Kinetic Energy Transport Research Articles

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.

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.

The NY-Ålesund TurbulencE Fiber Optic eXperiment (NYTEFOX): investigating the Arctic boundary layer, Svalbard

Abstract. The NY-Ålesund TurbulencE Fiber Optic eXperiment (NYTEFOX) was a field experiment at the Ny-Ålesund Arctic site (78.9∘ N, 11.9∘ E) and yielded a unique meteorological data set. These data describe the distribution of heat, airflows, and exchange in the Arctic boundary layer for a period of 14 d from 26 February to 10 March 2020. NYTEFOX is the first field experiment to investigate the heterogeneity of airflow and its transport of temperature, wind, and kinetic energy in the Arctic environment using the fiber-optic distributed sensing (FODS) technique for horizontal and vertical observations. FODS air temperature and wind speed were observed at a spatial resolution of 0.127 m and a temporal resolution of 9 s along a 700 m horizontal array at 1 m above ground level (a.g.l.) and along three 7 m vertical profiles. Ancillary data were collected from three sonic anemometers and an acoustic profiler (minisodar; sodar is an acronym for “sound detection and ranging”) yielding turbulent flow statistics and vertical profiles in the lowest 300 m a.g.l., respectively. The observations from this field campaign are publicly available on Zenodo (https://doi.org/10.5281/zenodo.4756836, Huss et al., 2021) and supplement the meteorological data set operationally collected by the Baseline Surface Radiation Network (BSRN) at Ny-Ålesund, Svalbard.

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

Abstract

STRUCTURE STATISTICS OF SCALE TO SCALE ENERGY TRANSFER OF WALL TURBULENCE BASED ON LBM

For the reason that the scale-to-scale energy transfer characteristics of wall bounded turbulence exhibit strong anisotropy in three dimensional physical space, understanding the spatial distribution of energy scale-to-scale transfer is of great importance for the further construction of high-fidelity anisotropic large eddy simulation models. Direct numerical simulation were performed at Reynolds number $Re_{\tau } =180$ by using lattice Boltzmann method (LBM). In comparison with the open source channel flow turbulence database, both the mean velocity and turbulent variables, such as Reynolds stress and velocity fluctuations, agree well with the results of Kim et al. (1987) and Moser et al. (2015). The ability and validity of LBM on simulating turbulent channel flow were verified. The filter-space technique is used to obtain the scale-to-scale transport of kinetic energy, and the statistical results show that the backward scatter and forward scatter contributions to the SGS dissipation were comparable. Combined with the novel structure identification method, the distribution and geometry properties of the energy flux structure is quantitatively investigated by the clustering methodology. The results show that small scale structures account for the majority in number, and the volume probability density distribution presents a -4/5 power law. The structures can further be divided into wall attached structures and wall detached structures according to their minimal distance to the wall. In spite of the relatively small number fraction, the attached structure accounts for most of volume fraction, which shows that most of the attached structures are large scale structures. Further statistics of the attached structures exhibit that the size of the structure has a certain power law relationship, indicating that the scale-to-scale energy transport structure also has the self similarity of the attached eddy hypothesis which proposed by Townsend. The forward and backward energy flux structure pairs tend to be arranged side by side along the span direction.

A prediction model for vertical turbulence momentum flux above infinite wind farms

Large wind farms can significantly change the vertical layered structures and some of the statistical characteristics of the atmospheric boundary layer (ABL). The vertical turbulence momentum flux (VTMF) above a wind farm, which quantifies the vertical transport of the ABL, is important to meteorological simulation and power absorption of the wind farm. However, we still lack a fast prediction model for the VTMF. To this end, a suite of large-eddy simulations (LESs) is performed for infinite wind farms with various turbine positionings. We show that, in the outer layer above a wind farm, the VTMF normalized by the wind farm's equivalent frictional velocity exhibits a linear relationship with height, which agrees well with the linear law for the canonical rough wall. In contrast, in both the wake layer and the inner layer, the VTMF is significantly dependent on the turbine positionings. Consequently, a prediction model for the VTMF in the outer layer of the ABL is proposed only using the mean velocity in the inner layer of the ABL (below the wind rotors). The kinetic energy transport downward to wind farms is also calculated using the proposed model.

Summer Regional Daily‐Precipitation Extreme Events in Huang‐Huai Rivers Region of China and Their Relationships With Rossby Wave Packet Activities

AbstractThe regional daily‐precipitation extreme events (RDPEs) have profound societal impacts. Based on NCEP/NCAR reanalysis and datasets of daily basic meteorological elements from China national meteorological stations, the statistical characteristics of RDPEs in the Huang‐Huai Rivers (HHR) region in eastern China from 1979 to 2016 and their relationships with Rossby wave activities are investigated. The results show that in the summers (June‐August) of 1979–2016, the 95 percentile threshold of regional extreme daily‐precipitation in HHR region is 27.32 mm/d. There are 77 RDPEs in total in the past 38 years. When RDPEs occur, HHR region is controlled by an anomalous cyclonic circulation in the middle and lower troposphere and an anomalous anticyclonic circulation in the upper troposphere. The water vapor is mainly transported from the Bay of Bengal and the South China Sea into HHR region. Rossby waves originate near the Caspian Sea and obviously disperse downstream‐ward, taking about 4 days to move to HHR region. The eddy kinetic energy at 200 hPa over HHR region reaches its maximum on the day before RDPEs occur and decrease from then on. This decrease is dominated by processes including advection transport of eddy kinetic energy and barotropic energy conversion by time‐mean flow. The intensification tendency of baroclinic conversion weakens while barotropic conversion play an important role in the weakening of eddy kinetic energy. The migrations of wave packets, meridional transports of warmer air and momentum over HHR region during 4 days before RDPEs occurrences may provide useful clues to forecasting RDPEs.

Physical space analysis of cross-scale turbulent kinetic energy transfer in premixed swirl flames

Understanding the cross-scale kinetic energy transport in turbulent flames is critical for physically-accurate modeling. This paper presents an experimental analysis of cross-scale kinetic energy transport in turbulent premixed swirl flames at Karlovitz numbers between 10 and 20 via physical space filtering. High-resolution tomographic particle image velocimetry and formaldehyde planar laser induced fluorescence measurements are used to obtain 3D velocity fields, as well as estimates for the progress variable and density fields. Filtering these fields at scales in the range of the laminar flame thickness (0.9<Δ/δL0<2.2) allows the kinetic energy transfer across the filter scale to be quantified. Mean kinetic energy transfer from sub-filter scales to larger scales (i.e. back-scatter) occurs internal to the flame structure across the range of conditions studied, with the maximum back-scatter occurring towards the center of the flame. Compared to equivalent non-reacting cases, considerably more back-scatter occurred in the reacting flows across all cases studied. At lower Karlovitz number, the magnitude of the back-scatter monotonically increased with increasing filter scale. At higher Karlovitz number, the back-scatter magnitude saturated at filter scales around Δ/δL0≈1.8. A scaling is proposed that quantifies the relative significance of the swirl-induced pressure gradient relative to the flame-induced pressure gradient on the pressure-work source of kinetic energy, indicating that swirling flow can significantly affect the kinetic energy dynamics. Overall, the results demonstrate that combustion significantly impacts the cross-scale kinetic energy transfer at scales in the range of the laminar flame thickness for conditions and configurations of practical relevance. These conclusions have implications for LES modelling strategies, providing evidence that models should allow for up-scale energy transfer in the vicinity of the flame.

Experimental investigation on the impingement of synthetic jet vortex rings onto a porous wall

This paper presents an experimental study on the effects of the Reynolds number (Resj = 300, 600, and 900) and porosity (ϕ = 20%–85%) on synthetic jet vortex rings impinging onto a porous wall. Laser-induced fluorescence and particle image velocimetry are used to acquire flow information qualitatively and quantitatively. When Resj is low (Resj = 300), ϕ plays a key role in determining the formation of transmitted vortex rings downstream. For the first time, a row of individual small-scale vortex rings that form at the lowest porosity (ϕ = 20%) have been observed in the synthetic jet/porous wall interaction. As Resj increases to 900, the triggered Kelvin–Helmholtz instability promotes the vorticity cancellation at a low porosity (ϕ = 30%), and thus contributes to the formation of a transmitted vortex ring. It is concluded that the vorticity cancellation is the dominant factor affecting the generation of a transmitted vortex ring. Time-averaged characteristics indicate that for a low Resj, the incoherence of the vortex ring is mainly due to the viscous effects. However, for a high Resj, it is the transition that leads to a significant enhancement in the turbulent kinetic energy. Measurements of flow macroscopic parameters show that the loss of the momentum flux exhibits a linear relationship with ϕ for all Resj, while the loss of the kinetic energy transport is nonlinearly dependent on ϕ. Incorporating ϕ, this study presents a more comprehensive similarity parameter, ϕln(Resj2dh*3), to characterize the synthetic jet/porous wall interaction.

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.

Dynamics of zonally elongated transient flows

Abstract

Noise characteristic analysis and sound sources identification for rod–airfoil interaction using different subgrid-scale models

Four subgrid-scale models based on large eddy simulation (LES), such as Smagorinsky–Lilly (SL), dynamic Smagorinsky–Lilly (DSL), wall-adapting local eddy-viscosity (WALE), and dynamic kinetic-energy transport (KET) were used and couple Ffowcs Williams–Hawkings equation to accurately analyze and identify the characteristics and position of the sound sources of rod–airfoil interaction. The results of four models were compared with experimental data. It was found that the DSL model was the optimal subgrid-scale model for the study of the interaction noise considering the calculation accuracy. Therefore, the DSL model was selected for analyzing and identifying the characteristics and location of the interaction noise source. During the calculation, solid and permeable data surfaces were used for acoustic integral surfaces. The results show that the impact of the quadrupole source is negligible at a low Mach number, and the dipole noise coming from the pressure fluctuations is dominant. Meanwhile, the dipole noise from the airfoil is louder than that from the rod; the leading edge of about 30% chord length of airfoil the is the main sound source of interference effect. Above results can provide guidance for research of blade-vortex interaction noise.

Turbulent kinetic energy in 2D isothermal interchange-dominated scrape-off layer E × B drift turbulence: Governing equation and relation to particle transport

This paper studies the turbulent kinetic energy (k⊥) in 2D isothermal electrostatic interchange-dominated E × B drift turbulence in the scrape-off layer and its relation to particle transport. An evolution equation for the former is analytically derived from the underlying turbulence equations. Evaluating this equation shows that the dominant source for the turbulent kinetic energy is due to interchange drive, while the parallel current loss to the sheath constitutes the main sink. Perpendicular transport of the turbulent kinetic energy seems to play a minor role in the balance equation. Reynolds stress energy transfer also seems to be negligible, presumably because no significant shear flow develops under the given assumptions of isothermal sheath-limited conditions in the open field line region. The interchange source of the turbulence is analytically related to the average turbulent E × B energy flux, while a regression analysis of TOKAM2D data suggests a model that is linear in the turbulent kinetic energy for the sheath loss. A similar regression analysis yields a diffusive model for the average radial particle flux, in which the anomalous diffusion coefficient scales with the square root of the turbulent kinetic energy. Combining these three components, a closed set of equations for the mean-field particle transport is obtained, in which the source of the turbulence depends on mean flow gradients and k⊥ through the particle flux, while the turbulence is saturated by parallel losses to the sheath. Implementation of this new model in a 1D mean-field code shows good agreement with the original TOKAM2D data over a range of model parameters.

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.

Impact of horizontal resolution on global ocean–sea ice model simulations based on the experimental protocols of the Ocean Model Intercomparison Project phase 2 (OMIP-2)

Abstract. This paper presents global comparisons of fundamental global climate variables from a suite of four pairs of matched low- and high-resolution ocean and sea ice simulations that are obtained following the OMIP-2 protocol (Griffies et al., 2016) and integrated for one cycle (1958–2018) of the JRA55-do atmospheric state and runoff dataset (Tsujino et al., 2018). Our goal is to assess the robustness of climate-relevant improvements in ocean simulations (mean and variability) associated with moving from coarse (∼ 1∘) to eddy-resolving (∼ 0.1∘) horizontal resolutions. The models are diverse in their numerics and parameterizations, but each low-resolution and high-resolution pair of models is matched so as to isolate, to the extent possible, the effects of horizontal resolution. A variety of observational datasets are used to assess the fidelity of simulated temperature and salinity, sea surface height, kinetic energy, heat and volume transports, and sea ice distribution. This paper provides a crucial benchmark for future studies comparing and improving different schemes in any of the models used in this study or similar ones. The biases in the low-resolution simulations are familiar, and their gross features – position, strength, and variability of western boundary currents, equatorial currents, and the Antarctic Circumpolar Current – are significantly improved in the high-resolution models. However, despite the fact that the high-resolution models “resolve” most of these features, the improvements in temperature and salinity are inconsistent among the different model families, and some regions show increased bias over their low-resolution counterparts. Greatly enhanced horizontal resolution does not deliver unambiguous bias improvement in all regions for all models.

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.