ENME 547 Final Project:

Analysis of Flow through an Obstructed Channel

Jaime Wong

December 10, 2010

Abstract This experiment attempted to verify a model used to simulate a water turbine in an unobstructed channel. A crude orifice was used in the place of a rotating, power-extracting turbine. Using ANSYS CFX, the behavior of the model was compared to the behavior expected of an ideal scaled model. While the ideal model would have a pressure difference between its front and back faces of approximately 1.9 kPa (under certain conditions), the model produced a pressured difference of approximately 1.8 kPa (under the same conditions). Although this is a reassuring result, the lack of a free surface produced anomalous recirculating behavior behind the turbine unlike that which would be expected in real life. Further tests may wish to explore free surface modeling in order to attempt to address this issue.

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Contents 1. Introduction ........................................................................................................................................ 2

2. Methods ............................................................................................................................................... 3

2.1. The Ideal Model........................................................................................................................... 3

2.2. Best Estimate of Proposed Model Dimensions ....................................................................... 4

2.3. The CFD Model ........................................................................................................................... 5

2.4. The CFX Solver ............................................................................................................................ 6

3.0. Results ............................................................................................................................................... 7

3.1. CFD Convergence Verification ................................................................................................. 7

3.2. CFD Model Verification ............................................................................................................. 8

3.3. Model Flaws ................................................................................................................................. 9

4. Discussion and Conclusions ........................................................................................................... 10

4.1. CFD Convergence Verification ............................................................................................... 10

4.2. Model Verification .................................................................................................................... 10

4.3. Model Flaws ............................................................................................................................... 10

Citations ............................................................................................................................................. 11

Figures Figure 1: A Sample of calculations performed in Excel ................................................................... 3Figure 2: Shape of Turbine Model ...................................................................................................... 4Figure 3: Areas of fine and coarse, structured and unstructured meshes. .................................... 5Figure 4: CFX Solver Equations ........................................................................................................... 6Figure 5: Boundary Layer Growth ...................................................................................................... 7Figure 6: Pressure Contour on Refined Mesh ................................................................................... 7Figure 7: Streamlines Colored by Pressure ........................................................................................ 8Figure 8: Pressures on front and rear of turbine ............................................................................... 8Figure 9: A single streamline ............................................................................................................... 9

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1. Introduction The VLH Turbine Group (ENME 538) was tasked with analyzing the effects of various obstructions upstream of a water turbine on the pressure field that the turbine observes. The VLH turbine is a novel design which is intended to be installed in existing hydrological infrastructure such as dams, locks, channels, weirs, and so forth. The project sponsor is currently doing a study on the turbine’s viability in Canada, and their ultimate goal is to obtain an efficiency number for typical Canadian installations. While that is not in the scope of this research, it is hoped that the pressure field eventually obtained will be useful in subsequent research undertaken by the project sponsor. However, before any conclusions can be drawn regarding the effects of these obstructions, first a baseline must be made to which they can be compared. The goal of open channel tests is to first build a set of data with which further results are to be compared; and secondly to verify that the model chosen is a useful and faithful representation of the behavior of a full-size turbine, and that assumptions are reasonable. Due to cost constrictions, and a lack of detailed drawings, it was decided a simplified model was preferable to a spinning, power-extracting turbine. In order to verify results, a requirement was drawn that tests must be run in both a physical water flume, and in CFD, limiting geometric complexity. The model chosen based on these requirements was a simple set of annular orifices that are to restrict flow through a reduction in area. Thus, the most immediate concern which is intended to be addressed herein is to what extent the chosen model replicates true flow patterns.

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2. Methods The goal of these tests is, as outlined in the introduction, was to verify that the model that has been produced can accurately represent the behavior of a real turbine to a reasonable degree, despite not being coupled to nearly the same extent. The steps taken to do so were as follows:

1. Determine analytically properties of an ideal scaled-model 2. Make a best estimate of how the ideal situation may be replicated with the proposed

model 3. Develop a computational model of the proposed model 4. Verify that the CFD computations are producing a reasonable solution of the model it

was given, through mesh refinement and sensitivity analysis, and lastly 5. Compare the results of the chosen model to that of the ideal model.

2.1. The Ideal Model Data was available from our project sponsor on full-scale turbine models (3500, 4000, and 5000 mm turbine diameters), regarding the effects of upstream head pressure and flow rate on downstream head pressure. These numbers were scaled using Froude and Reynolds Number similitude by Alex Yuen, another member of the VLH Project team. The calculations of Mr. Yuen showed the anticipated pressure change between the front and rear faces of the turbine to be 1.88 kPa for 191 mm of head pressure and 15 L/s of flow, shown in figure 1 below.

Figure 1: A Sample of calculations performed in Excel

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2.2. Best Estimate of Proposed Model Dimensions

The proposed model was of a fixed style. The turbine would be modeled as a set of holes between an outer diameter equal to that of a real turbine’s runner diameter, and an inner diameter equal to that of a real turbine’s hub assembly. However, there needed to be a first guess regarding what proportion of that area was to be open for flow versus closed in order to produce the pressure we were hoping to obtain. Such an estimate can be made using discharge coefficients, and our project sponsor, Wes Dick, suggested the use of a coefficient of 0.6 based on his experience. Assuming incompressible flow, it is possible to formulate an area requirement from Bernoulli’s Equation given a discharge coefficient of the form:

𝐴𝐴𝑜𝑜 =𝑄𝑄

𝐶𝐶𝑓𝑓�2∆𝑃𝑃𝜌𝜌

Where A0 is the area of a restriction required to produce a pressure drop of ΔP for a fluid of density ρ given a flow rate Q and discharge coefficient Cf. Given the parameters listen in section 2.1, the resulting area was 0.0129 m2. Thus, the model cross section looked as such:

Figure 2: Shape of Turbine Model

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2.3. The CFD Model The model to be tested in CFD (ANSYS CFX) was produced in a combination of Dassault SolidWorks, ANSYS Design Modeler, and ANSYS Mesher. To cover the steps only very briefly, a positive model was made in SolidWorks of a model of a cross section as shown in figure 2 of 70mm thickness, and placed on a stand angled 60 degrees from horizontal. Design Modeler was then used to convert this into a negative model: in CFD the negative image (the area where fluid will flow) is meshed. After these preliminary steps, the model was meshed in the ANSYS CFX-Mesh program. While most of the model was filled with unstructured, tetrahedral elements, there were several areas of concern which were not given such freedom. Inflated, prismatic elements were placed where boundary layers and interesting behavior was expected to occur. The coarsest of these were along the walls and floor the channel in which testing was to occur. The total thickness of the prismatic elements in these regions was up to 7.5 cm thick. Prismatic elements on the face of the turbine model were up to 1 cm thick, and in the surface of the orifices they were up to 0.5 cm in thickness, as illustrated in figure 3.

Figure 3: Areas of fine and coarse, structured and unstructured meshes.

In the area of greatest interest, the turbine, the mesh can be seen to be very fine. Further, on the front face the regions of structured and unstructured meshes are quite obvious and distinct. In total, there were approximately 1.1 million elements in the model, 350,000 of which prismatic and structured.

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The boundary conditions selected for this test were as follows:

Table 1: Model Boundary Conditions

Top Free-slip wall Walls, Floor No-slip wall

Turbine and stand No-slip wall Inlet 15 kg/s

Outlet 0 kPa relative pressure Furthermore, the working fluid was chosen to be water at 25° C, with a reference pressure of 1 atm.

2.4. The CFX Solver

ANSYS CFX solves the Navier-Stokes equations in their time-variant conservation form [1]. Although there are other equations available, they are largely unused or negligible in this test as they are concerned with head transfer and chemical reactions. These are illustrated in the CFX Solver documentation as follows:

Figure 4: CFX Solver Equations

These equations are discretized and used to form a coupled system of linear equations. These equations are solved using an Incomplete Lower Upper factorization technique. The solution process ends when a user-defined criteria is reached; by default this is a maximum value of residuals [2].

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3.0. Results

3.1. CFD Convergence Verification Discussed later, the following images can be used to verify the CFD model’s convergence.

Figure 5: Boundary Layer Growth

Figure 6: Pressure Contour on Refined Mesh

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3.2. CFD Model Verification

Similarly discussed in further sections, these images can be used to illustrate the model’s ability to replicate a significant quantity of the intended behavior. A significant note: CFX Post automatically subtracts the hydrostatic component of pressures when viewing with a reference pressure of 1 atm.

Figure 7: Streamlines Colored by Pressure

Figure 8: Pressures on front and rear of turbine

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3.3. Model Flaws The model that was developed is not perfect by any stretch. The most prominent example of this is shown below in figure 9.

Figure 9: A single streamline

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4. Discussion and Conclusions

4.1. CFD Convergence Verification The growth of a boundary layer is a very well understood fluid behavior. A simple method to check (but not necessarily verify) that CFD results are reasonable is to observe how boundary layers grow. Figure 5 illustrates this growth. The thin, but growing, dense gradient is a reasonable expectation for the slow (~0.1 m/s), low-Reynolds Number flow seen before the turbine.

Figure 6 is a much more thorough demonstration that results are convergent. It depicts the pressure contour on the symmetry plane of a refined mesh, showing values very similar to those seen in Figure 8 (or a less refined mesh). Due to limitations of student licensing, the 1.1 million elements of the standard mesh was very near the cutoff; as such the model was cut in half and the remaining half-model was meshed using approximately the same number of elements (the equivalent of a 2 million element full model). The similarities in pressure imply that the values obtained are near that of the true values for such conditions. In later tests it is planned to conduct a variable sensitivity study, however this has not been completed in time for this report. However, for the purposes of this report, and given the simplicity of geometry and boundary conditions, it would be reasonable to assume the results are a faithful solution.

4.2. Model Verification As mentioned in section 2.1, the expected pressure drop across the turbine was 1.88 kPa. Figure 7 illustrates the pressure being reduced in the orifice channels themselves, as expected. The pressure across the faces as shown in Figure 8, although varying across the faces (below the resolution of the contour plot) is approximately 1.8 kPa. This is a promising result, very much in line with our expectations.

4.3. Model Flaws Figure 9 is a plot of a single streamline entering the inlet, flowing through the turbine, and exiting only after a entering a large section of circulation. This is not what would be expected for a real turbine. While this is a problem, it does not necessarily show the CFD simulation to be completely faulty. In real life, a pressure drop would be represented by a shorter column of water behind the turbine, but as a simplification the entire area was modeled as a fluid, and no free surface was introduced. This problem may simply be an anomaly of this simplification. While the pressure drop explained in section 4.2 is reassuring, it cannot be held with a significant degree of confidence until further models with free surfaces can show that this recirculation is not significantly altering the flow conditions. Furthermore, it would be preferable to conduct a variable sensitivity study to confirm the stability of such computational results more rigorously.

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Citations

[1] ANSYS CFX-Solver Theory Guide, ANSYS Inc, Canonsburg, PA, 2006, pp. 23-24

[2] ANSYS CFX-Solver Theory Guide, ANSYS Inc, Canonsburg, PA, 2006, pp. 292-297