A study of non-oscillatory schemes based on LED principle for inviscid flow computation past airfoils

Summary Several high resolution non-oscillatory discretization schemes have been formulated in a finite volume framework for the solution of Euler equations in order to compute inviscid transonic flow fields past airfoils. The theory is based on the local extremum diminishing (LED) principle, initially proposed by Jameson [12], [13] in 1993 for nonlinear scalar conservation laws. Higher order non-oscillatory schemes satisfying the LED criterion have been generated by using a suitable switching function and also by the use of flux limiters. For the implementation of these schemes to the solution of a system of conservation laws, a number of flux splitting techniques have been considered in the present work. Extensive numerical experiments indicate that the flux limited dissipation schemes, viz. the SLIP and USLIP schemes hold the promise of improving the accuracy of the results. The switched scheme with different types of flux splitting has also proved successful in the resolution of shock waves without oscillation.     

Numerical analysis of the inviscid incompressible flow in two-dimensional radial-flow pump impellers

The flow through a two-dimensional centrifugal impeller fitted with equiangular blades of arbitrary geometry is investigated using a combination of conformal mapping with a boundary element technique. The blades can be thin or thick of arbitrary cross-section. A theoretical analysis and a numerical procedure are developed to determine the pressure distributions along the blade.     

A boundary element method for steady incompressible thermoviscous flow

A boundary element formulation is presented for moderate Reynolds number, steady, incompressible, thermoviscous flows. The governing integral equations are written exclusively in terms of velocities and temperatures, thus eliminating the need for the computation of any gradients. Furthermore, with the introduction of reference velocities and temperatures, volume modelling can often be confined to only a small portion of the problem domain, typically near obstacles or walls. The numerical implementation includes higher order elements, adaptive integration and multiregion capability. Both the integral formulation and implementation are discussed in detail. Several examples illustrate the high level of accuracy that is obtainable with the current method.     

A dual-time method for two-dimensional unsteady incompressible flow calculations

A method for computing unsteady incompressible viscous flows on moving or deforming meshes is described. It uses a well-established time-marching finite-volume flow solver, developed for steady compressible flows past rigid bodies. Time-marching methods cannot be applied directly to incompressible flows because the governing equations are not hyperbolic. Such methods can be extended to steady incompressible flows using an artificial compressibility scheme. A time-accurate scheme for unsteady incompressible flows is achieved by using an implicit real-time discretization and a dual-time approach, which uses a technique similar to the artificial compressibility scheme. Results are presented for test cases on both fixed and deforming meshes. Experimental, numerical and theoretical data have been included for comparison where available and reasonable agreement has been achieved. © 1998 John Wiley & Sons, Ltd.     

高效低噪的二维翼型优化设计

针对传统的气动优化设计未考虑气动噪声影响的局限性,开展了基于噪声预测模型的气动优化设计方法在二维翼型中的应用研究。建立了由几何外形参数化方法、径向基函数(Radial Basis Function,RBF)动网格技术、改进粒子群优化算法、气动分析方法、气动噪声预测方法等五大模块构成的优化设计系统,且各模块均采用标模算例进行验证。通过对二维SC(2)-0714超临界翼型进行了单点多目标优化设计。通过对比翼型几何形状、压力系数分布以及在不同迎角下的气动力系数曲线与总声压级的关系可得,翼型头部半径、厚度影响其头部压力峰值、压力恢复、逆压梯度等特性,从而影响升阻比和总声压级,逆压梯度越小,翼型的总声压级越小。优化结果表明,在设计状态下显著提高了升阻比、降低气动噪声,考虑气动噪声的二维翼型优化设计系统可在实际的工程设计中进行应用。     

A semi-implicit stabilized particle Galerkin method for incompressible free surface flow simulations

A new particle Galerkin method is introduced to solve the Naiver-Stokes equations in a Lagrangian fashion. The present method aims to suppress key numerical instabilities observed in the strong form Lagrangian particle methods such as smoothed particle hydrodynamics (SPH), incompressible SPH, and moving particle semi-implicit for incompressible free surface flow simulations. It is well-known that strong form Lagrangian particle methods usually rely on ad hoc particle stabilization techniques based on particle shifting, artificial viscosity, or density-invariant condition due to some formulation inconsistency issues. In the present method, we introduce a momentum-consistent velocity smoothing algorithm which is used to combine with the second-order rotational incremental pressure-correction scheme to stabilize the pressure field as well as to enforce the consistency of Neumann boundary condition. To further impose slip-free or nonslip boundary conditions for the fluid flow, a penalty method which is free of ghost or dummy particles is developed. Finally, a particle insertion-deletion adaptive scheme is proposed when the violent fluid flow is considered. Four numerical examples are studied to validate the accuracy and stability of the present method.     

A new particle method for simulation of incompressible free surface flow problems

A new Lagrangian particle method called the consistent particle method (CPM), which solves the Navier–Stokes equations in a semi‐implicit time stepping scheme, is proposed in this paper. Instead of using kernel function as in some particle methods, partial differential operators are approximated in a way consistent with Taylor series expansion. A boundary particle recognition method is applied to help define the changing liquid domain. The incompressibility condition of free surface particles is enforced by an adjustment scheme. With these improvements, the CPM is shown to be robust and accurate in long time simulation of free surface flow particularly for smooth pressure solution. Two types of free surface flow problems are presented to verify the CPM, that is, two‐dimensional dam break and liquid sloshing in a rectangular tank. In the dam break example, the CPM solutions of pressure and wave elevation are in good agreement with published experimental results. In addition, an experimental study of water sloshing in tank on a shake table was conducted to verify the CPM solutions. Copyright © 2011 John Wiley & Sons, Ltd.     

A numerical method for the analysis of flexible bodies in unsteady viscous flows

A two‐dimensional numerical model for unsteady viscous flow around flexible bodies is developed. Bodies are represented by distributed body forces. The body force density is found at every time‐step so as to adjust the velocity within the computational cells occupied by the body to a prescribed value. The method combines certain ideas from the immersed boundary method and the volume of fluid method. The main advantage of this method is that the computations can be effected on a Cartesian grid, without having to fit the grid to the body surface. This is particularly useful in the case of flexible bodies, in which case the surface of the object changes dynamically, and in the case of multiple bodies moving relatively to each other. The capabilities of the model are demonstrated through the study of the flow around a flapping flexible airfoil. The novelty of this method is that the surface of the airfoil is modelled as an active flexible skin that actually drives the flow. The accuracy and fidelity of the model are validated by reproducing well‐established results for vortex shedding from a stationary as well as oscillating rigid cylinder. Copyright © 2006 John Wiley & Sons, Ltd.     

Parallel computing for incompressible flow using a Nodal-Based method

In this paper, the development of a seamless system for parallel flow analysis using the “free-mesh method”, which is a kind of meshless method, is described. The system consists of two main parts: the computation of the global mass, advection, diffusion, gradient, and divergence matrices, and the time integration by the decoupled method with respect to velocity and pressure. This system is quite compatible with the parallel environment because the matrices are independently computed node-by-node without any node-element connectivity information, and furthermore because the fractional step method, with the interpolation functions for velocity and pressure being of equal order, is used with the conjugate gradient solver for the time integration. A parallel efficiency of approximately 83 was achieved for a large-scale problem with 480,000 degrees of freedom using 16 processors.     

Parallelization of lattice Boltzmann method for incompressible flow computations

Parallel computation of the two and three-dimensional decaying homogeneous isotropic turbulence using the lattice Boltzmann method are presented. BGK type approximation for collision term in 9 velocity square lattice model is used. It is found that the lattice Boltzmann method is able to reproduce the dynamics of decaying turbulence and could be an alternative for solving the Navier-Stokes equations. The lattice Boltzmann method is parallelized by using domain decomposition and implemented on a distributed memory computer, Hitachi SR2201. It is found that vertical decomposition gives the highest speedup. In the case of horizontal decomposition the longer the number of lattice units in horizontal direction of each subdomain, the shorter the CPU time. Extension to three-dimension is carried out using 15 velocity cubic lattice model. Compared with the result of two-dimensional case, a higher speedup is obtained than in the three-dimensional simulation. Further investigation is needed on the accuracy and efficiency of cubic lattice BGK model.     

A conservative embedded boundary method for an inviscid compressible flow coupled with a fragmenting structure

We present an embedded boundary method for the interaction between an inviscid compressible flow and a fragmenting structure. The fluid is discretized using a finite volume method combining Lax–Friedrichs fluxes near the opening fractures, where the density and pressure can be very low, with high‐order monotonicity‐preserving fluxes elsewhere. The fragmenting structure is discretized using a discrete element method based on particles, and fragmentation results from breaking the links between particles. The fluid‐solid coupling is achieved by an embedded boundary method using a cut‐cell finite volume method that ensures exact conservation of mass, momentum, and energy in the fluid. A time explicit approach is used for the computation of the energy and momentum transfer between the solid and the fluid. The embedded boundary method ensures that the exchange of fluid and solid momentum and energy is balanced. Numerical results are presented for two‐dimensional and three‐dimensional fragmenting structures interacting with shocked flows. Copyright © 2015 John Wiley & Sons, Ltd.     

A numerical method for non-linear flow about a submerged hydrofoil

Summary A numerical method is presented for computing two-dimensional potential flow about a wing with a cusped trailing edge immersed beneath the free surface of a running stream of infinite depth. The full non-linear boundary conditions are retained at the free surface of the fluid, and the conditions on the hydrofoil are also stated exactly. The problem is solved numerically using integral-equation techniques combined with Newton's method. Surface profiles and the pressure distribution on the body are shown for different body geometries.     

A numerical study of partitioned fluid-structure interaction applied to a cantilever in incompressible turbulent flow

This study presents an approach for partitioned fluid-structure interaction (FSI) applied to large structural deformations, where an incompressible turbulent solver is combined with a structural solver. The implementation is based upon two different open-source libraries by using MPI as a parallel communication protocol, the packages and OpenFOAM. FSI is achieved through a strongly-coupled scheme. The solver has been validated against cases with a submerged cantilever in a channel flow to which experiments, numerical calculations and theoretical solutions are available. The verification of the procedure is performed by using a solid-solid interaction (SSI) study. The solver has proven to be robust and has the same parallel efficiency as the fluid and the solid solver stand-alone.     

A thermodynamically consistent numerical method for transonic cascade flow simulation

The author's recent work on thermodynamically consistent numerical methods for the simulation of inviscid, adiabatic flow is extended to handle transonic flow problems of practical interest. The basic Singhal–Spalding scheme is developed and tested on two problems. The first one is the standard transonic nozzle flow. The computational results are shown to be in good agreement with the analytical solution. The second problem is a flow situation studied experimentlly by Sieverding. The inviscid results are in surprisingly good agreement with the principal qualitative features of the real folws. There are important quantitative discrepancies which are believed to be due to the inadequacies of the inviscid model rather than failings of the scheme itself. Arguments in support for this view are presented.     

Response of variations of free stream velocity on inviscid and incompressible flow past a wavy plate

This paper studies the several types of free stream flow past the wavy plate. The solution is obtained in terms of free stream function by regular perturbation. It may be noted that the introduction of small vorticity does not affect the primary flow due to uniform free stream; however it tends to increase the maximum pressure at the wall. As in the case of uniform free stream, the extrema of the pressure coefficient along the X-direction coincide with those of the wall. The perturbed flow fields due to the presence of the wavy shaped boundary die out transversally at the same rate as in case of uniform stream.     

Design and Optimization of airfoils in non-stalling incompressible flow with a prescribed range of the angle of attack

A simple and reliable method of aerodynamic design of airfoils is proposed for a given range of the angle of attack. The method is based on the solution of a new inverse boundary-value problem of aerohydrodynamics. In the problem the initial velocity distributions are given along the contour of the required airfoil as a function of the are co-ordinate for extreme values of the angle of attack from a fixed range. We justify a method of choice of these distributions which guarantees a non-stalling flow around the airfoil. The problem of airfoil optimization is also considered. Results of numerical calculations are presented.     

On the distribution of impulses in inviscid,incompressible flow — the induced downwash on a rotating wing

Summary We consider the prescribing of singularities in inviscid fluid flows by including Dirac delta functions in the Euler momentum equation. Examples are given of the modelling of the flows due to lifting bodies, in particular that due to a wing simultaneously translating and rotating and find the induced downwash due to the trailing vortex wake.With 2 Figures     

Hydrodynamics of deformable contiguous spherical shapes in an incompressible inviscid fluid

Summary An exact solution to the two-body interaction problem is presented for the case of spherical shapes moving in an incompressible and inviscid fluid. The spheres are assumed to translate in an arbitrary manner and to undergo radial deformation (or pulsation). The problem is formulated in terms of spherical harmonics and the force experienced by the spheres is obtained by employing the Lagally theorem. The expressions for the force are given as an infinite sum of coefficients which are found by solving an infinite set of linear equations. Three main geometries are considered, namely, two spheres exterior to each other, one sphere in the interior of the other and sphere in a rectangular channel. Numerical values for the added-mass coefficients as well as for the hydrodynamic forces are found for the case of rigid sphere moving toward or parallel to a rigid wall or a free surface, and a pulsating sphere in the proximity of these boundaries. Also given are numerical values for the transverse and the longitudinal addedmass coefficients for a sphere moving in a rectangular channel for different channel-blockage ratios.