Abstract
In this study, the unsteady flow and heat transfer characteristics of a laminar slot jet at low Reynolds numbers impinging on an isothermal plate surface in a two-dimensional confined space are numerically investigated. The investigations are performed at Reynolds numbers of 120, 150 and 200 based on the nozzle width and mean inlet velocity of the jet. Results show that the Reynolds numbers of 120, 150 and 200 correspond to different flow features, namely, a steady flow, an intermittent flapping motion of jet column and a continuous sinusoidal flapping state, respectively. Based on some time snapshots of the flow field, the dynamic characteristics and driving mechanism of the intermittent flapping motion of the jet column and the continuous sinusoidal flapping state are explained. When the jet flaps at the Reynolds number 150 and 200, there are other Nusselt number peaks outside the stagnation zone, which are related to the interference between the vortices shedding on both sides of the jet and the boundary layers of the plate surface. Furthermore, the dynamic mode decomposition is implemented to accurately extract flow modes with characteristic frequencies. For a Reynolds number of 150, there is a flapping mode, which describes the lateral flapping motion of the jet column. When the Reynolds number is 200, there are multiple modes related to the flapping motion of the jet, as well as a low-frequency mode, which reflects the periodic changes of the boundary contour and position of the recirculation zone.
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Abbreviations
- c p :
-
specific heat at constant pressure/J·(kg·K)−1
- e :
-
height ratio, e=H/W
- f :
-
Frequency/s−1
- H :
-
nozzle-plate spacing/m
- h :
-
convective heat transfer coefficient/W·(m2·K)−1
- k :
-
thermal conductivity/W·(m·K)−1
- L :
-
channel length/m
- Nu :
-
Nusselt number at the impingement surface, Nu=hW/k
- \(\overline {Nu} \) :
-
time-averaged Nusselt number at the impingement surface
- p :
-
dimensionless pressure, scaled with ρU2
- Pr :
-
Prandtl number, Pr=cpµ/k
- Re :
-
Reynolds number, Re=ρUW/µ
- St H :
-
Strouhal number, StH=fH/U
- T 0 :
-
inlet temperature of the jet/K
- T w :
-
temperature of the impinging surface/K
- t :
-
dimensionless time, scaled with W/U
- U :
-
mean inlet velocity of the jet/m·s−1
- u :
-
dimensionless velocity vector, scaled with U dimensionless transverse velocity component, scaled with U
- u y :
-
dimensionless streamwise velocity component, scaled with U
- W :
-
jet nozzle width/m
- x :
-
dimensionless transverse coordinates, scaled with W
- y :
-
dimensionless axial coordinates, scaled with W
- θ :
-
dimensionless temperature, \(\theta = {{\hat T - {T_0}} \over {{T_w} - {T_0}}}\)
- µ :
-
dynamic viscosity/Pa·s
- ρ :
-
density/kg·m−3
- ω z :
-
z component of dimensionless vorticity vector, scaled with U/W
- ^:
-
dimensional variable
- *:
-
conjugate transpose
- DMD:
-
dynamic mode decomposition
- FFT:
-
fast Fourier transform
- POD:
-
proper orthogonal decomposition
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Acknowledgment
The authors gratefully acknowledge the support for the research from the National Key R&D Program of China (2018YFB0604404).
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Shi, L., Sun, C., Zhu, X. et al. A Confined Laminar Slot Impinging Jet at Low Reynolds Numbers: Unsteady Flow and Heat Transfer Characteristics. J. Therm. Sci. 32, 753–769 (2023). https://doi.org/10.1007/s11630-022-1744-0
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DOI: https://doi.org/10.1007/s11630-022-1744-0