Large Eddy Motion Research Articles

Effects of Abrupt Cross-Section Area Change on theMultiparameter Propagation Characteristics of Premixed Methane–Air Explosion in Pipes

This paper explores the effects of an abrupt cross-section area change of gas pipes on the propagation law of explosion. For this, an explosion pipe experimental system was established, and a numerical research was conducted. By experimental and numerical simulation, the evolution of the overpressure, temperature, vorticity, and kinetic energy of shock waves of gas explosion in abrupt pipelines was investigated. This allowed us to obtain expressions for the attenuation coefficient, increase coefficient, and reflection coefficient of gas explosion overpressure. The study indicates that an abrupt increase of the pipeline cross-section area leads to a decrease of shock wave overpressure and vice versa. For a given change of cross-section area, the attenuation coefficient gradually increases as the initial peak overpressure rises, whereas the increase coefficient and reflection coefficient both present a decreasing trend. An abrupt change in the pipe structure can inhibit the propagation of gas explosion flames. The explosive gas is affected by the turbulence effect after passing through the middle large-diameter pipe, and the vorticity curve exhibits a clear peak. In addition, the large eddy motion caused by strong confinement increases the kinetic energy of the gas in pipes. The above research outcomes contribute to further enriching the basic theory of gas explosion for the study of gas explosion propagation in mining laneway.

Conservative compressible one-dimensional turbulence formulation and application to high-Reynolds-number compressible turbulent channel flows

One-dimensional turbulence (ODT) is an efficient stochastic methodology for turbulent flow simulation with dimensionality reduction. In this study, the conservative compressible ODT model is further developed and applied to address the challenge of accurately and economically modeling high-Reynolds-number wall-bounded compressible turbulent flows. The prohibitively costly direct numerical simulation (DNS) of multiscale motions for fully developed compressible turbulent channel flows is replaced by a much more economical simulation using the conservative compressible ODT model. The quantitative accuracy in capturing the main turbulent features, including the first-order mean statistics and the second-order and third-order turbulent fluctuation statistics, is verified by comparing the ODT results with different canonical DNS results at Mab = 0.5, 1.5, and 3.0. With its accuracy tested, the proposed ODT model is employed to capture the turbulent features of fully developed channel flows at Reynolds numbers widely ranging from 6000 to 60 000. The proposed ODT model reproduces Reynolds number effects in turbulent fluctuation statistics at all three Mach numbers mentioned above. Furthermore, considering the correspondence between the statistical effect of multiscale eddy events stochastically sampled in ODT and the effect of actual multiscale turbulent motions, a mechanism for Reynolds number effects is revealed by analyzing interactions between the multiscale eddy events from the ODT perspective. Evidence shows that the large-eddy motions in the outer region, rather than the small ones in the inner region, contribute to the Reynolds number effects when all these motions are plotted in inner-scaled units.

Effect of gap width on turbulent mixing of parallel flow in a square channel with a cylindrical rod

The turbulent mixing coefficient is an essential parameter to describe the energy and momentum transports between adjacent subchannels in a nuclear fuel assembly and affect the thermal–hydraulic characteristics in nuclear reactor core. Hence, its estimation is in close connection with the design and performance–prediction of nuclear reactor. In the present experimental study, the effect of gap width on the flow pulsation and turbulent mixing was investigated using PIV (Particle Image Velocimetry). The W/D (the ratio of distance to wall to rod diameter) covered from 1.03 to 1.14, and the single cylindrical rods with five different diameters were installed in a square channel to adjust the gap width. Among the W/D cases tested, in the W/D=1.03, 1.06, 1.08, and 1.10, the flow pulsation, a quasi-periodic oscillating flow motion, appeared at the rod gap center, while it was not observed for W/D=1.14. As an increase in Reynolds number and/or a decrease in W/D, the peak frequency and power spectral density of flow pulsation became higher and larger, respectively. On the other hand, the W/D cases with a flow pulsation exhibited higher RMS (Root–Mean–Square) values of lateral velocity than the case without a flow pulsation. The change in the RMS values of lateral velocity was more sensitive to the W/D conditions, particularly for the small W/D cases (i.e., W/D⩽1.10) showing the flow pulsation. This implies that the RMS values of lateral velocity are strongly influenced by the flow pulsation, which in turn, can determine the turbulent mixing between subchannels. To propose the turbulent mixing coefficient for nuclear reactor core application, the W/D ranges were divided into two groups dominated by (i) the large eddy motion of the flow pulsation, and (ii) the typical fluctuation of the turbulent flow. Finally, the empirical correlations of the turbulent mixing coefficient considering the effects of W/D and the Reynolds number were proposed using the RMS value of lateral velocity, which were in agreement with previous studies within a reasonable degree of accuracy.

초음속 유동에서 기저유동의 Detached Eddy Simulation

초음속 유동장 내의 축대칭 기저유동에 DES 기법을 적용하였다. 이 기법은 RANS 모드에서는 Spalart-Allmaras (S-A) 난류 모델을 사용하고, Large-eddy simulation (LES) 모드에서는 부격자 모델을 기반으로 하고 있다. LES 보다 비교적 적은 비용을 갖는 DES 기법을 사용하여 기저 유동장과 기저 압력을 정교게 예측할 수 있었다. 기저유동의 정확한 예측을 위해 경계층 두께, 운동량 두께, 표면마찰과 같은 기저 가장자리 유동 물성치를 Dutton 등의 실험과 비교하였다. DES는 하류영역에서의 전단층 말림, 큰 에디 운동, 재순환영역 내의 작은 에디 운동 같은 비정상 난류 운동의 물리적 현상을 잘 모사 하였다. 또한, 경험상수 <TEX>$C_{DES}$</TEX> 1.2를 사용한 현재 결과가 일반적인 경험상수 <TEX>$C_{DES}$</TEX> 0.65에 비해 실험과 잘 일치함을 보여준다. DES method is applied to an axisymmetric base flow at supersonic mainstream. The model is based on the Spalart-Allmaras (S-A) turbulence model in the RANS mode, and is based on the subgrid scale model in the Large-eddy simulation (LES) mode. Accurate predictions of the base flowfield and base pressure are successfully achieved by using the DES methodology which is less expensive than LES. Flow properties at the edge of base, such as boundary layer thickness, momentum thickness and skin fraction are compared with Dutton et al [experimental data to proper prediction of base flowfiled. From the present results, The DES accurately resolves the physics of unsteady turbulent motions, such as shear layer rollup, large-eddy motions in the downstream region and small eddy motions inside the recirculating region. Moreover, The present results of using an empirical constant <TEX>$C_{DES}$</TEX> of 1.2 shows good agreement with experimental data than conventional empirical constant <TEX>$C_{DES}$</TEX> of 0.65.

Existence theory of abstract approximate deconvolution models of turbulence

This report studies an abstract approach to modeling the motion of large eddies in a turbulent flow. If the Navier-Stokes equations (NSE) are averaged with a local, spatial convolution type filter, $$\overline{\bf \phi} = g_{\delta}\,*\,{\bf \phi}$$ , the resulting system is not closed due to the filtered nonlinear term $$\overline{\bf uu}$$ . An approximate deconvolution operator D is a bounded linear operator which is an approximate filter inverse $$D(\overline{\bf u}) = {\rm approximation\,of}\, {\bf u}.$$ Using this general deconvolution operator yields the closure approximation to the filtered nonlinear term in the NSE $$\overline{\bf uu} \simeq \overline{D(\overline{\bf u})D(\overline{\bf u})}.$$ Averaging the Navier-Stokes equations using the above closure, possible including a time relaxation term to damp unresolved scales, yields the approximate deconvolution model (ADM) $${\bf w}_{t} + \nabla \cdot \overline{D({\bf w})\,D({\bf w})} - \nu \triangle{\bf w}+\nabla q + \chi {\bf w}^* = \overline{\bf f} \quad {\rm and} \quad \nabla \cdot {\bf w} = 0.$$ Here $${\bf w} \simeq \overline{\bf u}$$ , χ ≥ 0, and w * is a generalized fluctuation, defined by a positive semi-definite operator. We derive conditions on the general deconvolution operator D that guarantee the existence and uniqueness of strong solutions of the model. We also derive the model’s energy balance.

On a well-posed turbulence model

This report considers mathematical properties, important for practical computations, of a model for the simulation of the motion of large eddies in a turbulent flow. In this model, closure is accomplished in the very simple way: <p align="center"> $\overline{u u} $˜ $\overline{\bar {u} \bar {u}}$, yielding the model<br> $\nabla \cdot w= 0, \quad w_{t} + \nabla \cdot (\overline{w w}) - \nu \Delta w + \nabla q = \bar {f}$. <p align="left" class="times"> In particular, we prove existence and uniqueness of strong solutions, develop the regularity of solutions of the model and give a rigorous bound on the modelling error, $||\bar {u} - w||$. Finally, we consider the question of non-physical vortices (false eddies), proving that the model correctly predicts that only a small amount of vorticity results when the total turning forces on the flow are small.

Computational Study of a Supersonic Base Flow Using Hybrid Turbulence Methodology

Large-eddy simulation/Reynolds-averaged Navier-Stokes (LES/RANS) hybrid methodology is applied to a high-Reynolds-number supersonic axisymmetric base flow. Accurate predictions of the base flowfield and base pressure are successfully achieved by using the LES/RANS hybrid methodology with less computational cost than that of pure LES and monotone integrated large-eddy simulation (MILES) approaches. Both the efficiency and reliability of the present LES/RANS hybrid methodology for the prediction of massively separated high-Reynolds-number flows are identified by comparison with the results obtained by LES, MILES, RANS, and the experiments in detail. The LES/RANS hybrid simulation accurately resolves the physics of unsteady turbulent motions, such as shear-layer rollup, large-eddy motions in the downstream region, small-eddy motions inside the recirculating region, and formation of large mushroom-shaped patterns in the end view

Hybrid Simulation Approach for Cavity Flows: Blending, Algorithm, and Boundary Treatment Issues

The maturation of high-performance computer architectures and computational algorithms has prompted the development of a new generation of models that attempt to combine the robustness and efficiency offered by the Reynolds averaged Navier-Stokes equations with the higher level of modeling offered by the equations developed for large eddy simulation. The application of a new hybrid approach is discussed, where the transition between these equation sets is controlled by a blending function that depends on local turbulent flow properties, as well as the local mesh spacing. The utilization of local turbulence properties provides added control in specifying the regions of the flow intended for each equation set, removing much of the burden from the grid-generation process. Moreover, the model framework allows for the combination of existing closure model equations, avoiding the difficulty of formulating a single set of closure coefficients that perform well in both Reynolds averaged and large eddy simulation modes. Simple modifications to common second-order accurate Reynolds averaged Navier-Stokes algorithms are proposed to enhance the capturing of large eddy motions

Hybrid Simulation Approach for Cavity Flows: Blending, Algorithm, and Boundary Treatment Issues

The maturation of high-performance computer architectures and computational algorithms has prompted the development of a new generation of models that attempt to combine the robustness and efficiency offered by the Reynolds averaged Navier-Stokes equations with the higher level of modeling offered by the equations developed for large eddy simulation. The application of a new hybrid approach is discussed, where the transition between these equation sets is controlled by a blending function that depends on local turbulent flow properties, as well as the local mesh spacing. The utilization of local turbulence properties provides added control in specifying the regions of the flow intended for each equation set, removing much of the burden from the grid-generation process. Moreover, the model framework allows for the combination of existing closure model equations, avoiding the difficulty of formulating a single set of closure coefficients that perform well in both Reynolds averaged and large eddy simulation modes. Simple modifications to common second-order accurate Reynolds averaged Navier-Stokes algorithms are proposed to enhance the capturing of large eddy motions

Large Eddy Simulation of Constant Heat Flux Turbulent Channel Flow With Property Variations: Quasi-Developed Model and Mean Flow Results

Turbulent planar channel flow has been computed for uniform wall heating and cooling fluxes strong enough to cause significant property variations using large eddy simulation. Channels with both walls either heated or cooled were considered, with wall-to-bulk temperature ratios as high as 1.5 for the heated case, and as low as 0.56 for the cooled case. An implicit, second order accurate finite volume scheme was used to solve the time dependent filtered set of equations to determine the large eddy motion, while a dynamic subgrid-scale model was used to account for the subgrid scale effects. Step-periodicity was used based on a quasi-developed assumption. The effects of strong heating and cooling on the flow were investigated and compared with the results obtained under low heating conditions.

Existence of weak solutions for a scale similarity model of the motion of large eddies in turbulent flow

In turbulent flow, the normal procedure has been seeking means of the fluid velocity u rather than the velocity itself. In large eddy simulation, we use an averaging operator which allows for the separation of large‐ and small‐length scales in the flow field. The filtered field denotes the eddies of size O(δ) and larger. Applying local spatial averaging operator with averaging radius δ to the Navier‐Stokes equations gives a new system of equations governing the large scales. However, it has the well‐known problem of closure. One approach to the closure problem which arises from averaging the nonlinear term is the use of a scale similarity hypothesis. We consider one such scale similarity model. We prove the existence of weak solutions for the resulting system.

Convergence of finite element approximations of large eddy motion

AbstractFluid motion in many applications occurs at higher Reynolds numbers. In these applications dealing with turbulent flow is thus inescapable. One promising approach to the simulation of the motion of the large structures in turbulent flow is large eddy simulation in which equations describing the motion of local spatial averages of the fluid velocity are solved numerically. This report considers “numerical errors” in LES. Specifically, for one family of space filtered flow models, we show convergence of the finite element approximation of the model and give an estimate of the error. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 689–710, 2002; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/num.10027.

Energy dissipation bounds for hear flows for a model in large eddy simulation

This report gives an upper bound for the time average of the energy dissipation rate, including energy dissipation due to viscous dissipation and turbulent diffusion in a model for the motion of large eddies in a turbulent flow. The bound is only a function of the reference velocity U, the domain diameter L, the eddy size δ, and surprisingly, the Reynolds number.

On "verifiability" of models of the motion of large eddies in turbulent flows

If the Navier-Stokes equations are averaged by a local, spacial filter (denoted by an over-bar) the following system results: $$\nabla \cdot {\overline{u}} = 0 \ \text{and}\ {\overline{u}}_t + {\overline{u}} \cdot \nabla {\overline{u}} - Re^{-1} \ \Delta {\overline{u}} + \nabla \cdot \mathbb R(u) + \nabla {\overline{p}} = {\overline{f}},$$ where $\mathbb R(u): = {\overline{u \ u}} - {\overline{u}} \ {\overline{u}}$ denotes the Reynold's stresses. To close this system, various models for the Reynold's stresses of the form $\mathbb R(u) \cong \tilde {\mathbb R}({\overline{u}})$ are used. The desire is that the solution to the resulting system (call it $w$) be close to ${\overline{u}}$. However, models are often validated instead by calculating $u$ and explicitly checking $||\mathbb R(u) - \tilde {\mathbb R}({\overline{u}})||$. This report studies conditions under which the latter being small implies $w$ is close to ${\overline{u}}$. (we call this {\it verifiability} of a model.) Since ${\overline{u}} \rightarrow u$ as $\delta \rightarrow 0$, we also study when it can be proven that $w\rightarrow u$ as $\delta \rightarrow 0$.

Analysis of Numerical Errors in Large Eddy Simulation

We consider the question of "numerical errors" in large eddy simulation. It is often claimed that straightforward discretization and solution using centered methods of models for large eddy motion can simulate the motion of turbulent flows with complexity independent of the Reynolds number and dependence only on the resolution ``$\delta$' of the eddies sought. This report considers this question analytically: Is it possible to prove error estimates for discretizations of actually used large eddy models whose error constants depend only on $\delta$ but not Re? We consider the most common, simplest, and most mathematically tractable model and the most mathematically clear discretization. In two cases, we prove such an error estimate and try to explain why our technique of proof fails in the most general case. Our analysis aims to assume as little time regularity on the true solution as possible.

Analysis of a Scale-Similarity Model of the Motion of Large Eddies in Turbulent Flows

In turbulent flow, the normal procedure has been to seek means ū of the fluid velocity u rather than the velocity itself. If these means are defined by local spacial averaging with an averaging radius of δ the approach is known as large eddy simulation, and ū denotes the eddies of size 0(δ) and larger. One approach to the closure problem which arises from averaging the nonlinear term is use of a scale-similarity hypothesis. We consider one such scale-similarity model. For this model we show the solution w to the model for ū converging to u as the averaging radius δ→0. We also show that the error ‖ū−w‖ is bounded by the modeling error (perhaps better termed “modeling residual”), evaluated on the true solution u. This last bound suggests one path to validating the model in either computational or physical experiments.

A Wind-Tunnel Study of Airflow in Waving Wheat: An EOF Analysis of the Structure of the Large-Eddy Motion

We have conducted an Empirical Orthogonal Functionanalysis (EOF) of a three dimensional, 2-pointvelocity covariance field, measured in a wind tunnel. The rate of convergence of the EOF sequence was usedas an objective test for the presence of distinctlarge turbulent structures. We found that in theroughness sublayer (2h > z > 0) the sequence convergedmuch more rapidly than in the lower surface layer(6h > z > 0), 75% of the total velocity variancebeing captured by the first three of 42 eigenmodes;h is the canopy height. The analysis was extended to three dimensions, whereover 50% of the variance and most of the spatialstructure of the covariance fields were captured by aneven smaller fraction of the total number ofeigenmodes. With some relatively weak additionalassumptions we were able to construct the velocityfield of a ‘characteristic eddy’ or large coherentstructure. This consisted of a pair ofcounter-rotating streamwise vortices centred above thecanopy. The sense of rotation of the vortex pair wasopposite to that found in the wall region of boundarylayers but matched that found in plane mixing layers. A strong gust or sweep motion generated between thevortices was responsible for most of the shear stresscarried by the large eddies. The region of significanttransport of streamwise momentum by the characteristiceddy is much smaller than the region of coherence of theeddy's velocity field.

Approximating the larger eddies in fluid motion V: Kinetic energy balance of scale similarity models

We first review a classical scale-similarity model used to simulate the motion of large eddies in a turbulent flow. The kinetic energy balance of this model is very unclear in theory. Experiments with it often have reported that an additional Smagorinski type subgridscale term is needed. This term is not benign; it can alter significantly the predicted long term dynamics of the large eddies. However, we also show that the principal of scale-similarity (introduced in 1980 by Bardina, Ferziger and Reynolds) can also give rise to other scale similarity models which have the correct kinetic energy balance.

Grid-averaged Lagrangian LES model for multiphase turbulent flow

A grid-averaged Lagrangian (GAL) model for dispersed particle motion in multiphase turbulent flow is presented to provide a large eddy simulation (LES) model for multiphase turbulent flow in which a quite large number of particles are involved. The GAL model is based on an averaging operation for a Lagrangian-type equation of motion of a particle over a computational grid volume and a procedure of reallocation of a dispersed particle cloud with its centroid movement to each grid. The model is therefore a mixed Eulerian–Lagrangian model which can effectively reduce computational time compared with existing Lagrangian-type models, without losing the advantage of Lagrangian-type models that they can properly describe the dynamical evolution of particles. Since the GAL model adopts the grid-volume averaging operation it can easily provide an effective SGS model for LES modeling of multiphase turbulent flow. The validity of the multiphase LES model developed, which is named the GAL-LES model, is confirmed through its application to a particle plume, in which the present model is found to simulate large-eddy motion usually observed in a jet and plume, and to give good agreements with experimental data.

An Air–Soil Layer Coupled Scheme for Computing Surface Heat Fluxes

Abstract An air–soil layer coupled scheme is developed to compute surface fluxes of sensible heat and latent heat from data collected at the Oklahoma Atmospheric Radiation Measurement–Cloud and Radiation Testbed (ARM–CART) stations. This new scheme extends the previous variational method of Xu and Qiu in two aspects: 1) it uses observed standard deviations of wind and temperature together with their similarity laws to estimate the effective roughness length, so the computed fluxes are nonlocal; that is, they contain the contributions of large-eddy motions over a nonlocal area of O(100 km2); and 2) it couples the atmospheric layer with the soil–vegetation layer and uses soil data together with the atmospheric measurements (even at a single level), so the computed fluxes are much less sensitive to measurement errors than those computed by the previous variational method. Surface skin temperature and effective roughness length are also retrieved as by-products by the new method.