Boundary layers and sepration

[M!Zare 48037]

Sports balls

 

Many games involve balls designed to use drag reduction brought about by surface roughness

 

Many sports balls have some type of surface roughness, such as the seams on baseballs or cricket balls and the fuzz on tennis balls

 

It is the Reynolds number (not the speed, per se) that determines whether the boundary layer is laminar or turbulent. Thus, the larger the ball, the lower the speed at which a rough surface can be of help in reducing the drag

 

 

Typically sports ball games that use surface roughness to promote an early transition of the boundary layer from a laminar to a turbulent flow are played over a Reynolds number range that is near the “trough” of the Cd versus Re curve, where drag is lowest

[M!Zare 48037]

Flow in reference frame relative to the ball

 

Note that we have been showing flow fields in the reference frame of the object, similar to the flow around the soccer ball shown here

 

[M!Zare 48037]

Flow in absolute reference frame

 

However, one should keep in mind that the flow in the absolute reference frame may look quite different, as shown here

 

[M!Zare 48037]

Airfoil - effect of angle of attack

 

The loss in pressure in the separated flow region behind solid bodies causes an imbalance between the upstream and downstream forces, contributing greatly to an increased net drag force

 

In the case of streamlined airfoils at low angle of attack, separation occurs only at the tip, with minimal losses. As the angle of attack increases, the separation point moves upstream, leading to increased drag

 

[M!Zare 48037]

Airfoil - effect of shape

 

The pressure field is changed by changing the thickness of a streamlined body placed in the flow. The acceleration and deceleration caused by a finite body width creates favorable and unfavorable pressure gradients

 

 

When the body is thin, there are only weak pressure gradients and the flow remains attached. As the body is made thicker, the adverse pressure gradient resulting from the deceleration near the rear leads to flow separation, recirculation, and vortex shedding

 

 

Focusing in on the rear region of the flow, it is seen that as the body is again reduced in thickness, the separated region disappears as the strengths of the adverse pressure gradient is diminished

 

[M!Zare 48037]

Suction

Just as flow separation can be understood in terms of the combined effects of viscosity and adverse pressure gradients, separated flows can be reattached by the application of a suitable modification to the boundary conditions

 

In this example, suction is applied to the leading edge of the airfoil at a sharp angle of attack, removing the early separation zone, and moving the separation point much farther downstream

 

[M!Zare 48037]

Blowing

 

Separation in external flows, such as the flow past a sudden expansion can be controlled not only by suction but also by blowing

 

In this video, the region of separated flow is eliminated by the introduction of high momentum fluid at a point near the separation point

 

This acts to eliminate the adverse pressure gradient by accelerating the fluid close to the boundary, leading to re-attachment of the flow

 

[M!Zare 48037]

The turbulent boundary layer

 

In turbulent flow, the boundary layer is defined as the thin region on the surface of a body in which viscous effects are important

 

The boundary layer allows the fluid to transition from the free stream velocity Ut to a velocity of zero at the wall

 

The velocity component normal to the surface is much smaller than the velocity parallel to the surface: v

 

The gradients of the flow across the layer are much greater than the gradients in the flow direction

 

The boundary layer thickness d is defined as the distance away from the surface where the velocity reaches 99% of the free-stream velocity

 

[M!Zare 48037]

The turbulent boundary layer

 

[M!Zare 48037]

[M!Zare 48037]

Boundary layer structure

 

[M!Zare 48037]

Standard wall functions

 

The experimental boundary layer profile can be used to calculate tw. However, this requires y+ for the cell adjacent to the wall to be calculated iteratively

 

In order to save calculation time, the following explicit set of correlations is usually solved instead

 

 

Here

Up is the velocity in the center of the cell adjacent to the wall

yp is the distance between the wall and the cell center

kp is the turbulent kinetic energy in the cell center

k is the von Karman constant (0.42

E is an empirical constant that depends on the roughness of the walls (9.8 for smooth surfaces

[M!Zare 48037]

Near-wall treatment - momentum equations

 

The objective is to take the effects of the boundary layer correctly into account without having to use a mesh that is so fine that the flow pattern in the layer can be calculated explicitly

 

Using the no-slip boundary condition at wall, velocities at the nodes at the wall equal those of the wall

 

The shear stress in the cell adjacent to the wall is calculated using the correlations shown in the previous slide

 

This allows the first grid point to be placed away from the wall, typically at 50

 

This approach is called the “standard wall function” approach

 

The correlations shown in the previous slide are for steady state (“equilibrium”) flow conditions. Improvements, “non-equilibrium wall functions,” are available that can give improved predictions for flows with strong separation and large adverse pressure gradients

[M!Zare 48037]

Two-layer zonal model

 

A disadvantage of the wall-function approach is that it relies on empirical correlations

 

The two-layer zonal model does not. It is used for low-Re flows or flows with complex near-wall phenomena

 

 

Zones distinguished by a wall-distance-based turbulent Reynolds number

 

The flow pattern in the boundary layer is calculated explicitly

 

Regular turbulence models are used in the turbulent core region

 

Only k equation is solved in the viscosity-affected region

 

e is computed using a correlation for the turbulent length scale

 

Zoning is dynamic and solution adaptive

[M!Zare 48037]

Near-wall treatment - turbulence

 

The turbulence structure in the boundary layer is highly anisotropic

 

e and k require special treatment at the walls

 

Furthermore, special turbulence models are available for the low Reynolds number region in the boundary layer

 

These are aptly called “low Reynolds number” models

 

This is still a very active area of research, and we will not discuss those here in detail

[M!Zare 48037]

Comparison of near-wall treatments

 

[M!Zare 48037]

Computational grid guidelines

 

 

First grid point in log-law region

 

Gradual expansion in cell size away from the wall

 

Better to use stretched quad/hex cells for economy

 

First grid point at y+ = 1

 

At least ten grid points within buffer and sublayers

 

Better to use stretched quad/hex cells for economy

[M!Zare 48037]

Obtaining accurate solutions

 

When very accurate (say 2%) drag, lift, or torque predictions are required, the boundary layer and flow separation require accurate modeling

 

The following practices will improve prediction accuracy:

Use boundary layer meshes consisting of quads, hexes, or prisms. Avoid using pyramid or tetrahedral cells immediately adjacent to the wall

 

After converging the solution, use the surface integral reporting option to check if y+ is in the right range, and if not refine the grid using adaption.

For best predictions use the two-layer zonal model and completely resolve the flow in the whole boundary layer

 

[M!Zare 48037]

Summary

 

The concept of the boundary layer was introduced

 

Boundary layers require special treatment in the CFD model

 

The influence of pressure gradient on boundary layer attachment showed that an adverse pressure gradient gives rise to flow separation

 

For accurate drag, lift, and torque predictions, the boundary layer and flow separation need to be modeled accurately

 

This requires the use of:

A suitable grid.

A suitable turbulence model.

Higher order discretization.

Deep convergence using the force to be predicted as a convergence monitor

[M!Zare 48037]

Summary

 

The concept of the boundary layer was introduced

 

Boundary layers require special treatment in the CFD model

 

The influence of pressure gradient on boundary layer attachment showed that an adverse pressure gradient gives rise to flow separation

 

For accurate drag, lift, and torque predictions, the boundary layer and flow separation need to be modeled accurately

 

This requires the use of

A suitable grid

A suitable turbulence model

Higher order discretization

Deep convergence using the force to be predicted as a convergence monitor