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Sensitivity study of momentum and turbulence models for subcooled boiling phenomena simulation

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Abstract

This sensitivity analysis of the momentum and turbulence equations uses the Eulerian two-phase approach and intends to achieve a validated modeling for subcooled boiling flows. The studied regime is relevant to many industry applications and to the critical heat flux phenomenon, an important process for design and safety analyses of water-cooled nuclear power plants. Ascending water flows in heated circular pipes are modeled under subcooled boiling condition and applying a combination of computational multi-fluid dynamics (CMFD) models, each one for the estimation of specific terms of the governing equations. Turbulence closure, drag, lift, turbulent interaction, turbulent dispersion, wall lubrication and interfacial area models are investigated through variations around a reference model set defined based on the literature review, changing each model one at a time to study their impacts on the simulation results. Key parameters, such as void fraction and temperature profiles, are chosen for the evaluation of the results. Despite the difficulty of tracking the contributions of simultaneously applied models, the Legendre–Magnaudet lift force and the Burns et al. turbulent dispersion force models show good agreement with the experimental data of a flow at 4.5 MPa used for the quality verification of the simulations. These models are also applied for flows with pressures ranging from 1.5 to 15 MPa, and they lead to promising results. This study gives interesting insights on the influence of the distinct models composing momentum and turbulence calculations, contributing to the validation effort of the CMFD approach for subcooled boiling flows.

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Abbreviations

A :

Area

A b :

Area covered with nucleate bubbles

A i :

Interphase interfacial area

C :

Reynolds stress convection term

C D :

Drag coefficient

Cke, Ctd :

Turbulence interaction model constants

C l :

Lift coefficient

c p :

Specific heat at constant pressure

C p :

Isobaric heat capacity

C wi :

Wall lubrication model i-th constant

C wl :

Wall lubrication coefficient

C μ :

Turbulence model coefficient

D :

Diameter

D L :

Reynolds stress molecular diffusion term

d p :

Droplets/particles diameter

\(\varvec{D}_{\text{pq}}\) :

Fluid-particulate dispersion tensor

D T :

Reynolds stress turbulent diffusion term

D t,pq :

Fluid-particulate dispersion scalar

D w :

Bubble departure diameter

Eo:

Eötvös number

f :

Drag function

F :

Reynolds stress system rotation term

f b :

Bubble departure frequency

\(\varvec{F}_{\text{drag}}\) :

Drag force

\(\varvec{F}_{\text{lift}}\) :

Lift force

\(\varvec{F}_{\text{td}}\) :

Turbulent dispersion force

\(\varvec{F}_{\text{vm}}\) :

Virtual mass force

\(\varvec{F}_{\text{wl}}\) :

Wall lubrication force

g :

Gravity magnitude

\(\varvec{g}\) :

Gravity vector

G :

Reynolds stress buoyance production term

h :

Volumetric heat transfer coefficient

\(\hat{h}\) :

Specific enthalpy

h c :

Single-phase heat transfer coefficient

h lv :

Latent heat of evaporation

Jasub :

Subcooled Jakob number

k :

Turbulent kinetic energy

K :

Interphase momentum exchange coefficient

m :

Power law constant

\(\dot{m}\) :

Interphase volumetric mass transfer

Mo:

Morton number

\(\varvec{n}_{\text{w}}\) :

Wall normal vector

N w :

Nucleate site density

Nu:

Nusselt number

p :

Pressure

P :

Reynolds stress production term

Pr:

Prandtl number

q :

Heat flux vector

\(\dot{q}\) :

Heat flux scalar

Q :

Interphase heat exchange

Re:

Reynolds number

\(\tilde{R}\) :

Reynolds stresses

S ϕ :

Generic source term

Sr:

Non-dimensional shear rate

t :

Time

T :

Temperature

\(\varvec{V}\) :

Velocity vector

y w :

Distance to the nearest wall

α :

Void fraction

γ :

Diffusion coefficient

\(\varGamma_{\phi }\) :

Generic diffusion coefficient

κ :

Thermal conductivity

µ :

Viscosity

ν :

Kinematic viscosity

ρ :

Density

σ :

Surface tension

σ pq :

Dispersion Prandtl number

ω :

Specific dissipation rate

\(\epsilon\) :

Turbulence dissipation rate

ϕ :

Generic turbulence scalar

\(\varPhi\) :

Reynolds stress pressure–strain term

\(\overline{\overline{\tau }}\) :

Stress–strain tensor

τ p :

Particulate relaxation time

τ t,p :

Characteristic time of the induced turbulence

λ RT :

Rayleigh–Taylor instability wavelength

μ t :

Turbulent viscosity

δt:

Time scale

\(\Delta T_{\text{sub}}\) :

Fluid subcooling

\(\Delta T_{\sup }\) :

Wall superheat

c:

Convective

cap:

Capped regime

dis:

Distorted regime

dr:

Drift

e:

Effective, evaporative

ij :

i-th and j-th element

l:

Liquid phase

m:

Mixture

p:

Secondary phase, vapor phase, particle

q:

Primary phase, liquid phase, quenching

sat:

Saturation

v:

Vapor phase

vis:

Viscous regime

w:

Wall

ω :

Vorticity

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  1. Instituto de Estudos Avançados (IEAv), Trevo Coronel Aviador José Alberto Albano do Amarante, 1, Putim, São José Dos Campos, SP, 12228-001, Brazil

    Brian de Lima Curtt & Francisco A. Braz Filho

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  1. Brian de Lima Curtt
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Correspondence to Brian de Lima Curtt.

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de Lima Curtt, B., Braz Filho, F.A. Sensitivity study of momentum and turbulence models for subcooled boiling phenomena simulation. J Braz. Soc. Mech. Sci. Eng. 42, 435 (2020). https://doi.org/10.1007/s40430-020-02500-5

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