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Hydraulic turbines have been elements of utmost importance to meet the energy needs of communities worldwide. These are used with elements that improve the flow behavior of water to the turbine so that its energy benefits are improved. Spiral chambers are circular elements where their cross-section is constantly changing and are used in reaction turbines, such as Francis turbines. Their main function is to distribute evenly the fluid into the impeller inlet. This paper sought to use engineering simulation tools (ANSYS - CFX) to compare behavior and performance from a discreet continuous spiral chamber in a virtual environment under the same physical operating conditions, providing a comparative view of the performance present between the two manufacturing methods of spiral chambers.

Las turbinas hidráulicas han sido un elemento de alta importancia para suplir las necesidades energéticas de las comunidades a nivel global, éstas son empleadas en conjunto con elementos que mejoren el comportamiento del flujo de agua hacia la turbina de tal manera que se mejoren las prestaciones energéticas de la misma. Las cámaras en espiral son elementos circulares dónde su sección transversal varía constantemente y son empleadas en turbinas de reacción, como las turbinas Francis, su función principal es distribuir uniformemente el fluido en la entrada del rodete, éste trabajo busca emplear herramientas ingenieriles de simulación (Ansys - CFX) para generar una comparativa del comportamiento y prestaciones entre una cámara en espiral discreta y una continua, en un entorno virtual bajo las mismas condiciones físicas y de operación, aportando una vista comparativa al rendimiento que se puede presentar entre los dos métodos de fabricación de las cámaras en espiral.

One way of producing electricity is through hydroelectric plants, which use the interaction of a mobile vane with a fluid in motion and, consequently, changes the amount of movement between the vane and the stream generate forces that work through the vane's displacement ^{[}^{1}^{]}. Said hydraulic turbines are classified with respect to their operating characteristics and geometry, as shown in

According to the flow conditions (Q) and pressure head (H), it is possible to select the type of turbine to implement, through any of the existing selection abacuses ^{[}^{2}^{]}, ^{[}^{3}^{]}.

Francis-type turbines are comprised of a runner, draft tube, stay vanes, wicket gate, and the spiral chamber (casing) ^{[}^{4}^{]}.

Spiral chambers are vitally important constitutive elements in the structure of hydraulic reaction turbines (Francis, Kaplan, propeller, and Deriaz) and are in charge of distributing water throughout the runner's periphery of said turbines ^{[}^{5}^{]}. In turn, these are in charge of changing the linear flow reaching the chamber inlet into radial and tangential flow, which will be delivered to the chamber outlet to be used by the turbine's vanes. During the interaction process between the fluid and the turbine, an exchange exists of the linear and angular moment of the axis moment and rotational speed pair in the turbine shaft, where the product between these last two amounts is the shaft power.

In spite of their proven importance in the generation of electric power, their design and construction is still precarious. Their design is achieved through trial and error in empirical practice, which implies high costs and in most cases inefficient designs. However, other methods have been applied for their design, for example, an analysis has been performed of the spiral chambers, starting with the potential flow theory, which is a valid approach in this case due to the irrotationality of the flow, as shown in the lines of current or streamlines obtained numerically by several studies ^{[}^{4}^{]}, ^{[}^{6}^{]}-^{[}^{8}^{]}. In their design, least squares regressions have also been used ^{[}^{3}^{]}, ^{[}^{5}^{]}. Additionally, the experimental analysis of the spiral chambers is normally conducted indirectly, given that what is analyzed is the turbine's global behavior ^{[}^{9}^{]}.

This work sought to compare two geometries of spiral chambers, one continuous and the other sectioned, and evaluate the velocities obtained for each at the outlet.

This project was structured into three stages. Initially, a design was made of the computational model of the spiral chamber, then, the system was simulated in Ansys® CFX; finally, the results are analyzed and discussed.

The computational model for each of the chambers was carried out under different CAD environments; the following provide details of each of the processes:

The computational model for the spiral-sectioned chamber was elaborated in the Siemens NX® 10.0 program, starting from a series of descriptive plans of real spiral chamber, measurements from which the chamber thickness was subtracted to achieve a representative volume of the water flow within the chamber. The spiral chamber's principal measurements are outlet diameter of 2.0 m and central diameter of 2.322 m.

Upon taking the measurements and making calculations through least squares regressions - as already done in methods, like that exposed by Professor Stefan Zarea ^{[}^{3}^{]}, ^{[}^{5}^{]}, a two-dimensional sketch was made of the chamber's internal volume (

The final design step extracted the inlet section (

A computational code developed in Mat lab® was applied for the continuous-spiral chamber, which travels radially the geometry and generates curves of different cross-sections. It is only necessary to indicate the inlet radius and the internal radius of the spiral chamber, these values were the same used to design the sectioned-spiral chamber. Upon ending the process, this program generates a file with the .IBL extension ready to be imported to a CAD program, said computational code is based on the equiangular spiral where programming of said codes helps to reduce design time and improve its precision ^{[}^{10}^{]}, ^{[}^{11}^{]}.

The curves were imported to the PTC Creo® 3.0 program (

This part of the work has two stages: discretization of the geometry and dynamic fluid analysis. In the first stage, the geometries are discretized in such a manner that a mesh is generated composed of a series of mathematical equations that permit the analysis module to recognize the geometry and the zones of interest. The second stage conducts a dynamic fluid analysis, which defines the physical conditions of standard behavior for both models.

The finite volume method (FVM) involves a spatial discretization of the domain using a mesh. The mesh is used as constructor of finite volumes in which the equations are applied ^{[}^{13}^{]}. In this case, the Ansys® 15.0 software meshing module is used to implement the FVM. This module generates a discretization of total volumes into smaller volumes, which permit evaluating the Navier-Stokes equations on fluid dynamics. The use of advanced meshing methods permits said discretization to comply with the parameters that facilitate the simulation convergence; said parameters include obliquity, whose values range between zero and one, which seek for the maximum value to be as far as possible from the upper limit. The maximum value of the aspect ratio is recommended to be <30; the maximum value for the orthogonal quality is required as close as possible to one.

Both geometries were imported to the Ansys® 16.02 geometry model to be recognized by the program; then, they were taken to the meshing module, where discretization of both models is performed, obtining as a result the discretized models with elements of tetrahedral volume. Thereafter, the same parameters were defined for both meshes, which are relevance of 100; face sizing was applied on the chamber inlet and ring outlet, identified as the purple zones in

B2. Computational Fluid Dynamics

During the 1970s, Computational Fluid Dynamics (CFD) was used as an acronym to express the combination of physics, numerical mathematics, and computational sciences to use computational tools from fluids simulation.

^{[}^{14}^{]}. By applying this technique, the hydrodynamic analysis is conducted of both spiral chambers in the CFX module of the Ansys® 16.02 software; wherein, the boundaries of the flow volumes are defined within the chambers. The conditions for both included domain of the environment (water) corresponding to the fluid within the chamber, with properties given by -4una reference pressure of 1 atm, given that for this case such is considered incompressible. Boundary conditions defined a normal velocity of 2 ms-1 and static pressure of 0 Pa at the ring outlet; the turbulence model selected was k-omega, based on prior studies on the theme by ^{[}^{15}^{]}. A model was established in stationary state with a limit of 1000 iterations to carry residues up to 10-4, to guarantee that calculation errors have the least possible significance. To guarantee equanimity in the results obtained, both simulations were developed in the same computer equipment, which has two Intel® Core i7-4770 processors with eight physical nuclei at 3.40 GHz, 12 Gb RAM memory, and a graphic processing unit (Nvidia® G-Force GT 460).

To observe the results graphically in the post-processing of the simulations, the study used the methodology developed by ^{[}^{15}^{]}, where a cylindrical revolution surface is generated that coincides with the turbine's outlet region. A set of plotted points is created of 360 angular positions and 21 axial positions (7560 in total). From each of these points the speed vector is obtained and its components on the X, Y, and Z axes. This information on the vector field flow at the turbine outlet is transferred to a database to process on MATLAB®. This graphic, in cylinder form, corresponds to the perimeter surface of a cylinder with a normal vector (radial) of velocity ar, where through a computational code this cylinder is cut forming a film (tape) on a 2D plane. The velocity film was analyzed at 50%, 75%, and 100% of its central area, given that it there where it had the highest flow density and, hence, its analysis is more representative ^{[}^{16}^{]}. Supervised techniques searches adjustment to input data and in the specific case of neural networks this technique had the best performance allowing to verify that variables chosen were appropriate. In addition, identifying the viability of these variables allowed to develop an additional model of particle swarm, whose comparison will be included in a future work.

Upon implementing the methodology described to obtain the absolute, tangential, and normal velocity profiles of the flow on the outlet of the spiral chambers, the following results were obtained: analysis of 100% of the area of the output absolute velocity profile (

To analyze the results, the average, maximum, and minimum mass flow velocities were taken as principal parameters at the outlet of the chambers, in normal manner and on the X, Y, and Z axes to provide validity to the comparison. The results obtained were compared quantitatively amongst them and, likewise, a qualitative comparison was performed of the velocity profiles obtained (

Normal velocity values (

This study permitted identifying higher velocities in the outlet region of the spiral chamber if it is compared to the input region, as in other studies ^{[}^{4}^{]}, ^{[}^{12}^{]}. Velocity contours at the outlet of the spiral chamber similar to those obtained by Zhu, which reach higher absolute velocities in the middle region of the chamber's radial outlet surface ^{[}^{8}^{]}.

This work provides a comparative view of the performance between both manufacturing methods of spiral chambers, by availing of existing computational simulation tools.

An experimental phase is required with scale models to assess geometry against geometry, the effects generated on the fluid's behavior.

Further research is needed on the theme, as well as evaluation of new conditions closer to the real world, which generate more significant differences in the velocities obtained, or that on the contrary reaffirm the results obtained in this research.

Although a difference exists when comparing the speeds between the spiral-sectioned chamber (higher speeds) and continuous chamber (lower speeds), the differences in the values obtained are not significant to give a final verdict, so that it is not feasible to determine a more optimal geometry for its application.

Sanchez, C, Graciano, J., Velez, S., Zuluaga, D.,