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The purpose of this paper is to investigate the feasibility of solving turbulent flows based on smoothed finite element method (S-FEM). Then, the differences between S-FEM and finite element method (FEM) in dealing with turbulent flows are compared.

The stabilization scheme, the streamline-upwind/Petrov-Galerkin stabilization is coupled with stabilized pressure gradient projection in the fractional step framework. The Reynolds-averaged Navier-Stokes equations with standard k-epsilon model are selected to solve turbulent flows based on S-FEM and FEM. Standard wall functions are applied to predict boundary layer profiles.

This paper explores a completely new application of S-FEM on turbulent flows. The adopted stabilization scheme presents a good performance on stabilizing the flows, especially for very high Reynolds numbers flows. An advantage of S-FEM is found in applying wall functions comparing with FEM. The differences between S-FEM and FEM have been investigated.

The research in this work is limited to the two-dimensional incompressible turbulent flow.

The verification and validation of a new combination are conducted by several numerical examples. The new combination could be used to deal with more complicated turbulent flows.

The applications of the new combination to study basic and complex turbulent flow are also presented, which demonstrates its potential to solve more turbulent flows in nature and engineering.

This work carries out a great extension of S-FEM in simulations of fluid dynamics. The new combination is verified to be very effective in handling turbulent flows. The performances of S-FEM and FEM on turbulent flows were analyzed by several numerical examples. Superior results were found compared with existing results and experiments. Meanwhile, S-FEM has an advantage of accuracy in predicting boundary layer profile.

A mathematical model has been developed to study incompressible, isothermal, turbulent, confined, swirling flows. The model solves the conservation equations of mass, momentum, and two additional equations for the turbulent kinetic energy and the rate of dissipation of turbulent kinetic energy. The numerical predictions show a recirculation zone in the form of a one‐celled toroidal vortex at the combustor centreline. High levels of turbulence characterize the recirculation zone. The length, diameter and maximum velocity of the recirculation zone first decrease and then increase as the magnitude of the outer swirl number is first decreased from counter‐swirl to zero and then increased to co‐swirl flow conditions. Counter‐swirl produces steeper velocity gradients at the inter‐jet shear layer and promotes faster mixing than co‐swirl. The numerical results also indicate that the mass of the recirculation zone first decreases and then increases as the outer swirl number is first decreased from counter‐swirl to zero and then increased to co‐swirl conditions. The diameter, maximum velocity and mass of the recirculation zone are monotonically increasing functions of the inner jet swirl number. The recirculation zone length, diameter and mass are almost independent of the Reynolds number and outer‐to‐inner jet axial velocity ratio.

The averaged Navier‐Stokes and the k‐e turbulence model equations are used to simulate turbulent flows in some internal flow cases. The discrete equations are solved by different variations of Multigrid methods. These include both steady state as well as time dependent solvers. Locally refined grids can be added dynamically in all cases. The Multigrid schemes result in fast convergence rates, whereas local grid refinements allow improved accuracy with rational increase in problem size. The applications of the solver to a 3‐D (cold) furnace model and to the simulation of the flow in a wind tunnel past an object prove the efficiency of the Multigrid scheme with local grid refinement.

A mathematical model has been developed to study turbulent, confined, swirling flows under reacting non‐premixed conditions. The model solves the conservation equations of mass, momentum, energy, species, and two additional equations for the turbulent kinetic energy and the turbulent length scale. Combustion has been modelled by means of a one‐step overall chemical reaction. The numerical predictions based on the eddy‐break‐up model of turbulent combustion show a recirculation zone in the form of a one‐celled toroidal vortex at the combustor centreline. High levels of turbulence characterize the recirculation zone, whose diameter and velocity first decrease and then increase as the magnitude of the outer swirl number is first decreased from counter‐swirl to zero and then increased to co‐swirl flow conditions. Counter‐swirl produces steeper velocity gradients at the inter‐jet shear layer, promotes faster mixing and yields better combustion efficiency than co‐swirl. The numerical results are compared with those obtained under non‐reacting conditions in order to assess the influence of the heat release on the size of the recirculation zone.

To provide an analysis of turbulent flow in plane diffusers for graduate and postgraduate students (researchers) which can help them to understand turbulent flows and turbulence modelling.

Steady, incompressible, turbulent flow in two‐dimensional plane diffusers, where Reynolds averaged Navier‐Stokes (RANS) equations were simplified using the theory of turbulent boundary layers in integral form adjusted for the internal flow. To close the RANS equations, the mixing length model proposed by Michel et al., which was previously used for the calculation of turbulent flow in a straight channel with a uniform cross section, is applied for the calculation of the turbulent flow in plane diffusers. Also, in this paper, the velocity profile is approximated in every cross‐section of the diffuser by a six‐order polynomial, whose coefficients depend upon the three form parameters. Using this transformation, the system of governing equations was reduced to the three ordinary differential equations which were solved numerically.

A comparison between results obtained (velocity profiles) and experimental data obtained using HWA and LDA shows very good agreement. The method of integral equations of boundary layer is a relatively old method and tends to be forgotten since more advanced methods have been introduced. However, the results obtained using this method for the calculation of turbulent flow in a plane diffuser show a very good agreement with experimental data. Therefore, in engineering applications when simplicity and low‐cpu times are required, the integral method can still be applied successfully.

This paper offers practical help to an individual starting his/her research in the computational fluid dynamics (turbulence modelling).

The purpose of this paper is to describe a variational multiscale finite element approximation for the incompressible Navier‐Stokes equations using the Boussinesq approximation to model thermal coupling.

The main feature of the formulation, in contrast to other stabilized methods, is that the subscales are considered as transient and orthogonal to the finite element space. These subscales are solution of a differential equation in time that needs to be integrated. Likewise, the effect of the subscales is kept, both in the nonlinear convective terms of the momentum and temperature equations and, if required, in the thermal coupling term of the momentum equation.

This strategy allows the approaching of the problem of dealing with thermal turbulence from a strictly numerical point of view and discussion important issues, such as the relationship between the turbulent mechanical dissipation and the turbulent thermal dissipation.

The treatment of thermal turbulence from a strictly numerical point of view is the main originality of the work.

This study aims to feature the application of the artificial compressibility method (ACM) for the numerical prediction of two-dimensional (2D) axisymmetric swirling flows.

The respective academic numerical solver, named IGal2D, is based on the axisymmetric Reynolds-averaged Navier–Stokes (RANS) equations, arranged in a pseudo-Cartesian form, enhanced by the addition of the circumferential momentum equation. Discretization of spatial derivative terms within the governing equations is performed via unstructured 2D grid layouts, with a node-centered finite-volume scheme. For the evaluation of inviscid fluxes, the upwind Roe’s approximate Riemann solver is applied, coupled with a higher-order accurate spatial reconstruction, whereas an element-based approach is used for the calculation of gradients required for the viscous ones. Time integration is succeeded through a second-order accurate four-stage Runge-Kutta method, adopting additionally a local time-stepping technique. Further acceleration, in terms of computational time, is achieved by using an agglomeration multigrid scheme, incorporating the full approximation scheme in a V-cycle process, within an efficient edge-based data structure.

A detailed validation of the proposed numerical methodology is performed by encountering both inviscid and viscous (laminar and turbulent) swirling flows with axial symmetry. IGal2D is compared against the commercial software ANSYS fluent – by using appropriate metrics and characteristic flow quantities – but also against experimental measurements, confirming the proposed methodology’s potential to predict such flows in terms of accuracy.

This study provides a robust methodology for the accurate prediction of swirling flows by combining the axisymmetric RANS equations with ACM. In addition, a detailed description of the convective flux Jacobian is provided, filling a respective gap in research literature.

The knowledge about the heat transfer and flow field in the ribbed internal passage is particularly important in industrial and engineering applications. The purpose of this paper is to identify and analyze the performance of the constrained large-eddy simulation (CLES) method in predicting the fully developed turbulent flow and heat transfer in a stationary periodic square duct with two-side ribbed walls.

The rib height-to-duct hydraulic diameter ratio is 0.1 and the rib pitch-to-height ratio is 9. The bulk Reynolds number is set to 30,000, and the bulk Mach number of the flow is chosen as 0.1 in order to keep the flow almost incompressible. The CLES calculated results are thoroughly assessed in comparison with the detached-eddy simulation (DES) and traditional large-eddy simulation (LES) methods in the light of the experimentally measured data.

It is manifested that the CLES approach can predict both aerodynamic and thermodynamic quantities more accurately than the DES and traditional LES methods.

This is the first time for the CLES method to be applied to simulation of heat and fluid flow in this widely used geometry.

The purpose of this paper is to simulate the behaviour of the symmetrical turn‐up vortex amplifier (STuVA) to obtain insight into its maximum through‐flow operation within the eight‐port STuVA, and understand the relation between its design parameters and flow characteristics. Furthermore, it is to test the performance of different turbulent models and near‐wall models using the same grid, the same numerical methods and the same computational fluid dynamics code under multiple impingement conditions.

Three turbulence models, the standard k‐ε, the renormalization group (RNG) k‐ε model and the Reynolds stress model (RSM), and three near‐wall models have been used to simulate the confined incompressible turbulent flow in an eight‐port STuVA using unstructured meshes. The STuVA is a special symmetrical design of turn‐up vortex amplifier, and the simulation focused on its extreme operation in the maximum flow state with no swirling. The predictions were compared with basic pressure‐drop flow rate measurements made using air at ambient conditions. The effect of different combinations of turbulence and near‐wall models was evaluated.

The RSM gave predictions slightly closer to the experimental data than the other models, although the RNG k‐ε model predicted nearly as accurately as the RSM. They both improved errors by about 3 per cent compared to the standard k‐ε model but took a long time for convergence. The modelling of complex flows depends not only on the turbulence model but also on the near‐wall treatments and computational economy. In this study a good combination was the RSM, the two layer wall model and the higher order discretization scheme, which improved accuracy by more than 10 per cent compared to the standard k‐ε model, the standard wall function and first order upwind.

The results of this paper are valid for the global pressure drop flow rate. It should be desirable to compare some local information with the experiment.

This paper provides insight into the maximum through‐flow operation within the eight‐port STuVA to understand the relation between its design parameters and flow characteristics and study the performance of turbulence and near wall models.

The results from a direct numerical simulation (DNS) of turbulent, incompressible flow through a square duct, with an imposed temperature difference between the horizontal walls, are presented. The vertical walls are assumed perfectly insulated, and the Reynolds number, based on the bulk velocity and the hydraulic diameter, is about 4400. Our results indicate that secondary motions do not affect dramatically global parameters, like the friction factor and the Nusselt number, with respect to the plane‐channel flow, but the distributions of the local shear stress and heat flux at the walls are highly non‐uniform, due to the presence of these secondary motions. It is also shown that an eddy‐diffusivity approach is capable to reproduce well the turbulent heat flux. All simulations were performed by an efficient finite volume algorithm. A description of the numerical algorithm, together with an analysis of time‐accuracy, is included. The OpenMP parallel programming language was exploited to obtain a moderately‐scalable application.