# Flow and heat transfer investigation of a circular jet issuing on different types of surfaces

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## Abstract

In the present study, flow and heat transfer characteristics of an impinging jet issuing from a circular cross-sectional pipe on a rectangular plate, convex and concave hemispheres were investigated numerically for various Reynolds numbers and jet-to-plate distances. Steady and three-dimensional Reynolds-Averaged Navier-Stokes equations were solved iteratively utilizing finite volume method. Turbulence model assessment study reveals that the transitional Shear Stress Transport k-ω turbulence model can be used for such a problem. Regardless of the geometry of the impinging surfaces, two different flow regions were detected around y/D = 3. The first region starts from the stagnation point (y/D = 0) to the edge of the rectangular plate and hemispheres (y/D = 3). In this region, the maximum heat transfer is obtained for the jet impinging on the rectangular plate. However, in the second region that covers the wall jet zone the impinging jet on the convex hemisphere provides the maximum while the concave causes the minimum heat transfer. The most efficient jet-to-plate distance is found as H/D = 2 in the first region while heat transfer does not change with distance in the wall jet zone. It was shown that Nusselt number increases with Reynolds number when the jet impinges on the concave and convex hemispheres as observed for the impinging jet on a flat plate.

## Keywords

Impinging jet heat transfer computational fluid dynamics turbulence convex surface concave surface## Nomenclature

- D
jet diameter (m)

- D
_{h} hydraulic diameter (m)

- H
distance between the pipe and the impinging surface (m)

- i, j
1, 2, 3

- I
turbulence intensity (–)

- k
turbulence kinetic energy (m

^{2}/s^{2})- K
thermal conductivity (W/mK)

- L
length of the pipe (m)

- Nu number
Nusselt number (–)

- P
pressure (N/m

^{2})- Re number
Reynolds number (–)

- T
temperature (K)

- u, v, w
velocity components in x-, y- an z-directions, respectively (m/s)

- x, y, z
streamwise, spanwise and normal directions, respectively (m)

## Greek letters

- \( \delta_{ij} \)
Kronecker delta (–)

- ε
dissipation rate of turbulence kinetic energy (m

^{2}/s^{3})- μ
dynamic viscosity of the fluid (kg/m.s)

- ν
kinematic viscosity of the fluid (m

^{2}/s)- ρ
density (kg/m

^{3})- ω
turbulence specific dissipation rate

## Abbreviations

- CFD
computational fluid dynamics

- CVP
counter-rotating vortices

- DNS
direct numerical simulation

- GCI
grid convergence index

- LES
large eddy viscosity

- RANS
Reynolds-averaged Navier-Stokes

- RNG
re-normalization group

- SIMPLE
semi-implicit method for pressure linked equations

- SST
shear stress transport

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