Minimum momentum flux ratio required to prevent air curtain breakthrough in case of cross-curtain pressure gradients: CFD versus analytical equation

Abstract

This paper presents a numerical study on the required momentum flux ratio to prevent air curtain breakthrough in case of cross-curtain (i.e. cross-jet) pressure gradients. 2D steady Reynolds-averaged Navier-Stokes (RANS) CFD simulations with the RNG k-ε turbulence model are employed for jet Reynolds numbers ranging from 5,000 to 30,000. First, the computational model is validated based on particle image velocimetry (PIV) measurements. Second, the influence of several jet parameters on the separation efficiency is evaluated for a moderate cross-jet pressure difference of 10 Pa. These are the ratio of the jet discharge momentum flux to the jet cross-flow momentum flux (momentum flux ratio), the jet height-to-width ratio and the jet discharge angle. Finally, the minimum deflection modulus to prevent jet breakthrough and the corresponding momentum flux ratio by an analytical equation and by CFD are compared. The results show that, for the configuration under study: (1) jets with the smallest height-to-width ratios (β = 18) provide the highest separation efficiency; (2) inclined jets with discharge angles α0 = 5° and 10° provide slightly higher separation efficiency than straight jets (α0 = 0°) and jets with α0 = 20°; (3) the maximum modified separation efficiency is reached at lower momentum flux ratios for jets with smaller height-to-width ratios and for inclined jets; (4) the analytical and CFD values of the optimal momentum flux ratio differ with up to 31.2%. This study shows how the separation efficiency of air curtains can be improved by adjusting certain jet parameters.

Abbreviations

d jet :

nozzle depth [m]

D :

depth [m]

D m :

deflection modulus [—]

D m,min :

minimum deflection modulus [—]

D s :

diameter of PIV seeding particles [m]

f middle :

solution for mean velocity obtained on the middle grid [m/s] solution for turbulent kinetic energy obtained on the middle grid [m2/s2]

f coarse :

solution for mean velocity obtained on the coarse grid [m/s] solution for turbulent kinetic energy obtained on the coarse grid [m2/s2]

FAC1.1:

factor of 1.1 of the observations [—]

FAC1.5:

factor of 1.5 of the observations [—]

F S :

safety factor used for grid convergence index [—]

g :

gravitational acceleration [m/s2]

h c :

height of contraction [m]

h jet :

jet height [m]

H :

height [m]

H d :

doorway height [m]

k :

turbulent kinetic energy [m2/s2]

L :

length [m]

M cf :

cross-flow momentum flux [kg/s2]

M jet :

jet discharge momentum flux [kg/s2]

M jet,min :

jet discharge momentum flux corresponding to Dm,min [kg/s2]

M jet,sf :

jet discharge momentum flux Mjet,min corrected by a safety factor of 2 [kg/s2]

n :

number of data points [—]

ni :

outward normal vector [—]

O i :

time-averaged values of mean velocity obtained from PIV experiments (observations) [m/s] time-averaged values of turbulent kinetic energy obtained from PIV experiments (observations) [m2/s2]

ΔP :

cross-jet static pressure gradient [Pa]

P i :

time-averaged values (predictions) of mean velocity obtained from CFD simulations [m/s] time-averaged values (predictions) of turbulent kinetic energy obtained from CFD simulations [m2/s2]

P l :

mean static pressure in left side of enclosure [Pa]

P r :

mean static pressure in right side of enclosure [Pa]

Q 0 :

heat or pollutant mass transfer rate by transport of outdoor air through the opening to the indoor environment without AC in operation (infiltration) [kg/s]

Q*0 :

heat or mass transfer rate by transport of indoor air through the opening to the outdoor environment (exfiltration) without AC in operation [kg/s]

Q ac :

heat or pollutant mass transfer rate by transport of outdoor air through the opening to the indoor environment (infiltration) with AC in operation [kg/s]

Q*ac :

heat or mass transfer rate by transport of indoor air through the opening to the outdoor environment (exfiltration) and by transport of air originating from the AC to the outdoor environment with AC in operation [kg/s]

p :

formal order of accuracy used for grid convergence index [—]

r :

linear grid refinement factor for grid sensitivity analysis [—]

Re :

Reynolds number [—]

Re y :

wall-distance-based Reynolds number [—]

Sc t :

turbulent Schmidt number [—]

U :

mean lateral (x-direction) velocity component [m/s]

U cf :

the average velocity of the cross-flow through the enclosure created by the pressure gradient for the case without AC in operation [m/s]

|V| :

mean velocity magnitude [m/s]

V→:

mean velocity vector [m/s]

|V0|:

mean jet velocity magnitude at the nozzle exit [m/s]

V :

mean streamwise (y-direction) velocity component [m/s]

V 0 :

mean streamwise jet velocity at the nozzle exit [m/s]

w jet :

jet width at the nozzle exit [m]

w jet :

jet width downstream the nozzle exit at y = hjet [m]

x :

Cartesian coordinate [m]

y :

Cartesian coordinate [m]

y*:

dimensionless wall distance [—]

Y cl :

clean water mass fraction [—]

Y pol :

pollutant mass fraction [—]

α :

angle of the jet centerline downstream of the nozzle exit at y = hjet [°]

α 0 :

jet discharge angle [°]

β :

jet height-to-width ratio [—]

γ :

momentum flux ratio [—]

γ CFD :

optimal momentum flux ratio as obtained from the CFD simulations [—]

γ min :

minimum momentum flux ratio as obtained from the analytical equation [—]

γ sf :

momentum flux ratio as obtained from the analytical equation and corrected by a safety factor [—]

δγ :

relative difference between momentum flux ratios [—]

ε :

turbulence dissipation rate [m2/s3]

η :

separation efficiency [—]

η*:

modified separation efficiency [—]

ρ :

fluid density [kg/m3]

ρ i :

density of indoor air [kg/m3]

ρ o :

density of outdoor air [kg/m3]

ρs:

density of the PIV seeding particles [kg/m3]

ρ w :

density of water [kg/m3]

ν :

kinematic viscosity [m2/s]

2D:

two-dimensional

3D:

three-dimensional

AC:

air curtain

AR:

aspect ratio, i.e. the ratio of nozzle depth djet to width wjet

CFD:

computational fluid dynamics

GCI:

grid convergence index

LES:

large eddy simulation

LRNM:

low-Reynolds number modeling

PIV:

particle image velocimetry

PTIJ:

plane turbulent impinging jet

RANS:

Reynolds-averaged Navier-Stokes

RNG:

renormalization group k-ε turbulence model

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Acknowledgements

Twan van Hooff is currently a postdoctoral fellow of the Research Foundation–Flanders (FWO) and acknowledges its financial support (project FWO 12R9718N). The authors acknowledge the partnership with ANSYS CFD.

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Correspondence to Adelya Khayrullina.

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Khayrullina, A., van Hooff, T., Alanis Ruiz, C. et al. Minimum momentum flux ratio required to prevent air curtain breakthrough in case of cross-curtain pressure gradients: CFD versus analytical equation. Build. Simul. 13, 943–960 (2020). https://doi.org/10.1007/s12273-020-0633-2

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Keywords

  • plane turbulent jet
  • air curtain
  • separation efficiency
  • CFD