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Comparative study on the influence of depth, number and arrangement of dimples on the flow and heat transfer characteristics at turbulent flow regimes

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Abstract

The ensuing study is dedicated to a series of numerical investigations concerning the effects of various geometric parameters of dimpled plates on the flow structure and heat transfer performance in a rectangular duct compared to the smooth plate. These parameters are the arrangement, number and depth of dimples. Two widely used staggered and square patterns in addition to a triangular arrangement, and three dimple depths (Δ = δ/d = 0.25, 0.375 and 0.5) have been chosen for this particular study. All studies have been conducted at three different Reynolds numbers Re = 25,000, 50,000 and 100,000. In order to capture the flow structures in the vicinity of dimples and contributing phenomena related to the boundary layer interactions, fully structured grids with y+ < 1 have been generated for all the cases. The realizable kt-ε two-layer model was selected as a proper turbulent model. It can be observed from the obtained results that higher effective area for heat transfer and a myriad of turbulent vortices mixing the hot fluid near the surface with the passing cold fluid generated from the downwind rims of dimples are the causes for improved average Nusselt number in the dimpled surface in comparison to the smooth plate. However, more pressure loss due to the higher friction drag and recirculation zones inside dimples will exist as a drawback in this system. Moreover, for all arrangements increasing dimple ratio Δ has a negative impact on the heat transfer augmentation and also deteriorates the pressure loss, which leads to this fact that Δ = 0.25 serves as the best option for the dimple depth.

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Abbreviations

c p :

Specific heat (J/kgK)

d :

Dimple diameter (m)

D h :

Hydraulic diameter (m) (=2HW/(H + W))

f :

Friction factor

f C :

Curvature correction factor

h :

Convective heat transfer coefficient (W/m2K) (=\( \dot{q}/\left({T}_w-{T}_{\operatorname{Re}f}\right) \))

H :

Height of channel (m)

k :

Thermal conductivity (W/m2K)

k t :

Turbulent kinetic energy (m2/s2)

l :

Length of dimple plate (m)

L :

Length of channel (m)

L ref :

Reference length (m)

\( \dot{m} \) :

Mass flow rate (kg/m3)

Nu :

Nusselt number

P :

Pressure (Pa)

P t, abs :

Absolute total pressure (Pa)

Pr :

PRANDTL number

\( \dot{q} \) :

Heat flux (W/m2)

Re :

Reynolds number

S :

Distance between each adjacent dimple (m)

T :

Temperature (K)

T Re f :

Reference temperature (taken at inlet)

T w :

Wall temperature

u :

Velocity vector (m/s)

V :

Average inlet velocity (m/s)

w :

Width of dimple plate

W :

Width of channel

x :

Coordinate in stream-wise direction

y :

Coordinate in span-wise direction

δ :

Dimple depth (m)

ρ :

Density (kg/m3)

Δ:

Dimple ratio

ΔP :

Pressure drop (Pa)

y + :

Dimensionless wall distance

η :

Performance factor \( \left(=\left(\overline{Nu}/\overline{Nu_o}\right)/{\left(f/{f}_o\right)}^{1/3}\right) \)

ε :

Dissipation rate (m2/s3)

μ :

Dynamic viscosity (Pa s)

i, j :

Components in the x- and y-directions

o :

Condition at smooth plate

f :

Face of an boundary or interface

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Authors and Affiliations

  1. Department of Energy and Process Engineering, Norwegian University of Science and Technology, Trondheim, Norway

    Saeed Nazari

  2. Department of Mechanical Engineering, Payame Noor University (PNU), P.O. Box 19395-3697, Tehran, Iran

    Mahdi Zamani

  3. Young Researchers and Elite Club, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran

    Sajad A. Moshizi

Authors
  1. Saeed Nazari
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  2. Mahdi Zamani
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  3. Sajad A. Moshizi
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Correspondence to Mahdi Zamani.

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Nazari, S., Zamani, M. & Moshizi, S.A. Comparative study on the influence of depth, number and arrangement of dimples on the flow and heat transfer characteristics at turbulent flow regimes. Heat Mass Transfer 54, 2743–2760 (2018). https://doi.org/10.1007/s00231-018-2307-5

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  • DOI: https://doi.org/10.1007/s00231-018-2307-5

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