Jules W. Lindau

A preconditioned Navier–Stokes method for two-phase flows with application to cavitation prediction

Abstract An implicit algorithm for the computation of viscous two-phase flows is presented in this paper. The baseline differential equation system is the multi-phase Navier–Stokes equations, comprised of the mixture volume, mixture momentum and constituent volume fraction equations. Though further generalization is straightforward, a three-species formulation is pursued here, which separately accounts for the liquid and vapor (which exchange mass) as well as a non-condensable gas field. The implicit method developed here employs a dual-time, preconditioned, three-dimensional algorithm, with multi-block and parallel execution capabilities. Time-derivative preconditioning is employed to ensure well-conditioned eigenvalues, which is important for the computational efficiency of the method. Special care is taken to ensure that the resulting eigensystem is independent of the density ratio and the local volume fraction, which renders the scheme well-suited to high density ratio, phase-separated two-fluid flows characteristic of many cavitating and boiling systems. To demonstrate the capabilities of the scheme, several two- and three-dimensional examples are presented.

Performance Analysis of Cavitating Flow in Centrifugal Pumps Using Multiphase CFD

A multi-phase CFD method is used to analyze centrifugal pump performance under developed cavitating conditions. The differential model employed is the homogeneous two-phase Reynolds-Averaged-Navier-Stokes equations, wherein mixture momentum and volume continuity equations are solved along with vapor volume fraction continuity. Mass transfer modeling is provided for the phase change associated with sheet cavitation. Quasi-three-dimensional (Q3D) and fully-three-dimensional analyses are performed for two impeller configurations. Using Q3D analysis, steady and time-dependent analyses were performed across a wide range of flow coefficients and cavitation numbers. Characteristic performance trends associated with offdesign flow and blade cavitation are observed. The rapid drop in head coefficient at low cavitation numbers (breakdown) is captured for all flow coefficients. Local flow field solution plots elucidate the principal physical mechanisms associated with the onset of breakdown. Results are also presented which illustrate the full three dimensional capability of the method.

High Reynolds Number, Unsteady, Multiphase CFD Modeling of Cavitating Flows

A preconditioned, homogeneous, multiphase, Reynolds Averaged Navier-Stokes model with mass transfer is presented. The model is preconditioned in order to obtain good convergence and accuracy regardless of phasic density ratio or flow velocity. Engineering relevant validative unsteady two and three-dimensional results are given. A demonstrative three-dimensional, three-field (liquid, vapor, noncondensable gas) transient is also presented. In modeling axisymmetric cavitators at zero angle-of-attack with 3-D unsteady RANS, significant asymmetric flow features are obtained

Propeller Cavitation Breakdown Analysis

A Reynolds-averaged Navier-Stokes computational model of homogeneous multiphase flow is presented. Cavitation driven thrust and torque breakdown over a wide range of advance ratios is modeled for an open propeller. Computational results are presented as a form of validation against water tunnel measured thrust and torque breakdown for the propeller. Successful validation of the computational model is achieved. Additional observations are made with regards to cavity size and shape as well as cavitation breakdown behavior.

Preconditioning Algorithms for the Computation of Multi-Phase Mixture Flows

Preconditioned time-marching algorithms are developed for a class of isothermal compressible multi-phase mixture flows, relevant to the modeling of sheetand super-cavitating flows in hydrodynamic applications. Using the volume fraction and mass fraction forms of the multi-phase governing equations, three closely related but distinct preconditioning forms are derived. The resulting algorithm is incorporated within an existing multi-phase code and several representative solutions are obtained to demonstrate the capabilities of the method. Comparisons with measurement data suggest that the compressible formulation provides an improved description of the cavitation dynamics compared with previous incompressible computations.

Two Fluid Modeling of Microbubble Turbulent Drag Reduction

An unstructured 3D multiphase CFD method has been adapted and applied for the modeling of high Reynolds number external flows with microbubble drag reduction (MDR). An ensemble averaged multi-field two-fluid baseline differential model is employed. Interfacial dynamics models are incorporated to account for drag, lift, virtual mass and dispersion. Wall kinematic constraints, porous-wall shear apportionment, coalescence, breakup and attendant turbulence attenuation are also accounted for. The results of several high Reynolds number applications are presented, including quasi-1D analysis of an equilibrium bubbly boundary layer, 2D analysis of flat plate flow across a range of gas injection flow rates, and 3D analysis of a notional high lift hydrofoil with MDR. For the flat plate analyses, quantitative comparisons are made with available experimental skin friction measurements, and qualitative comparisons are made with available volume fraction profile measurements. Though some accuracy shortcomings remain, the generally good agreement observed serves to validate the appropriateness of two-fluid modeling in these flows, while elucidating areas where modeling improvements can be made. It is observed that the extraction of turbulent kinetic energy from the liquid phase by the action of bubble breakup can be a significant source of skin friction reduction. Also, the role of mixture density in the boundary layer on wall shear stress is discussed in the context of the homogenous mixture and two-fluid simulations presented.Copyright

COMPUTATION OF COMPRESSIBLE MULTIPHASE FLOWS

A computational model capable of capturing fully compressible multiphase flow including energy conservation is presented. The model is a finite volume form based on the Reynolds Averaged Navier-Stokes Equations and is capable of considering fully general equations of state. The preconditioning matrix is presented and ensures a well conditioned eigensystem, essential for efficient and accurate multiphase computations. Solutions are given representing both the utility of the preconditioning method as well as the ability of the model to capture highly compressible multiphase flow fields. When considering compressible flows where thermal effects are significant and a general equation of state is necessary, energy conservation in a multiphase flow field is shown to be a requirement.

Multiphase Computations for Underwater Propulsive Flows

An algorithm for modeling compressible phenomena in multi-phase, reacting flows is developed. Time-marching preconditioned methodology is used as the algorithmic framework because of its inherent capability of handling multiple flow regimes, such as the incompressible bulk liquid flow, low Mach number compressible vapor flow and transonic/supersonic twophase mixture flow with predominant thermal effects. A preconditioning system is developed based on the onedimensional inviscid subsystem and shown to yield a well-conditioned eigensystem. Computational results representative of a hypothetical high-speed supercavitating-vehicle propulsion plume are presented to verify the capabilities of the formulation.

Noise generated by ventilated supercavities

The noise generated by ventilated supercavities has been explored experimentally in a water tunnel facility. The most prominent acoustical characteristic is the monopole behavior exhibited by a ventilated supercavity in its pulsating closure regime. The interior cavity pressure and near-field radiated sound are monotonic with a frequency that is related to the speed and length of waves propagating on the supercavity gas/water interface. The cavity interior pressure spectrum level is shown to be related to the near-field and far-field noise spectrum level through spherical spreading of the sound waves from the supercavity interface. As a result, the cavity interior pressure can be used as a measure of the radiated noise. The noise radiated by a pulsating supercavity at the pulsation frequency is at least 40 dB above that radiated by comparable re-entrant jet and twin vortex cavities.

Computational Investigations of Air Entrainment, Hysteresis, and Loading for Large-Scale, Buoyant Cavities

A complete physical model of ventilated supercavitation is not well established. Efforts documented display the ability, with a finite volume, locally homogeneous approach, to simulate supercavitating flows and obtain good agreement with experiments. Several modeling requirements appear critical, especially in physical hysteretic conditions or configurations. The hysteresis presented is due to obstruction of the flow with a solid object. The modeling approach taken correctly captures a full hysteresis loop and the corresponding dimensionless ventilation rate to cavity pressure (CQdelta) relationship. This correspondence supports the suggestion that the main mechanism of cavity gas entrainment is via shear layers attached to the cavity walls. With such validated solutions, additional insight into the flow within the cavity is gained.