A core objective of the undergraduate course Thermo-Fluids Design and Lab in the Department of Mechanical & Aerospace Engineering at the University of Florida (UF) is for students to use a hands-on approach to learn the fundamentals of the fluid mechanics of pumps. In the past, students have used traditional techniques such as Euler’s Turbomachine Equation and velocity triangles to predict pump performance, but these techniques can be inadequate. As a result, UF has begun to explore modern computational fluid dynamics (CFD) to improve these predictions and provide a fundamental understanding of these important concepts.

Under the guidance of UF Senior Lecturer Dr. John Abbitt, students design various centrifugal impeller models using traditional methods first and then run virtual tests of the designs using a proprietary 3-D CFD tool. They modify their designs based on these results, and, once they have a satisfactory design, they use 3-D printing to create hardware that is subsequently tested and compared with the CFD predictions.

## Traditional Techniques

The process begins with the application of Euler’s Turbomachine Equation to determine the blade angles for the impeller. Next, students add the blades to a template of the impeller hub provided by the instructor in a 3-D computer-aided design (CAD) program1 as shown in Figure 1.

The final product will be installed into the existing housing shown in Image 1. At this point in the design process, only classic design guidelines have been applied.

## Designing Using CFD

Once an initial design is created, the students begin the process of numerically analyzing the impeller’s performance. Numerical CFD simulations are used to test different blade shapes by generating curves of the head rise versus the flow rates and comparing the predictions with the desired performance.

Each of the design iterations involves a detailed process. First, the students create a CFD mesh to precisely conform to the geometry provided by the CAD. Then, they implement appropriate boundary and operating conditions. Finally, they select specific numerical parameters to perform virtual tests.

## Fluid Volume Mesh

First, the students create a model of the test rig and hub assembly using a NextEngine 3-D HD scanner and the CAD program. They then add their impeller designs in the CAD program and extract the system’s fluid volume, saving it in stereo lithographical (STL) format. The STL format includes the triangulation of the surfaces of the inlet, outlet, volute and impeller.

This file is imported into the CFD code and used to create the numerical mesh and boundaries needed for the simulation. A typical mesh size for these simulations is about 3 million cells. This process is automated, requiring less than 10 minutes to generate a mesh that captures details down to the order of microns. Students learn guidelines for generating a mesh that will produce accurate results while optimizing the calculation speed.

The students then enter the properties, boundary conditions and operating parameters corresponding to what would be done in a physical test. For the simulations, air is assumed as an ideal gas, and the pressure far from the inlet nozzle is atmospheric, with the exit pressure also atmospheric in accordance with subsonic nozzle flow theory.

Turbulence is modeled using the standard K-epsilon model2. The flow is regulated with 10 different smoothly contoured nozzles with cross-sectional areas corresponding to 5, 10, 15, 20, 25, 30, 40, 50 and 70 percent of the fully open flow at the outlet. The system is tested with the nine nozzles plus a shutoff plate (for no flow). The geometries of the nozzles, inlet, volute and outlet are included as part of the numerical model.

By specifying the geometry, inlet and exit pressures, and rotational speed of the impeller, the CFD code will predict the corresponding flow rate and the head rise.

## Numerical Parameters

In addition to the operating conditions, several numerical parameters—such as higher-order schemes and transient versus steady-state analysis—must be considered.

During the project, the advantage of higher-order numerical schemes in resolving the flow field is discussed and demonstrated. The project stresses and demonstrates the advantage of running full 3-D, transient simulations, which can account for pulsations, by comparing these simulations with the experimental data and the more common but less accurate steady-state analysis.

Once created, the numerical model can run in the same manner as a physical hardware test, generating data for different operating conditions. Specifically, the students can vary the revolutions per minute (rpm) and outlet area to predict the corresponding flow field, flow rates, pressures, torques, powers and loads throughout the blower. The students use the results to test different iterations of their prototype and select the best design.

As an example, the predicted pressure field throughout the test rig is show in Figure 2, and a cross-sectional view of the corresponding flow field in the housing is shown in Figure 3. This simulation took 35 minutes to reach a steady-state solution on a Dell Precision T5810 computer with an Intel Xeon CPU E5-1620 v3@3.5 GHz.

## Printing & Testing

Once a prototype design has been selected based on the CFD results, a Stratasys Dimension 1200es or a Fortus 360mc 3-D printer is used to create a physical impeller made of either acrylonitrile butadiene styrene (ABS) plastic or polycarbonate (see Image 2).

The printed impeller is subsequently mounted to the fan housing and tested in the UF Undergraduate Fan Performance test bed. The volumetric flow rate through the apparatus is computed by measuring the difference in static pressure in the calibrated inlet nozzle and atmospheric pressure, and computing the velocity based on the Bernoulli equation with an appropriate nozzle coefficient.

The students measure and include in the experimental data reduction certain ambient conditions including temperature, atmospheric pressure and relative humidity.

## Experimental Results

Students conduct experiments at two different rpms, 1,500 and 2,500, and obtain head rise for flow rates beginning at shutoff conditions. They then increase the outlet flow area until it is 100 percent open. The results are shown in Figure 4.

This impeller was designed to have a negative slope throughout its operating range. Using just the Euler Turbomachine Equation, a linear slope of -546 meters per cubic meters per second (m/[m3/s]) is predicted at 2,500 rpm, but the experimental curve deviates significantly from that prediction.

The Euler Equation predicts a maximum head of 111 meters at 2,500 rpm at shutoff conditions, while 43 meters was actually obtained. This corresponds to a prediction error of 175 percent. At 1,500 rpm, the Euler Equation predicts a slope of -327 m/(m3/s) and a maximum head of 40 meters at shutoff conditions, while 16 meters at shutoff was obtained in the experiment.

The results of the CFD predictions (transient) are compared with the experimental counterpart in Figure 5. As shown, the CFD results and experimental results are close over a large range of flow rates. At 2,500 rpm, the largest discrepancy is 20 percent at shutoff, but over the remaining flow rates from 0.02 to 0.11 m3/s, this correlation is excellent and within the experimental error (this includes 65 percent of the range of flow rates obtainable in the experimental apparatus). At 1,500 rpm, the difference between the experimental results and the CFD predictions is essentially negligible over the entire flow range.

## Lessons Learned

Prior to the application of CFD, the comparison between predicted performance using traditional methods and actual performance varied by as much as 100 percent. In contrast, the prediction of the actual performance curve using CFD has proven to be accurate over the range of flow rates.

This exercise has demonstrated that CFD can be used to accurately predict the performance of a design without hardware testing. Although the material is new to the students at the beginning of each semester, it is a practical way to introduce traditional theory, numerical simulation, fabrication and testing in one semester.

The partnership between students in the Department of Mechanical & Aerospace Engineering at UF and the CFD/CAD provider has been positive and has resulted in a comprehensive study of the fluid mechanics of turbomachinery. The partnership introduces approximately 400 students a year to modern analytical tools and design techniques for the industry.

**References**

1. solidworks.com

2. Ding, H., Visser, F.C., Jiang, Y. and Furmanczyk, M. 2011 “Demonstration and validation of a 3D CFD simulation tool predicting pump performance and cavitation for industrial applications”, J. Fluids Eng. – Trans ASME, 133(1), 011101