Reynolds Stress Profiles Research Articles

Numerical Investigation of Wall-Cooling Effect on Aero-Optical Distortions for Hypersonic Boundary Layer

Compressible wall-modeled large-eddy simulations of Mach 8 turbulent boundary-layer flows over a flat plate were carried out for the conditions of the hypersonic wind tunnel at Sandia National Laboratories. The simulations provide new insight into the effect of wall cooling on the aero-optical path distortions for hypersonic turbulent boundary-layer flows. Four different wall-to-recovery temperature ratios, 0.3, 0.48, 0.71, and 0.89, are considered. Despite the much lower grid resolution, the mean velocity, temperature, and resolved Reynolds stress profiles from the simulation for a temperature ratio of 0.48 are in good agreement with those from a reference direct numerical simulation. The normalized root-mean-square optical path difference obtained from the present simulations is compared with that from reference direct numerical simulations, Sandia experiments, as well as predictions obtained with a semi-analytical model by Notre Dame University. The present analysis focuses on the effect of wall cooling on the wall-normal density correlations, on key underlying assumptions of the aforementioned model such as the strong Reynolds analogy, and on the elevation angle effect on the optical path difference. Wall cooling is found to increase the velocity fluctuations and decrease the density fluctuations, resulting in an overall reduction of the normalized optical path distortion. Compared to the simulations, the basic strong Reynolds analogy overpredicts the temperature fluctuations for cooled walls. Also different from the strong Reynolds analogy, the velocity and temperature fluctuations are not perfectly anticorrelated. Finally, as the wall temperature is raised, the density correlation length, away from the wall but inside the boundary layer, increases significantly for beam paths tilted in the downstream direction.

Field inversion for transitional flows using continuous adjoint methods

Transition modeling represents one of the key challenges in computational fluid dynamics. While numerical efforts were traditionally devoted to either improving Reynolds-averaged Navier–Stokes-based turbulence modeling or developing scale-resolving simulations, cautious attention has been recently given to field inversion and machine learning techniques. This paper discusses an updated development of field inversion model for transitional flows based on k–ω shear stress transport model using the continuous adjoint approach, instead of the typical discrete adjoint method. The original model is modified by multiplying the production term of the turbulent kinetic energy equation by a spatially varying discrepancy function η(x). The adjoint equations and the relevant boundary conditions are specifically derived and integrated in OpenFOAM. The present model is validated using two zero pressure-gradient and four non-zero pressure-gradient from flow-over-flat-plate T3-series test cases. The gradient descent method is employed in the optimization process to minimize the discrepancy in the calculated shear stress. The inferred solution indicates a smooth transition to turbulence at the reported critical Reynolds numbers. The optimized model significantly improves the predictions of skin-friction coefficients, originally incorporated in the objective function. To demonstrate the usefulness of the present approach, the investigation is further extended to determine both velocity and shear Reynolds-stress profiles, which to our knowledge has not been reported before. Furthermore, a reduction in the percentage error from 50.2% to 7.3% is well observed in the predicted boundary layer thickness considering the laminar regime in the T3C5 test case.

The Wall-Jet Region of a Turbulent Jet Impinging on Smooth and Rough Plates

The study reports direct numerical simulations of a turbulent jet impinging onto smooth and rough surfaces at Reynolds number Re = 10,000 (based on the jet mean bulk velocity and diameter). Surface roughness is included in the simulations using an immersed boundary method. The deflection of the flow after jet impingement generates a radial wall-jet that develops parallel to the mean plate surface. The wall-jet is structured into an inner and an outer layer that, in the limit of infinite local Reynolds number, resemble a turbulent boundary layer and a free-shear flow. The investigation assesses the self-similar character of the mean radial velocity and Reynolds stresses profiles scaled by inner and outer layer units for varying size of the roughness topography. Namely the usual viscous units u_tau and delta _nu are used as inner layer scales, while the maximum radial velocity u_m and its wall-normal location z_m are used as outer layer scales. It is shown that the self-similarity of the mean radial velocity profiles scaled by outer layer units is marginally affected by the span of roughness topographies investigated, as outer layer velocity and length reference scales do not show a significantly modified behavior when surface roughness is considered. On the other hand, the mean radial velocity profiles scaled by inner layer units show a considerable scatter, as the roughness sub-layer determined by the considered roughness topographies extends up to the outer layer of the wall-jet. Nevertheless, the similar character of the velocity profiles appears to be conserved despite the profound impact of surface roughness.

Numerical Prediction of Turbulent Drag Reduction with Different Solid Fractions and Distribution Shapes over Superhydrophobic Surfaces

The exploration of superhydrophobic drag reduction has been and continues to be of significant interest to various industries. In the present work, direct numerical simulation (DNS) is utilized to investigate the effect of the parameters on the drag-reducing performance of superhydrophobic surfaces (SHS). Simulations with a friction Reynolds number of 180 were carried out at solid fraction values of ϕs=116,111, and 14, and three distribution shapes: aligned, staggered, and random. The top wall is the smooth one, and the bottom wall is a superhydrophobic surface (SHS). Drag reduction and Reynolds stress profiles are compared for all cases. The turbulent kinetic energy budget, including production, dissipation, and diffusion, is presented with respect to the solid fraction and type of distribution to investigate the drag reduction mechanism. The sizes of the longitudinal vortices and formation of hairpin vortices are investigated through the observation of coherent structures. The simulation of a post model is a useful method to study the drag reduction for different solid fraction values and distribution geometries. Our study demonstrates that the drag reduction could acquire 42% with the solid fraction value ϕs=116 and an aligned distribution shape for post superhydrophobic surface geometry. Our study also showed the relationship of the Reynolds stress component (R11, R22, and R33) to the drag reduction with the differences in the solid fraction values and distribution geometry. In which, the R11 component has the most change between an aligned distribution and a random one. The peak value of R11 tends to shift away from the SHS wall. In addition, the analysis of the TKE budget over the superhydrophobic surface was performed, which can be adopted as a useful resource in turbulence modeling based on RANS methodology.

Validation of a Large-Eddy Simulation Approach for Prediction of the Ground Roughness Influence on Wind Turbine Wakes

The ability of high-fidelity computational fluid mechanics simulation to quantitatively predict the influence of ground roughness on the evolution of the wake of a three-bladed horizontal axis wind turbine model is tested by comparison with wind tunnel measurements. The approach consists of the implicit approximate deconvolution large-eddy simulation formulation of Hickel et al., (2006), that is, for the first time, combined with a wall-stress model for flow over rough surfaces and with the actuator line approach (ALM) for modeling of the rotor. A recycling technique is used for the generation of turbulent inflow that matches shear exponents α=0.16 (medium roughness) and α=0.32 (high roughness) and turbulence level of the reference experiments at hub height. Satisfactory agreement of the spectral content in simulation and experiment is achieved for a grid resolution of 27 cells per rotor radius. Except for minor differences due to neglecting nacelle and tower in the simulation the LES reproduces the shapes of mean flow and Reynolds stress profiles in the wake. The deviations between measurement and simulation are more prominent in a vertical cut plane through the rotor center than in a horizontal cut plane. Simulation and experiment deviate with respect to the roughness influence on the development of the wake width; however, the relative change of the maximum wake deficit and of the vertical wake center position due to changes in ground roughness is reproduced very well.

Turbulent drag reduction of viscoelastic wormlike micellar gels

Long-chained, viscoelastic surfactant solutions (VES) have been widely employed in the oil and gas industry, particularly in hydraulic fracturing and gravel-packing operations, where turbulence is commonly reached due to high pumping rates. With this motivation, we experimentally investigate the turbulent duct flow of an under-studied class of wormlike micellar solutions that forms a gel at room temperature. The fluid is characterized via rotational rheometry, and the turbulent velocity and Reynolds stress profiles are measured via Laser Doppler Anemometry (LDA). Three surfactant concentrations are investigated at increasing Reynolds numbers. The turbulent flow fields of water, and semi-dilute solutions of partially hydrolysed polyacrylamide (HPAM) and xanthan gum (XG) are used as comparisons. Our study reveals that the gel-like structure of the wormlike micellar gel is mostly broken down during turbulent flow, especially in the near-wall region where the results indicate the presence of a water layer. Turbulent flow at low concentrations of surfactant show a Newtonian-like flow field throughout most of the duct, where the energy spectra shows a − 5 / 3 power law scale with wavenumber, whereas higher concentrations lead to drag reduction and lower power spectral densities at large wavenumbers. A comparison of the flow of polymeric fluids and the wormlike micellar solutions at maximum drag reduction (MDR) shows comparable drag-reduction effects, with a large decrease in Reynolds shear stresses, and increased turbulence anisotropy in the buffer layer due to the large streamwise fluctuations and near-zero wall-normal fluctuations. At the centreline of the duct, the power spectral densities of polymers and VES are significantly reduced at all wavenumbers probed. Additionally, the MDR regime was bounded by Virk’s asymptote for both polymers and the micellar gel, which implies a similar mechanism of drag reduction at MDR. • Turbulent flows of wormlike micellar gels (VES) are experimentally studied. • Turbulent flows of VES and polymeric liquids are quantified via LDA measurements. • Steady flow curves of VES are not representative of its rheology in turbulent flow. • At MDR, the VES and polymer solutions show decreased energy spectra. • Our results show similar drag reduction mechanisms between VES and polymers at MDR.

Three-Dimensional Simulation of Decaying Turbulent Swirling Flow Using Different Turbulence Models

This paper presents a numerical study of the turbulent swirling flow in a horizontal tangential inlet tube. The commercial CFD code ANSYS FLUENT 15 was used for solving the set of governing equations using different turbulence models. Eight turbulence models are tested which are, standard k–ε, realizable k–ε, RNG k–ε, SST k–ω, Non-Linear k–ε, v2-f, RSM (Quadratic Pressure-Strain Model), and RSM (Stress-Omega Model). All these turbulence models are available directly in the ANSYS FLUENT except the non-linear k–ε which was implemented in the solver using User Defined Functions (UDF). The numerical predictions are compared with experimental measurements from literature for tangential, axial velocity profiles and Reynolds stresses profiles within the tested tube. The results indicated that the axial velocity is predicted fairly well by the standard k–ε model while the tangential velocity is well predicted by RSM. On the other hand, v2-f model predicts the Reynolds stresses better than the other tested models. The statistical analysis of turbulence model performance showed that, the RSM (Quadratic Pressure-Strain) model gives the best agreement with all data of experiments followed by non-linear k–ε and standard k–ε turbulence models.

Numerical Study of Flow Structures Through Horizontal Double-Layered Vegetation Consisting of Combined Submergent and Emergent Vegetations

This study addresses the vivid internal flow structure variations through horizontal double-layered vegetation (HDLV) under subcritical flow conditions for an inland tsunami. The computational domain was built in ANSYS Workbench, while post-processing and simulation were performed using the computational fluid dynamics (CFD) tool FLUENT with the three-dimensional (3D) Reynolds stress model (RSM). Two alternative arrangements of HDLV were considered, namely Configuration 1 (short submergent layer [Formula: see text] emergent layer (Lt)) and Configuration 2 (tall emergent layer [Formula: see text] submergent layer (Ls)) along with varying flow depths. Strong inflections in velocity and Reynolds stress profiles were observed at the interface near the top of Ls, Whereas, these profiles were almost constant from bed to the top of vegetations inside Lt. A shear layer zone was formed above the top of Ls, which extended to the downstream region in Configuration 2 while it was restricted by Lt in Configuration 1. The normal Reynolds stresses at the bed were significantly greater within Ls in Configuration 2 than inside Lt in Configuration 1. Hence, Configuration 1 was performed relatively better than Configuration 2 in terms of reducing velocity within the vegetation, while Configuration 2 played a key role in attenuating the increased velocities and confining the shear layer above the short submergent layer.

EFFECT OF MOMENTUM PROVISION IN COMPUTATIONAL FLUID DYNAMICS ON TURBULENT STATISTICS IN URBAN BOUNDARY LAYER

To reproduce homogeneous flow fields above urban-like turbulent boundary layers in computational fluid dynamics (CFD), numerous CFDs with a limited numerical domain employ periodic boundary conditions in both lateral directions with artificial momentum provision to maintain airflows. Although such artificial momentum sources are clearly different from the momentum provision in wind-tunnel experiments, the effects of these numerical conditions on the airflow in the boundary layer are not well studied. In this paper, therefore, we investigate how the momentum provision differentiates the vertical Reynolds stress and turbulent kinetic energy profiles using large-eddy simulations of airflows over cubical block arrays.

Hydrodynamics of flow over a gradually varied bed roughness

Turbulence characteristics in a fully developed flow over a gradually varied bed roughness are investigated. The results of the Reynolds stress profiles indicate that they increase with an increase in bed roughness height. Their peaks occur within the wall-shear layer close to the bed. Besides, the bed shear stress rises in accordance with the roughness height. The roughness-induced layer grows as the roughness height increases with the streamwise distance. The velocity profiles fitted with the logarithmic law reveal that the zero-velocity level is elevated as the roughness height increases, but the zero-plane displacement is not influenced by the roughness. The turbulent kinetic energy (TKE) flux results indicate that an inrush of faster moving fluid parcels composing the sweep event is the dominant mechanism in the near-bed flow zone. The magnitude of the sweep event escalates, as the roughness height increases. On the other hand, a process of slowly moving fluid parcels forming the ejection event prevails in the outer flow layer. The TKE flux results agree with those obtained from the bursting analysis. Concerning the TKE budget, the peaks of the TKE production, dissipation, and pressure energy diffusion rates being positive appear near the bed and grow as the roughness height increases, whereas the peak of the TKE diffusion rate being negative behaves in the similar way as the other terms of the TKE budget behave.

Reynolds-Stress Model Computations of NASA Juncture Flow Experiment

Numerical simulations of the NASA Juncture Flow Experiment are carried out, employing a Reynolds-stress model. A transformation of the length-scale determining variable is suggested for improving the numerical robustness of the model. Results obtained with different unstructured flow solvers on different sets of grids show very good agreement, except for velocity and Reynolds-stress profiles in the vicinity of the predicted separation region. A recently developed length-scale correction and, particularly, prescribing transition on the fuselage and wing increase the predicted size of the separation region, where the variation is on the order of the experimental uncertainty. Detailed comparison of velocity and Reynolds-stress profiles with experimental data reveal a general deficiency of the model in predicting the peak of the streamwise normal stress and the distribution of all Reynolds stresses in the vicinity of the separation region. However, all predicted sizes of the separation region are in fair agreement with the experimental data.

Triple Hill’s Vortex Synthetic Eddy Method

The generation of initial or inflow synthetic turbulent velocity or scalar fields reproducing statistical characteristics of realistic turbulence is still a challenge. The synthetic eddy method, previously introduced in the context of inflow conditions for large eddy simulations, is based on the assumption that turbulence can be regarded as a superposition of coherent structures. In this paper, a new type of synthetic eddy method is proposed, where the fundamental eddy is constructed by superposing three Hill's vortices, with their axes orthogonal to each other. A distribution of Hill's vortices is used to synthesize an anisotropic turbulent velocity field that satisfies the incompressibility condition and match a given Reynolds stress tensor. The amplitudes of the three vortices that form the fundamental eddy are calculated from known Reynolds stress profiles through a transformation from the physical reference frame to the principal-axis reference frame. In this way, divergence-free anisotropic turbulent velocity fields are obtained that can reproduce a given Reynolds stress tensor. The model was tested on both isotropic and anisotropic turbulent velocity fields, in the framework of grid turbulence decay and turbulent channel flow, respectively. The transition from artificial to realistic turbulence in the proximity to the inflow boundary was found to be small in all test cases that were considered.

Passive separation control of shortfin mako shark skin in a turbulent boundary layer

This experimental investigation discusses the effectiveness of shortfin mako shark skin to passively control turbulent boundary layer separation. Experiments were conducted in a water tunnel facility with the shark skin specimens mounted on a smooth flat plate subjected to an adverse pressure gradient. The two skin specimens have shark scales with different sizes, shapes, and bristling angles. The flank region scales (B2) are slender, tall, and can bristle at 50°, while the scales in the region between flank and dorsal fin (B1) are wide, short, and can bristle at 30°. The adverse pressure gradient on the plate was generated by a rotating cylinder. DPIV measurements indicate that unpainted scales B2 can fully control or delay boundary layer separation and reduce the fraction of time the flow is reversed. The bristling of the scales caused fluctuation in the skin friction curve and the single spike intensity of the normal stress very close to the wall. These capabilities are directly related to the scale bristling angle. In contrast, the low bristling angle of the scales from region B1 did not impede the reversing flow, and therefore separation was enhanced. The increase in Reynold’s stress fluctuations away from the wall indicated that the separation region increased in size due to vortex structures further from the wall. Once the bristling mechanism of the B2 scales was eliminated by painting over the skin, the scales functioned as a rough surface but still promoted separation delay. In addition, the streamwise Reynolds stress profile for the flow over the painted scales measured after separation occurred, along with the high intensity of the normal stress near the surface are both characteristics of a flow over a rough surface. In summary, the shark skin surface showed an ability to both delay and increase flow separation depending on the capabilities of the scale bristling to inhibit reversing flow.

A direct comparison of turbulence in drag-reduced flows of polymers and surfactants

Abstract

Subtidal to Supertidal Variability of Reynolds Stresses in a Midlatitude Stratified Inner Shelf

AbstractWe describe the spatiotemporal variability and vertical structure of turbulent Reynolds stresses (RSs) in a stratified inner shelf with an energetic internal wave climate. The RSs are estimated from direct measurements of velocity variance derived from bottom-mounted acoustic Doppler current profilers. We link the RSs to different physical processes, namely, internal bores, midwater shear instabilities within vertical shear events related to wind-driven subtidal along-shelf currents, and nonturbulent stresses related to incoming nonlinear internal wave (NLIW) trains. The typical RS magnitudes are O(0.01) Pa for background conditions, with diurnal pulses of O(0.1–1) Pa, and O(1) Pa for the NLIW stresses. A NLIW train is observed to produce a depth-averaged vertical stress divergence sufficient to accelerate water 20 cm s−1 in 1 h, suggesting NLIWs may also be important contributors to the depth-averaged momentum budget. The subtidal stresses show significant periodic variability and are O(0.1) Pa. Conditionally averaged velocity and RS profiles for northward/southward flow provide evidence for downgradient turbulent momentum fluxes, but also indicate departures from this expected regime. Estimates of the terms in the depth-averaged momentum equation suggest that the vertical divergence of the RSs are important terms in both the cross-shelf and along-shelf directions, with geostrophy also present at leading-order in the cross-shelf momentum balance. Among other conclusions, the results highlight that internal bores and shoaling NLIWs may also be important dynamical players in other inner shelves with energetic internal waves.

Velocity Profile and Turbulence Structure Measurement Corrections for Sediment Transport-Induced Water-Worked Bed

When using point measurement for environmental or sediment laden flows, there is well-recognised risk for not having aligned measurements that causes misinterpretation of the measured velocity data. In reality, these kinds of mismeasurement mainly happen due to the misinterpretation of bed orientation caused by the complexity of its determination in natural flows, especially in bedload laden or rough bed flows. This study proposes a novel bed realignment method to improve the measured data benchmarking by three-dimensional (3D) bed profile orientation and implemented it into different sets of experimental data. More specifically, the effects of realignment on velocity profile and streamwise turbulence structure measurements were investigated. The proposed technique was tested against experimental data collected over a water-worked and an experimentally arranged well-packed beds. Different from the well-packed rough bed, the water-worked bed has been generated after long sediment transport and settling and hence can be used to verify the proposed bed-alignment technique thoroughly. During the flow analysis, the corrected velocity, turbulence intensity and Reynolds stress profiles were compared to the theoretical logarithmic law, exponential law and linear gravity (universal Reynolds stress distribution) profiles, respectively. It has been observed that the proposed method has improved the agreement of the measured velocity and turbulence structure data with their actual theoretical profiles, particularly in the near-bed region (where the ratio of the flow measurement vertical distance to the total water depth, z/h, is limited to ≤0.4).

Assessing and improving the accuracy of synthetic turbulence generation

Abstract

Characteristics of self-oscillating jets in a confined cavity

Jets emanating into a confined cavity exhibit self-oscillating behavior. This study is focused on evaluating characteristics of oscillating square and round jets. The jet exits from a submerged square or round nozzle of the same hydraulic diameter into a thin rectangular cavity at a Reynolds number of 54 000 based on the nozzle hydraulic diameter and average jet exit velocity. An investigation of the three-dimensional self-oscillatory flow structures is conducted using the unsteady Reynolds-averaged Navier–Stokes equations with the Reynolds stress turbulence model. Vortex identification using the λ2-criterion is used to investigate the flow dynamics. For the oscillating square jet, vortex rings initially have a square shape near the nozzle exit, before axis-switching and transforming into a circular ring. Upon impact on the walls, two tornado-like vortices are produced. The decay rate of oscillating square and round jets initially shows a trend traditionally noted in the corresponding free jets but changes significantly with distance from the nozzle as the effects of oscillation and confinement begin to dominate. Reynolds stress profiles for both types of jets are qualitatively similar and show two peaks on either side of the centerline, which convert to mild peaks farther downstream. Spread and decay rates of oscillating square jets are higher, while oscillating round jets have higher turbulence intensities near the jet center. Compared to free jets, more uniform Reynolds stresses at farther distances from the jet centerline in oscillating jets will enhance heat transfer over a larger area, making oscillating jets suitable in many cooling applications.

A numerical study of a rectangular jet along a shear free boundary: Surface jet

A numerical simulation of a rectangular surface jet is performed at a Reynolds number of Rej=4400. The global parameters of the jet e.g. maximum velocity decay, jet surface normal and lateral spread rates, entrainment, jet momentum flux and turbulent momentum flux are in agreement with several other studies reported in the literature. It is shown that the mean velocity and Reynolds stress profiles scale with the maximum local streamwise velocity and jet half width in the surface normal and lateral directions. The current simulation provides balance, explicitly calculated budgets for the turbulence kinetic energy, Reynolds normal and shear stresses. The surface jet develops a thin layer of fast moving fluid in the lateral direction near the surface. This layer is called the ‘surface current’. It has been suggested that the surface current arises due to the Reynolds stress anisotropy in the near surface region. The current study shows that this explanation is incomplete. The turbulence production for the Reynolds stress in the lateral direction is negative, which can drive the mean flow in the lateral direction. The higher level of negative production in the near surface region is responsible for the development of the surface current.

Mountain Waves Produced by a Stratified Shear Flow with a Boundary Layer. Part II: Form Drag, Wave Drag, and Transition from Downstream Sheltering to Upstream Blocking

AbstractThe nonhydrostatic version of the mountain flow theory presented in Part I is detailed. In the near-neutral case, the surface pressure decreases when the flow crosses the mountain to balance an increase in surface friction along the ground. This produces a form drag that can be predicted qualitatively. When stratification increases, internal waves start to control the dynamics and the drag is due to upward-propagating mountain waves as in Part I. The reflected waves nevertheless add complexity to the transition. First, when stability increases, upward-propagating waves and reflected waves interact destructively and low-drag states occur. When stability increases further, the interaction becomes constructive and high-drag states are reached. In very stable cases, the reflected waves do not affect the drag much. Although the drag gives a reasonable estimate of the Reynolds stress, its sign and vertical profile are profoundly affected by stability. In the near-neutral case, the Reynolds stress in the flow is positive, with a maximum around the top of the inner layer, decelerating the large-scale flow in the inner layer and accelerating it above. In the more stable cases, on the contrary, the large-scale flow above the inner layer is decelerated as expected for dissipated mountain waves. The structure of the flow around the mountain is also strongly affected by stability: it is characterized by nonseparated sheltering in the near-neutral cases, by upstream blocking in the very stable case, and at intermediate stability by the presence of a strong but isolated wave crest immediately downstream of the ridge.