Computational Fluid Dynamics Grid Research Articles

Local Wavelet Adaptation of Cartesian Grids in Computational Fluid Dynamics

Local Wavelet Adaptation of Cartesian Grids in Computational Fluid Dynamics

A Data-Driven Machine Learning Approach for Turbulent Flow Field Prediction Based on Direct Computational Fluid Dynamics Database

A novel approach is presented for predicting compressible turbulent flow fields using a neural network-based data-driven method. Accurate prediction in turbulent regions heavily relies on the resolution of available data. Traditional methods, employing image-based techniques by mapping scattered computational fluid dynamics (CFD) data onto Cartesian grids, encounter data scarcity in critical areas such as the boundary layer and wake. Recently, convolutional neural networks (CNN) have gained prominence as the most widely referenced technique in fluid dynamics, utilizing flow field images as datasets for flow field prediction. However, CNN requires datasets with a high pixel density to enhance training accuracy in crucial regions, thereby increasing the input data volume and machine training time. To address this challenge, our proposed method deviates from using flow field images and instead generates datasets directly from the flow field properties of CFD grid points. By employing this approach, several advantages are realized. Firstly, the network benefits from the favorable characteristics of unstructured grids, such as varying point spacing near the object surface and in the far field, which effectively reduces the amount of input data and consequently the machine training cost. Secondly, the construction of the training dataset eliminates the need for interpolation or extrapolation, thereby preserving the accuracy of CFD data. In this case, a simple multilayer perceptron can be trained using the proposed dataset. Various flow field properties, including static pressure, turbulent kinetic energy, and velocity components, can be predicted with high accuracy within a few seconds.

Numerical method used for the simulation of fluid–solid transitions based on the VOF and SAM models and prediction of snow distributions on large-span roofs

During a snowfall, the surfaces of the snow beds on roofs change dynamically with time and wind conditions. The generation of body-fitted computational fluid dynamics grids for simulating dynamic snow surfaces using the moving-grid method remains challenging. Therefore, a numerical method was developed to simulate the fluid–solid transition based on the volume of the fluid model and solidification and melting models. The snowfall process was divided into n stable steps, and a stable state calculation method was adopted to calculate the air and snow phases. The dynamic snow boundary was simulated at each stage by converting the fluid or solid characteristics of the domain in which the grids resided. Based on the results of the (n−1)th stage, the fluid domain grids buried by the snow were filled with liquid and frozen into the solid domain. Instead, the fluid in the frozen grids, where snow was about to be eroded, was evacuated and converted into fluid-domain grids. Thus, a complex and changeable snow boundary could be adapted without re-meshing. A modified wall friction velocity equation was derived to correct the wall friction velocity at the snow boundary owing to the serrated boundary of the solidified grids, thereby improving calculation accuracy. The numerical simulation results were verified via field observations of snow distribution on the stepped flat and gable roof models. The snow variation on a full-scale, three-span, suspended cable roof under snow-fall conditions was predicted using the proposed method.

Contribution of jet flow noise sources to the far-field sound power

Jet noise is the dominant source of noise during aircraft takeoff. This study uses direct numerical simulation (DNS) data of subsonic jet flow obtained from computational fluid dynamics (CFD) simulations to perform acoustic analyses. The non-negative contribution technique (NNC) is employed to identify aeroacoustic sources of jet noise with the greatest contribution to far-field sound power. The NNC technique uses the Lighthill source distribution with an acoustic impedance matrix constructed from radiation kernels of the free-field Green’s function. The fast multipole method (FMM) is integrated with the NNC technique to reduce computational cost arising from decomposition of the acoustic impedance matrix as well as from the high number of CFD grids associated with the DNS data. The results showed that the dominant aeroacoustic sources are associated with the first component of the Lighthill tensor (T11) and are concentrated along the jet centerline, downstream of the nozzle exit.

Numerical study of heat transfer across in-line circular cylinders for low to moderate Reynolds numbers

A computational fluid dynamics (CFD) model is generated to study the fluid flow and heat transfer from a series of six cylinders arranged in a horizontal row. The momentum and energy equations were solved using the finite volume method, with convective terms discretized using a second-order upwind method and diffusion terms discretized using central differencing. A second-order implicit technique was used for time integration. Simulations were run with four different values of the free stream Reynolds numbers 100, 200, 300, 400 and three different values of the longitudinal pitch (SL ) 1.5D, 2D, 2.5D to analyze the heat transfer behavior with fluid flow over a series of horizontal cylinders. First the grid independence test and CFD model validation are performed with the exact relation available in the literature. Next, the numerical results obtained from the developed CFD model for the row of cylinders were compared with the previously published analytical model, and correlation available in the literature, and were found to be in good agreement. The average Nusselt number calculated from the analytical and numerical models falls in the range of 8 to 10 for free stream Reynolds number equal to 100 for all values of dimensionless longitudinal pitches. Moreover, for the free stream Reynolds number equal to 400 with longitudinal pitch of 2.5D, the values of the average Nusselt number reach up to double the above-mentioned range. The maximum percentage error between the average Nusselt number obtained from the numerical and analytical solutions was less than 20% for larger free stream Reynolds number. The study found that the average Nusselt number for the array of cylinders increases with both the free stream Reynolds number and the dimensionless longitudinal pitch ratio increments. This information can be used to design more efficient heat exchangers or other fluid systems involving arrays of cylinders.

Comparative analysis on gas–solid drag models in MFIX-DEM simulations of bubbling fluidized bed

In this study, the open-source software MFIX-DEM simulations of a bubbling fluidized bed (BFB) are applied to assess nine drag models according to experimental and direct numerical simulation (DNS) results. The influence of superficial gas velocity on gas–solid flow is also examined. The results show that according to the distribution of time-averaged particle axial velocity in y direction, except for Wen–Yu and Tenneti–Garg–Subramaniam (TGS), other drag models are consistent with the experimental and DNS results. For the TGS drag model, the layer-by-layer movement of particles is observed, which indicates the particle velocity is not correctly predicted. The time domain and frequency domain analysis results of pressure drop of each drag model are similar. It is recommended to use the drag model derived from DNS or fine grid computational fluid dynamics–discrete element method (CFD-DEM) data first for CFD-DEM simulations. For the investigated BFB, the superficial gas velocity less than 0.9 m·s−1 should be adopted to obtain normal hydrodynamics.

Assessment of the Vortex Feature-Based Vorticity Confinement Method Applied to Rotor Aerodynamics and Aeroacoustics

The accurate prediction of helicopter rotor aerodynamics and aeroacoustics using Computational Fluid Dynamics (CFD) techniques still remains a challenge, as the over-dissipation of numerical schemes results in a higher diffusive rate of rotor wake and vortices than what can be expected from the fluid governing equations. To alleviate this issue, a vortex feature-based vorticity confinement (FVC2-L2) method that combines the locally normalized λ2 vortex detection method with the standard second vorticity confinement (VC2) scheme is presented to counterbalance the truncation error introduced by the numerical discretization of the convective term while avoiding the over-confinement inside the boundary layer. The FVC2-L2 scheme is adopted for helicopter rotor aerodynamic and aeroacoustic predictions through its implementation in the multi-block structured grid CFD solver ROSITA and coupling with the aeroacoustic code ROCAAP based on the permeable surface Ffowcs Williams–Hawkings (PS-FWH) equation. This approach is assessed in helicopter rotor flows via three databases. Firstly, the well-documented HART-II rotor in the baseline condition is used to evaluate the capability of the presented VC scheme in blade–vortex interaction (BVI) phenomena prediction. Subsequently, the UH-1H non-lifting hovering rotor and the AH-1/OLS low-speed descending flight rotor are adopted for assessment of such a method in aeroacoustics. The benefits of the FVC2-L2 scheme in terms of aerodynamics prediction, wake preservation, and noise signal prediction are well demonstrated by comparison with the experimental data and the results obtained without VC schemes. Particularly, the FVC2-L2 scheme mainly improves the highly unsteady airloads prediction, and results in an improvement of BVI noise prediction by more than 5 dB with respect to the case without VC schemes for AH-1/OLS rotor case. Additionally, some shortcomings of the approach are noticed in engineering applications. On the basis of a simplified convective vortex, some provisional guidelines on the required εo value in terms of number of cells per vortex diameter are provided: an εo value ranging from 0.01 to 0.04 for grids which may represent the vortex core diameter with 6 to 12 cells.

Computational fluid dynamics grid technology development

This paper reviews the development of computational fluid dynamics, especially computational aerodynamics. This paper summarizes the achievements of CFD in grid technology, analyzes the existing problems and perplexities, and prospects its development trend. The CFD grid technology includes structured grid, unstructured grid, hybrid grid and overlapping grid.

Fluid-structure interaction simulations of the ASPIRE SR01 supersonic parachute flight test

High-fidelity fluid-structure interaction (FSI) simulations of the ASPIRE SR01 supersonic parachute flight test are performed through the loose coupling of computational fluid dynamics (CFD) and computational structural dynamics (CSD) solvers. The CFD solver employs a Cartesian adaptive mesh refinement (AMR) grid paradigm with a ghost cell immersed boundary method to represent arbitrarily complex geometries, and the CSD solver uses MITC3 triangular shell and Timoshenko beam elements to discretize the parachute canopy and suspension lines. The CFD resolution required to capture the deficit of the dynamic pressure in the wake of the ASPIRE payload and the aerodynamic drag on the parachute canopy is systematically studied via grid refinement study before FSI simulations are conducted. FSI simulations presented consider the inflation of an initially folded parachute canopy in freestream conditions matching the line stretch event during the ASPIRE SR01 flight test. The total pull force at the instance of peak loading is predicted to within 10% of the flight test data. The sensitivity of the total pull force and canopy projected area to the grid resolution in the CFD and CSD domains is systematically studied via another grid refinement study, and grid convergence with respect to the CFD domain resolution is demonstrated. The pull force vs time curve predicted by each CFD and CSD grid resolution varies by less than 1% indicating a high degree of repeatability and low grid-related uncertainty. Remaining differences in the qualitative behavior of the pull force curve and quantitative difference in the peak pull force are thus determined to stem from modeling errors such as the lack of deceleration, and different initial parachute and flow states in the FSI simulations compared to the flight test.

Investigation of thermal evolution and fluid flow in the hot-end of a material extrusion 3D Printer using melting model

This work presents Computational Fluid Dynamics (CFD) simulations of the thermal evolution and fluid flow in the hot-end during material extrusion in fuse filament fabrication (FFF) additive manufacturing. The hot-end is the most fundamental and complex part of a FFF 3D printer. The fluid dynamics during material extrusion depend on the hot-end design while the printing speed depends on the speed at which the hot-end can melt the filament. In this work, a new melting model developed specifically for the FFF process is introduced. The CFD melting model incorporated the liquid fraction evolution to account for the presence of an air gap between the liquefier wall and the solid filament. For the first time, the thermal contact resistance was implemented using a melting model. The governing transport equations for the melting model were presented both in the dimensional primitive and non-dimensional primitive representations to understand the relevance of each term in a physical sense. The model equations were implemented with the aid of written user-defined function (UDF) codes coupled in the ANSYS Fluent. The grids were refined systematically to ensure that the influence of the mesh size on the computational results is minimized. The Richardson extrapolation technique was used to estimate the grid convergence index (GCI) and to quantify discretization error. The maximum discretization error is found to be 1.68%, which is an indication that the solution is in the asymptotic range. The thermal boundary conditions were implemented using simple liquid fraction-heat transfer coefficient relation and the results were validated using previously measured feeding force by Serdeczny et al. [1]. The predicted feeding force agrees reasonably with the measured feeding force. The model predicted a strong counter-clockwise recirculating vortex close to the barrel inlet. The further simulation revealed that the filament did not melt immediately at entry into the heated barrel, and variation in the barrel length indicates that the solid penetration depth ratio increases with an increase in the P é clet-number ( Pe ). Since high-speed 3D printing depends on the flow rate, an optimized thermal dissipation is desired in the hot-end. Our approach in presenting the model equations and subsequent results obtained should advance the understanding of the flow characteristics in the liquefier hot-end and thermal history within the barrel and the nozzle exit. Hence, the presented melt flow dynamics model would help in developing hot-end designs for 3D printers capable of melting filaments at an improved rate, by reducing the barrel length and printing at a higher liquefier temperature, while preheating the solid filament. • A new CFD melting model developed specifically for the FFF process is introduced. • Thermal contact resistance was implemented using the CFD melting model. • Effect of the air gap between the filament and the liquefier wall was implemented. • The true position of the melting front at the liquefier center was identified. • CFD Grid Sensitivity Analysis reveals solution is within the asymptotic limits.

ParTransgrid: A scalable parallel preprocessing tool for unstructured‐grid cell‐centered computational fluid dynamics applications

AbstractThe development of a basic scalable preprocessing tool is the key routine to accelerate the entire computational fluid dynamics (CFD) workflow toward the exascale computing era. In this work, a parallel preprocessing tool, called ParTransgrid, is developed to translate the general grid format like CFD General Notation System into an efficient distributed mesh data format for large‐scale parallel computing. Through ParTransgrid, a flexible face‐based parallel unstructured mesh data structure designed in Hierarchical Data Format can be obtained to support various cell‐centered unstructured CFD solvers. The whole parallel preprocessing operations include parallel grid I/O, parallel mesh partition, and parallel mesh migration, which are linked together to resolve the run‐time and memory consumption bottlenecks for increasingly large grid size problems. An inverted index search strategy combined with a multi‐master‐slave communication paradigm is proposed to improve the pairwise face matching efficiency and reduce the communication overhead when constructing the distributed sparse graph in the phase of parallel mesh partition. And we present a simplified owner update rule to fast the procedure of raw partition boundaries migration and the building of shared faces/nodes communication mapping list between new sub‐meshes with an order of magnitude of speed‐up. Experiment results reveal that ParTransgrid can be easily scaled to billion‐level grid CFD applications, the preparation time for parallel computing with hundreds of thousands of cores is reduced to a few minutes.

CFD modelling and grid uncertainty analysis of the free-falling water entry of 2D rigid bodies

The open source Computational Fluid Dynamics (CFD) library, OpenFOAM, is utilized to simulate the water impact of two-dimensional wedges and ship bow sections. For the free falling cases, the predicted results are validated against existing experimental data, and the parameter study is performed regarding the number of cells, time step, and width of the water domain applied in the numerical models. Grid uncertainty analysis for the CFD results is performed with a constant Courant–Friedrichs–Lewy number, to assess the consistency and accuracy of the CFD solver in solving the present problem. Three uncertainty estimation methods are compared on the peak slamming forces and pressures: Correction Factor (Cf), Factor of Safety (Fs), and Least-squares Fit (Lf) based approaches. All three of them can provide reliable uncertainty estimation for CFD simulations, as long as the right mesh configuration has been used. The variations of pressure distribution on wedge sections with various deadrise angles and initial entry velocities are analyzed. To examine the capability of the tool to predict the slamming loads for a section with roll motions two cases are simulated: one considering a free roll motion and another with constant roll angles. The predicted slamming loads are compared with the available experimental data and other numerical results.

Accelerated Estimation of Pulmonary Artery Stenosis Pressure Gradients with Distributed Lumped Parameter Modeling vs. 3D CFD with Instantaneous Adaptive Mesh Refinement: Experimental Validation in Swine.

Branch pulmonary artery stenosis (PAS) commonly occurs in congenital heart disease and the pressure gradient over a stenotic PA lesion is an important marker for re-intervention. Image based computational fluid dynamics (CFD) has shown promise for non-invasively estimating pressure gradients but one limitation of CFD is long simulation times. The goal of this study was to compare accelerated predictions of PAS pressure gradients from 3D CFD with instantaneous adaptive mesh refinement (AMR) versus a recently developed 0D distributed lumped parameter CFD model. Predictions were then experimentally validated using a swine PAS model (n = 13). 3D CFD simulations with AMR improved efficiency by 5 times compared to fixed grid CFD simulations. 0D simulations further improved efficiency by 6 times compared to the 3D simulations with AMR. Both 0D and 3D simulations underestimated the pressure gradients measured by catheterization (-1.87 ± 4.20and -1.78 ± 3.70mmHg respectively). This was partially due to simulations neglecting the effects of a catheter in the stenosis. There was good agreement between 0D and 3D simulations (ICC 0.88 [0.66-0.96]) but only moderate agreement between simulations and experimental measurements (0D ICC 0.60 [0.11-0.86] and 3D ICC 0.66 [0.21-0.88]). Uncertainty assessment indicates that this was likely due to limited medical imaging resolution causing uncertainty in the segmented stenosis diameter in addition to uncertainty in the outlet resistances. This study showed that 0D lumped parameter models and 3D CFD with instantaneous AMR both improve the efficiency of hemodynamic modeling, but uncertainty from medical imaging resolution will limit the accuracy of pressure gradient estimations.

Hybrid System Level and Coarse Grid CFD Tool for Three-Dimensional Natural Circulation, Mixing, and Stratification Modeling

Natural circulation, mixing, and stratification are important phenomena for the design and safety analysis of many advanced reactor designs with passive safety features as well as large open regions, such as pool reactor designs, spent fuel pools, and containments. Various modeling methods ranging from zero-dimensional (0-D) lumped volumes (or perfect mixing) to full three-dimensional (3-D) computational fluid dynamics (CFD) have been used. Historically, 0-D lumped volume approaches, combined with other modeling methods and assumptions, have been applied to perform so-called conservative analyses, but with the advancement of computational resources and best-estimate-plus-uncertainty methods, it is very desirable to have advanced, multidimensional modeling and simulation capabilities to improve the accuracy of reactor safety analyses, reduce modeling uncertainties, and eliminate the modeling distortions that can occur when simultaneously applying conservatisms. In the past decade there have been large investments in the pursuit of new, higher-fidelity modeling and simulation tools. However, GOTHICTM, which has been developed and maintained by Zachry Nuclear Engineering (formerly Numerical Applications, Inc.) since the mid-1980s, already provides these capabilities. GOTHIC is an industry-trusted, computationally efficient, coarse-grid multiphase CFD tool that also includes the important attributes of traditional system-level modeling tools, such as component-level models, control system capabilities, and neutron point kinetics models. GOTHIC applies a domain decomposition approach, allowing various levels of fidelity from 0-D to full 3-D to be applied in a single model, giving the user the ability to focus computational resources in the regions of interest while still capturing the integrated system response and important feedback effects. The result is a general-purpose, multiphysics engineering design and analysis tool that can be used for both light water reactor (LWR) and non-LWR designs. This paper provides an overview of 3-D finite volume modeling in GOTHIC, including the governing equations, turbulence model, and solution methods. Additionally, a few of the verification and validation tests from GOTHIC’s full test suite are presented to demonstrate fundamental capabilities, including laminar flow in a channel of parallel plates, square and rectangular cavity natural convection, natural convection through vertical and horizontal openings, and natural convection associated with a heated horizontal cylinder in a rectangular cavity. Based on the comparisons with the analytical solutions and experimental results, it is demonstrated that the multidimensional model can perform very well for a wide range of applications.

Solution adaptive refinement of cut‐cell Cartesian meshes can improve FDA nozzle computational fluid dynamics efficiency

AbstractTo be an effective tool in studying cardiovascular disease and designing new treatments, computational fluid dynamics (CFD) needs to move from the realm of “high performance” to “high throughput” computing by improving efficiency while retaining accuracy. Solution adaptive mesh refinement (AMR) has the potential to decrease simulation time and benefits would be greater if the mesh could dynamically adapt throughout a heartbeat. This study used cut‐cell Cartesian grids with AMR at each time step. The refinement criteria was based on subgrid scale (SGS). The potential efficiency improvements from AMR were investigated with the FDA nozzle benchmark case at Re 500, 3500 and 6500. Using AMR with SGS = 1% mean throat velocity simulations could be performed in under 24 h on 16 CPUs with high accuracy compared to both FDA particle image velocimetry experiments and refined uniform grid CFD. This was an efficiency improvement of over an order of magnitude compared to uniform grids and other AMR SGS values. Using AMR with SGS = 5 or 0.2% mean throat velocity did not result in large efficiency improvements. Lastly, simulations of pulsatile flow suggest that performance improvements for typical cardiovascular flows may be even greater than were found simulating the statistically stationary FDA nozzle experiments.

A forced ignition probability analysis method using kernel formation analysis with turbulent transport and Lagrangian flame particle tracking

A forced ignition probability analysis method is developed for turbulent combustion, in which kernel formation is analyzed with local kernel formation criteria, and flame propagation and stabilization are simulated with Lagrangian flame particle tracking. For kernel formation, the effect of turbulent scalar transport on flammability is modelled through the incorporation of turbulence-induced diffusion in a spherically outwardly propagating flame kernel model. The dependence of flammability limits on turbulent intensities is tabulated and serves as the flammability criterion for kernel formation. For Lagrangian flame particle tracking, flame particles are tracked in a structured grid with flow fields being interpolated from a Computational Fluid Dynamics (CFD) solution. The particle velocity follows a Langevin model consisting of a linear drift and an isotropic diffusion term. The Karlovitz number is employed for the extinction criterion, which compares chemical and turbulent timescales. The integration of the above two-step analysis approach with non-reacting CFD is achieved through a general interpolation interface suitable for general unstructured CFD grids. The method is demonstrated for a methane/air bluff-body flame, in which flow and fuel/air mixing characteristics are extracted from a non-reacting simulation. Results show that the computed ignition probability map agrees qualitatively with experimental results. A reduction of the ignition probability in the recirculation zone and a high ignition probability on the shear layer of the recirculation zone near the mean stoichiometric surface are well captured. The tools can facilitate optimization of spark placement and offer insights into ignition processes.

Modelling the effect of computation sampling on insight error in computational fluid dynamics scientific simulation

PurposeThe purpose of this paper is to collect data from humans as they generate insights from the visualised results of computational fluid dynamics (CFD) scientific simulation. The authors hypothesise the behaviour of their insight errors (IEs) and proceed to quantify the IEs provided by the crowd participants. They then use the insight framework to model the behaviours of the errors. Using the crowd responses and models from the framework, they test the hypotheses and use the results to validate the framework for the speedup of CFD applications.Design/methodology/approachThe authors use a randomised between-subjects experiment with blocking. CFD grid resolution is the independent variable while IE is the dependent variable. The experiment has one treatment factor with five levels. In case varying timestamps has an effect on insight variance levels, the authors block the responses by timestep. In total, 150 participants are randomly assigned to one of five groups and also randomly assigned to one of five blocks within a treatment. Participants are asked to complete a benchmark and open-ended task.FindingsThe authors find that the variances of insight and perception errors have a U-shaped relationship with grid resolution, that similar to the previously studied visualisation applications, the IE framework is valid for insights generated from CFD results and grid resolution can be used to predict the variance of IE resulting from observing CFD post-processing results.Originality/valueTo the best of the authors’ knowledge, no other work has measured IE variance to present it to simulation users so that they can use it as a feedback metric for selecting the ideal grid resolution when using grid resolution to speedup CFD simulation.

Shape optimisation of the sharp-heeled Kaplan draft tube: Performance evaluation using Computational Fluid Dynamics

Abstract A methodology to assess the performance of an elbow-type draft tube is outlined. This was achieved using Computational Fluid Dynamics (CFD) to evaluate the pressure recovery and mechanical energy losses along a draft tube design, while using open-source and commercial software to parameterise and regenerate the geometry and CFD grid. An initial validation study of the elbow-type draft tube is carried out, focusing on the grid-regeneration methodology, steady-state assumption, and turbulence modelling approach for evaluating the design’s efficiency. The Grid Convergence Index (GCI) technique was used to assess the uncertainty of the pressure recovery to the grid resolution. It was found that estimating the pressure recovery through area-weighted averaging significantly reduced the uncertainty due to the grid. Simultaneously, it was found that this uncertainty fluctuated with the local cross-sectional area along the geometry. Subsequently, a study of the inflow cone and outer-heel designs on the flowfield and pressure recovery was carried out. Catmull-Rom splines were used to parameterise these components, so as to recreate a number of proposed designs from the literature. GCI analysis is also applied to these designs, demonstrating the robustness of the grid-regeneration methodology.

On artificial density treatment for the pressure Poisson equation in the DEM-CFD simulations

The discrete element method (DEM) coupled with computational fluid dynamics (CFD) is regarded to be a standard approach in a numerical calculation of gas-solid flow. When the DEM-CFD method is applied to the simulation of industrial systems, we cannot shy away from the modeling of arbitrary shape wall boundaries. Very recently, we have developed an innovative wall boundary model in the DEM-CFD simulations, where the signed distance function (SDF) and the immersed boundary method (IBM) are used for the wall boundary in the DEM and CFD. The SDF makes it possible to create an arbitrary shape wall boundary based on the scalar field. The IBM can be used for the wall boundary model by reflecting the number of the SDF points on the local volume fraction in CFD grid. Thus, the arbitrary shape wall boundary can be easily created in the DEM-CFD method by combining the SDF with the IBM. On the other hand, the authors' group has pointed out the necessity of the density scale technique in CFD. In the density scale technique, the density scale coefficient is considered in the calculation of the pressure Poisson equation. When the SDF/IBM is applied to CFD without density scaling technique, an unnatural fluid flow might occur through the wall boundary object. The effect of the density scaling coefficient on a gas-solid flow has not been examined so far. From this background, the influence of the density scale coefficient on a gas-solid flow is investigated in the present study. Through this study, introduction of the density scaling technique is designated to be crucial when the IBM is used for the wall boundary in the DEM-CFD simulation. The density scaling coefficient is shown to be decided not by theory but by experience, and the value should become 100 to 1000 in a typical gas-solid flow system. Besides, it is illustrated that the calculation cost is not influenced by the value of the density scale coefficient in the DEM-CFD simulations.

Performance of the k-kL model for aerodynamics applications

PurposeThe purpose of this paper is to study the predictability of the recently proposed length scale-based two-equation k-kL model for external aerodynamic flows such as those also encountered in the high-lift devices.Design/methodology/approachThe two-equation k-kL model solves the transport equations of turbulent kinetic energy (TKE) and the product of TKE and the integral length scale to obtain the effect of turbulence on the mean flow field. In theory, the use of governing equation for length scale (kL) along with the TKE promises applicability in a wide range of applications in both free-shear and wall-bounded flows with eddy-resolving capability.FindingsThe model is implemented in the in-house unstructured grid computational fluid dynamics solver to investigate its performance for airfoils in difficult-to-predict situations, including stalling and separation. The numerical findings show the good capability of the model in handling the complex flow physics in the external aerodynamic computations.Originality/valueThe model performance is studied for stationary turbulent external aerodynamic flows, using five different airfoils, including two multi-element airfoils in high-lift configurations which, in the knowledge of the authors, have not been simulated with k-kL model until now.