Recent studies indicate that the transition from sheet to cloud cavitation depends on both cavitation number and Reynolds number. In the present paper this transition is investigated analytically and a physical model is introduced. In order to include the entire process, the model consists of two parts, a model for the growth of the sheet cavity and a viscous film flow model for the so-called re-entrant jet. The models allow the calculation of the length of the sheet cavity for given nucleation rates and initial nuclei radii and the spreading history of the viscous film. By definition, the transition occurs when the re-entrant jet reaches the point of origin of the sheet cavity, implying that the cavity length and the penetration length of the re-entrant jet are equal. Following this criterion, a stability map is derived showing that the transition depends on a critical Reynolds number which is a function of cavitation number and relative surface roughness. A good agreement was found between the model-based calculations and the experimental measurements. In conclusion, the presented research shows the evidence of nucleation and bubble collapse for the growth of the sheet cavity and underlines the role of wall friction for the evolution of the re-entrant jet.

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The transition from sheet to cloud cavitation

Hydraulic components failures due to cavitation erosion are mostly a common cause of false or unfavorable operating parameters. In a parameter study with a convergent divergent nozzle, we found a flow change from sheet cavitation to a more aggressive cloud cavitation. This transition occurs at a critical Reynolds number. The critical Reynolds number was found to be the same for water and a glycol water mixture (increased cinematic viscosity by a factor of 1.16) as one would expect on the grounds of the Bridgman postulate. The critical Reynolds number, hence the transition point, is predicted by a physical model developed on first principles: The transition point is reached, when the time for sheet growth is the same than the time needed for the reentrant jet to reach the sheet leading edge. If this is the case, the reentrant jets cut of the sheet and detach closed clouds. To predict the critical Reynolds number is of great value for the industry, since harm full operation points can be identified already in the design process.

On the Transition from Sheet to Cloud Cavitation

The three-dimensional interfacial waves due to a fundamental singularity steadily moving in a system of two semi-infinite immiscible fluids of different densities are investigated analytically. The two fluids are assumed to be incompressible and homogenous. There are three systems to be considered: one with two inviscid fluids, one with an upper viscous and a lower inviscid fluid, and one with an upper inviscid and a lower viscous fluid. The Laplace equation is taken as the governing equation for inviscid flows while the steady Oseen equations are taken for viscous flows. The kinematic and dynamic conditions on the interface are linearized for small-amplitude waves. The singularity immersed above or beneath the interface is modeled as a simple source in the inviscid fluid while as an Oseenlet in the viscous fluid. Based on the integral solutions for the interfacial waves, the asymptotic representations of wave profiles in the far field are explicitly derived by means of Lighthill’s two-stage scheme. An analytical solution is presented for the density ratio at which the maximum wave amplitude occurs. The effects of density ratio, immersion depth, and viscosity on wave patterns are analytically expressed. It is found that the wavelength of interfacial waves is elongated in comparison with that of free-surface waves in a single fluid.

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Interfacial waves due to a singularity in a system of two semi-infinite fluids

Physical investigation of transient dynamic behaviors of cavitation-induced vibration over a flexible hydrofoil

A generalized hybrid smoothed particle hydrodynamics–peridynamics algorithm with a novel Lagrangian mapping for solution and failure analysis of fluid–structure interaction problems

The closely coupled approach combined with the finite volume method (FVM) solver and the finite element method (FEM) solver is used to investigate the fluid-structure interaction (FSI) of a three-dimensional cantilevered hydrofoil in the water tunnel. The FVM solver and the coupled approach are verified and validated by comparing the numerical predictions with the experimental measurements, and good agreement is obtained concerning both the lift on the foil and the tip displacement. In the noncavitating flow, the result indicates that the growth of the initial incidence angle and the Reynolds number improves the deformation of the foil, and the lift on the foil is increased by the twist deformation. The normalized twist angle and displacement along the span of the hydrofoil for different incidence angles and Reynolds numbers are almost uniform. For the cavitation flow, it is shown that the small amplitude vibration of the foil has limited influence on the developing process of the partial cavity, and the quasi two-dimensional cavity shedding does not change the deformation mode of the hydrofoil. However, the frequency spectrum of the lift on the foil contains the frequency which is associated with the first bend frequency of the hydrofoil.

Fluid-structure interaction simulation of three-dimensional flexible hydrofoil in water tunnel

The steady partially cavitating flow around two-dimensional hydrofoils was simulated numerically by the low-order potential-based boundary integration method. The cavity shape and length are determined for given cavitating numbers in the course of iteration by satisfying the kinematic and dynamic boundary conditions. The re-entrant jet model and the pressure-recovery close model are adopted to replace the high turbulent and two-phase wake forming behind the cavity. The results are compared with the other published numerical ones.

On the partially cavitating flow around two-dimensional hydrofoils *

The derivations are carried out for the velocity potentials of singularities moving with an arbitrary path either in the upper fluid or in the lower fluid with or without a horizontal bottom when two fluids are present. In such a case, the pressure distribution is no longer equal to a constant or zero at the free interface. Taking the influence of an upper fluid upon the lower fluid into consideration, a series of fundamental solutions in closed forms are presented in this paper.

Analytical solutions of singularities moving with an arbitrary path when two fluids are present

Four turbulence models: algebraic Bladwin-Lomax model, two versions of Johnson-King model (J-K90A and J-K92) and two-equation k-g model, are described and evaluated for missile supersonic flow, NASA TN D-712 standard mode and the civil airplane wing-body configuration (two-block C-O mesh) transonic flows. We integrate numerically the 3-D compressible Reynolds averaged Navier-Stokes (RANS) equations, with central finite volume method and explicit multi-step Runge-Kutta algorithm. The turbulence equations of k-g model are explicitly solved in the same way as the RANS. The results show that all models could perform well for attached and mildly separated flows. For large angle-of-attack separated flows over the missile, the calculation with k-g and J-K92 models matches the experimental results better than those with B-L and J-K90A models. According to the B-L model with some modification the shock location logs behind those with the other three models for the civil airplane geometry. Model k-g, because of its advantages such as no use of normal-to-wall distance, simple source terms and straightforward boundary conditions, performs best in the four models for complex configuration with multi-block mesh system or multi-wall interference. B-L and J-K models, despite of cheapness and robustness, both base on empirical Prandtl mixing-length hypothesis and need to calculate the distance normal to the wall, undoubtedly limit the applications scope of these models for multi-block mesh system and complex geometry.

Application of Turbulence Models in Simulation of Complex Flow-Fields

A three-dimensional unsteady flow around the hydrofoil has been dealt with in this paper. Under the assumption of infinitesimal wave and thin hydrofoil, analytic solution of perturbation velocity potential induced by the unsteady flow of a hydrofoil which is simplified as a series of rectangular vortex rings is achieved and then the unsteady forces can be evaluated.

Lu Chuanjing

Papers

Fluid-structure interaction simulation of three-dimensional flexible hydrofoil in water tunnel

On the partially cavitating flow around two-dimensional hydrofoils *

Analytical solutions of singularities moving with an arbitrary path when two fluids are present

Application of Turbulence Models in Simulation of Complex Flow-Fields

Unsteady theory of the hydrofoil of finite span