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Nozzle exit conditions and the heat transfer in non-swirling and weakly swirling turbulent impinging jets

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Abstract

Investigations have been conducted into turbulent impinging jets but the exact flow dynamics and mechanisms leading to the observed heat transfer distributions at the impingement plane remain outstanding. In particular, use of different swirl generators (vanes, twisted inserts) means the role of varying inflow conditions (at the nozzle exit plane x/D = 0) should be studied to resolve its role on the observed convective heat transfer trends. The present paper studies axisymmetric turbulent weakly swirling (S = 0.31) jets (D = 40 mm) impinging onto a heated plate. Parameters varied include inflow conditions and the effects of impingement distance (H/D = 2, 4, and 6). The Reynolds Averaged Navier Stokes (RANS) equations are used to model the jets using the k-kl-ω turbulence model, which is benchmarked against other models. Three azimuthal (<w>) velocity profiles at a Reynolds (Re) number of 24,600 are used at the nozzle exit plane: Uniform (UP), Solid Body Rotation (SBR), and Parabolic Profiles (PP). The start of the wall jet region, designated through elevated levels of turbulent kinetic energy correlates well with the widely observed first peak in Nu distribution. This is however extremely sensitive to the imposition of any swirl, with the application of even weak swirl (S = 0.31) minimally modifying flow dynamics (in the upstream jet region) and leading to recirculation zones stabilized at the impingement plane. This occurs in near-field impingement (H/D) for some inflow conditions (S031-UP), but not others thereby highlighting the significance varied nozzle and swirl generation methods on trends observed in the literature. The imposition of elevated levels of turbulence at the nozzle inflow (x/D = 0) appreciably modifies the heat transfer distribution, particularly in far-field impingement (H/D = 6).

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Abbreviations

Ap :

Area of the jet exit plane or on the impingement surface (Experimental 0.06 m2)

Cμ :

Model constant (0.09)

Cp :

Pressure coefficient

cp:

Fluid heat capacity(J/K)

D:

Nozzle diameter at the exit plane

DL :

Anisotropic dissipation (kL)

DT :

Anisotropic dissipation (kT)

e:

Enthalpy (J/kg)

fW :

Inviscid near-wall damping function

fω :

Boundary layer wake term damping function

H:

Nozzle-to-plate distance

h:

Heat transfer coefficient

k:

Turbulent kinetic energy (J/kg)

Keff :

Effective thermal conductivity

kL :

Laminar kinetic energy

kT :

Turbulent kinetic energy(W/m2.k)

l:

Turbulent length scale (0.07D)

Nu(r):

Radially distributed Nusselt number

Nu0 :

Stagnation point Nusselt number

NuA :

Spatially averaged Nusselt number

P:

Pressure

P∞:

Ambient pressure

PKL :

Production of laminar kinetic energy by mean strain rate

PKT :

Production of turbulent kinetic energy by mean strain rate

Prt :

Turbulent Prandtl number

r:

Radial direction coordinate

RBP :

Bypass transition production term

Re:

Reynolds number

RNAT :

Natural transition production term

q:

Heat flux (Watts/m2)

S:

Swirl number

T:

Temperature (K)

t:

Time (s)

Tref :

Reference temperature (K)

Tw :

Heat wall temperature (K)

U:

Axial velocity (m/s)

Ub :

Bulk axial velocity at the nozzle exit plane (m/s)

ui,j :

Axial, radial and azimuthal velocity component (m/s)

u′ :

Axial, radial and azimuthal velocity fluctuations (m/s)

Wb :

Bulk tangential velocity at the nozzle exit plane (m/s)

xi,j :

Axial, radial and azimuthal coordinate

ρ:

Density

μ:

Dynamic viscosity

ν:

Kinematic viscosity

λ:

Thermal conductivity of the bulk air

δij :

Dirac’s delta

ω:

Specific rate of dissipation

ε:

Rate of dissipation

σA :

Standard deviation

αT :

Effective diffusivity for turbulence dependent variables

PP:

Parabolic tangential velocity profile

SBR:

Solid-body-rotation type tangential velocity profile

UP:

Uniform (top-hat) tangential velocity profile

SST:

Shear Stress Transport

RNG:

Re-Normalisation Group

RANS:

Reynolds-averaged Navier–Stokes

LES:

Large Eddy Simulation

DNS:

Direct Numerical Simulation

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Acknowledgements

This research is facilitated Edith Cowan University (ECU) research infrastructure. The corresponding author acknowledges ECU for awarding him an Edith Cowan University Postgraduate Research Scholarship (ECUPRS) to pursue a PhD research program. Dr. Zahir U Ahmed is also thanked for his advice.

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  1. School of Engineering, Edith Cowan University, 270 Joondalup Drive, Joondalup, WA, 6027, Australia

    Muhammad Ikhlaq, Yasir M. Al-Abdeli & Mehdi Khiadani

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Ikhlaq, M., Al-Abdeli, Y.M. & Khiadani, M. Nozzle exit conditions and the heat transfer in non-swirling and weakly swirling turbulent impinging jets. Heat Mass Transfer 56, 269–290 (2020). https://doi.org/10.1007/s00231-019-02710-1

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