# Turbulent Flow Through a 180 Degree Curved Channel

In this application, AcuSolve is used to simulate turbulent flow through a strongly curved two dimensional 180 degree U-duct channel. AcuSolve results are compared with experimental results adapted from Rumsey et al. (2000). The close agreement of AcuSolve results with experimental results validates the ability of AcuSolve to model turbulent cases with strong curvature effects.

## Problem Description

The problem consists of a fluid with properties similar to air flowing through a curved channel, as shown in the following image, which is not drawn to scale. The inlet channel height and remaining duct height is 0.0381 m. The bulk velocity (v) normal to the inlet is 31.1 m/s and an integrated outflow pressure is specified to allow the flow to pass through the channel. The flow develops into fully turbulent flow at a Reynolds's number (Re) of approximately 1,000,000. The density of the flow medium is 1.0 kg/m3 and the dynamic viscosity is 1.1818 X 10-6 kg/m-s. The simulation is conducted with the Reynolds Averaged Navier-Stokes equations using the Spalart Allmaras, Shear Stress Transport (SST), K-ω and Realizable K-ε turbulence models. The velocity field from the simulations is compared against experimental data at select measurement locations.

The simulation was performed as a two dimensional problem by restricting flow in the out-of-plane direction through the use of a mesh that is one element thick. The upper and lower walls are specified as no-slip, the inlet velocity and eddy viscosity are specified normal to the inlet face to match the experimental Reynolds Number.

## AcuSolve Results

The AcuSolve solution converged to a steady state and the results reflect the mean flow conditions. As the flow passes the inner convex wall it begins to accelerate before decelerating directly past the curved section due to the adverse pressure gradient that eventually leads to a local recirculation zone. On the outer concave wall, the flow remains attached, but is influenced by the adverse pressure gradient above the recirculation region.
The experimental value for the ratio of Velocity magnitude (Vm) to inlet bulk velocity (Vb=31.1 m/s) at different sections of the U-duct is presented with the corresponding AcuSolve result for each of the turbulence models tested in the following images. The images show black circles representing the experimental measurements (Rumsey 2000), solid red lines for the SA model, solid blue lines for the SST model, solid green lines for the K-ω model and solid cyan lines for the K-ε model.

## Summary

The AcuSolve solution compares well with experimental results for flow past the 180 degree U-duct. The experimental value for the ratio of Velocity magnitude to inlet bulk velocity at different sections of the U-duct is presented with the corresponding AcuSolve result for various turbulence models. The performance of the Spalart Allmaras turbulence model was found to improve when the rotation curvature correction is included in the numerical formulation. In this application, AcuSolve demonstrates the ability to predict the complex boundary layer separation and reattachment resulting from the curvature of the channel.

## Simulation Settings for Turbulent Flow Through a 180 Degree Curved Channel

AcuConsole database file: <your working directory>\curved_channel_simple_turbulent\curved_channel_simple_turbulent.acs

Global

• Problem Description
• Analysis type - Steady State
• Turbulence equation - Spalart Allmaras
• Auto Solution Strategy
• Relaxation factor - 0.4
• Material Model
• Air
• Type- Constant
• Density- 1.0 kg/m3
• Viscosity- 1.1818e-006 kg/m-sec

Model

• Volumes
• Fluid
• Element Set
• Material model- Air
• Surfaces
• Inlet
• Simple Boundary Condition
• Type- Wall
• Inflow type- Velocity
• Inflow velocity type- Normal
• Normal velocity- 31.1 m/sec
• Turbulence input type- Direct
• Eddy viscosity- 3.5547e-06 m2/sec
• ext1
• Simple Boundary Condition- Symmetry
• ext2
• Simple Boundary Condition- Symmetry
• Outlet
• Simple Boundary Condition
• Type- Outflow
• wall-bottom
• Simple Boundary Condition
• Type- Wall
• Turbulence wall type- Low Reynolds Number
• wall-top
• Simple Boundary Condition
• Type- Wall
• Turbulence wall type- Low Reynolds Number

## References

Christopher L. Rumsey, Thomas B. Gatski, and Joseph H. Morrison. "Turbulence Model Predictions of Strongly Curved Flow in a U-Duct", AIAA Journal, Vol. 38, No. 8 (2000), pp. 1394-1402.