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NASA NTRS1977

Numerical turbulence modeling

The underlying bases and developments in two techniques of detailed turbulence modeling are described where the flow is treated in the Eulerian sense, and one technique where the Lagrangian motions of vortices are followed. First, a technique is described for solving the single-point statistically averaged conservation equations. The Reynolds stresses that appear in these equations are evaluated by solving supplemental differential equations which contain terms that are modeled. A sequence of increasingly complex, but also increasingly general, modeling equations is described and computations based on these equations are compared with experimental data. The hierarchy of models described terminates with equations for the individual components of the Reynolds stress tensor. The second Eulerian technique approach to turbulence modeling is the direct numerical simulation of turbulent fields. In this approach, all three dimensional eddies between a predetermined range of sizes are computed in time within a specified volume of flow. Present day computers require a tradeoff between the size of the volume that can be considered and the degree of resolution of the turbulent eddies. Techniques of modeling the smallest eddies are described that permit enlarging the volume, or Reynolds number, that can be considered.

Rubesin, M. W.↗

NASA NTRS1991

Acoustic sources in the low Mach number turbulent boundary layer

The sources of sound production in a low Mach number turbulent boundary layer are examined. The sources are shown to be quadrupole in nature and to result from supersonically convecting wave-number components of the fluctuating Reynolds' normal stresses. The primary Tollmien-Schlichting instability of the boundary layer is found to radiate no sound. Analysis of various vortical phenomena suggests that the primary source is the process of formation of horseshoe vortices, with viscous sublayer bursts a possible secondary source.

Hardin, Jay C.↗

NASA NTRS1987

An investigation of the flow characteristics in the blade endwall corner region

Studies were undertaken to determine the structure of the flow in the blade end wall corner region simulated by attaching two uncambered airfoils on either side of a flat plate with a semicircular leading edge. Detailed measurements of the corner flow were obtained with conventional pressure probes, hot wire anemometry, and flow visualization. The mean velocity profiles and six components of the Reynolds stress tensor were obtained with an inclined single sensor hot wire probe whereas power spectra were obtained with a single sensor oriented normal to the flow. Three streamwise vortices were identified based on the surface streamlines, distortion of total pressure profiles, and variation of mean velocity components in the corner. A horseshoe vortex formed near the leading edge of the airfoil. Within a short distance downstream, a corner vortex was detected between the horseshoe vortex and the surfaces forming the corner. A third vortex was formed at the rear portion of the corner between the corner vortex and the surface of the flat plate. Turbulent shear stress and production of turbulence are negligibly small. A region of negative turbulent shear stress was also observed near the region of low turbulence intensity from the vicinity of the flat plate.

Hazarika, Birinchi K.↗

DOE OSTI2020

Needle-Like Ferroelastic Domains in Individual Ferroelectric Nanoparticles

Superior structural, physical and electronic properties make ferroelectric nanocrystals essential in enabling a range of next-generation devices. Ferroelectric responses are determined by crystal structure and domain morphology. The ability to reversibly displace, create and annihilate elastic domains is critical to device applications. Whereas electric-field control has been demonstrated for ferroelectric 180° surface domain walls and vortices, similar control of ferroelastic domains and domain boundaries within individual nanocrystals remains challenging. Using controlled external compressive and tensile axial stress, deterministic and reversible control of highly mobile ferroelastic domains and axial polarization in three dimensions is demonstrated in this study. While many studies exist on ferroelastic domains in thin films and bulk, little is known about ferroelastic interactions at the single nanoparticle level, especially involving domain boundaries. Through combining Bragg coherent X-ray diffractive imaging and Landau theory, strain gradients in individual BaTiO3 nanocrystals are shown to stabilize needle-like ferroelastic twin domains. These domains are highly labile under applied axial stress, producing a locally enhanced electric polarization mediated by a ferroelectric phase transition. The efficacy of Bragg coherent X-ray diffractive imaging in studying in operando domains in three-dimensions is demonstrated, while synergy with theory provides a paradigm for domain boundary engineering and potential for nanoscale functional devices.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Observations on the deformation of metal microspheres in shock-driven polymer flows

We report that solid particles can be fragmented by a fast-moving fluid if their velocity difference is great enough, such as during the atmospheric entry of meteoroids or the shock compression of engineered particulate composites. The extent of particle deformation and breakup in such systems is poorly understood because the necessary extreme conditions make observation difficult and data scarce. To meet this need, experiments combining ultrafast synchrotron-based radiography with plate impact loading were performed at the dynamic compression sector at the advanced photon source. Metal microspheres of several densities and strengths (Au, Ta, and W) were placed inside a polymer matrix. A planar shock wave was then produced in the polymer by the impact of a gun-launched flyer plate. X-ray images of the resulting flow were collected at ~150ns intervals. These images document the progression of particle deformation across a range of flow conditions and particle materials. They show that the extent of deformation is sensitive to the ratio of drag stress to particle strength. The deforming particle's shape is determined by the initial shock–particle interaction, fluid stagnation pressure, and vorticity, each acting on its own timescale. A set of scaling relationships is presented to capture these observations and enable comparison with prior hydrodynamic data. The result is a framework for predicting the conditions under which strong particles are severely deformed by a shock-driven flow.

36 MATERIALS SCIENCE↗

NASA NTRS1987

Mechanisms by which heat release affects the flow field in a chemically reacting, turbulent mixing layer

The mechanisms by which heat release affects the fluid dynamics in a turbulent reacting mixing layer are studied by direct numerical simulation. In agreement with previous laboratory experiments, the heat release is observed to lower the rate at which the mixing layer grows and to reduce the rate at which chemical products are formed. The baroclinic torque and thermal expansion in the mixing layer are shown to produce changes in the flame vortex structure that act to produce more diffuse vortices than in the constant density case, resulting in lower rotation rates of fluid elements. Previously unexplained anomalies observed in the mean velocity profiles of reacting jets and mixing layers are shown to result from vorticity generation by baroclinic torques. The density reductions also lower the generation rates of turbulent kinetic energy and the turbulent shear stresses, resulting in less turbulent mixing of fluid elements. Calculations of the energy in the various wave numbers show that the heat release has a stabilizing effect on the growth rates of individual modes. A linear stability analysis of a simlified model problem confirms this, showing that low density fluid in the mixing region will result in a shift of the frequency of the unstable modes to lower wave numbers (longer wavelengths). The growth rates of the unstable modes decrease, contributing to the slower growth of the mixing layer.

Riley, J. J.↗

DOE OSTI2021

An LES study of secondary motion and wall shear stresses in a pipe bend

In this study, large-eddy simulations (LES) of a single-phase, turbulent flow in a 90 ° pipe bend are performed at three Reynolds numbers (5300, 27 000, and 45 000) to investigate the correlation between secondary flow motion and wall shear stresses, which is suspected to be a potential mechanism responsible for material erosion. The isothermal flows are validated against available experimental and numerical data first. The snapshot proper orthogonal decomposition (POD) is applied for the medium and high Reynolds number flows to identify the secondary flow motions and the oscillation of the Dean vortices that are found to cause swirl-switching. Distinguished frequencies of the POD time coefficients at Strouhal numbers of 0.25 and 0.28 are identified for Reynolds numbers at 27 000 and 45 000, respectively. Moreover, shear stress on the pipe wall and the associated power spectral density are obtained and shown to have the same oscillating frequency as the swirl-switching.

42 ENGINEERING↗

NASA NTRS2003

Highly Inclined Jets in Cross Flow

Results from an experimental investigation of flow field generated by pitched and yawed jets discharging from a flat plate into a cross-flow are presented. The circular jet was pitched at alpha = 20deg and 45deg and yawed between Beta = 0deg and 90deg in increments of 15deg. The measurements were performed with two ×-wires providing all three components of velocity and turbulent stresses. These data were obtained at downstream locations of x = 3, 5, 10 and 20, where the distance x, normalized by the jet diameter, is measured from the center of the orifice. Data for all configurations were acquired at a momentum-flux ratio J = 8. Additionally, for selected angles and locations, surveys were conducted for J = 1.5, 4, and 20. As expected, the jet penetration is found to be higher at larger alpha. With increasing beta the jet spreads more. The rate of reduction of peak streamwise vorticity, ω max, with the downstream distance is significantly less at higher Beta but is found to be practically independent of alpha. Thus, at the farthest measurement station x = 20, ωxmax is about five times larger for Beta = 75deg compared to the levels at Beta = 0deg. Streamwise velocity within the jet-vortex structure is found to depend on the parameter J. At J = 1.5 and 4, 'wake-like' velocity profiles are observed. In comparison, a 'jet-like' overshoot is present at higher J. Distributions of turbulent stresses for various cases are documented. Peak normal stresses are found to occur within the core of the streamwise vortices. With yaw, at lower values of J, high turbulence is also observed in the boundary layer underneath the jet-vortex structure

Milanovic, I. M.↗

NASA NTRS1998

Turbulent Compressible Convection with Rotation: Mean Flows and Differential Rotation - 2

The effects of rotation on turbulent, compressible convection within stellar envelopes are studied through three-dimensional numerical simulations conducted within a local f-plane model. This work seeks to understand the types of differential rotation that can be established in convective envelopes of stars like the Sun, for which recent helioseismic observations suggest an angular velocity profile with depth and latitude at variance with many theoretical predictions. This paper analyzes the mechanisms that are responsible for the mean (horizontally averaged) zonal and meridional flows that are produced by convection influenced by Coriolis forces. The compressible convection is considered for a range of Rayleigh, Taylor, and Prandtl (and thus Rossby) numbers encompassing both laminar and turbulent flow conditions under weak and strong rotational constraints. When the nonlinearities are moderate, the effects of rotation on the resulting laminar cellular convection leads to distinctive tilts of the cell boundaries away from the vertical. These yield correlations between vertical and horizontal motions that generate Reynolds stresses that can drive mean flows, interpretable as differential rotation and meridional circulations. Under more vigorous forcing, the resulting turbulent convection involves complicated and contorted fluid particle trajectories, with few clear correlations between vertical and horizontal motions, punctuated by an evolving and intricate downflow network that can extend over much of the depth of the layer. Within such networks are some coherent structures of vortical downflow that tend to align with the rotation axis. These yield a novel turbulent alignment mechanism, distinct from the laminar tilting of cellular boundaries, that can provide the principal correlated motions and thus Reynolds stresses and subsequently mean flows. The emergence of such coherent structures that can persist amidst more random motions is a characteristic of turbulence with symmetries broken by rotation and stratification. Such structure is here found to play a crucial role in defining the mean zonal and meridional flows that coexist with the convection. Though they are subject to strong inertial oscillations, the strength and type of the mean flows are determined by a combination of the laminar tilting and the turbulent alignment mechanisms. Varying the parameters produces a wide range of mean motions. Among these, some turbulent solutions exhibit a mean zonal velocity profile that is nearly constant with depth, much as deduced by helioseismology at midlatitudes within the Sun. The solutions exhibit a definite handedness, with the direction of the persistent mean flows often prescribing a spiral with depth near the boundaries, also in accord with helioseismic deductions. The mean helicity has a profile that is positive in the upper portion of the domain and negative in the lower portion, a property bearing on magnetic dynamo processes that may be realized within such rotating layers of turbulent convection.

Brummell, Nicholas H.↗

NASA NTRS1988

Oscillations of drops in zero gravity with weak viscous effects

Nonlinear oscillations and other motions of large axially symmetric liquid drops in zero gravity are studied numerically by a boundary-integral method. The effect of small viscosity is included in the computations by retaining first-order viscous terms in the normal stress boundary condition. This is accomplished by making use of a partial solution of the boundary-layer equations which describe the weak vortical surface layer. Small viscosity is found to have a relatively large effect on resonant mode coupling phenomena.

Lundgren, T. S.↗

NASA NTRS1989

Three-dimensional structure of a plane mixing layer

An experimental study is reported which shows the spanwise structure of a plane mixing layer originating from laminar boundary layers. Quantitative measurements are obtained for the first time which show the origin and evolution of streamwise vortices within the mixing layer. After the first spanwise vortex rollup occurs, streamwise structures are triggered in clusters within the braid region of the mixing layer. Further downstream, they realign to form pairs of counterrotating vortices. The maximum vorticity diffuses rapidly with increasing downstream distance while the vortices grow, scaling with the mixing layer vorticity thickness. The presence of the streamwise vortices leads to significant spanwise distortions in the mean and turbulence properties of the mixing layer. A consistent peak in the secondary shear stress exists for each streamwise vortex.

Bell, James H.↗

NASA NTRS1994

A New K-epsilon Eddy Viscosity Model for High Reynolds Number Turbulent Flows: Model Development and Validation

A new k-epsilon eddy viscosity model, which consists of a new model dissipation rate equation and a new realizable eddy viscosity formulation, is proposed. The new model dissipation rate equation is based on the dynamic equation of the mean-square vorticity fluctuation at large turbulent Reynolds number. The new eddy viscosity formulation is based on the realizability constraints: the positivity of normal Reynolds stresses and Schwarz' inequality for turbulent shear stresses. We find that the present model with a set of unified model coefficients can perform well for a variety of flows. The flows that are examined include: (1) rotating homogeneous shear flows; (2) boundary-free shear flows including a mixing layer, planar and round jets; (3) a channel flow, and flat plate boundary layers with and without a pressure gradient; and (4) backward facing step separated flows. The model predictions are compared with available experimental data. The results from the standard k-epsilon eddy viscosity model are also included for comparison. It is shown that the present model is a significant improvement over the standard k-epsilon eddy viscosity model.

Shih, T.-H.↗

NASA NTRS1995

Effect of turbulence models on criticality conditions in swirling flows

The critical state of vortex cores downstream of vortex breakdown has been studied. Base vortical flows were computed using the Reynolds-averaged, axisymmetric Navier-Stokes equations. Standard K - epsilon, RNG and second-order Reynolds stress models were employed. Results indicate that the return to supercriticality is highly dependent on the turbulence model. The K - epsilon model predicted a rapid return of the vortex to supercritical conditions, the location of which showed little sensitivity to changes in the swirl ratio. The Reynolds stress model predicted that the vortex remains subcritical to the end of the domain for each of the swirl ratios employed, and provided results in qualitative agreement with experimental work. The RNG model produced intermediate results, with a downstream movement in the critical location with increasing swirl. Calculations for which area reductions were introduced at the exit in a subcritical flow were also performed using the Reynolds stress model. The structure of the resulting recirculation zone was altered significantly. However, when area reductions were employed within supercritical flows as predicted using the two-equation models, no significant influence on the recirculation zone was noted.

Gatski, Thomas B.↗

NASA NTRS2014

Flow Phenomena in the Very Near Wake of a Flat Plate with a Circular Trailing Edge

The very near wake of a flat plate with a circular trailing edge, exhibiting pronounced shedding of wake vortices, is investigated with data from a direct numerical simulation. The separating boundary layers are turbulent and statistically identical thus resulting in a wake that is symmetric in the mean. The focus here is on the instability of the detached shear layers, the evolution of rib-vortex induced localized regions of reverse flow that detach from the main body of reverse flow in the trailing edge region and convect downstream, and phaseaveraged velocity statistics in the very near wake. The detached shear layers are found to exhibit unstable behavior intermittently, including the development of shear layer vortices as in earlier cylinder flow investigations with laminar separating boundary layers. Only a small fraction of the separated turbulent boundary layers undergo this instability, and form the initial shed vortices. Pressure spectra within the shear layers show a broadband peak at a multiple of shedding frequency. Phase-averaged intensity and shear stress distributions of the randomly fluctuating component of velocity are compared with those obtained in the near wake. The distributions of the production terms in the transport equations for the turbulent stresses are also provided.

Turbulence↗

NASA NTRS1983

Embedded cavity drag in steady and unsteady flows

The numerical solution of the laminar boundary-layer flow over an embedded cavity is studied. The purpose is to examine the relevant drag characteristics of laminar cavity flow. The solution field is obtained in terms of velocity and vorticity variables, with the stream function and pressure derivable from the directly computed variables. An analysis and comparison is made among four square cavities, ranging in size from 0.25 to 1.00 boundary-layer thicknesses deep. The dominant flow features are examined in the vicinity of the cavity by means of the stream function and iso-vorticity contours. The dominant physics in the overall drag characteristics of the flow is examined by an analysis of the pressure and wall shear stress distributions in the cavity, and upstream and downstream of the cavity. Pressure forces and frictional forces in, and in the vicinity of, the cavity are determined. Stress relaxation distances, both upstream and downstream of the cavity, are calculated and analyzed. The flow dynamics of the boundary-layer flow over an embedded cavity is summarized. Finally, the relevance of the results to the control of flow separation in such flows is discussed.

Gatski, T. B.↗

NASA NTRS1984

Embedded cavity drag in steady and unsteady flows

The numerical solution of the laminar boundary-layer flow over an embedded cavity is studied. The purpose of the study is to examine the relevant drag characteristics of laminar cavity flow. The solution field is obtained in terms of velocity and vorticity variables, with the stream function and pressure derivable from the directly computed variables. An analysis and comparison is made among four square cavities, ranging in size from 0.25 to 1.00 boundary-layer thicknesses deep. The dominant flow features are examined in the vicinity of the cavity by means of the stream function and iso-vorticity contours. The dominant physics in the overall drag characteristics of the flow is examined by an analysis of the pressure and wall shear stress distributions in the cavity, and upstream and downstream of the cavity. Pressure forces and frictional forces in, and in the vicinity of, the cavity are determined. Stress relaxation distances, both upstream and downstream of the cavity, are calculated and analyzed. The flow dynamics of the boundary-layer flow over an embedded cavity is summarized. Finally, the relevance of the present results to the control of flow separation in such flows is discussed.

Gatski, T. B.↗

NASA NTRS1985

Evolution of a vortical structure associated with the bursting event in a channel flow

The temporal evolution of a horseshoe vortex structure in a channel is investigated by a numerical simulation. A spectral numerical method is employed to integrate the time-dependent, three-dimensional Navier-Stokes equations. The initial vortical structure is obtained by applying a conditional sampling technique to a data base generated from a direct simulation of a turbulent channel flow. The evolution of this vortical structure under the influence of the self-induced motion and the mean shear is presented. It is shown that the initial sheet-like vortical structure rolls up into a vortex tube as it is convected downstream. Turbulence structures associated with the vortex stretching are investigated. Production of vorticity stretching is high inside the vortex legs, although it is also substantial in the tip region and above the legs. High Reynolds shear stress is produced near the tip of the vortex.

Kim, J.↗

NASA NTRS1986

Navier-Stokes computations of lee-side flows over delta wings

Solutions to the Navier-Stokes equations for the flow over delta wings are computed with emphasis on the separated vortical flows developing on the lee side at high angles of attack. A recently developed implicit algorithm is used which employs upwind differencing for the pressure and convection terms and central differencing for the shear stress and heat transfer terms. Solutions to both the three-dimensional equations and the approximate conical flow equations are compared parametrically with an extensive experimental data base at supersonic speeds. The computations indicate that the conical flow approximation provides results in close agreement with the three-dimensional equations, even to angles of attack as high as 20 degrees. Good agreement with experimentally measured pressures and vapor screen photographs is obtained for the conditions investigated. The method predicts the classical pattern of vortical flow over a delta wing and transition to other flow patterns as the leading edge sweep angle and leading edge normal Mach number are varied.

Thomas, J. L.↗