1126 PART LOAD PARAMETER ID FOR CHILLER
PURPOSE:
Identification of the internal power of the compressor when all the cylinders
are unloaded. The pressure drop at the exhaust of the compressor cylinders is
taken into account.
MAJOR RESTRICTIONS:
-The surrounding heat exchanges are neglected.
-The compression is assumed to be isentropic.
-Perfect (ideal) gas properties are used.
-The chiller is supposed to work with only one compressor.
SUBROUTINES CALLED:
-PROPERTY - attached at the end of the code
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CONCEPTUAL SCHEMAS
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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")
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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.
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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
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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".
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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.
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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.
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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