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1 Theoretical Modelling of an Absorption THEORETICAL MODELLING OF AN ABSORPTION REFRIGERATION CYCLE COMBINED WITH STEAM JET THERMAL ICE STORAGE Jorge A. J. Caeiro, Ian W. Eames The Bartlett School of Graduate Studies, Faculty of the Built Environment, (Torrington Place Site), Gower Street, London WC1E 6BT, email: [email protected] Abstract This paper describes the theoretical study of an innovative single effect LiBr-H2O absorption refrigeration cycle combined with Steam Jet Thermal Ice Storage . The main objective of this combination is to create an entirely heat powered system that enables the LiBr absorption refrigerator to benefit from all the technical and economical advantages associated to coupling with ice storage. The novel cycle is an environmentally friendly and economically competitive alternative to conventional chillers that can be powered by low grade waste heat and uses water as working fluid, an inexpensive and innocuous refrigerant. Keywords: Absorption refrigeration combined cycles, Ice storage, Steam ejectors 1.Introduction In order to promote the displacement of electrical energy consumption in buildings more attention has been given in recent years to thermally activated refrigeration technologies. There is one heat-powered refrigeration technology widely used already namely the absorption cycle (using either LiBr – H 2O or NH 3-H2O). LiBr – H 2O systems can use relatively low temperature energy as their power source. LiBr- H2O absorption chillers utilize water as the refrigerant and are therefore limited to refrigeration temperatures above 00C. This limitation means that absorption chillers cannot benefit directly from the important advantages brought by ice storage systems over other commonly used cold storage technologies, namely chilled water and eutectic salt. These advantages include a higher energy storage capacity per unit of media mass, a lower storage temperature, tank modularity and shape flexibility, and comparatively lower storage costs for small and medium installations ( Hasnain , 1998). The proposed system evaluated in this study combines a LiBr-H2O absorption refrigeration system with a steam ejector refrigerator and overcomes this limitation. Figure 1 shows a schematic layout of the innovative system. The system can be operated in three different modes: Charge, discharge or a single effect absorption refrigerator. While operating in the charging mode the steam ejector refrigeration system vacuum freezes the storage media. This would normally match to a period of the day when there is a surplus of heat and there is no or low cooling demand. The ice store, however, cannot be charged whilst simultaneously providing cold to the building. The singularity of this process over conventional ejector refrigeration systems is that the vapour entrained by the ejector is compressed into the absorber rather than into a condenser. When operating in the discharge mode the cold previously stored as latent heat is used to top up the cooling capacity of the absorption system. Under normal operating conditions this would correspond to a period of the day when the building demand for chilled water exceeds the cooling capacity that the absorption system can provide. Finally, the system can be operated as an independent single effect absorption system without the contribution of the ice store. Under normal operating conditions this mode would be suitable for periods of the year when the cooling demand is low or when maintenance works need to be undertaken in the ice store. 1 Nomenclature At nozzle throat cross section area Subscripts AZ mixing cross section area a absorber COP coefficient of performance ARC absorption refrigeration cycle h specific enthalpy [kJ / kg] c condenser hfg latent heat of evaporation [kJ / kg] cc ice store charging cycle hig latent heat of sublimation [kJ / kg] dc ice store discharging cycle m& mass flow rate (kg/s) e evaporator P stagnation or total pressure [Pa] evap water evaporated q heat transfer per unit of mass [kJ / kg] ERC ejector refrigeration cycle Q& heat transfer rate [kW] g generator Rm entrainment ratio s secondary flow SHX Solution Heat Exchanger st strong solution TIS Thermal Ice Store w weak solution T temperature [ 0C, K] 1,2,3… numbers for the states x mass concentration [kg / kg] Greek α non-dimensional factor λ solution circulation factor Steam generator SHX Condenser Absorber Ice store Evaporator Figure 1 – Single effect LiBr-H2O absorption combined with ice storage system schematic 2. Theoretical analysis of the novel combined system In this section the individual analysis of the charging and discharging cycles is made. Separate steady flow analyses are made for each cycle and for each individual thermal process based on the first law of 2 thermodynamics and on the principle of mass conservation. The system’s performance was simulated for different operating conditions taking into account the features of the technologies involved and the properties of the working fluid. 2.1. Description of the charge cycle The system operates under three different pressure levels. At the high pressure level the condenser saturation temperature determines the pressure in the generator. On its turn at the intermediate level either the ejector outlet pressure, or the temperature of the weak solution determine the pressure in the absorber. The lowest pressure level is determined by the freezing point of water. The configuration of the combined system in the charge mode is shown schematically in Figure 2 as well as the heat and mass flow directions. Referring to Figure 2 , high-pressure primary steam driven from the boiler causes the ejector to entrain vapour from the TIS lowering its pressure down to the triple point of water. The ejector’s mixed stream of vapour is after compressed into the absorber where it finally condenses. In the meantime the weakened Lithium Bromide solution is pumped into the boiler where the concentration process takes place by release of the excess of condensed water. The cycle is completed when part of the high pressure vapour generated reaches the ejector being the rest, equalling m& s , condensed after the two streams split. Q& Q& c g m& s m& Condenser 7 Generator Pc;T c Pg;T g;x g 12 3 4 m SHX m & w & st 2 5 W& p 11 1 6 m 14 Absorber & p P ;T ;x a a a 13 Q&TIS m& s Q&a TIS P ;T TIS TIS Figure 2–Layout of the charge cycle 2.2 – Assessment of the charging cycle theoretical energy efficiency Each component of the combined system can be treated as a control volume with inlet and outlet streams, heat transfer and/or work. In order to simplify the first law analysis of the proposed arrangement it is assumed that there are no heat losses to the system surroundings. Using subscripts according to the notation of Figure 2 to indicate the specific enthalpies at the various points in the cycle, the principle of mass conservation and the steady flow energy equation was applied to each 3 component in turn. For each of the points within the cycle, the thermodynamic state of the fluid was specified. The enthalpy values of the refrigerant and solution, and the LiBr concentration were specified by the respective thermodynamic state, temperature and pressure at each point. The state depends on the operating conditions of the adjoining points therefore the system is coupled. In order to determine the enthalpies and hence the cycle performance a system of equations had to be solved simultaneously. The governing equations of mass and species conservation for a steady state system are respectively, ∑ (m& ) in − ∑ (m& ) out = 0 (1) ∑ (m& x ) in − ∑ (m& x ) out = 0 (2) Where m& is the mass flow rate and x is is the mass concentration of LiBr in the solution. The first law of thermodynamics readily yields the energy balance of each component of the combined system. (mh) − (mh) + Q& − Q& + W& = 0 (3) ∑ & in ∑ & out (∑ in ∑ out ) Where the Q&'s are the heat transfer rates between the control volume and its surroundings, and W& is positive if work rate is performed on the system. In this approach neither the external heat transfer processes nor the exergy changes will be considered. The power input to the absorber’s solution circulation pump is also neglected because it is usually small when compared with the other energy transfers. Based on the principle of mass continuity the following equalities are verified and the number of independent variables can thus be reduced, m& = m&7 = m&14 ;m& p = m&11 ;m& s = m&12 = m&13 m& st = m& 4 = m& 5 = m& 6 ;m& w = m&1 = m& 2 = m& 3 (4) Assuming that there are no losses in the fluid transport the pressures and solution concentrations at the different points of the high-pressure level are respectively, Pg = P2 = P3 = P4 = P5 = P7 = P11 = P12 xst = f (Tg , Pg ); xst = x4 = x5 = x6 (5) The pressures and solution concentrations at the different points of the intermediate-pressure level are, Pa = P1 = P6 = P14 xw = f (Ta , Pa ); xw = x1 (6) Assuming that the generator outlet vapour stream is pure water, x7 = x11 = x12 = x13 = x14 = 0 (7) Having characterized the thermodynamic state of the working fluid for each point of the system and the mass and energy balances for each individual component, the energy performance of the charging cycle, given by the ratio of the ejector’s cooling capacity over the heat input to the generator, will be defined as, Q&TIS m& shig 13, COP cc = = (8) Q& g m& st h4 − m& wh3 + m& h7 4 If Q& g is expressed in terms of the circulation factor, λ, the COP of the charging cycle ( COP CC ) can be rewritten as, h m& s ig 13, COP cc = (9) m& []h7 − h3 + λ(h4 − h3 ) Considering that m& = m& s + m& p , the COP CC can be turned into a function of the ejector entrainment ratio, Rm hig 13, COP cc = (10) 1+ Rm []h7 − h3 + λ(h4 − h3 ) If both the numerator and denominator of the right hand side term of Equation 10 are multiplied by the heat of vaporization of the ARC , qe, then the COP cc can be expressed as function of COP ARC , qe qe COP cc = α ⋅ = α ⋅ = α ⋅COP ARC (11) []h7 − h3 + λ(h4 − h3 ) qg Where, h , R α = ig 13 m (12) qe 1+ Rm 1.0 0.9 0 0.8 0 .7 .6 14 0.
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