A Heat Exchanger with Water Vapor Condensation on the External Surface of a Vertical Pipe
Abstract
:1. Introduction
2. Experiment
2.1. Experimental Device
2.2. Analytical Model
2.3. Experimental Setup
- (a)
- 24 mm channel: 10; 12; 15; 20; 25; 30 and 35 kg∙h−1, which corresponds to the vapor velocity range, in front of the first testing pipe, from 0.67 to 1.96 m∙s−1.
- (b)
- 20 mm channel: 10; 12; 15; 20; 25 and 30 kg∙h−1, which corresponds to the vapor velocity range, in front of the first testing pipe, from 0.81 to 2.32 m∙s−1.
3. Results and Comparison
3.1. Results of the Experiments
3.2. Steam Flow Identification by Computational Modeling
3.3. Comparison with Other Studies
3.3.1. Model S1
3.3.2. Model S2
3.3.3. Model S3
3.3.4. Model S4
3.3.5. Comparing the Models with the Experimental Results
- (a)
- The basic variant when the authors calculate the Reynolds number from the maximum velocity; see Equation (31). The maximum velocity is determined on the basis of the pipe bundle geometry (spacing of the pipes/row), where, in our case, another adjacent pipe is the channel wall. The velocity considered in this variant is that in front of the first pipe.
- (b)
- Another variant is the mean value of the vapor velocity in front of all the three pipes, i.e., the average value of the vapor velocity in front of the first, second and third pipes. This value is then adjusted as in the previous variant, i.e., it is substituted into Equation (32) and then into Equation (31).
- (c)
- Based on Equations (13) and (14), the maximum velocity at the narrowest point around the first pipe is determined. The amount of condensed vapor in front of the narrow section is . This velocity is directly substituted into the calculation of the maximum Reynolds number in Equation (31).
- (d)
- As in the previous variant, the maximum vapor velocity is calculated at the first, second and third pipes, and these values are used to calculate the average maximum velocity. This velocity is directly substituted into the calculation of the maximum Reynolds number in Equation (31).
4. Conclusions
- (a)
- The width of the channel is negligible, and deviations fall within the statistical error margins.
- (b)
- The heat flow in the exchanger increases with a decreasing input temperature of the cooling water. By decreasing the temperature of the cooling water by 20 °C, the output of the exchanger increases by approx. 25%, on average.
- (c)
- At the moment when not all the vapor condenses in the exchanger, the influence of the vapor velocity at the inlet into the exchanger decreases.
- (d)
- It holds for the particular exchanger geometry that with a higher vapor mass flow rate, and thus, a higher velocity, the condensation heat transfer coefficient also increases up to a flow rate of 25 kg·h−1, where the maximum is reached; with a further increase in the flow rate, it starts decreasing.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
cp | specific heat capacity, J∙kg−1∙K−1 |
d | tube diameter, m |
g | gravity acceleration, m∙s−2 |
Gr | Grashof number, - |
Δhc | latent heat of condensation, J∙kg−1 |
i | Enthalpy, J∙kg−1 |
Ja | Jacob number, - |
kc | overall HTC, W∙m−1∙K−1 |
L | characteristic length, m |
Mass flow rate, kg∙s−1 | |
Nu | Nusselt number, - |
p | absolute pressure, Pa |
Pr | Prandtl number |
heat transferred, W | |
Re | Reynolds number, - |
t | temperature, °C |
T | temperature, K |
Volume flow rate, m3∙s−1 | |
w | speed, m∙s−1 |
Greek letters | |
α | HTC, W∙m−2∙K−1 |
η | dynamic viscosity, Pa∙s |
λ | thermal conductivity, W∙m−1∙K−1 |
ν | kinematic viscosity, m2∙s−1 |
ρ | density, kg∙m−3 |
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Model | Average Error [%] | Standard Deviation [%p] |
---|---|---|
S1 | −131.3 | ±28.5 |
S2 | −121.9 | ±27.3 |
S3 | −14.7 | ±14.4 |
S4—a | 23.4 | ±19.3 |
S4—b | 34.1 | ±19.5 |
S4—c | 45.3 | ±13.2 |
S4—d | 53.6 | ±13.1 |
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Kracík, P.; Toman, F.; Pospíšil, J.; Kraml, S. A Heat Exchanger with Water Vapor Condensation on the External Surface of a Vertical Pipe. Energies 2022, 15, 5636. https://doi.org/10.3390/en15155636
Kracík P, Toman F, Pospíšil J, Kraml S. A Heat Exchanger with Water Vapor Condensation on the External Surface of a Vertical Pipe. Energies. 2022; 15(15):5636. https://doi.org/10.3390/en15155636
Chicago/Turabian StyleKracík, Petr, Filip Toman, Jiří Pospíšil, and Stanislav Kraml. 2022. "A Heat Exchanger with Water Vapor Condensation on the External Surface of a Vertical Pipe" Energies 15, no. 15: 5636. https://doi.org/10.3390/en15155636
APA StyleKracík, P., Toman, F., Pospíšil, J., & Kraml, S. (2022). A Heat Exchanger with Water Vapor Condensation on the External Surface of a Vertical Pipe. Energies, 15(15), 5636. https://doi.org/10.3390/en15155636