CE 319F - Laboratory #7
Laminar and Turbulent Flow


 
List of Figures: 
  • Fig. 7.1 - Lagrangian pathlines in turbulent flow 
  • Fig. 7.2 - Eulerian velocity distributions at different times 
  • Fig. 7.3 - Time history of Eulerian velocity at a point 
  • Fig. 7.4 - Osborne Reynolds Apparatus 
  • Fig. 7.5 - Sontex Acoustic Doppler Velocimeter 

Objective

The objective of this laboratory experiment is to demonstrate the differences between laminar, turbulent, and transitional fluid flow, and the Reynold's numbers at which each occurs.

Theory

Fluid flow can be characterized as laminar, turbulent, or transitional. The dimensionless Reynold's number (Re) can be used to determine the fluid flow condition. The Reynold's number is defined as

where r = the fluid density, V = the velocity of the fluid, L = an important length dimension for the flow, m = the dynamic viscosity, and n = the kinematic viscosity where n =m/r. For pipe flow, L is taken as the pipe diameter (D).

Re can be interpreted as the ratio of the flow's inertial forces to its viscous forces. For large viscous forces (low Re, normally Re < 2000 for pipe flows), viscous effects are great enough to damp any disturbances or perturbations in the flow and the flow remains laminar. Any combination of low velocity, small diameter, or high kinematic viscosity which results in Re < 2000 for pipe flow will produce laminar flow. The flow is called "laminar" because the flow takes place in layers. The only mixing that occurs is molecular mixing between the layers or between different parts of the flow. For large inertial forces (large Re, normally Re > 4000 for pipe flows), there is not enough viscous damping to remove any disturbances in the flow. Again, any combination of V, D, and n giving Re > 4000 will produce turbulent flow. As Re increases, the viscous damping of flow disturbances or perturbations decreases relative to the inertial effects. Because of a lack of viscous damping, disturbances are amplified until the entire flow breaks down into in irregular motion. There is still a definite flow direction, but there is an irregular motion superimposed on the average motion. Thus, for turbulent flow in a pipe, the fluid is flowing in the downstream direction, but fluid particles have an irregular motion in addition to the average motion. This effect is illustrated by the pathlines in Fig. 7.1; pathlines give a Lagrangian description of flow. The turbulent fluctuations are inherently unsteady and three dimensional. As a result, particles which pass though a given point in the flow do not follow the same path in turbulent flow even though they all are flowing generally downstream.
 
Fig. 7.1 - Lagrangian pathlines in turbulent flow
 
Since the velocities of all fluid particles are continually changing, the Eulerian velocities at a point or at several points are also changing. This effect is shown in the next two figures. Fig. 7.2 shows the time averaged velocity distribution across a diameter of a pipe and then illustrates the unsteadiness in the turbulent components of the velocities. Fig. 7.3 shows the time-averaged velocity at a point and the continual variation of instantaneous velocity due to the turbulent fluctuations.
Fig. 7.2 - Eulerian velocity distributions at different times
Fig. 7.3 - Time history of Eulerian velocity at a point

The instability or unsteadiness in turbulent flows is sometimes viewed as being due to parcels of fluid that are rotating in an irregular fashion as the fluid flows. These rotating parcels of fluid are sometimes called billows or eddies. Time-lapse pictures of clouds moving across the sky illustrate the billowing or eddy character of turbulent flows.

Flows with 2000 < Re < 4000 are called transitional. The flow can be unstable and the flow switch back and forth between turbulent and laminar conditions. This transitional flow was seen in the first lab with water flow from the 1/4 in. copper tube. The pulsating jet of water from the end of the tube was an indication of the transitional flow with the flow switching back and forth between being laminar and turbulent.

Laboratory Apparatus

Two types of equipment will be used in this laboratory. The first is called the Osborne Reynolds Apparatus (Fig. 7.4). This apparatus has a vertical tube through which water flows. The marbles in the water tank are to calm the inflow so there will be no turbulence in the top tank to get into the flow tube in the tube. As the flow rate in the tube is changed, the Reynold's number changes since Re = VD/n = (Q/A)D/n = 4Q/(pDn). For Re < 2000, laminar flow exists and the streakline is a smooth, straight line. For higher flow rates with Re > 4000, the flow is turbulent. The dye streak then moves around in the tube in response to the unsteady turbulent fluctuations of velocities and the eddies in the turbulence.
 
 
a) Photograph 
 
b) Dye streaks 
Fig. 7.4 - Osborne Reynolds Apparatus

The second apparatus is an Acoustic Doppler Velocimeter (ADV), shown in Fig. 7.5.  The probe on the apparatus has three prongs or fingers. In the main probe shaft, there is a sonic transmitter and three sonic receivers at the ends of the prongs. The receivers are focused on a small sampling or measurement volume 5 cm below the bottom of the prongs and straight down from the shaft of the probe. The emitted sonic pulses are reflected in all directions by very small solid particles in the flow. The frequency of the reflected sound wave depends on the frequency of the emitted wave and the velocity of the particles that reflect the wave. The receivers and the signal analysis hardware and software provide all three Cartesian velocity components at a frequency of 25 Hz, i.e., there are 25 measurements of the three velocity components each second or one measurement every 40 ms. More information on the principles of operation can be obtained from http://www.sontek.com/princop/adv/advpo.htm. The probe is put into a small channel with water flow. The signal from the ADV for the longitudinal flow direction is similar to Fig. 7.3. The other two components fluctuate about a zero average velocity.

 
Fig. 7.5 - Sontex Acoustic Doppler Velocimeter

Procedures

  1. For the Osborne Reynolds Apparatus, the out flow valve can be adjusted so that there are different velocities in the pipe. For a low flow rate, the dye streak will be a straight smooth line. For this condition, there is laminar flow in the tube. The flow rate can be measured and the Reynold's number calculated from Re = 4Q/pDn. to verify that Re < 2000.
  2. The second experiment is similar to the first except with a larger flow rate so Re > 4000. For this turbulent flow, the dye streak will be unsteady and move about laterally in the flow.
  3. The third experiment uses the ADV. It will be set into a water flow in a small open channel. The display of the instantaneous velocities will show the unsteadiness in the turbulence and the inherent three dimensional nature of turbulence. In addition, moving the probe vertically in the flow will show that the time-averaged velocity is different at different vertical positions and that the turbulent fluctuations of velocity are larger nearer to the boundary even though the time-averaged velocity is smaller.