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Rayleigh–Bénard convection in water is studied by means of direct numerical simulations, taking into account the variation of properties. The simulations considered a three-dimensional (3-D) cavity with a square cross-section and its two-dimensional (2-D) equivalent, covering a Rayleigh number range of $10^{6}\leqslant Ra\leqslant 10^{9}$ and using temperature differences up to 60 K. The main objectives of this study are (i) to investigate and report differences obtained by 2-D and 3-D simulations and (ii) to provide a first appreciation of the non-Oberbeck–Boussinesq (NOB) effects on the near-wall time-averaged and root-mean-squared (r.m.s.) temperature fields. The Nusselt number and the thermal boundary layer thickness exhibit the most pronounced differences when calculated in two dimensions and three dimensions, even though the $Ra$ scaling exponents are similar. These differences are closely related to the modification of the large-scale circulation pattern and become less pronounced when the NOB values are normalised with the respective Oberbeck–Boussinesq (OB) values. It is also demonstrated that NOB effects modify the near-wall temperature statistics, promoting the breaking of the top–bottom symmetry which characterises the OB approximation. The most prominent NOB effect in the near-wall region is the modification of the maximum r.m.s. values of temperature, which are found to increase at the top and decrease at the bottom of the cavity.

Thermally driven flows can be approximated as constant property flows only when temperature differences are relatively small. In that case, the Oberbeck-Boussinesq approximation holds and the set of governing equations is simplified. For larger temperature differences, the variation of the fluid properties with temperature cannot be ignored and in the case of gasses the governing equations take the low-Mach form. This significantly complicates the numerical solution of variable property against constant property flows because of the emergence of a variable coefficient Poisson equation for the pressure. In the present study, a numerical methodology for the direct numerical simulation of thermally driven low-Mach flows is presented. In this framework, a pressure-splitting scheme is utilised to transform the variable coefficient Poisson equation for the pressure into a constant coefficient Poisson equation, improving the efficiency of the numerical solution. The consistent boundary conditions for the pressure are derived and presented. Furthermore, the proposed methodology is validated for the natural convection of air inside a differentially heated cavity, for a wide range of temperature differences, both within and outside the limits of applicability of the Oberbeck-Boussinesq approximation. Finally, to demonstrate the potential of this methodology, the three-dimensional natural convection of air inside a differentially heated cavity is simulated for a Rayleigh number Ra = 2.0 × 10 9 and for temperature differences Δ T = 50 K, 100 K, and 200 K. It is found that, with increasing temperature difference, the symmetry around the centre of the cavity that characterises the Oberbeck-Boussinesq solution is lost. In addition, the laminar-turbulent transition point on the heated and cooled walls changes position, moving to a more upstream position on the heated wall and a more downstream position on the cooled wall.

The Oberbeck-Boussinesq (OB) form of the Navier-Stokes equations can provide reliable solutions only for problems where the density differences are relatively small and all other material properties can be considered constant. For heat transfer problems at large temperature differences, the dependence of the material properties on temperature is the main source of non-Oberbeck-Boussinesq (NOB) effects. When a numerical solution is attempted for this category of problems, due to the density variations of the heated medium, a variable coefficient Poisson equation for the pressure emerges which is difficult to solve in a computationally efficient manner. In the present study, an efficient methodology to treat incompressible flows with variable properties outside the range of validity of the OB approximation is proposed. In the context of this methodology, the variable coefficient Poisson equation for the pressure is transformed into a constant coefficient Poisson equation using a pressure-correction scheme. In addition, all thermophysical properties are considered to be temperature dependent for all terms of the conservation equations. The proposed methodology is validated against results provided by previous studies on the natural convection flow of air, water and glycerol. Moreover, the potential of this methodology is demonstrated with the direct numerical simulation (DNS) of the NOB Rayleigh-Bénard convection of water inside a three-dimensional (3D) cavity. The comparison between two-dimensional (2D) and 3D results reveals significant differences, highlighting the need for efficient methodologies capable to accurately simulate NOB problems in 3D. © 2018 Elsevier Ltd 125 1156 1168 1156-1168

We address the task of modelling numerically turbulent flows within random arrays of circular cylinders, relevant for several industrial and environmental applications. Numerical simulations are employed to model infinite domains of randomly placed emergent and rigid cylinders validated by a laboratory database acquired by a PIV system. The main goals are: (i) to discuss the effect of the numerical domain size and the grid resolution on the first and second order moments and (ii) to characterise the spatial distribution of mean flow and turbulence variables in the drag-wake controlled stratum. Five domains of different sizes (9–44 cylinders) and four grid resolutions were independently tested. The results show that the time-averaged velocity field and the Reynolds stress tensor were not significantly affected by the size of the tested numerical domains. The analysis of the grid resolution influence shows how the results improve with mesh refinement, while none of the tested meshes produces un-physical results. The present work provides guidance on the acceptable compromises, in terms of mesh resolution and domain size, when predicting, with eddy resolving computational fluid mechanics tools, first and second-order moments of turbulent flows within infinite arrays or randomly placed cylinders. © 2018 Elsevier Ltd 80 245 261 245-261

A series of unsteady, three-dimensional numerical simulations of the incompressible, oscillatory flow around a near-bed pipeline is presented. A flow at Reynolds number equal to Re α o = 20,000 with respect to the oscillatory amplitude and maximum oscillation velocity is considered. The ratio of the pipeline diameter to the oscillatory amplitude examined is in the range of D / α o = 0.1 − 1.0 , with the pipeline located at a distance of G / D = 0.0 − 1.0 . The numerical simulations are conducted by means of Large Eddy Simulation (LES), using Cartesian grids. The presence of solid boundaries is taken into account by means of the Immersed Boundary method. For turbulence modelling, two different subgrid scale models are tested, the classical Smagorinsky and the Filtered Structure Function (FSF) models. The results in terms of vortex shedding are compared against previously reported data demonstrating very good agreement. Vortex shedding patterns are presented, indicating suppression of the boundary layer separation of the lower side of the pipeline for gap lengths G / α o ≤ 1 / 20 . The characteristic values of the hydrodynamic forcing in terms of the drag and lift coefficients and the three significant oscillation frequencies extracted from the temporal variation of the forcing signals are associated with the flow regimes and wall proximity. The pipeline experiences hydrodynamic loading which is found to oscillate with the external flow frequency along the direction of the flow. Along the wall-normal direction, the forces exerted on the pipe oscillate with several frequencies of high power spectral density. However, the three significant oscillation frequencies of the lift coefficient appear to have almost constant values. The presented results can provide trends for design purposes in similar flow conditions for a wide range of engineering applications.

Direct numerical simulations (DNS) of the thermally-driven flow of air inside differentially heated cavities (DHC) are presented. The variation of air properties is taken into account using the low-Mach approximation, to obtain solutions outside the limits of the Oberbeck–Boussinesq (OB) approximation. The effects of the cavity’s aspect-ratio A and large temperature differences ΔT were investigated over the range 1 ≤ A ≤ 8 and ΔT ≤ 720 K. The Rayleigh and Prandtl numbers were set at R a = 10 9 and P r = 0.7 , considering a reference temperature of T 0 = 600 K. Time-averaged and r.m.s. statistics of the temperature field along with other derived quantities are presented and discussed. It is found that the time-averaged temperature fields vary significantly between non-Oberbeck–Boussinesq (NOB) and OB cases for larger aspect-ratios. This is also true for the instantaneous temperature and temperature r.m.s. fields which demonstrate significant qualitative differences. In addition, as the temperature difference increases and the property variations become more intense, the boundary layers at the vertical walls become turbulent at lower positions. The relocation of the laminar-turbulent transition point is found to be strongly dependent on the cavity’s aspect-ratio. An explanation of this phenomenon is given, based on the disruption of the vertical boundary layers by horizontal streams originating from the downstream part of the vertical walls.

In the present work, the forces exerted on spherical sand particles by oscillatory boundary layer flows at Re = 25 , 000 and Re = 55 , 000 are examined by means of Large Eddy Simulations. The particles move within the carrier fluid under the influence of the Stokes Drag, Gravity, Added Mass, Pressure Drag and Basset forces. The model has been validated for the cases of a particle accelerating within a stagnant fluid under the influence of gravity and for a particle within an oscillatory flow. The Basset force is computed in an efficient way, by calculating the Basset integral only for a specific time in the particle’s immediate history, called “window time”. In order to define the window time, existing literature approaches have been implemented. The rest of the particle’s history is calculated by an efficient second order methodology suitable for a large number of particles moving within the carrier fluid. The importance of each of the hydrodynamic forces has been examined when the particles are released far from the horizontal bed and when they are released in the boundary layer region, in the absence of gravity. The results indicate that Stokes Drag, Basset force and Pressure Drag are equally important. The contribution from the Added Mass force was found to be orders of magnitude smaller and the acceleration components in the other directions are also negligible. Furthermore, in the boundary layer region, a near-wall zone of negative mean Stokes Drag and positive mean Basset force has been identified. Moving away from the wall but still in the boundary layer region, another zone of positive mean Stokes Drag and negative mean Basset have been identified.

Kolokythas, G.A.; Grigoriadis, D.G.E., and Dimas, A.A., 2018. Dynamic friction coefficient in formulas of bed-load transport induced by waves over vortex orbital ripples. Empirical formulas for the computation of bed sediment transport induced by wave propagation over sand ripples often depend on, among other parameters, the dynamic friction coefficient, μd, of the sand grain motion. Here, a new approach is presented for the determination of μd based on the physics of the interaction between flow and sediment transport. Specifically, the correlation of μd to the wave, ripple, and sand grain characteristics was obtained using coupled numerical simulations of the flow over the rippled bed, the bed-load transport, and the bed morphology evolution. Flow results were obtained by two different numerical methods, one for wave boundary layer flow and one for purely oscillatory flow, both based on the solution of the Navier-Stokes equations. The bed-load transport rate, which drives the bed morphology evo...