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# Kaplan Hydro Turbine Evaluation, ANSYS Fluent CFD Simulation Training

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This project is going to study the hydrodynamics of the Kaplan turbine by ANSYS Fluent software.

This product includes Geometry & Mesh file and a comprehensive Training Movie.

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## Introduction

The Kaplan turbine is a propeller-type water turbine that has adjustable blades. Also, the Kaplan turbine is an inward flow reaction turbine, which means that the working fluid changes pressure as it moves through the turbine and gives up its energy. Power is recovered from both the hydrostatic head and from the kinetic energy of the flowing water. The design combines features of radial and axial turbines.

Since water tunnel experiments are expensive in terms of costs and time, another way to study the turbomachinery behavior of the rotors is to use CFD. As we know, CFD resolves the fluid dynamic equations, and it is undoubtedly a practical method. In this regard, many scientists across the world employ CFD to evaluate their experiments.

## Project Description

In this project, we are going to study the hydrodynamics of the Kaplan turbine by ANSYS Fluent software. The geometry included a small size Kaplan turbine with 125 [mm] as a new prototype. Our static domain consists of 8 [m] long rectangle, and our rotary domain is the Kaplan geometry with 16.5 RPM as the angular velocity. For our boundaries, we set a constant mass flow of 1000 kg/s as our inlet, a zero gauge pressure as our outlet, and finally, we have considered all the side walls as symmetry since they are far from the domain of interest. Besides getting to understand the physics involved with this geometry, we have also investigated the performance of the current Kaplan turbine by evaluating the drag force.

## Mathematical Modeling

To study the current water turbine, one must solve the flow equations in the differential form. By assuming an isothermal and incompressible condition for the water around the blades, two forces are known as the Coriolis, and centripetal accelerations are the important source terms that are exerting on the flow elements. These forces are appearing as the rotating zone starts to move in the current simulation. Briefly, the governing mass and momentum equations are as follows:  ## Kaplan Geometry and Mesh

As illustrated below figures, the blue face is the inlet of the domain, while the red face on the other side is the outlet. Also, the turbine walls are gray, and the side symmetry walls are as transparent white faces. For the current problem, a mesh count of 9,861,922 elements was created to represent the geometry. Regarding the quality of the mesh, the maximum skewness of 0.6 with an average of 0.21 is a satisfactory mesh for the current problem. In addition, for an interested reader, we have depicted the quality distribution of mesh. Lastly, we have considered 5 prism layers adjacent to our turbine walls to calculate the boundary layer accurately. Finally, while the original mesh is generated through ANSYS-Meshing software, we have transformed our elements to polyhedral inside ANSYS FLUENT via make polyhedral option.     ### Geometry & Mesh Note

As a final note, a cylindrical zone has been separated from the whole computational geometry due to having a turbomachinery simulation. This grey cylinder is the part of the domain that will be defined with the frame motion rotation and later represented as the rotary geometry.     ## Kaplan CFD Simulation Settings

By importing the mesh into the ANSYS-FLUENT solver, the calculation procedure is started. However, three important issues must be discussed before going through the solution calculations. First, we have selected the kw-SST model for the current calculation since it gives the highest accuracy that eddy viscosity models can provide. Second, we have considered the frame-motion technique to simulate the rotation. Thus, transient data processing would not be needed. Third, we have utilized the PRESTO method to discretize pressure. This discretization technique works well for the cases with big source-terms such as Coriolis and centripetal accelerations. Finally, other details of the solution setup are as follows:

## CFD Simulation

 Solver settings: Type: Pressure-based Velocity formulation: Absolute Time setting: Steady-state Gravity: Off Energy: Off Model: k-w-SST Zone: Static fluid zone: Rectangular Box: default Rotary fluid zone: Cylindrical: Frame-Motion Axis: Y-direction Axis point: (0,0,0) Rotational Speed: 16.5 RPM Boundary conditions: Turbine Walls: No-slip Inlet: mass-flow inlet: 1000 kg/s Outlet: pressure outlet FarWalls: Symmetry Operating Condition: Reference Pressure Point: 101325 Pa Solver Properties: Solution methods: SIMPLE Pressure interpolation scheme: PRESTO Momentum: First -Order Turbulence: First-Order Relaxation: Default Number of Iterations = 1000 Initialization: Standard > from inlet Material used: Fluid: Water – constant properties Density: 998 kg/(m3) Viscosity: 0.001003 (Pa.s) Monitor: Drag Value of Blade wall in Y-direction

Results

After converging our solution to our desired accuracy, we could now go through the post-processing stage. Meanwhile, as an assurance for a valid convergence, we have monitored our drag values per iterations. This study decided that the solution is converged when the drag force value reached a constant rate and our residuals were below 10-4 values.

After that, we have evaluated the y+ values as an initial check on how well the boundary layer was modeled. This issue has the highest degree of importance when we are about to give information on drag, lift, and other forces generated within the viscous sub-layer of our domain. Fortunately, for our current case, the maximum y+ value was calculated to be less than 10, which is located inside the laminar sub-layer. As a result, the solution was found to be accurate from the perspective of near-wall treatment.

Discussions

Afterward, we investigated the results regarding the pressure and the velocity field in different locations of our domain. As depicted in the below figures, the leading edge of the turbine wall corresponding to the lowest pressure is entirely logical since the velocity has the highest value on the tip of the turbine blade. Also, the velocity at the different radial locations of the Kaplan turbine is depicted, which efficiently shows that as we go farther from the turbine axis, the rotational velocity and the influence of our source terms would be increased.

Besides our parameters evaluated on the turbine walls, we need to understand how our Kaplan geometry would affect our domain flow field. Therefore, we have evaluated the velocity and the pressure distribution inside our domain. Depicted in the below pictures, the pressure distribution adjacent to the turbine walls formed two significant sections. The first section corresponds to the high-pressure zone before the flow interacts with the Kaplan turbine. The low-pressure zone, however, is the zone behind the Kaplan geometry.

## Analysis

Interestingly, the same observations were reported for the velocity distribution but with a single significant difference: velocity was at its peak only at the tip of the turbine’s blades. This was later confirmed through the figure that depicted either the velocity or pressure distribution vertical to the turbine’s axis.

Additionally, the flow vectors illustrate the quality of the flow streams resolved in the wake section, which is the core challenge of aerodynamic simulation. Understood from the flow vectors, we have observed the suction mechanism at the lower parts of the turbine, while we have illustrated the blowing mechanism for the upper section. Moreover, we have given the core vortex adjacent to the turbine body to inform us regarding how the flow field would be manipulated close to our rotary walls.

## Results

Finally, we have dived into the force-momentum analysis of the current simulation. Based on the specifications discussed above, we have calculated the drag force to be 0.66097 (N) and the momentum of 0.0527 (N.m), both in the Y-axis. The noted values were valid for a small-sized 125 [mm] prototype with a low angular speed of 16.5 RPM.

You can obtain Geometry & Mesh file and a comprehensive Training Movie that presents how to solve the problem and extract all desired results.

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