Modelling Turbulent Flows near Coastal Structures Using Various Turbulence Models

This paper is devoted to the challenges arising in Reynolds-Averaged Navier-Stokes (RANS) modeling of confined coaxial jet mixing. The main drawbacks of the gradient diffusion hypothesis and of the constant turbulent Schmidt number approach for the considered flow type are elucidated. In the first part of the present work, the mean and fluctuating velocity and scalar fields obtained in RANS simulations are directly validated against experimental data and compared with large-eddy simulation (LES) results. Three different turbulence models and three different turbulent Schmidt numbers values are selected for the present RANS computations. The accuracy given by LES is superior in comparison to RANS results especially for scalar mixing. The inability of the chosen RANS approach to represent counter-gradient diffusion in the axial direction characteristic for the considered test case is discussed. In the second part of the present study, the time-averaged mean and fluctuating velocity and scalar fields from LES are used for the evaluation of turbulent viscosities, turbulent scalar diffusivities, and turbulent Schmidt numbers as they appear in the RANS equations. Specific problems of the evaluation of these parameters from LES data are addressed. The importance of accounting for the turbulent scalar fluxes in all coordinate directions for evaluation of turbulent scalar diffusivity is revealed. The values obtained from LES results are compared with those given by RANS modeling. The deviations and their consequences for RANS predictions are discussed.

A computational study of the HyShot II combustor performance

Oscillatory flows over a flat plate are studied by using Large Eddy Simulation (LES) and Reyn- olds-Average Navier-Stokes (RANS) methods. A dynamic subgrid scale (SGS) model is employed in LES, while the Saffman's turbulence model in RANS. The mean velocity profile, the turbulence intensity, and the wall shear stress are computed and compared with earlier experimental and numerical works. The results indicate that the flow behaviors are quite different during the accelerating and decelerating phases of the oscillating cycle. The transition from laminar to turbulent is also investigated as a function of the Reynolds number, R, which represents the square of the ratio of the oscillation amplitude at free stream to the thickness of the Stokes layer at the plate. The present results both from LES and RANS show that the transition occurs in the range of 5 3 10 4 < R <5 3 10 5 . The evolution of the flow structure in the Stokes layer during the transition from laminar to turbulent is clearly demonstrated from the numerical results. The friction coefficient of the amplitude of oscil- latory surface shear stress varies as R 20.5 with a phase angle of 457 in laminar regime and transition to R 20.23 with a phase angle of about 107 in turbulence regime. These variations in the surface shear stress with the Reynolds number are in excellent agreement with the earlier experimental results of Kamphuis and the numerical results of Blondeaux. The excellent agreement between the LES and RANS demonstrated that Saffman's tur- bulence model, as originally intended by Saffman, is applicable for unsteady flows.

The critical review discusses the most accurate methods for description of turbulent flows: the computationally very expensive direct numerical simulation (DNS) and slightly less accurate and slightly less expensive large eddy simulation (LES) methods. Both methods have found their way into nuclear thermal hydraulics as tools for studies of the fundamental mechanisms of turbulence and turbulent heat transfer. In the first section of this critical review, both methods are briefly introduced in parallel with the basic properties of the turbulent flows. The focus is on the DNS method, the so-called quasi-DNS approach, and the coarsest turbulence modeling approach discussed in this work, which is still on the very small-scale, wall-resolved LES. Other, coarser turbulence modeling approaches (such as wall-modeled LES, Reynolds Averaged Navier-Stokes (RANS)/LES hybrids, or RANS) are beyond the scope of the present work. Section II answers the question: “How do the DNS and LES methods work?” A short discussion of the computational requirements, numerical approaches, and computational tools is included. Section III is about the interpretation of the DNS and LES results and statistical uncertainties. Sections IV and V give some examples of the DNS and wall-resolved LES results relevant for nuclear thermal hydraulics. The last section lists the conclusions and some of the challenges that might be tackled with the most accurate techniques like DNS and LES.

The goal of this study is to develop advanced numerical models and algorithms to improve the accuracy of engine spray combustion simulation. This study developed a large eddy simulation (LES) turbulence model and adaptive mesh refinement (AMR) algorithms to enhance the accuracy and computational efficiency of engine simulation. The LES approach for turbulence modeling is advantageous over the traditional Reynolds Averaged Navier Stokes (RANS) approach due to its capability to obtain more detailed flow information by resolving large-scale structures which are strongly geometry dependent. The current LES approach used a one-equation, non-viscosity, dynamic structure model for the sub-grid stress tensor and also used a gradient method for the sub-grid scalar fluxes. The LES implementation was validated by comparing the predicted spray penetrations and structures in a non-evaporating diesel spray. The present LES model, when coupled with spray breakup and detailed chemistry models, were able to predict the overall cylinder pressure history, heat release rate data, and the trends of NOx and soot emissions with respect to different injection timings and EGR levels in a heavy-duty diesel engine. Results also indicated that the LES model could predict the unsteadiness of in-cylinder flows and have the potential to provide more detailed flow structures compared to the RANS model. AMR algorithms were also developed to improve transient engine spray simulation. It is known that inadequate spatial resolution can cause inaccuracy in spray simulation using the stochastic Lagrangian particle approach due to the over-estimated diffusion and inappropriate

The explicit filtering method for large eddy simulations of a turbulent premixed flame

The flow field developing inside the stator-rotor disc cavities of gas turbines is characterized by highly complex and unsteady behavior driven by strong vortical structures and transient interactions. These features pose significant challenges for accurate prediction using standard Computational Fluid Dynamics models. In particular, the inherent unsteadiness of the flow field has a considerable impact on the sealing performance of the rim, especially when predicted by steady Reynolds-Averaged Navier-Stokes (RANS) methods, which tend to overestimate the sealing effectiveness by more than an order of magnitude. In this study, a series of numerical simulations were conducted using RANS, unsteady RANS (URANS), and large Eddy Simulation (LES) approaches to gain insight into the behaviour of the rim seal flow. The main objective was to compare the numerical results with experimental data obtained from the test rig at the University of Florence, in order to validate the accuracy of different numerical approaches. The RANS, URANS and LES simulations all demonstrated satisfactory agreement in terms of steady-state measurements of pressure coefficients and velocity fields, offering valuable insight into the time-averaged behavior of the flow. However, the Reynolds-averaged models failed to effectively capture the turbulent fluctuations between the main flow and the secondary flow. In contrast, LES simulations accurately captured the development of vortices and replicated more realistic flow conditions, resulting in a closer match with experimental data. Therefore, the resolution of these fluctuations, which are nowadays considered to be one of the fundamental factors driving the ingestion of mainstream flow into the cavity, appeared to be crucial to accurately understand the unsteady interaction between mainstream and secondary flows. Although the high computational cost and long transient phases required to reach periodic convergence make LES a resource-intensive approach, it demonstrates great potential for accurately predicting this interaction and providing valuable insights into the complex flow dynamics of rim seal flows.

Beach lowering and the effects of scour in front of coastal defences and erosion protection structures are recognised as a principle cause of their failure including collapse/breaching and washing out of fill materials. Both localised scour and more widespread beach lowering can lead to undermining of the Toe (see Figure 1 for definition). This can promote structural instability and result in partial or total collapse with subsequent reduction in, or loss of performance for flood defence or erosion protection. Lowering of the ‘ground levels’ in front of seawalls, revetments or other coastal structures is a common phenomenon not only in the U.K. but also around the world. Toe scour is a serious and costly problem – moreover, it is one which is not limited to any particular coastal environment or to any particular type of defence structure. The prevention of, design for, and management of beach lowering and scour at the Toe of coastal structures is an important factor in the management of those structures. Understanding, designing for and managing toe scour at coastal structures therefore is a key issue for coastal managers, designers and engineers. To date there has been no guidance available tailored specifically to meet these needs. Recognising this, the Defra/ Environment Agency Flood and Coastal Risk Management programme commissioned the development of guidance on the management of the Toe of coastal structures in 2008 (Toe Scour Guide). The guide draws together recent key research and development work on beach lowering and scour including ‘Understanding the Lowering of Beaches in Front of Coastal Defence Structures’ (Sutherland et al, 2006, 2008). It is also integrating work on performance and reliability of coastal structures developed through the Performance-based Asset Management Project (PAMS) including performance analysis and asset inspection methods. This paper reflects on and highlights some of the developments made in the preparation of the guide.

Dynamic procedures, typically motivated by scale-similarity concepts, have proven highly successful and are widely used in Large Eddy Simulation (LES) for determining model coefficients. However, in hybrid Reynolds-Averaged Navier–Stokes (RANS)/LES approaches, excessively coarse grids can undermine scale-similarity-based dynamic procedures: the turbulence mode implied by the test filter scale may be inconsistent with that of the grid filter. In this study, we derive a consistent dynamic model (CDM) by minimizing dependence of stress on the turbulence-resolution length scale, thereby ensuring consistency between RANS and LES modes. The CDM is capable of recovering the standard dynamic model (SDM) in regions far from the wall, while smoothly transitioning to the RANS mode near the wall. A priori tests in homogeneous isotropic turbulence show that, as filter width increases, the SDM coefficient quickly decays toward zero, whereas the CDM remains consistent with Direct Numerical Simulation (DNS)-calibrated values, demonstrating broader applicability. A posteriori tests in turbulent channel flow confirm that the CDM avoids underprediction of CDES near the wall and accurately distinguishes between RANS and LES regions without additional wall treatments. Consequently, mean and fluctuating quantities predicted on coarse grids agree better with experimental data and scaling laws than those from LES and the SDM. In periodic hill simulations, the CDM also predicts separation and reattachment points closer to high-resolution LES, further validating its ability to capture separated flows on coarse grids.

The separated turbulent flow past an inclined flat plate with sharp leading and trailing edges was computed based on three different simulation approaches for a reynolds number Rec= 20000 and a high angle of attack α=18°. The simulation techniques applied were the Reynolds‐averaged Navier–Stokes (RANS) equations combined with a one‐equation Spalart–Allmaras turbulence model, the large‐eddy simulation (LES) based on an algebraic eddy‐viscosity model, and a hybrid approach known as detached‐eddy simulation (DES) applying a slightly modified Spalart–Allmaras model in the entire integration domain. DES is a non‐zonal coupling technique of RANS and LES developed in the hope of reducing the large computational resources required for LES computations of turbulent flows with practical relevance. However, the objective of the present study was not to compare the resources (CPU time, memory) required for all three techniques but to investigate and evaluate the quality of the predicted results for RANS, DES and LES. For this purpose, a test case which is favourable to the basic concept of DES and which places special emphasis on the LES part of the DES concept was chosen. This last issue was important since the modified Spalart–Allmaras model applied as a subgrid scale model in the LES part is not as well validated as other models usually applied in LES. For this purpose, an LES prediction on a very fine grid served as a reference case for the evaluation. For all three techniques, predictions with different grid resolutions were carried out and compared with each other based on important integral parameters (e.g. Strouhal number, mean drag and lift coefficients and their standard deviations), the instantaneous and time‐averaged flow structures, and higher‐order statistics. As expected, the pure RANS calculation, although applied as unsteady RANS, failed to predict the unsteady characteristics of the separated flow. In contrast, the DES approach yielded reasonably the shedding phenomenon and some integral parameters. However, analysing the results in more detail led to remarkable deviations between the DES and LES predictions also when the same grid resolution was applied. Especially the free shear layer originating from the leading edge of the plate was not well reproduced by DES, showing strong deficiencies of the model applied as a subgrid scale model. The reasons for this behaviour of the model were analysed in detail. Two basic causes were identified; the first is given by some near‐wall corrections in the finite Reynolds number version of the model which are not working properly in the LES mode of DES. The second is a modified definition of the filter width typically applied for DES, leading to strongly increased values of the eddy viscosity. A revised version of the S–A model taking both issues seriously into account was used as a subgrid scale model in the LES mode. As a direct consequence, much better agreement with the reference LES solution was found for the DES prediction on the coarse grid, eliminating the deficiencies of the original formulation. Copyright© 2003 John Wiley &amp; Sons, Ltd.

Aero-thermal characteristics of transitional flow through a highly loaded transonic linear turbine are studied at the design incidence using computational methods. The three-dimensional compressible turbulent flow through a turbine inlet guide vane is simulated using finite-volume method-based fluid flow solutions using both Reynolds-averaged Navier Stokes (RANS) equations-based turbulence models, and a dynamic large eddy simulation (LES) approach which is based on a Smagorinsky-Lilly subgrid scale (SGS) model. The calculations are made for exit isentropic Mach numbers ranging from 0.7 to 1.1, and for Reynolds numbers ranging from 5 × 105 to 2 × 106. The numerical results obtained from different turbulence model simulations are compared with each other, and with the experimental data available in the open literature in terms of integrated flow parameters, such as pressure and heat transfer coefficients for varying exit Mach and Reynolds numbers. The present numerical approach indicates a guide line that the present LES approach can be a reliable choice for turbomachinery flows.

The continuous casting of steel in commercial use: K. P. Korotkovet al.: (Translated from the Russian). Pergamon Press, Oxford, 1960. 171 pp. + ix, 50s

Numerical simulations based on Reynolds-averaged Navier Stokes (RANS) models are still the work-horse tool in engineering design involving turbulent flows. Two decades ago, when LES started gaining popularity thanks to the increasing availability of computational resources, it was widely expected that it would have gradually replaced RANS methods in industrial CFD for decades to come. In the past two decades, however, while LES-based methods gained widespread applications and the earlier hope did not diminish, the predicted time when LES would replace RANS has been significantly delayed. Most industrial users are probably decades away from any routine use of scale resolving simulations, not to mention the cost, time and user skill it take to run these computations. In brief, RANS solvers, particularly those based on standard eddy viscosity models (e.g k-e, k-ω, S-A and k-ω SST) are expected to remain the workhorse in the CFD of high Reynolds number flows for decades. However, predictions from RANS simulations are known to have large discrepancies in many flows of engineering relevance, including those with swirl, pressure gradients, or mean streamline curvature. It is a consensus that the dominant cause for such discrepancies is the RANS-modeled Reynolds stresses. In light of the long stagnation in traditional turbulence modeling, researchers explored machine learning as an alternative to improve RANS modeling by leveraging data from highfidelity simulations. The goal is to make use of vast amounts of turbulent flows data, machine learning techniques and current understanding of turbulence physics to develop models with better predictive capabilities in the context of RANS simulations. Recently, in a seminar work, Ling et al (2016) developed a neural network architecture capable of embedding invariance properties into the Reynolds stress tensor predicted in output. Such a network, named the tensor basis neural network (TBNN), was applied to a variety of flow fields with encouraging results compared to both classical turbulence models and neural networks that do not preserve Galilean invariance. Yet, as in most data driven turbulence modelling approaches, the TBNN was used as a post-processing tool to correct the Reynolds stress tensor field predicted by a RANS simulation run with standard closure models. This means that, theoretically, the network can be applied only to correct the Reynolds stress tensor for the same RANS model on which it has been trained since, in general, different turbulence models yield different results depending on the flow type. Moreover, there is no physisical insight that suggests a relation between the RANS velocity gradients - used as inputs of the machine learning model - and the true Reynolds stress tensor. Differently, in this work a network with a similar architecture to the Ling’s one was trained and tested on a database of high-fidelity data of eight different flows to learn a functional mapping between the inputs of Pope’s General Eddy Viscosity Model and the anisotropic part of the Reynolds stress tensor. Then the network was embedded into a CFD RANS solver as a replacement of the standard closure model - and therefore called at every solver’s iteration. Lasty, the RANS solver with embedded TBNN was be tested on a canonical flow case - turbulent channel flow - to evaluate its performances. As for the organization of this work: in Chapter 1 further details on the data driven turbulence modelling will be given, RANS models and equations will be introduced and also an introduction to Neural Networks will be presented. In Chapter 2, it will be given a detailedexplanation of the RANS CFD solver and the neural network’s implementation. In Chapter 3, the method will be tested on a turbulent channel flow case and the results will be discussed. Lastly, in Chapter 4, some meaningful conclusions will be drawn.

The work presents comparative results between wall friction and pressure coefficient predictions from Large Eddy Simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) computations in channel flows with an adverse pressure gradient created by a 2-D bump. LES results are obtained using the semi-spectral code, MFLOPS3D, developed at Laboratoire de Mecanique de Lille, while RANS solutions are computed using a commercial code based on 2nd-order finite volume discretization with typical two-equation turbulence models and one seven-equation Reynolds stress transport model. Reynolds numbers range from Reτ = 617 to 2000, based on the friction velocity at the channel inlet. It is found that LES produces very consistent results when compared to DNS or other highly resolved LES. Two-equation and seven-equation RANS models are found to correctly predict friction coefficients in zero and favorable pressure gradient regions, but they fail in regions of adverse pressure gradients. The Reynolds stress transport model shows a better performance when compared to two-equation eddy-viscosity models, particularly in the higher Reynolds number cases. However, none of the RANS models is able to capture the full physics of turbulence related with adverse pressure gradients. The limitations of RANS models are observed both in separated and attached flow conditions at the rear portion of the bump. Such limitations seem to be related to the fact that these models do not correctly describe the evolution of the turbulent kinetic energy close to the walls in adverse pressure gradient regions.

Turbulent flow and heat transfer past a cube (L × L × L) mounted on one wall of a channel of height 2L have served as a benchmark problem to validate computational methods and turbulence models because of the richness in the flow features induced by an unassumingly simple geometry. These include an unstable bi-modal horse-shoe vertical structure upstream of the cube, vortex shedding from the two sides of the cube that extend to the aft of the cube, and periodic separation from the top of the cube. In this study, simulations based on steady and unsteady Reynolds-Averaged Navier-Stokes (RANS and URANS) and large-eddy simulations (LES) were performed to understand the nature of the flow and how that flow affects pressure, drag, and surface heat transfer distributions. For RANS and URANS, the following turbulence models were assessed: the realizable k−ε model, the shear-stress transport (SST) model with and without corrections for curvature, the Reynolds stress model with linear pressure strain (RSM-LPS), and the stress-omega Reynolds stress model. In this study, the RANS and URANS results were generated by using the ANYSYS Fluent code, and the LES results were generated by using the PowerFlow code. Results obtained show RANS to be unacceptable in predicting the reattachment of the separation bubble downstream of the cube. URANS by being able to resolve the oscillatory shedding from the two sides of the cube was able to predict the reattachment with reasonable accuracy. URANS with the SST model that has the curvature correction gave the best results for the reattachment length downstream of the cube (relative error within 5% of the experimental data). Also, this model was able to capture all details of the flow features revealed in the experimental oil-flow study with considerable accuracy. However even with this model, the predicted pressure just downstream of the cube is incorrect by up to 50%. This is because URANS was unable to predict the unstable bi-modal, horse-shoe vortex system upstream of the cube induced by interactions between the spanwise vortices in the turbulent boundary layer and the horsehoe vortex system. This interaction was found to cause the separation bubble on top of the cube to shed periodically. By being able to capture this interaction, LES was able to better predict the pressure just downstream of the cube. This shows why LES is needed and why RANS and URANS are inadequate unless those models can be modified to account for these unsteady interactions. Steady and unsteady RANS based on the SST model were also employed to study the heat transfer about the surface of the cube. Reasonably good results were obtained for the leading and trailing faces of the cube but not for the top and the two side faces. A parametric study on the effects of the turbulent Prandtl number show the connection between the turbulent eddy viscosity and the turbulent thermal conductivity cannot be represented by a simple algebraic equation, the Prandtl number. Thus, better RANS models are needed to capture the physics embedded in the correlations between the fluctuating velocities and temperatures. A paper on this work is being prepared. The order of authorship will be X. Chi, K, Adeel Ahmad, Surya Muthukannan Chinnamani, and T. I-P. Shih. The author of this abstract thanks his students who worked on the different parts of this problem.