boundary23ofT Boundary function for region boundary between regions 2 and 3 (input temperature)
	boundary23ofp Boundary function for region boundary between regions 2 and 3 (input pressure)
	hlowerofp5 Explicit lower specific enthalpy limit of region 5 as function of pressure
	hupperofp5 Explicit upper specific enthalpy limit of region 5 as function of pressure
	slowerofp5 Explicit lower specific entropy limit of region 5 as function of pressure
	supperofp5 Explicit upper specific entropy limit of region 5 as function of pressure
	hlowerofp1 Explicit lower specific enthalpy limit of region 1 as function of pressure
	hupperofp1 Explicit upper specific enthalpy limit of region 1 as function of pressure (meets region 4 saturation pressure curve at 623.15 K)
	slowerofp1 Explicit lower specific entropy limit of region 1 as function of pressure
	supperofp1 Explicit upper specific entropy limit of region 1 as function of pressure (meets region 4 saturation pressure curve at 623.15 K)
	hlowerofp2 Explicit lower specific enthalpy limit of region 2 as function of pressure (meets region 4 saturation pressure curve at 623.15 K)
	hupperofp2 Explicit upper specific enthalpy limit of region 2 as function of pressure
	slowerofp2 Explicit lower specific entropy limit of region 2 as function of pressure (meets region 4 saturation pressure curve at 623.15 K)
	supperofp2 Explicit upper specific entropy limit of region 2 as function of pressure
	d1n Density in region 1 as function of p and T
	d2n Density in region 2 as function of p and T
	dhot1ofp Density at upper temperature limit of region 1
	dupper1ofT Density at upper pressure limit of region 1
	hl_p_R4b Explicit approximation of liquid specific enthalpy on the boundary between regions 4 and 3
	hv_p_R4b Explicit approximation of vapour specific enthalpy on the boundary between regions 4 and 3
	sl_p_R4b Explicit approximation of liquid specific entropy on the boundary between regions 4 and 3
	sv_p_R4b Explicit approximation of vapour specific entropy on the boundary between regions 4 and 3
	rhol_p_R4b Explicit approximation of liquid density on the boundary between regions 4 and 3
	rhov_p_R4b Explicit approximation of vapour density on the boundary between regions 4 and 2
	boilingcurve_p Properties on the boiling curve
	dewcurve_p Properties on the dew curve
	hvl_p
	hl_p Liquid specific enthalpy on the boundary between regions 4 and 3 or 1
	hv_p Vapour specific enthalpy on the boundary between regions 4 and 3 or 2
	hvl_p_der Derivative function for the specific enthalpy along the phase boundary
	rhovl_p
	rhol_p Density of saturated water
	rhov_p Density of saturated vapour
	rhovl_p_der
	sl_p Liquid specific entropy on the boundary between regions 4 and 3 or 1
	sv_p Vapour specific entropy on the boundary between regions 4 and 3 or 2
	rhol_T Density of saturated water
	rhov_T Density of saturated vapour
	region_ph Return the current region (valid values: 1,2,3,4,5) in IF97 for given pressure and specific enthalpy
	region_ps Return the current region (valid values: 1,2,3,4,5) in IF97 for given pressure and specific entropy
	region_pT Return the current region (valid values: 1,2,3,5) in IF97, given pressure and temperature
	region_dT Return the current region (valid values: 1,2,3,4,5) in IF97, given density and temperature
	hvl_dp Derivative function for the specific enthalpy along the phase boundary
	dhl_dp Derivative of liquid specific enthalpy on the boundary between regions 4 and 3 or 1 w.r.t. pressure
	dhv_dp Derivative of vapour specific enthalpy on the boundary between regions 4 and 3 or 1 w.r.t. pressure
	drhovl_dp
	drhol_dp Derivative of density of saturated water w.r.t. pressure
	drhov_dp Derivative of density of saturated steam w.r.t. pressure

This information is part of the Modelica Standard Library maintained by the Modelica Association.

Package description

Package Regions contains a large number of auxiliary functions which are needed to compute the current region of the IAPWS/IF97 for a given pair of input variables as quickly as possible. The focus of this implementation was on computational efficiency, not on compact code. Many of the function values calculated in these functions could be obtained using the fundamental functions of IAPWS/IF97, but with considerable overhead. If the region of IAPWS/IF97 is known in advance, the input variable mode can be set to the region, then the somewhat costly region checks are omitted. The checking for the phase has to be done outside the region functions because many properties are not differentiable at the region boundary. If the input phase is 2, the output region will be set to 4 immediately.

Package contents

The main 4 functions in this package are the functions returning the appropriate region for two input variables.

• Function region_ph compute the region of IAPWS/IF97 for input pair pressure and specific enthalpy.
• Function region_ps compute the region of IAPWS/IF97 for input pair pressure and specific entropy
• Function region_dT compute the region of IAPWS/IF97 for input pair density and temperature.
• Function region_pT compute the region of IAPWS/IF97 for input pair pressure and temperature (only in phase region).

In addition, functions of the boiling and condensation curves compute the specific enthalpy, specific entropy, or density on these curves. The functions for the saturation pressure and temperature are included in the package Basic because they are part of the original IAPWS/IF97 standards document. These functions are also aliased to be used directly from package Water.

• Function hl_p computes the liquid specific enthalpy as a function of pressure. For overcritical pressures, the critical specific enthalpy is returned. An approximation is used for temperatures > 623.15 K.
• Function hv_p computes the vapour specific enthalpy as a function of pressure. For overcritical pressures, the critical specific enthalpy is returned. An approximation is used for temperatures > 623.15 K.
• Function sl_p computes the liquid specific entropy as a function of pressure. For overcritical pressures, the critical specific entropy is returned. An approximation is used for temperatures > 623.15 K.
• Function sv_p computes the vapour specific entropy as a function of pressure. For overcritical pressures, the critical specific entropy is returned. An approximation is used for temperatures > 623.15 K.
• Function rhol_T computes the liquid density as a function of temperature. For overcritical temperatures, the critical density is returned. An approximation is used for temperatures > 623.15 K.
• Function rhol_T computes the vapour density as a function of temperature. For overcritical temperatures, the critical density is returned. An approximation is used for temperatures > 623.15 K.

All other functions are auxiliary functions called from the region functions to check a specific boundary.

• Function boundary23ofT computes the boundary pressure between regions 2 and 3 (input temperature)
• Function boundary23ofp computes the boundary temperature between regions 2 and 3 (input pressure)
• Function hlowerofp5 computes the lower specific enthalpy limit of region 5 (input p, T=1073.15 K)
• Function hupperofp5 computes the upper specific enthalpy limit of region 5 (input p, T=2273.15 K)
• Function slowerofp5 computes the lower specific entropy limit of region 5 (input p, T=1073.15 K)
• Function supperofp5 computes the upper specific entropy limit of region 5 (input p, T=2273.15 K)
• Function hlowerofp1 computes the lower specific enthalpy limit of region 1 (input p, T=273.15 K)
• Function hupperofp1 computes the upper specific enthalpy limit of region 1 (input p, T=623.15 K)
• Function slowerofp1 computes the lower specific entropy limit of region 1 (input p, T=273.15 K)
• Function supperofp1 computes the upper specific entropy limit of region 1 (input p, T=623.15 K)
• Function hlowerofp2 computes the lower specific enthalpy limit of region 2 (input p, T=623.15 K)
• Function hupperofp2 computes the upper specific enthalpy limit of region 2 (input p, T=1073.15 K)
• Function slowerofp2 computes the lower specific entropy limit of region 2 (input p, T=623.15 K)
• Function supperofp2 computes the upper specific entropy limit of region 2 (input p, T=1073.15 K)
• Function d1n computes the density in region 1 as function of pressure and temperature
• Function d2n computes the density in region 2 as function of pressure and temperature
• Function dhot1ofp computes the hot density limit of region 1 (input p, T=623.15 K)
• Function dupper1ofTcomputes the high pressure density limit of region 1 (input T, p=100MPa)
• Function hl_p_R4b computes a high accuracy approximation to the liquid enthalpy for temperatures > 623.15 K (input p)
• Function hv_p_R4b computes a high accuracy approximation to the vapour enthalpy for temperatures > 623.15 K (input p)
• Function sl_p_R4b computes a high accuracy approximation to the liquid entropy for temperatures > 623.15 K (input p)
• Function sv_p_R4b computes a high accuracy approximation to the vapour entropy for temperatures > 623.15 K (input p)
• Function rhol_p_R4b computes a high accuracy approximation to the liquid density for temperatures > 623.15 K (input p)
• Function rhov_p_R4b computes a high accuracy approximation to the vapour density for temperatures > 623.15 K (input p)

Version Info and Revision history

• First implemented: July, 2000 by Hubertus Tummescheit

Authors: Hubertus Tummescheit, Jonas Eborn and Falko Jens Wagner
Modelon AB
Ideon Science Park
SE-22370 Lund, Sweden
email: hubertus@modelon.se

• Initial version: July 2000
• Revised and extended for inclusion in Modelica.Thermal: December 2002