Inter-comparison and validation of computational fluid dynamics codes in two-stage meandering channel flows

This paper presents a study in the inter-comparison and validation of three-dimensional computational fluid dynamics codes which are currently used in river engineering. Finite volume codes PHOENICS, FLUENT and SSIIM; and finite element code TELEMAC3D are considered in this study. The work has been carried out by competent hydraulic modellers who are users of the codes and not involved in their development. This paper is therefore written from the perspective of independent practitioners of the techniques. In all codes, the flow calculations are performed by solving the three-dimensional continuity and Reynolds-averaged Navier–Stokes equations with the k–ε turbulence model. The application of each code was carried out independently and this led to slightly different, but nonetheless valid, models. This is particularly seen in the different boundary conditions which have been applied and which arise in part from differences in the modelling approaches and methodology adopted by the different research groups and in part from the different assumptions and formulations implemented in the different codes. Similar finite volume meshes are used in the simulations with PHOENICS, FLUENT and SSIIM while in TELEMAC3D, a triangular finite element mesh is used. The ASME Journal of Fluids Engineering editorial policy is taken as a minimum framework for the control of numerical accuracy. In all cases, grid convergence is demonstrated and conventional criteria, such as Y⁺, are satisfied. A rigorous inter-comparison of the codes is performed using large-scale experimental data from the UK Flood Channel Facility for a two-stage meandering channel. This example data set shows complex hydraulic behaviour without the additional complications found in natural rivers. Standardised methods are used to compare each model with the available experimental data. Results are shown for the streamwise and transverse velocities, secondary flow, turbulent kinetic energy, bed shear stress and free surface elevation. They demonstrate that the models produce similar results overall, although there are some differences in the predicted flow field and greater differences in turbulent kinetic energy and bed shear stress. This study is seen as an essential first step in the inter-comparison of some of the computational fluid dynamics codes used in the field of river engineering.     

Modeling of a continuous pretreatment reactor using computational fluid dynamics

Computational fluid dynamic simulations are employed to predict flow characteristics in a continuous auger driven reactor designed for the dilure acid pretreatment of biomass. Slurry containing a high concentration of biomass solids exhibits a high viscosity, which poses unique mixing issues within the reactor. The viscosity increases significantly with a small increase in solids concentration and also varies with temperature. A well-mixed slurry is desirable to evenly distribute acid on biomass, prevent buildup on the walls of the reactor, and provides an uniform final product. Simulations provide flow patterns obtained over a wide range of viscosities and pressure distributions, which may affect reaction rates. Results provide a tool for analyzing sources of inconsistencies in product quality and insight into future design and operating parameters.     

MPI+X: task-based parallelisation and dynamic load balance of finite element assembly

The main computing phases of numerical methods for solving partial differential equations are the algebraic system assembly and the iterative solver. This work focuses on the first task, in the context of a hybrid MPI+X paradigm. The matrix assembly consists of a loop over the elements, faces, edges or nodes of the MPI partitions to compute element matrices and vectors and then of their assemblies. In a MPI+X hybrid parallelism context, X has consisted traditionally of loop parallelism using OpenMP, with different techniques to avoid the race condition, but presenting efficiency or implementation drawbacks. We propose an alternative, based on task parallelism using some extensions to the OpenMP programming model. In addition, dynamic load balance will be applied, especially efficient in the presence of hybrid meshes. This paper presents the proposed methodology, its implementation and its validation through the solution of large computational mechanics problems up to 16k cores.     

Numerical analysis of a synthetic jet using an automated adaptive method

An automated adaptive remeshing methodology is applied to a synthetic jet. A set of two‐dimensional, axisymmetric, time‐dependent Computational Fluid Dynamics analyses are performed. Grid independence is achieved via successive levels of adaptive refinement using a novel methodology. The method employs adaptive remeshing, performed in an automated fashion. Adaptation criteria are based upon the undivided differences in select field variables. Sensors are placed at strategic locations within the flow field, which are used to aid in judging grid independence. The resulting analytical predictions are compared to an experimental dataset. The automated methodology yields both a verified and validated set of analysis results for the synthetic jet. Copyright © 2011 John Wiley & Sons, Ltd.     

Coupled solution of the species conservation equations using unstructured finite‐volume method

A coupled solver was developed to solve the species conservation equations on an unstructured mesh with implicit spatial as well as species‐to‐species coupling. First, the computational domain was decomposed into sub‐domains comprised of geometrically contiguous cells—a process similar to additive Schwarz decomposition. This was done using the binary spatial partitioning algorithm. Following this step, for each sub‐domain, the discretized equations were developed using the finite‐volume method, and solved using an iterative solver based on Krylov sub‐space iterations, that is, the pre‐conditioned generalized minimum residual solver. Overall (outer) iterations were then performed to treat explicitness at sub‐domain interfaces and nonlinearities in the governing equations. The solver is demonstrated for both two‐dimensional and three‐dimensional geometries for laminar methane–air flame calculations with 6 species and 2 reaction steps, and for catalytic methane–air combustion with 19 species and 24 reaction steps. It was found that the best performance is manifested for sub‐domain size of 2000 cells or more, the exact number depending on the problem at hand. The overall gain in computational efficiency was found to be a factor of 2–5 over the block (coupled) Gauss–Seidel procedure. All calculations were performed on a single processor machine. The largest calculations were performed for about 355 000 cells (4.6 million unknowns) and required 900 MB of peak runtime memory and 19 h of CPU on a single processor. Copyright © 2009 John Wiley & Sons, Ltd.     

Gun tunnel flow calibration: defining input conditions for hypersonic flow computations

The procedures used to calibrate a hypersonic gun tunnel nozzle flow are described. The values obtained using these methods are then used as input conditions for computations of hypersonic flow over a long slender test body. Only by completely specifying the flow field, including the effects of nozzle flow angularity, can the best agreement between experiment and computations be achieved. Received 18 February 2000 / Accepted 7 July 2000     

On relaxation times in the Navier-Stokes-Voigt model

We study analytically and numerically the relaxation time of flow evolution governed by the Navier-Stokes-Voigt (NSV) model. We first show that for the Taylor–Green vortex decay problem, NSV admits an exact solution which evolves slower than true fluid flow. Secondly, we show numerically for a channel flow test problem using standard discretisation methods that although NSV provides more regular solutions compared to usual Navier-Stokes solutions, NSV approximations take significantly longer to reach the steady state.     

Hybrid mechanistic approach in the estimation of flow properties in cylindrical membrane modules

A hybrid computational approach was employed for simulation of molecular separation using polymeric membranes. The considered system is a cylindrical membrane module in which the mass transfer equations were solved numerically using CFD (Computational Fluid Dynamics) to obtain the concentration of the species, and then the simulation results were used in machine learning models. Indeed, the CFD simulation results were used as the inputs for several machine learning models to obtain the hybrid model. We have a dataset with more than 2000 data points and two input features (r and z). Also, the only output is C which is the concentration of the species in the feed channel of membrane module. KNN (K nearest neighbor), PLSR (Partial Least Square Regression), and SGD (Stochastic Gradient Descent) are the models employed in this research to analyze the mentioned data set. Models were optimized with their hyper-parameters and finally evaluated with different statistical metrics. MAE error metric is 3.4, 5.1, and 5.5 for KNN, SGD, and PLSR. Also, they have 0.998, 0.997, 0.896 coefficient of determination (R²) respectively. Finally, based on the overall results, KNN with K = 8 is selected as the best model in this study for simulation of the membrane system. The final maximum error is also 1.35E+02.     

Numerical study of unsteady compressible flow driven by supersonic jet injected into elliptical cell with small exit hole

The unsteady behavior of flow driven by a jet suddenly injected into an elliptical cell is numerically studied by solving the axisymmetric two-dimensional compressible Navier–Stokes equations. This system is a model of laser ablation of a certain duration followed by a discharging process through the exit hole at the downstream end of the cell. The parameters for the calculations are the exit diameter of the cell, the Mach number and duration of the injected jet. The injected jet becomes a traveling plume approaching the downstream end of the elliptical cell and discharges from the cell through an exit hole. The plume generates and interacts with a shock wave in the elliptical cell. The unsteady flow properties downstream of the cell are found to be attenuated by the combination of the phenomena occurring in the cell and at the exit. Monitoring the velocity at the exit hole is used to clarify the characteristics of the flow and apply them to applications in pulse laser ablation. The results show that the vortex in the plume head with the same radius as the exit diameter (i.e., D_e/D_j = 2.7, where D_e is the exit diameter and D_j is the injected jet diameter) causes a relatively constant velocity at the exit for about 10 μs. In the downstream flow characteristics, the suddenly injected jet makes a single or double peak in the velocity variation outside the cell depending on the combination of parameters. This suggests that a single laser pulse might generate two beams through the exit hole of a cell, which could increase the efficiency of beam generation with the combination of an elliptical cell and the laser ablation. It is also found that the wave form of the variations and their level are roughly determined by the durations of the jet and the exit diameters of the cell exit, respectively. PACS 51.35.+a; 47.40.Nm     

Heat transfer behaviour of nanofluids in a uniformly heated circular tube fitted with helical inserts in laminar flow

The CFD simulation of heat transfer characteristics of a nanofluid in a circular tube fitted with helical twist inserts under constant heat flux has been explained using Fluent version 6.3.26 in laminar flow. Al₂O₃ nanoparticles in water of 0.5%, 1.0% and 1.5% concentrations and helical twist inserts of twist ratios 2.93, 3.91 and 4.89 has been used for the simulation. All thermophysical properties of nanofluids are temperature dependent. The heat transfer enhancement increases with Reynolds number and decreases with twist ratio with maximum for the twist ratio 2.93. By comparing the heat transfer rates of water and nanofluids, the increase in Nusselt number is 5%–31% for different helical inserts and different volume concentrations. The maximum heat transfer enhancement is 31.29% for helical insert of twist ratio 2.93 and for the volume concentration of 1.5% corresponding to the Reynolds number of 2039. The data obtained by simulation match with the literature value of water with the discrepancy of less than ±10% for plain tube and tube fitted with helical tape inserts for Nusselt number.