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Turbulent flow investigation inside and outside plain-orifice atomizers with rounded orifice inlets

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Abstract

The performances of three linear eddy viscosity models (LEVM) and one algebraic Reynolds stress model (ARSM) on the simulation of the internal and external flows in the plain-orifice atomizers with rounded orifice inlets are evaluated. The validity of the computational model is first assessed through the testing of a backward facing step flow, a sudden expansion pipe flow and a liquid column collapsing problem. Then the atomizer internal and external flows are analyzed by comparing the computed discharge coefficients with available experimental data and by comparing the turbulence intensity profiles at the orifice exit. The results are also illustrated by the fluid/air interface plot. It is found that the turbulence models investigated exhibit zonal behaviors, i.e., none of the models investigated performs well throughout the entire flow field. It is worthwhile to note that the standard k-εmodel is not necessarily the worst among the models investigated. In average, the ARSM model gives better results as compared to the standard k-εmodel and the low Reynolds number models. The turbulence strength has a significant influence on the global characteristics of the flow field. The models with better predictions of the turbulence kinetic energy, such as Gatski–Speziale’s ARSM model and Nagano–Hishida’s low Reynolds number model, can yield better predictions of the global characteristics of the flow field, e.g., the reattachment lengths for the backward-facing step flow and the sudden expansion pipe flow, and the discharge coefficient for the atomizer flow.

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Abbreviations

Cε1, Cε2, Cμ:

Turbulence model coefficients

C d :

discharge coefficient

d :

orifice diameter

D :

inlet pipe diameter; also LRN turbulence model function

E :

LRN turbulence model function

f :

volume fraction

f1, f2, fμ:

viscous damping functions for LRN turbulence model

g :

gravitational acceleration

H :

characteristic length

k :

non-dimensionalized turbulence intensity; ≡ k*/u *2in

l/d:

orifice length/diameter ratio

p :

non-dimensionalized pressure; \( \equiv \frac{{p^* - p_{{\text{ref}}}^* }} {{\rho _l^* u_{{\text{in}}}^{*2} }}\) for atomizer flow; \( \equiv \frac{{p^* - p_{{\text{ref}}}^* }} {{\rho ^* u_{{\text{in}}}^{*2} }}\) for other flows

Re:

Reynolds number; \( \equiv \rho _l^* \bar u_{\text{e}}^* d/\mu _l^* \) for atomizer flow; \( \equiv \rho ^* u_{{\text{in}}}^* H/\mu ^* \) for other flows

\(\tilde R_k^{} \) :

turbulent Reynolds number; \( \equiv \frac{{\sqrt {k^* } y^* }} {{\upsilon ^* }}\)

\(\tilde R_t^{} \) :

turbulent Reynolds number; \( \equiv \frac{{k^{*2} }} {{\upsilon ^* \varepsilon ^* }}\)

S Φ :

source term

t :

time

(u,v):

non-dimensionalized physical velocity; ≡ (u*, v*)/u *in

We:

Weber number; ≡ (ρ * l u *2in d)/γ

(x,y):

non-dimensionalized coordinates; ≡(x*, y*)/d for atomizer flow; ≡(x*, y*)/H for other flows

y n :

normal distance between wall and neighboring grid point

y + :

uτ y*/ν*; \(u_\tau = \sqrt {\frac{{\tau _{\text{w}} }} {{\rho ^* }}} \)

Yc:

Yap correction

ΓΦ:

diffusion coefficient

Φ:

dependent variable

γ:

surface tension coefficient

ɛ:

non-dimensionalized turbulence dissipation rate; ≡ ɛ*/(u *3in /d) for atomizer flow; ≡ ɛ */(u *3in /H) for other flows

μ:

non-dimensionalized viscosity; ≡ μ*/μ * l for atomizer flow; ≡ 1 for other flows

μ t :

non-dimensionalized turbulent viscosity; ≡ μ t */μ * l for atomizer flow; ≡ μ t */μ * for other flows

ρ:

non-dimensionalized density; ≡ ρ */ρ * l for atomizer flow; ≡ 1 for other flows

σk, σε:

turbulent diffusion coefficients for k and ε, respectively

τ:

non-dimensionalized time; ≡ (u *in /d)t for atomizer flow; ≡ (u *in /H)t for other flows

τ w :

wall shear stress

ν:

non-dimensionalized kinematic viscosity; ≡ μ/ρ

a:

air

e:

atomizer exit

in:

entrance pipe inlet; also inlet for other flows

l:

liquid

nb:

neighboring grid points

P:

main grid point

ref:

reference state

w:

water; also wall

*:

dimensional quantity

–:

average quantity

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Acknowledgements

The author gratefully acknowledges the grant support from the National Science Council, R.O.C., under the contract NSC93-2212-E-150-018.

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  1. Department of Aeronautical Engineering, National Formosa University, Huwei, Yunlin 632, Taiwan, R.O.C

    Chun-Lang Yeh

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Yeh, CL. Turbulent flow investigation inside and outside plain-orifice atomizers with rounded orifice inlets. Heat Mass Transfer 41, 810–823 (2005). https://doi.org/10.1007/s00231-005-0632-y

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