Compressible Flow Critical Flow

Calculate gas critical over stagnation flow ratios and gas properties for isentropic and isothermal flow.

The flow ratios are calculated as critical value over stagnation value, eg critical pressure over stagnation pressure. Critical properties are calculated at M = 1 for isentropic flow, and M = 1 / √k for isothermal flow, where k is the specific heat ratio (Cp/Cv). The stagnation properties are calculated at stationary conditions (M = 0). The temperature and pressure can be defined at either stagnation conditions, or at critical conditions. For isothermal flow the critical temperature is assumed equal to the stagnation temperature at M = 0. The stagnation temperature is constant for isentropic flow, and varies with Mach number for isothermal flow. Phase changes are ignored.

Tool Input

• fluidtype : Fluid Type
  • γu : User Defined Specific Heat Ratio
  • SGu : User Defined Gas Specific Gravity
• zfactype : Compressibility Factor Type
  • Zu : User Defined Compressibility Factor
• presstype : Critical Pressure Type
  • Pou : User Defined Stagnation Pressure
  • Pcu : User Defined Critical Flowing Pressure
  • Tou : User Defined Stagnation Temperature
  • Tcu : User Defined Critical Flowing Temperature
• flowtype : Fluid Flow Type
• ID : Inside Diameter

Tool Output

• γ : Specific Heat Ratio
• ρc : Critical Density
• ρc/ρo : Density Ratio
• ρo : Stagnation Density
• Cc : Critical Speed Of Sound
• Cc/Co : Speed Of Sound Ratio
• Co : Stagnation Speed Of Sound
• Gc : Critical Mass Flux (Mass Flow Rate Per Area)
• Mc : Critical Mach Number
• Pc : Critical Pressure
• Pc/Po : Pressure Ratio
• Po : Stagnation Pressure
• Rg : Specific Gas Constant
• SG : Gas Specific Gravity
• Tc : Critical Temperature
• Tc/To : Temperature Ratio
• To : Stagnation Temperature (M = 0)
• Toc : Critical Stagnation Temperature (M = Mc)
• Vc : Critical Fluid Velocity
• Z : Compressibility Factor
• mc : Critical Mass Flow Rate
• mmg : Gas Molar Mass
• nc : Critical Mole Flow Rate

Calculate gas header frictional flow critical ratios for adiabatic (constant enthalpy) and isothermal (constant temperature) flow.

Critical flow conditions occur when the exit Mach number equals the critical Mach number and the critical exit pressure is greater than or equal to ambient pressure. For adiabatic flow the critical exit Mach number = 1 (eg sonic flow conditions). For isothermal flow the critical exit Mach number = √γ.

Use the Result Plot option to plot critical pressure loss factor versus inlet Mach number and either flow type or specific heat ratio; or pressure ratio, temperature ratio, density ratio, speed of sound ratio, and velocity ratio, versus either Mach number or pressure loss factor, and versus either flow type or specific heat ratio (Fanno lines). The plot range is set from the calculated value of either the inlet Mach number, or the pressure loss factor in the main calculation. Change the main calculation values to change the plot range.

Tool Input

• fluidtype : Fluid Type
  • γu : User Defined Specific Heat Ratio
• fldtype : Pressure Loss Factor Type
  • Mciu : User Defined Inlet Mach Number
  • fL/Du : User Defined Pressure Loss Factor
• flowtype : Fluid Flow Type

Tool Output

• γ : Specific Heat Ratio
• ρi/ρ* : Inlet Density Over Critical Exit Density Ratio
• Ci/C* : Inlet Speed Of Sound Over Critical Exit Speed Of Sound Ratio
• M* : Critical Exit Mach Number
• Mi : Inlet Mach Number
• Pi/P* : Inlet Pressure Over Critical Exit Pressure Ratio
• Ti/T* : Inlet Temperature Over Critical Exit Temperature Ratio
• Vi/V* : Inlet Velocity Over Critical Velocity Ratio
• cvg : Convergence Factor (≅ 1)
• fL/D* : Critical Duct Pressure Loss factor

Calculate steam table properties from temperature and pressure (IAPWS R7-97 Steam Table).

Steam table values can be calculated for water and steam, saturated water, saturated steam, saturated water and steam, metastable water, and metastable steam. The calculations for water and steam are valid between 273.15 K and 1073.15 K (0 to 100 MPa), and between 1073.15 K and 2273.15 K (0 to 50 MPa).

The saturated water and steam calculations are valid between 273.15 K and 647.096 K.

The metastable calculation is valid between 273.15 K and 647.096 K, and for pressure from the saturated vapour line to the 5% equilibium moisture line (user defined). Use the Result Plot option to plot the steam properties versus temperature and pressure.

Note : There is an anomaly in the steam calculation for region 3 between the saturated vapour line, the regions 2/3 boundary, and the critical pressure. Select either region 2 or region 3 for calculations in the anomaly zone.

Reference : IAPWS R7-97 Industrial Formulation for thermodynamic Properties of Water and Steam

Tool Input

• anomtype : Region 2/3 Anomaly Type
• proptype : Steam Phase
  • Pu : User Defined Pressure
  • Tu : User Defined Temperature
  • Xu : User Defined Saturated Steam Quality

Tool Output

• ρ : Density
• Cp : Specific Heat Constant Pressure
• Cp-Cv : Delta Specific Heat (Cp - Cv)
• Cp/Cv : Specific Heat Ratio
• Cv : Specific Heat Constant Volume
• P : Pressure
• T : Temperature
• Vc : Speed Of Sound
• Z : Compressibility Factor
• cvg : Convergence Check
• h : Enthalpy
• s : Entropy
• u : Internal Energy
• vg : Mole Specific Volume
• vm : Specific Volume
• wv : Specific Weight