Flow through an axisymmetrical parameterized contraction nozzle of limited size with area contraction ratio 21.8 and total length 6 cm is studied for moderate Reynolds numbers 300 < Re < 20,200. The transverse flow profiles at the nozzle exit are characterized by hot film anemometry for two different spatial step sizes. The flow at the exit is laminar and uniform in its core. Boundary layer characteristics at the nozzle exit are estimated from the transverse velocity profiles. Flow throughout the nozzle is modeled by implementing Thwaites laminar axisymmetrical boundary layer solutions in an iterative algorithm for which both universal functions, describing the shape factor and skin friction parameters respectively, are altered by adding a constant. The value of the constants is determined by fitting the modified universal functions to tabulated values reported in Blevins (Blevins, R., 1992, Applied Fluid Dynamics Handbook. Krieger, Malabar, FL.). The model is validated on the measured data. Adding nonzero constants to the universal functions improves the prediction of boundary layer characteristics so that the range of Reynolds numbers for which the discrepancy with experimental findings is less than 4% is extended from Re > 3000 to Re > 1000. Therefore, the studied contraction nozzle is of use for applications requiring a small nozzle with known low turbulence flow at the exit such as moderate Reynolds number free jet studies or bio fluid mechanics (respiration, speech production,…) and the flow at the exit of the nozzle can be accurately described by a simple boundary layer algorithm for Re > 1000.

References

References
1.
Blevins
,
R.
, 1992,
Applied Fluid Dynamics Handbook
,
Krieger
,
Malabar, FL
.
2.
Kachhara
,
N.
,
Wilcox
,
P.
, and
Livesey
,
J.
, 1974, “
A Theoretical and Experimental Investigation of Flow Through Short Axisymmetric Contractions
,” in
Proceedings of the 5th Australian Conference on Hydraulics and Fluid Mechanics
, pp.
82
89
.
3.
Morel
,
T.
, 1975, “
Comprehensive Design of Axisymmetric Wind Tunnel Contractions
,”
J. Fluid Eng.
,
97
, pp.
225
233
.
4.
Mikhail
,
M.
, 1979, “
Optimum Design of Wind Tunnel Contractions
,”
AIAA J.
,
17
, pp.
471
477
.
5.
Metha
,
R.
, and
Bradshaw
,
P.
, 1979, “
Design Rules for Small Low Speed Wind Tunnels
,”
Aeronaut. J. R. Aeronaut. Soc.
,
18
, pp.
443
449
.
6.
Watmuff
,
J.
, 1986, “
Wind Tunnel Contraction Design
,” in
Proceedings of 9th Australian Fluid Mechanics Conference
, pp.
82
89
.
7.
Bell
,
J.
, and
Mehta
,
R.
, 1988, “
Contraction Design for Small Low-Speed Wind Tunnels
,” NASA STI/Recon Technical Report No. 89.
8.
Fang
,
F.
, 1997, “
A Design Method for Contractions With Square End Sections
,”
J. Fluid Eng.
,
119
, pp.
454
458
.
9.
Fang
,
F.
,
Chen
,
J.
, and
Hong
,
Y.
, 2001, “
Experimental and Analytical Evaluation of Flow in a Square-To-Square Wind Tunnel Contraction
,”
J. Wind Eng. Indust. Aerodyn.
,
89
, pp.
247
262
.
10.
Todde
,
V.
,
Spazzini
,
P.
, and
Sandberg
,
M.
, 2009, “
Experimental Analysis of Low-Reynolds Number Free Jets: Evolution Along the Jet Centerline and Reynolds Number Effects
,”
Exp. Fluids
,
47
, pp.
279
294
.
11.
Mi
,
J.
,
Nobes
,
D.
, and
Nathan
,
G.
, 2001, “
Influence of Jet Exit Conditions on the Passive Scalar Field of an Axisymmetric Free Jet
,”
J. Fluid Mech.
,
432
, pp.
91
125
.
12.
Malmström
,
T.
,
Kirkpatrick
,
A.
,
Christensen
,
B.
, and
Knappmiller
,
K.
, 1997, “
Centreline Velocity Decay Measurements in Low-Velocity Axisymmetric Jets
,”
J. Fluid Mech.
,
246
, pp.
363
377
.
13.
Lee
,
T.
, and
Budwig
,
R.
, 1991, “
Two Improved Methods for Low-Speed Hot-Wire Calibration
,”
Meas. Sci. Technol.
,
2
, pp.
643
646
.
14.
Yue
,
Z.
, and
Malmström
,
T.
, 1998, “
A Simple Method for Low-Speed Hot-Wire Anemometer Calibration
,”
Meas. Sci. Technol.
,
9
, pp.
1506
1510
.
15.
Johnstone
,
A.
,
Uddin
,
M.
, and
Pollard
,
A.
, 2005, “
Calibration of Hot-Wire Probes Using Non-Uniform Mean Velocity Profiles
,”
Exp. Fluids
,
39
, pp.
1432
1114
.
16.
Daniloff
,
R.
,
Schuckers
,
G.
, and
Feth
,
L.
, 1980,
The Physiology of Speech and Hearing
,
Prentice-Hall
,
Upper Saddle River, N.J.
17.
Shadle
,
C.
, 1985, “
The Acoustics of Fricative Consonants
,” PhD thesis, Massachusetts Institute of Technology, Boston.
18.
Stevens
,
K.
, 1998,
Acoustic Phonetics
,
MIT Press
,
London
.
19.
White
,
F.
, 1991,
Viscous Fluid Flow
,
McGraw-Hill
,
New York
.
20.
Schlichting
,
H.
, and
Gersten
,
K.
, 2000,
Boundary Layer Theory
,
Springer Verlag
,
Berlin
.
21.
Bruun
,
H.
, 1995,
Hot-Wire Anemometry
,
Oxford Science
,
New York
.
22.
Cebeci
,
T.
, and
Cousteix
,
J.
, 2005,
Modeling and Computation of Boundary-Layer Flows
,
Springer
,
Berlin
.
23.
Thwaites
,
B.
, 1947, “
On the Momentum Equation in Laminar Boundary-Layer Flow. A New Method of Uni-Parametric Calculation
,” Tech. Rep. No. 2587.
24.
Thwaites
,
B.
, 1949, “
Approximate Calculations of Laminar Boundary Layers
,”
Aeronaut. Quart.
,
1
, pp.
245
280
.
25.
Rosenhead
,
L.
, 1963,
Laminar Boundary Layers
,
Dover
,
U.K
.
26.
Curle
,
N.
, 1962,
The Laminar Boundary Layer Equations
,
Clarendon Press
,
London
.
27.
Kavence
,
G.
, and
Oka
,
S.
, 1973, “
Correcting Hot-Wire Readings for Influence of Fluid Temperature Variations
,”
DISA Info
,
15
, pp.
21
24
.
28.
Grandchamp
,
X.
,
Van Hirtum
,
A.
, and
Pelorson
,
X.
, 2010, “
Hot Film/Wire Calibration for Low to Moderate Flow Velocities
,”
Meas. Sci. Technol.
,
21
, pp.
1
5
.
29.
Grandchamp
,
X.
, 2009, “
Modélisation Physique des Écoulements Turbulents Appliquée aux Voies Aériennes Supérieures Chez L’humain
,” PhD thesis, Grenoble University, Grenoble.
30.
Benedict
,
L.
, and
Gould
,
R.
, 1996, “
Towards Better Uncertainty Estimates for Turbulence Statistics
,”
Exp. Fluids
,
22
, pp.
129
136
.
31.
Michalke
,
A.
, and
Hermann
,
G.
, 1982, “
On the Inviscid Instability of a Circular Jet With External Flow
,”
J. Fluid Mech.
,
114
, pp.
343
359
.
32.
Zagarola
,
M.
,
Perry
,
A.
, and
Smits
,
A.
, 1997, “
Log Laws or Power Laws: The Scaling in the Overlap Region
,”
Phys. Fluids
,
9
, pp.
2094
2100
.
You do not currently have access to this content.