## Engineering Challenge

This benchmark study looks at turbulence modeling over curved boundaries. The case of liquid flow through a 2-dimensional slot with a hill has been documented by Almeida, Durao, and Heitor [1] with experimental data available via laser-doppler measurements. Particular attention is paid to the recirculating flows that occur in the lee of the hill.

## Azore Solution

Existing experimental data was compared to the Azore simulation results for multiple turbulence models, along with simulation results from a well-know commercial CFD package. Both tools make similar comparisons that represent the general flow structure.

## Introduction

Almeida et al. collected data for water flow in a 2-dimensional slot, 170 mm in height. Within the slot, flow passes over a 28mm high hill. Figure 1 shows the geometry of the model used for this simulation.

*Figure 1. Geometry of the two-dimension slot and hill*

The red lines in Figure 2 denote the locations where velocity traverse data was collected along the slot.

*Figure 2. Experimental data locations*

The basic flow structure of the benchmark case is displayed in Figure 3. A parabolic velocity profile approaches the hill, and the flow accelerates as it passes over the hill feature. In the wake of the hill, there is a low velocity recirculation zone. Further downstream, the fluid begins to reattach to the lower wall.

*Figure 3. Basic flow structure*

#### Model Set-up

Sufficient inlet length in the model was found to be very important in accurately predicting the flow profile of the inlet section. The original benchmark case used a 3m inlet. Increasing the inlet length by an additional 6m led to an improved prediction at the inlet to the hill, located at the first red line. This additional length facilitates full development of the velocity profile of the inlet section, where both the upper and lower boundary layers seem to combine.

The domain inlet was set with a uniform velocity of 1.959748 m/s entering the slot. The fluid properties are assumed to be standard water (ρ=998 kg/m3 and μ=1.0e-3 kg/(m-s) ). A close-up view of the mesh topology is shown in Figure 4. Boundary layer cells with a high aspect ratio (>3) are used along the walls where the flow is primarily 1-dimensional. Around the hill, the boundary layer cells have a lower aspect ratio, since the boundary layer is changing and the flow structure becomes more 2-dimensional. Shorter mesh length scales are chosen in the area downstream of the hill to capture the steep gradients in that area.

*Figure 4. Mesh topology of the computational domain*

#### Model Results

The simulation was performed in both Azore and ANSYS Fluent using both the k-epsilon and k-omega SST turbulence models. The results of the simulation compared to the experimental data are shown in the figures below. The curves indicate the velocity magnitude at each red reference line, and the vertical axis shows the vertical position in the slot.

*Figure 5. Velocity profiles near the hill*

The simulation results show minimal variation between Azore and Fluent, along with minimal variation between the two turbulence models. All of the models show strong agreement with the experimental data.

*Figure 6. Velocity profiles immediately after the hill*

*Figure 7. Recovery Velocity Profiles*

For a deep dive into this benchmark case with Azore’s lead developer, check out the video below. Dr. Jeff Franklin, P.E. walks through the test case along with lessons learned for CFD and turbulence modeling.

[1] G. P. Almeida, D. F. G. Durao, and M. V. Heitor, Wake flows behind two dimensional hills, Exp. Thermal Fluid Science 7 (1992), 87.