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A Finite Volume Procedure for Thermofluid System Analysis in a Flow Network

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50 Years of CFD in Engineering Sciences

Abstract

This paper describes a finite volume procedure for network flow analysis in a thermofluid system. A flow network is defined as a group of interconnected control volumes called ‘nodes’ that are connected by ‘branches.’ The mass and energy conservation equations are solved at the nodes and momentum conservation equations are solved at the branches. The flow network also includes solid nodes to account for fluid to solid heat transfer. The heat conduction equation is solved at the solid nodes in conjunction with the flow equations. The properties of a real fluid are calculated using a thermodynamic property program and used in the conservation equations. The system of equations describing the fluid–solid network is solved by a hybrid numerical method that is a combination of the Newton-Raphson and successive substitution method. This procedure has been incorporated into a general-purpose computer program, the Generalized Fluid System Simulation Program (GFSSP). This paper also presents the application and verification of the method by comparison with test data for several applications that include (1) internal flow in a rocket engine turbopump, (2) pressurization and loading of a cryogenic propellant tank, (3) fluid transient during a sudden opening of the valve for priming of an evacuated feed line, and (4) chilldown of a cryogenic transfer line with phase change and two-phase flows. This paper also presents the extension of this finite volume-based network flow method to perform multidimensional flow calculation.

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Abbreviations

A :

Area

C L :

Flow coefficient

c i,k :

Mass concentration of kth specie at ith node

C p :

Specific heat

D :

Diameter

f :

Darcy friction factor

g :

Gravitational acceleration

g c :

Conversion constant (=32.174 lb-ft/lbf-s2) for English unit (=1 for SI unit)

h :

Enthalpy

h ij :

Heat transfer coefficient

J :

Mechanical equivalent of heat (778 ft-lbf/Btu) for English unit (=1 for SI unit)

K :

Nondimensional head loss factor

K f :

Flow resistance coefficient

K rot :

Slip factor of rotating branch

k :

Thermal conductivity

L :

Length

LH 2 :

Liquid hydrogen

LN 2 :

Liquid nitrogen

LO 2 :

Liquid oxygen

m :

Resident mass

\(\dot{m}\) :

Mass flow rate

Nu:

Nusselt number

n :

Number of branches connected to a node

Pr:

Prandtl number

P R :

Ratio of reservoir pressure and air pressure

p :

Pressure

Q, q:

Heat source

Re:

Reynolds number (Re = ρuD/μ)

R :

Gas constant

r :

Radius

S :

Momentum source

s :

Entropy

T :

Fluid temperature

T s :

Solid temperature

u :

Velocity

V :

Volume

x :

Quality and mass fraction

Y :

Two-phase factor in Miropolsky correlation

z :

Compressibility factor

α :

Void fraction of air

γ :

Specific heat ratio

Δ :

Time step

Δh :

Head loss

ε :

Absolute roughness

ε/D :

Relative roughness

ε ij :

Emissivity

θ :

Angle between branch flow velocity vector and gravity vector (deg)

μ :

Viscosity

ρ :

Density

σ :

Stefan-Boltzmann constant

τ :

Time

ν :

Kinematic viscosity

ω :

Angular velocity

a :

Ambient

c :

Convection

cr :

Critical

f :

Fluid

g :

Generation

i :

Node index

ij :

Branch index

k :

Fluid index

p :

Index for neighboring branch

r :

Radiation

s :

Solid, surface area for shear

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Acknowledgements

This paper is dedicated to the memory of Professor D. B. Spalding who inspired and guided the author to develop understanding and expertise in the fascinating field of computational thermofluid dynamics and heat transfer. The author wants to acknowledge NASA Marshall Space Flight Center for the opportunity and resources for the continuous development of GFSSP for the last 25 years. The author also appreciates the contribution and support of Dr. Andre LeClair, Mr. Derek Moody, and other members of the GFSSP development team.

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Authors and Affiliations

  1. NASA Marshall Space Flight Center, Huntsville, AL, 35812, USA

    Alok Majumdar

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  1. Alok Majumdar
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Correspondence to Alok Majumdar .

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Editors and Affiliations

  1. ACRI, The CFD Innovators, Los Angeles, CA, USA

    Akshai Runchal

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Majumdar, A. (2020). A Finite Volume Procedure for Thermofluid System Analysis in a Flow Network. In: Runchal, A. (eds) 50 Years of CFD in Engineering Sciences. Springer, Singapore. https://doi.org/10.1007/978-981-15-2670-1_7

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  • DOI: https://doi.org/10.1007/978-981-15-2670-1_7

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-2669-5

  • Online ISBN: 978-981-15-2670-1

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