# Turbulent Flow Past a Convex Curve in a Channel

In this application, AcuSolve is used to simulate fully developed turbulent flow through a channel containing a convex curve in the lower wall. AcuSolve results are compared with experimental results as described in Smits (1979) and on the NASA Langley Research Center Turbulence Modeling Resource webpage. The close agreement of AcuSolve results with experimental data and reference turbulence model performance validates the ability of AcuSolve to model cases with turbulent flow moving past a convex curved wall.

## Problem Description

The problem consists of a fluid with material properties close to air flowing through a channel containing a 30° swept wall, with a lower convex wall. The inlet channel height and remaining duct height is 0.127 m. The bulk velocity (v) normal to the inlet is 31.9 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 2,100,000. The density of the flow medium is 1.225 kg/m3 and the dynamic viscosity is 1.8608 X 10-5 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 flow conditions are compared against experimental data and the current state-of-the-art performance for coefficient of pressure and coefficient of friction.
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 within the channel. As the fluid enters the channel it develops into fully turbulent flow exhibiting a steep parabolic velocity profile across the width of the channel. The flow begins to accelerate near the lower wall and decelerate near the top wall as it approaches the 30° bend. The results show that the upper (concave) wall destabilizes the boundary layer, increasing the eddy viscosity and forcing the flow velocity to decrease. The following figures show the flow conditions within the channel.
Upstream of the curved section of the channel, the flow normal to the channel opening increases as the distance from the lower wall increases until it reaches the centerline of the channel and then begins decreasing until it reaches zero at the top wall. As the flow approaches the curved section, it begins to accelerate, requiring that the flow velocity near the upper wall decrease to conserve momentum. The relatively low angle of curvature in the channel does not cause the accelerated fluid to recirculate. The images below show the coefficient of pressure (Cp) and coefficient of skin friction (Cf) along the lower wall of the channel. The images show black circles representing the experimental measurements (Smiths 1979), solid red lines for the SA model, solid blue lines for the SST model, solid green lines for the K-ω model and a solid cyan line for the K-ε model, representing the AcuSolve results. The coefficient of pressure within the channel is predicted nearly identically compared to the experiment for each of the turbulence models. It appears that the SST and K-ε models capture the low velocity region with the best accuracy, demonstrating that the flow velocity decreases significantly, but does not recirculate within the channel. This is shown in the friction coefficient plot, where the coefficient of friction, and subsequently the wall shear stress, does not decrease below zero.

## Summary

In this application, a turbulent flow through a curved channel at a Reynolds number of 2,100,000 is simulated and compared against experimental data. The AcuSolve results compare well with the experimental data for pressure coefficient and skin friction coefficient within the channel. The performance of the Spalart Allmaras turbulence model was found to be consistent with previously published results for flow through a convex-curved channel (NASA 2015) and the SST turbulence model appears to predict the shear stress on the lower wall most accurately. AcuSolve demonstrates the ability to predict the complex boundary layers resulting from the curvature of the channel and accurately predicts the propagation of the flow further downstream.

## Simulation Settings for Turbulent Flow past a Convex Curve in a Channel

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

Global

• Problem Description
• Analysis type - Steady State
• Turbulence equation - Spalart Allmaras
• Auto Solution Strategy
• Max time steps - 100
• Convergence tolerance - 0.0001
• Relaxation factor - 0.4
• Material Model
• Fluid
• Density - 1.225 kg/m3
• Viscosity - 1.8603e-5 kg/m-sec

Model

• Volumes
• Fluid - elbow
• Element Set
• Material model - Fluid
• Fluid - inlet
• Element Set
• Material model - Fluid
• Fluid - outlet
• Element Set
• Material model - Fluid
• Surfaces
• -Y
• Simple Boundary Condition
• Type - Slip
• +Y
• Type - Slip
• Inlet
• Simple Boundary Condition
• Type - Inflow
• Inflow type - Velocity
• Inflow velocity type - Normal
• Normal velocity - 31.9 m/sec
• Turbulence input type - Direct
• Eddy viscosity - 1.3671e-7 m2/sec
• Internal
• Simple Boundary Condition - (disabled)
• Lower Wall
• Simple Boundary Condition
• Type - Wall
• Turbulence wall type - Low Reynolds Number
• Outlet
• Simple Boundary Condition
• Type - Outflow
• Upper Wall
• Simple Boundary Condition
• Type - Wall
• Turbulence wall type - Low Reynolds Number

## References

A. J. Smits, S. T. B. Young, and P. Bradshaw. "The Effect of Short Regions of High Surface Curvature on Turbulent Boundary Layers". Journal of Fluid Mechanics. 94(2):209-242. 1979

NASA Langley Research Center Turbulence Modeling Resource webpage. http://turbmodels.larc.nasa.gov/smitscurve_val.html. Accessed May 2015.