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ABSTRACT
In the present research, considering the importance of appropriate design of steam turbines, a combination of scalar and convective upwind split pressure (CUSP) with known value of z schemes is used for numerically modeling condensation of the 2D nucleating steam flow. Considering the importance of z parameter in the CUSP scheme, effects of several different values of this parameter on the modeling of steam flows are subjected to sensitivity analysis using the combination method. Results of the improved numerical method across sensitive nucleation condensation shock zone are in good agreement with experimental data. Furthermore, numerical errors are lower than those conventional methods by up to about 80% with the mass flow rate being well stable, which indicates better satisfaction of conservation laws, and revealing efficiency of the proposed novel combination method.
Nomenclature
| A | = | the element area (m2) |
| CFL | = | Courant number |
| e | = | internal energy (kJ/kg) |
| Fp | = | flux vector of the pressure in the CUSP |
| Fx,Fy | = | flux vector |
| ΔG | = | Gibbs energy (kJ) |
| G | = | vapor-phase symbol |
| h | = | enthalpy (kJ/kg) |
| h0 | = | the total enthalpy |
| J | = | nucleation rate (no. of droplet/m3 · s) |
| kn | = | Knudsen number |
| k | = | Boltzmann’s constant |
| L | = | heat latent (kJ) or liquid phase symbol or symbols left by CUSP |
| L(u,v) | = | switch function of artificial dissipation |
| = | mean free path of vapor molecules (m) | |
| m | = | mass flow or the mass of a molecule (kg or kg/s) |
| M | = | Mach number |
| MP | = | mid-passage (center line) |
| N | = | number of droplets per unit mass |
| P | = | static pressure (kPa) |
| P0 | = | stagnation pressure (kPa) |
| = | unknown parameters | |
| PS | = | pressure side |
| r | = | radius droplet (m) |
| q | = | condensation factor |
| Q | = | displacement flux |
| R | = | gas constant or symbol in the right of CUSP (kJ/kg · K) |
| SS | = | suction side |
| Sx, Sy | = | x and y directions of the vector elements |
| T | = | static temperature (K) |
| T0 | = | stagnation temperature (K) |
| TG | = | steam temperature (K) |
| TL | = | droplet temperature (K) |
| Ts | = | saturation temperature (K) |
| u,v | = | components of velocity (m/s) |
| ΔV | = | elements size (m3) |
| V | = | velocity (m/s) |
| w | = | flux |
| x,y | = | to coordinate the flow perpendicular to it |
| z | = | convergence parameter on CUSP’s method |
| Greek symbols | = | |
| α | = | heat transfer coefficient of droplet with vapor |
| σ | = | surface tension (N/m) |
| ν | = | kinematic viscosity or correction factor in the nucleation equation (m2/s) |
| λ | = | thermal conductivity (W/m K) |
| ρ | = | density (kg/m3) |
Nomenclature
| A | = | the element area (m2) |
| CFL | = | Courant number |
| e | = | internal energy (kJ/kg) |
| Fp | = | flux vector of the pressure in the CUSP |
| Fx,Fy | = | flux vector |
| ΔG | = | Gibbs energy (kJ) |
| G | = | vapor-phase symbol |
| h | = | enthalpy (kJ/kg) |
| h0 | = | the total enthalpy |
| J | = | nucleation rate (no. of droplet/m3 · s) |
| kn | = | Knudsen number |
| k | = | Boltzmann’s constant |
| L | = | heat latent (kJ) or liquid phase symbol or symbols left by CUSP |
| L(u,v) | = | switch function of artificial dissipation |
| = | mean free path of vapor molecules (m) | |
| m | = | mass flow or the mass of a molecule (kg or kg/s) |
| M | = | Mach number |
| MP | = | mid-passage (center line) |
| N | = | number of droplets per unit mass |
| P | = | static pressure (kPa) |
| P0 | = | stagnation pressure (kPa) |
| = | unknown parameters | |
| PS | = | pressure side |
| r | = | radius droplet (m) |
| q | = | condensation factor |
| Q | = | displacement flux |
| R | = | gas constant or symbol in the right of CUSP (kJ/kg · K) |
| SS | = | suction side |
| Sx, Sy | = | x and y directions of the vector elements |
| T | = | static temperature (K) |
| T0 | = | stagnation temperature (K) |
| TG | = | steam temperature (K) |
| TL | = | droplet temperature (K) |
| Ts | = | saturation temperature (K) |
| u,v | = | components of velocity (m/s) |
| ΔV | = | elements size (m3) |
| V | = | velocity (m/s) |
| w | = | flux |
| x,y | = | to coordinate the flow perpendicular to it |
| z | = | convergence parameter on CUSP’s method |
| Greek symbols | = | |
| α | = | heat transfer coefficient of droplet with vapor |
| σ | = | surface tension (N/m) |
| ν | = | kinematic viscosity or correction factor in the nucleation equation (m2/s) |
| λ | = | thermal conductivity (W/m K) |
| ρ | = | density (kg/m3) |