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Using property values of aqueous solutions and ice to estimate ice concentrations and enthalpies of ice slurries
International Journal of Refrigeration 28 (2005) 13–19 www.elsevier.com/locate/ijrefrig
Using property values of aqueous solutions and ice to estimate ice concentrations and enthalpies of ice slurries ˚ . Melinder*, E. Granryd A Department of Energy Technology, Division of Applied Thermodynamics and Refrigeration, The Royal Institute of Technology (KTH), S-100 44, Stockholm, Sweden Received 10 February 2003; received in revised form 14 June 2004; accepted 16 July 2004
Abstract For ice slurry calculations and modeling, it is important that they are performed with accurate thermophysical property values of the aqueous solution and of ice. For ice slurry applications there is a need for accurate freezing point data and for more basic thermophysical property data at low concentrations. The article covers some phenomena in connection with freezing of aqueous solutions. Charts with ice concentration curves as a function of temperature and additive concentration are given for a number of aqueous solutions. A main purpose of using ice slurry is to benefit from the latent heat or enthalpy difference at melting. The article shows how an enthalpy-phase diagram can be constructed, gives charts with enthalpy values and charts giving apparent specific heat as a function of temperature and concentration for aqueous solution of propylene glycol, ethyl alcohol and potassium formate. These charts for ethyl alcohol–water are in good agreement with works earlier reported on. q 2004 Elsevier Ltd and IIR. All rights reserved. Keywords: Two-phase secondary refrigerant; Ice slurry; Aqueous solution; Thermal property; Physical property; Temperature; Heat capacity; Concentration; Propylene glycol; Alcohol; Potassium
Utilisation des proprie´te´ des solutions aqueuses et de la glace a fin d’e´valuer les concentrations de glace et les enthalpies des coulis de glace Mots cle´s: Frigoporteur diphasique; Coulis de glace; Solution aqueuse; Proprie´te´ thermique; Proprie´te´ physique; Tempe´rature; Chaleur massique; Concentration; Propyle`ne glycol; Alcool; Potassium
1. Introduction A number of aqueous solutions are used as liquid secondary refrigerants in indirect heat pump and refrigeration
* Corresponding author. Tel.: C46-8-790-7454; fax: C46-8-203007. E-mail address: [email protected] ( Melinder). 0140-7007/$35.00 q 2004 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2004.07.013
systems to transport energy from the cooling object to the evaporator. The same liquids may be used for ice slurry applications, but it is important to have accurate thermophysical property values of ice and of the water solution used as a start for ice slurry calculations and modeling. The IIRpublication by Melinder [1] contains thermophysical property values for a number of aqueous solutions. The reliability of these values is reported in Refs. [3,4]. However, for ice slurry
A˚ Melinder, E. Granryd / International Journal of Refrigeration 28 (2005) 13–19
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Nomenclature c cp h DhM cI m t
mass concentration (kg kg-1 sol.) specific heat (J kg-1 K-1) enthalpy (J kg-1) heat of mixing (J kg-1) ice concentration (kg ice kg-1 sol.) mass (kg) temperature (8C)
applications there is a need for more data at lower additive concentrations and that was treated in Ref. [2]. CRC Handbook of Chemistry and Physics [5] gives reliable values of freezing point as a function of the concentration. Handbooks with data for heats of mixing give enthalpy values at a reference temperature (tRZ0 or 25 8C) for a number of aqueous solutions. For calculation purposes of an ice slurry, we can view the solution as consisting of ice crystals of pure water that freeze out, and the rest of the solution with a higher concentration of the freezing point depressant substance. A mass balance of the salt concentration gives the amount of frozen ice and of concentrated solution. A main purpose of using ice slurry is naturally to benefit from the latent heat or enthalpy difference at melting. This reduces the volume flow rate needed for a given heating power or cooling capacity. The paper gives charts with ice concentration as a function of the concentration of the added substance for a number of aqueous solutions. Charts with enthalpy values as a function of temperature and concentration of the freezing point depressant substance and with approximate ice concentration curves are given for aqueous solutions of propylene glycol, ethyl alcohol and potassium formate. The attached charts for ethyl alcohol are in good agreement with earlier works presented during the last few years.
2. Phase changing secondary refrigerants Most secondary refrigerants are aqueous solutions, mixtures of water and a freezing point depressant substance. Let us consider some phenomena in connection with freezing of aqueous solutions and enthalpy diagrams of phase changing secondary refrigerants used as ice slurries. A main purpose with such phase changing secondary refrigerants is to benefit from the latent heat or enthalpy difference at melting, which can reduce the volume flow rate needed for a given heating power or cooling capacity. In ice slurry applications, small ice crystals are produced as a slurry in water or aqueous solution and distributed to the cooling object from which heat is removed when some of the ice crystals melt. For aqueous solutions, the available latent heat has its maximum at temperatures just below the
Index E F I O R S 0, R
eutectic freezing point ice original, initial reference solution, concentrated water at reference temperature
freezing point and it decreases at lower temperatures. This also means that for temperatures just below the freezing point a certain concentration of ice can be produced with a small temperature reduction, while this is not the case for lower temperatures.
3. Freezing point and ice concentration Fig. 1 shows how the freezing point is changed with the composition of the mixture. The diagram can be used for any of the aqueous solutions, but let us use the example of a salt in water. An increased concentration of the freezing point depressant substance lowers the freezing point temperature. This continues until we reach the concentration where salt and water form an eutectic solution. The freezing point is raised when the concentration becomes higher than the eutectic. The over-eutectic part of the freezing point curve is generally not of interest for this application. Note that only certain solutions have well defined eutectic points. Let us assume a solution with the concentration c0 and note what happens when it is cooled down from A to the freezing point F (c0, tF,0) and below that temperature. If the temperature is decreased below the freezing point and the process takes place in equilibrium, a separation of the mixture takes place. Ice crystals that ideally consist of pure water freeze out and are separated from the rest of the solution that as a consequence gets increasingly higher concentration of the freezing point depressant substance.
Fig. 1. Freezing point diagram.
A˚ Melinder, E. Granryd / International Journal of Refrigeration 28 (2005) 13–19
Fig. 2. (a–f) Ice concentration as a function of the temperature for six types of aqueous solutions.
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Fig. 2 (continued)
When the temperature has been lowered so that it corresponds to K in Fig. 1, there are ice crystals with the condition (cIZ0, tF,S) as well as solution with the condition (cS, tF,S). A consequence of what is said is further that the solution does not freeze to a solid mass when the freezing point is passed, an ice slurry is formed. It is first when the temperature goes down to the eutectic temperature that the solution fully solidifies. We need also to remember that we in practice often get sub-cooling phenomena. The first ice crystals are often not formed until one or two degrees under the freezing point indicated by the freezing point curve. When some ice crystals have been formed the continued process seems easier to take place in equilibrium. The concentration of the remaining solution is given by a mass balance based on the condition that the mixture totally has unchanged amount of salt. Let us call the mass of pure ice as mI and the mass of solution with mS, the concentration of which is cS. Then the amount of salt is mScS. In the original solution, the salt amount was evidently c0(mICmS). As the amount of salt has not changed, it follows that mScSZc0(mICmS), that also can be written as mS(cSKc0)Z mIc0. The ice concentration, cI, can then easily be calculated from cI Z mI =ðmI C mS Þ Z ðcS K c0 Þ=cS
(1)
Some extensive works on ice slurry properties, such as
Fig. 3. Enthalpy-phase diagram of sodium chloride–water as a function of additive concentration.
A˚ Melinder, E. Granryd / International Journal of Refrigeration 28 (2005) 13–19
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Fig. 4. (a–b) Charts giving enthalpy and apparent specific heat of ethyl alcohol (EA). (c–d) Charts giving enthalpy and apparent specific heat of propylene glycol (PG). (e–f) Charts giving enthalpy and apparent specific heat of potassium formate (KF) (on next page).
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A˚ Melinder, E. Granryd / International Journal of Refrigeration 28 (2005) 13–19
Figs. 2a–f gives in the same manner ice concentration as a function of the temperature for various concentrations of the freezing point depressant substance for the following aqueous solutions: (a) propylene glycol, (b) ethyl alcohol, (c) sodium chloride, (d) potassium carbonate, (e) potassium acetate and (f) potassium formate. Property values are taken from Ref. [5] and an Excel program based on polynom equations and coefficients (not valid for low concentrations) in Refs. [1,10].
4. Enthalpy diagrams of aqueous solutions
Fig. 4 (continued )
Bel et al. [6] and Guilpart et al. [7], present ice concentration as a function of the temperature for various concentrations of the freezing point depressant substance, usually for ethyl alcohol–water. Suitable equations of ice slurries are also given in Kauffeld et al. [8] and Lottin et al. [9].
A main purpose with phase changing secondary refrigerants is to benefit from the latent heat or enthalpy difference at melting. This use of latent heat reduces the volume flow rate needed for a given heating power or cooling capacity. The amounts of heat exchanged in connection with the freezing process just described can be calculated if we have access to enthalpy values, as from an enthalpy diagram for the solution in question. Fig. 3 shows as an example a diagram for a mixture of sodium chloride– water, partly based on a more extensive diagram from Bosˇnjakovic´ [11]. The additive concentration is given in [kg NaCl/kg solution]. The vertical axis gives the enthalpy, h, expressed in kJ kgK1 mixture. The heat of melting of water can be seen as the enthalpy difference between N and P. Following Granryd, et al. [12], the freezing point curve is in Fig. 3 represented by the line N–E, where E is the eutectic point. The diagram also shows a few isothermal lines. Let us follow the cooling process for a mixture with the condition A, having the temperature tAZ0 8C. If the temperature is lowered, the freezing point, tFZK5 8C is passed in F. If more heat is removed from the mixture we move further down in the diagram and the temperature has reached tKZK10 8C in point K. As mentioned earlier, we can view the ice slurry solution as consisting of ice crystals of pure water that freeze out, and the rest of the solution with a higher concentration of the freezing point depressant substance. Point K then represents a condition of mixture between pure ice at tKZK10 8C (point H), and solution with the freezing point tKZK10 8C (point L). The amount of heat that has to be removed for each kg original solution can be seen as the enthalpy difference hAKhK. During cooling below the freezing point of a mixture that does not have eutectic composition, ice slurry is first formed, as we earlier discussed. The forming of solid mass first takes place at a temperature equal to that of the eutectic point, E. A solution with eutectic composition of sodium chloride freezes to solid ice between E and M. The enthalpy difference between E and M is the latent heat of phase change of the eutectic solution. The variation with concentration of enthalpy values for an isothermal line (for instance, tZ0 8C) relates to the heat of mixing. Bosˇnjakovic´ [11] and Rant [13] give enthalpy
A˚ Melinder, E. Granryd / International Journal of Refrigeration 28 (2005) 13–19
phase diagrams as a function of additive concentration and temperature also for other aqueous solutions than sodium chloride. In order to construct enthalpy-phase diagrams, the solution may be assumed as consisting of ice crystals of pure water that freeze out, and the rest of the solution with a higher concentration of the additive, the freezing point depressant substance. Enthalpy values of an aqueous solution can then be estimated with the help of specific heat values of the aqueous solution down to the freezing point curve, heat of melting of ice and heat of mixing data of the solution. The enthalpy of the ice slurry can (with the nomenclature from Fig. 1) be expressed by the following correlation h Z hI ðtS ÞcI C hS ðcS ; tS Þð1 K cI Þ
(2)
where the enthalpy of ice, hI(tS) can be expressed as hI ðtS Þ Z KðhN K hP Þ C ðhH K hP Þ
(3)
In Eq. (3), the heat of melting of ice hNKhPZ 332.4 kJ kg-1, and hHKhPZKcp,ItS, where the average specific heat of ice is cp,IZ2.09 kJ kg-1 K-1. The enthalpy of the remaining solution, hS(cS,tS) can be expressed as ð tS (4) hS ðcS ; tS Þ Z h0;R C DhM ðcS ; tR Þ C cp dt tR
where h0,R is the enthalpy of water at the reference temperature and DhM(cS, tR) is the heat of mixing for the concentration cS. Values of heat of mixing, DhM (usually at tRZ0 or 25 8C) are taken from Heats of Mixing Data Collection [14], Handbook of Heats of Mixing [15], Landolt-Bo¨rnstein [16] and an internal report from Norsk Hydro Research Center [17]. Some works on ice slurry properties give enthalpy, and at times apparent specific heat, as a function of the temperature for various concentrations of the freezing point depressant substance, usually ethyl alcohol–water [6,7]. Fig. 4a–f give similar graphs with enthalpy and apparent specific heat for aqueous solutions of ethyl alcohol, propylene glycol and for potassium formate. Lines for constant ice concentrations (0.1, 0.2, 0.3, 0.4 and 0.5) are indicated in the enthalpy charts.
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References ˚ . Melinder, Thermophysical properties of liquid secondary [1] A refrigerants, Tables and diagrams for the refrigeration industry, IIF/IIR, Paris, 1997. ˚ . Melinder, Accurate thermophysical property values of [2] A aqueous solutions are important for ice slurry modeling and calculations, Third Workshop of the International Institute of Refrigeration on Ice Slurries, Lucern, 2001 p. 19–26. ˚ . Melinder, Thermophysical properties of liquid secondary [3] A refrigerants, A critical review on literature references and laboratory measurements, KTH, Stockholm, 1998. ˚ . Melinder, A critical review on thermo-physical properties [4] A of liquid secondary refrigerants, Natural Working Fluids’98, IIR Gustav Lorentzen Conference, Oslo, 1998 p. 505–15. [5] CRC handbook of chemistry and physics, 69th ed.; 1988–89. [6] O. Bel, A. Lallemand, Study of a two-phase secondary refrigerant. 1. Intrinsic thermophysical properties of an ice slurry, Int J Refrig, IIR/IIF, Paris 22 (1999) 164–174. [7] J. Guilpart, L. Fournaison, M.A. Ben Lakhdar, Calculation method of ice slurries thermophysical properties—application to water/ethanol mixture, Int Congr Refrig, IIR/IIF, Sydney 1999. [8] M. Kauffeld, K.G. Christensen, S. Lund, T.M. Hansen, Experience with ice slurry, Int Congr Refrig, IIR/IIF, Sydney 1999. [9] O. Lottin, C. Epiard, Thermodynamic properties of some currently used water-antifreeze mixtures when used as ice slurries, Eighth Int Refrig, Purdue, USA 2000; 391–398. ˚ Melinder, Thermophysical properties of liquid secondary [10] A refrigerants, charts and tables, Swedish Society of Refrigeration, Stockholm, 1997. [11] F. Bosˇnjakovic´, Technische Thermodynamik, Teil II, Band 12, in: Wa¨rmelehre und Wa¨rmewirtschaft in Einzeldarstellungen, Dresden/Leipzig, 1961. ˚ . Melinder, Secondary refrigerants for indirect [12] E. Granryd, A systems in: E. Granryd et al. (Ed.),, Refrigerating engineering, KTH, Stockholm, 1999, pp. 6:2–6:6. [13] Z. Rant, Diagramm-Mappe zu Band 13, Verdampfen in Theorie und Praxis, in: Wa¨rmelehre und Wa¨rmewirtschaft in Einzeldarstellungen, Dresden/Leipzig, 1961. [14] J.J. Christensen, J. Gmehling, P. Rasmussen, U. Weidlich, Heats of mixing data collection, 1, Binary Systems 1986. [15] C. Christensen, R.W. Hanks, R.M. Izatt, Handbook of heats of mixing 1982. [16] Landolt-Bo¨rnstein, Numerical data and functional relationships in science and technology, Group IV. Heats Mixing Solution 1976;2. [17] Norsk Hydro Research Centre, Internal report; 2001.
Using property values of aqueous solutions and ice to estimate ice concentrations and enthalpies of ice slurries ˚ . Melinder*, E. Granryd A Department of Energy Technology, Division of Applied Thermodynamics and Refrigeration, The Royal Institute of Technology (KTH), S-100 44, Stockholm, Sweden Received 10 February 2003; received in revised form 14 June 2004; accepted 16 July 2004
Abstract For ice slurry calculations and modeling, it is important that they are performed with accurate thermophysical property values of the aqueous solution and of ice. For ice slurry applications there is a need for accurate freezing point data and for more basic thermophysical property data at low concentrations. The article covers some phenomena in connection with freezing of aqueous solutions. Charts with ice concentration curves as a function of temperature and additive concentration are given for a number of aqueous solutions. A main purpose of using ice slurry is to benefit from the latent heat or enthalpy difference at melting. The article shows how an enthalpy-phase diagram can be constructed, gives charts with enthalpy values and charts giving apparent specific heat as a function of temperature and concentration for aqueous solution of propylene glycol, ethyl alcohol and potassium formate. These charts for ethyl alcohol–water are in good agreement with works earlier reported on. q 2004 Elsevier Ltd and IIR. All rights reserved. Keywords: Two-phase secondary refrigerant; Ice slurry; Aqueous solution; Thermal property; Physical property; Temperature; Heat capacity; Concentration; Propylene glycol; Alcohol; Potassium
Utilisation des proprie´te´ des solutions aqueuses et de la glace a fin d’e´valuer les concentrations de glace et les enthalpies des coulis de glace Mots cle´s: Frigoporteur diphasique; Coulis de glace; Solution aqueuse; Proprie´te´ thermique; Proprie´te´ physique; Tempe´rature; Chaleur massique; Concentration; Propyle`ne glycol; Alcool; Potassium
1. Introduction A number of aqueous solutions are used as liquid secondary refrigerants in indirect heat pump and refrigeration
* Corresponding author. Tel.: C46-8-790-7454; fax: C46-8-203007. E-mail address: [email protected] ( Melinder). 0140-7007/$35.00 q 2004 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2004.07.013
systems to transport energy from the cooling object to the evaporator. The same liquids may be used for ice slurry applications, but it is important to have accurate thermophysical property values of ice and of the water solution used as a start for ice slurry calculations and modeling. The IIRpublication by Melinder [1] contains thermophysical property values for a number of aqueous solutions. The reliability of these values is reported in Refs. [3,4]. However, for ice slurry
A˚ Melinder, E. Granryd / International Journal of Refrigeration 28 (2005) 13–19
14
Nomenclature c cp h DhM cI m t
mass concentration (kg kg-1 sol.) specific heat (J kg-1 K-1) enthalpy (J kg-1) heat of mixing (J kg-1) ice concentration (kg ice kg-1 sol.) mass (kg) temperature (8C)
applications there is a need for more data at lower additive concentrations and that was treated in Ref. [2]. CRC Handbook of Chemistry and Physics [5] gives reliable values of freezing point as a function of the concentration. Handbooks with data for heats of mixing give enthalpy values at a reference temperature (tRZ0 or 25 8C) for a number of aqueous solutions. For calculation purposes of an ice slurry, we can view the solution as consisting of ice crystals of pure water that freeze out, and the rest of the solution with a higher concentration of the freezing point depressant substance. A mass balance of the salt concentration gives the amount of frozen ice and of concentrated solution. A main purpose of using ice slurry is naturally to benefit from the latent heat or enthalpy difference at melting. This reduces the volume flow rate needed for a given heating power or cooling capacity. The paper gives charts with ice concentration as a function of the concentration of the added substance for a number of aqueous solutions. Charts with enthalpy values as a function of temperature and concentration of the freezing point depressant substance and with approximate ice concentration curves are given for aqueous solutions of propylene glycol, ethyl alcohol and potassium formate. The attached charts for ethyl alcohol are in good agreement with earlier works presented during the last few years.
2. Phase changing secondary refrigerants Most secondary refrigerants are aqueous solutions, mixtures of water and a freezing point depressant substance. Let us consider some phenomena in connection with freezing of aqueous solutions and enthalpy diagrams of phase changing secondary refrigerants used as ice slurries. A main purpose with such phase changing secondary refrigerants is to benefit from the latent heat or enthalpy difference at melting, which can reduce the volume flow rate needed for a given heating power or cooling capacity. In ice slurry applications, small ice crystals are produced as a slurry in water or aqueous solution and distributed to the cooling object from which heat is removed when some of the ice crystals melt. For aqueous solutions, the available latent heat has its maximum at temperatures just below the
Index E F I O R S 0, R
eutectic freezing point ice original, initial reference solution, concentrated water at reference temperature
freezing point and it decreases at lower temperatures. This also means that for temperatures just below the freezing point a certain concentration of ice can be produced with a small temperature reduction, while this is not the case for lower temperatures.
3. Freezing point and ice concentration Fig. 1 shows how the freezing point is changed with the composition of the mixture. The diagram can be used for any of the aqueous solutions, but let us use the example of a salt in water. An increased concentration of the freezing point depressant substance lowers the freezing point temperature. This continues until we reach the concentration where salt and water form an eutectic solution. The freezing point is raised when the concentration becomes higher than the eutectic. The over-eutectic part of the freezing point curve is generally not of interest for this application. Note that only certain solutions have well defined eutectic points. Let us assume a solution with the concentration c0 and note what happens when it is cooled down from A to the freezing point F (c0, tF,0) and below that temperature. If the temperature is decreased below the freezing point and the process takes place in equilibrium, a separation of the mixture takes place. Ice crystals that ideally consist of pure water freeze out and are separated from the rest of the solution that as a consequence gets increasingly higher concentration of the freezing point depressant substance.
Fig. 1. Freezing point diagram.
A˚ Melinder, E. Granryd / International Journal of Refrigeration 28 (2005) 13–19
Fig. 2. (a–f) Ice concentration as a function of the temperature for six types of aqueous solutions.
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Fig. 2 (continued)
When the temperature has been lowered so that it corresponds to K in Fig. 1, there are ice crystals with the condition (cIZ0, tF,S) as well as solution with the condition (cS, tF,S). A consequence of what is said is further that the solution does not freeze to a solid mass when the freezing point is passed, an ice slurry is formed. It is first when the temperature goes down to the eutectic temperature that the solution fully solidifies. We need also to remember that we in practice often get sub-cooling phenomena. The first ice crystals are often not formed until one or two degrees under the freezing point indicated by the freezing point curve. When some ice crystals have been formed the continued process seems easier to take place in equilibrium. The concentration of the remaining solution is given by a mass balance based on the condition that the mixture totally has unchanged amount of salt. Let us call the mass of pure ice as mI and the mass of solution with mS, the concentration of which is cS. Then the amount of salt is mScS. In the original solution, the salt amount was evidently c0(mICmS). As the amount of salt has not changed, it follows that mScSZc0(mICmS), that also can be written as mS(cSKc0)Z mIc0. The ice concentration, cI, can then easily be calculated from cI Z mI =ðmI C mS Þ Z ðcS K c0 Þ=cS
(1)
Some extensive works on ice slurry properties, such as
Fig. 3. Enthalpy-phase diagram of sodium chloride–water as a function of additive concentration.
A˚ Melinder, E. Granryd / International Journal of Refrigeration 28 (2005) 13–19
17
Fig. 4. (a–b) Charts giving enthalpy and apparent specific heat of ethyl alcohol (EA). (c–d) Charts giving enthalpy and apparent specific heat of propylene glycol (PG). (e–f) Charts giving enthalpy and apparent specific heat of potassium formate (KF) (on next page).
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A˚ Melinder, E. Granryd / International Journal of Refrigeration 28 (2005) 13–19
Figs. 2a–f gives in the same manner ice concentration as a function of the temperature for various concentrations of the freezing point depressant substance for the following aqueous solutions: (a) propylene glycol, (b) ethyl alcohol, (c) sodium chloride, (d) potassium carbonate, (e) potassium acetate and (f) potassium formate. Property values are taken from Ref. [5] and an Excel program based on polynom equations and coefficients (not valid for low concentrations) in Refs. [1,10].
4. Enthalpy diagrams of aqueous solutions
Fig. 4 (continued )
Bel et al. [6] and Guilpart et al. [7], present ice concentration as a function of the temperature for various concentrations of the freezing point depressant substance, usually for ethyl alcohol–water. Suitable equations of ice slurries are also given in Kauffeld et al. [8] and Lottin et al. [9].
A main purpose with phase changing secondary refrigerants is to benefit from the latent heat or enthalpy difference at melting. This use of latent heat reduces the volume flow rate needed for a given heating power or cooling capacity. The amounts of heat exchanged in connection with the freezing process just described can be calculated if we have access to enthalpy values, as from an enthalpy diagram for the solution in question. Fig. 3 shows as an example a diagram for a mixture of sodium chloride– water, partly based on a more extensive diagram from Bosˇnjakovic´ [11]. The additive concentration is given in [kg NaCl/kg solution]. The vertical axis gives the enthalpy, h, expressed in kJ kgK1 mixture. The heat of melting of water can be seen as the enthalpy difference between N and P. Following Granryd, et al. [12], the freezing point curve is in Fig. 3 represented by the line N–E, where E is the eutectic point. The diagram also shows a few isothermal lines. Let us follow the cooling process for a mixture with the condition A, having the temperature tAZ0 8C. If the temperature is lowered, the freezing point, tFZK5 8C is passed in F. If more heat is removed from the mixture we move further down in the diagram and the temperature has reached tKZK10 8C in point K. As mentioned earlier, we can view the ice slurry solution as consisting of ice crystals of pure water that freeze out, and the rest of the solution with a higher concentration of the freezing point depressant substance. Point K then represents a condition of mixture between pure ice at tKZK10 8C (point H), and solution with the freezing point tKZK10 8C (point L). The amount of heat that has to be removed for each kg original solution can be seen as the enthalpy difference hAKhK. During cooling below the freezing point of a mixture that does not have eutectic composition, ice slurry is first formed, as we earlier discussed. The forming of solid mass first takes place at a temperature equal to that of the eutectic point, E. A solution with eutectic composition of sodium chloride freezes to solid ice between E and M. The enthalpy difference between E and M is the latent heat of phase change of the eutectic solution. The variation with concentration of enthalpy values for an isothermal line (for instance, tZ0 8C) relates to the heat of mixing. Bosˇnjakovic´ [11] and Rant [13] give enthalpy
A˚ Melinder, E. Granryd / International Journal of Refrigeration 28 (2005) 13–19
phase diagrams as a function of additive concentration and temperature also for other aqueous solutions than sodium chloride. In order to construct enthalpy-phase diagrams, the solution may be assumed as consisting of ice crystals of pure water that freeze out, and the rest of the solution with a higher concentration of the additive, the freezing point depressant substance. Enthalpy values of an aqueous solution can then be estimated with the help of specific heat values of the aqueous solution down to the freezing point curve, heat of melting of ice and heat of mixing data of the solution. The enthalpy of the ice slurry can (with the nomenclature from Fig. 1) be expressed by the following correlation h Z hI ðtS ÞcI C hS ðcS ; tS Þð1 K cI Þ
(2)
where the enthalpy of ice, hI(tS) can be expressed as hI ðtS Þ Z KðhN K hP Þ C ðhH K hP Þ
(3)
In Eq. (3), the heat of melting of ice hNKhPZ 332.4 kJ kg-1, and hHKhPZKcp,ItS, where the average specific heat of ice is cp,IZ2.09 kJ kg-1 K-1. The enthalpy of the remaining solution, hS(cS,tS) can be expressed as ð tS (4) hS ðcS ; tS Þ Z h0;R C DhM ðcS ; tR Þ C cp dt tR
where h0,R is the enthalpy of water at the reference temperature and DhM(cS, tR) is the heat of mixing for the concentration cS. Values of heat of mixing, DhM (usually at tRZ0 or 25 8C) are taken from Heats of Mixing Data Collection [14], Handbook of Heats of Mixing [15], Landolt-Bo¨rnstein [16] and an internal report from Norsk Hydro Research Center [17]. Some works on ice slurry properties give enthalpy, and at times apparent specific heat, as a function of the temperature for various concentrations of the freezing point depressant substance, usually ethyl alcohol–water [6,7]. Fig. 4a–f give similar graphs with enthalpy and apparent specific heat for aqueous solutions of ethyl alcohol, propylene glycol and for potassium formate. Lines for constant ice concentrations (0.1, 0.2, 0.3, 0.4 and 0.5) are indicated in the enthalpy charts.
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References ˚ . Melinder, Thermophysical properties of liquid secondary [1] A refrigerants, Tables and diagrams for the refrigeration industry, IIF/IIR, Paris, 1997. ˚ . Melinder, Accurate thermophysical property values of [2] A aqueous solutions are important for ice slurry modeling and calculations, Third Workshop of the International Institute of Refrigeration on Ice Slurries, Lucern, 2001 p. 19–26. ˚ . Melinder, Thermophysical properties of liquid secondary [3] A refrigerants, A critical review on literature references and laboratory measurements, KTH, Stockholm, 1998. ˚ . Melinder, A critical review on thermo-physical properties [4] A of liquid secondary refrigerants, Natural Working Fluids’98, IIR Gustav Lorentzen Conference, Oslo, 1998 p. 505–15. [5] CRC handbook of chemistry and physics, 69th ed.; 1988–89. [6] O. Bel, A. Lallemand, Study of a two-phase secondary refrigerant. 1. Intrinsic thermophysical properties of an ice slurry, Int J Refrig, IIR/IIF, Paris 22 (1999) 164–174. [7] J. Guilpart, L. Fournaison, M.A. Ben Lakhdar, Calculation method of ice slurries thermophysical properties—application to water/ethanol mixture, Int Congr Refrig, IIR/IIF, Sydney 1999. [8] M. Kauffeld, K.G. Christensen, S. Lund, T.M. Hansen, Experience with ice slurry, Int Congr Refrig, IIR/IIF, Sydney 1999. [9] O. Lottin, C. Epiard, Thermodynamic properties of some currently used water-antifreeze mixtures when used as ice slurries, Eighth Int Refrig, Purdue, USA 2000; 391–398. ˚ Melinder, Thermophysical properties of liquid secondary [10] A refrigerants, charts and tables, Swedish Society of Refrigeration, Stockholm, 1997. [11] F. Bosˇnjakovic´, Technische Thermodynamik, Teil II, Band 12, in: Wa¨rmelehre und Wa¨rmewirtschaft in Einzeldarstellungen, Dresden/Leipzig, 1961. ˚ . Melinder, Secondary refrigerants for indirect [12] E. Granryd, A systems in: E. Granryd et al. (Ed.),, Refrigerating engineering, KTH, Stockholm, 1999, pp. 6:2–6:6. [13] Z. Rant, Diagramm-Mappe zu Band 13, Verdampfen in Theorie und Praxis, in: Wa¨rmelehre und Wa¨rmewirtschaft in Einzeldarstellungen, Dresden/Leipzig, 1961. [14] J.J. Christensen, J. Gmehling, P. Rasmussen, U. Weidlich, Heats of mixing data collection, 1, Binary Systems 1986. [15] C. Christensen, R.W. Hanks, R.M. Izatt, Handbook of heats of mixing 1982. [16] Landolt-Bo¨rnstein, Numerical data and functional relationships in science and technology, Group IV. Heats Mixing Solution 1976;2. [17] Norsk Hydro Research Centre, Internal report; 2001.