Turbulent Kinetic Energy Transport Research Articles

Outlier detection for PIV statistics based on turbulence transport

The occurrence of data outliers in PIV measurements remains nowadays a problematic issue; their effective detection is relevant to the reliability of PIV experiments. This study proposes a novel approach to outliers detection from time-averaged three-dimensional PIV data. The principle is based on the agreement of the measured data to the turbulent kinetic energy (TKE) transport equation. The ratio between the local advection and production terms of the TKE along the streamline determines the admissibility of the inquired datapoint. Planar and 3D PIV experimental datasets are used to demonstrate that in the presence of outliers, the turbulent transport (TT) criterion yields a large separation between correct and erroneous vectors. The comparison between the TT criterion and the state-of-the-art universal outlier detection from Westerweel and Scarano (Exp Fluids 39:1096–1100, 2005) shows that the proposed criterion yields a larger percentage of detected outliers along with a lower fraction of false positives for a wider range of possible values chosen for the threshold.Graphical abstract

Study of unsteady cavitating flow around Clark-Y hydrofoil using nonlinear PANS model with near-wall correction

In this paper, we describe the use of a new nonlinear partially-averaged Navier–Stokes (PANS) model with near-wall correction for simulating the cavitating flow around a Clark-Y hydrofoil. For comparison, the standard [Formula: see text]–[Formula: see text] PANS model is also used. The results demonstrate that compared to [Formula: see text]–[Formula: see text] PANS and experiment, the new PANS model shows better performance for cavitation flow, including time-averaged velocity, root mean square (rms) velocity and cavity shedding processing. Through the calculation of the lift and drag coefficient at [Formula: see text] and [Formula: see text], it can be concluded that the cavitation will decrease the lift and increase the drag of the hydrofoil, resulting in a decrease of the lift-to-drag ratio. From the analysis of different terms in both the turbulent kinetic energy (TKE) and dissipation rate transport equations of the cloud cavitation, it is found that the production term and the dissipation term are dominant in the turbulent transport, and they are mainly distributed in the vapor–liquid interface and the trailing edge of the hydrofoil.

3D numerical investigation of trans-critical heat transfer enhancement in regeneration cooling channel with crescent rib

In this study, a numerical simulation of the trans-critical flow and heat transfer performance of n-decane in a regenerative cooling microrib structure channel is conducted. The shear stress transfer k-ω numerical model is used to compare the heat transfer enhancement mechanism between straight and crescent ribs to improve heat transfer deterioration in a smooth channel. Within the specific dimensions and operative conditions of the test case, the results demonstrate that the average temperature in a channel with crescent ribs was 70 K less than one with rectangular ribs, and the average Nusselt number in a channel with crescent ribs was 50 greater than one with rectangular ribs. When compared with the rectangular rib channel, the thermal performance in the crescent rib channel increased by 59.1%–66.4%, and the overall heat transfer performance increased by 18.3%–25.9%. Saw-tooth distribution was observed along the rib channel, breaking the thermal boundary layer and avoiding heat transfer deterioration. Two spanwise vortices produced by the crescent ribs enhanced the flow mixing and turbulence kinetic energy transport near the sidewall region, which is a significant reason for the superior thermal performance of the crescent rib channel.

Modeling the interstitial fluid effect in turbulent disperse slurry flow in a vertical pipe

A numerical study was conducted to assess the performance of a Two-Fluid Model (TFM) developed for gas-solid flow in predicting liquid-solid flow, as well as a TFM specifically modified for liquid-solid flow, which considers the effect of the interstitial fluid. Both cases use the Kinetic Theory of Granular Flow (KTGF) for prediction of the solid phase flow features. Some of the physics involved in gas-solid and liquid-solid flows is intuitively different, and some model terms that can be neglected in a gas-solid formulation turn out to be important for liquid-solid flow. For instance, the much larger density and viscosity of the liquid compared to a gas suggest that the solid particle fluctuations and collisions are reduced. Three intermediate model formulations were developed to assess the relevance of the interstitial terms. The intermediate model formulations, together with the two base case models, were assessed based on their predictions for the case of fully developed, turbulent, steady flow of a liquid solid mixture in a vertical pipe. The main differences in the model formulations pertain to the transport equations for the streamwise liquid momentum, granular temperature and turbulence kinetic energy. The predictions considered such flow features as: the velocity profiles of both the liquid and solid phases, the solids volume fraction profile and budgets of the transport equations for the granular temperature and turbulence kinetic energy. The results obtained were used to identify the most significant model terms. These include modified formulations for the solids viscosity and granular temperature conductive coefficient to include the effects of the interstitial fluid. The single most important term was the model for the long-range particle fluctuations through the fluid, which played a dominant role in the balance of the turbulence kinetic energy and granular temperature transport equations. The present analysis demonstrates that this term should be reconfigured as a sink term in the granular temperature equation and a source term in the turbulence kinetic energy equation. With this modification, the numerical predictions were much closer to the experimental data, especially in terms of the solids volume fraction profile.

Coherent Velocity Structures in the Mixed Layer: Characteristics, Energetics, and Turbulent Kinetic Energy Budget

AbstractVelocity, hydrographic, and microstructure observations collected under moderate to high winds, large surface waves, and significant ocean-surface heat losses were utilized to examine coherent velocity structures (CVS) and turbulent kinetic energy (TKE) budget in the mixed layer on the outer shelf in the northern Gulf of Mexico in February 2017. The CVS exhibited larger downward velocities in downwelling regions and weaker upward velocities in broader upwelling regions, elevated vertical velocity variance, vertical velocity maxima in the upper part of the mixed layer, and phasing of crosswind velocities relative to vertical velocities near the base of the mixed layer. Temporal scales ranged from 10 to 40 min, and estimated lateral scales ranged from 90 to 430 m, which were 1.5–6 times as large as the mixed layer depth. Nondimensional parameters, Langmuir and Hoenikker numbers, indicated that plausible forcing mechanisms were surface-wave-driven Langmuir vortex and destabilizing surface buoyancy flux. The rate of change of TKE, shear production, Stokes production, buoyancy production, vertical transport of TKE, and dissipation in the TKE budget were evaluated. The shear and Stokes productions, dissipation, and vertical transport of TKE were the dominant terms. The buoyancy production term was important at the sea surface, but it decreased rapidly in the interior. A large imbalance term was found under the unstable, high-wind, and high–sea state conditions. The cause of this imbalance cannot be determined with certainty through analyses of the available observations; however, our speculation is that the pressure transport is significant under these conditions.

Turbulence Properties of a Deep‐Sea Hydrothermal Plume in a Time‐Variable Cross‐Flow: Field and Model Comparisons for Dante in the Main Endeavour Field

AbstractA large eddy simulation is used to study a high temperature hydrothermal vent plume in a stratified and tidally modulated crossflow, in order to identify its turbulence and mixing characteristics. The model parameters and source conditions that are comparable to the vertical velocity and refractive index fluctuations measured 20 m above the Dante sulfide mound in the Main Endeavour vent Field are a heat transport of 50 MW over a cross‐sectional area of 4 × 4.5 m2. With these model source conditions and output results taken at 20 m above the source with 1 Hz sampling, the shear production of turbulent kinetic energy (TKE), the vertical transport of TKE, and the buoyancy production/dissipation are quantified showing that shear production dominates. Similarly, thermal variance production, and its vertical transport, is also quantified showing that the advective term dominates. Because of enhanced entrainment of ambient water into the plume during strong crossflows, all mean and turbulent quantities show tidally modulated values. Assuming steady state, the dissipation rates are evaluated. During strong crossflows, the tilting of the vertical velocity contours and isotherms plays a critical role in the stability of the plume and in creating high shear and thermal gradients on the upstream side of the plume center axis. These dissipation rates are used to quantify the refractive index fluctuations, and given the high thermal dissipation quantity it is the main contributing factor in acoustic forward scatter.

Inertial Effects and Anisotropy for the Flow in a Domain of Close Packed Spheres with a Bounding Wall

We present results for a direct numerical simulation study of isothermal incompressible flow in a regularly packed pebble-bed domain with a bounding wall. We focus specifically on the near-wall behavior of the flow. Our simulation is carried out at a Reynolds number of 9308 to facilitate cross verification with available high-fidelity data. To reduce the required time to achieve statistically stationary results, we implemented an ensemble-averaging scheme that allowed for multiple simulation runs to be carried out concurrently. The close packing of the spheres in the domain causes significant acceleration effects in the domain, which result in boundary layer detachment and reattachment. Presented results include selected first- and second-order turbulence statistics, as well as selected terms of the turbulent kinetic energy transport equation. The acceleration effects in the near-wall region of the domain cause negative production of turbulent kinetic energy. The presented data may be useful for benchmarking Reynolds-averaged Navier-Stokes–based simulations of pebble beds.

Physics-based universal outlier detector for flow statistics

Outlier detection for PIV velocity fields is still nowadays an active field of research. In the last decades, several image pre-processing and processing algorithms have been developed aiming at increasing the dynamic velocity range of PIV measurements and reducing the measurement uncertainty. Nevertheless, PIV velocity fields are still often characterised by the presence of outliers, which potentially hamper the correct interpretation of the flow physics and negatively affect the evaluation of the flow statistics. The outlier detection strategies presented in literature are mainly based on the statistical analysis of the velocity vector with its immediate neighbour. Most of these algorithms have been demonstrated to be effective for instantaneous flow fields, where the errors associated with the outliers are order of magnitude larger than the expected measurement uncertainty. However, these approaches are not as effective for the flow statistics, where the outliers yield errors of the same order of the measurement uncertainty. To overcome this limitation, this paper proposed an outlier detection approach based on the agreement of the flow statistics to the constitutive equations, more specifically to the turbulent kinetic energy (TKE) transport equation. The focus is posed on the ratio between the local advection terms of TKE and a robust estimation of the TKE production along the local streamline. It is demonstrated that, in presence of outliers, the proposed principle yields a clear separation between the correct and the erroneous vectors. In order to assess the performance of the proposed principle, three different test cases are considered. For all of them, the results are compared with a reference outlier detection methodology, namely the universal outlier detection method proposed by Westerweel and Scarano (2005). The proposed turbulence transport-based approach exhibits higher performance in terms of percentage of outliers correctly identified in the flow statistics.

Stability influences on interscale transport of turbulent kinetic energy and Reynolds shear stress in atmospheric boundary layers interacting with a tall vegetation canopy

Abstract

Numerical simulation of rotating channel flow based on a modified DES model

A new type of nonlinear sub-grid scale (SGS) model is adopted based on the helicity analysis and is verified by predicting the internal flow in a rotating channel. A stress term that contains helicity constraint is introduced into the original SGS model to construct a nonlinear sub-grid model. This additional term representing the helicity constraint effect in the momentum equations is shown to give predictions that are in better agreement with the experimental data. In this paper, the Detached-Eddy Simulation (DES) and the nonlinear SGS model are used to further study the turbulence statistics of the rotating channel flow. Combining with the Reynolds stress transport equations and the turbulent kinetic energy transport equation, the change of turbulence statistics near the wall of the rotating channel is analyzed. The newly added term changes the turbulent viscosity near the wall, which changes the velocity gradient near the wall and further affects other turbulence statistics near the wall.

Rayleigh–Taylor instability with gravity reversal

We present results from Direct Numerical Simulations (DNS) of Rayleigh–Taylor instability at Atwood numbers up to 0.9. After the layer width had developed substantially, additional branched simulations have been run under reversed and zero gravity conditions. We focus on the modifications of the mixing layer structure and turbulence in response to the acceleration change. After the gravity reversal, the flow undergoes a complex transient process in which the vertical mass flux changes sign multiple times and, consequently, the buoyancy term in the turbulent kinetic energy transport equation changes its role back and forth from production to destruction. This behavior is examined in detail using the turbulent kinetic energy and mass flux transport equations and time instances when the vertical mass at the centerline crosses zero and reaches local minima and maxima. While the transient process significantly affects the flow anisotropy at all scales, other turbulence characteristics, like the alignment between the vorticity and eigenvectors of the strain rate tensor, retain their fully developed turbulence behavior in the interior of the layer. In addition, after the gravity reversal, the edges of the layer also exhibit characteristics closer to those of the turbulent interior, even as the fluids become more mixed. None of these changes affects the mean density profile, which still collapses among various cases. Such significant changes in some turbulence quantities and not others are difficult to capture with existing turbulence models.

Direct numerical simulation of turbulent flow separation induced by a forward-facing step

Direct numerical simulation is used to investigate turbulent flow separations generated by a forward-facing step exposed to an incoming fully-developed turbulent plane channel flow at Reτ=180. The step height is 25% of the inlet channel height. The results are analyzed in terms of the topology of the Reynolds stresses, transport of turbulence kinetic energy (TKE) and unsteadiness of separation bubbles using a broad range of post-processing techniques, including the Lumley triangle, quadrant analysis, auto-correlation, joint probability density function, proper orthogonal decomposition and linear stochastic estimation. The incoming turbulence intensity is elevated as the step is approached and peaks along the mean separating streamline over the step. The topology of the Reynolds stresses switches from two-component to axisymmetric along the mean separating streamline over the step. The production term of TKE peaks in the separated shear layer, while the turbulent diffusion term tends to transport TKE away from the shear layer. An expanded separation bubble upstream of the step is typically associated with a contracted separation bubble over the step. This pattern is captured by the first proper orthogonal decomposition (POD) mode. In the first POD mode, the streamwise and vertical fluctuating velocities switch signs abruptly near the mean separating streamline over the step. This is characterized by two pairs of counter-rotating vortices: one pair of counter-rotating vortices leaning over the step and another pair of opposite-signed counter-rotating vortices near the top surface of the step.

Exact Solutions of a Nonlinear Diffusion Equation with Absorption and Production

We provide closed form solutions for an equation which describes the transport of turbulent kinetic energy in the framework of a turbulence model with a single equation.

Energy transport characteristics of converging Richtmyer–Meshkov instability

In this paper, the Richtmyer–Meshkov (RM) instability in spherical and cylindrical converging geometries with a Mach number of about 1.5 is investigated by using the direct numerical simulation method. The heavy fluid is sulfur hexafluoride, and the light fluid is nitrogen. The shock wave converges from the heavy fluid into the light fluid. The main focus is on the energy transport characteristics in the mixing layer during the entire development process from early instability to late-time turbulent mixing. First, the turbulence kinetic energy transport equation is analyzed, and it is found that the production and dissipation mechanisms of the turbulence induced by the spherical and cylindrical converging RM instabilities in the mixing layer are the same. The turbulent diffusion terms are crucial in the whole development processes of the mixing layers. Before the reflected shock waves transit the interfaces, the dissipation terms can be ignored relative to other terms, and after that, the dissipation terms are close to the production terms and play an important role. The compressibility terms are approximate to the production terms and promote the production of turbulence kinetic energy in the later stage. The viscous diffusion terms can be ignored throughout the process. Then, the enstrophy transport equation is researched, and it is found that, in the mixing layers, the baroclinicity terms play a leading role in the early stage, while the vortex stretching terms play a leading role in the later stage, and the vortex stretching term of the spherical converging geometry develops faster than that of the cylindrical converging geometry. The compressibility terms are positive in the early stage, which promote the production of enstrophy. After the reflected shock waves transit the interfaces, the compressibility terms become negative, which inhibit the production of enstrophy. In addition, the results of the present direct numerical simulation also show that the density fluctuation spectra in the centers of the mixing layers of the spherical and cylindrical converging RM instabilities present the obvious −5/3 scaling law.

Direct numerical simulation of a turbulent Couette-Poiseuille flow, part 2: Large- and very-large-scale motions

A direct numerical simulation dataset of a fully developed turbulent Couette-Poiseuille flow is analyzed to investigate the spatial organization of streamwise velocity-fluctuating u-structures on large and very large scales. Instantaneous and statistical flow fields show that negative-u structures with a small scale on a stationary bottom wall grow throughout the centerline due to the continuous positive mean shear, and they penetrate to the opposite moving wall. The development of an initial vortical structure related to negative-u structures on the bottom wall into a large-scale hairpin vortex packet with new hairpin vortices, which are created upstream and close to the wall, is consistent with the auto-generation process in a Poiseuille flow (Zhou et al., J. Fluid Mech., vol. 387, 1999, pp. 353–396). Although the initial vortical structure associated with positive-u structures on the top wall also grows toward the bottom wall, the spatial development of the structure is less coherent with weak strength due to the reduced mean shear near the top wall, resulting in less turbulent energy on the top wall. The continuous growth of the structures from a wall to the opposite wall explains the enhanced wall-normal transport of the streamwise turbulent kinetic energy near the centerline. Finally, an inspection of the time-evolving instantaneous fields and conditional averaged flow fields for the streamwise growth of a very long structure near the centerline exhibits that a streamwise concatenation of adjacent large-scale u-structures creates a very-large-scale structure near the channel centerline.

Direct numerical simulation of turbulent flow through a ribbed square duct

Abstract

Assessing the turbulent kinetic energy budget in an energetic tidal flow from measurements of coupled ADCPs.

Two coupled four-beam acoustic Doppler current profilers were used to provide simultaneous and independent measurements of the turbulent kinetic energy (TKE) dissipation rate ε and the TKE production rate [Formula: see text] over a 36 h long period at a highly energetic tidal energy site in the Alderney Race. The eight-beam arrangement enabled the evaluation of the six components of the Reynolds stress tensor which allows for an improved estimation of the TKE production rate. Depth-time series of ε, [Formula: see text] and the Reynolds stresses are provided. The comparison between ε and [Formula: see text] was performed by calculating individual ratios of ε corresponding to [Formula: see text]. The depth-averaged ratio [Formula: see text] averaged over whole flood and ebb tide were found to be 2.2 and 2.8 respectively, indicating that TKE dissipation exceeds TKE production. It is shown that the term of diffusive transport of TKE is significant. As a result, non-local transport is important to the TKE budget and the common assumption of a local balance, i.e. a balance between production and dissipation, is not valid at the measurement site. This article is part of the theme issue 'New insights on tidal dynamics and tidal energy harvesting in the Alderney Race'.

Mixing behavior in a confined jet with disparate viscosity and implications for complex reactions

Turbulent shear-driven mixing in a coaxial and co-flowing configuration is studied using experiments and computations to understand and model the effect of viscosity gradients in the flow field. Two liquids with a large disparity in dynamic viscosity are mixed, with a low viscosity, high momentum jet directed into a high viscosity, low momentum co-flow in a pipe. Simultaneous experimental measurements of the velocity and concentration fields are made using high-resolution PIV and PLIF to obtain their turbulent cross-correlation statistics for viscosity ratios of 1 and 40. LES simulations are also performed using dynamic mixing sub-grid model to investigate the three dimensional mixing structure of the flow for the two cases. The overall structure of turbulent mixing in the coaxial confined jet configuration is studied to identify the mixing regions of the flow and the effect of viscosity gradients on the dynamics of the same. Besides the effect of Reynolds number between the two cases that manifests as reduced mixing, it was noted that the transport of turbulent kinetic energy and scalar concentration variance shows significant asymmetries that arise from the viscosity gradients in the field. The scalar mixing structure between the two cases is studied in detail with relevance to complex mixing-limited reactions frequently encountered in such environments. It was found that turbulence production and associated scalar mixing is highly skewed in variable viscosity flows, where the low viscosity regions show enhanced turbulence activity. The implications of such turbulence skewness on the chemistry of reaction systems involving variable viscosity environments are discussed in further detail.

Turbulent kinetic energy transfer and dissipation in thermoviscous fluid flow

Turbulent flow of thermoviscous liquid is studied in a three-dimensional region with periodicity in two directions. Flow characteristics are described in the terms of equation for turbulent kinetic energy: this allows to differentiate contributions from different components related to generation, transport, and dissipation of turbulent kinetic energy. Those terms can be calculated from averaging the moments of different order. The previous studies demonstrated that thermoviscous liquid flow occurs through several stages of evolution, including the unsteady turbulence. This allows discussing the problem of mathematical rigorous statement and applicability of different methods for averaging. Existence of spatial periodicity allow using a combined spatial-time averaging for different values on the interval of steady turbulence. Results are presented as a set of Z—t-diagrams. Besides, the paper presents analysis of flow development on the basis of direct visualization of velocity and temperature.

An analytical description of the energy balance in turbulent, round, free jets

This brief contribution provides a quantification of the terms of the turbulent kinetic energy transport equation for a round steady turbulent free jet. The analysis is based on the assumption of flow self-similarity, and it is performed by means of a simple analytical asymptotic analysis. The results are in good agreement with the experimental findings of Panchapakesan and Lumley [J. Fluid Mech. 246, 197–223 (1993)] and with the large eddy simulations of Bogey and Bailly [J. Fluid Mech. 627, 129–160 (2009)], hence providing a theoretical interpretation of such findings.