Numerical Assessment of Flow Energy Harvesting Potential in a Micro-Channel
Abstract
:1. Introduction
2. Set-Up of the CFD Model
2.1. Flow Domain Geometry
2.2. Assumptions Involved in the Simulations
- The flexible diaphragm is considered to be a rigid wall, fluid–structure interaction phenomena are ignored, displacement of the fluid due to the diaphragm motion is ignored, and feedback effects from the diaphragm to the flow are neglected.
- The diaphragm has small inertia and oscillates with the frequency of vortex shedding; the piezoelectric film is supposed to be strained laterally following the vibrations of the diaphragm and, according to the piezoelectric phenomenon, produce electrical power.
- Although the actual geometry is three-dimensional, two-dimensional simulations along the symmetry plane of the channel are performed to model the phenomenon.
- The greater the calculated vortex shedding intensity, the better the expected performance of the device.
2.3. Governing Equations and Numerical Solver
2.4. Description of Case Studies
2.4.1. Cases to Study the Effect of Blockage Ratio and Reynolds Number
2.4.2. Cases to Find the Value of Blockage Ratio Causing Suppression of Vortex Shedding
2.5. Fluid Data for the Simulations
2.6. Definition of Metrics to Assess the Energy Harvesting Potential of the Device
- The position (point Pi,max among the 21 points) where the maximum pressure fluctuation amplitude Δpi,max is predicted.
- The value of the maximum pressure fluctuation amplitude Δpi,max and the corresponding non-dimensional quantity (pressure coefficient) Cpi,max = Δpi,max/0.5ρVin2.
- The frequency and the non-dimensional frequency, i.e., Strouhal number St = fD/Vin of the pressure signal at point Pi,max.
- The average pressure drop Δpdrop in the duct, calculated as the difference between inlet and outlet average pressures, as well as the same quantity in non-dimensional form, i.e., Cpdrop = Δpdrop/0.5ρVin2.
3. Selection of Grid Size and Time-Step
3.1. Grid Generation
3.2. Grid Independence Study
3.3. Time-Step Selection
4. Results and Discussion
4.1. Effect of Reynolds Number and Blockage Ratio
4.1.1. Effect of Reynolds Number—Baseline Geometry
4.1.2. Effect of Reynolds Number—Various Blockage Ratios
- An almost linear increase of pressure amplitude with inlet velocity is noticed for all BR; this increase becomes steeper for greater values of BR.
- The pressure amplitude increases with the increase of BR for the same inlet velocity.
- An almost linear variation is predicted for all the values of BR; all curves have about the same inclination.
- For the same inlet velocity, contrary to pressure amplitude, the frequency decreases with the increase of BR.
4.1.3. Effect of Blockage Ratio—Various Reynolds Numbers
4.2. Investigation of Vortex Shedding Suppression Due to Blockage Ratio Increase
Discussion on the Estimation of the Critical BR
4.3. Further Discussion on the Results
- Δpmax is over the BR range from 1.3 to 2.6 times the value of ΔpS (about double in average), and the same is valid for Δpdrop. This means that if the diaphragm was positioned with its center at S at point P5, the achieved pressure amplitude could be multiplied by the corresponding ratio (greater than 100% increase).
- The value of Δpdrop is of the order of that of ΔpS and definitely lower than Δpmax.
5. Conclusions–Future Research
5.1. Conclusions
- The maximum pressure amplitude (Δpmax) in all cases occurs at the same position, located upstream of the center of the diaphragm (at a distance of 8 mm from its beginning). Thus, in order to maximize the effect of vortex shedding on the diaphragm, the center of the latter should be placed upstream at the point where the maximum pressure amplitude is predicted.
- The maximum pressure amplitude increases almost linearly with the inlet velocity for all the values of the blockage ratio (BR); the greater the BR, the more abrupt the increase. Thus, using a greater inlet velocity and greater blockage ratio, a greater maximum pressure fluctuation amplitude can be achieved.
- The fundamental frequency of the predicted pressure signal at the point where Δpmax occurs increases almost linearly with inlet velocity for all values of BR; the slope of the linear increase remains almost constant for all BR. This frequency slightly decreases with the increase of BR for the same Reynolds number. Since a high frequency is rather desired, maximizing the pressure amplitude (as proposed above) will also lead to a frequency increase.
- The channel pressure drop (Δpdrop) increases with the square of inlet velocity for all values of BR. For the same inlet velocity, the pressure drop increases with BR. As expected, an increase in pressure amplitude causes an increase in pressure drop.
- As a contribution of this work, from a designer point of view and under the prerequisite that these results would be validated by experiments, a great value of BR but lower than its critical one seems to provide a great value of amplitude in the expense of a moderate pressure drop (Figure 20).
5.2. Future Research
- To study of the effect of the distance between the two bluff bodies on the device performance since there is already experimental evidence [26] that a greater distance between the bodies may lead to a greater pressure amplitude.
- To study the device performance for a particular membrane and attempt to correlate the maximum pressure fluctuation amplitude predicted by CFD with the measured electric power from the corresponding experiments, i.e., to extract the operational curve of the device.
- To perform design optimization studies with respect to characteristic geometric quantities (location and distance between the two bodies, location of the diaphragm, channel blockage ratio, etc.) for maximum performance. A stochastic-based approach can be implemented (e.g., genetic algorithms), which would utilize either the present CFD solver or any reduced-order model of the phenomenon. The solution of a multiobjective problem could be sought, e.g., maximization of Δpmax with minimization of Δpdrop. Furthermore, this could be a constrained problem, e.g., by requiring the frequency to be near the resonant frequency of the membrane.
- To model the phenomenon more accurately, like, for example, to compare 3D against 2D simulations and/or model membrane dynamics and to consider fluid–structure interaction in the simulations.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Case | C1 | C2 | C3 | C4 | C5 | C6 | C7 | |
---|---|---|---|---|---|---|---|---|
Re | 4278 | 4860 | 5442 | 6024 | 6606 | 7188 | 7770 | BR |
16.3 | 18.5 | 20.7 | 22.9 | 25.1 | 27.3 | 29.6 | 0.24 | |
14.7 | 16.7 | 18.7 | 20.7 | 22.7 | 24.7 | 26.7 | 0.27 | |
13.0 | 14.8 | 16.6 | 18.3 | 20.1 | 21.9 | 23.6 | 0.30 | |
Vin (m/s) | 11.8 | 13.4 | 15.1 | 16.7 | 18.3 | 19.9 | 21.5 | 0.33 |
10.8 | 12.3 | 13.8 | 15.3 | 16.7 | 18.2 | 19.7 | 0.36 | |
10.0 | 11.4 | 12.7 | 14.1 | 15.5 | 16.8 | 18.2 | 0.39 | |
9.3 | 10.6 | 11.8 | 13.1 | 14.4 | 15.6 | 16.9 | 0.42 |
Name | G1.0 | G0.7 | G0.5 | G0.4 | G0.3 | G0.25 | G0.2 |
---|---|---|---|---|---|---|---|
Mesh size (mm) | 1.00 | 0.70 | 0.50 | 0.40 | 0.30 | 0.25 | 0.20 |
# Nodes | 6415 | 12,623 | 21,433 | 30,490 | 56,529 | 87,216 | 105,783 |
# Elements | 12,086 | 24,230 | 41,491 | 59,288 | 110,840 | 171,737 | 208,238 |
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Koubogiannis, D.G.; Benetatos, M.V.N. Numerical Assessment of Flow Energy Harvesting Potential in a Micro-Channel. Fluids 2023, 8, 222. https://doi.org/10.3390/fluids8080222
Koubogiannis DG, Benetatos MVN. Numerical Assessment of Flow Energy Harvesting Potential in a Micro-Channel. Fluids. 2023; 8(8):222. https://doi.org/10.3390/fluids8080222
Chicago/Turabian StyleKoubogiannis, Dimitrios G., and Marios Vasileios N. Benetatos. 2023. "Numerical Assessment of Flow Energy Harvesting Potential in a Micro-Channel" Fluids 8, no. 8: 222. https://doi.org/10.3390/fluids8080222