Development of computationally efficient augmented Lagrangian SPH for incompressible flows and its quantitative comparison with WCSPH simulating flow past a circular cylinder

In Lagrangian particle-based methods such as smoothed particle hydrodynamics (SPH), computing totally divergence-free velocity field in a flow domain with the smallest error possible is the most critical issue, which might be achieved through solving pressure Poisson equation implicitly with higher particle resolutions. However, implicit solutions are computationally expensive and may be particularly challenging in the solution of multiphase flows with highly nonlinear deformations as well as fluid-structure interaction problems. Augmented Lagrangian SPH (ALSPH) method is a new alternative algorithm as a prevalent pressure solver where the divergence-free velocity field is achieved by iterative calculation of velocity and pressure fields. This study investigates the performance of the ALSPH technique by solving a challenging flow problem such as two-dimensional flow around a cylinder within the Reynolds number range of 50 to 500 in terms of improved robustness, accuracy, and computational efficiency. The same flow conditions are also simulated using the conventional weakly compressible SPH (WCSPH) method. The results of ALSPH and WCSPH solutions are not only compared in terms of numerical validation/ verification studies, but also rigorous investigations are performed for all related physical flow characteristics, namely, hydrodynamic coefficients, frequency domain analyses, and velocity divergence fields.     

Modelling of the break up mechanism in gas atomization of liquid metals Part II. The gas flow model

An analytical model for the gas flow produced by a close coupled atomization assembly is described. The algorithm is based on physical arguments and it fully accounts for the expansion of compressible gas from cylindrical gas jets and the convergence/divergence of the subsequent turbulent flow. A critical input parameter of the model, the radius of the convergence area of the individual jet flows, established elsewhere [G. Antipas, PhD Thesis, University of Surrey, UK, 1995] to be 3 mm by high speed photography, is in tight agreement with the predictions of the model. Pitot tube gas velocity measurements compared well with model predictions.     

On cycle-averaged pressure in a G-M type pulse tube refrigerator

An experimental investigation has been carried out on dynamical pressures of the viscous compressible flow oscillating at different locations in a Gifford-McMahon (G-M) type pulse tube refrigerator operating at cycle-steady states. Measurements show that the oscillating amplitude of the pressure was largest at the hot end of the regenerator while the cycle-averaged pressure was the largest in the reservoir. The latter characteristics can be explained based on a cycle-averaged and cross-sectional averaged of the governing equations for a compressible viscous oscillating flow. The reason why the cycle-averaged pressure of the compressible flow oscillating at low frequencies in a tube increases from the wave generator toward the reservoir is analyzed. In addition, the effect of the cycle-averaged pressure on the refrigeration performance is discussed, which can be used to explain why the system with proper asymmetric charging and discharging periods has a better performance than a symmetric one in a G-M type pulse tube refrigerator.     

An efficient numerical method for highly loaded transonic cascade flow

In this paper, an efficient numerical method for transonic viscous flow in a highly loaded turbine vane cascade, where the interaction of a shock wave and boundary layer often leads to very complicated flow phenomena, is developed. The numerical code, a modified implicit flux-vector-splitting solver of the Navier–Stokes equations (MIFVS), is extended to simulate such transonic cascade flow. A compressible low-Reynolds-number k–ɛ model, together with a transition-modified damping function, has been implemented into the MIFVS code. With this extended MIFVS solver, the main feature of transonic flow and shock and boundary-layer interactions in the highly loaded transonic turbine vane are efficiently predicted with satisfactory accuracy. The convergence rate is found to be three times faster than that of flux-vector-splitting (FVS) methods.     

振动叶栅中振荡欧拉流场求解的一种简化方法

从线化的三维可压非定常欧拉方程组(时间相关的双曲型方程组)出发,将非定常流场的振荡现象看作是若干频率成份的简谐振动的叠加,根据实际的研究对象,通过合理的数学方法,得到一个有广泛应用背景的振荡欧拉流场求解的简化方法,并通过比较,证明这一简化方法不但简单易行,而且具有较高精度。     

Interfacial waves and hydraulic falls: Some applications to atmospheric flows in the lee of mountains

Two dimensional flow of a layer of constant density fluid over arbitrary topography, beneath a compressible, isothermal and stationary fluid is considered. Both downstream wave and critical flow solutions are obtained using a boundary integral formulation which is solved numerically by Newton's method. The resulting solutions are compared against waves produced behind similar obstacles in which the compressible upper layer is absent (single layer flow) and against the predictions of a linearised theory. The limiting waves predicted by the full non-linear equations are contrasted with those predicted by the forced Korteweg-de Vries theory. In particular, it is shown that at some parameter values a multiplicity of solutions exists in the full nonlinear theory.     

A numerical simulation of the flow development behind a circular cylinder started from rest and a criterion for investigating unsteady separating flows

Summary The numerical solution of the Navier-Stokes equations for an unsteady compressible flow is employed to follow the development of periodic vortex shedding behind a circular cylinder starded from rest. The periodic vortex shedding is found to be a direct consequence of the interaction between the upper and lower primary vortices behind the cylinder, while the topological instability of the full saddle-point joining the vortices and the outer flow can be seen to play a predominant role in the process. A criterion based upon the rate of distortion of fluid elements and derived from the previous Lagrangian analysis of boundary-layer separation has been applied to the present study of unsteady separating flow and is found to be instrumental in revealing critical regions and surfaces in the flow where the fluid elements are extremely deformed.With 12 FiguresAt DFVLR-Institute for Theoretical Fluid Mechanics on Alexander-von-Humboldt Senior-Scientist Award.At DFVLR-Institute for Theoretical Fluid Mechanics on leave from Beijing Institute of Aeronautics and Astronautics.     

The stability of low-amplitude three-dimensional disturbances in a nonequilibrium compressible boundary layer

The stability of Tollmien-Schlichting waves propagating at an angle to the main flow in a nonequilibrium compressible supersonic boundary layer is investigated within the linear theory of hydrodynamic stability. The dependences of the critical Reynolds number on the degree of disequilibrium and on the Mach number of undisturbed flow are found at different angles of wave propagation. It is demonstrated that the critical Reynolds number in a nonequilibrium medium may decrease appreciably with increasing degree of disequilibrium, which results in the reduction of the characteristic length of the linear region of transition to turbulence.     

On the unsteady inviscid force on cylinders and spheres in subcritical compressible flow

The unsteady inviscid force on cylinders and spheres in subcritical compressible flow is investigated. In the limit of incompressible flow, the unsteady inviscid force on a cylinder or sphere is the so-called added-mass force that is proportional to the product of the mass displaced by the body and the instantaneous acceleration. In compressible flow, the finite acoustic propagation speed means that the unsteady inviscid force arising from an instantaneously applied constant acceleration develops gradually and reaches steady values only for non-dimensional times c(infinity)t/R approximately >10, where c(infinity) is the freestream speed of sound and R is the radius of the cylinder or sphere. In this limit, an effective added-mass coefficient may be defined. The main conclusion of our study is that the freestream Mach number has a pronounced effect on both the peak value of the unsteady force and the effective added-mass coefficient. At a freestream Mach number of 0.5, the effective added-mass coefficient is about twice as large as the incompressible value for the sphere. Coupled with an impulsive acceleration, the unsteady inviscid force in compressible flow can be more than four times larger than that predicted from incompressible theory. Furthermore, the effect of the ratio of specific heats on the unsteady force becomes more pronounced as the Mach number increases.     

High‐Throughput Continuous Production of Shear‐Exfoliated 2D Layered Materials using Compressible Flows

2D nanomaterials are finding numerous applications in next‐generation electronics, consumer goods, energy generation and storage, and healthcare. The rapid rise of utility and applications for 2D nanomaterials necessitates developing means for their mass production. This study details a new compressible flow exfoliation method for producing 2D nanomaterials using a multiphase flow of 2D layered materials suspended in a high‐pressure gas undergoing expansion. The expanded gas–solid mixture is sprayed in a suitable solvent, where a significant portion (up to 10% yield) of the initial hexagonal boron nitride material is found to be exfoliated with a mean thickness of 4.2 nm. The exfoliation is attributed to the high shear rates ( > 10⁵ s^?1) generated by supersonic flow of compressible gases inside narrow orifices and converging‐diverging channels. This method has significant advantages over current 2D material exfoliation methods, such as chemical intercalation and exfoliation, as well as liquid phase shear exfoliation, with the most obvious benefit being the fast, continuous nature of the process. Other advantages include environmentally friendly processing, reduced occurrence of defects, and the versatility to be applied to any 2D layered material using any gaseous medium. Scaling this process to industrial production has a strong possibility of reducing the cost of creating 2D nanomaterials.     

A cut‐cell non‐conforming Cartesian mesh method for compressible and incompressible flow

This paper details a multigrid‐accelerated cut‐cell non‐conforming Cartesian mesh methodology for the modelling of inviscid compressible and incompressible flow. This is done via a single equation set that describes sub‐, trans‐, and supersonic flows. Cut‐cell technology is developed to furnish body‐fitted meshes with an overlapping mesh as starting point, and in a manner which is insensitive to surface definition inconsistencies. Spatial discretization is effected via an edge‐based vertex‐centred finite volume method. An alternative dual‐mesh construction strategy, similar to the cell‐centred method, is developed. Incompressibility is dealt with via an artificial compressibility algorithm, and stabilization achieved with artificial dissipation. In compressible flow, shocks are captured via pressure switch‐activated upwinding. The solution process is accelerated with full approximation storage (FAS) multigrid where coarse meshes are generated automatically via a volume agglomeration methodology. This is the first time that the proposed discretization and solution methods are employed to solve a single compressible–incompressible equation set on cut‐cell Cartesian meshes. The developed technology is validated by numerical experiments. The standard discretization and alternative methods were found equivalent in accuracy and computational cost. The multigrid implementation achieved decreases in CPU time of up to one order of magnitude. Copyright © 2007 John Wiley & Sons, Ltd.     

Solution methods for gas flow in ducts through the whole pressure regime

In vacuum technology it is frequently necessary to calculate gas flows over a wide range of pressures and flow conditions. Ideally, it is desirable to be able to conduct calculations for long and short ducts and for large and small pressure differences and flow rates. The basic requirement for a general purpose flow calculation method is a combined continuum/molecular model that provides a smooth transition between the flow regimes. Since gases are compressible a generally applicable model requires the application of thermodynamic flow relations.The thermodynamic flow equations are introduced and, in particular, a form applicable to laminar flow conditions together with equations that relate flow velocities to the applied boundary conditions (not generally covered in the fluid dynamics literature).In addition to circular cross-section ducts it is desirable to be able to include other common cross-section shapes so the equations discussed are generalised to include annular and rectangular cross-sections. Continuum flow formulas for these shapes are well known but there appear to be no published formulas for molecular flow in rectangular or annular cross-section ducts of arbitrary length. Empirical formulas which have been developed by the author for annular and rectangular ducts are presented.     

Application of a coupled Eulerian–Lagrangian method to simulate interactions between deformable composite structures and compressible multiphase flow

Interactions between deformable composite structures and compressible multiphase flow are common for many marine/submarine problems. Recently, there has been an increased interest in the application of composite structures in marine industry (e.g. propulsion system, ship hulls, marine platforms, marine turbines, etc) to take advantage their high stiffness to weight and strength to weight ratios, and high impact/shock resistance characteristics. It is therefore important to evaluate the performance of composite structures subject to dynamic loads. In this paper, a coupled Eulerian–Lagrangian numerical method is proposed to model the two‐dimensional (2D) or axisymmetric response of deformable composite structures subject to shock and blast loads. The method couples an Eulerian compressible multiphase fluid solver with a general Lagrangian solid solver using an interface capturing method, and is validated using analytical, numerical, and experimental results. A 2D case study is shown for an underwater explosion beneath a three‐layered composite structure with clamped ends. The importance of 2D fluid–structure interaction effects on the transient response between composite structures and compressible multiphase flow is discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Effect of the geometric parameters on a flexible fiber motion in a tangentially injected divergent swirling tube flow

A particle-level simulation method is employed to study the effects of some geometric parameters, such as the injector diameter, the injection angle and position on fiber motions in a 3D compressible decaying swirling flow in a divergent tube. The flexibility of the fiber is defined by the bending and twisting displacements. The fiber-wall collision and compressible effects are considered here. The fiber with different complex configurations moves as spiral orbit with stream-wise direction. With the increase in the injector diameter, the deformation degree of the fiber increases. For a larger injector diameter, the fiber appears to be closed coil loops or asymmetric S-loopturn. The larger the injection angle is, the earlier the fiber starts to swirl and the larger the number of ‘turn’ is. The complex coiled configurations with entanglement can be observed under small injection angle. Especially, a ‘zigzag’ configuration is formed for larger injection angle and injection position.     

A note on critical flow section in collector channels

Generalized solution for the location of critical flow section in collector channels is presented. Based on the concept of the singularity, the dynamic equation of spatially varied flow (SVF) is solved using the flow resistance equations of von Karman (for rough regime) and Jain (for transitional and smooth regimes). The advantage of using Jain’s equations is that they provide the explicit forms of the Colebrook-White and Nikuradse equations. Computational steps for the determination of critical flow section in a collector channel, being dependent on channel geometry, roughness, longitudinal bed slope and inflow discharge, are given for different channel shapes.     

The flow of a compressible dust-gas medium in tubes,in several thermal and structural regimes

We examine the one-dimensional motion of a compressible dust-gas medium in tubes in the case of critical pressure differences and great flow-rate concentrations of a finely dispersed material, with the latter exhibiting various distribution structures in the flow.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 16, No. 5, pp. 826–834, May, 1969.     

Detonation gas model for combined finite‐discrete element simulation of fracture and fragmentation

The equation of state for expansion of detonation gas together with a model for gas flow through fracturing solid is proposed and implemented into the combined finite‐discrete element code. The equation of state proposed enables gas pressure to be obtained in a closed form for both reversible and irreversible adiabatic expansion, while the gas flow model proposed considers only 1D compressible flow through cracks, hence avoiding full 2D or 3D gas flow through the fracturing solid. When coupled with finite‐discrete element algorithms for solid fracture and fragmentation, the model proposed enables gas pressure to be predicted and energy balance to be preserved. Copyright © 2000 John Wiley & Sons, Ltd.     

Application of Cosserat-spectrum theory to the weakly compressible Stokes flow past a sphere

The Cosserat-spectrum theory, which provides an eigenfunction-expansion solution to the Navier equations of linear elasticity, has recently been applied successfully to a number of problems in elasticity, thermoelasticity and viscoelasticity. In this work the theory's extension to fluid mechanics is explored and the example problem of the weakly compressible Stokes flow past a sphere is solved in closed form.     

A CFD/CSD Model for Transonic Flutter

In this paper, a rapid deforming technique is developed to generate dynamic, three-dimensional, multi-block, mesh. The second-order Runge-Kutta time-marching method is used to solve the structural equations of motion. A dual-time method and finite volume discretization are applied for the unsteady Euler/Navier-Stokes equations to calculate the aerodynamic forces, in which the physical time step is synchronous with the structural equations of motion. The Spalart-Allmaras turbulence model is adopted for a turbulent flow. Due to mass dissimilarity, exiting in flutter calculations for a compressible flow, methods of variable mass and variable stiffness are developed to calculate the dynamic pressure of flutter at the point of mass similarity, and the flutter characteristics are then obtained in accordance with similarity rule. For completeness, the calculated transonic flutter characteristic results are presented and discussed for a double-wing and an aircraft model.     

The cylinder in the wind tunnel,revisited

Analytical comparative solutions are often needed to assess the accuracy of proposed elements or proposed iterative schemes for potential flow numerical calculations. Traditionally, the flow over a circular cylinder, placed in a wind tunnel, has served for such a test and the results compared to what is thought to be an exact solution. We point out here that there is no exact solution for the flow over a circular cylinder in a wind tunnel, for practical values of wind tunnel height to cylinder radius, but that an exact solution can only be found for the flow over an oval cylinder. We derive that exact solution and provide numerical comparisons, using triangular elements, with both the stream function and the velocity potential for the incompressible case. In addition, numerical results for compressible flows up to critical Mach number are presented.