The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Turbulence, Coherent Structures, Dynamical Systems and SymmetryP. Holmes, J. L. Lumley, G. Berkooz, and C. W. Rowley, 2nd ed., Cambridge University Press, Cambridge, England, U.K., 2012, 386 pp., $90

Cemented paste backfill for mineral tailings management: Review and future perspectives

This paper mainly summarizes the recent progresses for the cavitation study in the hydraulic machinery including turbo-pumps, hydro turbines, etc.. Especially, the newly developed numerical methods for simulating cavitating turbulent flows and the achievements with regard to the complicated flow features revealed by using advanced optical techniques as well as cavitation simulation are introduced so as to make a better understanding of the cavitating flow mechanism for hydraulic machinery. Since cavitation instabilities are also vital issue and rather harmful for the operation safety of hydro machines, we present the 1-D analysis method, which is identified to be very useful for engineering applications regarding the cavitating flows in inducers, turbine draft tubes, etc. Though both cavitation and hydraulic machinery are extensively discussed in literatures, one should be aware that a few problems still remains and are open for solution, such as the comprehensive understanding of cavitating turbulent flows especially inside hydro turbines, the unneglectable discrepancies between the numerical and experimental data, etc.. To further promote the study of cavitation in hydraulic machinery, some advanced topics such as a Density-Based solver suitable for highly compressible cavitating turbulent flows, a virtual cavitation tunnel, etc. are addressed for the future works.

A review of cavitation in hydraulic machinery

Numerical analysis of unsteady cavitating turbulent flow and shedding horse-shoe vortex structure around a twisted hydrofoil

A robust CFD model is described, suitable for general three-dimensional flows with extensive cavitation at large density ratios. The model utilizes a multiphase approach, based on volume-scalar-equations, a truncated RayleighPlesset equation for bubble dynamics, and specific numerical modifications (in a finite-volume solution approach) to promote robust solutions when cavitation is present. The model is implemented in the CFD software CFX TASCflow 2.12. The validation of the model was done on an inducer designed and tested at LEMFI. First, The physical model and the numerical aspects are described. Then, the experimental and numerical methodologies, at cavitating regime, are presented. Finally, for several flow rates, the comparisons between experimental and simulated results on the overall performances, head drop and cavitation figures, are discussed. For a range of flow rates, good agreement between experiment and prediction was found.

/pdf/numerical-and-experimental-investigations-of-the-cavitating-33zr4dl7to.pdf

Numerical and Experimental Investigations of the Cavitating Behavior of an Inducer

This work aims at studying the influence of adding splitter blades on the performance of a hydraulic centrifugal pump. The studied machine is an ENSIVAL-MORET MP 250.200.400 pump (diameter = 408 mm, 5 blades, specific speed = 32), whose impeller is designed with and without splitter blades. Velocity and pressure fields are computed using unsteady Reynolds-averaged Navier-Stokes (URANS) approach at different flow rates. The sliding mesh method is used to model the rotor zone motion in order to simulate the impeller-volute casing interaction. The flow morphology analysis shows that, when adding splitter blades to the impeller, the impeller periphery velocities and pressures become more homogeneous. An evaluation of the static pressure values all around the impeller is performed and their integration leads to the radial thrust. Global and local experimental validations are carried out at the rotating speed of 
900 rpm, for both the original and the splitter blade impellers. The head is evaluated at various flow rates: 50 % , 80 % , 100 % , and 120 % of the flow rate at the best efficiency point (BEP). The pressure fluctuations are measured at four locations at the BEP using dynamic pressure sensors. The experimental results match the numerical predictions, so that the effect of adding splitter blades on the pump is acknowledged. Adding splitters has a positive effect on the pressure fluctuations which decrease at the canal duct.

/pdf/influence-of-splitter-blades-on-the-flow-field-of-a-38srxq0rkw.pdf

Influence of Splitter Blades on the Flow Field of a Centrifugal Pump:Test-Analysis Comparison

A 3D-CFD simulation of the impeller and volute of a centrifugal pump has been performed using CFX codes. The pump has a specific speed of 32 (metric units) and an outside impeller diameter of 400 mm. First, a 3D flow simulation for the impeller with a structured grid is presented. A sensitivity analysis regarding grid quality and turbulence models were also performed. The final impeller model obtained was used for a 3D quasi-unsteady flow simulation of the impeller-volute stage. A procedure for designing the volute, the nonstructured grid generation in the volute, and the interface flow passage between the impeller and volute are discussed. This flow simulation was carried out for several impeller blades and volute tongue relative positions. As a result, velocity and pressure field were calculated for different flow rates, allowing to obtain the radial thrust on the pump shaft.

/pdf/numerical-modelization-of-the-flow-in-centrifugal-pump-svnfa7wb2u.pdf

Numerical Modelization of the Flow in Centrifugal Pump: Volute Influence in Velocity and Pressure Fields

Predicting tonal noise from a high rotational speed centrifugal fan

The paper presents full 3D numerical simulations and experimental investigations of the cavitating flow through three axial inducers. These inducers are identified by the tip blade angle at the leading edge β 1T =8, 10, and 13 deg. The numerical and experimental investigations were carried out at the LEMFI laboratory (Laboratoire d'Energetique et de Mecanique de Fluides Interne) of the ENSAM-Paris center (Ecole rationale Superieure d'Arts et Metiers). A review of the cavitating regime modeling and the cavitation homogeneous model used for this paper's calculations is first presented. The numerical model is based on a combination of the multiphase flow equations with a truncated version of the Rayleigh-Plesset model predicting the complicated growth and collapse processes of bubbles. The mass transfers due to cavitation are source/sink terms in continuity equations of the liquid and vapor phases

Farid Bakir

Papers

Numerical and Experimental Investigations of the Cavitating Behavior of an Inducer

Influence of Splitter Blades on the Flow Field of a Centrifugal Pump:Test-Analysis Comparison

Numerical Modelization of the Flow in Centrifugal Pump: Volute Influence in Velocity and Pressure Fields

Predicting tonal noise from a high rotational speed centrifugal fan

Comparison of Computational Results Obtained From a Homogeneous Cavitation Model With Experimental Investigations of Three Inducers