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ABSTRACT
In order to study the flow behavior and optimize separation performance, a three-dimensional numerical model of an improved supersonic separator was developed. The proposed model takes into account the compressible and strong swirling effect. Four widely-used turbulence models include Sparlart–Allmaras model, realizable k–ε model, shear-stress transport (SST) k–ω model, and Reynolds stress model (RSM) were validated and compared by the experimental date reported in the literature. The comparison results indicated that RSMs have great potential to predict the flow inside supersonic separator. Based on the established numerical model, the distribution of critical parameters such as temperature, pressure, and Mach number was obtained. The influence of the pressure loss ratio on the shockwave location occurred at the divergence section of the Laval nozzle was systematically studied. Analysis about the relationship between the pressure effect and shock wave location was carried out to explore the principal factors that limit the performance of the supersonic separator.
Nomenclature
| c | = | Corresponding sound speed |
| di | = | Diameter of the supersonic separator inlet, mm |
| dt | = | Diameter of the Laval nozzle, mm |
| ds | = | Diameter of the straight tube, mm |
| dh | = | Diameter of the straight tube, mm |
| L1 | = | Length of the entrance smooth section, mm |
| L2 | = | Length of the convergent section of the Laval nozzle, mm |
| L3 | = | Length of the divergent section of the Laval nozzle, mm |
| L4 | = | Length of the swirling flow generator, mm |
| L5 | = | Length of the straight tube, mm |
| L6 | = | Length of the diffuser part, mm |
| n | = | Specific heat ratio of air |
| e | = | Internal energy |
| = | Gravitational acceleration, kg⋅m⋅s−2 | |
| m | = | Mass flow rate, kg/s |
| Ma | = | Mach number |
| k | = | Turbulence kinetic energy, m2⋅s−2 |
| ke | = | Effective conductivity, W⋅m−1⋅K−1 |
| = | Velocity components in x, y and z direction, m/s | |
| Cp | = | Specific heat at constant pressure, J⋅kg−1⋅K−1 |
| E | = | Volumetric total energy, J |
| Gb | = | Generation of turbulence kinetic energy due to buoyancy, m2⋅s−2 |
| = | External body forces, N | |
| YM | = | Contribution of the fluctuating dilatation |
| pinlet | = | Static pressure at the inlet, MPa |
| poutlet | = | Static pressure at the outlet, MPa |
| pb | = | Back pressure of the separator, MPa |
| pe | = | Pressure at the exit section of the Laval Nozzle, MPa |
| Rm | = | Gas constant, J/(kg⋅K) |
| T | = | Static temperature inside the supersonic separator, K |
| vT | = | Tangential velocity |
| vA | = | Axial velocity |
| Tinlet | = | Static temperature at the inlet, K |
| I | = | Unit tensor |
Greek symbols
| μ | = | Molecular viscosity, Pa⋅s |
| υ | = | Specific volume of the working fluid |
| κ | = | Ratio of specific heats |
| ω | = | Turbulence specific dissipation rate, s−1 |
| ε | = | Turbulence dissipation rate, m2⋅s−3 |
| ρ | = | Density, kg⋅m−3 |
| = | Stress tensor, N⋅m−2 | |
| Θ | = | Dimensionless temperature |
| γ | = | Pressure loss ratio |
| σε | = | Turbulent Prandtl numbers for ε |
| σk | = | Turbulent Prandtl numbers for k |
| Γk | = | Effective diffusivity of k |
| Γε | = | Effective diffusivity of ε |
| Ωk | = | Mean rate-of-rotation tensor |
| ξ | = | Cold fluid mass fraction |
| Δp | = | Pressure difference between inlet and outlet, MPa |
Subscripts
| Inlet | = | Inlet gas of the supersonic separator |
| outlet | = | Outlet gas of the supersonic separator |
Funding
This study is supported by the National Natural Science Foundation of China [grant number 50676002] and the Specialized Research Fund for the Doctoral Program of Higher Education [grant number 20040005008]