A numerical model was included in a three-dimensional viscous solver to account for real gas effects in the compressible Reynolds averaged Navier-Stokes (RANS) equations. The behavior of real gases is reproduced by using gas property tables. The method consists of a local fitting of gas data to provide the thermodynamic property required by the solver in each solution step. This approach presents several characteristics which make it attractive as a design tool for industrial applications. First of all, the implementation of the method in the solver is simple and straightforward, since it does not require relevant changes in the solver structure. Moreover, it is based on a low-computational-cost algorithm, which prevents a considerable increase in the overall computational time. Finally, the approach is completely general, since it allows one to handle any type of gas, gas mixture or steam over a wide operative range. In this work a detailed description of the model is provided. In addition, some examples are presented in which the model is applied to the thermo-fluid-dynamic analysis of industrial turbomachines.

Issue Section:
Technical Papers
Keywords:
computational fluid dynamics, gas mixtures, compressible flow, Navier-Stokes equations, computational complexity
Topics:
Computation, Computational fluid dynamics, Design, Flow (Dynamics), Fluids, Impellers, Interpolation, Pressure, Steam, Turbomachinery, Density, Algorithms, Temperature, Blades, Fittings, Gases, Reynolds-averaged Navier–Stokes equations, Computer simulation
1.
Young
,
J. B.
,
1988
, “
An Equation of State for Steam for Turbomachinery and Other Flow Computations
,”
ASME J. Fluids Eng.
,
110
, pp.
1
–
7
.
2.
Benedict
,
M.
,
Webb
,
G. B.
, and
Rubin
,
L. C.
,
1951
, “
An Empirical Equation for Thermodynamic Properties of Light Hydrocarbons and Their Mixtures
,”
Chem. Eng. Prog.
,
47
(
8
), p.
419
419
.
3.
Jacobsen
,
R. T.
, and
Stewart
,
R. B.
,
1973
, “
Thermodynamic Properties of Nitrogen Including Liquid and Vapor Phases From 63 K to 2000 K With Pressures to 10,000 Bar
,”
J. Phys. Chem. Ref. Data
,
2
, pp.
757
–
922
.
4.
Cravero, C., and Satta, A., 2000, “A CFD Model for Real Gas Flows,” ASME Paper 2000-GT-518.
5.
Pa´tek
,
J.
,
1996
, “
Functional Forms to Describe Thermodynamic Properties of Gases for Fast Calculations
,”
ASME Journal of Engineering for Gas Turbine and Power
,
118
, pp.
210
–
213
.
6.
Dierckx, P., 1993, Curve and Surface Fitting With Splines, Oxford University Press, New York.
7.
IAPWS, 1997, “IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam,” IAPWS Release, IAPWS Secretariat, Technical Report.
8.
Harvey, A. H., Peskin, A. P., and Klein, S. A., 2000, “NIST/ASME Steam Properties,” NIST Standard Reference Database 10, Version 2.2, Standard Reference Data Program, National Institute of Standards and Technology, Gaithersburg, MD.
9.
Wagner
,
W.
,
Cooper
,
J. R.
,
Dittmann
,
A.
,
Kijima
,
J.
,
Kretzschmar
,
H.-J.
,
Kruse
,
A.
,
Maresˇ
,
R.
,
Oguchi
,
K.
,
Sato
,
H.
,
Sto¨cker
,
I.
,
Sˇifner
,
O.
,
Takaishi
,
Y.
,
Tanishita
,
I.
,
Tru¨benbach
,
J.
, and
Willkommen
,
T.
,
2000
, “
The IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam
,”
ASME J. Eng. Gas Turbines Power
,
122
, pp.
150
–
182
.
10.
Benzler
,
H.
, and
Koch
,
A. V.
,
1955
, “
Ein Zustandsdiagram fu¨r Athylen bis zu 10,000 Ata Druck
,”
Chem.-Ing.-Tech.
,
27
(
2
), p.
71
71
.
11.
Schultz
,
J. M.
,
1962
, “
The Polytropic Analysis of Centrifugal Compressors
,” ASME J. Eng. Gas Turbines Power, 69.
12.
Cooper
,
H. W.
, and
Goldfrank
,
J. C.
,
1967
, “
B-W-R Constants and New Correlations
,”
Hydrocarbon Process.
,
46
(
12
), p.
141
141
.
13.
Lee
,
B. I.
, and
Kesler
,
M. G.
,
1975
, “
A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States
,” AIChE J., 21(3).
14.
Lin
,
H.
, and
Chao
,
K.
,
1984
, “
Correlation of Critical Properties and Acentric Factor of Hydrocarbons and Derivatives
,” AIChE J., 30(6).
15.
Arnone
,
A.
,
Liou
,
M. S.
, and
Povinelli
,
L. A.
,
1993
, “
Multigrid Calculation of Three-Dimensional Viscous Cascade Flows
,”
J. Propul. Power
,
9
(
4
), pp.
605
–
614
.
16.
Baldwin, B. S., and Lomax, H., 1978, “Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows,” AIAA paper, 78, p. 257.
17.
Arnone
,
A.
, and
Pacciani
,
R.
,
1998
, “
IGV-Rotor Interaction Analysis in a Transonic Compressor Using the Navier-Stokes Equations
,”
ASME J. Turbomach.
,
120
(
1
), pp.
143
–
155
.
18.
Spalart, P., and Allmaras, S., 1992, “A One-Equation Turbulence Model for Aerodynamic Flows,” AIAA Paper 92-0439.
19.
Menter, F. R., 1993, “Zonal Two-Equations k-ω Turbulence Models for Aerodynamic Flows,” AIAA Paper 93-2906.
20.
Arnone
,
A.
,
1994
, “
Viscous Analysis of Three-Dimensional Rotor Flow Using a Multigrid Method
,”
ASME J. Turbomach.
,
116
, pp.
435
–
445
.
21.
Rogers, D. F., and Adams, J. A., 1990, Mathematical Elements for Computer Graphics, WBC/McGraw-Hill, New York.
Copyright © 2004
 by ASME
You do not currently have access to this content.