MEHB221
Fluid Mechanics Lab
2012
Experiment No. 2 FLOW VISUALIZATION
Objectives To study the flow lines and path lines in fluids mechanics (steady flow), and investigate the influence of different shaped bodies on the flow.
Apparatus Flow Visualization Unit, FM 22 (Figure 4). Hydraulic Bench, FM 110.
Summary of Theory Timelines, Pathlines, Streaklines and Streamlines (Flow lines) In the analysis of problems in fluid mechanics, frequently it is advantageous to obtain a visual representation of a flow field. Such a representation is provided by timelines, pathlines, streaklines, and streamlines (flow lines). If a number of adjacent fluid particles in a flow field are marked at a given instant, they form a line in the fluid at that instant; this line is called a timeline. A pathline is the path or trajectory traced out by a moving fluid particle. To make a pathline visible, we might identify a fluid particle at a given instant, e.g., by the use of dye, and then take a long exposure photograph of its subsequent motion. The line traced out by the particle is a pathline. On the other hand, we might choose to focus our attention on a fixed location in space and identify, again by the use of dye, all fluid particles passing through this point. After a short period of time we would have a number of identifiable fluid particles in the flow, all of which had, at some time, passed through one fixed location in space. The line joining these fluid particles is defined as a streakline. Streamlines (flow lines) are lines drawn in the flow field so that at a given instant they are tangent to the direction of flow at every point in the flow field. Since the streamlines are tangent to the velocity vector at every point in the flow field, there can be no flow across a streamline. In steady flow, the velocity at each point in the flow field remains constant with time and, consequently, the streamlines do not vary from one instant to the next. This implies that a particle located on a given streamline will remain on the same streamline. Furthermore,
1
MEHB221
Fluid Mechanics Lab
2012
consecutive particles passing through a fixed point in space will be on the same streamline and, subsequently, will remain on this streamline. Thus in a steady flow, pathlines, streaklines, and streamlines are identical lines in the flow field. The shape of the streamlines may vary from instant to instant if the flow is unsteady. In the case of unsteady flow, pathlines, streaklines, and streamlines do not coincide.
Flow Vector Visualization Various visualization approaches have been developed for vector data. For steady flows, (where flow at a given position does not change over time), one can use streamlines, contour lines, or glyph plots. Streamlines are lines that follow the tangent of the velocity vector, while contour lines delineate areas with similar values of some scalar field (e.g. velocity magnitude). Glyph plots use small arrows or oriented icons to indicate direction and magnitude of flow at specified points, placed either at random or on a regular grid. Experimental flow visualization technique uses smoke or dye injected into the flow field. As shown in Figure 1, if the particles are placed close together along a line segment in space and released at regular (but long) time intervals, timelines are produced. Conversely, if the particles are released further apart in space and at short time intervals, streaklines are created. Note for steady flows streaklines are equivalent to streamlines.
Figure 1: Streaklines and timelines for steady flow.
Standard seed points (starting positions of particles) for streamlines or timelines are usually along a line or regular grid. Important features in a flow field are called critical points. Depending on the nature of the flow, critical points can be classified into six groups, as illustrated in Figure 2.
2
MEHB221
Fluid Mechanics Lab
2012
Figure 2: Classification of critical points.
Viscous Effects A body immersed in a flowing fluid is acted on by both pressure and viscous forces from the flow. The sum of the forces (pressure, viscous, or both) that act normal to the freestream direction is equal to the lift, and the sum that act parallel to the free-stream direction is equal to the drag. It is customary to consider two components of drag. The transfer of momentum perpendicular to the body surface resulted in a tangential shear stress or drag on the smooth surface parallel to the direction of flow. This force exerted by the fluid on the solid in the direction of the flow is called skin or wall drag. For any surface in contact with a flowing fluid, skin friction will exist. In addition to skin friction, if the fluid is not flowing parallel to the surface but must change direction to pass around a solid body like a cylinder, significant additional frictional losses will occur; this is called form drag. In Figure 3a, the flow of fluid is parallel to the smooth surface of the flat, solid plate, and the force, F on an element of surface, dA of the plate is the wall shear stress, τw times the area, dA, or τwdA. The total force is the sum of the integrals of these quantities evaluated over entire area of the plate. Here the transfer of momentum to the surface results in a tangential stress or skin drag on the surface. In many cases, however, the immersed body is a blunt-shaped solid which presents various angles to the direction of the fluid flow. As shown in Figure 3b, the free-stream velocity is uniform on approaching the blunt shaped body suspended in fluid flow. The flow streamlines represent the path of fluid elements around the suspended body. The thin boundary layer adjacent to the solid surface is shown as a dashed line; at the edge of this layer the velocity is essentially the same as the bulk fluid velocity adjacent to it. At the front center of the body, called the stagnation point, the fluid velocity will be zero; boundary-layer growth begins at this point and continues over the surface until the layer separates. The tangential stress on the body because of the velocity gradient in the
3
MEHB221
Fluid Mechanics Lab
2012
boundary layer is the skin friction. Outside the boundary layer the fluid changes direction to pass around the solid and also accelerates near the front and the thenn decelerates. Because of these effects, an additional force is exerted by the fluid on the body. This phenomenon, called form drag, is an addition to the skin drag in the boundary layer. andd a wake, covering the In Figure 3b,, as shown, separation of the boundary layer occurs an entire rear of the object, occurs where large eddies are present and contribute to the form drag. The point of separation depends on the shape of the body, Reynolds number, etc. Form drag for bluffed bodies can be minimized by strea streamlining mlining the body Figure 3c, which forces the separation point toward the rear of the body, greatly reducing the size of the wake.
Figure 3: Flow past immersed objects: (a) flat plate (b) cylinder (c) streamline object object.
4
MEHB221
Fluid Mechanics Lab
2012
Procedures Part I To study the flow lines and path lines in fluids mechanics (steady flow). 1. 2. 3. 4.
5. 6. 7. 8. 9. 10.
Fill the ink container with ink. Make sure the ink flow regulating valve is closed. Open slightly the water flow control valve, V1. Make sure all valves in water sinks manifold and water sources manifold is fully closed. Open the water supply (pipe) slowly until enough water is supplied to the apparatus. Flow control valve may also need to be adjusted to control the water. Check for any leaking of water from the water chamber. Tighten the screw if necessary. Open the ink flow regulating valve slightly to release some ink into the water chamber. Study the flow pattern shown by the ink. Obtain the flow pattern of uniform velocity flow (steady flow). Take the photo of the resulting flow pattern. Close the ink flow regulating valve. Close the flow control valve.
Part II To investigate the influence of different shaped bodies on the flow. 1. 2. 3. 4. 5. 6. 7. 8. 9.
Open the water chamber gently (do not break the glass). Place the aerofoil shape body into the flow field (in the middle). Close the water chamber gently. Open the water flow control valve slowly until enough water is flowing through the water chamber and check for any water leakage. Open the ink flow regulating valve slightly to release some ink into the water chamber. Adjust the water or ink (if necessary) to obtain a clear visual of the flow pattern formed. Take the photo of the resulting flow pattern. Close the ink flow regulating valve. Repeat the experiment with different shaped bodies (cylinder-shaped 2-D body, reversed triangle-shaped 2-D body, and quadrate-shaped 2-D body).
5
MEHB221
Fluid Mechanics Lab
Results, Analysis and Discussion (combined). • • • • • •
Explain about timelines, pathlines, streaklines, and streamlines. Explain about steady and non-steady fluid flow. Show the photo obtained in Part I. Comment your photo. Explain about skin drag and form drag. Show the photos obtained in Part II. Comment your photos. List the possible sources of errors and safety precaution.
Figure 4: The Flow Visualization Unit (Model: FM 22)
1. Dye/Ink Container
6. Drain
2. Dye/Ink Flow Regulating Valve
7. Water Sources Manifold
3. Water Flow Control Valve, V1
8. Water Inlet
4. Drag Bodies
9.
5. Water Sinks Manifold
10. Flow Chamber
6
Dye/Ink
2012
