Resolved Reynolds Stresses Research Articles

Advanced detached-eddy simulation of the MD 30P-30N three-element airfoil

An experimental version in the Detached-Eddy Simulation (DES) family (called Advanced DES or ADES) is introduced and tested on a geometry that is fairly complex but two-dimensional. The essential change in ADES is that the user is given control of the regions treated with full turbulence modelling (RANS) and those treated with Large-Eddy Simulation (LES). This zonal character makes the approach more powerful, but less practical, so that in its current state it is not ready for industrial CFD. The grid requirements of the two regions are very different, and multi-block grid structure is natural. Another key feature is a Volumetric Synthetic Turbulence Generator (VSTG), installed to feed the LES region with viable resolved turbulence, so that the resolved Reynolds stresses rapidly substitute for the modelled Reynolds stresses present in the RANS region. The VSTG operates in a volume, rather than on a surface and can be active in attached boundary layers, at a trailing edge, or after separation. The well-known McDonnell-Douglas 30P-30N airfoil is simulated with periodic lateral boundary conditions. The VSTG is successful, and the desired nature of simulation is obtained in each region. ADES involves zonal decisions, but appears robust. An inertial range is clearly indicated in frequency spectra. A grid-refinement study is included, as well as variations in lateral domain size and STG positions; this led to a matrix of 11 simulations. Cases are shown at four angles of attack and with three RANS models in addition to ADES. Pressure and friction distributions and velocity and shear stress profiles are compared in detail. The prospects for an evolution of ADES into a practical routine approach in the long term are discussed.

Mean flow and turbulence in unsteady canopy layers

Non-stationarity is the rule in the atmospheric boundary layer (ABL). Under such conditions, the flow may experience departures from equilibrium with the underlying surface stress, misalignment of shear stresses and strain rates, and three-dimensionality in turbulence statistics. Existing ABL flow theories are primarily established for statistically stationary flow conditions and cannot predict such behaviours. Motivated by this knowledge gap, this study analyses the impact of time-varying pressure gradients on mean flow and turbulence over urban-like surfaces. A series of large-eddy simulations of pulsatile flow over cuboid arrays is performed, programmatically varying the oscillation amplitude $\alpha$ and forcing frequency $\omega$ . The analysis focuses on both longtime-averaged and phase-dependent flow dynamics. Inspection of longtime-averaged velocity profiles reveals that the aerodynamic roughness length $z_0$ increases with $\alpha$ and $\omega$ , whereas the displacement height $d$ appears to be insensitive to these parameters. In terms of oscillatory flow statistics, it is found that $\alpha$ primarily controls the oscillation amplitude of the streamwise velocity and Reynolds stresses, but has a negligible impact on their wall-normal structure. On the other hand, $\omega$ determines the size of the region affected by the unsteady forcing, which identifies the so-called Stokes layer thickness $\delta _s$ . Within the Stokes layer, phase-averaged resolved Reynolds stress profiles feature substantial variations during the pulsatile cycle, and the turbulence is out of equilibrium with the mean flow. Two phenomenological models have been proposed that capture the influence of flow unsteadiness on $z_0$ and $\delta _s$ , respectively.

Development of an Interpolated RANS-LES solver for wall-bounded turbulent fluid flows

Scale-resolving hybrid RANS-LES models are being increasingly used to numerically simulate wall-bounded turbulent flows since they are computationally efficient compared to LES (Large Eddy Simulation) while also being more accurate compared to RANS (Reynolds-Averaged Navier–Stokes) models. Existing hybrid RANS-LES models typically either suffer from modeled stress depletion or they can introduce a sharp jump in the mean Reynolds stress across the RANS-LES zone. We present a novel interpolated RANS-LES (IRL) solver implemented in OpenFOAM, in which the RANS equations (for eddy-viscosity) and LES equations (for filtered velocity) are evolved simultaneously on the same computational grid. Based on the distance from the no-slip wall, the flow domain is demarcated into a near-wall, free-stream, and a “hybrid” region, sandwiched between the near-wall and free-stream regions. Spalart Allmaras (S-A) model has been used to evolve the RANS eddy viscosity, while the Wall Adapting Local Eddy Viscosity (WALE) model is used for evolving the filtered LES velocity. Using a novel scheme based on solving a partial differential equation, the turbulent eddy-viscosity is interpolated between the RANS eddy viscosity in the near wall region and the effective eddy viscosity from the resolved LES fluctuations in the free-stream region. The mean subgrid stress in the LES momentum equation is then corrected in the near-wall and hybrid regions using the interpolated turbulent eddy-viscosity. IRL’s grid resolution requirements are the same as DES’s (Detached Eddy Simulation). Grid convergence and sensitivity studies have been carried out for two canonical flow geometries. For turbulent channel flow simulations, the IRL solver does not display the typical mean stress depletion observed in DES while also predicting resolved Reynolds stresses accurately in the free-stream region. For simulations of flow over backward facing step, the IRL solver can predict the friction factor and coefficient of pressure better than that DES, especially after the reattachment point.

Deep learning closure models for large-eddy simulation of flows around bluff bodies

Near-wall flow simulation remains a central challenge in aerodynamics modelling: Reynolds-averaged Navier–Stokes predictions of separated flows are often inaccurate, and large-eddy simulation (LES) can require prohibitively small near-wall mesh sizes. A deep learning (DL) closure model for LES is developed by introducing untrained neural networks into the governing equations and training in situ for incompressible flows around rectangular prisms at moderate Reynolds numbers. The DL-LES models are trained using adjoint partial differential equation (PDE) optimization methods to match, as closely as possible, direct numerical simulation (DNS) data. They are then evaluated out-of-sample – for aspect ratios, Reynolds numbers and bluff-body geometries not included in the training data – and compared with standard LES models. The DL-LES models outperform these models and are able to achieve accurate LES predictions on a relatively coarse mesh (downsampled from the DNS mesh by factors of four or eight in each Cartesian direction). We study the accuracy of the DL-LES model for predicting the drag coefficient, near-wall and far-field mean flow, and resolved Reynolds stress. A crucial challenge is that the LES quantities of interest are the steady-state flow statistics; for example, a time-averaged velocity component $\langle {u}_i\rangle (x) = \lim _{t \rightarrow \infty } ({1}/{t}) \int _0^t u_i(s,x)\, {\rm d}s$ . Calculating the steady-state flow statistics therefore requires simulating the DL-LES equations over a large number of flow times through the domain. It is a non-trivial question whether an unsteady PDE model with a functional form defined by a deep neural network can remain stable and accurate on $t \in [0, \infty )$ , especially when trained over comparatively short time intervals. Our results demonstrate that the DL-LES models are accurate and stable over long time horizons, which enables the estimation of the steady-state mean velocity, fluctuations and drag coefficient of turbulent flows around bluff bodies relevant to aerodynamics applications.

Two-phase flow simulations of surface waves in wind-forced conditions

The paper is devoted to two-phase flow simulations and investigates the ability of a diffusive interface Cahn–Hilliard volume-of-fluid model to capture the dynamics of the air–sea interface at geophysically relevant Reynolds numbers. It employs a hybrid filtered/averaging improved detached eddy simulation method to model turbulence and utilizes a continuum model to account for surface tension if the diffuse interface is under-resolved by the grid. A numerical wind-wave tank is introduced, and results obtained for two known wind-wave conditions are analyzed in comparison to experimental data at matched Reynolds numbers. The focus of the comparison is on both time-averaged and wave-coherent quantities, and includes pressure, velocity as well as modeled and resolved Reynolds stresses. In general, numerical predictions agree well with the experimental measurements and reproduce many wave-dependent flow features. Reynolds stresses near the water surface are found to be especially important in modulating the critical layer height. It is concluded that the diffusive interface approach proves to be a promising method for future studies of air–sea interface dynamics in geophysically relevant flows.

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.

Application of immersed boundary based turbulence wall modeling to the Ahmed body aerodynamics

This paper applies a recently developed immersed boundary-turbulence wall modeling approach to turbulent flows over a generic car geometry, known as the Ahmed body, under massive flow separation within a lattice Boltzmann solver. Although the immersed boundary method combined with hierarchical Cartesian grid offers high flexibility in automatic grid generation around complex geometries, the near-wall solution is significantly deteriorated compared to the body-fitted simulation, especially when coupled to wall models for turbulent flows at high Reynolds number. Enhanced wall treatments have been proposed in the literature and validated for attached flow configurations. In this work, the Ahmed body with a slant surface of angle 35° is considered where the flow separates massively over the slant surface and the vertical base. The large eddy simulation is performed with a Reynolds stress constraint near-wall. The eddy viscosity is computed dynamically by taking into account the actually resolved Reynolds stresses. It approaches the mixing length eddy viscosity in attached boundary layers and returns to the subgrid eddy viscosity in detached boundary layers. An explicit equilibrium wall model has also been proposed to accelerate the calculation. Comparison with the no-slip boundary condition on the separated surfaces shows that the near-wall treatments with the equilibrium wall model operate reasonably well on both attached and detached boundary layers.

Implicit Subgrid-Scale Modeling of a Mach 2.5 Spatially Developing Turbulent Boundary Layer.

We employ numerically implicit subgrid-scale modeling provided by the well-known streamlined upwind/Petrov–Galerkin stabilization for the finite element discretization of advection–diffusion problems in a Large Eddy Simulation (LES) approach. Whereas its original purpose was to provide sufficient algorithmic dissipation for a stable and convergent numerical method, more recently, it has been utilized as a subgrid-scale (SGS) model to account for the effect of small scales, unresolvable by the discretization. The freestream Mach number is 2.5, and direct comparison with a DNS database from our research group, as well as with experiments from the literature of adiabatic supersonic spatially turbulent boundary layers, is performed. Turbulent inflow conditions are generated via our dynamic rescaling–recycling approach, recently extended to high-speed flows. Focus is given to the assessment of the resolved Reynolds stresses. In addition, flow visualization is performed to obtain a much better insight into the physics of the flow. A weak compressibility effect is observed on thermal turbulent structures based on two-point correlations (IC vs. supersonic). The Reynolds analogy ( vs. ) approximately holds for the supersonic regime, but to a lesser extent than previously observed in incompressible (IC) turbulent boundary layers, where temperature was assumed as a passive scalar. A much longer power law behavior of the mean streamwise velocity is computed in the outer region when compared to the log law at Mach 2.5. Implicit LES has shown very good performance in Mach 2.5 adiabatic flat plates in terms of the mean flow (i.e., and ). iLES significantly overpredicts the peak values of , and consequently Reynolds shear stress peaks, in the buffer layer. However, excellent agreement between the turbulence intensities and Reynolds shear stresses is accomplished in the outer region by the present iLES with respect to the external DNS database at similar Reynolds numbers.

The Influence of WENO Schemes on Large-Eddy Simulations of a Neutral Atmospheric Boundary Layer

AbstractThis work explores the influence of Weighted Essentially Non-Oscillatory (WENO) schemes on Cloud Model 1 (CM1) large-eddy simulations (LES) of a quasi-steady, horizontally homogeneous, fully developed, neutral atmospheric boundary layer (ABL). An advantage of applying WENO schemes to scalar advection in compressible models is the elimination of acoustic waves and associated oscillations of domain-total vertical velocity. Applying WENO schemes to momentum advection in addition to scalar advection yields no further advantage, but has an adverse effect on resolved turbulence within LES. As a tool designed to reduce numerically generated spurious oscillations, WENO schemes also suppress physically realistic instability development in turbulence-resolving simulations. Thus, applying WENO schemes to momentum advection reduces vortex stretching, suppresses the energy cascade, reduces shear-production of resolved Reynolds stress, and eventually amplifies the differences between the surface-layer mean wind profiles in the LES and the mean wind profiles expected in accordance with the filtered law of the wall (LOTW). The role of WENO schemes in adversely influencing surface-layer turbulence has inspired a concept of anti-WENO (AWENO) schemes to enhance instability development in regions where energy-containing turbulent motions are inadequately resolved by LES grids. The success in reproducing the filtered LOTW via AWENO schemes suggests that improving advection schemes is a critical component toward faithfully simulating near-surface turbulence and dealing with other "Terra Incognita" problems.

On the suitability of second-order accurate finite-volume solvers for the simulation of atmospheric boundary layer flow

Abstract. The present work analyzes the quality and reliability of an important class of general-purpose, second-order accurate finite-volume (FV) solvers for the large-eddy simulation of a neutrally stratified atmospheric boundary layer (ABL) flow. The analysis is carried out within the OpenFOAM® framework, which is based on a colocated grid arrangement. A series of open-channel flow simulations are carried out using a static Smagorinsky model for subgrid scale momentum fluxes in combination with an algebraic equilibrium wall-layer model. The sensitivity of the solution to variations in numerical parameters such as grid resolution (up to 1603 control volumes), numerical solvers, and interpolation schemes for the discretization of nonlinear terms is evaluated and results are contrasted against those from a well-established mixed pseudospectral–finite-difference code. Considered flow statistics include mean streamwise velocity, resolved Reynolds stresses, velocity skewness and kurtosis, velocity spectra, and two-point autocorrelations. A quadrant analysis along with the examination of the conditionally averaged flow field are performed to investigate the mechanisms responsible for momentum transfer in the flow. It is found that at the selected grid resolutions, the considered class of FV-based solvers yields a poorly correlated flow field and is not able to accurately capture the dominant mechanisms responsible for momentum transport in the ABL. Specifically, the predicted flow field lacks the well-known sweep and ejection pairs organized side by side along the cross-stream direction, which are representative of a streamwise roll mode. This is especially true when using linear interpolation schemes for the discretization of nonlinear terms. This shortcoming leads to a misprediction of flow statistics that are relevant for ABL flow applications and to an enhanced sensitivity of the solution to variations in grid resolution, thus calling for future research aimed at reducing the impact of modeling and discretization errors.

A new method of LES verification and validation for attached turbulent cavitating flow

The large eddy simulation (LES) is used to resolve the flow structure in the cavitating turbulent flow around the Clark-Y hydrofoil coupled with a homogeneous cavitation model. A new method is proposed in this paper to calculate the LES error of the time-averaged streamwise velocity for the LES verification and validation (V&V). From the instantaneous cavity patterns, it is demonstrated that the predicted results agree fairly well with the experimental data. With this new proposed method, the LES errors can be easily and effectively calculated with a limited mesh number, and the method might be used in the other applications of the LES V&V. Results of the LES errors obtained by the new method show that the relatively steady flow can be simulated with small errors, while the complex flow structures at the cavity shedding region might lead to an increase of errors in the LES modeling. In addition, the distributions of the resolved Reynolds stresses are used to estimate the influences of the cavitation on the turbulent fluctuations. Results indicate that the turbulent fluctuations for the cavitating flow are much larger in magnitude as compared to the cases without cavitation.

Statistical Properties of Subgrid-Scale Turbulence Models

This review examines large eddy simulation (LES) models from the perspective of their a priori statistical characteristics. The most well-known statistical characteristic of an LES subgrid-scale model is its dissipation (energy transfer to unresolved scales), and many models are directly or indirectly formulated and tuned for consistency of this characteristic. However, in complex turbulent flows, many other subgrid statistical characteristics are important. These include such quantities as mean subgrid stress, subgrid transport of resolved Reynolds stress, and dissipation anisotropy. Also important are the statistical characteristics of models that account for filters that do not commute with differentiation and of the discrete numerical operators in the LES equations. We review the known statistical characteristics of subgrid models to assess these characteristics and the importance of their a priori consistency. We hope that this analysis will be helpful in continued development of LES models.

High-Resolution Measurements of Heat Transfer, Near-Wall Intermittency, and Reynolds-Stresses Along a Flat Plate Boundary Layer Undergoing Bypass Transition

Abstract A new experimental dataset focusing on the influence of high freestream turbulence and large pressure gradients on boundary layer transition is presented. The experiments are conducted in a new wind tunnel equipped with a flat plate test section and a new kind of turbulence generator, which allows for a continuous variation of turbulence intensity. The flat plate is mounted midway between contoured top and bottom walls. Two different wall contours can be implemented to create pressure distributions on the flat plate that are typical for the pressure and suction side of high pressure turbine cascades. A large variation of Reynolds number from 3.0 × 105 to 7.5 × 105 and inlet turbulence intensity between 1.1% and 8% is realized, resulting in more than 100 test cases. Measurements comprise highly resolved heat transfer, near-wall intermittency and freestream Reynolds stress distributions. Near-wall intermittency is measured using a traversable hotfilm sensor while freestream Reynolds stresses are measured simultaneously at the same position with a revolvable X-wire probe. Additionally, turbulent length scales are analyzed using the X-wire signal along the flat plate. Results show that heat transfer and near-wall intermittency distributions are in good agreement and that heat transfer at high turbulence levels increases prior to the formation of first turbulence spots. Transition onset is found to be influenced by the turbulence Reynolds number, i.e., turbulent length scales. At constant inlet turbulence intensity, transition onset moves upstream, when the turbulent Reynolds number is decreased.

Application of numerical transition control method to enhance turbulence in a natural convection boundary layer over a vertical heated plate

The present paper describes the application of local perturbations in Large Eddy Simulation to enhance transition to turbulence applied on the heated wall of a natural convection boundary layer. Simulations are carried out with a Prandtl number Pr=0.71 and a maximum Grashof number of Gr=4.1×1011. The purpose of this work is to accelerate the transition process in the numerical domain, reducing the needed simulation effort to reach the turbulent regime in a natural convection boundary layer flow. A parametric study has been performed to identify the fastest transition to turbulence in the proposed technique. The obtained results are compared with experimental, empirical and other numerical reference data to assess the method’s performance. The analysis of the transition method contemplates its effect in the mean flow field, as well as in the resolved Reynolds stresses and turbulent heat fluxes.

Resolution-induced anisotropy in large-eddy simulations

Large eddy simulation (LES) of turbulence in complex geometries and domains is often conducted with high aspect ratio resolution cells of varying shapes and orientations. The effects of such anisotropic resolution are often simplified or neglected in subgrid model formulation. Here, we examine resolution induced anisotropy and demonstrate that, even for isotropic turbulence, anisotropic resolution induces mild resolved Reynolds stress anisotropy and significant anisotropy in second-order resolved velocity gradient statistics. In large eddy simulations of homogeneous isotropic turbulence with anisotropic resolution, it is shown that commonly used subgrid models, including those that consider resolution anisotropy in their formulation, perform poorly. The one exception is the anisotropic minimum dissipation model proposed by Rozema et al. (Phys. of Fluids 27, 085107, 2015). A simple new model is presented here that is formulated with an anisotropic eddy diffusivity that depends explicitly on the anisotropy of the resolution. It also performs well, and is remarkable because unlike other LES subgrid models, the eddy diffusivity only depends on statistical characteristics of the turbulence (in this case the dissipation rate), not on fluctuating quantities. In other subgrid modeling formulations, such as the dynamic procedure, limiting flow dependence to statistical quantities in this way could have advantages.

A time-average filtering technique to improve the efficiency of two-layer wall models for large eddy simulation in complex geometries

Two-Layer wall models have been recurrently studied since they represent a good physical model for Large Eddy Simulations with underresolved wall regions. Specifically, those based on the Reynolds Averaged Navier-Stokes equations are of special interest, since they can be applied to a wide range of conditions including non-equilibrium flows. Nonetheless, these models are affected by two recurrent problems, the “log-layer mismatch” and the resolved Reynolds stresses inflow, which until now, have been dealt with separated techniques. In this work, a time-filtering methodology is applied to tackle both issues at once with a single and low-computational-cost step, easily applicable to complex three-dimensional geometries. The time-filtering technique has already been applied to other types of wall models to mitigate the “log-layer mismatch.” Now, it is applied for the first time in the Two-Layer wall model context, showing its ability not only in avoiding the mismatch issue but also in blocking the resolved Reynolds stress inflow, dramatically improving the wall model performance and generality compared to other existing implementations. A methodology to determine the necessary temporal filter length is proposed and validated in equilibrium and non-equilibrium conditions. Additionally, the filter size influence on large-scale unsteady flow motions is assessed. Good results are obtained in steady and unsteady flow regimes by suppressing the LES highest frequencies while taking into account large-scale temporal effects.

LES grid resolution requirements for the modelling of gravity currents

The influence of the grid resolution on the large eddy simulation (LES) of a lock-exchange turbidity current is investigated. The simulations are performed using a finite volume Boussinesq code with a Smagorinsky turbulence model for a range of buoyancy Reynolds numbers, ranging from transitional currents (Reb=1,000) to fully-developed turbulence (Reb=60,000). The general features of the flow and the relative independence of the current front for Reb>10,000 are correctly predicted. In agreement with previous research, the spanwise two-point correlations are found to be the most useful quantities to assess the mesh resolution. In addition, velocity power spectrum densities are used to provide information on the maximum cell size required to ensure the LES filter cutoff wavelength is inside the inertial range of the turbulence spectra. We show that at low Reynolds numbers, the turbulence model is too restrictive and direct resolution (DNS) is preferable. For 10,000<Reb<60,000, the combination of the different criteria lead to a minimum resolution of 1140 × 37 × 74 cells for coarse LES, and 1925 × 62 × 125 cells for well-resolved LES, regardless of the Reynolds number. Finally, recommendations are made on how to achieve a well-resolved LES based on examination of the vertical profiles of the ratio of SGS viscosity to molecular viscosity, and of the SGS shear-stress to the resolved Reynolds stress.

LES mesh resolution requirements for particledriven gravity currents

In this study we investigate the influence of grid resolution on a near-wall resolved LES model of a lock-exchange particle-driven gravity current. The simulations are performed using the finite volume Boussinesq code SnS with a Smagorinsky turbulence model for a buoyant Reynolds number of 60,000 on 4 grid sizes. According to previous studies, two-point correlations are most appropriate to estimate LES resolution. With the largest scales of the flow being resolved by more than 20 cells, well-resolved LES is obtained for grid resolutions of 1925×62×125 and finer. In addition, in order to apply the turbulence model correctly, we show that the velocity power spectrum densities provide useful information for the maximum cell size. The ratio of the subgrid scale viscosity to the molecular viscosity and the subgrid scale shear-stress to the resolved Reynolds stress show good convergence with grid refinement. The ratios vSGS / &lt;0.3 above the current and τSGS (u'v')ave &lt; 0.05 inside the mixing layer, are chosen as threshold values, based on our evaluation study.

An Eulerian two-phase model for steady sheet flow using large-eddy simulation methodology

Abstract A three-dimensional Eulerian two-phase flow model for sediment transport in sheet flow conditions is presented. To resolve turbulence and turbulence-sediment interactions, the large-eddy simulation approach is adopted. Specifically, a dynamic Smagorinsky closure is used for the subgrid fluid and sediment stresses, while the subgrid contribution to the drag force is included using a drift velocity model with a similar dynamic procedure. The contribution of sediment stresses due to intergranular interactions is modeled by the kinetic theory of granular flow at low to intermediate sediment concentration, while at high sediment concentration of enduring contact, a phenomenological closure for particle pressure and frictional viscosity is used. The model is validated with a comprehensive high-resolution dataset of unidirectional steady sheet flow (Revil-Baudard et al., 2015, Journal of Fluid Mechanics, 767, 1–30). At a particle Stokes number of about 10, simulation results indicate a reduced von Karman coefficient of κ ≈ 0.215 obtained from the fluid velocity profile. A fluid turbulence kinetic energy budget analysis further indicates that the drag-induced turbulence dissipation rate is significant in the sheet flow layer, while in the dilute transport layer, the pressure work plays a similar role as the buoyancy dissipation, which is typically used in the single-phase stratified flow formulation. The present model also reproduces the sheet layer thickness and mobile bed roughness similar to measured data. However, the resulting mobile bed roughness is more than two times larger than that predicted by the empirical formulae. Further analysis suggests that through intermittent turbulent motions near the bed, the resolved sediment Reynolds stress plays a major role in the enhancement of mobile bed roughness. Our analysis on near-bed intermittency also suggests that the turbulent ejection motions are highly correlated with the upward sediment suspension flux, while the turbulent sweep events are mostly associated with the downward sediment deposition flux.

On the turbulent flow in piston engines: Coupling of statistical theory quantities and instantaneous turbulence

Planar particle image velocimetry (PIV) and tomographic PIV (TPIV) measurements are utilized to analyze turbulent statistical theory quantities and the instantaneous turbulence within a single-cylinder optical engine. Measurements are performed during the intake and mid-compression stroke at 800 and 1500 RPM. TPIV facilitates the evaluation of spatially resolved Reynolds stress tensor (RST) distributions, anisotropic Reynolds stress invariants, and instantaneous turbulent vortical structures. The RST analysis describes distributions of individual velocity fluctuation components that arise from unsteady turbulent flow behavior as well as cycle-to-cycle variability (CCV). A conditional analysis, for which instantaneous PIV images are sampled by their tumble center location, reveals that CCV and turbulence have similar contributions to RST distributions at the mean tumble center, but turbulence is dominant in regions peripheral to the tumble center. Analysis of the anisotropic Reynolds stress invariants reveals the spatial distribution of axisymmetric expansion, axisymmetric contraction, and 3D isotropy within the cylinder. Findings indicate that the mid-compression flow exhibits a higher tendency toward 3D isotropy than the intake flow. A novel post-processing algorithm is utilized to classify the geometry of instantaneous turbulent vortical structures and evaluate their frequency of occurrence within the cylinder. Findings are coupled with statistical theory quantities to provide a comprehensive understanding of the distribution of turbulent velocity components, the distribution of anisotropic states of turbulence, and compare the turbulent vortical flow distribution that is theoretically expected to what is experimentally observed. The analyses reveal requisites of important turbulent flow quantities and discern their sensitivity to the local flow topography and engine operation.