CFD Based Non-Dimensional Characterization of Energy Dissipation Due to Verticle Slosh
Abstract
:1. Introduction
- We validate the accuracy of the CFD code Elemental® for modelling violent vertical slosh physics relevant to this article.
- We detail the CFD based energy budget used to quantify effects of scaling non-dimensional properties on the system.
- We present a non-dimensional analysis of a SDOF tank under vertical slosh, isolating the functional relationship characterising slosh induced energy dissipation.
- We define the non-dimensional parameter space of interest for the problem under consideration (to include both experimental and full scales).
- Finally, we develop novel scaling-laws which correlate the slosh induced energy dissipation as a function of the identified non-dimensional parameters. This is done via curve fitting of CFD generated data.
- The developed novel scaling laws are finally applied to quantify ideal (representative of full scale aircraft) experimental slosh induced energy dissipation.
2. Validation of CFD Model
3. Energy Analysis
4. Dimensional Analysis
5. Scaling of Violent Sloshing Systems
5.1. Froude Scaling Rules
5.2. Practical Considerations
6. Non-Dimensional Property Parameter Space
7. Non-Dimensional Study Results and Analysis
8. Dissipated Energy Scaling Laws
9. Scaling-Laws Application
10. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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(%) | |
---|---|
Quantity | Units | ||||
---|---|---|---|---|---|
M | L | T | |||
Liquid Viscosity | [Pa·s] | 1 | −1 | −1 | |
Liquid Density | [kg·m] | 1 | −3 | 0 | |
Gas Density | [kg·m] | 1 | −3 | 0 | |
Liquid Surface Tension | [N·m] | 1 | 0 | −2 | |
liquid–solid Contact Angle | [rad] | 0 | 0 | 0 | |
v | Fluid speed | [m·s] | 0 | 1 | −1 |
g | Gravity | [m·s] | 0 | 1 | −2 |
m | Solid Mass | [kg] | 1 | 0 | 0 |
k | Structural Stiffness | [N·m] | 1 | 0 | −2 |
c | Structural Damping | [Ns·m] | 1 | 0 | −1 |
h | Tank Height | [m] | 0 | 1 | 0 |
l | Tank Length | [m] | 0 | 1 | 0 |
Height of fluid | [m] | 0 | 1 | 0 | |
Initial tank offset (spring displacement) | [m] | 0 | 1 | 0 |
Quantity | Factor |
---|---|
Length | |
Time | |
Mass | |
Velocity | |
Acceleration | |
Viscosity | |
Surface Tension | |
Force | |
Energy |
f [Hz] | ||
---|---|---|
Required | 3.35 | 1.65 |
Achieved | 7.0 | 3.44 |
Actual | Froude Scaled | Aircraft | |
---|---|---|---|
Protospace | Protospace | ||
0 | 0 | ||
Parameter | Property Range |
---|---|
− | |
kg·m | |
Pa·s | |
N·m | |
Hz |
Protospace | Protospace | Protospace * | Aircraft | |
---|---|---|---|---|
(Water) | (Cold Kerosene) | (Ideal) | (Cold Kerosene) | |
Protospace | Protospace | Protospace * | |
---|---|---|---|
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Wright, M.D.; Gambioli, F.; Malan, A.G. CFD Based Non-Dimensional Characterization of Energy Dissipation Due to Verticle Slosh. Appl. Sci. 2021, 11, 10401. https://doi.org/10.3390/app112110401
Wright MD, Gambioli F, Malan AG. CFD Based Non-Dimensional Characterization of Energy Dissipation Due to Verticle Slosh. Applied Sciences. 2021; 11(21):10401. https://doi.org/10.3390/app112110401
Chicago/Turabian StyleWright, Michael Dennis, Francesco Gambioli, and Arnaud George Malan. 2021. "CFD Based Non-Dimensional Characterization of Energy Dissipation Due to Verticle Slosh" Applied Sciences 11, no. 21: 10401. https://doi.org/10.3390/app112110401