The buoyancy-driven fluid flow and heat transfer in a square cavity with partially active side walls filled with Cu–water nanofluid is investigated numerically. The active parts of the left and the right side walls of the cavity are maintained at temperatures and , respectively, with . The enclosure’s top and bottom walls as well as the inactive parts of its side walls are kept insulated. The governing equations in the two-dimensional space are discretized using the control volume method. A proper upwinding scheme is employed to obtain stabilized solutions. Using the developed code, a parametric study is undertaken, and the effects of the Rayleigh number, the locations of the active parts of the side walls, and the volume fraction of the nanoparticles on the fluid flow and heat transfer inside the cavity are investigated. It is observed from the results that the average Nusselt number increases with increasing both the Rayleigh number and the volume fraction of the nanoparticles. Moreover, the maximum average Nusselt number for the high and the low Rayleigh numbers occur for the bottom–middle and the middle–middle locations of the thermally active parts, respectively.
The onset of bio-thermal convection in a suspension containing both nanoparticles and gyrotactic microorganisms, such as algae, is considered. Physical mechanisms responsible for the slip velocity between the nanoparticles and the base fluid, such as Brownian motion and thermophoresis, are included in the model. The suspension occupies a horizontal layer of finite depth. The lower boundary of the layer is assumed rigid while at the upper boundary both cases of either rigid or stress-free top boundaries are considered. A linear instability analysis is performed and the resulting eigenvalue problem is solved analytically using the Galerkin method. The cases of oscillatory and non-oscillatory convection are studied. Investigation of the dependence of the thermal Rayleigh number on the nanoparticle Rayleigh number and the bioconvection Rayleigh number is performed. The boundaries of oscillatory and non-oscillatory instability are established. The effect of nanoparticles can be either stabilizing or destabilizing, depending on whether the basic nanoparticle distribution is bottom-heavy or top-heavy. The effect of upswimming microorganisms is generally destabilizing.
The impeller of a centrifugal pump experiences a significant radial load when operating at off-design conditions. Its average magnitude can be reasonably estimated at the design stage by existing formulas. In contrast, the unsteady component is difficult to estimate since it is affected by the transient properties of the flow. This paper explores the use of a commercial CFD code to estimate the total radial load on the impeller of two test pumps. The full 3D-URANS equations were solved for several flow rates between 10%–130% of rated conditions. The predictions were validated with experimental data of global characteristics and unsteady pressure distribution round the impeller. The code was used to estimate the total radial load (steady and unsteady components) on the impellers as a function of flow rate. It was observed that the unsteady component can represent about a 40%–70% of the average magnitude when operating at off-design conditions.
To describe the strongly nonlinear dynamics of waves propagating in the final stages of shoaling and in the surf and swash zones, fully nonlinear models are required. The ability of the Serre or Green Naghdi (S–GN) equations to reproduce this nonlinear processes is reviewed. Two high-order methods for solving S–GN equations, based on Finite Volume approaches, are presented. The first one is based on a quasi-conservative form of the S–GN equations, and the second on a hybrid Finite Volume/Finite Difference method. We show the ability of these two approaches to accurately simulate nonlinear shoaling, breaking and runup processes.
A novel tool for tsunami wave modeling is presented. This tool has the potential of being used for operational purposes: indeed, the numerical code is able to handle the complete life cycle of a tsunami (generation, propagation and run-up along the coast). The algorithm works on unstructured triangular meshes and thus can be run in arbitrary complex domains. This paper contains a detailed description of the finite volume scheme implemented in the code. The numerical treatment of the wet/dry transition is explained. This point is crucial for accurate run-up/run-down computations. The majority of tsunami codes use semi-empirical techniques at this stage, which are not always sufficient for tsunami hazard mitigation. Indeed the decision to evacuate inhabitants is based on inundation maps, which are produced with these types of numerical tools. We present several realistic test cases that partially validate our algorithm. Comparisons with analytical solutions and experimental data are performed. Finally, the main conclusions are outlined and the perspectives for future research presented.
The simulation of cavitating flows is a challenging problem both in terms of modelling the physics and developing robust numerical methodologies. Such flows are characterized by important variations of the local Mach number, compressibility effects on turbulence and involve thermodynamic phase transition. To simulate these flows by applying homogeneous models and Reynolds averaged codes, the turbulence modelling plays a major role in the capture of unsteady behaviours. This paper presents a one-fluid compressible Reynolds-Averaged Navier–Stokes (RANS) solver with a simple equation of state (EOS) for the mixture. A special focus is devoted to the turbulence model influence. Unsteady numerical results are given for Venturi geometries and comparisons are made with experimental data.
Similarity solutions are essential for understanding nonlinear viscous fluid flow. The similarity transform reduces the Navier–Stokes equations to a set of nonlinear ordinary differential equations, which can be solved to yield universal curves. This paper reviews the advances in similarity solutions of a viscous fluid due to a stretching boundary.
The aim of this paper is to describe a turbulence model for the particle method Smoothed Particle Hydrodynamics (SPH). The model makes few assumptions, conserves linear and angular momentum, satisfies a discrete version of Kelvin’s circulation theorem, and is computationally efficient. Furthermore, the results from the model are in good agreement with the experimental and computational results of Clercx and Heijst for two-dimensional turbulence inside a box with no-slip walls. The model is based on a Lagrangian similar to that used for the Lagrangian averaged Navier–Stokes (LANS) turbulence model, but with a different smoothed velocity. The smoothed velocity preserves the of the spectrum of the unsmoothed velocity, but reduces the magnitude for short length scales by an amount which depends on a parameter . We call this the SPH- model. The effectiveness of the model is indicated by the fact that the second and fourth order velocity correlation functions calculated using the smoothed velocity and a coarse resolution, are in good agreement with a calculation using a resolution which is finer by a factor 2, and therefore requires 8 times as much work to integrate to the same time.
In this paper, a thorough numerical investigation of the performance of several linear and nonlinear turbulence model variants in various jet flow applications is carried out. Three based turbulence models are considered, namely the standard model, the model, and the nonlinear model. The selected turbulence models are applied for the prediction of simple as well as complex jet flow applications to underpin knowledge about the accuracy obtained from the two-equation turbulence models. The numerical code developed by the present authors solves the unsteady RANS equations by using the control volume approach on a non-staggered grid system. Three jet flow applications are selected, namely a turbulent free jet, a turbulent jet impinging on a flat plate, and a turbulent wall jet. In order to validate the numerical results obtained and to investigate the performance of the different turbulence models considered, different experimental measurements from the literature are used. The present work is primarily motivated by the desire to provide a rational way for deciding how complex the turbulence model is required to be for a given application and to find out how the accuracy changes with model complexity. Due to the superior predictive performance of modern turbulence models in a wide range of complex industrial and engineering applications, it was believed that a ‘universal’ turbulence model might exist. In general, that is not true. Simple flows can be analysed using standard two-equation models. The present numerical investigation showed that the linear turbulence model could give good results in simple (non-impinging) jet flows. However, in complicated flows, such as impinging jet problems or wall jet flows, a more elaborate level of modeling is required. In such contexts, nonlinear models are appropriate for predicting the turbulent viscosity structure, namely the inhomogeneous near-wall flow region and the anisotropic Reynolds stresses, which is a vital part of turbulent jet flow prediction.
In the last three decades, great improvements have been made towards knowledge of the hydrodynamics and general processes occurring in the surf zone, widely affected by the breaking of the waves. Nevertheless, the turbulent flow structure is still very complicated to investigate. The aim of this work is to present and discuss the results obtained by simulating two-dimensional breaking waves by solving the Navier–Stokes equations, in air and water, coupled with a dynamic subgrid scale turbulence model (Large Eddy Simulation, LES). First, the ability of the numerical tool to capture the crucial features of this complicated turbulent two-phase flow is demonstrated. Numerical results are compared with experimental observations provided by Kimmoun and Branger (2007) . Spilling/plunging breaking regular waves are considered. Generally, there is good agreement and the model provides a precise and efficient tool for the simulation of the flow field and wave transformations in the nearshore.
We show that a free surface water flow of constant nonzero vorticity beneath a wave train and above a flat bed has to be two-dimensional and the vorticity must have only one nonzero component which points in the horizontal direction orthogonal to the direction of wave propagation. The obtained results are of relevance to studies of resonant wave train interactions in flows of constant nonzero vorticity: in contrast to irrotational flows, all wave trains have to propagate in the same direction. An important practical aspect of these considerations lies in that wave trains of constant vorticity model the interaction of swell with tidal currents, negative vorticity being appropriate for the flood current and positive vorticity for the ebb current.
The Serre equations are a pair of strongly nonlinear, weakly dispersive, Boussinesq-type partial differential equations. They model the evolution of the surface elevation and the depth-averaged horizontal velocity of an inviscid, irrotational, incompressible, shallow fluid. They admit a three-parameter family of cnoidal wave solutions with improved kinematics when compared to KdV theory. We examine their linear stability and establish that waves with sufficiently small amplitude/steepness are stable while waves with sufficiently large amplitude/steepness are unstable.
A study has been carried out to clarify vortical structures and behaviour resultant from imposing inclined exits along either the major or minor plane of an elliptic nozzle. Laser-induced fluorescence (LIF) flow visualizations show production of inclined vortex roll-ups along the inclined planes, with corresponding narrowing of jet columns along the non-inclined planes. Minor-plane inclined nozzles result in significant growths in the jet spread along the inclined plane, while major-plane inclined nozzles produce little variations. Formation of rib structures is observed to be suppressed in minor-plane inclined nozzles and linked to braid vortices inducing the formation of streamwise vortices along the minor plane. Particle-image velocimetry measurements show that increasing the incline angle in major-plane inclined nozzles reduce the strengths of the discrete vortex roll-ups, while the opposite occurs in minor-plane inclined nozzles. Although Reynolds shear stress variations correspond well with changes in incline angle and vortex roll-up strength in major-plane inclined nozzles, they demonstrate a non-monotonic relationship in minor-plane inclined nozzles. LIF visualizations further clarify how strong asymmetric interactions between the inclined vortex roll-ups and braid vortices lead to suppression of axis-switching in major-plane inclined nozzles but not in minor-plane inclined nozzles. The more complex flow behaviour in the latter is responsible for the non-linear relationship in Reynolds shear stress levels observed earlier. Comparisons of the half-jet width profiles confirm the suppression of axis-switching in major-plane inclined nozzles only, while momentum thickness profiles show significant variations in the mixing layer characteristics between major- and minor-plane inclined nozzles.
Rarefied gas flow through a thin slit is studied on the basis of the direct simulation Monte Carlo method. The flow rate and flow field are calculated over the whole range of gas rarefaction for various values of the pressure ratio. It is found that at all values of the pressure ratio a significant variation of the flow rate occurs in the transition regime between the free-molecular and hydrodynamic regimes. In the hydrodynamic regime, the flow rate tends to a constant value. In the case of finite pressure ratio, the flow field qualitatively differs from that for outflow into vacuum, namely, vortices appear in the down-flow container in the vicinity of the hydrodynamic regime. Then, in the hydrodynamic regime the gas flow forms a strong jet.
A good prediction of wave celerity in the surf zone is essential for wave propagation modelling in the nearshore. This paper is devoted to a study of wave celerity based on the analysis of data collected during the ECORS 2008 field experiment that took place at Truc Vert Beach, SW France. Here we analyze and quantify the effects of non-linearities and evaluate the predictive ability of several non-linear celerity predictors for high-energy wave conditions. The asymptotic behaviour of the different models for high values of the non-linearity parameter is investigated. Besides, comparisons with data show that the classic bore model is inappropriate for describing wave dynamics when approaching the swash zone. The influence of very low frequency pulsations of the wave-induced circulation on wave celerity is also discussed.
We study the effects of the Maxwell–Cattaneo (MC) law of heat conduction on the flow of a Newtonian fluid in a vertical slot subject to both vertical and horizontal temperature gradients. Working in one spatial dimension (1D), we employ a spectral expansion involving Rayleigh’s beam functions as the basis set, which are especially well-suited to the fourth order boundary value problem (b.v.p.) considered here, and the stability of the resulting dynamical system for the Galerkin coefficients is investigated. It is shown that the absolute value of the (negative) real parts of the eigenvalues are reduced, while the absolute values of the imaginary parts are somewhat increased, under the MC law. This means that the presence of the time derivative of the heat flux increases the order of the system, thus leading to more oscillatory regimes in comparison with the usual Fourier case. Moreover, no eigenvalues with positive real parts were found, which means that in this particular situation, the inclusion of thermal relaxation does not lead to destabilization of the motion.