def psy_chart(self, x, θo, φo):
"""
Plot results on psychrometric chart.
Parameters
----------
x : θM, wM, θs, ws, θC, wC, θS, wS, θI, wI,
QtCC, QsCC, QlCC, QsHC, QsTZ, QlTZ
results of self.solve_lin or self.m_ls
θo, φo outdoor point
Returns
-------
None.
"""
# Processes on psychrometric chart
wo = psy.w(θo, φo)
# Points: O, s, S, I
θ = np.append(θo, x[0:10:2])
w = np.append(wo, x[1:10:2])
# Points O s S I Elements
A = np.array([
[-1, 1, 0, 0, 0, 1], # MX1
[0, -1, 1, 0, 0, 0], # CC
[0, 0, -1, 1, -1, 0], # MX2
[0, 0, 0, -1, 1, 0], # HC
[0, 0, 0, 0, -1, 1]
]) # TZ
psy.chartA(θ, w, A)
θ = pd.Series(θ)
w = 1000 * pd.Series(w) # kg/kg -> g/kg
P = pd.concat([θ, w], axis=1) # points
P.columns = ['θ [°C]', 'w [g/kg]']
output = P.to_string(formatters={
'θ [°C]': '{:,.2f}'.format,
'w [g/kg]': '{:,.2f}'.format
})
print()
print(output)
Q = pd.Series(x[10:],
index=['QtCC', 'QsCC', 'QlCC', 'QsHC', 'QsTZ', 'QlTZ'])
# Q.columns = ['kW']
pd.options.display.float_format = '{:,.2f}'.format
print()
print(Q.to_frame().T / 1000, 'kW')
return None
def RecAirVAV(alpha=1, beta=0.1,
tSsp=30, tIsp=18, phiIsp=0.49, tO=-1, phiO=1,
Qsa=0, Qla=0, mi=2.18, UA=935.83):
"""
Created on Fri Apr 10 13:57:22 2020
Heating & Adiabatic humidification & Re-heating
Recirculated air
VAV Variable Air Volume:
mass flow rate calculated to have const. supply temp.
INPUTS:
alpha mixing ratio of outdoor air, -
beta by-pass factor of the adiabatic humidifier, -
tS supply air, °C
tIsp indoor air setpoint, °C
phiIsp indoor relative humidity set point, -
tO outdoor temperature for design, °C
phiO outdoor relative humidity for design, -
Qsa aux. sensible heat, W
Qla aux. latente heat, W
mi infiltration massflow rate, kg/s
UA global conductivity bldg, W/K
System:
MX1: Mixing box
HC1: Heating Coil
AH: Adiabatic Humidifier
MX2: Mixing in humidifier model
HC2: Reheating coil
TZ: Thermal Zone
BL: Building
Kw: Controller - humidity
Kt: Controller - temperature
o: outdoor conditions
0..5 unknown points (temperature, humidity ratio)
<----|<-------------------------------------------------|
| |
| |-------| |
-o->MX1--0->HC1--1->| MX2--3->HC2--F-----4->TZ--5-|
| |->AH-2-| | | | || |
| | |-Kt4-| BL |
| | |
| |<-----Kt----------|<-t5
|<------------------------------Kw----------|<-w5
16 Unknowns
0..5: 2*6 points (temperature, humidity ratio)
QsHC1, QsHC2, QsTZ, QlTZ
"""
from scipy.optimize import least_squares
def Saturation(m):
"""
Used in VAV to find the mass flow which solves tS = tSsp
Parameters
----------
m : mass flow rate of dry air
Returns
-------
tS - tSsp: difference between supply temp. and its set point
"""
x = ModelRecAir(m, alpha, beta,
tSsp, tIsp, phiIsp, tO, phiO, Qsa, Qla, mi, UA)
tS = x[8]
return (tS - tSsp)
plt.close('all')
wO = psy.w(tO, phiO) # hum. out
# Mass flow rate
res = least_squares(Saturation, 5, bounds=(0, 10))
if res.cost < 1e-10:
m = float(res.x)
else:
print('RecAirVAV: No solution for m')
print(f'm = {m: 5.3f} kg/s')
x = ModelRecAir(m, alpha, beta,
tSsp, tIsp, phiIsp, tO, phiO, Qsa, Qla, mi, UA)
# DtS, m = 2, 1 # initial temp; diff; flow rate
# while DtS > 0.01:
# m = m + 0.01
# # Model
# x = ModelRecAir(m, tSsp, mi, tO, phiO, alpha, beta)
# tS = x[8]
# DtS = -(tSsp - tS)
t = np.append(tO, x[0:12:2])
w = np.append(wO, x[1:12:2])
# Adjancy matrix
# Points o 0 1 2 3 4 5 Elements
A = np.array([[-1, 1, 0, 0, 0, 0, -1], # MX1
[0, -1, 1, 0, 0, 0, 0], # HC1
[0, 0, -1, 1, 0, 0, 0], # AH
[0, 0, -1, -1, 1, 0, 0], # MX2
[0, 0, 0, 0, -1, 1, 0], # HC2
[0, 0, 0, 0, 0, -1, 1]]) # TZ
psy.chartA(t, w, A)
t = pd.Series(t)
w = 1000*pd.Series(w)
P = pd.concat([t, w], axis=1) # points
P.columns = ['t [°C]', 'w [g/kg]']
output = P.to_string(formatters={
't [°C]': '{:,.2f}'.format,
'w [g/kg]': '{:,.2f}'.format
})
print()
print(output)
Q = pd.Series(x[12:], index=['QsHC1', 'QsHC2', 'QsTZ', 'QlTZ'])
# Q.columns = ['kW']
pd.options.display.float_format = '{:,.2f}'.format
print()
print(Q.to_frame().T/1000, 'kW')
return None
def RecAirCAV(alpha=1, beta=0.1,
tS=30, tIsp=18, phiIsp=0.49, tO=-1, phiO=1,
Qsa=0, Qla=0, mi=2.18, UA=935.83):
"""
Model:
Heating and adiabatic humidification
Recycled air
CAV Constant Air Volume:
mass flow rate calculated for design conditions
maintained constant in all situations
INPUTS:
alpha mixing ratio of outdoor air, -
beta by-pass factor of the adiabatic humidifier, -
tS supply air, °C
tIsp indoor air setpoint, °C
phiIsp indoor relative humidity set point, -
tO outdoor temperature for design, °C
phiO outdoor relative humidity for design, -
Qsa aux. sensible heat, W
Qla aux. latente heat, W
mi infiltration massflow rate, kg/s
UA global conductivity bldg, W/K
System:
MX1: Mixing box
HC1: Heating Coil
AH: Adiabatic Humidifier
MX2: Mixing in humidifier model
HC2: Reheating coil
TZ: Thermal Zone
BL: Building
Kw: Controller - humidity
Kt: Controller - temperature
o: outdoor conditions
0..5 6 unknown points (temperature, humidity ratio)
<----|<-------------------------------------------|
| |
| |-------| |
-o->MX1--0->HC1--1->| MX2--3->HC2--4->TZ--5-|
| | | | || |
| |->AH-2-| | BL |
| | |
| |<-----Kt----|<-t5
|<------------------------------Kw----|<-w5
16 Unknowns
0..5: 2*6 points (temperature, humidity ratio)
QsHC1, QsHC2, QsTZ, QlTZ
Returns
-------
None
"""
plt.close('all')
wO = psy.w(tO, phiO) # hum. out
# Mass flow rate for design conditions
# Supplay air mass flow rate
# QsZ = UA*(tO - tIsp) + mi*c*(tO - tIsp)
# m = - QsZ/(c*(tS - tIsp)
# where
# tO, wO = -1, 3.5e-3 # outdoor
# tS = 30 # supply air
# mid = 2.18 # infiltration
QsZ = UA*(tOd - tIsp) + mid*c*(tOd - tIsp)
m = - QsZ/(c*(tS - tIsp))
print(f'm = {m: 5.3f} kg/s constant for design conditions:')
print(f' [tSd = {tS: 3.1f} °C, mi = 2.18 kg/S, tO = -1°C, phi0 = 100%]')
# Model
x = ModelRecAir(m, alpha, beta,
tS, tIsp, phiIsp, tO, phiO, Qsa, Qla, mi, UA)
t = np.append(tO, x[0:12:2])
w = np.append(wO, x[1:12:2])
# Adjancy matrix
# Points o 0 1 2 3 4 5 Elements
A = np.array([[-1, 1, 0, 0, 0, 0, -1], # MX1
[0, -1, 1, 0, 0, 0, 0], # HC1
[0, 0, -1, 1, 0, 0, 0], # AH
[0, 0, -1, -1, 1, 0, 0], # MX2
[0, 0, 0, 0, -1, 1, 0], # HC2
[0, 0, 0, 0, 0, -1, 1]]) # TZ
psy.chartA(t, w, A)
t = pd.Series(t)
w = 1000*pd.Series(w)
P = pd.concat([t, w], axis=1) # points
P.columns = ['t [°C]', 'w [g/kg]']
output = P.to_string(formatters={
't [°C]': '{:,.2f}'.format,
'w [g/kg]': '{:,.2f}'.format
})
print()
print(output)
Q = pd.Series(x[12:], index=['QsHC1', 'QsHC2', 'QsTZ', 'QlTZ'])
# Q.columns = ['kW']
pd.options.display.float_format = '{:,.2f}'.format
print()
print(Q.to_frame().T/1000, 'kW')
return None
def RecAirVAV(alpha=0.5,
tSsp=30,
tIsp=18,
phiIsp=0.5,
tO=-1,
phiO=1,
Qsa=0,
Qla=0,
mi=2.12,
UA=935.83):
"""
CAV Variable Air Volume:
mass flow rate calculated s.t.
he supply temp. is maintained constant in all situations
INPUTS:
INPUTS:
m mass flow of supply dry air kg/s
alpha mixing ratio of outdoor air
tS supply air °C
tIsp indoor air setpoint °C
phiIsp -
tO outdoor temperature for design °C
phiO outdoor relative humidity for design -
Qsa aux. sensible heat W
Qla aux. latente heat W
mi infiltration massflow rate kg/s
UA global conductivity bldg W/K
System (CAV & m introduced by the Fan is cotrolled by tS )
HC: Heating Coil
VH: Vapor Humidifier
TZ: Thermal Zone
F: Supply air fan
Kw: Controller - humidity
Kt: Controller - temperature
o: outdoor conditions
12 Unknowns
0, 1, 2, 3 points (temperature, humidity ratio)
QsHC, QlVH, QsTZ, QlTZ
<----|<--------------------------------|
| |
-o->MX--0->HC--1->VH--F-----2-->TZ--3-->
/ / | | || |
| | | | BL |
| | | | |
| | |_Kt2_|_t2 |
| | |
| |_____Kw_________|_w3
|_____________Kt_________|_t3
Mass-flow rate (VAV) I-controller:
start with m = 0
measure the supply temperature
while -(tSsp - tS)>0.01, increase m (I-controller)
"""
plt.close('all')
wO = psy.w(tO, phiO) # hum. out
# Mass flow rate
DtS, m = 2, 0 # initial temp; diff; flow rate
while DtS > 0.01:
m = m + 0.01
# Model
x = ModelRecAir(m, alpha, tSsp, tIsp, phiIsp, tO, phiO, Qsa, Qla, mi,
UA)
tS = x[4]
DtS = -(tSsp - tS)
print('Winter Rec_air VAV')
print(f'm = {m: 5.3f} kg/s')
# Processes on psychrometric chart
# Points o 0 1 2 3 Elements
A = np.array([
[-1, 1, 0, 0, -1], # MX
[0, -1, 1, 0, 0], # HC
[0, 0, -1, 1, 0], # VH
[0, 0, 0, -1, 1]
]) # TZ
t = np.append(tO, x[0:8:2])
print(f'wO = {wO:6.5f}')
w = np.append(wO, x[1:8:2])
psy.chartA(t, w, A)
t = pd.Series(t)
w = 1000 * pd.Series(w)
P = pd.concat([t, w], axis=1) # points
P.columns = ['t [°C]', 'w [g/kg]']
output = P.to_string(formatters={
't [°C]': '{:,.2f}'.format,
'w [g/kg]': '{:,.2f}'.format
})
print()
print(output)
Q = pd.Series(x[8:], index=['QsHC', 'QlVH', 'QsTZ', 'QlTZ'])
pd.options.display.float_format = '{:,.2f}'.format
print()
print(Q.to_frame().T / 1000, 'kW')
return None
def RecAirCAV(alpha=0.5,
tS=30,
tIsp=18,
phiIsp=0.5,
tO=-1,
phiO=1,
Qsa=0,
Qla=0,
mi=2.12,
UA=935.83):
"""
CAV Constant Air Volume:
mass flow rate calculated for design conditions
maintained constant in all situations
INPUTS:
alpha mixing ratio of outdoor air
tS supply air °C
tIsp indoor air setpoint °C
phiIsp -
tO outdoor temperature for design °C
phiO outdoor relative humidity for design -
Qsa aux. sensible heat W
Qla aux. latente heat W
mi infiltration massflow rate kg/s
UA global conductivity bldg W/K
System:
HC: Heating Coil
VH: Vapor Humidifier
TZ: Thermal Zone
Kw: Controller - humidity
Kt: Controller - temperature
o: outdoor conditions
12 Unknowns
0, 1, 2, 3 points (temperature, humidity ratio)
QsHC, QlVH, QsTZ, QlTZ
<-3--|<-------------------------|
| |
-o->MX--0->HC--1->VH--2->TZ--3-->
/ / || |
| | BL |
| | |
| |_____Kw__|_w3
|_____________Kt__|_t3
"""
plt.close('all')
wO = psy.w(tO, phiO) # hum. out
# Mass flow rate for design conditions
# Supplay air mass flow rate
# QsZ = UA*(tO - tIsp) + mi*c*(tO - tIsp)
# m = - QsZ/(c*(tS - tIsp)
# where
# tOd, wOd = -1, 3.5e-3 # outdoor
# tS = 30 # supply air
# mid = 2.18 # infiltration
QsZ = UA * (tOd - tIsp) + mid * c * (-1 - tIsp)
m = -QsZ / (c * (tS - tIsp))
print('Winter Recirculated_air CAV')
print(f'm = {m: 5.3f} kg/s constant (from design conditions)')
print(f'Design conditions tS = {tS: 3.1f} °C,'
f'mi = {mid:3.1f} kg/s, tO = {tOd:3.1f} °C, '
f'tI = {tIsp:3.1f} °C')
# Model
x = ModelRecAir(m, alpha, tS, tIsp, phiIsp, tO, phiO, Qsa, Qla, mi, UA)
# (m, tS, mi, tO, phiO, alpha)
# Processes on psychrometric chart
# Points o 0 1 2 3 Elements
A = np.array([
[-1, 1, 0, 0, -1], # MX
[0, -1, 1, 0, 0], # HC
[0, 0, -1, 1, 0], # VH
[0, 0, 0, -1, 1]
]) # TZ
t = np.append(tO, x[0:8:2])
print(f'wO = {wO:6.5f}')
w = np.append(wO, x[1:8:2])
psy.chartA(t, w, A)
t = pd.Series(t)
w = 1000 * pd.Series(w)
P = pd.concat([t, w], axis=1) # points
P.columns = ['t [°C]', 'w [g/kg]']
output = P.to_string(formatters={
't [°C]': '{:,.2f}'.format,
'w [g/kg]': '{:,.2f}'.format
})
print()
print(output)
Q = pd.Series(x[8:], index=['QsHC', 'QlVH', 'QsTZ', 'QlTZ'])
pd.options.display.float_format = '{:,.2f}'.format
print()
print(Q.to_frame().T / 1000, 'kW')
return None
def AllOutAirVAV(tSsp=30,
tIsp=18,
phiIsp=0.5,
tO=-1,
phiO=1,
Qsa=0,
Qla=0,
mi=2.12,
UA=935.83):
"""
All out air
Heating & Vapor humidification
VAV Variable Air Volume:
mass flow rate calculated to have const. supply temp.
INPUTS:
tS supply air °C
tIsp indoor air setpoint °C
phiIsp -
tO outdoor temperature for design °C
phiO outdoor relative humidity for design -
Qsa aux. sensible heat W
Qla aux. latente heat W
mi infiltration massflow rate kg/s
UA global conductivity bldg W/K
System:
HC: Heating Coil
VH: Vapor Humidifier
TZ: Thermal Zone
BL: Building
Kw: Controller - humidity
Kt: Controller - temperature
o: outdoor conditions
10 Unknowns
0, 1, 2 points (temperature, humidity ratio)
QsHC, QlVH, QsTZ, QlTZ
--o->HC--0->VH--F-----1-->TZ--2-->
/ / | | || |
| | | | BL |
| | |_Kt1_| |
| | |
| |<----Kw---------|-w2
|<------------Kt---------|-t2
Mass-flow rate (VAV) I-controller:
start with m = 0
measure the supply temperature
while -(tSsp - tS)>0.01, increase m (I-controller)
"""
plt.close('all')
wO = psy.w(tO, phiO) # outdoor mumidity ratio
# Mass flow rate
DtS, m = 2, 0 # initial temp; diff; flow rate
while DtS > 0.01:
m = m + 0.01 # mass-flow rate I-controller
# Model
x = ModelAllOutAir(m, tSsp, tIsp, phiIsp, tO, phiO, Qsa, Qla, mi, UA)
tS = x[2]
DtS = -(tSsp - tS)
print('Winter All_out_air VAV')
print(f'm = {m: 5.3f} kg/s')
# Processes on psychrometric chart
t = np.append(tO, x[0:5:2])
w = np.append(wO, x[1:6:2])
# Points o 0 1 2 Elements
A = np.array([
[-1, 1, 0, 0], # HC
[0, -1, 1, 0], # VH
[0, 0, 1, -1]
]) # TZ
psy.chartA(t, w, A)
t = pd.Series(t)
w = 1000 * pd.Series(w)
P = pd.concat([t, w], axis=1) # points
P.columns = ['t [°C]', 'w [g/kg]']
output = P.to_string(formatters={
't [°C]': '{:,.2f}'.format,
'w [g/kg]': '{:,.2f}'.format
})
print()
print(output)
Q = pd.Series(x[6:], index=['QsHC', 'QlVH', 'QsTZ', 'QlTZ'])
# Q.columns = ['kW']
pd.options.display.float_format = '{:,.2f}'.format
print()
print(Q.to_frame().T / 1000, 'kW')
return None
def AllOutAirCAV(tS=30,
tIsp=18,
phiIsp=0.5,
tO=-1,
phiO=1,
Qsa=0,
Qla=0,
mi=2.12,
UA=935.83):
"""
All out air
CAV Constant Air Volume:
mass flow rate calculated for design conditions
maintained constant in all situations
INPUTS:
m mass flow of supply dry air kg/s
tS supply air °C
tIsp indoor air setpoint °C
phiIsp -
tO outdoor temperature for design °C
phiO outdoor relative humidity for design -
Qsa aux. sensible heat W
Qla aux. latente heat W
mi infiltration massflow rate kg/s
UA global conductivity bldg W/K
System:
HC: Heating Coil
VH: Vapor Humidifier
TZ: Thermal Zone
BL: Building
Kw: Controller - humidity
Kt: Controller - temperature
o: outdoor conditions
10 Unknowns
0, 1, 2 points (temperature, humidity ratio)
QsHC, QlVH, QsTZ, QlTZ
--o->HC--0->VH--1->TZ--2-->
/ / || |
| | BL |
| | |
| |<----Kw--|-w2
|<------------Kt--|-t2
"""
plt.close('all')
wO = psy.w(tO, phiO) # hum. out
# Mass flow rate for design conditions
# tOd = -1 # outdoor design conditions
# mid = 2.18 # infiltration design
QsZ = UA * (tOd - tIsp) + mid * c * (tOd - tIsp)
m = -QsZ / (c * (tS - tIsp))
print('Winter All_out_air CAV')
print(f'm = {m: 5.3f} kg/s constant (from design conditions)')
print(f'Design conditions tS = {tS: 3.1f} °C,'
f'mi = {mid:3.1f} kg/s, tO = {tOd:3.1f} °C, '
f'tI = {tIsp:3.1f} °C')
# Model
x = ModelAllOutAir(m, tS, tIsp, phiIsp, tO, phiO, Qsa, Qla, mi, UA)
# Processes on psychrometric chart
t = np.append(tO, x[0:5:2])
w = np.append(wO, x[1:6:2])
# Adjancy matrix: rows=lines; columns=points
# Points O 0 1 2 Elements
A = np.array([
[-1, 1, 0, 0], # HC
[0, -1, 1, 0], # VH
[0, 0, 1, -1]
]) # TZ
psy.chartA(t, w, A)
t = pd.Series(t)
w = 1000 * pd.Series(w)
P = pd.concat([t, w], axis=1) # points
P.columns = ['t [°C]', 'w [g/kg]']
output = P.to_string(formatters={
't [°C]': '{:,.2f}'.format,
'w [g/kg]': '{:,.2f}'.format
})
print()
print(output)
Q = pd.Series(x[6:], index=['QsHC', 'QlVH', 'QsTZ', 'QlTZ'])
# Q.columns = ['kW']
pd.options.display.float_format = '{:,.2f}'.format
print()
print(Q.to_frame().T / 1000, 'kW')
return x