Spectral simulations of an unsteady compressible flow past a circular cylinder

An unsteady compressible viscous wake flow past a circular cylinder has been successfully simulated using spectral methods. A new approach in using the Chebyshev collocation method for a periodic problem is introduced. We have further proved that the eigenvalues associated with the differentiation matrix are purely imaginary, reflecting the periodicity of the problem. It has been shown that the solution of a model problem has exponential growth in time if an ‘improper’ boundary conditions procedure is used. A characteristic boundary conditions, which is based on the characteristics of the Euler equations of gas dynamics, has been derived for the spectral code. The primary vortex shedding frequency computed agrees well with the results in the literature for Mach = 0.4, Re = 80. No secondary frequency is observed in the power spectrum analysis of the pressure data.     

Collapse of micrometer-sized cavitation bubbles near a rigid boundary

The interaction of cavitation bubbles with a rigid boundary and its dependence on the distance between bubble and boundary is investigated experimentally. Individual cavitation bubbles, with a maximum radius of 150?μm, are generated by using pulsed high-intensity focused ultrasound. Observations are made with high-speed photography with framing rates of up to 200?million frames per second and exposure time of 5?ns, and the spatial resolution is in the order of a few micrometers. The significant parameter of this study is the non-dimensional stand-off parameter, γ, defined as the distance between the ultrasound focus and the rigid boundary scaled by the maximum bubble radius. Both the velocity of the liquid jet developed during bubble collapse and the maximum pressure of the shock wave emitted during bubble rebound show a minimum for γ?≈?1 and a constant value for γ?>?3. The maximum jet velocity is slightly smaller than the corresponding values obtained in the case of millimeter-sized bubbles and ranges from 80?m/s (at γ?≈?1) to 130?m/s (for γ?>?3). No jet formation was observed for γ?>?3. The shock wave pressure, measured at a distance of 5?mm from the emission center, ranges from 0.2?MPa (at γ?≈?1) to 0.65?MPa (for γ?>?3). These values are an order of magnitude smaller than those obtained in the case of millimeter-sized bubbles. The shock wave duration is almost independent of γ at a value of about 75?ns. For large γ values (γ?>?3), a large percentage of the bubble energy (up to 60?%) is transformed into the mechanical energy of the shock wave emitted during bubble rebound but, for γ?≈?1, the conversion efficiency decreases to 30?%. Independent of the relative distance between bubble and rigid boundary, the shock pressure decays proportionally to r ^?1 with increasing distance r from the emission center. The results are discussed with respect to cavitation damage and collateral effects in pulsed high-intensity focused ultrasound surgery.     

Preconditioned methods for simulations of low speed compressible flows

A time-derivative preconditioned system of equations suitable for the numerical simulation of inviscid compressible flow at low speeds is formulated. The preconditioned system of equations are hyperbolic in time and remain well-conditioned in the incompressible limit. The preconditioning formulation is easily generalized to multicomponent/multiphase mixtures. When applying conservative methods to multicomponent flows with sharp fluid interfaces, nonphysical solution behavior is observed. This stimulated the authors to develop an alternative solution method based on the nonconservative form of the equations which does not generate the aforementioned nonphysical behavior. Before the results of the application of the nonconservative method to multicomponent flow problems is reported, the accuracy of the method on single component flows will be demonstrated. In this report a series of steady and unsteady inviscid flow problems are simulated using the nonconservative method and a well-known conservative scheme. It is demonstrated that the nonconservative method is both accurate and robust for smooth low speed flows, in comparison to its conservative counterpart.     

Numerical dissipation and the bottleneck effect in simulations of compressible isotropic turbulence

The piece-wise parabolic method (PPM) is applied to simulations of forced isotropic turbulence with Mach numbers ∼0.1 … 1. The equation of state is dominated by the Fermi pressure of an electron-degenerate fluid. The dissipation in these simulations is of purely numerical origin. For the dimensionless mean rate of dissipation, we find values in agreement with known results from mostly incompressible turbulence simulations. The calculation of a Smagorinsky length corresponding to the rate of numerical dissipation supports the notion of the PPM supplying an implicit subgrid scale model. In the turbulence energy spectra of various flow realisations, we find the so-called bottleneck phenomenon, i.e., a flattening of the spectrum function near the wave number of maximal dissipation. The shape of the bottleneck peak in the compensated spectrum functions is comparable to what is found in turbulence simulations with hyperviscosity. Although the bottleneck effect reduces the range of nearly inertial length scales considerably, we are able to estimate the value of the Kolmogorov constant. For steady turbulence with a balance between energy injection and dissipation, it appears that C ≈ 1.7. However, a smaller value is found in the case of transonic turbulence with a large fraction of compressive components in the driving force. Moreover, we discuss length scales related to the dissipation, in particular, an effective numerical length scale Δ_eff, which can be regarded as the characteristic smoothing length of the implicit filter associated with the PPM.     

Gas-kinetic schemes for compressible flow of real gases

This paper extends gas-kinetic schemes to the Euler equations for real gases. In the current scheme, the maxwell-Boltzmann gas distribution function is modified to recover macroscopic flow equations. More specifically, the internal degree of freedom of the gas distribution function becomes a function of flow variables according to the general equation of state. The numerical results confirm the accuracy and robustness of the gas-kinetic approach.     

Numerical simulations for the motion of soap bubbles using level set methods

In this paper, we develop appropriate equations for bubble motions depending on curvature using the level set methodology. Our method consists of an appropriate finite difference scheme for solving our model equations and a level set approach for capturing the complicated motion between the bubbles. Results indicate that our models and the level set methods can handle complicated interfacial motions and topology changes, and that they can numerically simulate many of the physical features of bubble motions.     

文丘里管中空化流场的数值模拟

基于FLUENT软件,采用标准k-ε模型和空化泡动力学模型,对三种不同几何形状的文丘里管内空化流场进行数值模拟,计算了文丘里管内空化区的空化数、压力分布和汽含率分布,研究了操作条件、文丘里管的结构形式对空化效果的影响。结果表明,理论计算的空化区汽含率分布与实验拍摄的空化云雾区图像有较好的吻合性;水力空化装置的操作条件,以及文丘里管的结构形式对空化效果有着明显的影响。     

Numerical analysis of unsteady compressible laminar boundary layer flow

The unsteady compressible laminar boundary layer flow on an arbitrary cylinder due to an incident stream whose velocity varies arbitrarily with time is considered. The method presented is based on the separation between the convective and diffusive quantities. By defining some new variables, the splitting appears rather naturally, and the initialisation problem can be solved without difficulty. The transformed equations are solved with the help of a semi-implicit finite difference scheme which is unconditionally linearly stable. The computations have been applied to flows past a cylinder with constant and fluctuating free-stream velocities.     

Discontinuous Galerkin solution of compressible flow in time-dependent domains

This work is concerned with the simulation of inviscid compressible flow in time-dependent domains. We present an arbitrary Lagrangian–Eulerian (ALE) formulation of the Euler equations describing compressible flow, discretize them in space by the discontinous Galerkin method and introduce a semi-implicit linearized time stepping for the numerical solution of the complete problem. Special attention is paid to the treatment of boundary conditions and the limiting procedure avoiding the Gibbs phenomenon in the vicinity of discontinuities. The presented computational results show the applicability of the developed method.     

Parallel single grid and multigrid solution of industrial compressible flow problems

The Euler and Navier-Stokes equations with a k-ε turbulence model are solved numerically in parallel on a distributed memory machine IBM SP2, a shared memory machine SGI Power Challenge, and a cluster of SGI workstations. The grid is partitioned into blocks and the steady state solution is computed using single grid and multigrid iteration. The multigrid algorithm is analyzed leading to an estimate of the elapsed time per iteration. Based on this analysis, a heuristic algorithm is devised for distributing and splitting the blocks for a good static load balance. Speed-up results are presented for a wing, a complete aircraft and an air inlet.     

Analysis of unsteady compressible boundary layer flow via finite elements

This paper is concerned with the discrete formulation and numerical solution of unsteady compressible boundary layer flows using the Galerkin-finite element method. Linear interpolation functions for the velocity, density, temperature and pressure are used in the momentum equation and equations of continuity, energy and state. The coupled nonlinear finite element equations are approximated by a third order Taylor series expansion as temporal operator to integrate in time with Newton-Raphson type iterations performed until convergence within each time step. As an example, a boundary layer problem of a perfect gas behind a normal shock wave is solved. A comparison of the results with those by other method indicates a favorable agreement.     

Large-eddy simulation of vortex breakdown in compressible swirling jet flow

Vortex breakdown in a compressible swirling jet flow is investigated by large-eddy simulation (LES) using the approximate deconvolution model. Conditions are chosen similar to recent experimental investigations by Liang and Maxworthy [Liang H, Maxworthy T. An experimental investigation of swirling jets. J Fluid Mech 2005;525:115] for incompressible flow. LES results are presented for two simulations of a swirling jet at Mach number Ma = 0.6 with and without inflow forcing by imposed linear instability disturbances. Both the forced and the self-excited jet show three-dimensional helical waves developing in the jet breakdown zone. The features observed in the two simulations are compared to each other as well as to the experiments with respect to flow statistics and instability behaviour. Both simulations show favourable qualitative agreement with the experiment.     

Efficient numerical approximation of compressible multi-material flow for unstructured meshes

We consider the numerical approximation of multi-dimensional multi-material flows. This is a difficult topic related to the numerical smearing of contact discontinuities (or material interfaces or slip lines). Any Eulerian scheme will produce an artificial mixing zone. In this artificial mixture, the computation of thermodynamical variables (pressure, sound speed, temperature, …) is difficult to achieve correctly. For the stiff cases considered in this paper, with solid-liquid-gas interfaces, small errors on the thermodynamical variables lead to the blow up of the computation in many cases. In this paper, we review and explain this problem, then we propose solutions for 1D and 2D flows. Contrarily to front-tracking techniques, our schemes use the same formulation everywhere on the mesh. We provide several examples with the stiffened gas equation of state (EOS): inert materials (water-air), and chemically reactive materials (solid explosive-Plexiglass-air).     

Development of a MEMS-based control system for compressible flow separation

A MEMS-based sensor and actuator system has been designed and fabricated for separation control in the compressible flow regime. The MEMS sensors in the system are surface-micromachined shear stress sensors and the actuators are bulk-micromachined balloon vortex generators (VGs). A three-dimensional (3-D) wing model embedded with the shear stress sensors and balloon VGs was tested in a transonic wind tunnel to evaluate the performance of the control system in a range of Mach number between 0.2 and 0.6. At each Mach number tested, the shear stress sensors quantify the boundary layer on the surface of the wing model while the balloon VGs interact with the boundary layer in an attempt to provide flow control. The shear stress measurements indicate the presence of a separated flow on the trailing ramp section of the wing model at all Mach numbers tested when the balloon VGs are not activated. This result is confirmed by total pressure measurements downstream from the wing model where a wake profile is observed. When the balloon VGs are activated, the shear stress level on the trailing ramp increases with the Mach number. At the highest Mach number tested, this increase elevates the shear stress on the ramp to almost the same level as the unseparated flow, suggesting the possibility of a boundary layer reattachment. This result is supported by the downstream pressure measurements which show a large pressure recovery when the balloon VGs are activated. The wind tunnel experiment successfully demonstrated two aspects of the MEMS flow control system: the effectiveness of the microshear stress sensors in measuring the separation characteristics of a high-speed compressible flow and the ability of the microballoons in positively enhancing the aerodynamic performance of a high-speed wing through boundary layer modification.     

A volume-of-fluid method for simulation of compressible axisymmetric multi-material flow

A two-dimensional Eulerian hydrodynamic method for the numerical simulation of inviscid compressible axisymmetric multi-material flow in external force fields for the situation of pure fluids separated by macroscopic interfaces is presented. The method combines an implicit Lagrangian step with an explicit Eulerian advection step. Individual materials obey separate energy equations, fulfill general equations of state, and may possess different temperatures. Material volume is tracked using a piecewise linear volume-of-fluid method. An overshoot-free logically simple and economic material advection algorithm for cylinder coordinates is derived, in an algebraic formulation. New aspects arising in the case of more than two materials such as the material ordering strategy during transport are presented. One- and two-dimensional numerical examples are given.     

Mesoscopic simulations of electroosmotic flow and electrophoresis in nanochannels

We review recent dissipative particle dynamics (DPD) simulations of electrolyte flow in nanochannels. A method is presented by which the slip length δB at the channel boundaries can be tuned systematically from negative to infinity by introducing suitably adjusted wall-fluid friction forces. Using this method, we study electroosmotic flow (EOF) in nanochannels for varying surface slip conditions and fluids of different ionic strength. Analytic expressions for the flow profiles are derived from the Stokes equation, which are in good agreement with the numerical results. Finally, we investigate the influence of EOF on the effective mobility of polyelectrolytes in nanochannels. The relevant quantity characterizing the effect of slippage is found to be the dimensionless quantity κδB, where 1/κ is an effective electrostatic screening length at the channel boundaries.     

High-fidelity simulations of unsteady flow through turbopumps and flowliners

High-fidelity computations were carried out to analyze the orbiter liquid hydrogen (LH₂) feedline flowliner and the low-pressure-fuel-turbopump (LPFTP). Computations were performed on the Columbia platform which is a 10,240-processor supercluster consisting of 20 Altix nodes with 512 processors each. Various computational models were used to characterize the unsteady flow features in the turbopump, including the orbiter LPFTP inducer, the orbiter manifold and an experimental test article used to represent the manifold. Unsteady flow originating from the orbiter LPFTP inducer is one of the major contributors to the high-frequency cyclic loading that results in high cycle fatigue damage to the gimbal flowliners just upstream of the LPFTP. The flowfields for the orbiter manifold and representative test article are computed and analyzed for similarities and differences. An incompressible Navier–Stokes flow solver INS3D, based on the artificial compressibility method, was used to compute the flow of liquid hydrogen in each test article.     

A hybrid numerical method and its application to inviscid compressible flow problems

An improved version of the artificially upstream flux vector scheme, is developed to efficiently compute inviscid compressible flow problems. This numerical scheme, named AUFSR (Tchuen et al. 2011), is obtained by hybridizing the AUFS scheme with Roe’s solver. This approach handles difficulties encountered by the AUFS scheme, in the case where the flux vector does not check the homogeneous property. The present scheme for multi-dimensional flows introduces a certain amount of numerical dissipation to shear waves, as Roe’s splitting. The AUFSR scheme is not only robust for shock-capturing, but also accurate for resolving shear layers. Numerical results for 1D Riemann problems and several 2D problems are investigated to show the capability of the method to accurately compute inviscid compressible flow when compared to AUFS, and Roe solvers.     

Strict error estimation for a spectral method of compressible fluid flow

In this paper, a Fourier Spectral method for compressible flow in n-dimensional space with periodic boundary conditions is constructed. We give a strict error estimation, from which the convergence follows with some assumptions.