def chartA(t,
wv,
A,
t_range=np.arange(-10, 50, 5),
w_range=np.arange(0, 0.030, 0.01)):
"""
Parameters
----------
t : np.array, no. equal to no. points in the psy-chart
temperatures, °C
wv: np.array, wv.shape = t.shape
weight vapor, kg/kg_da
A : np.array [no. processes, no. points = no. temperatures]
adjancy matrix: -1 flow our of node, 1 flow in node, 0 no connection
t_range : np.arange
range of temperature
the default is np.arange(-10, 50, 0.1).
temperature vector t = np.arange(-10, 50, 0.1)
w_range : np.arange
humidity ration vector
The default is np.arange(0, 0.030, 0.01).
Returns
-------
None.
"""
import matplotlib.pyplot as plt
import psychro as psy
fig = plt.figure()
ax = fig.add_subplot(111)
ax.yaxis.tick_right()
plt.xlabel(r'Temperature $\theta$ [°C]')
ax.yaxis.set_label_position("right")
plt.ylabel(r'Humidity ratio w [kg/kg]')
plt.grid(True)
plt.plot(t_range, psy.w(t_range, 1), linewidth=2) # saturation curve
# Plot relative humidity curves
for phi in np.arange(0, 1, 0.2):
w4t = psy.w(t_range, phi)
plt.plot(t_range, w4t, linewidth=0.5)
phi100 = phi * 100
s_phi = "%3.0f" % phi100
ax.annotate(s_phi + ' %', xy=(t_range[-1] - 3, w4t[-1]))
for k in range(0, A.shape[0]):
tk = np.nonzero(A[k, :])
wk = np.nonzero(A[k, :])
plt.plot(t[tk], wv[wk], linewidth=3) # processes
# plot no. point
for j in range(0, np.shape(tk)[1]):
plt.text(t[tk][j], wv[tk][j], str(tk[0][j]))
return None
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 chart(t,
w,
t_range=np.arange(-10, 50, 0.1),
w_range=np.arange(0, 0.030, 0.0001)):
"""
Parameters
----------
t_range : temperature vector t = np.arange(-10, 50, 0.1)
w_range : humidity ration vector w = np.arange(0, 0.030, 0.0001)
Returns
-------
None. Psycrometric chart
"""
import matplotlib.pyplot as plt
import psychro as psy
fig = plt.figure()
ax = fig.add_subplot(111)
ax.yaxis.tick_right()
plt.xlabel(r'Temperature $\theta$ [°C]')
ax.yaxis.set_label_position("right")
plt.ylabel(r'Humidity ratio w [kg/kg]')
plt.grid(True)
plt.plot(t_range, psy.w(t_range, 100), linewidth=2) # saturation curve
# Plot relative humidity curves
for phi in np.arange(0, 100, 20):
w4t = psy.w(t_range, phi)
plt.plot(t_range, w4t, linewidth=0.5)
s_phi = "%3.0f" % phi
ax.annotate(s_phi + ' %', xy=(t_range[-1] - 3, w4t[-1]))
plt.plot(t, w, linewidth=3) # processes
return None
def solve_lin(self, θs0):
"""
Finds saturation point on saturation curve ws = f(θs).
Solves iterativelly *lin_model(θs0)*:
θs -> θs0 until ws = psy(θs, 1).
Parameters
----------
θs0 initial guess saturation temperature
Method from object
---------------------
*self.lin_model(θs0)*
Returns (16 unknowns)
---------------------
x of *self.lin_model(self, θs0)*
"""
Δ_ws = 10e-3 # kg/kg, initial difference to start the iterations
while Δ_ws > 0.01e-3:
x = self.lin_model(θs0)
Δ_ws = abs(psy.w(x[2], 1) - x[3]) # psy.w(θs, 1) = ws
θs0 = x[2] # actualize θs0
return x
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 β_ls(self, value, sp):
"""
Bypass β controls supply temperature θS or indoor humidity wI.
Finds β which solves value = sp, i.e. minimizes ε = value - sp.
Uses *scipy.optimize.least_squares* to solve the non-linear system.
Parameters
----------
value string: 'θS' od 'wI' type of controlled variable
sp float: value of setpoint
Calls
-----
*ε(m)* gives (value - sp) to be minimized for m
Returns (16 unknowns)
---------------------
x given by *self.lin_model(self, θs0)*
"""
from scipy.optimize import least_squares
def ε(β):
"""
Gives difference ε = (values - sp) function of β
ε calculated by self.solve_lin(ts0)
β bounds=(0, 1)
Parameters
----------
β : by-pass factor of the cooling coil
From object
Method: self.solve.lin(θs0)
Variables: self.actual <- m (used in self.solve.lin)
Returns
-------
ε = value - sp: difference between value and its set point
"""
self.actual[2] = β
x = self.solve_lin(θs_0)
if value == 'θS':
θS = x[6] # supply air
return abs(sp - θS)
elif value == 'φI':
wI = x[9] # indoor air
return abs(sp - wI)
else:
print('ERROR in ε(β): value not in {"θS", "wI"}')
β0 = self.actual[2] # initial guess
β0 = 0.1
if value == 'φI':
self.actual[4] = 0
sp = psy.w(self.actual[7], sp)
# gives m for min(θSsp - θS); θs_0 is the initial guess of θs
res = least_squares(ε, β0, bounds=(0, 1))
if res.cost < 1e-5:
β = float(res.x)
# print(f'm = {m: 5.3f} kg/s')
else:
print('RecAirVBP: No solution for β')
self.actual[2] = β
x = self.solve_lin(θs_0)
return x
def m_ls(self, value, sp):
"""
Mass flow rate m controls supply temperature θS or indoor humidity wI.
Finds m which solves value = sp, i.e. minimizes ε = value - sp.
Uses *scipy.optimize.least_squares* to solve the non-linear system.
Parameters
----------
value string: 'θS' od 'wI' type of controlled variable
sp float: value of setpoint
Calls
-----
*ε(m)* gives (value - sp) to be minimized for m
Returns (16 unknowns)
---------------------
x given by *self.lin_model(self, θs0)*
"""
from scipy.optimize import least_squares
def ε(m):
"""
Gives difference ε = (values - sp) function of m
ε calculated by self.solve_lin(ts0)
m bounds=(0, m_max); m_max hard coded (global variable)
Parameters
----------
m : mass flow rate of dry air
From object
Method: self.solve.lin(θs0)
Variables: self.actual <- m (used in self.solve.lin)
Returns
-------
ε = value - sp: difference between value and its set point
"""
self.actual[0] = m
x = self.solve_lin(θs_0)
if value == 'θS':
θS = x[6] # supply air
return abs(sp - θS)
elif value == 'φI':
wI = x[9] # indoor air
return abs(sp - wI)
else:
print('ERROR in ε(m): value not in {"θS", "wI"}')
m0 = self.actual[0] # initial guess
if value == 'φI':
self.actual[4] = 0
sp = psy.w(self.actual[7], sp)
# gives m for min(θSsp - θS); θs_0 is the initial guess of θs
res = least_squares(ε, m0, bounds=(0, m_max))
if res.cost < 0.1e-3:
m = float(res.x)
# print(f'm = {m: 5.3f} kg/s')
else:
print('RecAirVAV: No solution for m')
self.actual[0] = m
x = self.solve_lin(θs_0)
return x
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 lin_model(self, θs0):
"""
Linearized model.
Solves a set of 16 linear equations.
Saturation curve is linearized in θs0.
s-point (θs, ws):
- is on a tangent to φ = 100 % in θs0;
- is **not** on the saturation curve (Apparatus Dew Point ADP).
Parameter from function call
----------------------------
θs0 °C, temperature for which the saturation curve is liniarized
Parameters from object
---------------------
m, mo, θo, φo, θIsp, φIsp, β, mi, UA, Qsa, Qla = self.actual
Equations (16)
-------------
+-------------+-----+----+-----+----+----+----+----+----+
| Element | MX1 | CC | MX2 | HC | TZ | BL | Kθ | Kw |
+=============+=====+====+=====+====+====+====+====+====+
| N° equations| 2 | 4 | 2 | 2 | 2 | 2 | 1 | 1 |
+-------------+-----+----+-----+----+----+----+----+----+
Returns (16 unknowns)
---------------------
x : θM, wM, θs, ws, θC, wC, θS, wS, θI, wI,
QtCC, QsCC, QlCC, QsHC, QsTZ, QlTZ
"""
"""
<=4================================m==========================
|| ||
4 (m-mo) =======0======= ||
|| || (1-β)m || ||
θo,φo=>[MX1]==0==|| [MX2]==2==[HC]==F==3==>[TZ]==4==||
mo || || / / // |
===0=[CC]==1=== s m sl |
/\\ βm | || |
t sl | [BL]<-mi |
| | // |
| | sl |
| | |
| |<------[K]-----------+<-wI
|<------------------------[K]-----------+<-θI
"""
m, mo, β, Kθ, Kw, θo, φo, θIsp, φIsp, mi, UA, Qsa, Qla = self.actual
wo = psy.w(θo, φo) # hum. out
A = np.zeros((16, 16)) # coefficents of unknowns
b = np.zeros(16) # vector of inputs
# MX1
A[0, 0], A[0, 8], b[0] = m * c, -(m - mo) * c, mo * c * θo
A[1, 1], A[1, 9], b[1] = m * l, -(m - mo) * l, mo * l * wo
# CC
A[2, 0], A[2, 2], A[2, 11], b[2] = (1 - β) * m * c, -(1 - β) * m * c,\
1, 0
A[3, 1], A[3, 3], A[3, 12], b[3] = (1 - β) * m * l, -(1 - β) * m * l,\
1, 0
A[4, 2], A[4, 3], b[4] = psy.wsp(θs0), -1,\
psy.wsp(θs0) * θs0 - psy.w(θs0, 1)
A[5, 10], A[5, 11], A[5, 12], b[5] = -1, 1, 1, 0
# MX2
A[6, 0], A[6, 2], A[6, 4], b[6] = β * m * c, (1 - β) * m * c,\
- m * c, 0
A[7, 1], A[7, 3], A[7, 5], b[7] = β * m * l, (1 - β) * m * l,\
- m * l, 0
# HC
A[8, 4], A[8, 6], A[8, 13], b[8] = m * c, -m * c, 1, 0
A[9, 5], A[9, 7], b[9] = m * l, -m * l, 0
# TZ
A[10, 6], A[10, 8], A[10, 14], b[10] = m * c, -m * c, 1, 0
A[11, 7], A[11, 9], A[11, 15], b[11] = m * l, -m * l, 1, 0
# BL
A[12, 8], A[12, 14], b[12] = (UA + mi * c), 1, (UA + mi * c) * θo + Qsa
A[13, 9], A[13, 15], b[13] = mi * l, 1, mi * l * wo + Qla
# Kθ indoor temperature controller
A[14, 8], A[14, 10], b[14] = Kθ, 1, Kθ * θIsp
# Kw indoor humidity ratio controller
A[15, 9], A[15, 13], b[15] = Kw, 1, Kw * psy.w(θIsp, φIsp)
x = np.linalg.solve(A, b)
return x
m=self.actual[0], mo=self.actual[1], β=self.actual[2]))
self.psy_chart(x, θo, φo)
return x
# TESTS: uncomment
# Recyclage p. 6/19
Kθ, Kw = 1e10, 0 # Kw can be 0
β = 0
m, mo = 3.093, 0.94179
θo, φo = 32, 0.5
θIsp, φIsp = 26, 0.5
mi = 15e3 / (l * (psy.w(θo, φo) - psy.w(θIsp, φIsp))) # kg/s
UA = 45e3 / (θo - θIsp) - mi * c # W/K
Qsa, Qla = 0, 0 # W
print(f'QsTZ = {(UA + mi * c) * (θo - θIsp): ,.1f} W')
print(f'QlTZ = {mi * l * (psy.w(θo, φo) - psy.w(θIsp, φIsp)): ,.1f} W')
parameters = m, mo, β, Kθ, Kw
inputs = θo, φo, θIsp, φIsp, mi, UA, Qsa, Qla
cool = MxCcRhTzBl(parameters, inputs)
# # 1. CAV
# print('\nCAV: m given')
# cool.CAV_wd()
# cool.CAV_wd(θo, φo, θIsp, φIsp, mi, UA, Qsa, Qla)
# # 2.
length = 20 # m width = 30 # m height = 3.5 # m persons = 100 # m sens_heat_person = 60 # W / person latent_heat_person = 40 # W / person load_m2 = 20 # W/m2 solar_m2 = 150 # W/m2 of window area ACH = 1 # Air Cnhnages per Hour U_wall = 0.4 # W/K, overall heat transfer coeff. walls U_window = 3.5 # W/K, overall heat transfer coeff. windows θo, φo = 32, 0.5 # outdoor temperature & relative humidity θI, φI = 26, 0.5 # indoor temperature & relative humidity wo = psy.w(θo, φo) wI = psy.w(θI, φI) floor_area = length * width surface_envelope = 2 * (length + width) * height + floor_area surface_wall = 0.9 * surface_envelope surface_window = surface_envelope - surface_wall # building conductance, W/K UA = U_wall * surface_wall + U_window * surface_window # infiltration mass flow rate, kg/s mi = ACH * surface_envelope * height / 3600 * ρ # gains, W solar_gains = solar_m2 * surface_window
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 ModelAllOutAir(m, tS, tIsp, phiIsp, tO, phiO, Qsa, Qla, mi, UA):
"""
Model:
All outdoor air
CAV Constant Air Volume:
mass flow rate given
control of indoor condition (t2, w2)
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
OUTPUTS:
x vector 10 elements:
t0, w0, t1, w1, t2, w2, QsHC, QlVH, QsTZ, QlTZ
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
"""
Kt, Kw = 1e10, 1e10 # controller gain
wO = psy.w(tO, phiO) # outdoor mumidity ratio
wIsp = psy.w(tIsp, phiIsp) # indoor mumidity ratio
# Model
A = np.zeros((10, 10)) # coefficents of unknowns
b = np.zeros(10) # vector of inputs
# HC heating coil
A[0, 0], A[0, 6], b[0] = m * c, -1, m * c * tO
A[1, 1], b[1] = m * l, m * l * wO
# VA vapor humidifier
A[2, 0], A[2, 2], b[2] = -m * c, m * c, 0
A[3, 1], A[3, 3], A[3, 7], b[3] = -m * l, m * l, -1, 0
# TZ thermal zone
A[4, 2], A[4, 4], A[4, 8], b[4] = -m * c, m * c, -1, 0
A[5, 3], A[5, 5], A[5, 9], b[5] = -m * l, m * l, -1, 0
# BL building
A[6, 4], A[6, 8], b[6] = UA + mi * c, 1, (UA + mi * c) * tO + Qsa
A[7, 5], A[7, 9], b[7] = mi * l, 1, mi * l * wO + Qla
# Kt indoor temperature controller
A[8, 4], A[8, 8], b[8] = Kt, 1, Kt * tIsp
# Kw indoor hum.ratio controller
A[9, 5], A[9, 9], b[9] = Kw, 1, Kw * wIsp
# Solution
x = np.linalg.solve(A, b)
return x
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 ModelRecAir(m, alpha, tS, tIsp, phiIsp, tO, phiO, Qsa, Qla, mi, UA):
"""
Model:
Heating and vapor humidification
Recycled 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
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
OUTPUTS:
x vector 12 elements:
t0, w0, t1, w1, t2, w2, t3, w3, QsHC, QlVH, QsTZ, QlTZ
System:
MX: Mixing Box
HC: Heating Coil
VH: Vapor Humidifier
TZ: Thermal Zone
BL: Buildings
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
"""
Kt, Kw = 1e10, 1e10 # controller gain
wO = psy.w(tO, phiO) # hum. out
wIsp = psy.w(tIsp, phiIsp) # hum. in set point
# Model
A = np.zeros((12, 12)) # coefficents of unknowns
b = np.zeros(12) # vector of inputs
# MX mixing box
A[0, 0], A[0, 6], b[0] = m * c, -(1 - alpha) * m * c, alpha * m * c * tO
A[1, 1], A[1, 7], b[1] = m * l, -(1 - alpha) * m * l, alpha * m * l * wO
# HC hearing coil
A[2, 0], A[2, 2], A[2, 8], b[2] = m * c, -m * c, 1, 0
A[3, 1], A[3, 3], b[3] = m * l, -m * l, 0
# VH vapor humidifier
A[4, 2], A[4, 4], b[4] = m * c, -m * c, 0
A[5, 3], A[5, 5], A[5, 9], b[5] = m * l, -m * l, 1, 0
# TZ thermal zone
A[6, 4], A[6, 6], A[6, 10], b[6] = m * c, -m * c, 1, 0
A[7, 5], A[7, 7], A[7, 11], b[7] = m * l, -m * l, 1, 0
# BL building
A[8, 6], A[8, 10], b[8] = (UA + mi * c), 1, (UA + mi * c) * tO + Qsa
A[9, 7], A[9, 11], b[9] = mi * l, 1, mi * l * wO + Qla
# Kt indoor temperature controller
A[10, 6], A[10, 8], b[10] = Kt, 1, Kt * tIsp
# Kw indoor humidity controller
A[11, 7], A[11, 9], b[11] = Kw, 1, Kw * wIsp
# Solution
x = np.linalg.solve(A, b)
return x
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 ModelRecAir(m, alpha, beta, tS, tIsp, phiIsp, tO, phiO, Qsa, Qla, mi, UA):
"""
Model:
Heating and adiabatic humidification
Recycled 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
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--4->TZ--5-|
/ | | / || |
| |->AH-2-| | BL |
| | |
| |<-----Kt----|<-t5
|<------------------------------Kw----|<-w5
Returns
-------
x vector 16 elem.:
t0, w0, t1, w1, t2, w2, t3, w3, t4, w4, t5, w5,...
QHC1, QHC2, QsTZ, QlTZ
"""
Kt, Kw = 1e10, 1e10 # controller gain
wO = psy.w(tO, phiO) # hum. out
wIsp = psy.w(tIsp, phiIsp) # indoor mumidity ratio
# Model
ts0, Del_ts = tS, 2 # initial guess saturation temp.
A = np.zeros((16, 16)) # coefficents of unknowns
b = np.zeros(16) # vector of inputs
while Del_ts > 0.01:
# MX1
A[0, 0], A[0, 10], b[0] = m*c, -(1 - alpha)*m*c, alpha*m*c*tO
A[1, 1], A[1, 11], b[1] = m*l, -(1 - alpha)*m*l, alpha*m*l*wO
# HC1
A[2, 0], A[2, 2], A[2, 12], b[2] = m*c, -m*c, 1, 0
A[3, 1], A[3, 3], b[3] = m*l, -m*l, 0
# AH
A[4, 2], A[4, 3], A[4, 4], A[4, 5], b[4] = c, l, -c, -l, 0
A[5, 4], A[5, 5] = psy.wsp(ts0), -1
b[5] = psy.wsp(ts0)*ts0 - psy.w(ts0, 1)
# MX2
A[6, 2], A[6, 4], A[6, 6], b[6] = beta*m*c, (1-beta)*m*c, -m*c, 0
A[7, 3], A[7, 5], A[7, 7], b[7] = beta*m*l, (1-beta)*m*l, -m*l, 0
# HC2
A[8, 6], A[8, 8], A[8, 13], b[8] = m*c, -m*c, 1, 0
A[9, 7], A[9, 9], b[9] = m*l, -m*l, 0
# TZ
A[10, 8], A[10, 10], A[10, 14], b[10] = m*c, -m*c, 1, 0
A[11, 9], A[11, 11], A[11, 15], b[11] = m*l, -m*l, 1, 0
# BL
A[12, 10], A[12, 14], b[12] = (UA+mi*c), 1, (UA+mi*c)*tO + Qsa
A[13, 11], A[13, 15], b[13] = mi*l, 1, mi*l*wO + Qla
# Kt & Kw
A[14, 10], A[14, 12], b[14] = Kt, 1, Kt*tIsp
A[15, 11], A[15, 13], b[15] = Kw, 1, Kw*wIsp
x = np.linalg.solve(A, b)
Del_ts = abs(ts0 - x[4])
ts0 = x[4]
return x
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
