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Cavitation erosion is caused in solids exposed to strong pressure waves developing in an adjacent fluid field. The knowledge of the transient distribution of stresses in the solid is important to understand the cause of damaging by comparisons with breaking points of the material. The modeling of this problem requires the coupling of the models for the fluid and the solid. For this purpose we employ a strategy based on the solution of coupled Riemann problems that has been originally developed for the coupling of two fluids. This concept is exemplified for the coupling of a linear elastic structure with an ideal gas. The coupling procedure relies on the solution of a nonlinear equation. Existence and uniqueness of the solution is proven. The coupling conditions are validated by means of quasi-1D problems for which an explicit solution can be determined. For a more realistic scenario a 2D application is considered where in a compressible single fluid a hot gas bubble at low pressure collapses in a cold gas at high pressure near an adjacent structure. This article is protected by copyright. All rights reserved.
The main purpose of this article is to develop a forced reduced-order model based on the proper orthogonal decomposition (POD)/Galerkin projection (on isentropic Navier-Stokes equations) and perturbation method on the compressible Navier-Stokes equations. The resulting forced reduced-order model will be used in optimal control of the separated flow over a NACA23012 airfoil at Mach number of 0.2, Reynolds number of 800, and high incidence angle of 24°. The main disadvantage of the POD/Galerkin projection method for control purposes is that controlling parameters do not show up explicitly in the resulting reduced-order system. The perturbation method and POD/Galerkin projection on the isentropic Navier-Stokes equations introduce a forced reduced-order model that can predict the time varying influence of the controlling parameters and the Navier-Stokes response to external excitations. An optimal control theory based on forced reduced-order system is used to design a control law for a nonlinear reduced-order system, which attempts to minimize the vorticity content in the flow field. The test bed is a laminar flow over NACA23012 airfoil actuated by a suction jet at 12% to 18% chord from leading edge and a pair of blowing/suction jets at 15% to 18% and 24% to 30% chord from leading edge, respectively. The results show that wall jet can significantly influence the flow field, remove separation bubbles, and increase the lift coefficient up to 22%, while the perturbation method can predict the flow field in an accurate manner.
The main purpose of this article is to develop a forced reduced-order model based on the proper orthogonal decomposition/Galerkin projection and perturbation method on the compressible Navier-Stokes equations. The model will be used in optimal control of the laminar separated flow over a NACA23012 airfoil at M = 0.2, Re = 800, and incidence angle of 24°. The airfoil is actuated by a suction jet at 12% to 18% chord from leading edge and a pair of blowing/suction jets at 15% to 18% and 24% to 30% chord from leading edge.
We present a novel approach to wall modeling for the Reynolds-averaged Navier-Stokes equations within the discontinuous Galerkin method. Wall functions are not used to prescribe boundary conditions as usual, but they are built into the function space of the numerical method as a local enrichment, in addition to the standard polynomial component. The Galerkin method then automatically finds the optimal solution among all shape functions available. This idea is fully consistent and gives the wall model vast flexibility in separated boundary layers or high adverse pressure gradients. The wall model is implemented in a high-order discontinuous Galerkin solver for incompressible flow complemented by the Spalart-Allmaras closure model. As benchmark examples, we present turbulent channel flow starting from Reτ=180 and up to Reτ=100000 as well as flow past periodic hills at Reynolds numbers based on the hill height of ReH=10595 and ReH=19000.
We present a novel approach to wall modeling for the Reynolds-averaged Navier-Stokes equations within the discontinuous Galerkin method. The velocity profile in a turbulent boundary layer is composed of the standard polynomial component plus an enrichment component, which is constructed using Spalding's law-of-the-wall. This composition results in a much higher degree of flexibility in strong nonequilibrium boundary layers and mesh independence than common wall functions can provide.
No abstract is available for this article.
In this paper, we present the numerical solution of 2-phase flow problems of engineering significance with a space-time finite element method that allows for local temporal refinement. Arbitrary temporal refinement is applied to preselected regions of the mesh and is governed by a quantity that is part of the solution process, namely, the interface position in 2-phase flow. Because of local effects such as surface tension, jumps in material properties, etc, the interface can in general be considered a region that requires high flexibility and high resolution, both in space and in time. The new method, which leads to tetrahedral (for 2D problems) and pentatope (for 3D problems) meshes, offers an efficient yet accurate approach to the underlying 2-phase flow problems.
The main goal of this paper was to demonstrate how adaptive temporal refinement can be applied in the area of evolving fronts, by means of space-time FE. Firstly, tetrahedral (2D) and pentatope (3D) meshes are used for simulating two-phase flow problems and their behavior is compared to that of the usual prismatic space-time elements. Furthermore, a hybrid tetrahedral space-time grid is used for the filling of a step cavity, giving us the flexibility to use a type of local time-stepping.
This paper presents a novel model reduction method: deep learning reduced order model, which is based on proper orthogonal decomposition and deep learning methods. The deep learning approach is a recent technological advancement in the field of artificial neural networks. It has the advantage of learning the nonlinear system with multiple levels of representation and predicting data. In this work, the training data are obtained from high fidelity model solutions at selected time levels. The long short-term memory network is used to construct a set of hypersurfaces representing the reduced fluid dynamic system. The model reduction method developed here is independent of the source code of the full physical system.
The reduced order model based on deep learning has been implemented within an unstructured mesh finite element fluid model. The performance of the new reduced order model is evaluated using 2 numerical examples: an ocean gyre and flow past a cylinder. These results illustrate that the CPU cost is reduced by several orders of magnitude whilst providing reasonable accuracy in predictive numerical modelling.
This paper presents a novel model reduction method: deep learning reduced order model, which is based on proper orthogonal decomposition and deep learning methods. The reduced order model based on deep learning has been implemented within an unstructured mesh finite element fluid model. The performance of the new reduced order model is evaluated using 2 numerical examples: an ocean gyre and flow past a cylinder. These results illustrate that the CPU cost is reduced by several orders of magnitude whilst providing reasonable accuracy in predictive numerical modelling.
We report our recent development of the high-order flux reconstruction adaptive mesh refinement (AMR) method for magnetohydrodynamics (MHD). The resulted framework features a shock-capturing duo of AMR and artificial resistivity (AR), which can robustly capture shocks and rotational and contact discontinuities with a fraction of the cell counts that are usually required. In our previous paper, we have presented a shock-capturing framework on hydrodynamic problems with artificial diffusivity and AMR. Our AMR approach features a tree-free, direct-addressing approach in retrieving data across multiple levels of refinement. In this article, we report an extension to MHD systems that retains the flexibility of using unstructured grids. The challenges due to complex shock structures and divergence-free constraint of magnetic field are more difficult to deal with than those of hydrodynamic systems. The accuracy of our solver hinges on 2 properties to achieve high-order accuracy on MHD systems: removing the divergence error thoroughly and resolving discontinuities accurately. A hyperbolic divergence cleaning method with multiple subiterations is used for the first task. This method drives away the divergence error and preserves conservative forms of the governing equations. The subiteration can be accelerated by absorbing a pseudo time step into the wave speed coefficient, therefore enjoys a relaxed CFL condition. The AMR method rallies multiple levels of refined cells around various shock discontinuities, and it coordinates with the AR method to obtain sharp shock profiles. The physically consistent AR method localizes discontinuities and damps the spurious oscillation arising in the curl of the magnetic field. The effectiveness of the AMR and AR combination is demonstrated to be much more powerful than simply adding AR on finer and finer mesh, since the AMR steeply reduces the required amount of AR and confines the added artificial diffusivity and resistivity to a narrower and narrower region. We are able to verify the designed high-order accuracy in space by using smooth flow test problems on unstructured grids. The efficiency and robustness of this framework are fully demonstrated through a number of two-dimensional nonsmooth ideal MHD tests. We also successfully demonstrate that the AMR method can help significantly save computational cost for the Orszag-Tang vortex problem.
High-order flux reconstruction method is extended for solving magnetohydrodynamic equations for the first time. The shock-capturing duo of adaptive mesh refinement and artificial resistivity achieves sharply defined shock profile with a fraction of cells of uniformly refined cell, as shown in the above Orszag-Tang vortex case. When plasma beta is low, a decoupled hyperbolic cleaning method is capable of thoroughly removing the divergence error in a multiple sweep fashion.
In this paper, we present a two-dimensional computational framework for the simulation of fluid-structure interaction problems involving incompressible flexible solids and multiphase flows, further extending the application range of classical immersed computational approaches to the context of hydrodynamics. The proposed method aims to overcome shortcomings such as the restriction of having to deal with similar density ratios among different phases or the restriction to solve single-phase flows. First, a variation of classical immersed techniques, pioneered with the immersed boundary method (IBM), is presented by rearranging the governing equations, which define the behaviour of the multiple physics involved. The formulation is compatible with the “one-fluid” formulation for two-phase flows and can deal with large density ratios with the help of an anisotropic Poisson solver. Second, immersed deformable structures and fluid phases are modelled in an identical manner except for the computation of the deviatoric stresses. The numerical technique followed in this paper builds upon the immersed structural potential method developed by the authors, by adding a level set–based method for the capturing of the fluid-fluid interfaces and an interface Lagrangian-based meshless technique for the tracking of the fluid-structure interface. The spatial discretisation is based on the standard marker-and-cell method used in conjunction with a fractional step approach for the pressure/velocity decoupling, a second-order time integrator, and a fixed-point iterative scheme. The paper presents a wide d range of two-dimensional applications involving multiphase flows interacting with immersed deformable solids, including benchmarking against both experimental and alternative numerical schemes.
In this paper, we present a two-dimensional computational framework for the simulation of fluid-structure interaction problems involving incompressible flexible solids and multiphase flows. The numerical technique followed in this paper builds upon the Immersed Structural Potential Method developed by the authors, by adding a Level Set based method for the capturing of the fluid-fluid interfaces and an interface Lagrangian based meshless technique for the tracking of the fluid-structure interface.
With the increasing heterogeneity and on-node parallelism of high-performance computing hardware, a major challenge is to develop portable and efficient algorithms and software. In this work, we present our implementation of a portable code to perform surface reconstruction using NVIDIA's Thrust library. Surface reconstruction is a technique commonly used in volume tracking methods for simulations of multimaterial flow with interfaces. We have designed a 3D mesh data structure that is easily mapped to the 1D vectors used by Thrust and at the same time is simple to use and uses familiar data structure terminology (such as cells, faces, vertices, and edges). With this new data structure in place, we have implemented a piecewise linear interface reconstruction algorithm in 3 dimensions that effectively exploits the symmetry present in a uniform rectilinear computational cell. Finally, we report performance results, which show that a single implementation of these algorithms can be compiled to multiple backends (specifically, multi-core CPUs, NVIDIA GPUs, and Intel Xeon Phi processors), making efficient use of the available parallelism on each. We also compare performance of our implementation to a legacy FORTRAN implementation in Message Passing Interface (MPI) and show performance parity on single and multi-core CPU and achieved good parallel speed-ups on GPU. Our research demonstrates the advantage of performance portability of the underlying data-parallel programming model.
In this work, we present the implementation of a portable code PINION to perform surface reconstruction using NVIDIA's Thrust Library. Performance comparison of the RAGE and PINION codes for a sphere of radius 0.25 (A) and 0.45 (B), a cylinder (C), and the Stanford bunny (D) is given in the above Figure.
The paper addresses a numerical approach for solving the Baer-Nunziato equations describing compressible two-phase flows. We are developing a finite-volume method where the numerical flux is approximated with the Godunov scheme based on the Riemann problem solution. The analytical solution to this problem is discussed, and approximate solvers are considered. The obtained theoretical results are applied to develop the discrete model that can be treated as an extension of the Rusanov numerical scheme to the Baer-Nunziato equations. Numerical results are presented that concern the method verification and also application to the deflagration-to-detonation transition (DDT) in porous reactive materials.
A leading-edge suction parameter (LESP) that is derived from potential flow theory as a measure of suction at the airfoil leading edge is used to study initiation of leading-edge vortex (LEV) formation in this article. The LESP hypothesis is presented, which states that LEV formation in unsteady flows for specified airfoil shape and Reynolds number occurs at a critical constant value of LESP, regardless of motion kinematics. This hypothesis is tested and validated against a large set of data from CFD and experimental studies of flows with LEV formation. The hypothesis is seen to hold except in cases with slow-rate kinematics which evince significant trailing-edge separation (which refers here to separation leading to reversed flow on the aft portion of the upper surface), thereby establishing the envelope of validity. The implication is that the critical LESP value for an airfoil–Reynolds number combination may be calibrated using CFD or experiment for just one motion and then employed to predict LEV initiation for any other (fast-rate) motion. It is also shown that the LESP concept may be used in an inverse mode to generate motion kinematics that would either prevent LEV formation or trigger the same as per aerodynamic requirements.
The motion of a heavy finite-size tracer is numerically calculated in a two-dimensional shear-driven cavity. The particle motion is computed using a discontinuous Galerkin-finite-element method combined with a smoothed profile method resolving all scales, including the flow in the lubrication gap between the particle and the boundary. The centrifugation of heavy particles in the recirculating flow is counteracted by a repulsion from the shear-stress surface. The resulting limit cycle for the particle motion represents an attractor for particles in dilute suspensions. The limit cycles obtained by fully resolved simulations as a function of the particle size and density are compared with those obtained by one-way coupling using the Maxey–Riley equation and an inelastic collision model for the particle–boundary interaction, solely characterized by an interaction-length parameter. It is shown that the one-way coupling approach can faithfully approximate the true limit cycle if the interaction length is selected depending on the particle size and its relative density.
Numerical simulation and theoretical analysis were performed to investigate the upstream topology of a jet–crossflow interaction. The numerical results were validated with mathematical theory as well as a juncture flow structure. The upstream critical point satisfies the condition of occurrence for a saddle point of attachment in the horseshoe vortex system. In addition to the classical topology led by a saddle point of separation, a new topology led by a saddle point of attachment was found for the first time in a jet–crossflow interaction. The degeneration of the critical point from separation to attachment is determined by the velocity ratio of the jet over the crossflow, and the boundary layer thickness of the flat plate. When the boundary layer thickness at the upstream edge of the jet is close to one diameter of the jet, the flow topology is led by a saddle point of attachment. Variation of the velocity ratio does not change the topology but the location of the saddle point. When the boundary layer thickness is less than 0.255 of the jet flow diameter, large velocity ratio can generate a saddle point of attachment without spiral horseshoe vortex; continuously decreasing the velocity ratio will change the flow topology to saddle point of the separation. The degeneration of the critical point from attachment to separation was observed.
Boundary layer flows over concave wall can be unstable to disturbances giving rise to streamwise counter-rotating vortices known as Görtler vortices. These vortices in its nonlinear form are responsible for a strong distortion of the streamwise velocity profiles in the wall-normal and spanwise directions. The resulting inflectional velocity profiles are unstable to unsteady disturbances. These disturbances are called secondary instabilities and can develop into horseshoe vortices or a sinuous motion of the Görtler vortices. These types of secondary instabilities are known as even (varicose) and odd (sinuous) modes, respectively. Although many studies focused this subject, it has not been stated which mode dominates the transition process. In the present study the secondary instability of Görtler flow is investigated using high-order spatial numerical simulation. Multi-frequency unsteady disturbances are introduced with the same spanwise wavelength as the Görtler vortices, but different spanwise phases. Three different spanwise phases are used and the effect on the secondary instability is analyzed. Both, even and odd secondary instabilities are observed, according to the relative spanwise position of the unsteady disturbances. The growth analysis for each secondary crossplane instability mode is made using a temporal Fourier analysis and the physics is explored with the aid of the flow structures visualization. The results introducing disturbances that give rise to odd and even modes simultaneously show that, for the spanwise wavelength analyzed, the odd modes grow first and dominate the transition process.
Transition from steady to oscillatory buoyancy convection of air in a laterally heated cubic box is studied numerically by straight-forward time integration of Boussinesq equations using a series of gradually refined finite volume grids. Horizontal and spanwise cube boundaries are assumed to be either perfectly thermally conducting or perfectly thermally insulated, which results in four different sets of thermal boundary conditions. Critical Grashof numbers are obtained by interpolation of numerically extracted growth/decay rates of oscillation amplitude to zero. Slightly supercritical flow regimes are described by time-averaged flows, snapshots, and spatial distribution of the oscillation amplitude. Possible similarities and dissimilarities with two-dimensional instabilities in laterally heated square cavities are discussed. Break of symmetries and sub- or supercritical character of bifurcations are examined. Three consequent transitions from steady to the oscillatory regime, from the oscillatory to the steady regime, and finally to the oscillatory flow, are found in the case of perfectly insulated horizontal and spanwise boundaries. Arguments for grid and time-step independence of the results are given.
The dynamic mode decomposition (DMD)—a popular method for performing data-driven Koopman spectral analysis—has gained increased popularity for extracting dynamically meaningful spatiotemporal descriptions of fluid flows from snapshot measurements. Often times, DMD descriptions can be used for predictive purposes as well, which enables informed decision-making based on DMD model forecasts. Despite its widespread use and utility, DMD can fail to yield accurate dynamical descriptions when the measured snapshot data are imprecise due to, e.g., sensor noise. Here, we express DMD as a two-stage algorithm in order to isolate a source of systematic error. We show that DMD’s first stage, a subspace projection step, systematically introduces bias errors by processing snapshots asymmetrically. To remove this systematic error, we propose utilizing an augmented snapshot matrix in a subspace projection step, as in problems of total least-squares, in order to account for the error present in all snapshots. The resulting unbiased and noise-aware total DMD (TDMD) formulation reduces to standard DMD in the absence of snapshot errors, while the two-stage perspective generalizes the de-biasing framework to other related methods as well. TDMD’s performance is demonstrated in numerical and experimental fluids examples. In particular, in the analysis of time-resolved particle image velocimetry data for a separated flow, TDMD outperforms standard DMD by providing dynamical interpretations that are consistent with alternative analysis techniques. Further, TDMD extracts modes that reveal detailed spatial structures missed by standard DMD.
Concentric, counter-rotating vortex ring formation by transient jet ejection between concentric cylinders was studied numerically to determine the effects of cylinder gap ratio, \(\frac{\Delta R}{R}\) , and jet stroke length-to-gap ratio, \(\frac{L}{\Delta R}\) , on the evolution of the vorticity and the trajectories of the resulting axisymmetric vortex pair. The flow was simulated at a jet Reynolds number of 1000 (based on \(\Delta R\) and the jet velocity), \(\frac{L}{\Delta R} \) in the range 1–20, and \(\frac{\Delta R}{R}\) in the range 0.05–0.25. Five characteristic flow evolution patterns were observed and classified based on \(\frac{L}{\Delta R} \) and \(\frac{\Delta R}{R}\) . The results showed that the relative position, relative strength, and radii of the vortex rings during and soon after formation played a prominent role in the evolution of the trajectories of their vorticity centroids at the later time. The conditions on relative strength of the vortices necessary for them to travel together as a pair following formation were studied, and factors affecting differences in vortex circulation following formation were investigated. In addition to the characteristics of the primary vortices, the stopping vortices had a strong influence on the initial vortex configuration and effected the long-time flow evolution at low \(\frac{L}{\Delta R}\) and small \(\frac{\Delta R}{R}\) . For long \(\frac{L}{\Delta R} \) and small \(\frac{\Delta R}{R}\) , shedding of vorticity was sometimes observed and this shedding was related to the Kelvin–Benjamin variational principle of maximal energy for steadily translating vortex rings.
In this paper, the motion of high deformable (healthy) and low deformable (sick) red blood cells in a microvessel with and without stenosis is simulated using a combined lattice Boltzmann-immersed boundary method. The RBC is considered as neo-Hookean elastic membrane with bending resistance. The motion and deformation of the RBC under different values of the Reynolds number are evaluated. In addition, the variations of blood flow resistance and time-averaged pressure due to the motion and deformation of the RBC are assessed. It was found that a healthy RBC moves faster than a sick one. The apparent viscosity and blood flow resistance are greater for the case involving the sick RBC. Blood pressure at the presence of stenosis and low deformable RBC increases, which is thought of as the reason of many serious diseases including cardiovascular diseases. As the Re number increases, the RBC deforms further and moves easier and faster through the stenosis. The results of this study were compared to the available experimental and numerical results, and good agreements were observed.
The flow of two-dimensional drops on an inclined channel is studied by numerical simulations at finite Reynolds numbers. The effect of viscosity ratio on the behaviour of the two-phase medium is examined. The flow is driven by the acceleration due to gravity, and there is no pressure gradient along the flow direction. An implicit version of the finite difference/front-tracking method was developed and used in the present study. The lateral migration of a drop is studied first. It is found that the equilibrium position of a drop moves away from the channel floor as the viscosity ratio increases. However, the trend reverses beyond a certain viscosity ratio. Simulations with 40 drops in a relatively large channel show that there exists a limiting viscosity ratio where the drops behave like solid particles, and the effect of internal circulation of drops becomes negligible. This limiting condition resembles the granular flow regime except that the effect of interstitial fluid is present. The limiting viscosity ratio depends on the flow conditions (80 for \(Re=10\) , and 200 for \(Re=20\) ). There are two peaks in the areal fraction distribution of drops across the channel which is different from granular flow regime. It is also found that the peak in areal fraction distribution of drops moves away from the channel floor as the inclination angle of the channel increases.
Görtler vortices develop along concave walls as a result of the imbalance between the centrifugal force and radial pressure gradient. In this study, we introduce a simple control strategy aimed at reducing the growth rate of Görtler vortices by locally modifying the surface geometry in spanwise and streamwise directions. Such wall deformations are accounted in the boundary region equations by using a Prandtl transform of dependent and independent variables. The vortex energy is then controlled via a classical proportional control algorithm for which either the wall-normal velocity or the wall shear stress serves as the control variable. Our numerical results indicate that the control algorithm is quite effective in minimizing the wall shear stress.
