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Numerical investigation of turbulent free jet flows issuing from rectangular nozzles: the influence of small aspect ratio

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Abstract

In this research, the fluid and thermal characteristics of a rectangular turbulent jet flow is studied numerically. The results of three-dimensional jet issued from a rectangular nozzle are presented. A numerical method employing control volume approach with collocated grid arrangement was employed. Velocity and pressure fields are coupled with SIMPLEC algorithm. The turbulent stresses are approximated using k–\({\varepsilon}\) model with two different inlet conditions. The velocity and temperature fields are presented and the rates of their decay at the jet centerline are noted. The velocity vectors of the main flow and the secondary flow are illustrated. Also, effect of aspect ratio on mixing in rectangular cross-section jets is considered. The aspect ratios that were considered for this work were 1:1 to 1:4. The results showed that the jet entrains more with smaller AR. Special attention has been drawn to the influence of the Reynolds number (based on hydraulic diameter) as well as the inflow conditions on the evolution of the rectangular jet. An influence on the jet evolution is found for smaller Re, but the jet is close to a converged state for higher Reynolds numbers. The inflow conditions have considerable influence on the jet characteristics.

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Abbreviations

AR:

Nozzle aspect ratio (AR = L zi /L yi )

c μ :

k–\({\varepsilon}\) Turbulence model constant

c 1 :

k–\({\varepsilon}\) Turbulence model constant

c 2 :

k–\({\varepsilon}\) Turbulence model constant

D :

Equivalent circular jet diameter, m

I :

Turbulence intensity

k :

Mean turbulence kinetic energy per unit mass, m2 s−2

L x :

Length of the computational domain in the x-direction, m

L y :

Length of the computational domain in the y-direction, m

L yi :

Half-length of the inlet vent in the y-direction, m

L z :

Length of the computational domain in the z-direction, m

L zi :

Half-length of the inlet vent in the y-direction, m

M :

Momentum, kgms−2

p :

Pressure, Pa

P k :

Turbulence production due to viscous forces, kgm−1 s−3

Pr :

Prandtl number

Prt :

Turbulent Prandtl number

Re :

Reynolds number based on hydraulic diameter

T :

Temperature, K

u :

Time-averaged velocity component in the x-direction, ms−1

\({{u}^{\prime}_i}\) :

Velocity fluctuations in the x i directions, ms−1

v :

Time-averaged velocity component in the y-direction, ms−1

w :

Time-averaged velocity component in the z-direction, ms−1

x :

Cartesian coordinate along the stream-wise length of domain, m

y :

Cartesian coordinate along the span-wise length of domain, m

y 1/2 :

Half-velocity width in the y-direction based on the u-velocity [u(y 1/2) = u cl/2], m

yt 1/2 :

Half-temperature width in the y-direction [T(yt 1/2) = T cl/2], m

z :

Cartesian coordinate along the lateral length of domain, m

z 1/2 :

Half-velocity width in the z direction based on the u-velocity [u(z 1/2) = u cl/2], m

α :

Thermal diffusivity, m2 s

α t :

Turbulent thermal diffusivity, m2 s

\({\delta_{ij}}\) :

Kronecker delta

\({\varepsilon}\) :

Turbulent dissipation rate, m2 s−3

μ :

Dynamic viscosity, Nsm−2

μ t :

Eddy viscosity, Nsm−2

ρ :

Density, kgm−3

\({\sigma_k}\) :

Turbulence model constant for the k equation

\({\sigma_\varepsilon }\) :

k–\({\varepsilon}\) Turbulence model constant

cl:

At the jet centerline

in:

At inlet plane of jet

inf:

At ambient

max:

Maximum

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Authors and Affiliations

  1. School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

    Ehsan Faghani, Reza Maddahian & Bijan Farhanieh

  2. Department of Civil Engineering, University of Tehran, Tehran, Iran

    Pedram Faghani

Authors
  1. Ehsan Faghani
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  2. Reza Maddahian
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  3. Pedram Faghani
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  4. Bijan Farhanieh
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Correspondence to Ehsan Faghani.

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Faghani, E., Maddahian, R., Faghani, P. et al. Numerical investigation of turbulent free jet flows issuing from rectangular nozzles: the influence of small aspect ratio. Arch Appl Mech 80, 727–745 (2010). https://doi.org/10.1007/s00419-009-0340-z

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