CFX Simulation of a Free Surface Water Chanel Flow over a Step

Colin Hartloper

December 3, 2010

Presentation Outline

• Problem Background

• Theory

• Geometry and Meshing

• Boundary Conditions

• Results

Problem Background

• VLHT – Low head turbine (less than 3.2m)

• CPL wants to install in North America, but has concerns.

• One such concern is the effect of an upstream geometry on the turbine performance.

Free Surface Flow

• “Free Surface” refers to atm. pressure at the water surface

• Model water flowing in an open channel rather than through a duct

• Requires two materials in simulation– Air and water

• Requires slightly more sophisticated boundary conditions

Governing Equations

Conservation of Mass

• Incompressible, steady state

• Two equations (one for water, one for air)

Conservation of Momentum

• Incompressible, steady state

• Three equations (x, y, and z momentum)

Turbulence Model

• Proper modeling of turbulence requires very fine mesh– Very small relative length scale

• Therefore, use of k-epsilon model– k is magnitude of energy

– ε is length scale

– Use because it is useful for relatively small pressure gradients

Critical Flow (theoretical verification)

• Governed by Froude number

• Fr < 1 is sub-critical, Fr > 1 is super-critical– Analogous to sub/supersonic gas flow

Geometry – Side View

Element Types

• Tetrahedral Element– Suitable for modeling general fluid flow

• Wedge Element (inflation)– Suitable for modeling fluid flow close to a wall,

where a boundary layer exists

Meshing – Coarse

13812 Nodes, 55960 Elements

Meshing – Coarse with Inflation

22818 Nodes, 74039 Elements

Meshing – Fine with Inflation

27864 Nodes, 96271 Elements

Boundary Conditions

• “Infinately wide channel”– Actual model thickness of 30mm

• Free surface conditions

Results – Boundary Layer

Coarse Coarse with Inflation

Velocity Profile Location

Velocity Profile – Convergence?

Swirling

Validation – Froude Number

• For flow over step, Fr = 0.24 (sub-critical)

Comparison to Super-Critical

• For flow over bump, Fr = 1.33 (super-critical)

Questions?