Local Heat Transfer Dynamics in the In-Line Tube Bundle under Asymmetrical Pulsating Flow
Abstract
:1. Introduction
2. Mathematical Model
2.1. Computational Domain and Boundary Conditions
2.2. Modeling Approach
2.3. Methodology for Evaluating Results of Simulation
2.4. Model Verification
3. Results and Discussion
3.1. Effect of Amplitude and Frequency of Pulsations on the Flow and Heat Transfer Characteristics
3.2. Effect of Amplitude and Frequency of Pulsations on Local Flow Characteristics and Heat Transfer
3.3. Contour Plots of Temperature, Effective Thermal Conductivity, and Plots of the Velocity Vector
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
A | Dimensional amplitude of pulsation, m |
A/D | Dimensionless relative amplitude of pulsation |
D | Diameter of the tubes in tube bundle, m |
Dj | Diameter of the hydraulic model elements, m |
f | Frequency of pulsation, Hz |
F(φ,r) | Area of the sector around the cylinder in the tube bundle, m2 |
g | Gravity acceleration, m s−2 |
H | Pressure in the hydraulic model elements, mH2O |
Hh | Pressure on the surface of the liquid in the hydraulic accumulator, mH2O |
Hp.c. | Pressure on the surface of the liquid in the pulsation chamber, mH2O |
k | Hydraulic resistance coefficient of the hydraulic model elements |
l | Length of the hydraulic model elements, m |
Nu | Nusselt number |
P | Pressure, Pa |
q | Heat flux, W m−2 |
Q | Volumetric flow rate in the hydraulic model elements, m3 s−1 |
Re | Reynolds numbers |
rmin/D | Minimum cell size in the near-wall region |
S | Area of the hydraulic model elements, m2 |
s/D | Relative transverse and longitudinal pitch of tube bundle |
Sh0 | Hole area at the bottom of the hydraulic accumulator, m2 |
Sp.c.0 | Hole area at the bottom of the pulsation chamber, m2 |
St | Strouhal number |
tf | Flow temperature at the inlet of the tube bundle, °C |
ts | Temperature around central cylinder in the fifth row of the tube bundle, °C |
tw | Tube bundle wall temperature, °C |
u | Flow velocity at inlet of the tube bundle, m s−1 |
U | Velocity around central cylinder in the fifth row of the tube bundle, m s−1 |
Ux,y | Velocity components, m s−1 |
ymax/D | Maximum mesh size related to the tube diameter |
z1 | Liquid level in the hydraulic accumulator, m |
z2 | Liquid level in the pulsation chamber, m |
T | Period of the pulsation, s |
T1 | First half-period of the pulsation, s |
T2 | Second half-period of the pulsation, s |
x | x-coordinate |
y | y-coordinate |
Greek symbols | |
η | Kinematic viscosity, m2 s−1 |
λ | Thermal conductivity, W m−1 K−1 |
λeff | Effective thermal conductivity, W m−1 K−1 |
λturb | Turbulent thermal conductivity, W m−1 K−1 |
τ | Time, s |
τ1 | Start time of the pulsation period, s |
τ2 | End time of the pulsation period, s |
Δt | Temperature difference, °C |
Subscripts | |
st | Steady flow |
p | Pulsating flow |
o | Averaged value over the surface of the cylinder wall in the tube bundle |
a | Averaged value over the annular area around the cylinder in the tube bundle |
φ | Averaged value depending on the azimuth angle |
δ | Enhancement factor |
Notations | |
〈 〉 | Averaged value over one period of the pulsation |
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Haibullina, A.; Khairullin, A.; Balzamov, D.; Ilyin, V.; Bronskaya, V.; Khairullina, L. Local Heat Transfer Dynamics in the In-Line Tube Bundle under Asymmetrical Pulsating Flow. Energies 2022, 15, 5571. https://doi.org/10.3390/en15155571
Haibullina A, Khairullin A, Balzamov D, Ilyin V, Bronskaya V, Khairullina L. Local Heat Transfer Dynamics in the In-Line Tube Bundle under Asymmetrical Pulsating Flow. Energies. 2022; 15(15):5571. https://doi.org/10.3390/en15155571
Chicago/Turabian StyleHaibullina, Aigul, Aidar Khairullin, Denis Balzamov, Vladimir Ilyin, Veronika Bronskaya, and Liliya Khairullina. 2022. "Local Heat Transfer Dynamics in the In-Line Tube Bundle under Asymmetrical Pulsating Flow" Energies 15, no. 15: 5571. https://doi.org/10.3390/en15155571