This article is intended to help you build your own cross-flow turbine, also known as a Mitchell-Banki turbine. Mitchell is the original inventor of the turbine around Banki took up this design and explained its theory of operation in The results of the experiments were produced in this document titled the Banki Water Turbine by C. The low efficiency that Mockmore and Merryfield achieved may be due in part to the nozzle design; the Banki nozzle was close coupled to the turbine such that the nozzle outlet pressure may have been higher than atmospheric, as compared to the Mockmore and Merryfield design that came in at atmospheric pressure. Their nozzle is also close-coupled and the water enters many turbine blades perhaps being responsible for the higher efficiency.

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The paper refers to the numerical analysis of the internal flow in a hydraulic cross-flow turbine type Banki. The simulation includes nozzle, runner, shaft, and casing. The objectives of this study were to analyze the velocity and pressure fields of the cross-flow within the runner and to characterize its performance for different runner speeds. Absolute flow velocity angles are obtained at runner entrance for simulations with and without the runner. Flow recirculation in the runner interblade passages and shocks of the internal cross-flow cause considerable hydraulic losses by which the efficiency of the turbine decreases significantly.

The CFD simulations results were compared with experimental data and were consistent with global performance parameters. The utilization of these turbines in large-scale power plants has been limited due to its low efficiency compared to other turbines used commercially. In order to make them more competitive, it is imperative that their efficiency be improved. This can only be achieved by means of studying the turbine operation and determining the parameters and phenomena that affect their performance.

Nowadays, numerical tools are regarded as an industry standard for this process. The improvements in CFD tools have allowed the modeling and obtaining of numerical accuracy of flow fields in turbomachines than previously attained.

Turbomachinery designers regularly use numerical methods for predicting performance of hydraulic reaction pumps [ 1 ] and turbines [ 2 ]. However, numerical methods for predicting the action turbine performance with free surface flow conditions have slowly emerged due to the complex nature of this physic phenomenon.

One-dimensional 1D and quasi-three-dimensional Q-3D approaches for turbomachinery design and analysis can be considered well adapted and powerful enough for most applications. Researchers such as Mockmore and Merryfield [ 3 ] have used 1D theoretical analysis methods and experiments to improve the cross-flow turbines performance.

However, for designing a high-performance Banki turbine, it is necessary to determine accurately the internal flow in the static passages and the cross-flow within the runner [ 4 ]. In the literature, CFD simulation results with regard to nozzle flow are consistent with experimental results. The numerical results are consistent with the experimental data collected when the runner was not present. This approach has also been used by Marchegiani and Montiveros [ 6 ], where the effect of the turbine injector geometry is studied.

In another approach by Arzola et al. With this approach, certain differences were found between water and water-air CFD results with regard to the flow velocity angles towards the 1st stage of the runner. Global performance parameters were presented for different operating conditions. Fukutomi et al. On the other hand, Choi et al. With this approach, the authors studied the influence of nozzle shape, runner blade angle, and runner blade number on the turbine performance.

Moreover, the important role of the air layer on the numerical calculation was verified. The purpose of the present study is to perform a 3D-CFD steady state flow simulation of a hydraulic cross-flow turbine type Banki including nozzle, runner, shaft, and casing in order to analyze and understand the fluid dynamic behavior of the multiphase flow within the runner.

The study is focused on achieving a better use of small hydraulic resources with future cross-flow turbine designs. An extensive bibliographical review on the development of the cross-flow turbines can be found in the works of Khosrowpanah et al. The works included details concerning the influence of the number of blades, outside diameter of the runner and admission arc of the nozzle on the turbine efficiency.

Fiuzat and Akerkar [ 13 ] led a study to improve the cross-flow turbine efficiency by means of using a guide tube inside the runner to collect and guide the flow that crosses the interior towards the 2nd stage of the runner. In their study, these authors conclude that the low efficiency of the turbine is attributed to a certain portion of the flow that crosses the runner blade being lost in the 2nd stage leaving it without transferring energy; this flow only generates power in the 1st stage.

A scheme of this flow distribution is shown in Figure 1. Furthermore, Fiuzat and Akerkar [ 14 ] carried out another study with the intention of identifying the contribution of each one of the cross-flow turbine stages to the power output generation.

The authors conclude, after this study, that the 2nd stage plays a significant role in the total efficiency of the cross-flow turbine, which could be increased if the research carried out by Nakase et al. They established that the flow in a Banki turbine is divided in two types of flow, as can be observed in Figure 1.

This would not improve the efficiency of the 1st stage, but it would increase the cross-flow towards the 2nd stage. The hydraulic efficiency of the 1st stage is greater because the angle of incidence of the fluid can be calculated and controlled with an appropriate nozzle design.

In the 2nd stage the efficiency falls due to the hydraulic losses that take place inside the runner. The flow angles at the inlet of this 2nd stage cannot be controlled. Figure 2 shows for different streamlines, the velocity triangles when the flow is coming out of the 1st stage of the runner blade.

The effective turbine head is given by the application of the Euler equation, which expresses that the energy acquired from the fluid that flows through the runner is a function of the angular moment variation. In the cross-flow turbine case, the Euler equation can be expressed as follows:. The Euler equation considers the variation of the velocity triangles from runner inlet to outlet of the 1st stage and then from runner inlet to outlet of the 2nd stage.

The relevant velocity triangles within the runner are schematized in Figure 3. According to the figure, for design conditions , and. The global efficiency of the turbine is given by 2. Furthermore, for this study it is important to mention the hydraulic efficiency, which considers the losses due to hydraulic effects. The hydraulic efficiency can be expressed as. A hydraulic cross-flow turbine with a specific speed of 63 metric units is used as the test object.

This facility was designed to characterize the performance of the turbine [ 18 ]. Through the tests were obtained the global performance parameters of the turbine for different runner speeds, at each flow rate and head tested.

With the processing of all this data, the hill diagram of the turbine was constructed. Other relevant parameters are presented in Table 1. Due to the great computational costs and time that the study of this complex flow through the turbine entails, all the simulations were carried out at the design conditions varying the runner speed. This near-wall treatment can be applied on arbitrarily fine grids and allows the user to perform a consistent grid refinement independent of the Reynolds number of the application.

More details can be found in [ 19 ]. Given that the flow considered in this study is a two-phase flow water-air , where the fluids are separated by a distinct interface, the standard homogeneous free surface model is used. Thus, both fluids share the same velocity, pressure, and turbulence fields.

It was not possible to apply the buoyancy model, since the software does not allow it when there is a numeric domain in rotation, such as the runner. More details of the numerical modeling can be found in [ 20 , 21 ]. In areas where the gradients change sharply, a first-order upwind scheme is used to maintain robustness. The boundary conditions are as follows: i inlet : velocity normal to face, and , ii outlet : static pressure, type opening, and , iii periodic : two symmetry surfaces positioned in the middle of the blade passages, iv wall : general boundary condition by default no-slip.

This means that the frame of reference is changed, but the relative orientation among the components across the interface is fixed. This analysis is useful when the circumferential variation of the flow is large. More details are in [ 22 ]. For the runner, a structured grid was created using the Turbogrid v. For the rest of fluid domains, unstructured tetrahedral grids with inflated layers at the walls were created. As in any CFD simulation, a sensibility analysis was performed to guarantee that results are not dependent on grid size.

Figure 4 shows how the calculated pressure drop reaches an asymptotic value as the number of elements increases. According to this figure, the grids highlighted are considered to be sufficiently reliable to ensure mesh independence.

The total number of elements inside domain I was 1,, and for domain II was 1,, Table 2 presents the detailed number of elements in each domain.

The closest nodes to the solid walls are located at a distance of between 0. The radial unit vector shown on the figure is considered positive regarding the radial velocities further addressed in this study. For the validation of this numerical investigation, the conducted CFD computations are compared to global performance parameters.

The parameters considered are global and hydraulic efficiency. The experimental efficiency is calculated according to 2 and the numerical efficiency according to 3 , which means that the volumetric and mechanical efficiencies are not numerically estimated.

In this first part of the results section two main issues are addressed for the design test conditions : firstly, the analysis and discussion of the multiphase flow field with respect to water-air volume fraction and water velocity variations at midspan location. Secondly, the investigation of the absolute flow velocity angles variations that would come to the runner inlet 1st stage. The study is conducted for the assembly nozzle-casing, but focusing on the nozzle outlet. In Figures 7 and 8 , the water volume fraction contour and water velocity vectors at the midspan are, respectively, illustrated for the flow design condition.

A free surface flow with a well-defined interface between the water and air homogenous flows can be observed. The water flow velocity field reaches the maximum velocities at nozzle outlet, where the runner 1st stage inlet would be.

The transfer of energy from pressure into speed is important in any action turbine. However, according to 3 , maintaining a specific flow angle at runner entrance is of equal importance. Water volume fraction variation is also shown. The numerical grid could account, at least partially, for some of the small oscillations seen in angle.

Nevertheless, according to the grid validation in Figure 4 the numerical grid selected not seems to influence the turbine performance noticeably.

Arzola et al. The explanation for this flow behavior is probably the standard supposition of potential flow when the nozzle was designed. In this section, the fluid dynamic behavior of the cross-flow turbine is addressed for the design test conditions.

First, the 1st and 2nd runner stages are quantitative studied for the design runner speed. Next, the assessment of the numerical and experimental calculations by comparing the global performance parameters for different runner speeds is presented. Furthermore, the water volume fraction and water flow velocity contours are addressed for different runner speeds.

Particular attention is paid to the nominal speed. Next, the significant absolute and relative flow velocity angles are investigated for the 1st and 2nd runner stages at design speed. Finally, the absolute flow velocity angles found for domains I and II are compared.

Definition of Runner Stages To estimate the cross-flow turbine hydraulic efficiency through the CFD simulations on Domain II, it is important to establish clearly the angular limits at each stage of energy transfer.

FM 3-100.4 PDF

## Cross-flow turbine

The paper refers to the numerical analysis of the internal flow in a hydraulic cross-flow turbine type Banki. The simulation includes nozzle, runner, shaft, and casing. The objectives of this study were to analyze the velocity and pressure fields of the cross-flow within the runner and to characterize its performance for different runner speeds. Absolute flow velocity angles are obtained at runner entrance for simulations with and without the runner.

FUKUOKA STEVEN HOLL PDF

## Numerical Investigation of the Internal Flow in a Banki Turbine

Michell obtained patents for his turbine design in , and the manufacturing company Weymouth made it for many years. Today, the company founded by Ossberger is the leading manufacturer of this type of turbine. Unlike most water turbines , which have axial or radial flows, in a cross-flow turbine the water passes through the turbine transversely, or across the turbine blades. As with a water wheel , the water is admitted at the turbine's edge. After passing to the inside of the runner, it leaves on the opposite side, going outward.

CITRUS LIMONUN RISSO PDF

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