Toshiaki Ikohagi

Dynamics of attached turbulent cavitating flows

Abstract Stationary and non-stationary characteristics of attached, turbulent cavitating flows around solid objects are reviewed. Different cavitation regimes, including incipient cavitation with traveling bubbles, sheet cavitation, cloud cavitation, and supercavitation, are addressed along with both visualization and quantitative information. Clustered hairpin type of counter-rotating vapor vortices at incipient cavitation, and finger-like structure in the leading edge and an oscillatory, wavy structure in the trailing edge with sheet cavitation are assessed. Phenomena such as large-scale vortex structure and rear re-entrant jet associated with cloud cavitation, and subsequent development in supercavitation are described. Experimental evidence indicates that the lift and drag coefficients are clearly affected by the cavitating flow structure, reaching minimum and maximum, respectively, at cloud cavitation. Computationally, progress has been made in Navier–Stokes (N–S) based solution techniques. Issues including suitable algorithm development for treating large density jump across phase boundaries, turbulence and cavitation models, and interface tracking are discussed. While satisfactory predictions in wall pressure distribution can be made in various cases, aspects such as density and stress distributions exhibit higher sensitivity to modeling details. A perspective of future research needs in computational modeling is offered.

High-speed observation of ultrahigh-speed submerged water jets

Some peculiar phenomena occur around ultrahigh-speed submerged water jets accompanied by very severe cavitation erosion. Using the flow visualization technique with a xenon flash, the water jets were carefully observed, and the spatial distributions of highly erosive impulsive pressures around the jets were measured by means of a pressure-sensitive film technique. The effects of the injection pressure and the nozzle configuration are systematically clarified. Thus, the characteristics and structures of ultrahigh-speed submerged water jets are clearly shown.

Numerical Study of Sheet Cavitation Breakoff Phenomenon on a Cascade Hydrofoil

2-D unsteady cavity flows through hydrofoils in cascade which is the most fundamental element of turbomachinery are numerically calculated. In particular, attention was paid to instability phenomena of the sheet cavity in transient cavitation condition and the mechanism of break-off phenomenon was examined. A TVD MacCormacks scheme employing a locally homogeneous model of compressible gas-liquid two-phase media was applied to analyze above cavity flows. The present method permits us to treat the whole cavitating/noncavitating unsteady flow field. By analyzing numerical results in detail, it became clear that there are at least two mechanisms in the break-off phenomena of sheet cavity; one is that re-entrant jets play a dominant role in such a break-off phenomenon, and the other is that pressure waves propagating inside the cavity bring about an another type of break-off phenomenon accompanied with cavity surface waves.

Numerical Analysis of Cavitation Instabilities Arising in the Three-Blade Cascade

Three types of cavitation instabilities through flat plate cascades, which are similar to forward rotating cavitation, rotating-stall cavitation and cavitation surge occurring in high-speed rotating fluid machinery, are represented numerically under the three-blade cyclic condition. A numerical method employing a locally homogeneous model of compressible gas-liquid two-phase medium is applied to solve the above flow fields, because this permits the entire flow field inside and outside the cavity to be treated through only one system of governing equations. In addition, the numerical method suites to analyze unsteady cavitating flow with a long time evolution. From the calculated results of the present numerical simulation with wide range of cavitation number and flow rate, we obtain a cavitation performance curve of the present three-blade cyclic cascade, analyze the aspects of unsteady cavitation, and discuss the characteristics and mechanisms of cavitation

Finite-difference schemes for steady incompressible Navier-Stokes equations in general curvilinear coordinates

Abstract Time-marching finite-difference schemes for solving the steady incompressible Navier-Stokes equations are proposed. In these schemes, the fractional-step method and the SMAC method are applied to a general curvilinear coordinates grid, so that the continuity condition can be satisfied identically. The momentum equations of contravariant velocities are newly derived for the accurate and easy treatment of the boundary conditions and are formulated concisely by introducing the contravariant vorticities. Spurious errors and numerical instabilities can be reasonably suppressed by employing the staggered grid and the upwind difference for moderate-to-high Reynolds number flows. Numerical results for two-dimensional laminar duct flow over a backward-facing step are shown, and compared with existing results to assess the reliability of the present schemes.

Application of an implicit time-marching scheme to a three-dimensional incompressible flow problem in curvilinear coordinate systems☆

Abstract An implicit finite-difference scheme based on the SMAC method for solving steady three-dimensional incompressible viscous flows is proposed. The three-dimensional incompressible Navier-Stokes equations in general curvilinear coordinates, in which the contravariant velocities and the pressure are used as the unknown variables, have been derived by the authors. The momentum equations for the contravariant velocity components and the elliptic equation for the pressure are solved directly in the transformed space by applying the delta-form approximate-factorization scheme and the Tschebyscheff SLOR method, respectively. The present implicit scheme is stable under correctly imposed boundary conditions, since the spurious error and the numerical instabilities can be suppressed by satisfying the continuity condition identically, and by employing the staggered grid and the TVD upwind scheme. Some numerical results for three-dimensional flow over a backward-facing step are shown to demonstrate the reliability of the present scheme and to clarify the three-dimensional effects of such complex flows.

Influence of Thermodynamic Effect on Synchronous Rotating Cavitation

Synchronous rotating cavitation is known as one type of cavitation instability, which causes synchronous shaft vibration or head loss. On the other hand, cavitation in cryogenic fluids has a thermodynamic effect on cavitating inducers because of thermal imbalance around the cavity. it improves cavitation performances due to delay of cavity growth. However, relationships between the thermodynamic effect and cavitation instabilities are still unknown. To investigate the influence of the thermodynamic effect on synchronous rotating cavitation, we conducted experiments in which liquid nitrogen was set at different temperatures (74 K, 78 K, and 83 K). We clarified the thermodynamic effect on synchronous rotating cavitation in terms of cavity length, fluid force, and liquid temperature. Synchronous rotating cavitation occurs at the critical cavity length of Lc/h ≅ 0.8, and the onset cavitation number shifts to a lower level due to the lag of cavity growth by the thermodynamic effect, which appears significantly with rising liquid temperature. Furthermore, we confirmed that the fluid force acting on the inducer notably increases under conditions of synchronous rotating cavitation.

Thermodynamic Effect on Subsynchronous Rotating Cavitation and Surge Mode Oscillation in a Space Inducer

The relationship between the thermodynamic effect and subsynchronous rotating cavitation was investigated with a focus on cavity fluctuations. Experiments on a three-bladed inducer were conducted with liquid nitrogen at different temperatures (74, 78, and 83 K) to confirm the dependence of the thermodynamic effects. Subsynchronous rotating cavitation appeared at lower cavitation numbers in liquid nitrogen at 74 K, the same as in cold water. In contrast, in liquid nitrogen at 83 K the occurrence of subsynchronous rotating cavitation was suppressed because of the increase of the thermodynamic effect due to the rising temperature. Furthermore, unevenness of cavity length under synchronous rotating cavitation at 83 K was also decreased by the thermodynamic effect. However, surge mode oscillation occurred simultaneously under this weakened synchronous rotating cavitation. Cavity lengths on the blades oscillated with the same phase and maintained the uneven cavity pattern. It was inferred that the thermodynamic effect weakened peripheral cavitation instability, i.e., synchronous rotating cavitation, and thus axial cavitation instability, i.e., surge mode oscillation, was easily induced due to the synchronization of the cavity fluctuation with an acoustic resonance in the present experimental inlet-pipe system.

Numerical Prediction Method of Cavitation Erosion

Bubble behavior in cavitating flow is analyzed for the development of practical erosion prediction method. CFD analysis with cavitation model is carried out for the flow field around a hydrofoil. Afterwards computation of bubble dynamics is carried out coupled with flow field CFD results by one way approach. For the bubble dynamic calculation, Rayleigh-Plesset equation is adopted. Bubble behaviors in the collapse of cloud cavitaion and in the break off of sheet cavity are analyzed. Bubble behavior at the trailing edge of sheet cavity is also calculated. It is observed that steep pressure change in the flow causes oscillation of the bubbles. Based on this qualitative information of bubble behaviors, numerical cavitation aggressiveness is simply defined. This numerical cavitation aggressiveness is a function of local void fraction and pressure over the solid surface and can be calculated directly from the cavitating flow field CFD results without concerning bubble dynamics.Copyright

Simulation of Flow Through Francis Turbine by Les Method

The traditional approach of Francis turbine design which is based on the steady potential flow theory and heavily dependent on model testing and engineering experience, has come a long way in producing efficient and relatively cavitation free turbines. But further improvement of performance for design and off design operating conditions will be extremely difficult with the traditional method because it will depend more on those phenomena such as, boundary layer separation, vortex dynamics, interactions between different components, vibrations, etc., which are not predictable with conventional approach and difficult to measure in physical models.