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Unsteady flow and heat transfer analysis of an impinging synthetic jet

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Abstract

The present paper focuses on the analysis of unsteady flow and heat transfer regarding an axisymmetric impinging synthetic jet on a constant heat flux disc. Synthetic jet is a zero net mass flux jet that provides an unsteady flow without any external source of fluid. Present results are validated against the available experimental data showing that the SST/k − ω turbulence model is more accurate and reliable than the standard and low-Re k − ε models for predicting heat transfer from an impinging synthetic jet. It is found that the time-averaged Nusselt number enhances as the nozzle-to-plate distance is increased. As the oscillation frequency in the range of 16–400 Hz is increased, the heat transfer is enhanced. It is shown that the instantaneous Nu distribution along the wall is influenced mainly by the interaction of produced vortex ring and wall boundary layer. Also, the fluctuation level of Nu decreases as the frequency is raised.

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Abbreviations

D :

Nozzle diameter (m)

f :

Oscillation (diaphragm vibration) frequency (s−1)

H :

Nozzle-to-plate distance (m)

h :

Heat transfer coefficient \( \left( {{\frac{\text{W}}{{{\text{m}}^{ 2} \, {\text{K}}}}}} \right) \)

k :

Turbulence kinetic energy \( \left( {{\frac{{{\text{m}}^{ 2} }}{{{\text{s}}^{ 2} }}}} \right) \)

L 0 :

Stroke length of synthetic jet (m)

N u :

Instantaneous Nusselt number \( \left( { = {\frac{hD}{\kappa }}} \right) \)

Nu′:

Root-mean-squared fluctuations of instantaneous Nusselt number

\( \overline{Nu} \) :

Mean Nusselt number (averaged across the surface)

Nu avg :

Time-averaged Nusselt number in one cycle

Nu s :

Nusselt number of stagnation point

P :

Static pressure (Pa)

P atm :

Atmospheric pressure (Pa)

Re :

Reynolds number \( \left( {{\frac{{\rho U_{ 0} D}}{\mu }}} \right) \)

r :

Radial coordinate (m)

T :

Oscillation (diaphragm vibration) period \( \left( { = {\frac{ 2\pi }{f}}} \right) \)(s)

t :

Time (s)

U 0 :

Equivalent synthetic jet velocity \( \left( {{\frac{\text{m}}{\text{s}}}} \right) \)

u(t):

Velocity \( \left( {{\frac{\text{m}}{\text{s}}}} \right) \)

\( \overline{{u_{i} }} \) :

Mean velocity components (for turbulent velocity) \( \left( {{\frac{\text{m}}{\text{s}}}} \right) \)

u′:

Fluctuation velocity components (for turbulent velocity) \( \left( {{\frac{\text{m}}{\text{s}}}} \right) \)

u max :

Maximum velocity of synthetic jet in one cycle \( \left( {{\frac{\text{m}}{\text{s}}}} \right) \)

y:

Axial coordinate (m)

α:

Thermal diffusivity \( \left( {{\frac{{{\text{m}}^{ 2} }}{\text{s}}}} \right) \)

ε:

Dissipation rate of turbulence kinetic energy

θ:

Temperature (K)

κ:

Thermal conductivity \( \left( {{\frac{\text{W}}{{{\text{m}} \, {\text{K}}}}}} \right) \)

μ:

Dynamic viscosity \( \left( {{\frac{\text{kg}}{{{\text{m}} \, {\text{s}}}}}} \right) \)

μ t :

Turbulent eddy viscosity \( \left( {{\frac{\text{kg}}{{{\text{m}} \, {\text{s}}}}}} \right) \)

ρ:

Density \( \left( {{\frac{\text{kg}}{{{\text{m}}^{ 3} }}}} \right) \)

\( - \rho \overline{{u^{\prime}_{i} u^{\prime}_{j} }} \) :

Reynolds stress \( \left( {{\frac{\text{kg}}{{{\text{m}} \, {\text{s}}^{ 2} }}}} \right) \)

ϕ:

Phase angle (degree)

ω:

Turbulence eddy frequency \( \left( {{\frac{ 1}{\text{s}}}} \right) \)

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Authors and Affiliations

  1. School of Mechanical Engineering, Iran University of Science and Technology, 16846-13114, Tehran, Iran

    Farzad Bazdidi-Tehrani, Mahdi Karami & Mehdi Jahromi

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  1. Farzad Bazdidi-Tehrani
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  2. Mahdi Karami
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  3. Mehdi Jahromi
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Correspondence to Farzad Bazdidi-Tehrani.

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Bazdidi-Tehrani, F., Karami, M. & Jahromi, M. Unsteady flow and heat transfer analysis of an impinging synthetic jet. Heat Mass Transfer 47, 1363–1373 (2011). https://doi.org/10.1007/s00231-011-0801-0

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