Distribution and Deposition of Cylindrical Nanoparticles in a Turbulent Pipe Flow
Abstract
:1. Introduction
2. Models and Equations
2.1. Flow Laden with Cylindrical Nanoparticles
2.2. Reynolds Stress
2.3. Mean Probability Density Function for Orientation of Cylindrical Nanoparticles
2.4. Volume Fraction Φ of Cylindrical Nanoparticles
2.5. Penetration Efficiency
3. Numerical Method and Main Steps of Simulation
- (1)
- Equations (1), (2), (4)–(6) with Φ = μa = Sk = Sε = 0 are solved to get , k, ε and .
- (2)
- Equations (10)–(12) are solved to get and Φ.
- (3)
- Substitute Φ into Equation (2) to get ρm and μa.
- (4)
- Substitute , k, ε and Equation (8) into Equation (9) and solve it to get .
- (5)
- Substitute into Equation (3) to get and .
- (6)
- Substitute ρm, μa, and into Equations (1), (4)–(6) to get , k, ε and .
- (7)
- Turn to step (2) based on the new values of , k, ε and if necessary.
- (8)
- Calculate the particle volume V with Equation (12).
- (9)
- Calculate the deposited particle volume Vde with Equation (14) and penetration efficiency PE with Equation (13).
4. Validation
5. Results and Discussion
5.1. Distribution of Particle Volume Concentration and Orientation at Different Axial Positions
5.2. Distribution of Particle Number Concentration and Orientation at Outlet
5.2.1. Distribution of Particle Orientation
5.2.2. Effect of the Particle Aspect Ratio
5.2.3. Effect of the Reynolds Number
5.3. Penetration Efficiency
5.3.1. Effect of the Particle Aspect Ratio
5.3.2. Effect of the Particle Aspect Ratio
5.3.3. Effect of Pipe Length-to-Diameter Ratio
5.3.4. Relationship of Penetration Efficiency and Related Parameters
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
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Lin, W.; Shi, R.; Lin, J. Distribution and Deposition of Cylindrical Nanoparticles in a Turbulent Pipe Flow. Appl. Sci. 2021, 11, 962. https://doi.org/10.3390/app11030962
Lin W, Shi R, Lin J. Distribution and Deposition of Cylindrical Nanoparticles in a Turbulent Pipe Flow. Applied Sciences. 2021; 11(3):962. https://doi.org/10.3390/app11030962
Chicago/Turabian StyleLin, Wenqian, Ruifang Shi, and Jianzhong Lin. 2021. "Distribution and Deposition of Cylindrical Nanoparticles in a Turbulent Pipe Flow" Applied Sciences 11, no. 3: 962. https://doi.org/10.3390/app11030962
APA StyleLin, W., Shi, R., & Lin, J. (2021). Distribution and Deposition of Cylindrical Nanoparticles in a Turbulent Pipe Flow. Applied Sciences, 11(3), 962. https://doi.org/10.3390/app11030962