Study of the Gas Distribution in a Multiphase Rotodynamic Pump Based on Interphase Force Analysis
Abstract
:1. Introduction
2. Test System
3. Numerical Methodology
3.1. Governing Equations
3.2. Interphase Forces
3.3. Structured Mesh Information
3.4. Boundary Conditions and Numerical Solution Settings
4. Results and Discussions
4.1. Model Validation
4.2. Phase Interaction Characteristics in Impeller and Guide Vane
4.3. Gas Distribution in the Impeller Passage
4.4. Gas Distribution in the Guide Vane Passage
5. Conclusions
- (1)
- For the interphase forces in impeller and guide vane passages at IGVF = 21%, the magnitude ratio of non-drag forces to drag was generally less than 1, while the magnitude ratio of turbulent dispersion force to drag was always less than 0.2, which indicates that the drag was dominant and the turbulent dispersion force was very small relative to the drag in the multiphase rotodynamic pump.
- (2)
- Due to the rotation of the impeller and the rotor-stator interaction, the interphase forces of drag, added mass, and lift near the inlet and outlet of the impeller increased significantly. Meanwhile, with the increased IGVF, the variation range of interphase forces in the impeller was greater than that in the guide vane.
- (3)
- Due to the rotation effect of the impeller and the adverse pressure gradient in the flow passages, the gas in the impeller mainly accumulated near the hub of the impeller outlet. The higher the IGVF, the higher the aggregation degree and gas inhomogeneity therein, thus resulting in the increased interphase forces in the impeller passage.
- (4)
- The regularities of gas distribution in the guide vane were similar at different IGVFs, mainly accumulating near the guide vane hub, and gradually spreading to the mainstream region along the streamwise direction. Additionally, due to the divergent structure of the guide vane, obvious vortexes emerged at the hub. With increased IGVF, the degree of aggregation of gas and the range of gas vortexes—which are both located near the guide vane hub—became larger.
Author Contributions
Acknowledgments
Conflicts of Interest
Nomenclature
Ak | Additional mass force of phase k, N/m3 |
Model constant, dimensionless | |
CA | Coefficient of additional mass force, dimensionless |
CD | Drag coefficient, dimensionless |
CL | Lift coefficient, dimensionless |
cm2 | Meridional velocity at impeller outlet, m/s |
CT | Coefficient of turbulent dispersion force, dimensionless |
Db | Bubble diameter, mm |
Dh1 | Hub diameter of impeller inlet, mm |
Dh2 | Hub diameter of impeller outlet, mm |
Dh3 | Hub diameter of guide vane inlet, mm |
Dh4 | Hub diameter of guide vane outlet, mm |
Dk | Drag force of phase k, N/m3 |
Ds1 | Impeller shroud diameter, mm |
Ds2 | Guide vane shroud diameter, mm |
F2 | Blending function in SST-k-ω model |
f | Mass force relevant to the rotation of the impeller, m/s2 |
H | Pump head, m |
Hd | Pump design head, m |
Hl | Impeller axial length, mm |
H2 | Guide vane axial length, mm |
IGVF | Inlet gas void fraction, dimensionless |
k | Turbulent kinetic energy, m2/s2 |
Lk | Lift force of phase k, N/m3 |
Mk | Total interphase force per unit volume, N/m3 |
n | Rotational speed, r/min |
ns | Specific speed, m3/4·s−3/2 |
p | Static pressure, kPa |
Q | Q-criterion |
qv | Discharge, m3/s |
Re | Reynolds number, dimensionless |
SkΦ | Source item |
S | Invariant measure of the strain rate |
Tk | Turbulent dispersion force of phase k, N/m3 |
Ug | Gas velocity, m/s |
Ul | Liquid velocity, m/s |
u2 | Velocity of the impeller outlet, m/s |
w | Relative velocity, m/s |
Z1 | Impeller blade numbers, mm |
Z2 | Guide vane blade numbers, mm |
Greek symbols | |
αk | Volume fraction of phase, % |
β′ | Model constant, dimensionless |
ΓkΦ | Diffusion coefficient, dimensionless |
σ | Surface tension coefficient, N/m |
μk,t | Turbulent viscosity, Pa·s |
μ | Molecular viscosity, Pa·s |
μkeff | Effective viscosity, Pa·s |
Density of phase k, kg/m3 | |
Mixture density of phases, kg/m3 | |
Φk | Universal variable |
φ | Discharge coefficient, dimensionless |
ψ | Head coefficient, dimensionless |
ω | Rotational frequency of the impeller, 1/s |
Subscripts | |
k | Phase |
g | Gas phase |
l | Liquid phase |
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Multiphase Pump | Items | Values | Units |
---|---|---|---|
Impeller | Shroud diameter Ds1 | 150 | mm |
Hub diameter of inlet Dh1 | 120 | ||
Hub diameter of outlet Dh2 | 134 | ||
Axial length Hl | 60 | ||
Blade numbers Z1 | 4 | dimensionless | |
Guide vane | Shroud diameter Ds2 | 150 | mm |
Hub diameter of inlet Dh3 | 134 | ||
Hub diameter of outlet Dh4 | 120 | ||
Axial length H2 | 40 | ||
Blade numbers Z2 | 11 | dimensionless | |
Design condition | Rotational speed n | 2950 | r/min |
Discharge coefficient φ | 0.168 | dimensionless | |
Head coefficient ψ | 0.274 | ||
Specific speed ns | 166 | m3/4·s−3/2 |
Items | Mesh I | Mesh II | Mesh III | Mesh IV |
---|---|---|---|---|
Inlet pipe | 54,516 | 54,516 | 54,516 | 54,516 |
Impeller | 165,096 × 4 | 306,660 × 4 | 590,416 × 4 | 809,361 × 4 |
Guide vane | 35,168 × 11 | 56,280 × 11 | 105,840 × 11 | 129,472 × 11 |
Outlet pipe | 99,540 | 99,540 | 99,540 | 99,540 |
Total (million) | 1.20 | 2.00 | 3.68 | 4.82 |
Head coefficient | 0.261 | 0.259 | 0.256 | 0.256 |
Efficiency/% | 58.23 | 57.73 | 57.14 | 57.13 |
Items | Inlet Pipe | Impeller | Guide Vane | Outlet Pipe |
---|---|---|---|---|
Mesh type | hexahedral mesh | |||
Orthogonality angle (0°–90°) | 88.7 | 82.2 | 73.6 | 85.9 |
Mesh expansion factor (0–20) | 1.0 | 1.2 | 4.9 | 1.0 |
Aspect ratio (0–100) | 2.4 | 13.9 | 18.2 | 2.8 |
y+ | 233 | 66 | 10 | 331 |
Items | Settings |
---|---|
Analysis type | Steady state |
Advection scheme | Second order |
Turbulence numerics | Second order |
Residual RMS | <1 × 10−4 |
Discharge coefficient φ | 0.168 |
Inlet gas void fraction IGVF | 9%, 15%, 21% |
Results | ψ_CFD (m) | ψ_EXP (m) | Error (%) | |
---|---|---|---|---|
Conditions | ||||
IGVF = 0% | 0.312 | 0.303 | 2.97 | |
IGVF = 9% | 0.296 | 0.290 | 2.07 | |
IGVF = 15% | 0.282 | 0.273 | 3.30 | |
IGVF = 21% | 0.269 | 0.265 | 1.51 |
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Zhang, W.; Yu, Z.; Zahid, M.N.; Li, Y. Study of the Gas Distribution in a Multiphase Rotodynamic Pump Based on Interphase Force Analysis. Energies 2018, 11, 1069. https://doi.org/10.3390/en11051069
Zhang W, Yu Z, Zahid MN, Li Y. Study of the Gas Distribution in a Multiphase Rotodynamic Pump Based on Interphase Force Analysis. Energies. 2018; 11(5):1069. https://doi.org/10.3390/en11051069
Chicago/Turabian StyleZhang, Wenwu, Zhiyi Yu, Muhammad Noaman Zahid, and Yongjiang Li. 2018. "Study of the Gas Distribution in a Multiphase Rotodynamic Pump Based on Interphase Force Analysis" Energies 11, no. 5: 1069. https://doi.org/10.3390/en11051069