated effects. In the present paper the magnetohydrodynamic boundary-layer equation is also expressed in a simple form that is especially convenient for physical interpretation. This is done by adapting methods to magnetic forces which in the past have been used for forces due to gravitational or centrifugal action. The simplified approach is used to develop some new solutions of boundary-layer flow and to reinterpret certain solutions existing in the literature. An asymptotic boundary-layer solution representing a fixed velocity profile and shear is found. Special emphasis is put on estimating skin friction and heat-transfer rates.

Hess, Robert V.↗
NASA NTRS2011

Direct Numerical Simulations of Transitional/Turbulent Wakes

The interest in transitional/turbulent wakes spans the spectrum from an intellectual pursuit to understand the complex underlying physics to a critical need in aeronautical engineering and other disciplines to predict component/system performance and reliability. Cylinder wakes have been studied extensively over several decades to gain a better understanding of the basic flow phenomena that are encountered in such flows. Experimental, computational and theoretical means have been employed in this effort. While much has been accomplished there are many important issues that need to be resolved. The physics of the very near wake of the cylinder (less than three diameters downstream) is perhaps the most challenging of them all. This region comprises the two detached shear layers, the recirculation region and wake flow. The interaction amongst these three components is to some extent still a matter of conjecture. Experimental techniques have generated a large percentage of the data that have provided us with the current state of understanding of the subject. More recently computational techniques have been used to simulate cylinder wakes, and the data from such simulations are being used to both refine our understanding of such flows as well as provide new insights. A few large eddy and direct numerical simulations (LES and DNS) of cylinder wakes have appeared in the literature in the recent past. These investigations focus on the low Reynolds number range where the cylinder boundary layer is laminar (sub-critical range). However, from an engineering point of view, there is considerable interest in the situation where the upper and/or lower boundary layer of an airfoil is turbulent, and these turbulent boundary layers separate from the airfoil to contribute to the formation of the wake downstream. In the case of cylinders, this only occurs at relatively large unit Reynolds numbers. However, in the case of airfoils, the boundary layer has the opportunity to transition to turbulence on the airfoil surface at a relatively lower unit Reynolds number because the characteristic length of the airfoil is typically one to two orders of magnitude larger than the trailing edge diameter. This transition to turbulence would occur unless there is a strong favorable pressure gradient that results in the boundary layer remaining laminar or transitional over the surface of the airfoil. This presentation will focus on two direct numerical simulations that have been performed at NASA ARC. The first is of a cylinder wake with laminar separating boundary layers. The second is the wake of a flat plate with a circular trailing edge. The upper and lower plate surface boundary layers are both turbulent and statistically identical. Thus the computed wake is symmetric in a statistical sense. This flow is more representative of airfoil wakes than cylinder wakes. Results from the two simulations including flow visualization and turbulence statistics in the near wake will be presented at the seminar.

wakes↗
NASA NTRS2000

The Turbulent/Non-Turbulent Interface Bounding a Far-Wake

The velocity fields of a turbulent wake behind a flat plate obtained from the direct numerical simulations of Moser et al. are used to study the structure of the flow in the intermittent zone where there are, alternately, regions of fully turbulent flow and non-turbulent velocity fluctuations either side of a thin randomly moving interface. Comparisons are made with a wake that is 'forced' by amplifying initial velocity fluctuations. There is also a random temperature field T in the flow; T varies between constant values of 0.0 and 1.0 on the sides of the wake. The value of the Reynolds number based on the centreplane mean velocity defect and halfwidth b of the wake is Re approx. = 2000. It is found that the thickness of the continuous interface is about equal to 0.07b, whereas the amplitude of fluctuations of the instantaneous interface displacement y(sub I)(t) is an order of magnitude larger, being about 0.5b. This explains why the mean statistics of vorticity in the intermittent zone can be calculated in terms of the probability distribution of y(sub I) and the instantaneous discontinuity in vorticity across the interface. When plotted as functions of y - y(sub I), the conditional mean velocity (U) and temperature (T) profiles show sharp jumps Delta(U) and Delta(T) at the interface adjacent to a thick zone where (U) and (T) vary much more slowly. Statistics for the vorticity and velocity variances, available in such detail only from DNS data, show how streamwise and spanwise components of vorticity are generated by vortex stretching in the bulges of the interface. Flow fields around the interface, analyzed in terms of the local streamline pattern, confirm previous results that the advancement of the vortical interface into the irrotational flow is driven by large-scale eddy motion. It is argued that because this is an inviscid mechanism the entrainment process is not sensitive to the value of Re, and that small-scale nibbling only plays a subsidiary role. While mean Reynolds stresses decrease gradually in the intermittent zone, conditional stresses are found to decrease sharply towards zero at the interface. Using one-point turbulence models applied to either unconditional or conditional statistics for the turbulent region and then averaged, the entrainment rate E(sub b) would, if calculated exactly, be zero. But if computed with standard computational methods, E(sub b) would be non-zero because of numerical diffusion. It is concluded that the current practice in statistical models of approximating entrainment by a diffusion process is computationally arbitrary and physically incorrect. An analysis shows how E(sub b) is related to Delta(U) and the jump in shear stress at the interface, and correspondingly to Delta(T) and the heat flux.

Bisset, David K.↗