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Influence of the elliptical and circular orifices on the local heat transfer distribution of a flat plate impinged by under-expanded jets

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Abstract

Experimental study is carried out to explore the influence of nozzle profile on heat transfer for underexpanded impinging jets. Circular and elliptical orifices are used to generate underexpanded jets for underexpantion ratio ranging from 1.25 to 2.67. The supply pressure maintained in the present study ranges from 2.36 to 5.08 times the ambient pressure. IR thermal imaging camera is used to measure surface temperature of thin foil at different nozzle to plate distances. Shadowgraph and pressure distribution are used to understand the flow structure and distribution of circular and elliptical nozzle. It is observed that plate shock and pressure distribution over the plate have significant influence on the local heat transfer. The performance of the circular orifice is far better at lower z/d. The axis switching is observed for an elliptical orifice. Correlation for local heat transfer predicts Nusselt number comparable within 15 % of experimental results.

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Abbreviations

A :

Exit area of the orifice, m2

C p :

Specific heat of air at constant pressure, kJ/kg K

c :

Velocity of sound, m/sec

D :

Diameter meter of the supply pipe, m

d :

Equivalent diameter of orifice, m

h :

Heat transfer coefficient, W/m2K

I :

Current, A

k :

Thermal conductivity of air, W/mK

l :

Length of pipe, m

\( \dot{m} \) :

Mass flow rate, kg/sec

M :

Design Mach number, M = U ∞ /c

Nu :

Nusselt number, \( \left( {\frac{hd}{k}} \right) \)

Nu avg :

Average Nusselt number

Nu o :

Nusselt Number at the stagnation point

NPR :

Nozzle pressure ratio (P s /P ∞ )

P 0 :

Supply pressure, Pa

P ∞ :

Ambient pressure, Pa

P e :

Nozzle exit pressure, Pa

p :

Perimeter, m

Pr :

Prandtl number, (μCp/k)

q :

Heat transfer rate, W/m2

\( q_{conv} \) :

Heat carried out by convection from impinging jet, W/m2

\( q_{nat } \) :

Heat carried out by convection from back side of plate, W/m2

\( q_{joule} \) :

Total heat supplied, W/m2

\( q_{loss} \) :

Heat loss by radiation and convection from the plate, W/m2

\( q_{rad\left( b \right)} \) :

Heat loss by radiation from the back side, W/m2

\( q_{{rad\left( {f } \right)}} \) :

Heat loss by radiation from the front side, W/m2

R :

Recovery factor

r :

Radial distance from the stagnation point, m

Re :

Reynolds number, \( \left( {\rho U_{\infty } d/\mu = 4\dot{m}/\pi \mu d} \right) \)

T aw :

Adiabatic wall temperature, K

T aw :

Adiabatic wall temperature, K

T d :

Jet dynamic temperature, K

T i :

Jet initial temperature, K

T j0 :

Jet total temperature, K

T js :

Jet static temperature, K

T jd :

Jet dynamic temperature, K

T w :

Wall temperature, K

U ∞ :

Velocity, (\( U_{\infty } = \frac{{\dot{m}}}{A\rho } \)), m/sec

V :

Voltage, V

z :

Nozzle to plate distance, m

γ :

Specific heat ratio

µ :

Viscosity of fluid, Pa.s

ρ :

Density of fluid, kg/m3

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Acknowledgments

Authors acknowledge the efforts put in by Mr. Vittoba Kharat and Mr. Rahul Shirsat in building the experimental setup and fixing the mechanical problems during the course of the experiments.

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Authors and Affiliations

  1. Department of Mechanical Engineering, DIAT, Pune, India

    Ravish Vinze

  2. R & D E (E), DRDO, Pune, India

    M. D. Limeye

  3. Department of Mechanical Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai, 400 076, India

    S. V. Prabhu

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  1. Ravish Vinze
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  2. M. D. Limeye
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Correspondence to S. V. Prabhu.

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Vinze, R., Limeye, M.D. & Prabhu, S.V. Influence of the elliptical and circular orifices on the local heat transfer distribution of a flat plate impinged by under-expanded jets. Heat Mass Transfer 53, 1439–1455 (2017). https://doi.org/10.1007/s00231-016-1902-6

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