The influence of surface roughness on cloud cavitation flow around hydrofoils

The aim of this study is to investigate experimentally the effect of surface roughness on cloud cavitation around Clark-Y hydrofoils. High-speed video and particle image velocimetry(PIV) were used to obtain cavitation patterns images(Prog. Aerosp. Sci. 37: 551–581, 2001), as well as velocity and vorticity fields. Results are presented for cloud cavitating conditions around a Clark-Y hydrofoil fixed at angle of attack of α = 8?for moderate Reynolds number of Re = 5.6 × 10~5. The results show that roughness had a great influence on the pattern, velocity and vorticity distribution of cloud cavitation. For cavitating flow around a smooth hydrofoil(A) and a rough hydrofoil(B), cloud cavitation occurred in the form of finger-like cavities and attached subulate cavities, respectively. The period of cloud cavitation around hydrofoil A was shorter than for hydrofoil B.Surface roughness had a great influence on the process of cloud cavitation. The development of cloud cavitation around hydrofoil A consisted of two stages:(1) Attached cavities developed along the surface to the trailing edge;(2) A reentrant jet developed, resulting in shedding and collapse of cluster bubbles or vortex structure. Meanwhile, its development for hydrofoil B included three stages:(1) Attached cavities developed along the surface to the trailing edge, with accumulation and rotation of bubbles at the trailing edge of the hydrofoil affecting the flow field;(2) Development of a reentrant jet resulted in the first shedding of cavities. Interaction and movement of flows from the pressure side and suction side brought liquid water from the pressure side to the suction side of the hydrofoil, finally forming a reentrant jet. The jet kept moving along the surface to the leading edge of the hydrofoil, resulting in large-scale shedding of cloud bubbles. Several vortices appeared and dissipated during the process;(3) Cavities grew and shed again.     

Computer simulation of flow past arbitrary hydrofoils with partial cavitation

A method of the numerical investigation of cavitation flow past an arbitrary hydrofoil or a system of hydrofoils and flow past a hydrofoil in a channel or near a free boundary is developed on the basis of the generalized integral Green relation and direct iteration procedure. Emphasis is placed on the numerical analysis of smooth separation of the cavity boundary from a curvilinear surface. The comparison with available analytical and numerical solutions shows a high efficiency of the method proposed.     

Influence of cavitation on the hydroelastic stability of hydrofoils

This work numerically examines the effect of turbulent and cavitating flow on the hydroelastic response and stability of a hydrofoil. A cantilevered, rectangular, chordwise rigid hydrofoil is modeled as a 2-degrees-of-freedom structure for its spanwise bending and torsional flexibilities. The fluid flow is modeled with the incompressible, Unsteady Reynolds Averaged Navier–Stokes equations using an eddy-viscosity turbulence closure model that is corrected for the presence of cavitation, and with a transport equation based cavitation model. The results show that, in general, massive cavitation tends to: (i) reduce the mean lift, (ii) increase the mean drag, (iii) lower the mean deformations, and (iv) delay static divergence, while unsteady sheet/cloud cavitation promotes flow induced vibrations. Such vibrations and load fluctuations could be as large as (and even greater than) the mean values for cases with unsteady cavitation, so dynamic and viscous fluid–structure models are needed to simulate flexible hydrofoils in cavitating flows. In general, the flow induced vibrations, and hence the drag force, are higher with decreasing stiffness. For small leading edge partial cavitation, increasing foil flexibility increases the maximum cavity length and reduces the cavity shedding frequency; however, the influence of foil flexibility is limited for cases where the maximum cavity length is near or beyond the foil trailing edge, because of the relocation of the center of pressure at the elastic axis, near the mid-chord. The results show that the mean deformations are generally limited by stall, and by the quasi-steady linear theory predictions at the fully-wetted and supercavitating limits. Furthermore, frequency focusing can occur when the cavity shedding frequency is near the fundamental system resonance frequencies, and broadening of the frequency spectrum can occur due to excitation of the sub-harmonics and/or modulation induced by the fluctuating cavities, if the cavity shedding frequency is away from the fundamental system resonance frequencies.     

Numerical and experimental investigations on the cavitating flow in a cascade of hydrofoils

The cavitating flow in a cascade of three hydrofoils was investigated by experimental means and numerical simulation. Experiments on the 2D-hydrofoils cascade were carried out at Darmstadt University of Technology in a rectangular test section of a cavitation tunnel. A numerical model developed at LEGI (Grenoble) to describe the unsteady behaviour of cavitation, including the shedding of vapour structures, was applied to the hydrofoils cascade geometry. Results of both experimental and numerical studies show a strong interaction between the cavities of each flow channel besides the typical self-oscillation of cloud cavitation. A detailed comparison of the results allows an interpretation of the interaction mechanisms to be proposed.     

A numerical model for cloud cavitation based on bubble cluster

The cavitation cloud of different internal structures results in different collapse pressures owing to the interaction among bubbles. The internal structure of cloud cavitation is required to accurately predict collapse pressure. A cavitation model was developed through dimensional analysis and direct numerical simulation of collapse of bubble cluster. Bubble number density was included in proposed model to characterize the internal structure of bubble cloud. Implemented on flows over a projectile, the proposed model predicts a higher collapse pressure compared with Singhal model. Results indicate that the collapse pressure of detached cavitation cloud is affected by bubble number density.     

Multiscale tow-phase flow modeling of sheet and cloud cavitation

A multiscale two-phase flow model based on a coupled Eulerian/Lagrangian approach is applied to capture the sheet cavitation formation, development, unsteady breakup, and bubble cloud shedding on a hydrofoil. No assumptions are needed on mass transfer. Instead natural free field nuclei and solid boundary nucleation are modelled and enable capture of the sheet and cloud dynamics. The multiscale model includes a micro-scale model for tracking the bubbles, a macro-scale model for describing large cavity dynamics, and a transition scheme to bridge the micro and macro scales. With this multiscale model small nuclei are seen to grow into large bubbles, which eventually merge to form a large scale sheet cavity. A reentrant jet forms under the sheet cavity, travels upstream, and breaks the cavity, resulting in the emission of high pressure peaks as the broken pockets shrink and collapse while travelling downstream. The method is validated on a 2D NACA0015 foil and is shown to be in good agreement with published experimental measurements in terms of sheet cavity lengths and shedding frequencies. Sensitivity assessment of the model parameters and 3D effects on the predicted major cavity dynamics are also discussed.     

A Stokes model with cavitation for the numerical simulation of hydrodynamic lubrication

We present a cavitation model based on the Stokes equation and formulate adaptive finite element methods for its numerical solution. A posteriori error estimates and adaptive algorithms are derived, and numerical examples illustrating the theory are supplied, in particular with comparison to the simplified Reynolds model of lubrication. Copyright © 2010 John Wiley & Sons, Ltd.     

The numerical and experimental simulation of hypervelocity flow around the HYFLEX vehicle forebody

Numerical and experimental techniques are used to model the flow and pressure distribution around the forebody of the HYFLEX hypersonic flight vehicle. We compare numerical simulation results with modified Newtonian theory and flight data to determine the accuracy of the computational fluid dynamics (CFD) technique used. The numerical simulations closely match the trends in flight data, and show that real gas effects have a small but significant influence on the nose pressure distribution. We also present pressure results from a scale-model tested in a shock tunnel, and compare them with simulation results. For the shock tunnel experiment, the model was placed such that part of the upper surface was in a region of the test flow where nonuniformities were significant, and it was shown that the numerical simulation could adequately capture these experimental flow features. The binary scaling parameter (describing the similarity in species dissociation between flight and model) was used to design the scale-model tests in the shock tunnel, and its effectiveness is discussed. We find that matching the flight Mach number in the shock tunnel experiment is not critical for reproducing flight pressure data, so long as flight velocity is matched, and binary scaling is maintained. Received 11 June 1998 / Accepted 1 September 1998     

A numerical method for simulation of attached cavitation flows

A new numerical algorithm for attached cavitation flows is developed. A cavitation model is implemented in a viscous Navier–Stokes solver. The liquid–vapour interface is assumed as a free surface boundary of the computation domain. Its shape is determined with an iterative procedure to match the cavity surface to a constant pressure boundary. The pressure distribution, as well as its gradient along the wall, is taken into account in updating the cavity shape iteratively. A series of computations are performed for the cavitating flows across three kinds of headform/cylinder bodies: conic, ogival and hemispheric heads. A range of cavitation numbers is investigated for each headform/cylinder body. The obtained results are reasonable and the iterative procedure of cavity shape updating is quite stable. The superiority of the developed cavitation model and algorithm is demonstrated. Copyright © 2006 John Wiley & Sons, Ltd.     

Metal matrix composite solidification in the presence of cooled fibers: numerical simulation and experimental observation

Attempts have been made to alter the solidification microstructures of fiber reinforced aluminum composites by cooling the ends of the fibers extending out of the mold. Experimental observations indicate that cooling the extended ends of the reinforcement results in finer microstructures in the matrix and changes the nature of the interface. In this paper, numerical simulation is performed on a two-dimensional axi-symmetric model to investigate the solidification process of metal matrix composite (MMC) with the extended ends of the fibers cooled by a heat sink. The numerical simulation is based on the source-based enthalpy method with finite volume discretization. The temperature profiles obtained by simulation are compared to the cooling curves measured experimentally in order to validate the current mathematical model. It is found that the simulation result matches the experimental data with reasonable agreement.     

Comparison of experimental data with the numerical simulation of planar entry flow: Role of the constitutive equation

The goal of this research was to determine whether there is any interaction between the type of constitutive equation used and the degree of mesh refinement, as well as how the type of constitutive equation might affect the convergence and quality of the solution, for a planar 4:1 contraction in the finite eiement method. Five constitutive equations were used in this work: the Phan-Thien–Tanner (PTT), Johnson–Segalman (JS), White–Metzner (WM), Leonov-like and upper convected Maxwell (UCM) models. A penalty Galerkin finite element technique was used to solve the system of non-linear differential equations. The constitutive equations were fitted to the steady shear viscosity and normal stress data for a polystyrene melt. In general it was found that the convergence limit based on the Deborah number De and the Weissenberg number We varied from model to model and from mesh to mesh. From a practical point of view it was observed that the wall shear stress in the downstream region should also be indicated at the point where convergence is lost, since this parameter reflects the throughput conditions. Because of the dependence of convergence on the combination of mesh size and constitutive equation, predictions of the computations were compared with birefringence data obtained for the same polystyrene melt flowing through a 4:1 planar contraction. Refinement in the mesh led to better agreement between the predictions using the PTT model and flow birefringence, but the oscillations became worse in the corner region as the mesh was further refined, eventually leading to the loss of convergence of the numerical algorithm. In comparing results using different models at the same wall shear stress conditions and on the same mesh, it was found that the PTT model gave less overshoot of the stresses at the re-entrant corner. Away from the corner there were very small differences between the quality of the solutions obtained using different models. All the models predicted solutions with oscillations. However, the values of the solutions oscillated around the experimental birefringence data, even when the numerical algorithm would not converge. Whereas the stresses are predicted to oscillate, the streamlines and velocity field remained smooth. Predictions for the existence of vortices as well as for the entrance pressure loss (ΔP_ent) varied from model to model. The UCM and WM models predicted negative values for ΔP_ent.     

3D numerical simulation on fluid-structure interaction of structure subjected to underwater explosion with cavitation

In the underwater-shock environment,cavitation occurs near the structural surface.The dynamic response of fluid-structure interactions is influenced seriously by the cavitation effects.It is also the difficulty in the field of underwater explosion.With the traditional boundary element method and the finite element method(FEM),it is difficult to solve the nonlinear problem with cavitation effects subjected to the underwater explosion.To solve this problem,under the consideration of the cavitation effects and fluid compressibility,with fluid viscidity being neglected,a 3D numerical model of transient nonlinear fluid-structure interaction subjected to the underwater explosion is built.The fluid spectral element method(SEM) and the FEM are adopted to solve this model.After comparison with the FEM,it is shown that the SEM is more precise than the FEM,and the SEM results are in good coincidence with benchmark results and experiment results.Based on this,combined with ABAQUS,the transient fluid-structure interaction mechanism of the 3D submerged spherical shell and ship stiffened plates subjected to the underwater explosion is discussed,and the cavitation region and its influence on the structural dynamic responses are presented.The paper aims at providing references for relevant research on transient fluid-structure interaction of ship structures subjected to the underwater explosion.     

Study on the numerical schemes for hypersonic flow simulation

Hypersonic flow is full of complex physical and chemical processes, hence its investigation needs careful analysis of existing schemes and choosing a suitable scheme or designing a brand new scheme. The present study deals with two numerical schemes Harten, Lax, and van Leer with Contact (HLLC) and advection upstream splitting method (AUSM) to effectively simulate hypersonic flow fields, and accurately predict shock waves with minimal diffusion. In present computations, hypersonic flows have been modeled as a system of hyperbolic equations with one additional equation for non-equilibrium energy and relaxing source terms. Real gas effects, which appear typically in hypersonic flows, have been simulated through energy relaxation method. HLLC and AUSM methods are modified to incorporate the conservation laws for non-equilibrium energy. Numerical implementation have shown that non-equilibrium energy convect with mass, and hence has no bearing on the basic numerical scheme. The numerical simulation carried out shows good comparison with experimental data available in literature. Both numerical schemes have shown identical results at equilibrium. Present study has demonstrated that real gas effects in hypersonic flows can be modeled through energy relaxation method along with either AUSM or HLLC numerical scheme.     

The manipulated transitional backward-facing step flow: an experimental and direct numerical simulation investigation

Results from a joint experimental and direct numerical simulation (DNS) investigation are presented for the flow over a backward-facing step manipulated by low-amplitude time-periodic (harmonic) blowing/suction excitation through a narrow slot at the edge of the step. For a Reynolds number of Re_h=3000 (based on step height, h, and inflow velocity, U_o) and for laminar inflow, a 33% reduction of the mean recirculation length (in comparison to the non-manipulated reference case) could be obtained with a forcing amplitude of the order of one per cent of U_o. Based on the momentum thickness, θ, of the incoming laminar boundary layer (at the edge of the step), the corresponding optimum Strouhal number is St_θ=f_optθ/U_o=0.012. From the experimental data it can be concluded that, in our flow case, the optimum frequency, f_opt=50 Hz , was the most amplified frequency in the transition-to-turbulence process of the separated laminar shear layer. Detailed comparison of the experimental data with data from the numerical simulation shows that DNS and experimental data agree up to second-order statistics. The joint experimental and numerical investigations exhibit a complementary nature in the sense that, on the one hand, the main advantage of the experiment was the relative ease with which a wide range of forcing parameters could be tested and, on the other hand, DNS could provide spatio-temporal details of the flow which could not be so easily obtained in the experiment.     

Visualisation and les simulation of cavitation cloud formation and collapse in an axisymmetric geometry

Visualisation and Large Eddy Simulations (LES) of cavitation inside the apparatus previously developed by Franc (2011) for surface erosion acceleration tests and material response monitoring are presented. The experimental flow configuration is a steady-state closed loop flow circuit where pressurised water, flowing through a cylindrical feed nozzle, is forced to turn 90° and then, move radially between two flat plates towards the exit of the device. High speed images show that cavitation is forming at the round exit of the feed nozzle. The cavitation cloud then grows in the radial direction until it reaches a maximum distance where it collapses. Due to the complexity of the flow field, direct observation of the flow structures was not possible, however vortex shedding is inferred from relevant simulations performed for the same conditions. Despite the axisymmetric geometry utilized, instantaneous pictures of cavitation indicate variations in the circumferential direction. Image post-processing has been used to characterize in more detail the phenomenon. In particular, the mean cavitation appearance and the cavity length have been estimated, showing good correlation with the erosion zone. This also coincides with the locations of the maximum values of the standard deviation of cavitation presence. The dominant frequency of the ‘large-scale’ cavitation clouds has been estimated through FFT. Cloud collapse frequencies vary almost linearly between 200 and 2000 Hz as function of the cavitation number and the downstream pressure. It seems that the increase of the Reynolds number leads to a reduction of the collapse frequency; it is believed that this effect is due to the agglomeration of vortex cavities, which causes a decrease of the apparent frequency. The results presented here can be utilized for validation of relevant cavitation erosion models which are currently under development.     

薄膜结构流固耦合的CFD数值模拟研究

基于弱耦合分区求解策略,在CompaqVisualFortran6．5环境下搭建了薄膜结构三维流固耦合效应的CFD数值模拟平台。程序采用模块化编程思想,主要包含几何建模、流体分析、结构分析和数据交换四个模块。其中几何建模模块采用自行编制的膜结构找形分析程序,流体分析模块采用经过二次开发的计算流体力学软件FLUENT6．0,结构分析模块采用自行编制的膜结构动力分析程序MDLFX;在数据交换模块中,编制了基于薄板样条法的插值计算程序,以实现流固交界面上不同区域网格间的数据传递问题,编制了基于代数法和迭代法的动网格变形程序,以实现流固耦合运算中的动网格更新。基于该软件平台,对单向柔性屋盖和鞍形膜结构屋盖进行了流固耦合数值模拟,验证了方法的有效性。     

Time-dependent numerical simulation of viscoelastic flow and stability

The 4×4 mixed finite-element method is extended in order to calculate time-dependent viscoelastic flow. The basic algorithm uses a fully implicit technique with a predictor-corrector control of the time step for monitoring the accuracy. Excellent agreement is found with analytical test cases. Several decoupled schemes are also developed with a view to reducing the cost of the time-dependent calculations. However, none of them reaches that goal on actual flow problems because of a drastic reduction of the time step.The time-dependent algorithm is used for verifying the stability of steady-state viscoelastic flow solutions. The approach consists of using a steady-state solution as a set of initial conditions for a time-dependent algorithm with the hope that, in case of instability, the system will lead to a stable solution. More precisely, we consider the flow of an Oldroyd-B fluid through a four-to-one contraction. Starting from a steady-state flow, we impose a pressure impulse in the entry section and calculate the approach toward another steady-state. For planar contractions, we do not constrain the flow to be symmetric while, for circular contractions, the flow is endowed with swirling capabilities. It is found that the stable or unstable character of the flow depends upon the mesh as well as upon the method of discretization.     

Direct numerical simulation of fluid flow laden with many particles

Two-dimensional channel flow of fluid laden with many particles is studied by direct numerical simulation using the Navier–Stokes equation coupled with the equation of motion for respective particles. Fractional four-step method with Crank–Nicolson scheme and ALE technique is adopted for P2P1 mixed finite element formulation of the governing equations for fluid motion. The motion and distribution of particles in the fluid is virtually described and the calculated relative viscosity is compared with previous results within the limits of possibility. The effect of the ratio of channel gap to particle diameter on the relative viscosity and the tubular pinch effect are also delineated.     

膛口反应流并行数值模拟

采用轴对称多组分N-S方程对含有高速运动弹丸的膛口反应流进行了数值模拟.控制方程采用时间分裂方法并在大型计算机上采用MPI方法进行多核并行求解,其中对流项采用二阶AUSM+格式和MUSCL插值方法进行处理,燃气采用氢气-空气混合气,反应机理为9组分19步基元反应.对于弹丸引起的网格运动,采用嵌套网格法处理.并行验证算例与串行计算结果一致,采用20个CPU计算时效率为64％.根据数值结果详细讨论了发射过程中的气体动力学和化学动力学过程,并且通过对两种条件下的计算结果比较分析了化学反应对膛口流场发展的影响.结果表明,上述算法能够较为正确地模拟弹丸和化学反应对膛口流场的影响,并大大提高了计算速度.     

Direct numerical simulation of turbulent pipe flow

Fully developed turbulent pipe flow at low Re-number is studied by means of direct numerical simulation (DNS). In contrast to many previous DNS's of turbulent flows in rectangular geometries, the present DNS code, developed for a cylindrical geometry, is based on the finite volume technique rather than being based on a spectral method. The statistical results are compared with experimental data obtained with two different experimental techniques. The agreement between numerical and experimental results is found to be good which indicates that the present DNS code is suited for this kind of numerical simulations.