from __future__ import division, print_function, absolute_import
from math import log,exp
from CoolProp.CoolProp import HAPropsSI, cair_sat
from .FinCorrelations import WavyLouveredFins, HerringboneFins, PlainFins
[docs]class DWSVals():
"""
Empty Class for passing data with DryWetSegment
"""
def __init__(self):
#Don't do anything
pass
[docs]def DryWetSegment(DWS):
"""
Generic solver function for dry-wet mixed surface conditions for a given element.
Can handle superheated, subcooled and two-phase regions.
Does not handle the pressure drops, only HT required to get the dry/wet interface
"""
#List of required parameters
RequiredParameters=['Tin_a','h_a','cp_da','eta_a','A_a','pin_a','RHin_a','Tin_r','pin_r','h_r','cp_r','A_r','mdot_r','Fins','FinsType']
#Check that all the parameters are included, raise exception otherwise
for param in RequiredParameters:
if not hasattr(DWS,param):
raise AttributeError("Parameter "+param+" is required for DWS class in DryWetSegment")
#Retrieve values from structures defined above
Tin_a=DWS.Tin_a
h_a=DWS.h_a
cp_da=DWS.cp_da
eta_a=DWS.eta_a #from fin correlations, overall airside surface effectiveness
A_a=DWS.A_a
pin_a=DWS.pin_a
RHin_a=DWS.RHin_a
mdot_da=DWS.mdot_da
Tin_r=DWS.Tin_r
pin_r=DWS.pin_r
h_r=DWS.h_r
cp_r=DWS.cp_r
A_r=DWS.A_r
mdot_r=DWS.mdot_r
#Calculate the dewpoint (amongst others)
omega_in=HAPropsSI('W','T',Tin_a,'P',pin_a,'R',RHin_a)
Tdp=HAPropsSI('D','T',Tin_a,'P',pin_a,'W',omega_in)
hin_a=HAPropsSI('H','T',Tin_a,'P',pin_a,'W',omega_in) #[J/kg_da]
# Internal UA between fluid flow and outside surface (neglecting tube conduction)
UA_i=h_r*A_r #[W/K], from Shah or f_h_1phase_Tube-fct -> Correlations.py
# External UA between wall and free stream
UA_o=eta_a*h_a*A_a #[W/K], from fin correlations
# Internal Ntu
Ntu_i=UA_i/(mdot_r*cp_r) #[-]
# External Ntu (multiplied by eta_a since surface is finned and has lower effectiveness)
Ntu_o=eta_a*h_a*A_a/(mdot_da*cp_da) #[-]
if DWS.IsTwoPhase: #(Two-Phase analysis)
UA=1/(1/(h_a*A_a*eta_a)+1/(h_r*A_r)); #overall heat transfer coefficient
Ntu_dry=UA/(mdot_da*cp_da); #Number of transfer units
epsilon_dry=1-exp(-Ntu_dry); #since Cr=0, e.g. see Incropera - Fundamentals of Heat and Mass Transfer, 2007, p. 690
Q_dry=epsilon_dry*mdot_da*cp_da*(Tin_a-Tin_r);
Tout_a=Tin_a-Q_dry/(mdot_da*cp_da); #outlet temperature, dry fin
T_so_a=(UA_o*Tin_a+UA_i*Tin_r)/(UA_o+UA_i); #inlet surface temperature
T_so_b=(UA_o*Tout_a+UA_i*Tin_r)/(UA_o+UA_i); #outlet surface temperature
if T_so_b>Tdp:
#All dry, since surface at outlet dry
f_dry=1.0
Q=Q_dry #[W]
Q_sensible=Q #[W]
hout_a=hin_a-Q/mdot_da #[J/kg_da]
# Air outlet humidity ratio
DWS.omega_out = omega_in #[kg/kg]
else:
if T_so_a<Tdp:
#All wet, since surface at inlet wet
f_dry=0.0
Q_dry=0.0
T_ac=Tin_a #temp at onset of wetted wall
h_ac=hin_a #enthalpy at onset of wetted surface
else:
# Partially wet and dry (i.e T_so_b<Tdp<T_so_a)
# Air temperature at the interface between wet and dry surface
# Based on equating heat fluxes at the wall which is at dew point UA_i*(Tw-Ti)=UA_o*(To-Tw)
T_ac = Tdp + UA_i/UA_o*(Tdp - Tin_r)
# Dry effectiveness (minimum capacitance on the air side by definition)
epsilon_dry=(Tin_a-T_ac)/(Tin_a-Tin_r)
# Dry fraction found by solving epsilon=1-exp(-f_dry*Ntu) for known epsilon from above equation
f_dry=-1.0/Ntu_dry*log(1.0-epsilon_dry)
# Enthalpy, using air humidity at the interface between wet and dry surfaces, which is same humidity ratio as inlet
h_ac=HAPropsSI('H','T',T_ac,'P',pin_a,'W',omega_in) #[J/kg_da]
# Dry heat transfer
Q_dry=mdot_da*cp_da*(Tin_a-T_ac)
# Saturation specific heat at mean water temp (c_s : partial derivative dh_sat/dT @ Tsat_r)
c_s=cair_sat(Tin_r)*1000 #[J/kg-K]
# Find new, effective fin efficiency since cs/cp is changed from wetting
# Ratio of specific heats [-]
DWS.Fins.Air.cs_cp=c_s/cp_da
DWS.Fins.WetDry='Wet'
#Compute the fin efficiency based on the user choice of FinsType
if DWS.FinsType == 'WavyLouveredFins':
WavyLouveredFins(DWS.Fins)
elif DWS.FinsType == 'HerringboneFins':
HerringboneFins(DWS.Fins)
elif DWS.FinsType == 'PlainFins':
PlainFins(DWS.Fins)
eta_a_wet=DWS.Fins.eta_a_wet
UA_o=eta_a_wet*h_a*A_a
Ntu_o=eta_a_wet*h_a*A_a/(mdot_da*cp_da)
# Wet analysis overall Ntu for two-phase refrigerant
# Minimum capacitance rate is by definition on the air side
# Ntu_wet is the NTU if the entire two-phase region were to be wetted
UA_wet=1/(c_s/UA_i+cp_da/UA_o)
Ntu_wet=UA_wet/(mdot_da)
# Wet effectiveness [-]
epsilon_wet=1-exp(-(1-f_dry)*Ntu_wet)
# Air saturated at refrigerant saturation temp [J/kg]
h_s_s_o=HAPropsSI('H','T',Tin_r, 'P',pin_a, 'R', 1.0) #[kJ/kg_da]
# Wet heat transfer [W]
Q_wet=epsilon_wet*mdot_da*(h_ac-h_s_s_o)
# Total heat transfer [W]
Q=Q_wet+Q_dry
# Air exit enthalpy [J/kg]
hout_a=h_ac-Q_wet/mdot_da
# Saturated air temp at effective surface temp [J/kg_da]
h_s_s_e=h_ac-(h_ac-hout_a)/(1-exp(-(1-f_dry)*Ntu_o))
# Effective surface temperature [K]
T_s_e = HAPropsSI('T','H',h_s_s_e,'P',pin_a,'R',1.0)
# Outlet dry-bulb temp [K]
Tout_a = T_s_e+(T_ac-T_s_e)*exp(-(1-f_dry)*Ntu_o)
#Sensible heat transfer rate [kW]
Q_sensible=mdot_da*cp_da*(Tin_a-Tout_a)
#Outlet is saturated vapor
Tout_r=DWS.Tdew_r
else: #(Single-Phase analysis)
#Overall UA
UA = 1 / (1 / (UA_i) + 1 / (UA_o));
# Min and max capacitance rates [W/K]
Cmin = min([cp_r * mdot_r, cp_da * mdot_da])
Cmax = max([cp_r * mdot_r, cp_da * mdot_da])
# Capacitance rate ratio [-]
C_star = Cmin / Cmax
# Ntu overall [-]
Ntu_dry = UA / Cmin
if Ntu_dry<0.0000001:
print("warning: NTU_dry in dry wet segment was negative. forced it to positive value of 0.001!")
Ntu_dry=0.0000001
# Counterflow effectiveness [-]
#epsilon_dry = ((1 - exp(-Ntu_dry * (1 - C_star))) /
# (1 - C_star * exp(-Ntu_dry * (1 - C_star))))
#Crossflow effectiveness (e.g. see Incropera - Fundamentals of Heat and Mass Transfer, 2007, p. 662)
if (cp_r * mdot_r)<(cp_da * mdot_da):
epsilon_dry= 1-exp(-C_star**(-1)*(1-exp(-C_star*(Ntu_dry))))
#Cross flow, single phase, cmax is airside, which is unmixed
else:
epsilon_dry=(1/C_star)*(1-exp(-C_star*(1-exp(-Ntu_dry))))
#Cross flow, single phase, cmax is refrigerant side, which is mixed
# Dry heat transfer [W]
Q_dry = epsilon_dry*Cmin*(Tin_a-Tin_r)
# Dry-analysis air outlet temp [K]
Tout_a_dry=Tin_a-Q_dry/(mdot_da*cp_da)
# Dry-analysis outlet temp [K]
Tout_r=Tin_r+Q_dry/(mdot_r*cp_r)
# Dry-analysis air outlet enthalpy from energy balance [J/kg]
hout_a=hin_a-Q_dry/mdot_da
# Dry-analysis surface outlet temp [K]
Tout_s=(UA_o*Tout_a_dry+UA_i*Tin_r)/(UA_o+UA_i)
# Dry-analysis surface inlet temp [K]
Tin_s=(UA_o*Tin_a+UA_i*Tout_r)/(UA_o+UA_i)
# Dry-analysis outlet refrigerant temp [K]
Tout_r_dry=Tout_r
# Dry fraction [-]
f_dry=1.0
# Air outlet humidity ratio [-]
DWS.omega_out = omega_in
# If inlet surface temp below dewpoint, whole surface is wetted
if Tin_s<Tdp:
isFullyWet=True
else:
isFullyWet=False
if Tout_s<Tdp or isFullyWet:
# There is some wetting, either the coil is fully wetted or partially wetted
# Loop to get the correct c_s
# Start with the inlet temp as the outlet temp
x1=Tin_r+1 #Lowest possible outlet temperature
x2=Tin_a-1 #Highest possible outlet temperature
eps=1e-8
iter=1
change=999
while ((iter<=3 or change>eps) and iter<100):
if (iter==1):
Tout_r=x1;
if (iter>1):
Tout_r=x2;
Tout_r_start=Tout_r;
# Saturated air enthalpy at the inlet water temperature [J/kg]
h_s_w_i=HAPropsSI('H','T',Tin_r,'P', pin_a, 'R', 1.0) #[J/kg_da]
# Saturation specific heat at mean water temp [J/kg]
c_s=cair_sat((Tin_r+Tout_r)/2.0)*1000
# Ratio of specific heats [-]
DWS.Fins.Air.cs_cp=c_s/cp_da
# Find new, effective fin efficiency since cs/cp is changed from wetting
# Based on the user choice of FinsType
if DWS.FinsType == 'WavyLouveredFins':
WavyLouveredFins(DWS.Fins)
elif DWS.FinsType == 'HerringboneFins':
HerringboneFins(DWS.Fins)
elif DWS.FinsType == 'PlainFins':
PlainFins(DWS.Fins)
# Effective humid air mass flow ratio
m_star=mdot_da/(mdot_r*(cp_r/c_s))
#compute the new Ntu_owet
Ntu_owet = eta_a*h_a*A_a/(mdot_da*cp_da)
m_star = min([cp_r * mdot_r/c_s, mdot_da])/max([cp_r * mdot_r/c_s, mdot_da])
mdot_min = min([cp_r * mdot_r/c_s, mdot_da])
# Wet-analysis overall Ntu [-]
Ntu_wet=Ntu_o/(1+m_star*(Ntu_owet/Ntu_i))
if(cp_r * mdot_r> c_s * mdot_da):
Ntu_wet=Ntu_o/(1+m_star*(Ntu_owet/Ntu_i))
else:
Ntu_wet=Ntu_i/(1+m_star*(Ntu_i/Ntu_owet))
# Counterflow effectiveness for wet analysis
epsilon_wet = ((1 - exp(-Ntu_wet * (1 - m_star))) /
(1 - m_star * exp(-Ntu_wet * (1 - m_star))))
# Wet-analysis heat transfer rate
Q_wet = epsilon_wet*mdot_min*(hin_a-h_s_w_i)
# Air outlet enthalpy [J/kg_da]
hout_a=hin_a-Q_wet/mdot_da
# Water outlet temp [K]
Tout_r = Tin_r+mdot_da/(mdot_r*cp_r)*(hin_a-hout_a)
# Water outlet saturated surface enthalpy [J/kg_da]
h_s_w_o=HAPropsSI('H','T',Tout_r, 'P',pin_a, 'R', 1.0) #[J/kg_da]
#Local UA* and c_s
UA_star = 1/(cp_da/eta_a/h_a/A_a+cair_sat((Tin_a+Tout_r)/2.0)*1000/h_r/A_r)
# Wet-analysis surface temperature [K]
Tin_s = Tout_r + UA_star/h_r/A_r*(hin_a-h_s_w_o)
# Wet-analysis saturation enthalpy [J/kg_da]
h_s_s_e=hin_a+(hout_a-hin_a)/(1-exp(-Ntu_owet))
# Surface effective temperature [K]
T_s_e=HAPropsSI('T','H',h_s_s_e,'P',pin_a,'R',1.0)
# Air outlet temp based on effective temp [K]
Tout_a=T_s_e + (Tin_a-T_s_e)*exp(-Ntu_o)
#Sensible heat transfer rate [W]
Q_sensible = mdot_da*cp_da*(Tin_a-Tout_a)
# Error between guess and recalculated value [K]
errorToutr=Tout_r-Tout_r_start;
if(iter>500):
print("Superheated region wet analysis T_outr convergence failed")
DWS.Q=Q_dry;
return
if iter==1:
y1=errorToutr
if iter>1:
y2=errorToutr
x3=x2-y2/(y2-y1)*(x2-x1)
change=abs(y2/(y2-y1)*(x2-x1))
y1=y2; x1=x2; x2=x3
if hasattr(DWS,'Verbosity') and DWS.Verbosity>7:
print("Fullwet iter %d Toutr %0.5f dT %g" %(iter,Tout_r,errorToutr))
#Update loop counter
iter+=1
# Fully wetted outlet temperature [K]
Tout_r_wet=Tout_r
# Dry fraction
f_dry=0.0
if (Tin_s>Tdp and not isFullyWet):
#Partially wet and partially dry with single-phase on refrigerant side
"""
-----------------------------------------------------------
|
* Tout_a <---- * T_a,x <---- * Tin_a
|
____________Wet____________| Dry
----------------------------o T_dp ------------------------
|
* Tin_r ----> * T_w,x ----> * Tout_r
|
-----------------------------------------------------------
"""
iter = 1
# Now do an iterative solver to find the fraction of the coil that is wetted
x1=0.0001
x2=0.9999
eps=1e-8
while ((iter<=3 or error>eps) and iter<100):
if iter==1:
f_dry=x1
if iter>1:
f_dry=x2
K=Ntu_dry*(1.0-C_star)
expk = exp(-K*f_dry)
if cp_da*mdot_da < cp_r*mdot_r:
Tout_r_guess = (Tdp + C_star*(Tin_a - Tdp)-expk*(1-K/Ntu_o)*Tin_a)/(1-expk*(1-K/Ntu_o))
else:
Tout_r_guess = (expk*(Tin_a+(C_star-1)*Tdp)-C_star*(1+K/Ntu_o)*Tin_a)/(expk*C_star-C_star*(1+K/Ntu_o))
# Wet and dry effective effectivenesses
epsilon_dry = ((1 - exp(-f_dry*Ntu_dry * (1 - C_star))) /
(1 - C_star * exp(-f_dry*Ntu_dry * (1 - C_star))))
epsilon_wet = ((1 - exp(-(1-f_dry)*Ntu_wet * (1 - m_star))) /
(1 - m_star * exp(-(1-f_dry)*Ntu_wet * (1 - m_star))))
# Temperature of "water" where condensation begins
T_w_x=(Tin_r+(mdot_min)/(cp_r * mdot_r)*epsilon_wet*(hin_a-h_s_w_i-epsilon_dry*Cmin/mdot_da*Tin_a))/(1-(Cmin*mdot_min)/(cp_r * mdot_r * mdot_da)*epsilon_wet*epsilon_dry)
# Temperature of air where condensation begins [K]
# Obtained from energy balance on air side
T_a_x = Tin_a - epsilon_dry*Cmin*(Tin_a - T_w_x)/(mdot_da*cp_da)
# Enthalpy of air where condensation begins
h_a_x = hin_a - cp_da*(Tin_a - T_a_x)
# New "water" temperature (stored temporarily to be able to build change
Tout_r=(Cmin)/(cp_r * mdot_r)*epsilon_dry*Tin_a+(1-(Cmin)/(cp_r * mdot_r)*epsilon_dry)*T_w_x
# Difference between initial guess and outlet
error=Tout_r-Tout_r_guess
if(iter>500):
print("Superheated region wet analysis f_dry convergence failed")
DWS.Q=Q_dry
return
if iter==1:
y1=error
if iter>1:
y2=error
x3=x2-y2/(y2-y1)*(x2-x1)
change=abs(y2/(y2-y1)*(x2-x1))
y1=y2; x1=x2; x2=x3;
if hasattr(DWS,'Verbosity') and DWS.Verbosity>7:
print("Partwet iter %d Toutr_guess %0.5f diff %g f_dry: %g"%(iter,Tout_r_guess,error,f_dry))
#Update loop counter
iter+=1
# Wet-analysis saturation enthalpy [J/kg]
h_s_s_e=h_a_x+(hout_a-h_a_x)/(1-exp(-(1-f_dry)*Ntu_owet))
# Surface effective temperature [K]
T_s_e=HAPropsSI('T','H',h_s_s_e,'P',pin_a,'R',1.0)
# Air outlet temp based on effective surface temp [K]
Tout_a=T_s_e + (T_a_x-T_s_e)*exp(-(1-f_dry)*Ntu_o)
# Heat transferred [W]
Q=mdot_r*cp_r*(Tout_r-Tin_r)
# Dry-analysis air outlet enthalpy from energy balance [J/kg]
hout_a=hin_a-Q/mdot_da
#Sensible heat transfer rate [kW]
Q_sensible = mdot_da*cp_da*(Tin_a-Tout_a)
else:
Q=Q_wet
else:
# Coil is fully dry
Tout_a=Tout_a_dry
Q=Q_dry
Q_sensible=Q_dry
DWS.f_dry=f_dry
DWS.omega_out=HAPropsSI('W','T',Tout_a,'P',101325,'H',hout_a)
DWS.RHout_a=HAPropsSI('R','T',Tout_a,'P',101325,'W',DWS.omega_out)
DWS.Tout_a=Tout_a
DWS.Q=Q
DWS.Q_sensible=Q_sensible
DWS.hout_a=hout_a
DWS.hin_a=hin_a
DWS.Tout_r=Tout_r
DWS.Twall_s=Tout_r - Q/UA_i #inner wall temperature for gas cooler model