1135 FULL LOAD PARAMETER ID FOR CHILLER PURPOSE: Parameter identification based on a reciprocating chiller performance in a steady state regime. The pressure drop at the compressor exhaust can be taken into account. MAJOR RESTRICTIONS: -The surrounding heat exchanges are neglected. -The refrigerant leaves the evaporator and the condenser as saturated vapor and saturated liquid respectively. -Perfect (ideal) gas properties are used. -The maximum number of working point (operation points) is 82 -The compression is assumed to be isentropic SUBROUTINES CALLED: -PROPERTY - attached at the end of the code -ERROR - attached at the end of the code -FIT - contained in TRNSYS -TYPE88 - component 1101 (Full load chiller with reciprocating compressor) ------------------------------------------------------------------------------- CONCEPTUAL SCHEMAS ------------------------------------------------------------------------------- GENERAL CHILLER MODEL Refrigerant States State 1 : compressor inlet (saturated vapor) State 1': compressor at start of compression (superheated vapor) State 2 : condenser inlet (superheated vapor) State 3 : expansion valve inlet (saturated liquid) State 4 : evaporator inlet (inside vapor dome) States 1 to 1' : constant pressure heat addition due to compressor losses States 1 to 2 : constant entropy compression States 2 to 3 : constant pressure heat loss States 3 to 4 : constant enthalpy expansion States 4 to 1 : constant pressure heat addition This component models a chiller comprised of a reciprocating compressor, a condenser, an expansion valve, and an evaporator. In order to simplify the whole chiller simulation, the refrigerant leaves the condenser as saturated liquid and the evaporator as saturated vapor. This assumes a "perfect" adaptation of condenser transfer area and also a "perfect" control of the thermostatic valve. No heat exchange between this system and its environment is taken into account. This means that: Qdotcd = Wdot + Qdotev where Qdotcd = heat rejected in the condenser Wdot = power consumed by the compressor Qdotev = heat absorbed in the evaporator ("refrigerating capacity") ------------------------------------------------------------------------------- CONDENSER AND EVAPORATOR MODELING Both the condenser and evaporator are represented as classical heat exchangers. The refrigerant side is considered isothermal in both cases (the refrigerant is replaced by a fluid of infinite capacity flow rate). Liquid water is assumed to be the second fluid. The effectiveness of a semi-isothermal heat exchanger is defined by the following relationship: effectiveness = 1 - e^(-NTU) with NTU = (AU / Cdotmin) where AU = heat transfer coefficient Cdotmin = minimum of the two capacity flow rates = Mdotw*cpw MdotW = water mass flow rate cpw = water specific heat Water Side MdotW Twsu---> --->Twex Heat Exchanger Trex<--- <---Trsu MdotR Refrigerant Side Modeled as isothermal (Tr)su = (Tr)ex = Tev or Tcd The hypothesis of an isothermal refrigerant side is very crude for the condenser -- it neglects all the effect of refrigerant desuperheating and therefore underestimates the mean temperature difference between refrigerant and water in this heat exchanger. The systematic error will have to be compensated for by a significant overesitmate of the corresponding heat transfer coefficient (AU). Of course, the condenser and evaporator heat transfer coefficients will have to be identified. In the models proposed hereafter, these coefficients are assumed to remain constant. ------------------------------------------------------------------------------- COMPRESSOR MODELING The refrigerant is heated by electromechanical losses before being compressed. A simple linear model will be used to represent the "motor-transmission" subsystem: Wdot = Wdotlo + alpha * Wdotin + Wdotin where Wdot = electrical power for a hermetic or semi-hermetic compressor or shaft power for an open compressor Wdotlo = constant part of the electromechanical losses alpha = loss factor Wdotin = compressor "internal" power The two parameters, Wdotlo and alpha will have to be identified. The heat transfer is assumed to occur at constant pressure. The refrigerant passing from state 1 to state 1' undergoes a consant pressure heat addition: h1' = h1 + (Wdot - Wdotin)/MdotR where h1' = enthalpy after heat addition h1 = enthalpy at evaporator (compressor inlet) MdotR = mass flow rate of refrigerant Throttling processes will play an essential role in the compressor modeling. Any throttling can be represented by two steps: 1) an isentropic expansion (a-b) inside an ideal nozzle (throat area A) 2) an isobaric diffusion (b-c) where a = nozzle entrance b = nozzle throat c = nozzle exit Three different throttles will be considered: 1) at the compressor supply 2) at the compressor exhaust 3) inside the compressor itself, as "internal leakage" Classical nozzle theory will be used in order to calculate the throttling mass flow rate in relationship with the pressure drop and vice versa. Two limit cases are particularly easy to calculate: 1) If the pressure drop is much smaller than the entrance pressure, the fluid may be considered as quasi-incompressible: Mdot = A * (2*deltap/nu)^.5 where Mdot = mass flow rate A = nozzle throat area deltap = pressure drop nu = fluid specific volume 2) In other circumstances, the pressure ratio pa/pb = pa/pc is large enough to produce a choked flow (sonic velocity in the nozzle throat)and it remains: (Mdot*(Ta)^.5)/pa = constant where Ta = fluid temperature at nozzle entrance pa = fluid pressure at nozzle entrance ------------------------------------------------------------------------------- REFRIGERANT MODELING The refrigerant is represented as an ideal fluid, i.e. an ideal gas, an ideal liquid or mixture of both. This allows the intensive use of the following equations: p*nu = r * T (ideal gas equation) where p = pressure (Pa) nu = specific volume (m^3/kg) r = gas constant (J/kg*K) T = absolute temperature (K) h = hfo + hfgo + cp * (T-To) (enthalpy of an ideal gas) where h = enthalpy (J/kg) hfo = enthalpy of the saturated liquid at the reference temperature (J/kg) hfgo = enthalpy of the vaporization at the reference temperature (J/kg) cp = specific heat at constant pressure (J/kg*K) To = refence state temperature h = hfo + c * (T-To) + nu * (p-po) (enthalpy of an ideal liquid) where nu = specific volume, considered constant for ideal liquids (m^3/kg) c = specific heat (J/kg*K) nu = (1-x) * nuf + (x * nug) (specific volume of a mixture) where f = saturated liquid phase g = saturated gas phase x = vapor fraction (quality) h = (1-x) * hf + (x * hg) = hf+ (x * hfg) (enthalpy of a mixture) where hfg = hg-hf hg = approximated by the enthalpy of an ideal gas equation hf = apporximated by the enthalpy of an ideal liquid equation The saturation pressure is derived from the Clausius-Clapyfron equation: ln (ps) = A + B/T with A and B = constants. The isentropic processes are described by: p*(nu)^gamma = constant The parameters describing the refrigerant are: hfo = enthalpy of the saturated liquid at the reference temperature cf = mean specific heat in a saturated liquid state hfgo = enthalpy of vaporization at the reference temperature cp = mean specific heat at constant pressure in superheated vapor state r = gas constant gamma = mean isentropic coefficient A and B = coefficients in the Clausius-Clapyron equation eta = mean compressibility factor According to ideal gas theory: gamma = cp / (cp - r) but this constraint will not be used, as cp and gamma will be selected seperately. A constant compressiblity factor (eta) will also be introduced in the ideal gas state equation: p * nu = eta * r * T This ideal fluid model is not very accurate but it simplifies the calculations. It should be remembered that the 'refrigerant' is a ideal fluid replacing the real one. Also, the different parameters of the chiller model will have to be considered as ideal characteristics. Refinements on fluid properties modeling could be re-introduced by the user at a later stage (i.e. when more accuracy is required or better experimental data is available). The initial model is useful as a first approximation. Numerical data for R12, R134a, R114, R22, R502, and R717 is stored in the routine "PROPERTY". ------------------------------------------------------------------------------- MODELING OF SECONDARY FLUIDS Water is the only secondary fluid considered in the chiller model, but it is very easy to shift to other fluids. Two methods are outlined: 1) the use of water as a substitute fluid in place of the real one; 2) the use of a theoretical water loop connecting the component considered to another theoretical heat exchanger. Water as a Substitute Fluid Three components are considered: A) an air cooled condenser B) an evaporative condenser C) a direct expansion coil A) An air cooled condenser can be modeled as supplied by water providing that: MdotW = (cpa/cpw)*Mdota where MdotW = water flow rate cpa = air specific heat (approx. = 1005 J/Kg*K) cpw = liquid water specific heat at constant pressure = 4187 J/kg*K Mdota = air flow rate The water model has to be supplied with a reduced flow rate: MdotW = 0.24 * Mdota B) An evporative condenser can also be modeled as supplied by water: MdotW = (cpmodel/cpw) * Mdota (Tw)su=(Twb)su An iterative procedure can be used to catch the correct value cpmodel: cpmodel = (haex - hasu) / (Twbex - Twbsu) where haex = enthalpy of the air at the exhaust of the evaporative condenser = f ((Twb)ex) (assume the air is almost saturated) hasu = enthalpy of the air at in the supply of the evaporative condenser Twbsu = wet bulb temperature in the supply (weather data) in most situations (approximate values): cpmodel = cw (+/- 20%) MdotW = Mdota (+/- 20%) C) A direct expansion coil can also be simulated by using water. As for air cooling coils, two models will have to be run in parallel: - one dry regime, which is the same as the air cooled condenser - one wet regime, which is the same as the evaporative condenser A test will have to be introduced in the simulation in order to select the regime which gives the highest heat transfer absolute value. Theoretical Water Loops An evaporative condenser can be represented by the idealizecd association of a water cooled condenser to a cooling tower. A direct expansion coil can be represented by an association of a water heated evaporator to an air cooling coil. ------------------------------------------------------------------------------ CHILLERS WITH RECIPROCATING COMPRESSORS Full Load Regime An ideal mechanical cycle is assumed to occur in the compressor cylinders. This cycle includes: 1) an isobaric intake of the refrigerant into the cylinders 2) an isentropic compression 3) an isobaric exhaust of refrigerant from the cylinders 4) an isentropic expansion of the refrigerant remaining in the clearance volume at the end of the exhaust process Due to some refrigerant remaining in the cylinder after exhaust, the compressor refrigerant flow rate is a decreasing function of the pressure ratio: Vdot = VdotS *( 1 + Cf - Cf * (pex/psu)^(1/gamma)) where Vdot = volumetric flow rate VdotS = swept volume flow rate (geometric displacement of the compressor) Cf = clearance factor = Vclearance / Vswept pex = exhaust pressure psu = supply pressure Parameters VdotS and Cf will generally be actual values. They will be tuned in order to reproduce the behavior of the actual compressor. Described above are: Wdotlo = constant part of the electromechanical losses alpha = loss factor This four parameter model is not always able to reproduce accurately the electrical consumption variations of a real compressor. In some cases, it is justified to a introduce a fifth parameter: a fictitous nozzle throat area at the compressor exhaust. Part Load Regime Part load is modeled by varying the number of cylinders in use or by on/off cycling when the minimal number of cylinders in use is still giving too much refrigeration capacity). Electrical power is represented by the same equation used in the full load model: Wdot = Wdotlo + alpha * Wdotin + Wdotin Wdotin is now larger than the isentropic power (WdotsS) due to pumping losses: Wdotin = WdotS + (1 - (Nc/Ncfl) * Wdotpump where Nc = number of cylinders in use Ncfl = number of cylinders in use in full load regime Wdotpump= internal power of the compressor when all the cylinders are unloaded = pumping power The pumping power will also contribute to the refrigerant heating-up before compression. ------------------------------------------------------------------------------- ------------------------------------------------------------------------------- For further information, see section 3 of the HVAC 1 Toolkit, A Toolkit for Primary HVAC System Energy Calculation, prepared for ASHRAE by: Jean LEBRUN Laborataoire de Thermodynamique Universite de Liege Campus du SART TILMAN Parking P 33 - Batiment B 49 B-4000 Leige, Belgium Telephone: +32(0)41-664800 FAX: +46 243 73750 Developers: Jean Lebrun, Jean-Pascal Bourdouxhe, and Marc Grodent University of Liege, Belgium Date: October 7, 1993 Modified for TRNSYS: Mark Nott and Chad Marlett University of Wisconsin, Madison Date: December 6, 1994