绕三维水翼非定常空化流动结构的数值与实验研究

为了说明非定常空化的流动机理,该文采用数值与实验相结合的方法对绕三维水翼片状和云状空化流动结构进行了研究.实验在高速水洞中进行,采用高速录像技术观测了片状和云状空化阶段的空穴形态.数值计算基于均相流模型,汽液混合区域密度由质量传输方程调节.利用商业软件二次开发技术引入准确描述空化流场非定常特性的FBM 湍流模型,进行绕三维水翼的数值模拟,获得了随时间变化的空穴形态、压力和速度分布等流场结构.与实验结果对比发现,数值计算结果与实验基本一致.在片状空化阶段,空穴稳定地附着在水翼表面,只有空穴尾部不断的有小空泡团沿着翼弦方向脱落.在云状空化阶段,清楚得描述了空穴的产生-发展-脱落-溃灭的准周期性变化,并准确地捕捉到空泡脱落时,附着在翼型前端的U 型空穴和翼展方向不同强度的反向射流,脱落的空泡由翼型中前部旋涡状脱落.     

Calculation of a turbulent monodisperse flow in an axisymmetric channel

A stationary isothermal model of the aerodynamics of a two-phase flow in an axisymmetric channel has been constructed with allowance for the turbulent and pseudoturbulent mechanisms underlying the transfer of the solid phase momentum. The equations of dispersed phase motion are closed at the level of the equations for the second moments of the pulsation velocities of particles, whereas the equation of momentum transfer of the carrier is closed on the basis of a one-parameter model of turbulence extended to the case of two-phase turbulent flows. The results of calculations are compared with experimental data. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 5, pp. 844–855, September–October, 2008.     

Use of equations for transfer of particle pulsation characteristics for calculating two-phase flows in the stabilized section of a tube

A stationary isothermal system of equations defining the behavior of a two-phase rising flow in the region of steady motion of a gas suspension in an axially symmetric channel has been developed. The equation of motion of the carrying medium is closed using a one-parameter model of turbulence, and the equation of momentum transfer in the dispersed phase is closed with the use of the equations for the second, third, and fourth moments of the pulsation velocities of the particles. The main mechanisms of two-phase turbulent flows were numerically investigated. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 4, pp. 99–109, July–August, 2007.     

A BEM for the prediction of free surface effects on cavitating hydrofoils

 In this paper, a boundary element method (BEM) for cavitating hydrofoils moving steadily under a free surface is presented and its performance is assessed through systematic convergence studies, comparisons with other methods, and existing measurements. The cavitating hydrofoil part and the free surface part of the problem are solved separately, with the effects of one on the other being accounted for in an iterative manner. Both the cavitating hydrofoil surface and the free surface are modeled by a low-order potential based panel method using constant strength dipole and source panels. The induced potential by the cavitating hydrofoil on the free surface and by the free surface on the hydrofoil are determined in an iterative sense and considered on the right hand side of the discretized integral equations. The source strengths on the free surface are expressed by applying the linearized free surface conditions. In order to prevent upstream waves the source strengths from some distance in front of the hydrofoil to the end of the truncated upstream boundary are enforced to be equal to zero. No radiation condition is enforced at the downstream boundary or at the transverse boundary for the three-dimensional case. First, the BEM is validated in the case of a point vortex and some convergence studies are done. Second, the BEM is applied to 2-D hydrofoil geometry both in fully wetted and in cavitating flow conditions and the predictions are compared to those of other methods and of the measurements in the literature. The effects of Froude number, the cavitation number and the submergence depth of the hydrofoil from free surface are discussed. Then, the BEM is validated in the case of a 3-D point source. The effects of grid and of the truncated domain size on the results are investigated. Lastly, the BEM is applied to a 3-D rectangular cavitating hydrofoil and the effect of number of iterations and the effect of Froude number on the results are discussed. Received 6 November 2000     

基于拉格朗日方法的非定常空化流动研究

采用基于拉格朗日体系的有限时间李雅普诺夫指数、拉格朗日拟序结构和粒子追踪方法对绕水翼典型非定常云状空化流场进行研究。采用计算流体动力学方法获得空化流场数据数值,湍流模型采用经典大涡模拟方法,空化相变过程采用基于相间质量传输的Zwart模型进行处理。根据有限时间李雅普诺夫指数分布在空化核心区域定义了前缘拟序结构和尾缘拟序结构。在不同的空化发展阶段,两种拟序结构相互作用并呈现不同的分布规律,揭示不同空化发展阶段的典型流场结构。     

Calculation of turbulent momentum transfer in a solid phase based on equations for the second and third moments of particle-velocity pulsations

A chain of transfer equations for the second and third moments of dispersed-phase-velocity pulsations in the anisotropic field of energy of random particle motion is obtained based on the computational procedure developed. The interphase and interparticle interactions are allowed for. The turbulent characteristics of the gas are calculated on the basis of a one-parameter turbulence model generalized to the case of two-phase turbulent flows. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 2, pp. 60–70, March–April, 2007.     

Numerical simulation of cavitating flow of liquid helium in venturi channel

The fundamental characteristics of the two-dimensional cavitating flow of liquid helium through a venturi channel near the lambda point are numerically investigated to realize the further development and high performance of new multi-phase superfluid cooling systems. First, the governing equations of the cavitating flow of liquid helium based on the unsteady thermal nonequilibrium multi-fluid model with generalized curvilinear coordinates system are presented, and several flow characteristics are numerically calculated, taking into account the effect of superfluidity. Based on the numerical results, the two-dimensional structure of the cavitating flow of liquid helium though venturi channel is shown in detail, and it is also found that the generation of superfluid counterflow against normal fluid flow based on the thermomechanical effect is conspicuous in the large gas phase volume fraction region where the liquid-to-gas phase change actively occurs. Furthermore, it is clarified that the mechanism of the He I to He II phase transition caused by the temperature decrease is due to the deprivation of latent heat for vaporization from the liquid phase.     

Turbulence in a Roughness Layer

Consideration is given to a model of turbulent flow in a roughness layer; the model is formed by the equations for turbulent momentum and turbulence-energy density and by free boundary conditions at self-establishing boundaries of the turbulent zone in the entire layer and in roughness cells. The model describes the interactions of the flow with the elements of roughness and the processes in the cells of different scales. Certain calculated characteristics of turbulence in vegetation are given. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 78, No. 4, pp. 143–151, July–August, 2005.     

Numerical simulation of cryogenic cavitating flow by an extended transport-based cavitation model with thermal effects

Thermodynamic effects on cryogenic cavitating flow is important to the accuracy of numerical simulations mainly because cryogenic fluids are thermo-sensitive, and the vapour saturation pressure is strongly dependent on the local temperature. The present study analyses the thermal cavitating flows in liquid nitrogen around a 2D hydrofoil. Thermal effects were considered using the RNG k-ε turbulence model with a modified turbulent eddy viscosity and the mass transfer homogenous cavitation model coupled with energy equation. In the cavitation model process, the saturated vapour pressure is modified based on the Clausius-Clapron equation. The convection heat transfer approach is also considered to extend the Zwart-Gerber-Belamri model. The predicted pressure and temperature inside the cavity under cryogenic conditions show that the modified Zwart-Gerber-Belamri model is in agreement with the experimental data of Hord et al. in NASA, especially in the thermal field. The thermal effect significantly affects the cavitation dynamics during phase-change process, which could delay or suppress the occurrence and development of cavitation behaviour. Based on the modified Zwart-Gerber-Belamri model proposed in this paper, better prediction of the cryogenic cavitation is attainable.     

基于预处理方法的空化超空化流数值模拟

建立了一套水动力空化流数值计算方法,采用基于预处理方法的空化两相流模型计算二维空化问题,并通过添加源项来计算轴对称外型空化问题,发展了类比于Roe格式的空化两相流通量计算迎风格式,湍流模型采用经过修正的两方程模型,时间推进采用双时间步LU-SGS隐式方法,计算了二维水翼及轴对称体外型的全湿流、空化及超空化流动。数值结果表明,该文建立的基于预处理方法的空化两相流数值算法是有效的,可以对二维及轴对称外型的全湿流态以及空化、超空化的演化等现象进行数值预测。     

On the calculation of turbulent fan jets

The self-similar equations for the dynamic and temperature fields of a forced free fan jet have been numerically integrated within the framework of the standard k-ε model of turbulence. The tables of solutions obtained for the velocity, temperature, and kinetic turbulent energy of the jet, as well as the mean square of the jet-temperature fluctuations at different turbulent Prandtl numbers, are presented. The quantitative parameters of the evolution of the average and turbulent characteristics of the jet flow were determined. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 1, pp. 62–67, January–February, 2008.     

Dynamics of the viscous interaction of a ring vortex with a flat screen

A separation turbulent flow has been mathematically simulated on the basis of numerical solution of nonstationary Navier-Stokes equations for determining the dynamics of viscous interaction of a ring vortex with a flat screen. The problem was solved for an axisymmetric turbulent flow at Reynolds numbers falling within the range 10⁵–10⁷. On the basis of the calculation data obtained, the interaction of a ring vortex with a turbulent flow induced on the screen and with the secondary ring vortices was investigated. The data obtained are in qualitative agreement with the analogous data obtained by other authors with the use of the discrete-vortex method and the boundary-layer theory as well as with the available experimental and calculation data obtained for a laminar flow. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 1, pp. 184–190, January–February, 2008.     

Numerical simulation of unsteady cavitating flows using a homogenous equilibrium model

 Numerical simulations of two-dimensional cavity flows around a flat plate normal to flow and flows through a 90^∘ bent duct are performed to clarify unsteady behavior under various cavitation conditions. A numerical method applying a TVD-MacCormack scheme with a cavitation model based on a homogenous equilibrium model of compressible gas-liquid two-phase media proposed by the present authors, is applied to solve the cavitating flow. This method permits the simple treatment of the whole gas-liquid two-phase flow field including wave propagation and large interface deformation. Numerical results including detailed observations of unsteady cavity flows and comparisons of predicted results with experimental data are provided. Received: 5 August 2002 / Accepted: 6 January 2003     

Calculation of unsteady flow past a cube on the wall of a narrow channel using URANS and the Spalart–Allmaras turbulence model

The results of numerical simulation of fully developed turbulent flow in a channel with the cube on the lower wall (for the characteristic Reynolds number Re = 40,000) within the framework of the traditional approach to the solution of unsteady Reynolds-averaged Navier–Stokes equations (URANS) in combination with the semiempirical Spalart–Allmaras turbulence model (with a correction for rotation) have been presented. A detailed comparative analysis of the results of numerical simulation of local and integral flow characteristics and the Martinuzzi experimental data has shown that the self-oscillating regime of flow past the cube is a superposition of oscillations of the arms of a horseshoe vortex and the rear arched and detached vortex structures. Using fast Fourier transformation, it has been found that the oscillations are of a bimodal character in the longitudinal and vertical directions, whereas in the transverse direction, they are of a unimodal character.     

The evolution of homogeneous turbulence in a density-stratified medium. 3. Analysis of the near region

Development of a turbulent perturbation in a homogeneous flow moving within a medium that is linearly density-stratified across the direction of flow motion is described. The initial region of the evolution of turbulence with a large turbulent Reynolds numberR _λ is considered. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 70, No. 3, pp. 393–403, May–June, 1997.     

MHD boundary-layer flow due to a moving extensible surface

The flow due to a moving extensible sheet that obeys a more general stretching law is considered. The sheet occupies the negative x-axis and is moving continually in the positive x-direction, in an incompressible viscous and electrically conducting fluid. The sheet somehow disappears in a sink that is located at (x, y) = (0, 0). The governing system of partial differential equations is first transformed into a system of ordinary differential equations, and the transformed equations are solved numerically using a finite-difference scheme, namely the Keller-box method. The features of the flow and heat-transfer characteristics for different values of the governing parameters are analyzed and discussed. It is found that dual solutions exist for the flow near x = 0, where the velocity profiles show a reversed flow.     

Preliminary results on acoustic modelling of cavitating propellers

The numerical prediction of the acoustic pressure field induced by cavitating marine propellers is addressed. A hydrodynamic model for transient sheet cavitation on propellers in non–uniform inviscid flow is coupled with a hydroacoustic model based on the Ffowcs Williams–Hawkings equation. The proposed hydroacoustic approach, novel to marine applications, allows to split the noise signature into thickness and loading term contributions. Both hydrodynamic and hydroacoustic model equations are solved via boundary integral formulations. Numerical predictions of the propeller noise by using the Ffowcs Williams–Hawkings equation are compared to those obtained by a classical Bernoulli equation approach. The influence of cavitation on the noise waveforms is discussed by comparing non–cavitating and cavitating propeller flow results. The authors wish to thank Prof. S.A. Kinnas for providing a detailed documentation of the experiment used as the test case in the present analysis. The present work was supported by the Ministero dei Trasporti e della Navigazione in the frame of INSEAN Research Program 2000–02.     

Nonstationary radiation-gasdynamic model of a laser-plasma accelerator

Based on the system of two-dimensional axisymmetrical continuity equations, Navier-Stokes and energy equations, and the equations of selective heat radiation transfer, a computational model is constructed and conditions of unsteady subsonic flows in a cylindrical channel of a power unit of the laser-plasma accelerator type are investigated. The governing parameters of the model are calculated, at which numerical solutions can be obtained to describe steady laminar gas flow in the neighborhood of the region of heat release, nonstationary oscillatory motions, and nonstationary vortex motion. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 1, pp. 174–179, January–February, 2000.     

Numerical study of the two-phase flow characteristics of slush nitrogen

The fundamental two-phase flow characteristics of slush nitrogen in a pipe are numerically investigated to develop effective cooling performance for long-distance superconducting cable. First, the governing equations of two-phase slush nitrogen flow based on the unsteady thermal non-equilibrium two-fluid model are constructed and several flow characteristics are numerically calculated taking into account the effects of the slush volume fraction, the thermodynamic behavior of slush, and the duct shape. Furthermore, the numerical results are compared with previous experimental results on pressure loss measurement and visualization measurement in two-phase slush nitrogen flow along the longitudinal direction of the pipe. Results of this research show that it is possible to reduce the pressure loss by using a two-phase slush flow under the high Reynolds number condition and by applying the appropriate volume fraction of slush particles. The optimized thermal flow conditions for cryogenic two-phase slush nitrogen with practical use of latent heat for slush melting are predicted for the development of a new type of superconducting cooling system.     

A two-scale model for fluid flow in an unsaturated porous medium with cohesive cracks

A two-scale model is developed for fluid flow in a deforming, unsaturated and progressively fracturing porous medium. At the microscale, the flow in the cohesive crack is modelled using Darcy’s relation for fluid flow in a porous medium, taking into account changes in the permeability due to the progressive damage evolution inside the cohesive zone. From the micromechanics of the flow in the cavity, identities are derived that couple the local momentum and the mass balances to the governing equations for an unsaturated porous medium, which are assumed to hold on the macroscopic scale. The finite element equations are derived for this two-scale approach and integrated over time. By exploiting the partition-of-unity property of the finite element shape functions, the position and direction of the fractures are independent from the underlying discretization. The resulting discrete equations are nonlinear due to the cohesive crack model and the nonlinearity of the coupling terms. A consistent linearization is given for use within a Newton–Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach. The calculations indicate that the evolving cohesive cracks can have a significant influence on the fluid flow and vice versa.