Approximate Riemann Solvers

The aim of the present investigation is to model and analyze compressible three-dimensional (3D) cavitating liquid flows with special emphasis on the detection of shock formation and propagation. We recently developed the conservative finite volume method CATUM (Cavitation Technische Universitat Munchen), which enables us to simulate unsteady 3D liquid flows with phase transition at all Mach numbers. The compressible formulation of the governing equations together with the thermodynamic closure relations are solved by a modified Riemann approach by using time steps down to nanoseconds. This high temporal resolution is necessary to resolve the wave dynamics that leads to acoustic cavitation as well as to detect regions of instantaneous high pressure loads. The proposed two-phase model based on the integral average properties of thermodynamic quantities is first validated against the solution of the Rayleigh–Plesset equation for the collapse of a single bubble. The computational fluid dynamics tool CATUM is then applied to the numerical simulation of the highly unsteady two-phase flow around a 3D twisted hydrofoil. This specific hydrofoil allows a detailed study of sheet and cloud cavitation structures related to 3D shock dynamics emerging from collapsing vapor regions. The time dependent development of vapor clouds, their shedding mechanism, and the resulting unsteady variation of lift and drag are discussed in detail. We identify instantaneous local pressure peaks of the order of 100 bar, which are thought to be responsible for the erosive damage of the surface of the hydrofoil.

Numerical investigation of three-dimensional cloud cavitation with special emphasis on collapse induced shock dynamics

Large eddy simulation of turbulent cavitating flow in a venturi nozzle is conducted. The fully compressible Favre-filtered Navier-Stokes equations are coupled with a homogeneous equilibrium cavitation model. The dynamic Smagorinsky subgrid-scale turbulence model is employed to close the filtered nonlinear convection terms. The equations are numerically integrated in the context of a generalized curvilinear coordinate system to facilitate geometric complexities. A sixth-order compact finite difference scheme is employed for the Navier—Stokes equations with the AUSM + -up scheme to handle convective terms in the presence of large density gradients. The stiffness of the system due to the incompressibility of the liquid phase is addressed through an artificial increase in the Mach number. The simulation predicts the formation of a vapor cavity at the venturi throat with an irregular shedding of the small scale vapor structures near the turbulent cavity closure region. The vapor formation at the throat is observed to suppress the velocity fluctuations due to turbulence. The collapse of the vapor structures in the downstream region is a major source of vorticity production, resulting into formation of hairpin vortices. A detailed analysis of the vorticity transport equation shows a decrease in the vortex-stretching term due to cavitation. A substantial increase in the baroclinic torque is observed in the regions where the vapor structures collapse. A spectra of the pressure fluctuations in the far-field downstream region show an increase in the acoustic noise at high frequencies due to cavitation.

Large Eddy Simulation of Turbulent-Cavitation Interactions in a Venturi Nozzle

The objective of this paper is to investigate cavitating flows around a pitching hydrofoil via combined physical and numerical studies. The aims are to (1) improve the understanding of the interplay between unsteady cavitating flow, hydrofoil motion, and hydrodynamic performance, (2) quantify the influence of pitching rate on subcavitating and cavitating responses, and (3) quantify the influence of cavitation on the hydrodynamic load coefficients and surrounding flow structures. Results are presented for a NACA66 hydrofoil undergoing controlled, slow (α=6∘/s) and fast (α=63∘/s) pitching motions from α = 0° to α = 15° and back to α = 0° for both subcavitating and cavitating conditions at a moderate Reynolds number of Re = 750 000. The experimental studies were conducted in a cavitation tunnel at the French Naval Academy, France. The numerical simulations are performed by solving the incompressible, multiphase Unsteady Reynolds-Averaged Navier-Stokes Equations via the commercial code CFX using a transport...

Physical and numerical investigation of cavitating flows around a pitching hydrofoil

CFD analysis on the dynamic flow characteristics of the pilot-control globe valve

Prediction of cavitating flow noise by direct numerical simulation

A preconditioned numerical method for gas-liquid two-phase flows is applied to solve cavitating flow. The present method employs a finite-difference method of the dual time-stepping integration procedure and Roe's flux difference splitting approximation with the MUSCL-TVD scheme. A homogeneous equilibrium cavitation model is used. The present density-based numerical method permits simple treatment of the whole gas-liquid two-phase flow field, including wave propagation, large density changes and incompressible flow characteristics at low Mach number. Two-dimensional internal flows through a backward-facing step duct, convergent-divergent nozzles and decelerating cascades are computed using this method

Application of Preconditioning Method to Gas-Liquid Two-Phase Flow Computations

A numerical analysis of three dimensional incompressible turbulent flows through high pressure drop control valves was carried out by using a CFD-ACE code to develop anti-cavitation control valve used in LNG marine system. For this, numerical simulation was performed on several models of control valve that have different orifice diameters of anti-trim and the size of valve discharge. In this study, flow characteristics of control valves with complex flow fields including pressure drop, cavitation effect and variation of flow coefficient as well as correlation of discharge coefficient were investigated and analyzed. Comparing with conventional control valves, newly designed valves by using the CFD analysis showed an improved flow pattern with reduced cavitation and an anticipated performance characteristic.

Numerical analysis of 3-D flow through LNG marine control valves for their advanced design †

An experimental investigation on the effective shape of a floor splitter to reduce sub-surface vortices and cavitation which arise in the vicinity of the pump bells in pump sump is performed. A test model sump was designed based on the Froude number similitude for the recommended structure layout by HI-9.8 standard for pump intake design. To obtain an effective shape of the splitter as an anti-vortex device (AVD), three types of quadrilateral submerged bar with different shape and dimension in sectional area are considered. From the experimental results with and without the splitter attached on the floor under the bell mouth, it was confirmed that the installation of the AVD is very effective to reduce abnormal vortices including sub-surface vortices, pre-swirls and other undesirable hydraulic phenomena. Because of the splitter, sub-surface vortices under the bell mouth did not appear anymore and the swirl was dramatically weakened. The evaluation of AVD was made by the measurement of swirl angles indicating the strength of the vortices and pre-swirls. Splitters with square sections showed partly large swirl angles beyond the acceptable criteria of HI standard though a large square was more effective than a small one. Meanwhile, the splitter with trapezoidal section was showed swirl angle values of less than 5 degrees in all cases of pump operation. Among the three types of AVD, the trapezoidal splitter is the most effective one to suppress the vortices. It is very useful to reduce the occurrence of submerged vortices and to obtain stable inflow condition for designing a high performance pump sump.

An effective shape of floor splitter for reducing sub-surface vortices in pump sump

A numerical simulation on suction vortices behavior in a centrifugal pump was carried out to investigate their influence on the internal flow through impellers including formation and shedding of cavitation by using a finite-volume method and k-ω Shear Stress Transport turbulence model. For cavitating flow, a two phase homogeneous cavitation model was used. A full three-dimensional flow in a single-section centrifugal pump consisting of a six blade impeller and shroud ring was computed with structured mesh. A constant suction vortex is imposed as a boundary condition. Vortices behavior was investigated according to the variation of flow rates of two pump systems with and without suction vortices. From the results, suction vortices induced biased flow structure and more cavitations, especially at the low flow rate condition. Complicated internal flow phenomena through impellers such as formation of cavitations, growing and shedding of the vortex, flow separation and flow unsteadiness due to the suction vortices are investigated and discussed.

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Byeong Rog Shin

Papers

Prediction of cavitating flow noise by direct numerical simulation

Application of Preconditioning Method to Gas-Liquid Two-Phase Flow Computations

Numerical analysis of 3-D flow through LNG marine control valves for their advanced design †

An effective shape of floor splitter for reducing sub-surface vortices in pump sump

Numerical investigation of suction vortices behavior in centrifugal pump