General

PCM (phase change material) fluids are substances which store or give off the supplied or released energy by means of a phase change. Energy is needed for the phase change, so that the temperature remains constant in the process. Due to this, a large part of the energy exists as latent heat and the operation temperature ranges become smaller compared to sensible heat storage systems. The substances described here undergo a phase transition from solid to liquid (melting) or from liquid to solid (solidifying). The phase change takes place within a melting interval. To be able to carry out calculations in the two-phase range, an effective specific heat capacity is defined so that the integral over the melting interval corresponds to the effective specific melting enthalpy (sum of melting enthalpy and sensible enthalpy):

\[ \Delta h_{eff} = \Delta h_{mel} + \Delta h_{sens} = \int_{T_{0}}^{T_{1}} c_{p,eff}(T) dT \]

 

The PCM fluids can be found in EBSILON in the oil/melt line type.

Four predefined fluids are available altogether.

Moreover, it is possible to create a user-defined fluid on the basis of a JSON-Format.

Although the pressure has to be formally specified when activating the physical properties functions, the calculations exclusively depend on the temperature.

The following physical properties functions are available:

Physical Property	Material value call A	Material value callB	EbsScript-Names
Enthalpy h	h (p, T)	h (p, s)	FuncH_OF_PT, FuncH_OF_PS
Thermal conductivity λ	lambda (p, T)	lambda (p, h)	FuncLAMBDA_OF_PT, FuncLAMBDA_OF_PH
Entropy s	s (p, T)	s (p, h)	FuncS_OF_PT, FuncS_OF_PH
Density ρ	rho (p, T)	rho (p, h)	FuncRHO_OF_PT, FuncRHO_OF_PH
Temperature T	T (p, h)	T (p, s)	FuncT_OF_PH, FuncT_OF_PS
Kinematic viscosity ν	nue (p, T)	nue (p, h)	FuncNUE_OF_PH, FuncNUE_OF_PS
Dynamic viscosity η	eta (p, T)	eta (p, h)	FuncETA_OF_PH, FuncETA_OF_PS
Specific volume v	v (p, T)	v (p, h)	FuncCP_OF_PT, FuncCP_OF_PH
gaseous portion x	x (p, T)	x (p, h)	FuncX_OF_PT, FuncX_OF_PH
Specific isobaric heat capacity cp	cp (p, T)	cp (p, h)	FuncCP_OF_PT, FuncCP_OF_PH
Minimum/Maximum Fluid temperature Tmin, Tmax	Tmin (p)	Tmax (p)	FuncTMIN_OF_P, FuncTMAX_OF_P
Minimum/Maximum Fluid pressure pmin, pmax	pmin (T)	pmax (T)	FuncPMIN_OF_T, FuncPMAX_OF_T
Enthalpy of the solid at the beginning of melting / of the liquid at the beginning of freezing	h_melt (T)	h_freeze (T)	FuncHMELT_OF_T, FuncHFREEZE_OF_T
Temperature of the solid at the beginning of melting / of the liquid at the beginning of freezing	T_melt (p)	T_freeze (p)	FuncTMEL_OF_P, FuncTFREEZE_OF_P

 

Effective Physical Properties Functions for Phase Smoothing

When modeling the latent heat accumulator, it has proven useful to develop effective material value functions that have a smoothed curve at the phase transition, since singularities at the phase transition point cause numerical problems and special treatment of such cases should be avoided.
Outside a small range around the phase transition point (0.05 K upwards and downwards), these functions correspond to the real material value functions listed above. Within this range, there is a smoothed transition from one phase to the other.

The following effective material value functions are available:

Effective Physical Property	Material value call	EbsScript-Name
Effective Enthalpy h	heff (p, T)	FuncHEFF_OF_PT
Effective specific isobaric heat capacity	cpeff (p, T)	FuncCPEFF_OF_PT
Effective density	rhoeff (p, T)	FuncRHOEFF_OF_PT
Effective thermal conductivity	lambdaeff (p, T)	FuncLAMBDAEFF_OF_PT
Effektiver gaseous portion	xeff (p, T)	FuncXEFF_OF_PT
Effective phase	phaseefff (p, T)	FuncPHASEEFF_OF_PT

 

These functions are also available:

Efektive Physical Property	Stoffwertaufruf	EbsScript-Name
Effective phase transition enthalpy dh between the state x1 and the state x2	dheff (p, x1, x2)	FuncDHEFF_OF_XX
Effective Temperature Teff, which is assigned to the state x For example, for the phase transition solid (x=10) / liquid (x=11), the actual phase transition temperature is obtained for x=10.5, the lower limit of the smoothing range for x=10.0 and the upper limit for x=11.0.	Teff (p, x)	FuncTEFF_OF_PX

Predefined Fluids

The predefined fluids of the manufacturer Rubitherm are substances with an effective melting interval of about 15K, where the mean temperature roughly corresponds to the number in the brand name of the PCM. In addition, there are lower and upper melting interval temperatures, designated as t_trans_lower and t_trans_upper in the json interface, and the melting temperature t_melt and the solidifying temperature t_freeze. The melting interval temperatures indicate the limits of the temperature range in which the effective specific heat capacity contains the fractions of the melting enthalpy (see above) and thus rises. In the melting interval, the PCM fluid undergoes a phase transition from solid to liquid. When the melting temperature t_melt is exceeded, it is assumed that the PCM fluid is in the liquid state (important e.g. when considering the convection in Component 166). When the solidifying temperature t_freeze is fallen below, it is assumed that the PCM fluid is in the solid state.

In what follows, the most important properties of the fluids are summarized:

• RT44HC: paraffin, operation temperatures 25-70°C, effective melting interval 37-52°C, effective specific melting enthalpy 250.51 kJ/kg, melting temperature 41°C, solidifying temperature 44°C

• RT64HC: paraffin, operation temperatures 25-95°C, effective melting interval 57-72°C, effective specific melting enthalpy 243.66 kJ/kg, melting temperature 64°C, solidifying temperature 65°C

• RT80HC: fatty acid, operation temperatures 25-110°C, effective melting interval 73-88°C, effective specific melting enthalpy 198.11 kJ/kg, melting temperature 77°C, solidifying temperature 80°C   
• SP58p: salt hydrate (sodium acetate trihydrate), operation temperatures 25-80°C, effective melting interval 51-66°C, effective specific melting enthalpy 242.42 kJ/kg, melting temperature 58°C, solidifying temperature 58°C

User defined fluids

Please note: All predefined fluids are already available in the required JSON format and can be used as templates for user-defined fluids by copy-and-paste.

The user-defined PCMs are created by means of the JSON-Formats . The following details are required for the full functionality of the PCMs:

• Name („name")
• Minimum and maximum operation temperatures („t_min" and „t_max")
• Melting temperature “t_melt“ and solidifying temperature “t_freeze“ (solidus and liquidus temperature), used e.g. when considering the convection in Component 166
• The limits of the effective melting interval “t_trans_lower“ and “t_trans_upper“, required e.g. in the context of “region_polynomial“ and “region_cp_with_h_eff“
• Specific heat capacity („cp"). An example of typical cp function is shown on figure 1. The corresponding enthalpy function example curve is shown on figure 2.
• Density („rho")
• Thermal conductivity (“lambda“)
• Dynamic viscosity (“eta“)

Moreover, further optional details are available:

• Minimum and maximum operation pressures (“p_min“ and “p_max“)
  • set to 0.001-1000 bar by default
• Zero point definition by pressure, temperature, specific entropy and enthalpy
  • „t0", „p0", „h0" and „s0"
  • Set to 0 kJ/kg and 0 kJ/(kgK) at 1 bar and 25°C by default

Most characteristic values are described by means of primitive types. The physical material properties heat capacity, density, thermal conductivity, and dynamic viscosity have to be defined by various more complex JSON objects, which in turn presuppose one of the predefined types. In what follows, these types are listed and the specifications for the JSON format are described:

• „step_points" → depend on the physical material properties
  • o Heat capacity: piecewise constant function; points define the beginning of the constant value that is valid up to the next point
    • Advantage: enthalpy becomes piecewise linear function
  • Other physical material properties: piecewise linear function between the initial point and the terminal point
  • Definied as an array of points that, in turn, are arrays
• „polynomial"
  • The entire operation temperature range is defined by an individual polynomial of any degree
  • Defined as an array of the coefficients of the polynomial, beginning with the smallest coefficient a_0 (absolute term)
• „region_polynomial"
  • The solid and the liquid phase are described with an own polynomial in each case; the melting interval is interpolated in a linear way
  • Defined as an object with the properties “liquid“ and “solid“, which are assigned to the respective arrays of the polynomial coefficients
• „piecewise_polynomial"
  • The entire operation temperature range is defined by any number of polynomials
  • The entire operation temperature range must be covered and the polynomials must be specified sorted according to the definition range
  • Consists of an array of the piecewise defined polynomials
  • Polynomials defined as objects with upper and lower limit of the definition range (“t_min“ and “t_max“) as well as the array of the polynomial coefficients (“polynomial“)
  • For the dynamic viscosity eta only the liquid range between "t_trans_upper" and "t_max" has to be covered, because only in the liquid range the viscosity is defined.
• „expression": here t (temperature in °C) and p (pressure in bar) can be used as arguments 
  • Definition of a random temperature-dependent function by means of all common functions and operators by a simple string
  • Use of the conditional operator for the definition of different functions as a function of the temperature range

    • condition ? true case : false case
      

• „region_cp_with_h_eff“ → only available for the heat capacity: here t (temperature in °C) can be used as an argument
  • Solid and liquid phase defined by one of the previous types (except “region_polynomial“)
    • „solid“ and „liquid“ as objects with the respective type
  • The behavior in the two-phase range is calculated by specifying the effective specific melting enthalpy (“h_eff“)
    • Function in the two-phase range: \(cp(T) = a + b * (1 - tanh^{2}(c * T + d))\)
    • \(c\) can be specified by the user (by default 0.26). The value of c impacts the shape of the cp curve (see example on figure 1)
    • The remaining coefficients (a, b, d) are determined from the boundary conditions \( \Delta h_{eff} \) adhered to and continuity of the function at both margins

Figure 1. Example of Cp,eff as a funcion of temperature for a PCM fluid

Figure 2. Example of PCM fluid enthalpy as a funcion of temperature resulting from the integration of the corresponding Cp,eff function 

Below is a syntactically correct definition of a PCM fluid where each of the existing types is used. This is only an example of the different types and not a real fluid for calculations.

{
    "name" : "MyFluid",
    "p_min" : 0.1,
    "t_min" : 20,
    "t_max" : 60,
    "t_melt" : 38,
    "t_freeze" : 38,
    "t_trans_lower" : 35,
    "t_trans_upper" : 45,
    "t0" : 35,
    "p0" : 1,
    "h0" : 1000,
    "s0" : 0.8,
    "cp" : {
        "region_cp_with_h_eff" : {
            "h_eff" : 250,
            "c" : 0.4,
            "liquid" : {
                "step_points" : [
                    [45, 1.6],
                    [50, 1.7],
                    [60, 1.8]
                ]
            },
            "solid" : {
                "expression" : "t>30 ? 1.5E-2*t : sin(t+3)"
            }
        }
    },
    "rho" : {
        "polynomial" : [1700, 3.5, 4E-06]
    },
    "lambda" : {
        "region_polynomial" : {
            "liquid" : [0.2],
            "solid" : [0.1, 0.004]
        }
    },
    "eta" : {
        "piecewise_polynomial" : [
            {
                "t_min" : 45,
                "t_max" : 55,
                "polynomial" : [30]
            },
            {
                "t_min" : 55,
                "t_max" : 60,
                "polynomial" : [40]
            }
        ]
    }
}