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Lauren Gust
October 26, 2010
Laminar and Turbulent Flow Laminar flow:
Capillaries, microfluidics, low velocities
Prediction of fluid movement and streamlines
Tur u ent ow:
Aerodynamics
House piping
Energy storage
Heat exchangers
M Van Dyke, “An Album of Fluid Motion”
(Parabolic Press, Stanford, CA, 1982), p. 89.
Vortex Shedding Major loss of energy in flying objects
Airplanes, flag waving
US Geological Survey Website, http://landsat.gsfc.nasa.go/earthasart/vortices.html
Objectives To determine the velocity profile for laminar,
turbulent, and transition flow regimes
To study vortex shedding from cylindrical objects in air
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Reynolds Number
ρ = density (kg/m^3) v = velocity (m/s)
v
AvvD Re
2
μ = viscosity (Pa-s) D
Ratio of viscous forces to inertial forces
Low Re (<~2300) is the laminar regime
High Re (>~2300) is the turbulent regime
Laminar Flow
Straight streamlines
Minimal lossesM Van Dyke, “An Album of Fluid Motion”
(Parabolic Press, Stanford, CA, 1982), p. 89.
Laminar Velocity Distribution
2
0 1)( R
r ur u
Smooth streamlines lead
to parabolic distribution
Can be solved analytically
from the Navier‐Stokes
equation A. J. Smits, A Physical Introduction to Fluid Mechanics,
John Wiley & Sons, New York, 2000)
Turbulent Flow
Mixed streamlines with many vortices
Significant lossesM Van Dyke, “An Album of Fluid Motion”
(Parabolic Press, Stanford, CA, 1982), p. 89.
Turbulent Velocity Distribution Changes over time, so use time‐averaged flow
No analytic form so use correlations derived from
experimental data
A. J. Smits, A Physical Introduction to Fluid Mechanics, John Wiley & Sons, New York, 2000)
Turbulent Velocity Distribution
n
ave
R
r
n
nnur u
1
21
2
121)(
Data determined from numerical correlations performed on experimental data
)ln(/535.6085.1
)ln(
Re
Ren
MV Zagarola, AE Perry, and AJ Smits, “Log laws or power laws: The scaling in the overlap
region”, Phys. Fluids, 9(7):2094‐2100, July, 1997.
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Entrance Considerations Assume that the flow is fully developed : the
measuring position is far enough from the entrance of the pipe that entrance effects are irrelevant
, e =0.03
For turbulent flow, vortices lead to more mixing, shorter entry lengths: Le=10D‐40D
Vortex Shedding Bodies in flow exhibit vortex shedding: a stream of
vortices trails behind the object
These vortices have a constant frequency, dependent
B. J. Hughey and I. W. Hunter. “Fluid Flow Experiment Prelab”: 2.671 Course Material, MIT, Spring 2010 (unpublished).
Strouhal Number
v
fd Sr
mens on ess parame er or e requency o vor ex propagation
Find Sr from correlations with Re
To measure the frequency, read the velocity data in
the wake of a disturbance rod and take the FFT
Since the detector often reads both vortex streams,
expect peaks at f and 2f
Strouhal Number Correlations
B. J. Hughey and I. W. Hunter. “Fluid Flow Experiment Prelab”: 2.671 Course Material, MIT, Spring 2010 (unpublished).
Experiment Setup
Flow tube Anemometer
Stepper motor
Potentiometer and slide
DMMs
Pitot tube holder
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Linear Potentiometer and Motor Anemometer is driven on a linear
slide using a stepper motor.
Distance moved is correlated
using voltage output from a
linear potentiometer.
Pitot Tube Flow measurement based on the Bernoulli equation
Neglect pipe friction
The gas velocity is given by:
1212
PPuug
g
Hot Film Anemometer Thin metal film is heated by a power supply
Increased gas velocity across the film requires more voltage to maintain a constant temperature
Anemometer vo tage s re ate to ow ve oc ty y:
ganem uC C V 10
2
Anemometer Calibration Low‐speed (≤ 0.1 m/s) and high speed (2-4 m/s)
measurements were used to determine the calibration
constants C 0 and C 1
VanemVpress
8 V
N2 Gas, velocity ug
P2
2
1 P1 = ?
ug
Pa/mV
C0 , C 1
)(2
121 PPug
ganem uC C V 10
2
B. J. Hughey and I. W. Hunter. “Fluid Flow Experiment Prelab”: 2.671 Course Material, MIT, Spring 2010 (unpublished).
Calibration Constants
C0 = 4.791 V2/√m/s
C1 = 6.634 V2ganem uC C V 10
2
Measurement of Velocity Profiles Measurements were taken at 20 and 75 SLPM
Using the stepper motor, the anemometer was moved
across the flow tube and data was taken
Ve oc ty pro es were grap e or eac ow rate an
the Reynolds number was calculated for each profile
Entry length was calculated to determine whether flows were fully developed.
78.40 D
L
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Vortex Shedding Measurements A control measurement was taken at 35 SLPM with no
cylindrical obstruction.
A series of cylinders (1.59 mm – 4.75 mm) were
used to determine anemometer position
Data was taken and a Fourier
transform was performed to
determine peak frequency
Laminar Velocity Profile
Avg. velocity = 0.17±0.16 m/s
Re = 470±450
Le = 14±13D Fully developed
Turbulent Velocity Profile
Average velocity = 13.8±2.8 m/s
Re = (3.93±0.79)x104
Le = (10-40)D
Fully developed
Vortex Shedding
Peak frequency
1.5 mm cylinder
Doubling frequency
Strouhal Numbers
Diameter(mm) ReynoldsNumber
Predicted Strouhal Number
MeasuredStrouhal Number
1.59 70.53 0.254 0.094±0.046
2.38 105.73 0.259 0.090±0.044
3.15 140.05 0.261 0.109±0.053
4.75 211.02 0.240 0.136±0.066
Not an exact correlation between predicted and
measured values, but correct order of magnitude is as good as can be expected
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Conclusion Laminar and turbulent profiles fit theoretical profiles
Strouhal number in vortex shedding gave order of magnitude estimates
xper menta wea nesses
Noise in data
Anemometer motion
Air currents in environment
We can use our data to do analysis of laminar and turbulent systems.
Future experiments
AcknowledgementsThe authors would like to thank Robert Truax and Dr. Barbara Hughey for their assistance in collecting and
analyzing data and the generous donors who provided
lounge.