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Abstract
This main purpose of this experiment was to measure the boundary layer velocity and to observe the growth of the boundary layer for the flat plate with smooth and rough surface. The experiment was done by using test apparatus which is airflow bench that provide adjustable air stream. The velocity in the experiment was measure by using tools and static probe that connected to multi-tube manometer. This experiment also was done to study about the effect of surface roughness on the development of the boundary layer. 2.0)
Introduction
In physics and fluid mechanics, a boundary layer is that la yer of fluid in the immediate vicinity of a bounding surface. In the Earth's atmosphere, the planetary boundary layer is the air layer near the ground affected by b y diurnal heat, moisture or momentum transfer to or from the surface. On an aircraft wing the boundary layer is the part of the flow close to the wing. The boundary layer effect occurs at the field region in which all changes occur in the flow pattern. The boundary layer layer distorts surrounding non viscous flow. It is a phenomenon of viscous forces. This effect is related to the Reynolds number. Laminar boundary layers come in various forms and can be loosely classified according to their structure and the circumstances under which they are created. The thin shear la yer which develops on an oscillating body is an example of a Stokes boundary layer, whilst the Blasius boundary layer refers to the well-known similarity solution for the steady boundary layer attached to a flat plate held in an oncoming unidirectional flow. When a fluid rotates, viscous forces may be balanced by the Coriolis effect, rather than convective inertia, leading to the formation of an Ekman layer. Thermal boundary layers also exist in heat transfer. Multiple types of boundary layers can coexist near a surface simultaneously. 2.1)
Objective
1. To measure the boundary layer velocity layer and observed the growth of the boundary layer for the flat plate with smooth and rough rough surface. 2. To measure the boundary layer properties for the measured velocit y profile 3. To studied the effect of surface roughness on the development of the boundary layer
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Theory
The boundary layer thickness, δ is used for a thickness beyond which the velocity is essentially the free-stream velocity U. This is customarily defined as the distance from the wall to the point where
Figure 1: Boundary layer thickness
The displacement thickness,
the distance by which the solid boundary would have to
be displaced in a frictionless flow the same s ame deficit exists in the boundary layer. The mathematical definition of the displacement thickness for incompressible flow is given by
Figure 2: Displacement thickness
The momentum thickness
Ѳ, is defined as the thickness of the layer fluid velocity, U (free
stream velocity), for which the momentum flux is equal to the deficit of momentum flux through the boundary layer. Mathematically it is defined as
The equation for velocity measured by pitot tube is given as
) )
The Blasius’s exact solution to the laminar la minar boundary layer yields the following equation for the above properties
√
√
√
Due to the complexity of the flow, there is no exact solution to the turbulent boundary layer. The properties of the boundary layer are approximated using the momentum integral equation which result in the following expression:
)
)
)
Another measured of the boundary later is the shape factor , H which is the ratio displacement thickness to the momentum thickness, H= δ . For laminar flow, H increase from 2.6 to 3.5 at separation. For turbulent layer, H increase from 1.3 to approximately 2.5 at separation.
When a viscous fluid flows along a fixed impermeable wall, or past the rigid surface of an immersed body, an essential condition is that the velocit y at any point on the wall or other fixed surface is zero. The extent to t o which this condition modifies the general character of the flow depends upon the value of the viscosity. If the body is of strea mlined shape and if the viscosity is small without being negligible, the modifying e ff ect ect appears to be confined within narrow regions adjacent to the solid surfaces ; these are called boundary layers. Within such layers the fluid velocity changes rapidly from zero to its main-stream main-stream value, and this may imply a steep gradient of shea ring stress; as a consequence, not all the viscous terms in the equation of motion will be negligible, even though the viscosit y, which they contain as a factor, is itself very small. A more precise criterion for the existence of a well-defined well-defined laminar boundary layer is that the Reynolds number nu mber should be large, though not so large as to imply a breakdown of the laminar flow. flow.
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Procedure
1. The experiment was started with plate which have the smooth surface 2. The position of the central plate was adjusted to set the measurement plate at the required distance from leading edge of 50mm 3. The fan was switched on and the air flow speed was set with air stream velocity velocit y at medium speed 4. The reading of the total pressure of the pitot tube was taken at an interval of 0.25mm 5. The velocity profile was clearly define with reduc ing the increment of the advanced directly with the pressure fall 6. The step of 2 to 4 was repeated with measurement plane at 200mm 7. The entire experiment was repeated with plate of rough surface
5.0)
Experimental Experimental apparatus
1. Airflow bench is provide adjustable air stream which enables a series of experiment to be connected 2. Test apparatus is consists of rectangular duct with flat plate. One side of the plate is smooth and other rough. Pitot tube tip is set in the zero plane of scale. By moving the plate up and down, the the leading edge can be set to given distance from pitot tube tip. 3. Micrometer scale is to measure the displacement of pitot tube from wall 4. Velocity measurement is velocity measured using total and st atic probes which is connected to multi-tube manometer.
Pitot tube Rough plate
Plate holder
Smooth plate
9.0)
References
1. Boundary layer, Retrieved 7, October, October, 2014 from Yunus A.Cengal, John M.Cimbala, Fluid Mechanics , Third Edition in SI Unit , Unit , Mc Graw Hill Education, 2014, page 555 – 555 – 577. 577.
2. Boundary Layer on a Flat Plate, Retrieved 7, October, 2014 from http://farside.ph.utexas.edu/teaching/336L/Fluidhtml/node87.html
3. Boundary layer, Retrieved 7, October, 2014 from http://en.wikipedia.org/wiki/Boundary_layer
4. Boundary layer thickness, Retrieved 7, October, 2014 from http://en.wikipedia.org/wiki/Boundary_layer_thickness
5. Laminar and Turbulent Boundary Layers, Retrieved 7, October, 2014 from http://wwwmdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/fprops/in trovisc/node8.html
