Classical Computational Fluid Dynamics Research Articles

A hybrid lattice Boltzmann/immersed boundary method/finite-difference model for thermal fluid-solid interactions

Particulate flows are frequently observed in both industrial and natural environments, and their simulation becomes particularly challenging when heat transfer is involved. This study introduces a hybrid numerical approach, combining the lattice Boltzmann Method (LBM), Immersed Boundary Method (IBM), and Finite Difference (FD) energy solver to alleviate the limitations observed in double distributed lattice Boltzmann methods and classical Computational Fluid Dynamics (CFD). The model incorporates an enhanced Hermite polynomial-based central moments collision operator. This enhancement boosts stability and overcomes the Galilean-invariant issues observed in classical LBM. For heat transfer, a Finite-Difference technique is employed for resolving the energy equation, discretizing the advection term through a Weighted Essentially Non-Oscillatory (WENO) approach. The Boussinesq approximation handles buoyancy forces, while the direct-forcing IBM manages fluid-particle interaction. Validation across various test cases confirms the model's accuracy, showcasing its ability to account for variations in thermal properties like specific heat capacity Cp over a wide range. The model is further utilized to investigate a reactor containing 300 catalyst particles. In summary, this hybrid methodology is found to be a promising tool for comprehensively studying and designing particle-laden systems with thermal effects.

Thermo-mechanical coupled peridynamics simulation of concrete failure under fire scenarios

A coupled thermo-mechanical bond-based peridynamical (PD) method is developed to simulate thermal cracking processes in concrete. Based on the bond-based PD heat conduction and motion equations, the PD differential operator (PDDO) is used to express the classical computational fluid dynamics basic equations in a non-local integral form, establishing a PD model for the thermo-mechanical coupling problems. In this model, concrete is considered a heterogeneous material composed of aggregates and mortar, with material parameters assumed to be temperature-dependent. The multi-rate explicit time integration scheme is proposed to overcome the multi-scale time problem in coupled thermo-mechanical systems. The model is applied to simulate the transient heat transfer problem of a homogeneous plate. The results show good agreement with the analytical solution, providing evidence for the correctness and accuracy of the proposed coupled numerical method. The damage behavior of the borehole heated concrete plate is analyzed, followed by the simulation of the damage to the concrete plate under a fire scenario. The numerical results accurately predict the temperature distribution within the heterogeneous concrete and the resulting material damage. This study provides new theoretical basis for the fire resistance design and high-temperature performance improvement of concrete materials and structures.

Influences of geometry configurations on the performance of micro-nozzles

Micro-nozzles play a critical role in various applications, such as micro-/nano-satellites in aerospace and heat dissipation and cooling in microelectronic systems (MEMS). The flows inside micro-nozzles can experience both continuum and rarefied flow due to their small size. In this research, we explore the optimal geometry configuration of micro-nozzles to achieve comprehensive performance and size, as well as background pressure compensation. Using classical computational fluid dynamics (CFD) and direct simulation Monte Carlo methods (DSMC), we investigate the effects of the expansion ratio, cross-profile shape, and plug on the performance of micro-nozzles operating over a wide range of pressures (0.5−100kPa). The results reveal that micro-nozzle performance is influenced by the interplay between flow expansion and viscous loss induced by the subsonic layer next to the micro-nozzle wall. The findings show that micro-nozzle performance improves with increasing expansion ratio in slip and continuum flow regimes, but decreases in the transition flow regime. Additionally, the results indicate that the axisymmetric micro-nozzle (with a circular cross-profile) outperforms the linear micro-nozzle (with a rectangular cross-profile) in terms of both performance and size when subject to the same conditions, making it the recommended choice for practical applications. We also find that plugs designed at the throat decrease performance, but increase stability under diverse background pressures. This study provides valuable insights for the design of high-efficiency micro-nozzles in applications such as nanosats and MEMS heat dissipation units.

Scalable simulation of coupled adsorption and transport of methane in confined complex porous media with density preconditioning

The growing significance of shales and tight formations in the transition to less carbon-intensive and clean energy drives the research endeavor to understand the physics of gas flow within these systems. However, shales are composed of massively heterogeneous physical and chemical features. Most nano-sized pores connect to millimeter-scale fractures, leading to multiscale transport. These nano-scale pore throats demonstrate non-classical flow behavior, such as non-negligible slip velocities and adsorbed gas layers at the boundary. As a result, classical computational fluid dynamics models do not capture the physics. In this work, we develop a coupling scheme for the multiple-relaxation-time (MRT) lattice Boltzmann (LB) method that integrates the Peng-Robinson equation of state into a pseudo-potential interaction model to capture the physics of methane flow in irregular networks of channels that represent nano-scale porous media. We use atomistic simulations to calibrate and validate our model in slit nano-channels. We propose a preconditioning scheme to initialize the coupled transport and adsorption simulation of methane in complex porous media. The results of this implementation of LB agree with Direct Simulation Monte Carlo (DSMC) and Molecular Dynamics (MD) simulations. We then scale up the LB implementation through vectorization and indirect addressing. We parallelize it using Message Passing Interface (MPI) and OpenMP frameworks to simulate transport and adsorption in complex media with a million lattices. We analyze the differences between coupled and transport-only simulations in two case studies and show that considering phase behavior, i.e., adsorption, can significantly change the flow behavior. This work constitutes an important step towards bridging the gap between molecular flow and system-scale behavior of complex disordered porous media.

Hybrid data assimilation methods, Part I: Numerical comparison between GEIM and PBDW

Hybrid Data Assimilation (HDA) methods are a class of numerical methods that aim at integrating Model Order Reduction (MOR) techniques into a Data Assimilation (DA) framework, thus combining mathematical models and experimental data. The objective is to reduce the solution time using MOR algorithms whilst keeping the accuracy of the models at the desired level using observations, which serve as an update to the a priori prediction of the model. This two-part work investigated HDA techniques by applying them to two classes of problems: numerical benchmark cases (part 1) and experimental facilities (part 2). In particular, this paper discusses the former, focusing on the numerical formulation of the methodologies and on the effect of noisy data. Indeed, real-world experimental data are always polluted by errors and uncertainties; therefore, it is critical to first assess the performance of these techniques on numerical benchmark cases with the artificial introduction of random noise before applying them to real-world experimental facilities. As such, this paper applies the Generalised Empirical Interpolation Method (GEIM) and the Parameterised-Background Data-Weak (PBDW) formulation to a non-adiabatic airflow over the classical computational fluid-dynamics benchmark of the 3D Backward Facing Step (BFS). Results show how both algorithms are valuable tools to reconstruct the state of the system when measurements are available, whilst assessing the effect of noise on the available data; in particular, the GEIM is a bit better than the PBDW since a lower reconstruction error is achieved with fewer sensors.

Data-Driven Prediction of Complex Flow Field Over an Axisymmetric Body of Revolution Using Machine Learning

Abstract Computationally efficient and accurate simulations of the flow over axisymmetric bodies of revolution (ABR) have been an important desideratum for engineering design. In this article, the flow field over an ABR is predicted using machine learning (ML) algorithms (e.g., random forest (RF), artificial neural network (ANN), and convolutional neural network (CNN)) using trained ML models as surrogates for classical computational fluid dynamics (CFD) approaches. The data required for the development of the ML models were obtained from high fidelity Reynolds stress transport model (RSTM)-based simulations. The flow field is approximated as functions of x and y coordinates of locations in the flow field and the velocity at the inlet of the computational domain. The optimal hyperparameters of the trained ML models are determined using validation. The trained ML models can predict the flow field rapidly and exhibit orders of magnitude speedup over conventional CFD approaches. The predicted results of pressure, velocity, and turbulence kinetic energy are compared with the baseline CFD data. It is found that the ML-based surrogate model predictions are as accurate as CFD results. This investigation offers a framework for fast and accurate predictions for a flow scenario that is critically important in engineering design.

Solving Burgers\u2019 equation with quantum computing

Computational fluid dynamics (CFD) simulations are a vital part of the design process in the aerospace industry. Although reliable CFD results can be obtained with turbulence models, direct numerical simulation of complex bodies in three spatial dimensions (3D) is impracticable due to the massive amount of computational elements. For instance, a 3D direct numerical simulation of a turbulent boundary-layer over the wing of a commercial jetliner that resolves all relevant length scales using a serial CFD solver on a modern digital computer would take approximately 750 million years or roughly 20% of the earth’s age. Over the past 25 years, quantum computers have become the object of great interest worldwide as powerful quantum algorithms have been constructed for several important, computationally challenging problems that provide enormous speed-up over the best-known classical algorithms. In this paper, we adapt a recently introduced quantum algorithm for partial differential equations to Burgers’ equation and develop a quantum CFD solver that determines its solutions. We used our quantum CFD solver to verify the quantum Burgers’ equation algorithm to find the flow solution when a shockwave is and is not present. The quantum simulation results were compared to: (i) an exact analytical solution for a flow without a shockwave; and (ii) the results of a classical CFD solver for flows with and without a shockwave. Excellent agreement was found in both cases, and the error of the quantum CFD solver was comparable to that of the classical CFD solver.

ANALYSIS OF FREE SURFACE FLOW IN PELTON TURBINE USING LATTICE BOLTZMANN METHOD

Computational fluid dynamics (CFD) has become an indispensable tool in the development and optimization of various machines and devices in the last decade. In most cases, researchers deal with single-phase flows and internal flows where all externally wetted walls are defined. In some cases, it is also necessary to analyze multiphase flow and free-surface flow. Using classical numerical methods such as the finite element method (FEM) or the finite volume method (FVM), the results are highly dependent on the size and quality of the computational grids. Particular attention should be paid to the conditions at the boundary between the individual phases of the fluid. In most cases, it is necessary to consider non-stationary conditions and the necessity of using non-stationary numerical methods. All the above properties of multiphase flows and their consequences in performing numerical analyses lead us to very long computational times and consequently the use of very powerful computers. Industry often needs results in a relatively fast time therefore many simplifications need to be considered. Recently a new approach for numerical simulations of multiphase and free-surface flows based on the Lattice Boltzmann method (LBM) started to be used. The method is very useful especially for development of small-scale hydraulic turbines, where the expense for development process is usually very limited. In this paper, some examples of the use of LBM in the calculation of free-surface flows and compare the results using classical CFD methods have been presented.

ECONOMY AND POWER TUNING AN IC ENGINE FOR LOWER CO2 FOOTPRINT

Computational fluid dynamics (CFD) has become an indispensable tool in the development and optimization of various machines and devices in the last decade. In most cases, researchers deal with single-phase flows and internal flows where all externally wetted walls are defined. In some cases, it is also necessary to analyze multiphase flow and free-surface flow. Using classical numerical methods such as the finite element method (FEM) or the finite volume method (FVM), the results are highly dependent on the size and quality of the computational grids. Particular attention should be paid to the conditions at the boundary between the individual phases of the fluid. In most cases, it is necessary to consider non-stationary conditions and the necessity of using non-stationary numerical methods. All the above properties of multiphase flows and their consequences in performing numerical analyses lead us to very long computational times and consequently the use of very powerful computers. Industry often needs results in a relatively fast time therefore many simplifications need to be considered. Recently a new approach for numerical simulations of multiphase and free-surface flows based on the Lattice Boltzmann method (LBM) started to be used. The method is very useful especially for development of small-scale hydraulic turbines, where the expense for development process is usually very limited. In this paper, some examples of the use of LBM in the calculation of free-surface flows and compare the results using classical CFD methods have been presented.

Lbmpy: Automatic code generation for efficient parallel lattice Boltzmann methods

Lattice Boltzmann methods are a popular mesoscopic alternative to classical computational fluid dynamics based on the macroscopic equations of continuum mechanics. Many variants of lattice Boltzmann methods have been developed that vary in complexity, accuracy, and computational cost. Extensions are available to simulate multi-phase, multi-component, turbulent, and non-Newtonian flows. In this work we present lbmpy, a code generation package that supports a wide variety of different lattice Boltzmann methods. Additionally, lbmpy provides a generic development environment for new schemes. A high-level domain-specific language allows the user to formulate, extend and test various lattice Boltzmann methods. In all cases, the lattice Boltzmann method can be specified in symbolic form. Transformations that operate on this symbolic representation yield highly efficient compute kernels. This is achieved by automatically parallelizing the methods, and by various application-specific automatized steps that optimize the resulting code. This pipeline of transformations can be applied to a wide range of lattice Boltzmann variants, including single- and two-relaxation-time schemes, multi-relaxation-time methods, as well as the more advanced cumulant methods, and entropically stabilized methods. lbmpy can be integrated into high-performance computing frameworks to enable massively parallel, distributed simulations. This is demonstrated using the waLBerla multiphysics package to conduct scaling experiments on the SuperMUC-NG supercomputing system on up to 147 456 compute cores.

A NURBS-based finite element formulation for incompressible fluid dynamics and fluid-structure interaction with rigid bodies

Abstract A numerical investigation is performed here using a NURBS-based finite element formulation applied to classical Computational Fluid Dynamics (CFD) and Fluid-Structure Interaction (FSI) problems. Model capabilities related to refinement techniques are analyzed using a finite element formulation with NURBS (non uniform rational B-splines) basis functions, where B-splines and low-order Lagrangian elements can be considered as particular cases. An explicit two-step Taylor-Galerkin model is utilized for discretization of the fundamental flow equations and turbulence is considered using Large Eddy Simulation (LES) and the Smagorinsky’s sub-grid scale model. FSI is considered using an ALE kinematic formulation and a conservative partitioned coupling scheme with rigid body approach for large rotations is adopted. CFD and FSI applications are analyzed to evaluate the accuracy associated with the different refinement procedures utilized. Results show that high order basis functions with appropriate refinement and non-uniform parameterization lead to better predictions, compared with low-order Lagrangian models.

A modified discrete-vortex method algorithm with shedding criterion for aerodynamic coefficients prediction at high angle of attack

• New algorithm of the LDVM with a gain of a factor 2 in computing time. • Transient pitching motion: the leading edge vortex formation is two-dimensional. • Merging of vortices: decrease of the computing cost for long time simulations. • Evidence of the development of the lift coefficient between 30° and 90 ∘ . Low-order methods require less computing power than classical computational fluid dynamics and can be implemented on a laptop computer, which is needed for engineering tasks. Discrete vortex methods are such low order methods that can describe the unsteady separated flow around an airfoil . After a presentation of the leading edge suction parameter discrete vortex method, a modified algorithm is proposed, in order to reduce the computing cost, and compared with the previous one. Several reference unsteady airfoil motions are discussed in terms of gain in the computation time with comparisons between the previous scheme and the present one. The accuracy of the new method is demonstrated through aerodynamic coefficients . The application of the present discrete vortex method to a transient pitching motion of an airfoil is also presented, in order to understand the leading edge vortex formation, and its implication in terms of lift and drag coefficients. The method is not limited to unsteady or transient motions but can also simulate the flow around a constant angle of attack airfoil. In that case, an original method of fast summation of the vortices located far away from the airfoil, allows a linear dependence of the computation time versus the number of vortices shed, which is a great improvement over the quadratic dependence observed in the classical discrete vortex methods. The development of the aerodynamic coefficients with angle of attack, from values ranging between −10° and 90°, is obtained for a purely two-dimensional flow. In particular, the shape of the lift coefficient of the airfoil in the fully detached flow region is established. Comparisons with relevant experimental or computational fluid dynamics data are discussed in order to grasp the influence of upstream turbulence level and three-dimensional effects in the measured data in the fully detached flow region.

Porous and geometry-resolved CFD modelling of a lattice transmission tower validated by drag force and flow field measurements

The assessment of the aerodynamic forces acting on transmission towers is of crucial importance for their design. These predictions are mainly based on an extrapolation of wind tunnel measurements done on simple structures which are the base of the present design codes. This extrapolation results in an uncertainty which often leads to insufficiently accurate drag force predictions, because of a lack of agreement between the basis of the design codes and their use for tall and complex tower geometries. Therefore, in the present study drag forces are measured in a wind tunnel on a scaled transmission tower and three representative sections of it. Results show similar drag coefficients for the entire tower and the different sections it is composed of. Additionally, the flow fields in the wake of these structures are measured with PIV (Particle Image Velocimetry). With low lattice densities the effect of each lattice element can be seen in the wake, while the lattice structures act as a porous media for higher densities. Based on these results a CFD (Computational Fluid Dynamics) approach, in which the transmission tower is modelled as a porous media, is proposed in this paper. The CFD simulations are performed substituting the tower geometry with a representative porous model, decreasing considerably the computational time and cost of the simulations. A validation against the experiments and classical CFD simulations, where the detailed geometries are resolved, is performed and shows the applicability of the developed approach. The drag forces as well as the velocity deficit in the wake of the transmission tower are well predicted with the porous CFD simulations. For regions with low lattice densities the porous CFD simulations cannot predict the effect of individual lattice elements on the flow field, because the individual lattice elements are not explicitly resolved.

Coupled WRF-OpenFOAM study of wind flow over complex terrain

This study addresses turbulence modelling issues related to the simulation of flow over complex terrain using a coupling between NWP (numerical weather prediction) code and a classical CFD (computational fluid dynamics) code. A new planetary boundary layer (PBL) parameterization scheme, which is specifically formulated for coupling purposes, is presented. The capability of the developed closure models to be applied to the whole atmospheric boundary layer, not only to the surface layer is assessed by performing idealized simulations and comparing the results with the Leipzig dataset. CFD simulations sustained with inflow conditions acquired from mesoscale simulations are performed with different turbulence closures for the Askervein Hill case and their performances are evaluated in comparison with wind speed and turbulence kinetic energy measurements. Finally, the proposed turbulence modelling methodology is applied to the Ria de Ferrol Case. The new PBL scheme is implemented and tested with the open source mesoscale code, Weather Research and Forecasting (WRF) model. Microscale simulations and the turbulence model implementation are performed with the open source computational fluid dynamics (CFD) toolbox, OpenFOAM v. 2.3.1.

A REGULARIZED STIFFENED-GAS EQUATION OF STATE

An alternative to the stiffened-gas equation of state is proposed that corrects for unphysical behavior, namely the returning of negative pressure values for densities lower than the reference density. The question of generalizing a given isentropic equation of state is first addressed. Then, a regularized stiffened-gas equation of state is derived, which is the main goal of this work. Finally, the use of the new equation of state is briefly illustrated for a classical computational fluid dynamics benchmark concerning the evaluation of liquid impact on a wall.

Tomographic particle image velocimetry for the validation of hemodynamic simulations in an intracranial aneurysm.

Image-based blood flow simulations can provide detailed hemodynamic information in diseased vessels such as intracranial aneurysms. However, validation is essential to evaluate the accuracy of these computations and further improve their acceptance among physicians. In this regard, tomographic particle image velocimetry was used to measure the flow characteristics in a patient specific aneurysm phantom model. Additionally, computational fluid dynamics (CFD) simulations were carried out using a well accepted commercial software package and a clinical research prototype, respectively. The comparison between in-vitro measurement and in-silico computations reveals a good qualitative agreement. Further, computations based on classical CFD agreed well with results from a clinical research prototype. Hence, the results of this study demonstrate the usability of numerical methods to obtain realistic blood flow predictions in a clinical context.

A wavelet based numerical simulation technique for two-phase flows using the phase field method

In multiphase flow phenomena, bubbles and droplets are advected, deformed, break up into smaller ones, and coalesce with each other. A primary challenge of classical computational fluid dynamics (CFD) methods for such flows is to effectively describe a transition zone between phases across which physical properties vary steeply but continuously. Based on the van der Waals theory, Allen-Cahn phase field method describes the face-to-face existence of two fluids with a free-energy functional of mass density or molar concentration, without imposing topological constraints on interface as phase boundary. In this article, a CFD simulation methodology is described by solving the Allen-Cahn-Navier-Stokes equations using a wavelet collocation method. The second order temporal accuracy is verified by simulating a moving sharp interface. The average terminal velocity of a rising gas bubble in a liquid that is computed by the present method has agreed with that computed by a laboratory experiment. The calculation of the surface tension force by the present method also shows an excellent agreement with what was obtained by an experiment. The up-welling and down-welling disturbances in a Rayleigh-Taylor instability are computed and compared with that from a reference numerical simulation. These results show that the wavelet based phase-field method is an efficient CFD simulation technique for gas-liquid or liquid-liquid flows.

Flow characteristics of metallic powder grains for additive manufacturing

Directed energy deposition technologies for additive manufacturing such as laser selective melting (SLM) or electron beam melting (EBM) is a fast growing technique mainly due to its flexibility in product design. However, the process is a complex interaction of multi-physics on multiple length scales that are still not entirely understood. A particular challenging task are the flow characteristics of metallic powder ejected as jets from a nozzle and shielded by an inert turbulent gas flow. Therefore, the objective is to describe numerically the complex interaction between turbulent flow and powder grains. In order to include both several physical processes and length scales an Euler-Lagrange technology is applied. Within this framework powder is treated by the Discrete-Element-Method, while gas flow is described by Euler approaches as found in classical Computational Fluid Dynamics (CFD). The described method succeeded in delivering more accuracy and consistency than a standard approach based on the volume averaging technique and therefore, is suited for the solution of problems within an engineering framework.

Flow Simulation Around Cambered Airfoil by Using Conformal Mapping and Intermediate Domain in Lattice Boltzmann Method

In this paper the developed interpolation lattice Boltzmann method is used for simulation of unsteady fluid flow. It combines the desirable features of the lattice Boltzmann and the Joukowski transformation methods. This approach has capability to simulate flow around curved boundary geometries such as airfoils in a body fitted grid system. Simulation of unsteady flow around a cambered airfoil in a non-uniform grid for the first time is considered to show the capability of this method for modeling of fluid flow around complex geometries and complicated long-term periodic flow phenomena. The developed solver is also coupled with a fast adaptive grid generator. In addition, the new approach retains all the advantages of the standard lattice Boltzmann method. The Strouhal number, the pressure, the drag and the lift coefficients obtained from the simulations agree well with classical computational fluid dynamics simulations. Numerical studies for various test cases illustrate the strength of this new approach.

Recurrence CFD – A novel approach to simulate multiphase flows with strongly separated time scales

Classical Computational Fluid Dynamics (CFD) of long-time processes with strongly separated time scales is computationally extremely demanding if not impossible. Consequently, the state-of-the-art description of such systems is not capable of real-time simulations or online process monitoring.In order to bridge this gap, we propose a new method suitable to decouple slow from fast degrees of freedom in many cases. Based on the recurrence statistics of unsteady flow fields, we deduce a recurrence process which enables the generic representation of pseudo-periodic motion at high spatial and temporal resolution.Based on these fields, passive scalars can be traced by recurrence CFD. While a first, Eulerian Model A solves a passive transport equation in a classical implicit finite-volume environment, a second, Lagrangian Model B propagates fluid particles obeying a stochastic differential equation explicitly.Finally, this new concept is tested by two multiphase processes – a lab scale oscillating bubble column and an industrial scale steelmaking converter. Results of tracer distribution obtained by recurrence CFD are in very good agreement with full CFD simulations, while computational times are dramatically reduced. Actually, recurrence CFD is a promising candidate for online simulations of passive transport processes at full CFD resolution, which opens the door towards improved process monitoring.