Search Results (26)

Objectivity or material frame indifference is the indifference of material behavior to a Euclidean transformation (a general change of observer). This paper considers the objectivity of turbulent fields under a time-periodic change of the observer. At a given phase, the fluctuating velocity and Reynolds stress tensor fields are shown to be objective. This is further illustrated by presenting one-point statistics of two canonical flows: homogeneous isotropic turbulence and turbulent channel flow. The results also highlight that statistical symmetries such as homogeneity and stationarity found in the objective fields are carried over after a change of observer. The paper concludes with some final thoughts on objectivity and its usefulness for the advancement of turbulent theory. Full article

Investigating the creation of bed forms due to sediment transport and flow structure in the presence of bed forms in alluvial channels is a constant challenge for engineers and researchers, because of its complex nature. In this research, turbulent flow structure and turbulence anisotropy in the presence of two- and three-dimensional laboratory dunes were investigated. The results showed that, at the reattachment point, the turbulence anisotropy at the centerline of a three-dimensional dune was the largest. On the stoss slope, the turbulence anisotropy for two-dimensional dunes was at its highest at the bed form’s trough and below the crest. The results also demonstrated a tendency at the crest line toward the plane–strain limit for two-dimensional dunes and the centerline of three-dimensional dunes. However, at a 20 cm distance, turbulence anisotropy at the crest line tended toward asymmetric contraction to an oblate spheroid. Full article

The interrelation between Reynolds stresses and their dissipation rate tensors for different Karlovitz number values was analysed using a direct numerical simulation (DNS) database of turbulent statistically planar premixed H₂-air flames with an equivalence ratio of 0.7. It was found that a significant enhancement of Reynolds stresses and dissipation rates takes place as a result of turbulence generation due to thermal expansion for small and moderate Karlovitz number values. However, both Reynolds stresses and dissipation rates decrease monotonically within the flame brush for large Karlovitz number values, as the flame-generated turbulence becomes overridden by the strong isotropic turbulence. Although there are similarities between the anisotropies of Reynolds stress and its dissipation rate tensors within the flame brush, the anisotropy tensors of these quantities are found to be non-linearly related. The predictions of three different models for the dissipation rate tensor were compared to the results computed from DNS data. It was found that the model relying upon isotropy and a linear dependence between the Reynolds stress and its dissipation rates does not correctly capture the turbulence characteristics within the flame brush for small and moderate Karlovitz number values. In contrast, the models that incorporate the dependence of the invariants of the anisotropy tensor of Reynolds stresses were found to capture the components of dissipation rate tensor for all Karlovitz number conditions. Full article

A fully developed turbulent flow in a concentric annulus, Re $=\mathrm{10,000}$, $r_i/r_o=0.5$, with an inner rotating cylinder in the velocity range $N=U_{\omega }/U_b=0÷4$, is studied via a large-eddy simulation. Also, for comparison, simulations by steady-state, unstatiounary RANS k-$\omega$ SST (URANS), and Elliptic Blending Model (EBM) were made. The main focus of this study is on the effect of high rotation on the mean flow, turbulence statistics, and vortex structure. Distribution of the tangential velocity and the Reynolds stress tensor change their behaviour at $N>0.5\sim 1$. With rotation increases, the production of tangential fluctuation becomes dominant over axial ones and the position of turbulent kinetic energy maximum shifts towards the wall into the buffer zone. URANS and EBM approaches show good agreement with LES in mean flow, turbulent statistics, and integral parameters. The difference in pressure loss prediction between LES and URANS does not exceed 20%, but the average difference is about 11%. The EBM approach underestimates pressure losses up to 9% and on average not more than 5%. Vortex structures are described well by URANS. Full article

One of the most commonly used techniques in aerospace engineering is the RANS (Reynolds average Navier–Stokes) approach for calculating the transonic compressor flow field, where the accuracy of the computation is significantly affected by the turbulence model used. In this work, we use SA, SST, k-ɛ, and the PAFV turbulence model developed based on the side-biased mean fluctuations velocity and the mean strain rate tensor to numerically simulate the transonic compressor NASA Rotor 67 to evaluate the accuracy of turbulence modeling in numerical calculations of transonic compressors. The simulation results demonstrate that the four turbulence models are generally superior in the numerical computation of NASA Rotor 67, which essentially satisfies the requirements of the accuracy of engineering calculations; by comparing and analyzing the ability of the four turbulence models to predict the aerodynamic performance of transonic compressors and to capture the details of the flow inside the rotor. The errors of the Rotor 67 clogging flow rate calculated by the SA, SST, k-ɛ, and PAFV turbulence models with the experimental data are 0.9%, 0.8%, 0.7%, and 0.6%, respectively. The errors of the calculated peak efficiencies are 2.2%, 1.6%, 0.9%, and 4.9%. The SA and SST turbulence models were developed for the computational characteristics of the aerospace industry. Their computational stability is better and their outputs for Rotor 67 are comparable. The k-ɛ turbulence model calculates the pressure ratio and efficiency that are closest to the experimental data, but the computation of its details of the flow field near the wall surface is not ideal because the k-ɛ turbulence model cannot accurately capture the flow characteristics of the region of high shear stresses. The PAFV turbulence model has a better prediction of complex phenomena such as rotor internal shock wave location, shock–boundary layer interaction, etc., due to the use of a turbulent velocity scale in vector form, but the calculated rotor efficiency is small. Full article

Modeling has become firmly established as a methodology to close the Reynolds-averaged Navier–Stokes (RANS) equations, owing to theoretical and empirical efforts towards a complete formulation of the Reynolds stress tensor and, recently, breakthroughs in data-processing technology. However, mathematical exactness is not generally ensured by modeling, which is an intrinsic reason why the reliability of RANS closure models is not supposed to be consistent for all kinds of turbulent flow. Rather than straightforwardly overcoming this inherent limitation, most of the studies to date were reasonably directed towards broadening the range of turbulent flows, where reliable prediction accuracy can be obtained via modeling. In this paper, we present three identities between components of the Reynolds stress tensor, constructed via spatial mapping on the basis of the differential version of the Gauss–Bonnet formula. Further, we present a constraint condition that gives a set of equations as numerous as the parameters within a RANS model. Full article

This article focuses on entropy generation in the combustion field, which serves as a useful indicator to quantify the interaction between turbulence and combustion. The study is performed on the direct numerical simulations (DNS) of high pressure non-premixed and premixed swirling flames. By analyzing the entropy generation in thermal transport, mass transport, and chemical reactions, it is found that the thermal transport, driven by the temperature gradient, plays a dominant role. The enstrophy transport analysis reveals that the responses of individual terms to combustion can be measured by the entropy: the vortex stretching and the dissipation terms increase monotonically with the increasing entropy. In high entropy regions, the turbulence behaves as the “cigar shaped” state in the non-premixed flame, while as the axisymmetric state in the premixed flame. A substantial increase in the normal Reynolds stress with the entropy is observed. This is due to the competition between two terms promoted by the entropy, i.e., the velocity–pressure gradient correlation term and the shear production term. As a result, the velocity–pressure gradient correlation tends to isotropize turbulence by transferring energy increasingly from the largest streamwise component to the other smaller normal components of Reynolds stress and is dominated by the fluctuating pressure gradient that increases along the entropy. The shear production term increases with the entropy due to the upgrading alignment of the eigenvectors of strain rate and Reynolds stress tensors. Full article

This work presents a semi-analytical method for laminar steady-state channel and pipe flows of viscoelastic fluids using the Linear Phan-Thien-Tanner (LPTT) constitutive equation, with solvent viscosity contribution. For the semi-analytical method validation, it compares its results and two analytical solutions: the Oldroyd-B model and the simplified LPTT model (without solvent viscosity contribution). The results adopted different values of the dimensionless parameters, showing their influence on the viscoelastic fluid flow. The results include the distribution of the streamwise velocity component and the extra-stress tensor components in the wall-normal direction. In order to investigate the proposed semi-analytical method, different solutions were obtained, both for channel and pipe flows, considering different values of Reynolds number, solvent viscosity contribution in the homogeneous mixture, elongational parameter, shear parameter, and Weissenberg number. The results show that the proposed semi-analytical method can find a laminar solution using the non-Newtonian LPTT model with solvent viscosity contribution and verify the effect of the parameters in the resulting flow field. Full article

Liquid fuel nuclear reactors offer innovative possibilities in terms of nuclear reactor designs and passive safety systems. Molten Salts Reactors (MSRs) with a fast spectrum are a particular type of these reactors using liquid fuel. MSFRs often involve large open cavities in their core in which the liquid fuel circulates at a high speed to transport the heat generated by the nuclear reactions into the heat exchangers. This high-speed flow yields a turbulent field with large Reynolds numbers in the reactor core. Since the nuclear power, the neutron precursor’s transport and the thermal exchanges are strongly coupled in the MSFR’s core cavity, having accurate turbulent models for the liquid fuel flow is necessary to avoid introducing significant errors in the numerical simulations of these reactors. Nonetheless, high-accuracy simulations of the turbulent flow field in the reactor cavity of these reactors are usually prohibitively expensive in terms of computational resources, especially when performing multiphysics numerical calculations. Therefore, in this work, we propose a novel method using a modified genetic algorithm to optimize the calculation of the Reynolds Shear Stress Tensor (RST) used for turbulence modeling. The proposed optimization methodology is particularly suitable for advanced liquid fuel reactors such as the MSFRs since it allows the development of high-accuracy but still low-computational-cost turbulence models for the liquid fuel. We demonstrate the applicability of this approach by developing high accuracy Reynolds-Averaged Navier–Stokes (RANS) models (averaged flow error less than 5%) for a low and a large aspect ratio in a Backward-Facing Step (BFS) section particularly challenging for RANS models. The newly developed turbulence models better capture the flow field after the boundary layer tipping, over the extent of the recirculation bubble, and near the boundary layer reattachment region in both BFS configurations. The main reason for these improvements is that the developed models better capture the flow field turbulent anisotropy in the bulk region of the BFS. Then, we illustrate the interest in using this turbulence modeling approach for the case of an MSFR by quantifying the impact of the turbulence modeling on the reactor key parameters. Full article

Herein, hydrodynamic analysis from a large-eddy simulation in Couette–Taylor–Poiseuille (CTP) geometry is numerically investigated. The present geometry is inspired by a previous experimental work in which heat transport phenomena were investigated in a heat recovery system devoted to a rotary kiln facility. The streamwise and spanwise components of the velocity and the Reynolds stress tensor are firstly validated using an experimental benchmark. The effect of the axial flow rates is studied at a fixed rotational velocity. It is shown that the streamwise velocity component damps the vortex flow organization known in Couette–Taylor (CT) flow. The bulk region and its wall footprint are therefore characterized by various methods (spectral and statistical analysis, Q-criterion). It is shown that the turbulent kinetic energy of the streamwise component in the near-wall region is augmented leading to a multi-scale nature of turbulence. Full article

Methodologies to be used in numerical models based on Reynolds-averaged Navier–Stokes (RANS) equations and the volume of fluid (VoF) to deal with waves over coastal structures, which involve wave breaking and overtopping and porous structures, are shown in this manuscript. Two turbulence models, k-ε NLS (non-linear Reynolds stress tensor) and k-ε SCM (stabilized closure model), that are used to avoid the growth of the eddy viscosity, are implemented in the FLUENT^® numerical model. Additionally, equations of momentum and turbulence models are adapted to simulate porous media of coastal structures. Comparisons of performance of k-ε NLS, k-ε SCM and standards k-ε and k-ω SST models in several classical cases of regular and random waves on coastal structures are carried out. It was noticed that the standard k-ε turbulence model, and k-ω SST with less intensity, over-predicted eddy viscosity, caused the decay of the free surface elevation and under-estimated wave overtopping discharge. k-ε NLS and k-ε SCM turbulence models have similar performance, with slightly better results of k-ε NLS, showing good agreement with experimental ones. Full article

Direct numerical simulation (DNS) of a droplet-laden, turbulent Couette airflow over a waved water surface is performed modeling the marine atmospheric boundary (MABL) layer carrying idealized spume droplets. Both the instantaneous and mean flow properties, the characteristics of the vortex structures and the momentum exchange between air turbulence and waved water surface and droplet-mediated momentum transfer are investigated. A Eulerian–Lagrangian approach is employed in DNS where full, 3D Navier–Stokes equations for the carrier air are solved in a Eulerian frame, and the trajectories of individual droplets are simultaneously tracked in a Lagrangian frame. The impact of the droplets on the carrier air flow is modeled via a point force approximation. The droplets size is considered in the range of spume droplet sizes observed in MABL. Various water surface roughness and droplet injection scenarios are considered, and both instantaneous and phase-averaged flow fields, the Reynolds stresses and the eigenvalues of the local air velocity gradient tensor are evaluated in DNS. Numerical results show a strong dependence of the droplet-mediated airflow modification on-the-droplet injection mechanism. Droplets injected with the surrounding air velocity effectively mitigate the vortex structures by reducing their swirling strength and suppress the momentum flux from air turbulence to water surface by weakening both ejections and sweeping events, and thus accelerating the mean flow as compared to the droplet-free flow. On the other hand, droplets injected with the velocities of the Lagrangian particles of the water surface enhance both the swirling strength of the vortex structures and air-flow turbulent stresses and decelerate the mean wind. The results also show that these effects of droplet-mediated flow modification become less pronounced as the water surface wave steepness increases. Full article

The characterisation of small-scale turbulence has been an active area of research for decades and this includes, particularly, the analysis of small-scale isotropy, as postulated by Kolmogorov. In particular, the question if the dissipation tensor is isotropic or not, and how it is related to the anisotropy of the Reynolds stresses is of particular interest for modelling purposes. While this subject has been extensively studied in the context of isothermal flows, the situation is more complicated in turbulent reacting flows because of heat release. Furthermore, the landscape of Computational Fluid Dynamics is characterised by a multitude of methods ranging from Reynolds-averaged to Large Eddy Simulation techniques, and they address different ranges of scales of the turbulence kinetic energy spectrum. Therefore, a multiscale analysis of the anisotropies of Reynolds stress, dissipation and sub-grid scale tensor has been performed by using a DNS database of statistically planar turbulent premixed flames. Results show that the coupling between dissipation tensor and Reynolds stress tensor is weaker compared to isothermal turbulent boundary layer flows. In particular, for low and moderate turbulence intensities, heat release induces pronounced anisotropies which affect not only fluctuation strengths but also the characteristic size of structures associated with different velocity components. Full article

This work experimentally investigates the turbulent flow characteristics of developing and fully-developed flows over a rough bed channel that is subjected to downward seepage. Instantaneous 3D velocities were collected using an acoustic Doppler velocimeter (ADV) in the developing and fully-developed flow regions, along the channel centerline, to analyze different turbulent statistics. Observations revealed that the streamwise and vertical velocities were higher in developing flows, whereas the Reynolds shear stresses, and turbulence intensities, were smaller. The downward seepage would affect the velocity distributions and flow depth in both the developing and fully-developed regions. Therefore, new equations to represent the distribution of the turbulence intensities were proposed, and a comparison with the current literature is provided. The investigation of the Reynolds stress anisotropy tensors concludes that the degree of anisotropy in fully-developed flows is lower than for developing flows. Full article

Due to their interesting thermal properties, liquid metals are widely studied for heat transfer applications where large heat fluxes occur. In the framework of the Reynolds-Averaged Navier–Stokes (RANS) approach, the Simple Gradient Diffusion Hypothesis (SGDH) and the Reynolds Analogy are almost universally invoked for the closure of the turbulent heat flux. Even though these assumptions can represent a reasonable compromise in a wide range of applications, they are not reliable when considering low Prandtl number fluids and/or buoyant flows. More advanced closure models for the turbulent heat flux are required to improve the accuracy of the RANS models dealing with low Prandtl number fluids. In this work, we propose an anisotropic four-parameter turbulence model. The closure of the Reynolds stress tensor and turbulent heat flux is gained through nonlinear models. Particular attention is given to the modeling of dynamical and thermal time scales. Numerical simulations of low Prandtl number fluids have been performed over the plane channel and backward-facing step configurations. Full article