Investigations of Gas–Particle Two-Phase Flow in Swirling Combustor by the Particle Stokes Numbers
Abstract
:1. Introduction
2. Modeling and Governing Equations
2.1. Continuity and Momentum Equations
2.2. Momentum Transfer between Gas and Particle Phases
2.3. Reynolds Stress Transport Equations of Gas and Particle Phases
2.4. Particle Temperature Equation Coupled with Kinetic Frictional Stress Model
3. Computational Method and Experimental Setting
3.1. Experimental Setting
3.2. Numerical Algorithms
4. Results and Discussion
4.1. Experimental Validations for Gas and Particle Velocity
4.2. Gas Turbulence Modulations
4.3. Effects of St Number on the Distributions of Gas and Particle Velocity
4.4. Effects of St Number on the Distributions of Gas and Particle Fluctuation Velocity
4.5. Effects of St Number on Turbulence Kinetic Energy (TKE)
4.6. Effects of St Number on the Reynolds Shear Stresses of Gas and Particle Dispersions
4.7. Effects of St Number on the Tensor Stress Invariants
5. Concluding Remarks
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
CD | Drag coefficient, (dimensionless) |
dp | Diameter of particle, (m) |
D | Diffusion term, (dimensionless) |
e | Restitution coefficient of particle, (dimensionless) |
ew | Restitution coefficient of wall, (dimensionless) |
g | Gravitational acceleration, (m/s2) |
g0 | Radial distribution function, (dimensionless) |
I | Unit tensor, (dimensionless) |
kg | Turbulent kinetic energy of gas, (m2/s2) |
kp | Turbulent kinetic energy of particle, (m2/s2) |
p | Thermodynamic pressure, (Pa) |
pp | Particle pressure term, (Pa) |
pfp | Frictional particle pressure term, (Pa) |
P | Transport production term, (dimensionless) |
Q | Flow rates of gas and particle, (g/s) |
Rep | The Reynolds numbers of particle, (dimensionless) |
s | Swirling numbers of gas, (dimensionless) |
St | Stokes numbers of particle, (dimensionless) |
t | Time, (s) |
T | Transport interaction terms, (dimensionless) |
ug | Gas phase velocity, (m/s) |
up | Particle phase velocity, (m/s) |
Greek Alphabets | |
αg | Volume fraction of gas, (dimensionless) |
αp | Volume fraction of particle, (dimensionless) |
αp,max | Maximum volume fraction of particle, (dimensionless) |
βgp | Drag coefficient between gas–particle, (dimensionless) |
γ | Dissipation rate of particle collision, (kg/ms3) |
λ | Tensor eigenvalues, (dimensionless) |
δ | Kronecker Delta symbol, (dimensionless) |
ρg | Gas phase density, (kg/m3) |
ρp | Particle phase density, (kg/m3) |
εg | Turbulent energy dissipation rate of gas, (m2/s3) |
εp | Turbulent energy dissipation rate of particle, (m2/s3) |
μg | Gas phase dynamic viscosity, (Pa.s) |
μp | Particle phase shear viscosity, (Pa.s) |
τg | Gas stresses, (Pa) |
τp | Particle stresses, (Pa) |
ξs | Bulk viscosity of particle phase, (Pa.s) |
θ | Granular temperature, (m2/s2) |
Π | Pressure-strain, (dimensionless) |
ϕ | lending function, (dimensionless) |
Superscripts | |
′ | Fluctuations of gas and particle |
¯ | Averaged symbol |
Subscripts | |
an | Annular diameter |
i,j,k | Space |
in | Inlet |
f | Friction, or flow |
g,p | Gas phase, particle phase |
l | Laminar flow |
L | Length of geometry |
o | Outer diameter |
r | Relaxation time of particle |
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Parameters of Gas and Particle | Unit | Value |
---|---|---|
Diameter of EGP and CP, dp | μm | 45/1000 |
45/1000 | ||
Density of EGP and CP, ρp | kg/m3 | 21.9, 8900 |
Diameter of glass particle, dpg | μm | 45 |
Density of glass particle, ρpg | kg/m3 | 2500 |
Density of gas, ρg | kg/m3 | 1.225 |
Viscosity of gas, μg | Pa.s | 1.8 × 10−5 |
Wall restitution coefficient, ew | - | 0.99 |
Particles restitution coefficient, e | - | 0.90 |
Sphericity of particle, φ | - | 0.98 |
Diameter of inner tube, djn | mm | 32 |
Diameter of annular jet, dan | mm | 64 |
Diameter of chamber, do | mm | 194 |
Length of test section, L | mm | 960 |
Ratios of particle loadings, η | - | 0.034 |
Swirling number of gas flow, s | - | 0.47 |
Primary flow rates, Qs | g/s | 9.9 |
Flow rate in annular jet, Qan | g/s | 38.3 |
Inlet Reynolds number, Rein | - | 26,200 |
Copper Stokes numbers St, dp = 45, 160, 1000 μm | - | 0.087, 43.6 |
EGP Stokes numbers of St, dp = 45, 1000 μm | - | 0.0002, 0.11 |
Glass particle Stokes number St, dp = 45 μm | - | 0.025 |
Predictions | Experiment Data | |
---|---|---|
Primary jetting regions, (x, r) | (50.4 mm, 73.3 mm) | (52.5 mm, -) |
Secondary circulation zone, (x,r) | (117.4 mm, 61.1 mm) | (112.5 mm, -) |
Reattachment position, (x,r) | (53.5 mm, 93.5 mm) | (52.5 mm, -) |
The relative errors, % | 4.8 |
EGP | CP | |||
---|---|---|---|---|
Stokes number | 0.0002 | 0.11 | 0.087 | 43.6 |
Followability | Excellent | Good | Excellent | Worse |
Second recirculation | Entrained | Entrained | Entrained | Entrained |
Length of circulation region | Elongated | Elongated | Elongated | Elongated |
Preferential accumulation | Increased | Increased | Increased | Decreased |
Vortex formation | Help | Help | Unsensitive | Damage |
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Liu, Y.; Li, G. Investigations of Gas–Particle Two-Phase Flow in Swirling Combustor by the Particle Stokes Numbers. Processes 2021, 9, 951. https://doi.org/10.3390/pr9060951
Liu Y, Li G. Investigations of Gas–Particle Two-Phase Flow in Swirling Combustor by the Particle Stokes Numbers. Processes. 2021; 9(6):951. https://doi.org/10.3390/pr9060951
Chicago/Turabian StyleLiu, Yang, and Guohui Li. 2021. "Investigations of Gas–Particle Two-Phase Flow in Swirling Combustor by the Particle Stokes Numbers" Processes 9, no. 6: 951. https://doi.org/10.3390/pr9060951