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Compact finite-difference schemes have been recently used in several Direct Numerical Simulations of turbulent flows, in order to achieve high-order accuracy and high resolution. The development of compact finite-volume schemes is more involved, due to the appearance of surface and volume integrals. In this paper we select a staggered grid arrangement, whose good characteristics are advantageous in the simulation of incompressible flows. Compact schemes can be tuned to achieve very high resolution, for a given formal order of accuracy. In this respect, we develop and test high-resolution schemes by following a procedure first introduced by Lele (1992, J. Comp. Phys., 103). Numerical evidence of the good characteristics of the developed method is presented.

Riblets are well known as a passive mean for drag reduction in turbulent flow conditions, but their effectiveness for heat transfer is quite controversial. In this paper, we report our numerical results for fully developed laminar and turbulent flow and heat transfer in a channel with triangular riblets. Two different ribbed channels are considered, under a constant heat flux boundary condition. In the turbulent regime, the study is performed by means of direct numerical simulation at a Reynolds number, based on the wall-shear velocity, Re = 180, for a fluid with a Prandtl number Pr = 0.71. The results obtained are in good agreement, for the flow and turbulent quantities, with past experimental and numerical studies, but the predicted heat transfer effciency, in the turbulent regime, is lower than some of the experimental studies.

Most Direct Numerical Simulations (DNS) for turbulent flow and heat transfer are performed under the assumption of negligible buoyancy forces. Therefore, the temperature is treated as a passive scalar, and the velocityfield is independent on the temperature distribution. This simplification is not applicable in many situations of practical interest, where relevant buoyancy forces are present. In this study, we investigate, by means of DNS, a weakly turbulent, fully developed horizontal channel flow under unstable thermal stratification at two different Grashof numbers. Both the Reynolds number, based on shear velocity and channel half-height, and the Prandtl number are set at constant values of 150 and 0.71, respectively. It is found that an increase of the Grashof number leads to a monotonic increase of the Nusselt number, while the drag force initiallydecr eases, and eventually increases at higher values of the Grashof number.

Riblets are well known as a passive mean for drag reduction in turbulent flow conditions, but their effectiveness for heat transfer is quite controversial, since the available experimental and theoretical investigations did not clearly establish whether riblets, with different cross sections, produce a net variation in heat transfer in comparison to the flat plate value. In this paper, we report our preliminary numerical results for fully developed laminar and turbulent flow and heat transfer in a channel with triangular riblets. The study is performed by means of direct numerical simulation at a Reynolds number, based on the wall-shear velocity, Re = 10 and Re = 180 for the laminar and turbulent case, respectively, for a fluid with a Prandtl number Pr = 0.71. Two different ribbed channels are considered, under a constant heat flux boundary condition. The results obtained are in general agreement, for the flow and turbulent quantities, with past experimental and numerical studies, but the predicted heat transfer efficiency, in the turbulent regime, is significantly lower than some of the experimental studies.

Compact finite-difference schemes have been recently used in several Direct Numerical Simulations of turbulent flows, since they can achieve high-order accuracy and high resolution without exceedingly increasing the size of the computational stencil. The development of compact finite-volume schemes is more involved, due to the appearance of surface and volume integrals. While Pereira et al. [J. Comput. Phys. 167 (2001)] and Smirnov et al. [AIAA Paper, 2546, 2001] focused on collocated grids, in this paper we use the staggered grid arrangement. Compact schemes can be tuned to achieve very high resolution for a given formal order of accuracy. We develop and test high-resolution schemes by following a procedure proposed by Lele [J. Comput. Phys. 103 (1992)] which, to the best of our knowledge, has not yet been applied to compact finite-volume methods on staggered grids. Results from several one- and two-dimensional simulations for the scalar transport and Navier–Stokes equations are presented, showing that the proposed method is capable to accurately reproduce complex steady and unsteady flows.

One of the requirements for achieving high levels of safety in fourth generation nuclear power plants, is that core thermal-hydraulics can be simulated numerically at a good level of accuracy. To this aim, detailed validation of turbulent heat transfer models needs to be carried out and discussed, in relevant flow and heat transfer configurations, and for low Prandtl-number fluids. The focus of this research is the turbulent, fully developed convection in a heated rod bundle with a triangular arrangement, and a pitch-to-diameter ratio P / D = 1.4 . Statistics derived from a set of Direct Numerical Simulations (DNS) at the moderate Reynolds number of Re = 8290 are compared to Reynolds Averaged Navier-Stokes (RANS) solutions where the closure is provided by the two-equation model SST k- ω and by the Reynolds-Stress Model. Comparisons are drawn for forced flow and in mixed convection conditions ( Ri ≈ 0.25 ). Global quantities extracted from experiments performed in very similar conditions are also compared against the numerical results. Profiles of the turbulent Prandtl number about the unit flow cell are also displayed and discussed. This work clarifies through detailed comparison that if, on the one hand, only the Reynolds-Stress model is able to reasonably capture important flow features like secondary flow components, on the other hand also the SST k- ω two-equation model considered is acceptably accurate in predicting the integral quantities of interest.

Numerical results of laminar fully developed natural convection in an inclined composite channel are presented. The mathematical model relies on the Method of Volume Averaging and thus a single domain approach is applied. The Forchheimer correction and thermal dispersion effects are considered while local thermal equilibrium between the porous matrix and the fluid is assumed. Velocity and temperature profiles are displayed and their rather weak dependence upon porosity and fluid properties assessed. Forces acting on the fluid are identified and discussed. Thermal performances of the composite channel in laminar conditions are evaluated. One of the main results of the present investigation is that when non-Darcian effects and thermal dispersion are negligible, the Nusselt number of the composite system in natural convection regime is independent of the channel inclination.

In this paper we attack the problem of devising a finite volume method for computational fluid dynamics and related phenomena which can deal with complex geometries while attaining high-orders of accuracy and spectral convergence at a reasonable computational cost. As a first step towards this end, we propose a control volume finite element method for the solution of the advection–diffusion equation. The numerical method and its implementation are carefully tested in the paper where h- and p-convergence are checked by comparing numerical results against analytical solutions in several relevant test-cases. The numerical efficiency of a selected set of operations implemented is estimated by operation counts, ill-conditioning of coefficient matrices is avoided by using an appropriate distribution of interpolation points and control-volume edges.

Riblets are well-known as a passive mean for drag reduction in turbulent flow conditions, but their effectiveness for heat transfer is quite controversial. In this paper we present the numerical results for fully developed laminar and turbulent flow and heat transfer in a channel with triangular riblets. The turbulent study is performed by means of direct numerical simulation at a Reynolds number Reτ=180 based on the wall-shear velocity, for a fluid with a Prandtl number Pr=0.71. Four different ribbed channels are considered, under a constant heat flux boundary condition, and correspond to ridge angle α=45° and 60°, and riblet spacing s+=20 and s+=40. The results obtained, for the flow and turbulent quantities, are in good agreement with past experimental and numerical studies, and correctly reproduce drag reduction over the smaller s+=20 riblets and drag increase over the larger s+=40 riblets. The predicted heat transfer efficiency of riblets do not agree with some experimental results, and is below that of a flat plate for all the configurations. The conditions for heat transfer enhancement are discussed.