Abstract

A compressible flow with wall friction has been predicted in a constant cross section duct by means of a barotropic modeling approach, and new analytical formulas have been proposed that also allow any possible heat transfer to the walls to be taken into account. A comparison between the distributions of the steady-state flow properties, pertaining to the new formulas, and those of a classic Fanno analysis has been performed. In order to better understand the limits of the polytropic approach in nearly chocked flow applications, a numerical code, which adopts a variable polytropic coefficient along the duct, has been developed. The steady-state numerical distributions along the pipe, obtained for either a viscous adiabatic or an inviscid diabatic flow by means of this approach, coincide with those of the Fanno and Rayleigh models for Mach numbers up to 1. A constant polytropic exponent can be adopted for a Fanno flow that is far from choking conditions, while it cannot be adopted for the simulation of a Rayleigh flow, even when the flow is not close to choking conditions. Finally, under the assumption of diabatic flows with wall friction, the polytropic approach, with a constant polytropic exponent, is shown to be able to accurately approximate cases in which no local maximum is present for the temperature along the duct. The Mach number value at the location where the local maximum temperature possibly occurs has been obtained by means of a new analytical formula.

References

1.
Anderson
,
J.
,
2003
,
Modern Compressible Flow with Historical Perspective
, 3rd ed.,
McGraw-Hill
,
Boston, MA
.
2.
Urata
,
E.
,
2013
, “
A Flow-Rate Equation for Subsonic Fanno Flow
,”
Proc. Inst. Mech. Eng. Part C
,
227
(
12
), pp.
2724
2729
.10.1177/0954406213480295
3.
Rennels
,
C. D.
, and
Hudson
,
H. M.
,
2012
,
Pipe Flow: A Practical and Comprehensive Guide
,
Wiley
,
New York
.
4.
Cavazzuti
,
M.
,
Corticelli
,
M. A.
, and
Karayiannis
,
T. G.
,
2020
, “
Compressible Fanno Flows in Micro-Channels: An Enhanced Quasi-2D Numerical Model for Turbulent Flows
,”
Int. Commun. Heat Mass Transfer
,
111
, p.
104448
.10.1016/j.icheatmasstransfer.2019.104448
5.
Kirkland
,
W. M.
,
2019
, “
A Polytropic Approximation of Compressible Flow in Pipes With Friction
,”
ASME J. Fluids Eng.
,
141
(
12
), p.
121404
.10.1115/1.4043717
6.
Cavazzuti
,
M.
, and
Corticelli
,
M. A.
,
2017
, “
Numerical Modelling of Fanno Flows in Micro Channels: A Quasi-Static Application to Air Vents for Plastic Moulding
,”
Therm. Sci. Eng. Prog.
,
2
, pp.
43
56
.10.1016/j.tsep.2017.04.004
7.
Landram
,
C. S.
,
1997
, “
One-Dimensional, Steady Compressible Flow With Friction Factor and Uniform Heat Flux at the Wall Specified
,” Lawrence Livermore National Laboratory, Livermore, CA, Report No.
UCRL-ID-128670
.https://www.osti.gov/servlets/purl/591781
8.
Nouri-Borujerdi
,
A.
, and
Ziaei-Rad
,
M.
,
2009
, “
Simulation of Compressible Flow in High Pressure Buried Gas Pipelines
,”
Int. J. Heat Mass Transfer
,
52
(
25–26
), pp.
5751
5758
.10.1016/j.ijheatmasstransfer.2009.07.026
9.
Michaelides
,
E. E.
, and
Parikh
,
S.
,
1983
, “
The Prediction of Critical Mass Flux by the Use of Fanno Lines
,”
Nucl. Eng. Des.
,
75
(
1
), pp.
117
124
.10.1016/0029-5493(83)90085-7
10.
Noorbehesht
,
N.
, and
Ghaseminejad
,
P.
,
2013
, “
Numerical Simulation of the Transient Flow in Natural Gas Transmission Lines Using a Computational Fluid Dynamic Method
,”
Am. J. Appl. Sci.
,
10
(
1
), pp.
24
34
.10.3844/AJASSP.2013.24.34
11.
Deodhar
,
S. D.
,
Kothadia
,
H. B.
,
Iyer
,
K. N.
, and
Prabhu
,
S. V.
,
2015
, “
Experimental and Numerical Studies of Choked Flow Through Adiabatic and Diabatic Capillary Tubes
,”
Appl. Therm. Eng.
,
90
, pp.
879
894
.10.1016/j.applthermaleng.2015.07.073
12.
Agrawal
,
N.
, and
Bhattacharyya
,
S.
,
2007
, “
Adiabatic Capillary Tube Flow of Carbon Dioxide in a Transcritical Heat Pump Cycle
,”
Int. J. Energy Res.
,
31
(
11
), pp.
1016
1030
.10.1002/er.1294
13.
Kumar
,
N. S.
, and
Ooi
,
K. T.
,
2014
, “
One Dimensional Model of an Ejector With Special Attention to Fanno Flow Within the Mixing Chamber
,”
Appl. Therm. Eng.
,
65
(
1–2
), pp.
226
235
.10.1016/j.applthermaleng.2013.12.055
14.
Cioffi
,
M.
,
Puppo
,
E.
, and., and
Silingardi
,
A.
, “
Fanno Design of Blow-Off Lines in Heavy Duty Gas Turbine
,”
ASME
Paper No. GT2013-95024.10.1115/GT2013-95024
15.
Kawashima
,
D.
, and
Asako
,
Y.
,
2014
, “
Data Reduction of Friction Factor of Compressible Flow in Micro-Channels
,”
Int. J. Heat Mass Transfer
,
77
, pp.
257
261
.10.1016/j.ijheatmasstransfer.2014.05.009
16.
Cavazzuti
,
M.
,
Corticelli
,
M. A.
, and
Karayiannis
,
T. G.
,
2019
, “
Compressible Fanno Flows in Micro-Channels: An Enhanced Quasi-2D Numerical Model for Laminar Flows
,”
Therm. Sci. Eng. Prog.
,
10
, pp.
10
26
.10.1016/j.tsep.2019.01.003
17.
Dittus
,
F. W.
, and
Boelter
,
L. M. K.
,
1985
, “
Heat Transfer in Automobile Radiators of the Tubular Type
,”
Int. Commun. Heat Mass Transfer
,
12
(
1
), pp.
3
22
.10.1016/0735-1933(85)90003-X
18.
Sieder
,
E.
, and
Tate
,
G.
,
1936
, “
Heat Transfer and Pressure Drop of Liquids in Tubes
,”
Ind. Eng. Chem.
,
28
(
12
), pp.
1429
1435
.10.1021/ie50324a027
19.
Guo
,
Z. Y.
, and
Wu
,
X. B.
,
1997
, “
Compressibility Effect on the Gas Flow and Heat Transfer in a Microtube
,”
Int. J. Heat Mass Transfer
,
40
(
13
), pp.
3251
3524
.10.1016/S0017-9310(96)00323-7
20.
Forbes Dewey
,
C.
,
1965
, “
A Correlation of Convective Heat Transfer and Recovery Temperature Data for Cylinders in Compressible Flow
,”
Int. J. Heat Mass Transfer
,
8
(
2
), pp.
245
252
.10.1016/0017-9310(65)90111-0
21.
Cardemil
,
J. M.
, and
Colle
,
S.
,
2012
, “
A General Model for Evaluation of Vapor Ejector Performance for Application in Refrigeration
,”
Energy Convers. Manage.
,
64
, pp.
79
86
.10.1016/j.enconman.2012.05.009
22.
Stocker
,
W. F.
, and
Jones
,
J. W.
,
1982
,
Refrigeration and Air-Conditioning
,
McGraw-Hill
,
New York
.
23.
Chan
,
S. K.
, and
Woods
,
W. A.
,
1992
, “
On Rayleigh and Fanno Flows of Homogeneous Equilibrium Two-Phase Fluids
,”
Int. J. Heat Fluid Flow
,
13
(
3
), pp.
273
281
.10.1016/0142-727X(92)90041-7
24.
Kim
,
J. S.
, and
Singh
,
N. R.
,
2012
, “
A Novel Adiabatic Pipe Flow Equation for Ideal Gases
,”
ASME J. Fluids Eng.
,
134
(
1
), p.
011202
.10.1115/1.4005679
25.
Christians
,
J.
,
2012
, “
Approach for Teaching Polytropic Processes Based on the Energy Transfer Ratio
,”
Int. J. Mech. Eng. Edu.
,
40
(
1
), pp.
53
65
.10.7227/IJMEE.40.1.9
26.
Shapiro
,
A.
,
1953
,
The Dynamics and Thermodynamics of Compressible Fluid Flow
, Vol.
1
,
Wiley
,
New York
.
27.
Ferrari
,
A.
, and
Mittica
,
A.
,
2013
, “
Thermodynamic Formulation of the Constitutive Equations for Solids and Fluids
,”
Energy Convers. Manage.
,
66
, pp.
77
86
.10.1016/j.enconman.2012.09.028
28.
Toro
,
E. F.
,
2009
,
Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction
, 3rd ed.,
Springer Verlag
,
Heidelberg, Germany
.
29.
Zucker
,
R. D.
, and
Biblarz
,
O.
,
2002
,
Fundamental of Gas Dynamics
,
Wiley
,
New York
.
30.
Ferrari
,
A.
,
2019
,
Fondamenti di Termofluidodinamica per le Macchine
, Vol.
I
,
CittàStudi, De Agostini
,
Biella, Italy
.
You do not currently have access to this content.