numerical and experimental study of the leakage flow in guide vanes with different hydrofoils

Accepted Manuscript Numerical and experimental study of the leakage flow in guide vanes with different hydrofoils Sailesh Chitrakar, Biraj Singh Thapa, Ole Gunnar Dahlhaug, Hari Prasad Neopane PII: DOI: Reference: S2288-4300(16)30139-7 http://dx.doi.org/10.1016/j.jcde.2017.02.004 JCDE 85 To appear in: Journal of Computational Design and Engineering Received Date: Revised Date: Accepted Date: 18 November 2016 20 February 2017 20 February 2017 Please cite this article as: S Chitrakar, B.S Thapa, O.G Dahlhaug, H.P Neopane, Numerical and experimental study of the leakage flow in guide vanes with different hydrofoils, Journal of Computational Design and Engineering (2017), doi: http://dx.doi.org/10.1016/j.jcde.2017.02.004 This is a PDF file of an unedited manuscript that has been accepted for publication As a service to our customers we are providing this early version of the manuscript The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain Numerical and experimental study of the leakage flow in guide vanes with different hydrofoils Sailesh Chitrakar e-mail: sailesh.chitrakar@ntnu.no Department of Energy and Process Engineering, Norwegian University of Science and Technology, Norway Biraj Singh Thapa e-mail: biraj.s.thapa@ntnu.no Department of Energy and Process Engineering, Norwegian University of Science and Technology, Norway Ole Gunnar Dahlhaug e-mail: ole.g.dahlhaug@ntnu.no Department of Energy and Process Engineering, Norwegian University of Science and Technology, Norway Hari Prasad Neopane e-mail: hari@ku.edu.np Department of Mechanical Engineering, Kathmandu University, Nepal ABSTRACT Clearance gaps between guide vanes and cover plates of Francis turbines tend to increase in size due to simultaneous effect of secondary flow and erosion in sediment affected hydropower plants The pressure difference between the two sides of the guide vane induces leakage flow through the gap This flow enters into the suction side with high acceleration, disturbing the primary flow and causing more erosion and losses in downstream turbine components A cascade rig containing a single guide vane passage has been built to study the effect of the clearance gap using pressure sensors and PIV (Particle Image Velocimetry) technique This study focuses on developing a numerical model of the test rig, validating the results with experiments and investigating the behavior of leakage flow numerically It was observed from both CFD and experiment that the leakage flow forms a passage vortex, which shifts away from the wall while travelling downstream The streamlines contributing to the formation of this vortex have been discussed Furthermore, the reference guide vane with symmetrical hydrofoil has been compared with four cambered profiles, in terms of the guide vane loading and the consequent effect on the leakage flow A dimensionless term called Leakage Flow Factor (Lff) has been introduced to compare the performances of hydrofoils It is shown that the leakage flow and its effect on increasing losses and erosion can be minimized by changing the pressure distribution over the guide vane Keywords: Leakage flow, guide vane, clearance gap, PIV, CFD, hydrofoil INTRODUCTION The relation between the guide vane wear, leakage flow through clearance gaps and efficiency drop in high head Francis turbines was studied by Brekke [1] in 1980s It was seen that the erosion of the facing plates underneath the edges of guide vanes increased the size of the clearance gaps, adding to Corresponding author: Sailesh Chitrakar, Email: sailesh.chitrakar@ntnu.no, Tel No.: +47-46431989 the losses in the turbine Although this study was focused on power plants of Norway, the consequences was found to be more apparent and vulnerable in the power plants of Himalaya and Andes, which are exposed to hard sand particles in higher concentration [2-4] Figure shows the guide vanes in Nepalese power plants, which are eroded at the span ends These ends are connected to the facing plates leaving a small clearance, which provides possibility to change the opening angle based on operating conditions When the sand particles pass through these gaps with high acceleration, eroded grooves are formed, which eventually increase the gap size The pressure difference between the pressure and the suction side of the guide vane profile drives the flow into the clearance gap and mixes with the main flow in the suction side This flow contains circulations, which travels downstream into the runner, causing more damages and losses The simultaneous nature of the erosion and flow phenomena in Francis turbines and the role of guide vane in this process have been explained by Thapa [5] and Chitrakar [6] In Kaligandaki-A hydropower plant running with the net head and flow of 115m and 47 m/s3 respectively, Koirala et al [7] reported that the size of the clearance gap increased from the designed value of 0.6 mm to 2.5 mm in the leading edge and 4.2 mm in the trailing edge in average after 16500 operational hours due to erosion The practices of using numerical techniques (CFD) for predicting the flow fields and erosion in turbines can be found in literatures [2] [8] These techniques are also used to optimize the design of the turbine components and investigate the performances of several designs with minimum cost [9] [10] However, fidelity of the numerical results depend on the validation with the results from experiments In general, the prototype turbine is usually scaled down and/or simplified to minimize the cost and effort involved in experiments In recent studies, the prediction of flow phenomena in Francis turbines using Laser Doppler Anemometry (LDA) and Particle Image Velocimetry (PIV) are becoming popular An LDA measurement was conducted in a guide vane case rig to study the formation of wakes for different guide vane profiles [11] The wake flow and Rotor-Stator-Interaction (RSI) phenomena were studied through experimental TRPIV (Transient Particle Image Velocimetry) from a hydrofoil in a stream of m/s, using different angles of attack [12] A PIV experiment was performed in a complete Francis hydro-turbine model of diameter 0.15 m by using transparent vanes and covers and drilling a hole on the casing at the measurement location for capturing the flow [13] The leakage flow through clearance gaps and consequent vortices are studied in many turbomachinery applications The effect of reduced tip clearance was studied using 3D Navier-Stokes CFD code in a linear turbine cascade [14] The study focused on types of streamlines at different planes and vortices formed from the gap region for each line A Stereo Particle Image Velocimetry (SPIV) was used to study the tip leakage vortex (TLV) in a NACA0009 hydrofoil in a simplified case study [15] This study also used high-speed flow visualization and showed a strong influence of the wall proximity on the vortex path The authors explained that the shifting of TLV away from the hydrofoil as the result of potential flow effect Eide [16] explained by building a 2-D numerical model of guide vanes including clearance gap, that out of 5-6% of the total losses developed in a high head Francis runner, around 1.5% is due to the leakage flow in guide vanes Some qualitative experimental approaches for studying tip leakage vortex through hydrofoils and their effects on cavitation can also be found in literature [17] A single guide vane cascade rig was recently developed in the Waterpower Laboratory at the Norwegian University of Science and Technology [18] [19], which contains a 1:1 scale guide vane of Jhimruk Hydropower Plant, located in Nepal The power plant (3 x 4.2 MW) runs with a net head of 201.5 m, and 2.35 m3/s flow in each of the three units By using PIV, the velocity field around the guide vane can be measured The rig also allows the measurement of the effect of the clearance gap on the main flow by milling one end of the blade The pressure measurements can be carried out along the mid-span surface and another end of the blade The objective of this study is to perform numerical study of the flow inside the same test rig and validate with PIV results The numerical model is used to C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an compare the leakage flow between different hydrofoil shaped guide vanes Following sections contain definition of the quantities, which are used to compare the results between CFD and PIV, and between the hydrofoils studied numerically Measured quantities Figure shows the boundary of the measurement, which contains two guide vane passages (one on each side) The guide vane is oriented in the opening angle corresponding to the design condition The figure also shows the circumferential locations corresponding to stay vane outlet (SVout), guide vane inlet (GVin), guide vane outlet (GVout) and runner inlet (Rin) of the real turbine Although the rig does not include the runner, Rin position is required to investigate how the flow enters the runner The space between guide vane outlet and runner inlet represents vaneless region of the real turbine The secondary flow in the form of wakes and leakages through clearance gaps undergo dissipation in this space before reaching the runner inlet The dissipation of these flows can be visualized in between these two curves The velocities in Cartesian co-ordinate system is converted into the cylindrical co-ordinate system with the equations: Cm  u cos   v sin   (1) Cu  u sin   v cos   (2) The Cartesian velocity components u, v and the angle θ are explained in Figure The terms Cu and Cm are the tangential and meridional components of the velocity, which are analogous to the real turbine The velocities measured by PIV and calculated by CFD are in Cartesian co-ordinates initially, but are converted later to infer the flow condition of the real turbine Cu component is responsible for the work done and power produced by the turbine, whereas Cm component is responsible for directing the flow Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an downstream In the region inside the clearance gap, leakage flow factor has been defined in this study as the sum of the velocity component normal to the guide vane chord from leading edge to trailing edge, compared to a reference velocity In Figure 4, the velocities u and v are converted into Vx’ and Vy’ based on the angles α and β α represents the angle of the chord and β represents the direction of the velocity vector, with respect to horizontal The conversion of the co-ordinate system is based on following equations:  Y Y    tan 1    X  X1  v u (3)   tan 1   (4) Vx  V cos    (5) Vy  V sin    (6) The leakage flow factor, according to the above definition, is measured as: ( X ,Y2 ) L ff   i ( X ,Y1 ) V yi n  Vo (7) Where Vo is the reference velocity, n is the number of the points taken and L ff is the leakage flow factor In this study, the reference velocity is taken as the velocity at stay vane outlet (SVout) In the ideal Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an scenario, the flow is directed along the chord, such that V y’ is zero The pressure difference between the pressure and the suction side of the guide vane results in the velocity component in the direction normal to the chord The absolute value in the numerator takes into account the negative leakage flow and avoids canceling with the positive values Hydrofoils studied This study compares the performance of five different NACA profiles NACA0012 is the reference hydrofoil, which is symmetric along the chord and has the maximum thickness of 12% (of the chord length) at 30% chord Jhimruk hydropower plant currently uses the reference hydrofoil shaped guide vanes and the test rig present in the lab was designed according to this profile NACA1412, NACA2412 and NACA4412 are the cambered hydrofoils with similar configuration as the reference case, but has camber of 1%, 2% and 4% respectively at 40% chord NACA63212 has the maximum thickness of 12% at 35% chord and the maximum camber of 1.1% at 55% chord The test rig is designed for a particular thickness and profile of the guide vane Hence, to avoid the change in flow condition due to change in the passage area, all the studied profiles have the same maximum thickness The experiment was conducted with a maximum Reynold’s number of 1.15E+07, which was at 80% of the Best Efficiency Point (BEP) The comparison of the GVs were done at BEP, with the Reynold’s number of 1.52E+07 All the GVs compared had an equal chord length of 0.14 m Apart from the hydrofoil, the geometry of the test rig and operating conditions were kept constant As the neighboring walls were designed according to NACA0012, it was assumed that the change in the hydrofoil have a negligible influence on the overall flow behavior GV CASCADE RIG AND EXPERIMENT SETUP Figure shows the complete layout of the experimental setup, including the measuring devices The Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an flow was circulated inside a closed loop that contains the section of one GV cascade rig The maximum flow of 0.155 m3/s was developed in this study by a centrifugal pump The maximum pressure of 750 kPa was developed inside the pressure tank The outlet of the test rig contains a flowmeter and two pressure taps were fixed at inlet of the rig and outlet of the GV, to measure the correct operating point for measurement The flow was sent back to the pump, from where the loop continued The detail design of the rig is explained in a previous study [18] The actual PIV measurement was done inside the PIV room, indicated in Figure and shown in Figure using Dantec System A light plane was generated from two double cavity Nd-YAG lasers, which provides 120 mJ by pulse This plane was visualized as paired images by a HiSense 2M CCD PIV camera Fluorescent seeding particles with a density of 1.016 kg/m3 and mean diameter of 55µm were used These particles were inserted into the rig from the low pressure seeding point, as indicated in the figure The paired image was acquired at 70 µs, such that the particle movement was between 3-6 pixels depending upon the high and low velocity regions in the frame The PIV system was calibrated using a 2D calibration target in the planes of measurement The GV inside the rig contains a clearance gap of 2mm height at one end The captured field was two dimensional, but by measuring the velocities at several spans of the GV, the velocity profiles in the direction of the GV span could be inferred A single plane of measurement contained the boundary, as shown in Figure This study captured and measured the velocity field for two planes, one at the midspan and one at the clearance gap for validating the results of CFD The pressure distribution around the GV was measured to characterize the effect of GV loading on leakage flow 14 pressure taps were attached to the facing plate at the end opposite to the clearance gap These taps were distributed symmetrically around the GV profile with 2mm offset, one each at leading and trailing edge, and six each at pressure and suction side respectively Each pressure tap was Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an connected to a piezo-resistive pressure transducer, calibrated using deadweight calibrator NUMERICAL MODEL This study uses a 3D- Reynold’s Averaged Navier Stokes to solve the governing equations for an incompressible and isothermal flow The commercial CFD solver ANSYS-CFX-15.0 was used for numerical simulations in steady conditions The simulations used high-resolution discretization in advection scheme and first order upwind scheme in turbulence equations The convergence criteria of Root Mean Square (RMS) residuals less than 10-5 was used Some backgrounds of the governing equations, turbulence models and other parameters of the numerical model are explained below Governing equations and turbulence models The governing equations (equation of continuity and momentum) for an incompressible and isothermal fluid are written in the form of Navier-Stokes equations given as:      V  ρ  VV   ρg  p  μ 2V  t    (8) Where, 2  2 2 2   x y z (9)  This equation has four unknowns: velocity components in all directions, V and pressure, p Although there are four equations to solve four unknowns, they are highly non-linear Partial Derivative Equation (PDE), which generally requires computational approaches to solve This study follows Reynolds average method, where a variable, for example, u i is divided into an average component, u i and a fluctuating term, ui The substitution of these new terms in the original transport equation gives: Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an ui 0 xi (10) And, ui u p  uj i    t x j  xi x j  ui    uiu  j   x  j   (11) Where, u i = time-averaged velocity components, p = time-averaged pressure, ρ = fluid density,  = fluid kinematic viscosity, ui = fluctuating velocity components, t = time The Reynold’s averaging does not change the continuity equation, but this will result in an additional stress term acting on the mean flow due to the fluctuating velocity, which are called Reynold’s stress  ij  uiu j These terms arise from the non-linear convective term in the un-averaged equations and represents the effect of the turbulence on the mean flow Consequently, the governing equation contains unknowns, which are solved using different turbulence models The RANS turbulence models can be divided into eddy-viscosity models and Reynolds stress models The eddy viscosity model assumes that the Reynolds stress is related to the mean velocity gradients and eddy (turbulent) viscosity by the gradient diffusion (Boussinesq) hypothesis, such that:  u i  ij  u iu j   t   x j k  u j      k   t u k xi   x k   ij  (12) uiu j  = turbulent kinetic energy,  ij = Kronecker delta,  t = Turbulent or eddy viscosity In two-equation eddy-viscosity turbulence models, the velocity and turbulent length scale are solved using two separate transport equations, one for kinetic energy, k and one for turbulent dissipation rate, ε, or the specific dissipation rate, ω In k-ε model, the turbulence viscosity, t , is related to the turbulence kinetic energy, k and the dissipation rate, ε by the relation: Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an Fig 12 Velocity contour in the clearance gap from CFD (left) and PIV (right) Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an Fig 13 Vortex filament in CFD and experiment Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an Fig 14 Velocity profile at GV outlet and runner inlet in mid-span Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an Fig 15 Velocity contour in the clearance gap Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an Fig 16 Pressure difference around GV surface for hydro profiles Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an Fig 17 Velocity Vy along the chord length Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an Fig 18 Streamlines through the clearance gap Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an Fig 19 Erosion of runner inlet at connecting ends due to the vortex filament carrying sediment [2] [25] Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an Fig 20 Cu distribution at Rin for all GV Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an Fig 21 Velocity and pressure distribution around GV Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an Fig 22 Total Pressure contours for GV profiles away from GV TE on planes normal to the chord length Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an Table Discretization errors in the numerical solution Parameter r21 r32 Cu1 (m/s) Cu2 (m/s) Cu3 (m/s) Cuext21 (m/s) ea21 eext21 GCI21fine GCI32med GVout 2.03 1.87 20.12 21.41 23.55 18.87 0.0641 0.0660 0.0774 0.1421 Rin 2.03 1.87 33.96 33.85 33.76 34.07 0.0033 0.0032 0.0036 0.0040 Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an Table Leakage flow factor (Lff) for all GV profiles NACA Profiles Lff 0012 0.815 1412 0.788 2412 0.464 4412 0.183 63212 0.577 Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an Numerical and experimental study of the leakage flow in guide vanes with different hydrofoils Sediment erosion problem in Guide Vanes of Francis turbines Mesh developed on GV cascade rig for CFD analysis Experimental layout Comparison between CFD and PIV (Particle Image Velocimetry) Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn Leakage flow through the clearance gap of GVs with different design C.33.44.55.54.78.65.5.43.22.2.4 22.Tai lieu Luan 66.55.77.99 van Luan an.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.C.33.44.55.54.78.655.43.22.2.4.55.22 Do an.Tai lieu Luan van Luan an Do an.Tai lieu Luan van Luan an Do an Stt.010.Mssv.BKD002ac.email.ninhd 77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77.77.99.44.45.67.22.55.77.C.37.99.44.45.67.22.55.77t@edu.gmail.com.vn.bkc19134.hmu.edu.vn.Stt.010.Mssv.BKD002ac.email.ninhddtt@edu.gmail.com.vn.bkc19134.hmu.edu.vn