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Saturday, 17 November 2018

WHAT IS LAMINAR AND TURBULENT BOUNDARY LAYER?

We were discussing the basic concept of streamline and equipotential linedimensional homogeneityBuckingham pi theoremdifference between model and prototypebasic principle of similitude i.e. types of similarityvarious forces acting on moving fluid and Boundary layer theory in the subject of fluid mechanics, in our recent posts. 

Laminar boundary layer 

Before going to understand the basic principle and meaning of turbulent boundary layer, we will see here a brief introduction of laminar boundary layer and further we will understand here the basic concept of turbulent boundary layer with the help of this post. 

Let us consider the flow of a fluid over a smooth thin and flat plate. Let us assume that this thin and flat plate is located parallel to the direction of fluid flow as displayed here in following figure. 

Let us consider that fluid is flowing with free stream velocity U and with zero pressure gradient on one side of the stationary plate. 

As we have already discussed that when a real fluid will flow over a solid body or a solid wall, the particles of fluid will adhere to the boundary and there will be condition of no-slip. We can also conclude that the velocity of the fluid particles, close to the boundary, will have equal velocity as of the velocity of boundary.  

As we have assumed that plate is stationary and therefore the velocity of fluid flow over the surface of plate will be zero. 

If we move away from the plate, the velocity of fluid particles will also be increasing. Velocity of fluid particles will be changing from zero at the surface of stationary boundary to the free stream velocity (U) of the fluid in a direction normal to the plate. 

Therefore, there will be presence of velocity gradient, due to variation of velocity of fluid particles, near the surface of the fluid. 

This velocity gradient will develop shear resistance and this shear resistance will retard the fluid. Therefore, fluid with free stream velocity (U) is retarded in the surrounding area of the solid surface of the plate and boundary layer region will be started at the sharp leading edge. 

Once we will go away from the sharp leading edge, retardation of the fluid will be increased and therefore boundary layer region increases with increase in the retardation of the fluid. The increase in the region of boundary layer with increase in the retardation of the fluid will also be termed as growth of boundary layer. 

Near the leading edge of the surface of the plate, where thickness will be small, the flow in the boundary layer will be laminar and this layer of the fluid will be termed as laminar boundary layer. 

Let us see the above figure. AE indicates the laminar boundary layer. 

Laminar zone 

Length of the plate from the leading edge up to which laminar boundary layer exists will be termed as laminar zone. AB indicates the laminar zone in above figure. 

Length of the plate from the leading edge up to which laminar boundary layer exists i.e. laminar zone will be determined with the help of following formula as mentioned here. 
Where,
x = Distance from leading edge up to which laminar boundary layer exists
U = Free stream velocity of the fluid
v = Kinematic viscosity of the fluid 

Turbulent boundary layer fundamentals

If the length of plate is greater than the value of x which is determined from above equation, thickness of boundary layer will keep increasing in the downstream direction. 

Laminar boundary layer will become unstable and movement of fluid particles within it will be disturbed and irregular. It will lead to a transition from laminar to turbulent boundary layer. 

This small length over which the boundary layer flow changes from laminar to turbulent will be termed as transition zone. BC, in above figure, indicates the transition zone. 

Further downstream the transition zone, boundary layer will be turbulent and the layer of boundary will be termed as turbulent boundary layer. 

FG, in above figure, indicates the turbulent boundary layer and CD represent the turbulent zone. 

Further we will go ahead to start a new topic i.e. boundary layer thickness, in the subject of fluid mechanics, with the help of our next post. 

Do you have any suggestions? Please write in comment box. 

Reference: 

Fluid mechanics, By R. K. Bansal 
Image courtesy: Google  

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