Reynolds Normal Stresses Research Articles

A large eddy simulation study of cyclones: The effect of sub-models on efficiency and erosion prediction

In this study, first, the effect of different state-of-the-art dispersion and particle-wall collision models on the efficiency and erosion prediction are investigated. Second, the influence of particle size on the erosion pattern is explored. These assessments require reliable sub-model inputs, e.g. velocity statistics, which are provided through a large eddy simulation. The results reveal that a dispersion model for cyclone applications should account for the effect of anisotropic normal and shear Reynolds stresses and the “drift correction”. Furthermore, the erosion inside a cyclone can have four critical zones based on the particle size. It is also proven that the accurate prediction of erosion pattern necessitates the inclusion of the Saffman and Magnus lift forces on particles and realistic variable restitution coefficients in the particle-wall collision model. Finally, wall roughness increases the erosion rate of large particles through the combined impact of the “shadow effect” and energetic inner vortex on particles.

Characteristics of Flow Structure around Cylindrical Bridge Piers in Pressure-Flow Conditions

The emerging shift of extreme events, combined with an aging infrastructure and bridges, highlights the potential increase in the risk of damage and catastrophic failure of bridges with climate change. This article analyzes the behavior of the flow and turbulence features in proximity to bridge piers, at two different moments of the scour temporal evolution in free-surface and pressure-flow conditions. Bridge pressure-flow conditions occur when the water depth submerges a bridge deck during extreme events. A circular pier and two rectangular decks of different lengths were used for this research. All tests were carried out in clear water conditions at the sediment critical velocity. This paper studied first the rate of scour temporal evolution and scour morphologies. Second, velocity measurements were taken using a Nortek acoustic Velocimeter at 25 Hz sampling rate in both free-surface and pressure-flow conditions. The average three-dimensional flow velocities, turbulence intensities, Reynolds stress, and turbulent kinetic energy were studies for the cross section corresponding to the center of the pier. The results show that pressure flow conditions accelerate the scour rate. This rate approximately reaches twice the scour in free-surface conditions with a vertical contraction of about 17%. Flow and turbulence measurements clearly exhibit how, under pressure-flow conditions, the additional turbulence and accelerated velocity modifies the flow pattern and circulation, accelerating the scour evolution around the bridge base. While numerous studies exist for pier scour and turbulence in free-surface conditions, pressure flow conditions received limited attention in the past. These results provide essential information for understanding scour mechanisms and for facilitating the design of future structures to increase bridge safety and resilience.

A new turbulence analysis method based on the mean speed and mean free path theory of the molecule thermal motion—correction and Improvement

Based on the mean speed and mean free path theory of the molecule thermal motion, a mathematical formulation of the Reynolds stress by reasonable analysis and derivation has been obtained and the result have been published in the Journal of Physics A. In follow-up studies, certain flaws were detected in the mathematical derivation presented in my previous paper and therefore the final mathematical expressions of the Reynolds shear stress achieved are not very accurate. In this paper, these flaws have been fixed and a new form of mathematical expression of Reynolds shear stress has been proposed. In addition, the mathematical expression of the Reynolds normal stress was also derived.

On coherent structures in gas–solid fluidization

In this work, experimental data from the novel high speed particle image velocimetry (HSPIV) measurements and pressure fluctuations complemented by numerical predictions from TFM simulations are processed using advanced signal processing protocols to identify and characterize coherent structures in a gas–solid fluidized bed with Geldart D particles. The time-frequency properties of the bed dynamics were studied using the wavelet coherent analysis (WCA) and the Hilbert Huang transform. The WCA of numerical pressure drop signals at different measurement positions showed the existence of spatial-temporal coherent structures. At close measurement positions phase locked coherent phenomenon due to bubble generation dominate most of the frequency and time scales due the proximity to the distributor. At a wider measurement spacing the fast traveling waves are attenuated due to gas bubble/void coalescence and acceleration and only pockets of highly coherent oscillations are visible mostly in the frequency range of 0.5–3Hz at certain times. Multi-resolution of the particle fluctuations realized with the Hilbert–Huang transform. The structures were resolved into the micro, meso and macro scales of fluidization based on the energy and frequency distributions. The meso scale structures form the main contribution to the normal axial Reynolds stresses and bubble granular temperature and ultimately the mixing.

Three-Dimensional Experimental Study of Compressibility Effects on Turbulent Free Shear Layers

Turbulent planar mixing layers of varying compressibility levels have been studied experimentally via flow visualization techniques, pressure measurements, and stereoscopic particle image velocimetry. The experiments were conducted for five different convective Mach numbers (, 0.38, 0.55, 0.69, and 0.88). For each case, inflow conditions were thoroughly documented with planar particle image velocimetry. Results indicate that the incoming boundary layers are thin (less than or equal to 9% of channel height) and fully developed. Schlieren and Mie scattering images show that for increased levels of compressibility the large-scale turbulent structures are less organized, and the Brown–Roshko rollers that are dominant in the incompressible case are not found. Three-component velocity measurements made on the spanwise-central plane () via stereo particle image velocimetry confirm the reduction in the normalized growth rate with increasing that has been agreed upon widely. Turbulence statistics results show that the peak (normalized) streamwise normal kinematic Reynolds stress remains constant, while the spanwise normal, transverse normal, and primary shear kinematic Reynolds stress peak values all decrease with increasing . In addition, knowledge of all three normal stress components allows for the calculation of the full Reynolds stress anisotropy tensor, a novel result for compressible mixing layer experiments. Each anisotropy component remains constant across the shear layer center. As compressibility in the mixing layer increases, the streamwise normal stress anisotropy increases, transverse and spanwise normal stress anisotropies decrease, and the shear stress anisotropy remains constant. Conversely, the Reynolds stress correlation coefficient remains constant across all cases at approximately 0.47.

On the large- and small-scale motions in a separated, turbulent-boundary-layer flow

ABSTRACTAdverse-pressure-gradient turbulent boundary layer flow was inspected at Reynolds number based on momentum thickness, , using particle image velocimetry in a refractive-index-matching flume. Proper orthogonal decomposition was used to quantify the effect of large-scale motions on the Reynolds stresses at the onset of separation and within the separated flow. Results show that approximately of the Reynolds shear stress, , is due to large-scale motions containing of the turbulence kinetic energy at the tested Reynolds number. The decomposed velocity field revealed that only the first of the modes is sufficient to recover of the turbulence kinetic energy. In this partition, the large-scale motion contribution to the streamwise component of the Reynolds normal stress, , is about and continues to grow with flow separation. In addition, the large- and small-scale motions equally contributed to the vertical component of the Reynolds normal stress, , and the contribution of the large-scale motions increased as the flow separated. Overall, results emphasise the significant impact of the large-scale motions on the Reynolds stresses in the separated flow, which may impact flow control strategies.

Large eddy simulation on the turbulent flow and mixing in a 2 × 2 rod bundle

The turbulent flow and interchannel mixing in rod bundles is a concerned issue in the thermal-hydraulic design of fuel assemblies. In this paper, a large eddy simulation was performed to study the turbulent flow of water in a 2 × 2 rod bundle. The diameter of each rod and the pitch-to-diameter ratio were set to 20 mm and 1.25, respectively. The grid resolutions were carefully studied by examining the two-point correlation of velocity components along the streamwise direction, and by comparing the power spectral density with Kolmogorov’s −5/3 law. The numerical results showed that the root-mean-square (RMS) velocity is highly anisotropic in the gap area. The secondary flow on the cross-section of the rod bundle was nonuniform, and the intensity is strong close to the wall where small eddies were generated. The distributions of Reynolds normal and shear stresses and the budget of primary normal stress were presented.

Mathematical Modeling of Evolution of Swirling Turbulent Jet in Coflowing Stream

A numerical modeling of a swirling turbulent jet in a coflowing stream was carried out. The flow description involved two second-order mathematical models. The first one includes the averaged equations of motion and the differential equations for transfer of normal Reynolds stresses and dissipation rate in the thin shear layer approximation. The second model relies on the far wake approximation. The distances from the source of the jet in the calculations reached very large values. At small distances, the calculated profiles of the averaged velocity components agree well with the known experimental data from Lavrent’ev Institute of Hydrodynamics SB RAS. At large distances from the source, the flow becomes close to the self-similar one, with degeneration laws and normalized profiles consistent with the known theoretical concepts of the dynamics of swirling turbulent jets in a coflowing stream. The problem of asymptotic behavior of a nonswirling turbulent jet in a coflowing stream was also considered. A self-similar solution based on numerical experiments was obtained.

A comparative study of the velocity and vorticity structure in pipes and boundary layers at friction Reynolds numbers up to

This study presents findings from a first-of-its-kind measurement campaign that includes simultaneous measurements of the full velocity and vorticity vectors in both pipe and boundary layer flows under matched spatial resolution and Reynolds number conditions. Comparison of canonical turbulent flows offers insight into the role(s) played by features that are unique to one or the other. Pipe and zero pressure gradient boundary layer flows are often compared with the goal of elucidating the roles of geometry and a free boundary condition on turbulent wall flows. Prior experimental efforts towards this end have focused primarily on the streamwise component of velocity, while direct numerical simulations are at relatively low Reynolds numbers. In contrast, this study presents experimental measurements of all three components of both velocity and vorticity for friction Reynolds numbers$Re_{\unicode[STIX]{x1D70F}}$ranging from 5000 to 10 000. Differences in the two transverse Reynolds normal stresses are shown to exist throughout the log layer and wake layer at Reynolds numbers that exceed those of existing numerical data sets. The turbulence enstrophy profiles are also shown to exhibit differences spanning from the outer edge of the log layer to the outer flow boundary. Skewness and kurtosis profiles of the velocity and vorticity components imply the existence of a ‘quiescent core’ in pipe flow, as described by Kwonet al. (J. Fluid Mech., vol. 751, 2014, pp. 228–254) for channel flow at lower$Re_{\unicode[STIX]{x1D70F}}$, and characterize the extent of its influence in the pipe. Observed differences between statistical profiles of velocity and vorticity are then discussed in the context of a structural difference between free-stream intermittency in the boundary layer and ‘quiescent core’ intermittency in the pipe that is detectable to wall distances as small as 5 % of the layer thickness.

Assessment of Turbulence Models in a Hypersonic Cold-Wall Turbulent Boundary Layer

In this study, the ability of standard one- or two-equation turbulence models to predict mean and turbulence profiles, the Reynolds stress, and the turbulent heat flux in hypersonic cold-wall boundary-layer applications is investigated. The turbulence models under investigation include the one-equation model of Spalart–Allmaras, the baseline k - ω model by Menter, as well as the shear-stress transport k - ω model by Menter. Reynolds-Averaged Navier-Stokes (RANS) simulations with the different turbulence models are conducted for a flat-plate, zero-pressure-gradient turbulent boundary layer with a nominal free-stream Mach number of 8 and wall-to-recovery temperature ratio of 0.48 , and the RANS results are compared with those of direct numerical simulations (DNS) under similar conditions. The study shows that the selected eddy-viscosity turbulence models, in combination with a constant Prandtl number model for turbulent heat flux, give good predictions of the skin friction, wall heat flux, and boundary-layer mean profiles. The Boussinesq assumption leads to essentially correct predictions of the Reynolds shear stress, but gives wrong predictions of the Reynolds normal stresses. The constant Prandtl number model gives an adequate prediction of the normal turbulent heat flux, while it fails to predict transverse turbulent heat fluxes. The discrepancy in model predictions among the three eddy-viscosity models under investigation is small.

Flow Characteristics of Curved Rotor Stator Systems Using Large Eddy Simulation

In this paper, the new idea of application of a curved rotor disk in rotor stator systems is presented and analyzed by using the large eddy simulation technique. The geometry of the examined rotor-stator system consists of a stationary flat disk (stator), a rotating curved disk (rotor) and a stationary enclosing cylinder (shroud). A hole in the center of stator allows the flow to enter the cavity, and the clearance between the shroud and rotor enables the flow to exit the cavity. Employing elliptical bumps with different geometrical parameters on the rotor disk (creating a curvature on the rotor), the rotating curved disk is parametrized. Three cavity cases (one with a flat rotor disk, another with the maximum outflow total pressure, and the third with the highest mass flow rate) are selected for LES analysis and more detailed investigation of flow and turbulence structures. The Favre-filtered governing equations for LES analysis of compressible turbulent flows are solved for all three cases. Radial and circumferential flow velocities as well as shear and normal Reynolds stresses in different cavity regions are studied. The flow in a rotor-stator cavity is simultaneously affected by the inlet flow, rotor rotation, and the bump on rotor disk. Creating a bump on rotor disk causes increase of both the radial pressure gradient and the mass flow rate of fluid that enters the rotor-stator cavity.

Turbulence kinetic energy budget and conditional sampling of momentum, scalar, and intermittency fluxes in thermally stratified wind farms

ABSTRACTA description of the turbulence kinetic energy budget is investigated to understand the dynamics and turbulence energy transfer between the atmospheric boundary layer and large wind farms. The turbulence kinetic energy budget terms are a dominant factor in explaining the energy supply process in wind farms. Large eddy simulations are used to generate the thermally stratified wind turbine array boundary layer, where stable and unstable conditions are considered. The wakes represent a sink of mean kinetic energy, and turbulence transport redistributes energy in the wake region. The energy balance between the budget terms is dependent on the physical location in the wind farm. During the unstable scenario, turbulence is driven by the production, transport, and buoyancy terms. Further, the contribution of the turbulence kinetic energy budget terms is reduced with increasing atmospheric stability, especially above the shear layer, where the mechanical production is the dominant term. Pressure diffusion redistributes the turbulent energy from the streamwise direction into the other components of the normal Reynolds stresses. This distinctive feature of the changing thermal stratification is presented through the quadrant analysis. The momentum ejection and sweep frequencies are both comparable and dominant. The scalar flux shows an increase in the contribution of the negative correlation in the quadrants. The quadrant analysis is extended to account for intermittency based on the pointwise Hölder exponents. Positive correlations are dominant in the wake and in higher layers of the domain for both considered cases.

POD Analysis of Entropy Generation in a Laminar Separation Boundary Layer

Separation of laminar boundary layer is a great source of loss in energy and power machinery. This paper investigates the entropy generation of the boundary layer on the flat plate with pressure gradient. The velocity of the flow field is measured by a high resolution and time related particle image velocimetry (PIV) system. A method to estimate the entropy generation of each mode extracted by proper orthogonal decomposition (POD) is introduced. The entropy generation of each POD mode caused by mean viscous, Reynolds normal stress, Reynolds sheer stress, and energy flux is analyzed. The first order mode of the mean viscous term contributes almost 100% of the total entropy generation. The first three order modes of the Reynolds sheer stress term contribute less than 10% of the total entropy generation in the fore part of the separation bubble, while it reaches to more than 95% in the rear part of the separation bubble. It indicates that the more unsteady that the flow is, the higher contribution rate of the Reynolds sheer stress term makes. The energy flux term plays an important role in the turbulent kinetic energy balance in the transition region.

Decelerating bores in channels and estuaries

ABSTRACT Decelerating bores are commonly seen in shorelines, estuaries and rivers in forms of swash run-up, tidal bores, tsunami bores. A decelerating bore propagating upstream can gradually change its shape, finally becoming an arrested bore, i.e. a stationary hydraulic jump. New experiments on decelerating bores against an adverse slope were conducted. Observations highlighted various types of arrested bores: fully breaking jumps, partially breaking jumps and non-breaking undular jumps. Measurements were repeated at least 25 times to obtain ensemble-averaged data with regards to instantaneous median and fluctuations of free-surface elevation, velocity components and turbulent shear stresses. An abrupt rise of free-surface elevation and immediate decrease in stream-wise velocity were observed during the passage of a decelerating bore. The arrival of decelerating bores induced some drastic increase of instantaneous free-surface fluctuations and all velocity components. Large-amplitude Reynolds stresses and extreme Reynolds stress fluctuations occurred in the same phase during and after the passage of decelerating bores. Histogram analysis of instantaneous normal and tangential Reynolds stresses suggested a preponderance of relatively smaller amplitudes. The upstream propagation of decelerating bores increased the probability density of large normal and tangential Reynolds stresses, yielding extrema vastly exceeding the critical threshold for inception of sediment motion.

Direct numerical simulation of a wall jet: flow physics

A direct numerical simulation (DNS) of a plane wall jet is performed at a Reynolds number of$Re_{j}=7500$. The streamwise length of the domain is long enough to achieve self-similarity for the mean flow and the Reynolds shear stress. This is the highest Reynolds number wall jet DNS for a large domain achieved to date. The high resolution simulation reveals the unsteady flow field in great detail and shows the transition process in the outer shear layer and inner boundary layer. Mean flow parameters of maximum velocity decay, wall shear stress, friction coefficient and jet spreading rate are consistent with several other studies reported in the literature. Mean flow, Reynolds normal and shear stress profiles are presented with various scalings, revealing the self-similar behaviour of the wall jet. The Reynolds normal stresses do not show complete similarity for the given Reynolds number and domain length. Previously published inner layer budgets based on LES are inaccurate and those that have been measured are only available in the outer layer. The current DNS provides fully balanced, explicitly calculated budgets for the turbulence kinetic energy, Reynolds normal stresses and Reynolds shear stress in both the inner and outer layers. The budgets are scaled with inner and outer variables. The inner-scaled budgets in the near wall region show great similarity with turbulent boundary layers. The only remarkable difference is for the turbulent diffusion in the wall-normal Reynolds stress and Reynolds shear stress budgets. The outer layer interacts with the inner layer through turbulent diffusion and the excess energy from the wall-normal direction is transferred to the spanwise direction.

Hydrodynamics of water-worked and screeded gravel beds: A comparative study

The turbulence characteristics within flows over water-worked gravel beds (WGBs) and screeded gravel beds (SGBs) were examined by measuring the instantaneous flow velocity field using a two-dimensional particle image velocimetry system. To compare the responses of a WGB and an SGB to velocity and various turbulence characteristics, the flow Froude number was kept identical for both the beds that remained immobile. The roughness structures of both the beds were measured using a laser scanner. The results showed that the bed surface roughness was higher in the WGB than in the SGB. However, the longest axis of the gravels of WGBs was oriented streamwise owing to the action of water work, but the gravels of SGBs were randomly poised. The distribution of bed roughness fluctuations was negatively skewed in the WGB and positively skewed in the SGB. Double averaging methodology was applied to analyze the flow parameters. In this paper, the vertical profiles of the double-averaged streamwise velocity and the turbulence parameters, specifically the spatially averaged (SA) Reynolds shear and normal stresses, form-induced shear and normal stresses, turbulent kinetic energy (TKE) and form-induced TKE fluxes, quadrant analysis of SA Reynolds shear stress, etc., are presented and analyzed critically by focusing on comparisons between a WGB and an SGB. A comparative study reveals that in the near-bed flow zone, the SGB underestimates the turbulence parameters compared to the WGB. Therefore, in order to represent the prototypical flow in laboratory, the experiments should be performed in a WGB.

Direct numerical simulations of temporally decelerating turbulent pipe flows

Direct numerical simulations of temporally decelerating turbulent pipe flows are performed to examine the effects of temporal deceleration on the turbulence characteristics. The temporal decelerations are applied with three different values of the decelerating parameter f = |dUb/dt| based on the bulk mean velocity (Ub) to introduce weak, mild and strong decelerations, and the flow rates for all cases are linearly decreased with time. In order to highlight the variation of the turbulent statistics for an unsteady flow, five independent simulations of steady flows are conducted along with the Reynolds number. An inspection of the mean velocity profiles shows that the log law in the overlap region is established with a slight downward shift for the weakly decelerating flow, whereas this is not the case for the strong decelerating flow. A comparison of the Reynolds stress profiles between the unsteady and steady flows displays that the turbulence is highly intensified with an increase of f due to the enhanced vortical structures and that the radial propagation of the turbulence is delayed. An analysis of the turbulent production term of the Reynolds stress budget equation shows that frozen of the strong second-quadrant Reynolds shear stress event plays an important role in delaying the response of the turbulent energy with a decrease of the Reynolds number, leading to an increase in the Reynolds stress. In addition, spectral decomposition of the streamwise Reynolds normal stress into small- and large-scale components reveals that the enhanced turbulence throughout the entire flow for unsteady flows is a direct consequence of the delay of strong large-scale structures, although small-scale structures throughout the wall layer adjust rapidly to temporal deceleration.

Magnetic configuration effects on the Reynolds stress in the plasma edge

Breaking the poloidal symmetry of the magnetic shear induced tilt of turbulent structures, by either divertor X-point resistivity or limiter positions, can lead to a finite (residual) contribution to the flux-surface averaged radial-binormal Reynolds stress. This residual stress supports or works against the radial electric field at the plasma edge of a tokamak. The impact of divertor geometry on the poloidal pattern of the Reynolds stress is studied by flux-coordinate-independent fluid simulations. Clear modifications of the Reynolds stress are found due to the magnetic shear in the confined region. The impact of different poloidal limiter positions on the radial electric field and the Reynolds stress is studied by means of magnetic field aligned gyrofluid simulations. Only if the limiter is close to the outer midplane can its position have a substantial effect on the radial electric field.

Large eddy simulation of boundary layer transition flow around NACA0009 blunt trailing edge hydrofoil at high Reynolds number

The process of boundary layer transition is needed to be taken into account for better understanding of the flow around a hydrofoil. Based on the WALE model, this paper presents a large eddy simulation of the flow around NACA0009 blunt trailing edge hydrofoil to investigate the characteristics of the boundary layer transition at high Reynolds number. The accuracy of the WALE model in predicting the transition process is validated by comparing the calculated boundary layer velocity profiles, thicknesses and shape factors with experimental data. Moreover, the spatial development laws of velocity fluctuation in the transitional boundary layer are revealed by analyzing the profiles of resolved normal and shear Reynolds stress in both streamwise and transverse directions

Dynamics of a Swirling Turbulent Wake past a Sphere

Using a mathematical model, which includes the averaged motion equations, differential transport equations of normal Reynolds stresses and dissipation rate, we carried out numerical modeling of evolution of a swirling turbulent wake with nonzero total excess momentum and angular momentum. The calculations were done to very large distances from the body. For small distances from the body the calculated profiles of averaged motion velocities and intensities of turbulent fluctuations of the longitudinal velocity component are in good agreement with the known experimental data of the Lavrent’ev Institute of Hydrodynamics, SB RAS. A simplified model of the flow is constructed.