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Research Papers: Fundamental Issues and Canonical Flows

A Small Disturbance Model for Transonic Flow of Pure Steam With Condensation

[+] Author and Article Information
Akashdeep Singh Virk

Department of Mechanical, Aerospace
and Nuclear Engineering,
Rensselaer Polytechnic Institute,
110 8th Street,
Troy, NY 12180
e-mail: virka@rpi.edu

Zvi Rusak

Professor
Department of Mechanical, Aerospace
and Nuclear Engineering,
Rensselaer Polytechnic Institute,
110 8th Street,
Troy, NY 12180
e-mail: rusakz@rpi.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 21, 2018; final manuscript received August 29, 2018; published online October 5, 2018. Assoc. Editor: Samuel Paolucci.

J. Fluids Eng 141(3), 031204 (Oct 05, 2018) (13 pages) Paper No: FE-18-1109; doi: 10.1115/1.4041390 History: Received February 21, 2018; Revised August 29, 2018

A small-disturbance model to study transonic steady condensing flow of pure steam around a thin airfoil is developed. Water vapor thermodynamics is described by the perfect gas model and its dynamics by the compressible inviscid flow equations. Classical nucleation and droplet growth theory for homogeneous and nonequilibrium condensation is used to compute the condensate mass fraction. The model is derived from an asymptotic analysis of the flow and condensation equations in terms of the proximity of upstream flow Mach number to 1, the small thickness ratio of airfoil, the small quantity of condensate, and the small angle-of-attack. The flow field may be described by a nonhomogeneous and nonlinear partial differential equation along with a set of four ordinary differential equations for calculating condensate mass fraction. The analysis provides a list of similarity parameters that describe the flow physics. A numerical scheme, which is composed of Murman and Cole's algorithm for the computation of flow parameters and Simpson's integration method for calculation of condensate mass fraction, is applied. The model is used to analyze the effects of heat release due to condensation on the aerodynamic performance of airfoils operating in steam at high temperatures and pressures near the vapor–liquid saturation dome.

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References

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Figures

Grahic Jump Location
Fig. 2

Computational domain around the airfoil

Grahic Jump Location
Fig. 3

Pressure coefficient (−Cp) distribution at the NACA0012 airfoil surface for wet steam flow at Θ=0, S∞=1.17,T∞=400 K,  p∞=2.88 bar and M∞=0.8 using several meshes and for dry steam flow at same conditions

Grahic Jump Location
Fig. 4

Condensate mass fraction (g) distribution at the NACA0012 airfoil surface for wet steam flow at Θ=0,S∞=1.17,T∞=400 K,  p∞=2.88 bar and M∞=0.8 using several meshes

Grahic Jump Location
Fig. 5

Pressure–temperature phase diagram along the NACA0012 airfoil surface for wet steam flow at Θ=0,S∞=1.17,T∞=400 K,  p∞=2.88 bar, and M∞=0.8 using several meshes

Grahic Jump Location
Fig. 6

Pressure coefficient (−Cp) distribution along the suction and pressure surfaces of the NACA0012 airfoil for dry air flow at p∞=65,600 Pa, T∞=259 K, M∞=0.8, and θ=1.25deg

Grahic Jump Location
Fig. 7

Pressure coefficient (−Cp) distribution at the NACA0012 airfoil surface for wet steam flow at Θ=0, M∞=0.8,T∞=400 K, and various S∞

Grahic Jump Location
Fig. 8

Condensate mass fraction (g) distribution at the NACA0012 airfoil surface for wet steam flow at Θ=0, M∞=0.8,T∞=400 K, and various S∞

Grahic Jump Location
Fig. 9

Drag coefficient (Cd) of the NACA0012 airfoil for wet steam flow at Θ = 0, M = 0.8, T = 400 K, and various S

Grahic Jump Location
Fig. 10

Pressure coefficient (−Cp) distribution at the NACA0012 airfoil surface for wet steam flow at Θ = 0, M = 0.8, S = 0.985, and various T

Grahic Jump Location
Fig. 11

Condensate mass fraction (g) distribution at the NACA0012 airfoil surface for wet steam flow at Θ = 0, M = 0.8, S = 0.985, and various T

Grahic Jump Location
Fig. 12

Drag coefficient (Cd) of the NACA0012 airfoil for wet steam flow at Θ = 0, M = 0.8, S = 0.985, and various T

Grahic Jump Location
Fig. 13

Pressure coefficient (−Cp) distribution at the NACA0012 airfoil surface for wet steam flow at Θ = 0, T = 400 K, S = 1.1, and various M

Grahic Jump Location
Fig. 14

Condensate mass fraction (g) distribution at the NACA0012 airfoil surface for wet steam flow at Θ = 0, T = 400 K, S = 1.1, and various M

Grahic Jump Location
Fig. 15

Drag coefficient (Cd) of the NACA0012 airfoil for wet steam flow at Θ = 0, T = 400 K, S = 1.1, and various M

Grahic Jump Location
Fig. 16

Pressure coefficient (−Cp) distribution along the suction surface of the NACA0012 airfoil for wet steam flow at M = 0.8, T = 400 K, S = 1.0, and various θ

Grahic Jump Location
Fig. 17

Pressure coefficient (−Cp) distribution along the pressure surface of the NACA0012 airfoil for wet steam flow at M = 0.8, T = 400 K, S = 1.0, and various θ

Grahic Jump Location
Fig. 18

Condensate mass fraction (g) distribution along the suction surface of the NACA0012 airfoil for wet steam flow at M = 0.8, T = 400 K, S = 1.0, and various θ

Grahic Jump Location
Fig. 19

Drag coefficient (Cd) of the NACA0012 airfoil for wet steam flow at M = 0.8, T = 400 K, S = 1.0, and various θ

Grahic Jump Location
Fig. 20

Lift coefficient (Cl) of the NACA0012 airfoil for wet steam flow at M = 0.8, T = 400 K, S = 1.0, and various θ

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