Body-fitted Grid Research Articles

A new forcing approach for wall-modeled simulation of rough-wall turbulent flows

The effect of rough surface on turbulent flows is usually investigated using direct numerical simulation (DNS) with either body-fitted grids or immersed boundary method. Both methods, however, require a significant number of grids to resolve all rough scales, resulting in intolerable computational cost. In this paper, a new volume forcing approach is developed to simulate wall-bounded turbulent flows with surface roughness at the same computational cost as that with smooth walls. Specifically, two extra forcing terms are introduced in the Navier–Stokes equations to mimic roughness effects. One is the feedback force operating within the roughness cell and ensuring zero velocity at the grid points located therein. The other represents the vortex force around the roughness surface. A direct comparison with the model proposed in literature shows a significant improvement in the prediction of mean flow and Reynolds stresses. To further validate the new forcing model, simulation of channel flow with cubical roughnesses is implemented, which shows a good agreement with fully resolved DNS.

Coupling immersed boundary method with wall function for high Reynolds number compressible flows on adaptive Cartesian grids

In this paper, a high Reynolds number compressible flow simulation method based on the immersed boundary method (IBM) is developed on the adaptive Cartesian grids to address two problems: one is the ability of large-scale Cartesian grid generation, and the other is the resolution of thin shear layers. For the former, an efficient automatic parallel generation method of adaptive Cartesian grids is proposed based on the k-d tree theory. The method has good parallel scalability and computational efficiency, e.g., the generation of 1.41 × 109 cells by 2048 cores takes only 0.40 min. For the latter, an IBM-wall function coupling method is designed to simulate geometrical configurations with high Reynolds numbers in the parallel framework. Numerical experiments show that the presented method can yield results consistent with the use of body-fitted grids. In conclusion, the presented method can realize a fully automatic simulation of high Reynolds number compressible flows, significantly reducing the labor cost in the computational fluid dynamics process, and can improve the accuracy and efficiency of engineering applications.

Parallel Bayesian Optimization of Thermophysical Properties of Low Thermal Conductivity Materials Using the Transient Plane Source Method in the Body-Fitted Coordinate.

The transient plane source (TPS) method heat transfer model was established. A body-fitted coordinate system is proposed to transform the unstructured grid structure to improve the speed of solving the heat transfer direct problem of the winding probe. A parallel Bayesian optimization algorithm based on a multi-objective hybrid strategy (MHS) is proposed based on an inverse problem. The efficiency of the thermophysical properties inversion was improved. The results show that the meshing method of 30° is the best. The transformation of body-fitted mesh is related to the orthogonality and density of the mesh. Compared with parameter inversion the computational fluid dynamics (CFD) software, the absolute values of the relative deviations of different materials are less than 0.03%. The calculation speeds of the body-fitted grid program are more than 36% and 91% higher than those of the CFD and self-developed unstructured mesh programs, respectively. The application of body-fitted coordinate system effectively improves the calculation speed of the TPS method. The MHS is more competitive than other algorithms in parallel mode, both in terms of accuracy and speed. The accuracy of the inversion is less affected by the number of initial samples, time range, and parallel points. The number of parallel points increased from 2 to 6, reducing the computation time by 66.6%. Adding parallel points effectively accelerates the convergence of algorithms.

Numerical simulation of seismic waves in transversely isotropic media based on orthogonal body-fitted grids

Numerical simulation of seismic waves in transversely isotropic media based on orthogonal body-fitted grids

A numerical framework for modeling evaporation and combustion of isolated, spherically-symmetric, multi-component fuel droplets

This paper presents a comprehensive numerical framework for simulating the evaporation and combustion of isolated, spherically-symmetric, multi-component fuel droplets. The framework incorporates a detailed description of chemical reactions in the gaseous phase and is capable of modeling pure evaporation, autoignition, and hot-wire ignition scenarios.The transport equations for mass, species, and energy are solved in both the liquid (droplet) and gaseous (surrounding atmosphere) phases. Diffusion in the liquid phase is described using the Stefan–Maxwell theory, while in the gaseous phase, both molecular and thermal diffusion are considered. The model also includes the thermophoretic effect for carbonaceous particles and accounts for gas radiation through various models, ranging from optically-thin approximations to more complex methods like the P1 and discrete ordinate methods. Non-gray radiative effects are handled using the Weighted-Sum-of-Gray-Gases Model (WSGGM). Liquid/gas interface conditions are evaluated by imposing flux continuity of mass and energy, along with thermodynamic equilibrium for species. Deviations from ideal thermodynamic behavior in the liquid droplet are managed by incorporating a suitable activity coefficient or by using a proper cubic equation of state. Additionally, the presence of supporting fibers is modeled using a simplified one-dimensional approach. The transport equations are solved using the method of lines, with spatial discretization performed via the finite difference method on a body-fitted grid. The resulting system of Differential–Algebraic Equations (DAEs) is then solved using a fully-coupled approach.Thanks to its generality in terms of kinetic and thermodynamic descriptions and the reduced computational time, the proposed framework offers significant potential for advancing our understanding of the complex combustion processes of multi-component liquid fuels and for enhancing the planning and execution of experiments involving isolated fuel droplets.

Virtual body-fitted grid-based immersed boundary method for simulation of thermal flows with Dirichlet and Neumann boundary conditions

In this work, a virtual body-fitted grid-based immersed boundary method (IBM) combined with the thermal lattice Boltzmann flux solver (TLBFS) is proposed to efficiently simulate thermal flows with Dirichlet and Neumann boundary conditions. The method involves generating a virtual body-fitted grid along the immersed boundary and implementing the boundary conditions using a fractional step technique. In the prediction step, the finite-volume TLBFS is used to obtain the predicted flow field on the Eulerian mesh without considering the immersed boundary, while in the correction step, the correction process of the flow field is conducted on the virtual grid. Thus, the effect of the boundary is transferred to the fluid domain through the virtual grid indirectly. For Dirichlet boundary conditions, such as the no-slip condition and the specified temperature condition, the velocity and temperature corrections are considered unknowns and solved through a matrix system formed from enforcing the boundary conditions. As for the Neumann boundary condition, such as the specified heat flux condition, the temperatures at virtual layers inside the immersed body are regarded as unknowns and computed from those at virtual layers outside the wall according to the quadratic distribution. Several benchmark cases including natural, forced, and mixed convection problems are well simulated to validate the method. The numerical results are in good agreement with reference data, demonstrating the capacity of the present method to simulate thermal flows with Dirichlet and Neumann boundary conditions while requiring fewer Lagrangian points and achieving higher computational efficiency.

Enhancing topology optimization with colored body-fitted mesh using adaptive filter, dual re-meshing strategy, and OOP programming paradigm

This study introduces a novel topology optimization approach by employing power law-based material interpolation and adaptive filtering in the framework of the unstructured grids. As an extension of the established Solid Isotropic Material with Penalization (SIMP) method that utilizes the fixed structured mesh, the proposed Colored Body-Fitted Optimization (CBFO) method adopts the body-fitted grids to enhance efficiency, accuracy, and adaptability for diverse engineering applications. Notably, incorporating body-fitted meshes with intermediate density profiles enables improved flexibility in the numerical simulations and eliminates the need for re-meshing in each iteration. The dual re-meshing strategy drastically reduces computational costs, with only two re-meshing procedures required throughout the optimization process. This approach facilitates the generation of dense mesh regions around critical boundaries to augment solution accuracy while enabling sparse mesh configurations in the low-sensitivity regions, thereby boosting computational efficiency without compromising performance. The effectiveness, robustness, and efficiency of the CBFO method are validated through testing on multiple standard minimum compliance and compliant mechanism problems. The proposed optimization method can converge in dozens of iterations, obtain better objective function values, and save computational costs by up to 69 % compared to the previous method using the body-fitted mesh. Additionally, a concise MATLAB script implementing the proposed method using an Object-Oriented Programming (OOP) paradigm is provided in the appendix and the supplementary material, complete with annotations.

Investigations on Trimming Strategy and Unsteady Aerodynamic Characteristics of Tiltrotor in Conversion Procedure

Numerical simulations were conducted to analyze the unsteady aerodynamic characteristics of a tiltrotor aircraft with different conversion strategies. Firstly, the CFD method was established by taking the interaction between the rotor and wing into account, as well as the body-fitted grid of the tiltrotor. Then, the trimming approach of the rotor and wing was developed to ensure longitudinal balance of the aircraft, and the method for determining the conversion corridor of the tiltrotor aircraft was proposed by considering the limitations imposed by wing stall and the required power of the rotor. Finally, the aerodynamic characteristics of the rotor and wing during the continuous conversion process were investigated, considering various tilting angular velocities and horizontal accelerations of the tiltrotor. The numerical results indicated that a smaller acceleration can enhance the efficiency of the tiltrotor. However, this would increase the complexity of trimming the fuselage attitude angle. It was also found that excessive acceleration could exceed the required power limit of the tiltrotor, rendering the conversion strategy infeasible.

Generalized interpolation-supplemented cascaded lattice Boltzmann method for noise radiated from a circular cylinder

Flow past a stationary or vibrating body usually leads to intense noise radiation. In order to study this problem via direct simulations, a cascaded lattice Boltzmann method (CLBM) is developed in the moving frame of reference, and implemented in a body-fitted grid using the generalized interpolation-supplemented particle streaming. A far-field perfectly matched layer is also incorporated so as to avoid sound reflection. The proposed generalized interpolation-supplemented cascaded lattice Boltzmann method (GICLBM) is then validated through numerical experiments concerning fixed and forced oscillating circular cylinders, in terms of forces exerting on the cylinder, wall stress, near-field flow dynamics, and far-field sound radiation. Very good consistency is observed for all quantities discussed therein with previous benchmark tests. Furthermore, the noise radiated from a circular cylinder undergoing vortex-induced vibration (VIV) is investigated using the GICLBM, providing interesting results. Firstly, at a mass ratio of m⁎=2, the flow and vibration dynamics are found to be dependent on the Mach number, and the critical value is found to be approximately Ma=0.1. Secondly, through comparisons with scenarios involving a fixed cylinder and a forced vibrating cylinder, it is noted that the VIV generates significantly more complicated sound sources including monopole and drag dipole. Thirdly, in the lock-in condition, the increase in the reduced velocity only alters the magnitude of the radiated sound pressure but not the directivity. Through this study, a high-fidelity, efficient, and relatively simple framework for fluid-structure-sound interactions is proposed.

Low Mach number approximated linearized perturbed Euler equations-based unified computational flow-induced acoustic model for 2D planar/axisymmetric complex geometry

This article is on proposition of a unified 2D planar and axisymmetric differential formulation—for both fluid dynamics and acoustic governing equations. Further, using hydrodynamic splitting method for computational acoustics, a differential formulation is proposed by performing low Mach number approximation on Linearized Perturbed Euler Equations (LPEE). Finally, using the differential formulations, a unified numerical methodology is proposed for Computational Flow-induced Acoustics (CFiA)—involving complex geometry—on a body-fitted curvilinear grid. A finite volume and finite difference methods-based hybrid method is presented for algebraic formulation in CFiA. Further, solution methodology is presented with a semi-implicit pressure projection method for fluid flow, four step Runge-Kutta method along with sub time-stepping for acoustic perturbations, and a one-way explicitly coupled solution algorithm for the CFiA. A detailed validation study is presented separately for the present in-house computational-acoustic and CFiA solvers—by considering various test problems, involving 2D planar and axisymmetric complex geometry problems. Further, using an order of accuracy study, the present acoustic and CFiA solvers are demonstrated as IV-order and II-order accurate, respectively. Finally, using the CFiA solver, a superior performance is demonstrated for the proposed low Mach number approximated LPEE as compared to the traditional LPEE-based solver. For low Mach number CFiA, involving 2D planar and axisymmetric complex geometries, a novel method is presented here for computationally efficient CFiA development.

Aerodynamic interference analysis and modeling of heterogeneous rotors

During closed-range rotorcraft missions, strong aerodynamic disturbances occur between multiple aircraft, thus affecting the stability and safety of cooperative flight processes. However, owing to the numerous control variables in rotor models, the cost and complexity of experiments and body-fitted grid simulation methods are high, thereby resulting in low analysis efficiency and difficulty in establishing a highly applicable aerodynamic-interference model. In this study, the effectiveness of a two-dimensional quasi-steady momentum source method for calculating the aerodynamic interference of heterogeneous rotors is validated using the sliding-mesh method. Using Latin sampling and momentum source methods to obtain aerodynamic-interference data points, a multiparameter-coupled heterogeneous-rotor aerodynamic-interference model is proposed and validated. The results indicate that the proposed aerodynamic-interference model provides clear physical significance and demonstrates high accuracy under different rotor configurations. In validation samples, the correlation coefficient between the predicted aerodynamic loss on the lower rotor and the computational fluid dynamics (CFD) calculation results is approximately 0.99, with the maximum errors in predicting thrust and moment losses are less than 7 % and 2 %. Meanwhile, the correlation coefficient between the predicted values on the upper rotor and the CFD calculation results is 0.82, with the maximum errors in predicting the dimensionless thrust and moment losses are less than 5.5 % and 1 %. The rapid aerodynamic-interference analysis model proposed herein can serve as a reference for the safe-flight strategy of rotorcraft during close-range cooperative missions.

Hybrid lattice Boltzmann method using Cartesian and body-fitted grids for turbomachinery aeroacoustic simulations

In this study, we developed a hybrid approach using the lattice Boltzmann method (LBM) and finite-volume lattice Boltzmann method (FVLBM) to perform efficient aeroacoustic simulations with moving boundaries. An entire domain, including the flow and acoustic fields, was computed using the standard LBM with a Cartesian grid. Local domains around the moving objects were computed using the FVLBM with body-fitted grids. These simulations were coupled using the direct forcing method to consider moving boundaries. The hybrid method was validated for several problems including turbulent flows and flow-induced sounds under low-Mach-number conditions. These validation problems covered flows with Reynolds numbers up to 2.0×105 and Mach numbers less than 0.2. In the simulations of the aeolian tone generated from stationary and rotating cylinders, the hybrid method results were consistent with those of the conventional methods. In the simulation of the turbulent flow and broadband sound of the isolated airfoil, the hybrid method was 15 times faster than the standard LBM and produced results consistent with the experimental results. Furthermore, the application of a cross-flow fan demonstrated that the hybrid method successfully simulated the flow and acoustic fields around the rotor.

Implementation of a level-set-based volume penalization method for solving fluid flows around bluff bodies

A volume penalization-based immersed boundary technique is developed and thoroughly validated for fluid flow problems, specifically flow over bluff bodies. The proposed algorithm has been implemented in an open source field operation and manipulation (OpenFOAM), a computational fluid dynamics solver. The immersed boundary method offers the advantage of inserting a complex solid object inside a Cartesian grid system, and therefore, the governing equations can be applied to such a simpler grid arrangement. For capturing the fluid–solid interface more accurately, the grid is refined near the solid surface using topoSetDict and refineMeshDict utilities in OpenFOAM. In order to avoid any numerical oscillation and to compute the gradients accurately near the interface, the present volume penalization method (VPM) is integrated with a signed distance function, which is also referred to as a level-set function. Benchmark problems, such as flows around a cylinder and a sphere, are considered and thoroughly validated with the results available in the literature. For the flow over a stationary cylinder, the Reynolds number is varied so that it covers from a steady two-dimensional flow to an unsteady three-dimensional flow. The capability of the present solver has been further verified by considering the flow past a vibrating cylinder in the cross-stream direction. In addition, a flow over a sphere, which is inherently three-dimensional due to its geometrical shape, is validated in both steady and unsteady regimes. The results obtained by the present VPM show good agreement with those obtained by a body-fitted grid using the same numerical scheme as that of the VPM, and also with those reported in the literature. The present results indicate that the VPM-based immersed boundary technique can be widely applicable to scientific and engineering problems involving flow past stationary and moving bluff bodies of arbitrary geometry.

An immersed boundary velocity correction method combined with virtual body-fitted grid for simulation of incompressible flows

In this work, a virtual body-fitted grid is introduced into the velocity correction-based immersed boundary method (IBM) to simulate incompressible flows. The impact of the immersed boundary is indirectly transmitted to the flow field via a virtual body-fitted grid. In this method, the fractional step technique consisting of the predictor and the corrector is adopted. The prediction step is executed on the Eulerian mesh, and the correction step is done on the virtual grid to fulfill the no-slip boundary condition. After the correction step, the corrected velocity field on the virtual grid is then assigned to that on the Eulerian mesh to update the flow field. Being able to adjust the grid spacing flexibly, the virtual body-fitted grid alleviates the shortcomings of the conventional IBM that uses the smooth Dirac delta function to associate Lagrangian points with their surrounding Eulerian points. As a result, the present method is easy to apply to non-uniform Cartesian grids, which is inapplicable to the conventional IBM with the smooth Dirac delta function. Numerical experiments concerning flow past a circular cylinder and a NACA0012 airfoil demonstrate the advantages of the present method, i.e., fewer Lagrangian points are required to avoid the streamline penetration of boundary and the range of “diffuse interface” can be narrowed by reducing the normal grid spacing of the virtual body-fitted grid to improve numerical results on a coarse mesh. In addition, an accuracy assessment on the decaying vortex problem reveals that the present IBM has a second-order accuracy.

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.

Assessment of immersed boundary methods for hypersonic flows with gas-surface interactions

The efficacy of immersed boundary (IB) methods with adaptive mesh refinement (AMR) techniques is assessed in the context of atmospheric entry applications, including effects of chemical nonequilibrium (CNE) and gas-surface interactions (GSI). We scrutinize a conservative cut-cell IB method and two non-conservative ghost-cell IB methods, comparing their results with analytical solutions, data from the literature, and results obtained with a reference solver that operates on body-fitted grids. All solvers employ the same external thermochemistry library, ensuring that all observed differences can be attributed solely to differences in the underlying numerical methodologies. We present results for eight benchmark cases. Four verification cases verify the implementation of chemistry, transport properties, catalytic boundary conditions, and shock capturing. Four validation cases encompass blunt geometries with adiabatic and isothermal, as well as inert, catalytic and ablative boundary conditions. Overall, the results obtained with the IB solvers are in very good agreement with the reference data. Discrepancies arise in cases with large temperature or concentration gradients at the wall, and these are linked to conservation errors inherent to ghost-cell methods. Only a strictly conservative cut-cell IB method is on par with body-fitted grid methods.

Direct Numerical Simulation of Transitional and Turbulent Flows Over Multi-Scale Surface Roughness—Part I: Methodology and Challenges

Abstract High-fidelity simulation of transitional and turbulent flows over multi-scale surface roughness presents several challenges. For instance, the complex and irregular geometrical nature of surface roughness makes it impractical to employ conforming structured grids, commonly adopted in large-scale numerical simulations due to their high computational efficiency. One possible solution to overcome this problem is offered by immersed boundary methods, which allow wall boundary conditions to be enforced on grids that do not conform to the geometry of the solid boundary. To this end, a three-dimensional, second-order accurate boundary data immersion method (BDIM) is adopted. A novel mapping algorithm that can be applied to general three-dimensional surfaces is presented, together with a newly developed data-capturing methodology to extract and analyze on-surface flow quantities of interest. A rigorous procedure to compute gradient quantities such as the wall shear stress and the heat flux on complex non-conforming geometries is also introduced. The new framework is validated by performing a direct numerical simulation (DNS) of fully developed turbulent channel flow over sinusoidal egg-carton roughness in a minimal-span domain. For this canonical case, the averaged streamwise velocity profiles are compared against results from the literature obtained with a body-fitted grid. General guidelines on the BDIM resolution requirements for multi-scale roughness simulation are given. Momentum and energy balance methods are used to validate the calculation of the overall skin friction and heat transfer at the wall. The BDIM is then employed to investigate the effect of irregular homogeneous surface roughness on the performance of an LS-89 high-pressure turbine blade at engine-relevant conditions using DNS. This is the first application of the BDIM to realize multi-scale roughness for transitional flow in transonic conditions in the context of high-pressure turbines. The methodology adopted to generate the desired roughness distribution and to apply it to the reference blade geometry is introduced. The results are compared to the case of an equivalent smooth blade.

CFD simulations of vapour cloud explosions using PDRFoam

Computational Fluid Dynamics (CFD) has gained a lot of popularity in the consequence assessments of gas explosions in the past couple of decades. This work reviews Porosity/ Distributed Resistance (PDR) approach-based CFD solver (PDRFoam) for gas explosions. The PDR approach is used to model the effect of small-scale obstacles and only solve for the large scale congestion. PDR-based modified Favre averaged equations for mass, momentum, enthalpy, and regress variable are solved using PDRFoam solver, which is developed as a new application in OpenFOAM. The evaluation of the solver is done against medium-scale standard benchmark experiments. Further, the effect of block-age ratio, different types of fuels, and different obstacle diameters is explored. Using PDRFoam simulations, the pressure–time series, the flame arrival times, and the flame speeds are predicted and the same are compared with experiments. Compared to standard body-fitted grid simulations, the PDR approach is computationally economical; The predicted results are in good agreement with experiments.

A ghost-point based second order accurate finite difference method on uniform orthogonal grids for electromagnetic scattering around curved perfect electric conductors with corners

We propose a finite difference method to solve Maxwell's equations in time domain in the presence of a perfect electric conductor (PEC) that impedes the propagation of electromagnetic waves. Our method relies on the level set characterization of the interface and the PDE-based extension technique which allows us to construct fictitious ghost values inside the PEC without scrutinizing the local geometries of its boundaries. As opposed to a locally perturbed body fitting grid used in [1], we promote a much simpler uniform orthogonal grid which necessitates a new approach for the extension technique to work. A novelty of our work is the introduction of what we call guest values which are accurately estimated boundary values deliberately and carefully misplaced near the interface. We stipulate a mild requirement on the accuracy of our ghost values that they need only be locally second-order accurate. Nevertheless, the resulting accuracy of our method is second order thanks to the application of back and forth error correction and compensation, which also relaxes CFL conditions. We demonstrate the effectiveness of our approach with some numerical examples.

Numerical study of acoustic source localization of rotor using a novel discrete noise analysis strategy

In order to obtain the influence mechanism of the rotor noise and the local aerodynamic variation under different operating conditions, a novel discrete noise analysis strategy for the acoustic source localization is established. The analysis strategy has two aspects including the blade division method and the noise contribution calculation method. Firstly, the body-fitted rotor blade grids are preprocessed and refined at the division position before the flowfield simulation. Then, based on the flowfield result, the blade grids are divided into several blocks in the chordwise and spanwise directions, and the acoustic pressure of each block is predicted. Finally, a discriminant function for the contribution of the block to the rotor noise is proposed, and the acoustic source localization is carried out. The URANS equations and FW-H equations are used to capture high-fidelity flowfield and rotor acoustic pressure. Parameters such as the block position in different direction on the rotor blade and the collective pitches are quantified, and the relationship between air flow and aeroacoustics is discussed in detail. Some conclusions are obtained by analyzing the BO105 model rotor in hover. The acoustic pressure produced by the leading edge of the upper surface could cancel about 50% acoustic pressure of the remainder of these blocks. Increasing the force at this position will be benefit to the noise reduction. Acoustic source distribution is closely linked to the flow separation near the blade tip: the main acoustic source moves toward around 0.9 R section of the blade in the spanwise direction, and it moves from the leading edge towards the trailing edge in the chordwise direction.