Turbulent Flow Through a Wavy Channel

Problem Description

The problem consists of air flowing through a channel with a wavy bottom wall. The channel is 1.1 m high, 1.0 m wide, and is modeled as a section 1.0 m in length, as shown in the following image, which is not drawn to scale. The bottom wall wave shape has an amplitude of 0.1 m and a wavelength of 1 m. The mass flow rate through the channel is set to a constant value of 0.816 kg/s. The flow field develops as a result of the non-planar bottom wall and viscous stresses acting near the top and bottom walls. Collision of air with the peak of the wave on the channel floor causes an acceleration of the flow, followed by recirculation as the flow area expands into the valley.

Figure 1. Critical Dimensions and Parameters for Simulating Turbulent Flow Through a Wavy Channel

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 elements were extruded to the width of the channel.

Figure 2. Mesh Used for Simulating Turbulent Flow Through a Wavy Channel

AcuSolve Results

The AcuSolve solution converged to a steady state and the results reflect the mean flow conditions. The expansion of the cross section as the air passes the trough in the wave causes an adverse pressure gradient to form. This results in separation of the flow along the downward-slanting walls of the wavy surfaces. The recirculation zone establishes itself within the troughs of the wave. The remaining flow above the troughs maintains its velocity in the streamwise direction and distributes throughout the channel. The flow accelerates as it travels over the wave peak and the velocity continues to increase as a function of distance from the wall until it reaches a maximum velocity approximately 0.3 m away from the upper wall.

Figure 3. Velocity Contours in the X-Y Plane in a Wavy Channel (the Horizontal Line Represents the Reference for Wave Height - the Wave Crest is 0.1 m Above The Reference Height, and the Wave Valley is 0.1 m Below the Reference Height)

Figure 4. Close-Up View of Velocity Contours and Velocity Vectors in the X-Y Plane Near the Valley of a Wave

The X-velocity directly over the center of the wave valley initially decreases (backflow) as distance away from the bottom wall increases, with a maximum velocity in the -X direction at approximately 0.03 m above the valley floor. The X-velocity then increases to zero m/sec at 0.1 m above the valley, reflecting an end of the recirculation.

Figure 5. X-Velocity Plotted Against Vertical Location in the Channel Above the Valley Center (the Valley Floor is 0.1 m Below the Reference Height)

The X-velocity directly over the wave peak has different behavior due to the lack of recirculation. The velocity above the peak increases as distance away from the bottom wall increases, with a maximum velocity in the X direction at approximately 0.75 m. The velocity then decreases to zero at the top wall.

Figure 6. X-Velocity Plotted Against Vertical Location in the Channel Above the Wave Peak (the Wave Peak is 0.1 m Above the Reference Height)

Summary

The AcuSolve results compare well with the experimental data for X-velocity in a channel with a wavy floor. In this application, the flow is driven with a constant mass flow rate and periodic constraints are used to model a repeating array of channel segments with a wavy bottom wall. Separation of the flow occurs as a result of the adverse pressure gradient created by the changes in area. This leads to recirculation within the wave valleys. The flow separation occurs along the smoothly tapered wave wall, illustrating the ability of AcuSolve to accurately predict the separation point in this type of application. The X-velocity predicted by AcuSolve matches the experimental results with an overall coefficient of determination (R2) of 0.99 for each location shown in the plots.

Simulation Settings for Turbulent Flow Through a Wavy Channel

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

Global

• Problem Description
  • Analysis type - Steady State
  • Turbulence equation - Spalart Allmaras
• Auto Solution Strategy
  • Relaxation factor - 0.4
• Material Model
  • Air
    • Density - 1.0 kg/m3
    • Viscosity - 0.0001 kg/m-sec

  Model

• Volumes
  • Fluid
    • Element Set
      • Material model - Air
• Surfaces
  • Max_X
    • Simple Boundary Condition - (disabled to allow for periodic conditions to be set)
  • Max_Y
    • Simple Boundary Condition
      • Type - Wall
  • Max_Z
    • Simple Boundary Condition - (disabled to allow for periodic conditions to be set)
  • Min_X
    • Simple Boundary Condition - (disabled to allow for periodic conditions to be set)
    • Advanced Options
      • Integrated Boundary Conditions
        • Mass Flux
          • Type - Constant
          • Constant value - -0.816 kg/sec
  • Min_Y
    • Simple Boundary Condition
      • Type - Wall
  • Min_Z
    • Simple Boundary Condition - (disabled to allow for periodic conditions to be set)
• Periodics
  • Periodic-Crossflow
    • Periodic Boundary Condition
      • Type - Periodic
  • Periodic-Streamwise
    • Periodic Boundary Condition
      • Type - Periodic
    • Individual Periodic BCs
      • Velocity
        • Type - Periodic
      • Pressure
        • Type - Single Unknown Offset
      • Eddy Viscosity
        • Type - Periodic

References

J. D. Kuzan."Velocity Measurements for Turbulent Separated and Near-Separated Flows Over Solid Waves". Ph.D. thesis. Deptartment of Chemical Engineering. University of Illinois. University of Illinois. Urbana, IL. 1986