Direct Numerical Simulation of Vertical Rotating Turbulent Open-Channel Flow with Heat Transfer

Direct numerical simulation of vertical rotating open-channel flow with heat transfer has been carried out for the rotation number N_τ from 0 to 0.1, the Prandtl number 1, and the Reynolds number 180 based on the friction velocity of non-rotating flow and the height of the channel. The ob jective of this study is to reveal the effect of rotation on the characteristics of turbulent flow and heat transfer, in particular near the free surface and the wall of the open-channel. Statistical quantities, e.g., the mean velocity, temperature and their fluctuations, turbulent heat fluxes, and turbulence structures, are analyzed. The depth of surface-influenced layer decreases with the increase of the rotation rate. In the free surface-influenced layer, the turbulence and thermal statistics are suppressed due to the effect of rotation. In the wall-influenced region, two typical rotation regimes are identified. In the weak rotation regime with 0 < N_τ< 0.06 approximately, the turbulence and thermal statistics correlated with the spanwise velocity fluctuation are enhanced since the shear rate of spanwise mean flow induced by Coriolis force increases; however, the other statistics are suppressed. In the strong rotation regime with Nτ > 0.06, the turbulence and thermal statistics are suppressed significantly because the Coriolis force effect plays a dominant role in the rotating flow. To elucidate the effect of rotation on turbulent flow and heat transfer, the budget terms in the transport equations of Reynolds stresses and turbulent heat fluxes are investigated. Remarkable change of the direction of streak structures based on the velocity and temperature fluctuations is discussed.     

Turbulence significantly increases pressure and fluid shear stress in an aortic aneurysm model under resting and exercise flow conditions

The numerical models of abdominal aortic aneurysm (AAA) in use do not take into account the non-Newtonian behavior of blood and the development of local turbulence. This study examines the influence of pulsatile, turbulent, non-Newtonian flow on fluid shear stresses and pressure changes under rest and exercise conditions. We numerically analyzed pulsatile turbulent flow, using simulated physiological rest and exercise waveforms, in axisymmetric-rigid aortic aneurysm models (AAMs). Discretization of governing equations was achieved using a finite element scheme. Maximum turbulence-induced shear stress was found at the distal end of an AAM. In large AAMs (dilated to undilated diameter ratio = 3.33) at peak systolic flow velocity, fluid shear stress during exercise is 70.4% higher than at rest. Our study provides a numerical, noninvasive method for obtaining detailed data on the forces generated by pulsatile turbulent flow in AAAs that are difficult to study in humans and in physical models. Our data suggest that increased flow turbulence results in increased shear stress in aneurysms. While pressure readings are fairly uniform along the length of an aneurysm, the kinetic energy generated by turbulence impacting on the wall of the distal half of the aneurysm increases fluid and wall shear stress at this site. If the increased fluid shear stress results in further dilation and hence further turbulence, wall stress may be a mechanism for aneurysmal growth and eventual rupture.     

Investigation of Compressible Electromagnetic Flute Mode Instability in Finite Beta Plasma in Support of Z-Pinch and Laboratory Astrophysics Experiments

Flute mode turbulence plays an important role in numerous applications, such as tokamak, Z-pinch, space and astrophysical plasmas. In a low beta plasma flute oscillations are electrostatic and in the nonlinear stage they produce large scale density structures co-mingling with short scale oscillations. Large scale structures are responsible for the enhanced transport across the magnetic field and appearance of short scales leads to ion heating, associated with the ion viscosity. In the present paper nonlinear equations which describe the nonlinear evolution of the flute modes treated as compressible electromagnetic oscillations in a finite beta inhomogeneous plasma with nonuniform magnetic field are derived and solved numerically. For this purpose the 2D numerical code FLUTE was developed. Numerical results show that even in a finite beta plasma flute mode instability can develop along with formation of large scale structures co-existing with short scale perturbations in the nonlinear stage.     

Unsteady Flow Separation and High Performance of Airfoil with Local Flexible Structure at Low Reynolds Number

The unsteady flow separation of airfoil with a local flexible structure (LFS) is studied numerically in Lagrangian frames in detail, in order to investigate the nature of its high aerodynamic performance. For such aeroelastic system, the characteristic-based split (CBS) scheme combined with arbitrary Lagrangian-Eulerian (ALE) framework is developed firstly for the numerical analysis of unsteady flow, and Galerkin method is used to approach the flexible structure. The local flexible skin of airfoil, which can lead to self-induced oscillations, is considered as unsteady perturbation to the flow. Then, the ensuing high aerodynamic performances and complex unsteady flow separation at low Reynolds number are studied by Lagrangian coherent structures (LCSs). The results show that the LFS has a significant influence on the unsteady flow separation, which is the key point for the lift enhancement. Specifically, the oscillations of the LFS can induce the generations of moving separation and vortex, which can enhance the kinetic energy transport from main flow to the boundary layer. The results could give a deep understanding of the dynamics in unsteady flow separation and flow control for the flow over airfoil.     

Numerical Simulation of Glottal Flow in Interaction with Self Oscillating Vocal Folds: Comparison of Finite Element Approximation with a Simplified Model

In this paper the numerical method for solution of an aeroelastic model describing the interactions of air flow with vocal folds is described. The flow is modelled by the incompressible Navier-Stokes equations spatially discretized with the aid of the stabilized finite element method. The motion of the computational domain is treated with the aid of the Arbitrary Lagrangian Eulerian method. The structure dynamics is replaced by a mechanically equivalent system with the two degrees of freedom governed by a system of ordinary differential equations and discretized in time with the aid of an implicit multistep method and strongly coupled with the flow model. The influence of inlet/outlet boundary conditions is studied and the numerical analysis is performed and compared to the related results from literature.     

A Scalable Numerical Method for Simulating Flows Around High-Speed Train Under Crosswind Conditions

This paper presents a parallel Newton-Krylov-Schwarz method for the numerical simulation of unsteady flows at high Reynolds number around a high-speed train under crosswind. With a realistic train geometry, a realistic Reynolds number, and a realistic wind speed, this is a very challenging computational problem. Because of the limited parallel scalability, commercial CFD software is not suitable for supercomputers with a large number of processors. We develop a Newton-Krylov-Schwarz based fully implicit method, and the corresponding parallel software, for the 3D unsteady incompressible Navier-Stokes equations discretized with a stabilized finite element method on very fine unstructured meshes. We test the algorithm and software for flows passing a train modeled after China's high-speed train CRH380B, and we also compare our results with results obtained from commercial CFD software. Our algorithm shows very good parallel scalability on a supercomputer with over one thousand processors.     

An Improved Second-Order Finite-Volume Algorithm for Detached-Eddy Simulation Based on Hybrid Grids

A hybrid grid based second-order finite volume algorithm has been developed for Detached-Eddy Simulation (DES) of turbulent flows. To alleviate the effect caused by the numerical dissipation of the commonly used second order upwind schemes in implementing DES with unstructured computational fluid dynamics (CFD) algorithms, an improved second-order hybrid scheme is established through modifying the dissipation term of the standard Roe's flux-difference splitting scheme and the numerical dissipation of the scheme can be self-adapted according to the DES flow field information. By Fourier analysis, the dissipative and dispersive features of the new scheme are discussed. To validate the numerical method, DES formulations based on the two most popular background turbulence models, namely, the one equation Spalart-Allmaras (SA) turbulence model and the two equation k−ω Shear Stress Transport model (SST), have been calibrated and tested with three typical numerical examples (decay of isotropic turbulence, NACA0021 airfoil at 60^◦incidence and 65^◦swept delta wing). Computational results indicate that the issue of numerical dissipation in implementing DES can be alleviated with the hybrid scheme, the resolution for turbulence structures is significantly improved and the corresponding solutions match the experimental data better. The results demonstrate the potentiality of the present DES solver for complex geometries.     

Vortical Flow Structure in the Wake of an Estate Car

A finite volume simulation of unsteady vortical wake flow behind a square-back estate car is presented. The three-dimensional time-averaged incompressible Navier-Stokes equations are solved together with the Reynolds stress transport equations for turbulence. By virtue of the simulated surface streamlines, the physics of fluid can be extracted using the topological theory. In addition, the simulated topological singular points and lines of separation are plotted on the car surface. The vortical flow motions that developed behind the mirrors, wheels and car body are explored by means of the simulated time evolving vortex corelines. The formation and interaction of the vortex systems in the wake are examined by tracing the instantaneous streamlines in the vicinity of the simulated vortex corelines. The vortex street behind the estate car is also illustrated by the simulated streaklines. Finally the Hopf bifurcation phenomenon is revealed by the time-varying aerodynamic forces on the car.     

A Parallel Domain Decomposition Algorithm for Simulating Blood Flow with Incompressible Navier-Stokes Equations with Resistive Boundary Condition

We introduce and study a parallel domain decomposition algorithm for the simulation of blood flow in compliant arteries using a fully-coupled system of nonlinear partial differential equations consisting of a linear elasticity equation and the incompressible Navier-Stokes equations with a resistive outflow boundary condition. The system is discretized with a finite element method on unstructured moving meshes and solved by a Newton-Krylov algorithm preconditioned with an overlapping restricted additive Schwarz method. The resistive outflow boundary condition plays an interesting role in the accuracy of the blood flow simulation and we provide a numerical comparison of its accuracy with the standard pressure type boundary condition. We also discuss the parallel performance of the implicit domain decomposition method for solving the fully coupled nonlinear system on a supercomputer with a few hundred processors.     

Numerical Analyses for Low Reynolds Flow in a Ventricular Assist Device

Scientific and technological advances in blood pump developments have been driven by their importance in cardiac patient treatments and in the expansion of life quality in assisted people. To improve and optimize the design and development, numerical tools were incorporated into the analyses of these mechanisms and have become indispensable in their advances. This study analyzes the flow behavior with low impeller Reynolds number, for which there is no consensus on the full development of turbulence in ventricular assist devices (VAD). For supporting analyses, computational numerical simulations were carried out in different scenarios with the same rotation speed. Two modeling approaches were applied: laminar flow and turbulent flow with the standard, RNG and realizable κ ? ε; the standard and SST κ ? ω models; and Spalart–Allmaras models. The results agree with the literature for VAD and the range for transient flows in stirred tanks with an impeller Reynolds number around 2800 for the tested scenarios. The turbulent models were compared, and it is suggested, based on the expected physical behavior, the use of RNG, standard and SST , and Spalart–Allmaras models to numerical analyses for low impeller Reynolds numbers according to the tested flow scenarios.     

Solution Remapping Method with Lower Bound Preservation for Navier-Stokes Equations in Aerodynamic Shape Optimization

It is found that the solution remapping technique proposed in [Numer. Math. Theor. Meth. Appl., 2020, 13(4)] and [J. Sci. Comput., 2021, 87(3): 1-26] does not work out for the Navier-Stokes equations with a high Reynolds number. The shape deformations usually reach several boundary layer mesh sizes for viscous flow, which far exceed one-layer mesh that the original method can tolerate. The direct application to Navier-Stokes equations can result in the unphysical pressures in remapped solutions, even though the conservative variables are within the reasonable range. In this work, a new solution remapping technique with lower bound preservation is proposed to construct initial values for the new shapes, and the global minimum density and pressure of the current shape which serve as lower bounds of the corresponding variables are used to constrain the remapped solutions. The solution distribution provided by the present method is proven to be acceptable as an initial value for the new shape. Several numerical experiments show that the present technique can substantially accelerate the flow convergence for large deformation problems with 70%-80% CPU time reduction in the viscous airfoil drag minimization.     

A Parallel Computational Model for Three-Dimensional,Thermo-Mechanical Stokes Flow Simulations of Glaciers and Ice Sheets

This paper focuses on the development of an efficient, three-dimensional, thermo-mechanical, nonlinear-Stokes flow computational model for ice sheet simulation. The model is based on the parallel finite element model developed in [14] which features high-order accurate finite element discretizations on variable resolution grids. Here, we add an improved iterative solution method for treating the nonlinearity of the Stokes problem, a new high-order accurate finite element solver for the temperature equation, and a new conservative finite volume solver for handling mass conservation. The result is an accurate and efficient numerical model for thermo-mechanical glacier and ice-sheet simulations. We demonstrate the improved efficiency of the Stokes solver using the ISMIP-HOM Benchmark experiments and a realistic test case for the Greenland ice-sheet. We also apply our model to the EISMINT-II benchmark experiments and demonstrate stable thermo-mechanical ice sheet evolution on both structured and unstructured meshes. Notably, we find no evidence for the "cold spoke" instabilities observed for these same experiments when using finite difference, shallow-ice approximation models on structured grids.     

Aerodynamic Analysis of a Localized Flexible Airfoil at Low Reynolds Numbers

A localized flexible airfoil at low Reynolds numbers is modeled and the aerodynamic performance is analyzed numerically. With characteristic based split scheme, a fluid solver for two dimensional incompressible Navier-Stokes equations is developed under the ALE framework, coupled with the theory of shallow arch, which is approximated by Galerkin method. Further, the interactions between the unsteady flow and the shallow arch are studied in detail. In particular, the effect of the self-excited vibration of the structure on aerodynamic performance of the airfoil is investigated deeply at various angles of attack. The results show that the lift-to-drag ratio has been increased greatly compared with the rigid airfoil. Finally, the relationship between the self-excited vibration and the evolution of the flow is analyzed using FFT tools.     

Numerical Simulation of Compressible Vortical Flows Using a Conservative Unstructured-Grid Adaptive Scheme

A two-dimensional numerical scheme for the compressible Euler equations is presented and applied here to the simulation of exemplary compressible vortical flows. The proposed approach allows to perform computations on unstructured moving grids with adaptation, which is required to capture complex features of the flow-field. Grid adaptation is driven by suitable error indicators based on the Mach number and by element-quality constraints as well. At the new time level, the computational grid is obtained by a suitable combination of grid smoothing, edge-swapping, grid refinement and de-refinement. The grid modifications—including topology modification due to edge-swapping or the insertion/deletion of a new grid node—are interpreted at the flow solver level as continuous (in time) deformations of suitably-defined node-centered finite volumes. The solution over the new grid is obtained without explicitly resorting to interpolation techniques, since the definition of suitable interface velocities allows one to determine the new solution by simple integration of the Arbitrary Lagrangian-Eulerian formulation of the flow equations. Numerical simulations of the steady oblique-shock problem, of the steady transonic flow and of the start-up unsteady flow around the NACA 0012 airfoil are presented to assess the scheme capabilities to describe these flows accurately.     

Numerical Investigations of the Dynamical Behaviors and Instabilities for the Gierer-Meinhardt System

This work is concerned with the numerical simulations on the Gierer-Meinhardt activator-inhibitor models. We consider the case when the inhibitor time constant τ is non-zero. In this case, oscillations and pulse splitting are observed numerically. Numerical experiments are carried out to investigate the dynamical behaviors and instabilities of the spike patterns. The numerical schemes used are based upon an efficient moving mesh finite element method which distributes more grid points near the localized spike regions.     

An Implicit LU-SGS Scheme for the Spectral Volume Method on Unstructured Tetrahedral Grids

An efficient implicit lower-upper symmetric Gauss-Seidel (LU-SGS) solution approach has been applied to a high order spectral volume (SV) method for unstructured tetrahedral grids. The LU-SGS solver is preconditioned by the block element matrix, and the system of equations is then solved with a LU decomposition. The compact feature of SV reconstruction facilitates the efficient solution algorithm even for high order discretizations. The developed implicit solver has shown more than an order of magnitude of speed-up relative to the Runge-Kutta explicit scheme for typical inviscid and viscous problems. A convergence to a high order solution for high Reynolds number transonic flow over a 3D wing with a one equation turbulence model is also indicated.     

The Biharmonic Approach for Unsteady Flow Past an Impulsively Started Circular Cylinder

In this paper, a newly developed second order temporally and spatially accurate finite difference scheme for biharmonic semi linear equations has been employed in simulating the time evolution of viscous flows past an impulsively started circular cylinder for Reynolds number (Re) up to 9,500. The robustness of the scheme and the effectiveness of the formulation can be gauged by the fact that it very accurately captures complex flow structures such as the von Kármán vortex street through streakline simulation and the α and β-phenomena in the range 3,000≤Re≤9,500 among others. The main focus here is the application of the technique which enables the use of the discretized version of a single semi linear biharmonic equation in order to efficiently simulate different fluid structures associated with flows around a bluff body. We compare our results, both qualitatively and quantitatively, with established numerical and more so with experimental results. Excellent comparison is obtained in all the cases.     

Simulation of Two-Dimensional Scramjet Combustor Reacting Flow Field Using Reynolds Averaged Navier-Stokes WENO Solver

The non-equilibrium chemical reacting combustion flows of a proposed long slender scramjet system were numerically studied by solving the turbulent Reynolds averaged Navier-Stokes (RANS) equations. The Spalart-Allmaras one equation turbulence model is used which produces better results for near wall and boundary layer flow field problems. The lower-upper symmetric Gauss-Seidel implicit scheme, which enables results converge efficiently under steady state condition, is combined with the weighted essentially non-oscillatory (WENO) scheme to yield an accurate simulation tool for scramjet combustion flow field analysis. Using the WENO schemes high-order accuracy and its non-oscillatory solution at flow discontinuities, better resolution of the hypersonic flow problems involving complex shock-shock/shock-boundary layer interactions inside the flow path, can be achieved. Two types of scramjet combustor with cavity-based and strut-based fuel injector were considered as the testing models. The flow characteristics with and without combustion reactions of the two types of combustor models were studied with a transient hydrogen/oxygen combustion model. The detailed results of aerodynamic data are obtained and discussed, moreover, the combustion properties of varying the equivalent ratio of hydrogen, including the concentration of reacting species, hydrogen and oxygen, and the reacting products, water, are demonstrated to study the combustion process and performance of the combustor. The comparisons of flow field structures, pressure on wall and velocity profiles between the experimental data and the solutions of the present algorithms, showed qualitatively as well as the quantitatively in good agreement, and validated the adequacy of the present simulation tool for hypersonic scramjet reacting flow analysis.     

A Two-Phase Flow Simulation of Discrete-Fractured Media Using Mimetic Finite Difference Method

Various conceptual models exist for numerical simulation of fluid flow in fractured porous media, such as dual-porosity model and equivalent continuum model. As a promising model, the discrete-fracture model has been received more attention in the past decade. It can be used both as a stand-alone tool as well as for the evaluation of effective parameters for the continuum models. Various numerical methods have been applied to the discrete-fracture model, including control volume finite difference, Galerkin and mixed finite element methods. All these methods have inherent limitations in accuracy and applicabilities. In this work, we developed a new numerical scheme for the discrete-fracture model by using mimetic finite difference method. The proposed numerical model is applicable in arbitrary unstructured grid cells with full-tensor permeabilities. The matrix-fracture and fracture-fracture fluxes are calculated based on powerful features of the mimetic finite difference method, while the upstream finite volume scheme is used for the approximation of the saturation equation. Several numerical tests in 2D and 3D are carried out to demonstrate the efficiency and robustness of the proposed numerical model.