def right_boundary(linkp, pn, H0, V0, H, V, links1, p, pump, valve, dt, H10,
V10, utype, dtype):
"""MOC solution for an individual right boundary pipe.
Parameters
----------
linkp : object
Current pipe object
pn : int
Current pipe ID
H : numpy.ndarray
Head of current pipe at current time step [m]
V : numpy.ndarray
Velocity of current pipe at current time step [m/s]
links1 : list
Upstream adjacent pipes
p : list
pipe list
pump : list
Characteristics of the pump
valve : list
Characteristics of the valve
n : int
Number of discretization of current pipe
dt : float
Time step
H0 : numpy.ndarray
Head of current pipe at previous time step [m]
V0 : numpy.ndarray
Velocity of current pipe at previous time step [m/s]
H10 : list
Head of left adjacent nodes at previous time step [m]
V10 : list
Velocity of left adjacent nodes at previous time step [m/s]
utype : list
Upstream adjacent link type, and if not pipe, their name
dtype : list
Downstream adjacent link type, and if not pipe, their name
Returns
-------
H : numpy.ndarray
Head results of the current pipe at current time step. [m]
V : numpy.ndarray
Velocity results of the current pipe at current time step. [m/s]
"""
# Properties of current pipe
link1 = [p[abs(i) - 1] for i in links1]
f = linkp.roughness # unitless
D = linkp.diameter # m
g = 9.8 # m/s^2
a = linkp.wavev # m/s
n = linkp.number_of_segments # spatial discretization
for i in range(n + 1):
# Pipe start (inner boundary conditions)
if i == 0:
V1 = V10
H1 = H10 # upstream node
V2 = V0[i + 1]
H2 = H0[i + 1] # downstream node
if utype[0] == 'Pipe':
elev = linkp.start_node.elevation
emitter_coeff = linkp.start_node.emitter_coeff + linkp.start_node.demand_coeff
H[i], V[i] = add_leakage(emitter_coeff, link1, linkp, elev,
H1, V1, H2, V2, dt, g, i,
np.sign(links1), [-1])
elif utype[0] == 'Pump':
pumpc = pump[0]
H[i], V[i] = pump_node(pumpc, link1, linkp, H1, V1, H2, V2, dt,
g, i, np.sign(links1), [-1])
elif utype[0] == 'Valve':
valvec = valve[0]
H[i], V[i] = valve_node(valvec, link1, linkp, H1, V1, H2, V2,
dt, g, i, np.sign(links1), [-1])
# Pipe end (outer boundary conditions )
if i == n:
V1 = V0[i - 1]
H1 = H0[i - 1]
if dtype[0] == 'Reservoir' or dtype[0] == 'Tank':
H[i], V[i] = rev_end(H1, V1, H[i], i, a, g, f, D, dt)
if dtype[0] == 'Valve':
H[i], V[i] = valve_end(H1, V1, V[i], i, a, g, f, D, dt)
if dtype[0] == 'Junction':
H[i], V[i] = dead_end(linkp, H1, V1, i, a, g, f, D, dt)
# Interior points
if (i > 0) and (i < n):
V1 = V0[i - 1]
H1 = H0[i - 1]
V2 = V0[i + 1]
H2 = H0[i + 1]
H[i], V[i] = inner_node(linkp, linkp, 0, H1, V1, H2, V2, dt, g, i,
[1], [-1])
return H, V
def right_boundary(linkp, pn, H0, V0, H, V, links1, p, pump, valve, dt,
H10, V10, utype, dtype,
friction, dVdt, dVdx, dVdt10, dVdx10):
"""MOC solution for an individual right boundary pipe.
Parameters
----------
linkp : object
Current pipe object
pn : int
Current pipe ID
H : numpy.ndarray
Head of current pipe at current time step [m]
V : numpy.ndarray
Velocity of current pipe at current time step [m/s]
links1 : list
Upstream adjacent pipes
p : list
pipe list
pump : list
Characteristics of the pump
valve : list
Characteristics of the valve
n : int
Number of discretization of current pipe
dt : float
Time step
H0 : numpy.ndarray
Head of current pipe at previous time step [m]
V0 : numpy.ndarray
Velocity of current pipe at previous time step [m/s]
H10 : list
Head of left adjacent nodes at previous time step [m]
V10 : list
Velocity of left adjacent nodes at previous time step [m/s]
utype : list
Upstream adjacent link type, and if not pipe, their name
dtype : list
Downstream adjacent link type, and if not pipe, their name
friction: str
friction model, e.g., 'steady', 'quasi-steady', 'unsteady',
by default 'steady'
dVdt: numpy.ndarray
local instantaneous velocity approximation to be used
for unsteady friction calculation, 0 if not
in unsteady friction mode [m/s^2]
dVdx: numpy.ndarray
convective instantaneous velocity approximation to be used
for unsteady friction calculation, 0 if not
in unsteady friction mode [m/s^2]
dVdt10 : list
local instantaneous acceleration of left adjacent nodes at previous time step [m]
dVdx10 : list
convective instantaneous acceleration of left adjacent nodes at previous time step [m/s]
Returns
-------
H : numpy.ndarray
Head results of the current pipe at current time step. [m]
V : numpy.ndarray
Velocity results of the current pipe at current time step. [m/s]
"""
# Properties of current pipe
link1 = [p[abs(i)-1] for i in links1]
f = linkp.roughness # unitless
D = linkp.diameter # m
g = 9.8 # m/s^2
a = linkp.wavev # m/s
n = linkp.number_of_segments # spatial discretization
KD = linkp.roughness_height
# inner nodes
if friction == 'steady':
H[1:-1], V[1:-1] = inner_node_steady(linkp, H0, V0, dt, g)
elif friction == 'quasi-steady':
H[1:-1], V[1:-1] = inner_node_quasisteady(linkp, H0, V0, dt, g)
else:
H[1:-1], V[1:-1] = inner_node_unsteady(linkp, H0, V0, dt, g,
dVdx, dVdt)
# Pipe start (inner boundary conditions)
V1 = V10; H1 = H10 # upstream node
V2 = V0[1]; H2 = H0[1] # downstream node
dVdx1 = dVdx10 ; dVdx2 = dVdx[0]
dVdt1 = dVdt10 ; dVdt2 = dVdt[1]
if utype[0] == 'Pipe':
if linkp.start_node.transient_node_type == 'SurgeTank':
shape = linkp.start_node.tank_shape
H[0], V[0], Qs = surge_tank(shape, link1, linkp,
H1, V1, H2, V2, dt, g, 0, np.sign(links1), [-1],
friction, dVdx1, dVdx2, dVdt1, dVdt2)
linkp.start_node.water_level = H[0]
linkp.start_node.tank_flow = Qs
if linkp.start_node.transient_node_type == 'Chamber':
shape = linkp.start_node.tank_shape
H[0], V[0], Qs, zp = air_chamber(shape, link1, linkp,
H1, V1, H2, V2, dt, g, 0, np.sign(links1), [-1],
friction, dVdx1, dVdx2, dVdt1, dVdt2)
linkp.start_node.water_level = zp
linkp.start_node.tank_flow = Qs
else:
elev = linkp.start_node.elevation
emitter_coeff = linkp.start_node.emitter_coeff + linkp.start_node.demand_coeff
block_per = linkp.start_node.block_per
H[0], V[0] = add_leakage(emitter_coeff, block_per,link1, linkp, elev,
H1, V1, H2, V2, dt, g, 0, np.sign(links1), [-1],
friction, dVdx1, dVdx2, dVdt1, dVdt2)
elif utype[0] == 'Pump':
pumpc = pump[0]
H[0], V[0] = pump_node(pumpc, link1, linkp,
H1, V1, H2, V2, dt, g, 0, np.sign(links1), [-1],
friction, dVdx1, dVdx2, dVdt1, dVdt2)
elif utype[0] == 'Valve':
valvec = valve[0]
H[0], V[0] = valve_node(valvec, link1, linkp,
H1, V1, H2, V2, dt, g, 0, np.sign(links1), [-1],
friction, dVdx1, dVdx2, dVdt1, dVdt2)
# Pipe end (outer boundary conditions )
V1 = V0[n-1]; H1 = H0[n-1]
dVdx1 = dVdx[n-1]
dVdt1 = dVdt[n-1]
if dtype[0] == 'Reservoir' or dtype[0] == 'Tank':
H[n], V[n] = rev_end (H1, V1, H[n], n, a, g, f, D, dt,
KD, friction, dVdx1, dVdt1)
if dtype[0] == 'Valve':
H[n], V[n] = valve_end (H1, V1, V[n], n, a, g, f, D, dt,
KD, friction, dVdx1, dVdt1)
if dtype[0] == 'Junction':
elev = linkp.end_node.elevation
H[n], V[n] = dead_end (linkp ,H1, V1, elev, n, a, g, f, D, dt,
KD, friction, dVdx1, dVdt1)
return H, V
def inner_pipe(linkp, pn, dt, links1, links2, utype, dtype, p, H0, V0, H, V,
H10, V10, H20, V20, pump, valve):
"""MOC solution for an individual inner pipe.
Parameters
----------
linkp : object
Current pipe object
pn : int
Current pipe ID
dt : float
Time step
H : numpy.ndarray
Head of current pipe at current time step [m]
V : numpy.ndarray
Velocity of current pipe at current time step [m/s]
links1 : list
Upstream adjacent pipes
links2 : list
Downstream adjacent pipes
utype : list
Upstream adjacent link type, and if not pipe, their name
dtype : list
Downstream adjacent link type, and if not pipe, their name
p : list
pipe list
n : int
Number of discretization of current pipe
H10 : list
Head of left adjacent nodes at previous time step [m]
V10 : list
Velocity of left adjacent nodes at previous time step [m/s]
H20 : list
Head of right adjacent nodes at previous time step [m]
V20 : list
Velocity of right adjacent nodes at previous time step [m/s]
pump : list
Characteristics of the pump
valve : list
Characteristics of the valve
Returns
-------
H : numpy.ndarray
Head results of the current pipe at current time step. [m]
V : numpy.ndarray
Velocity results of the current pipe at current time step. [m/s]
"""
# Properties of current pipe
g = 9.8 # m/s^2
link1 = [p[abs(i) - 1] for i in links1]
link2 = [p[abs(i) - 1] for i in links2]
n = linkp.number_of_segments # spatial discretization
for i in range(n + 1):
# Pipe start
if i == 0:
V1 = V10
H1 = H10 #list
V2 = V0[i + 1]
H2 = H0[i + 1]
if utype[0] == 'Pipe':
elev = linkp.start_node.elevation
emitter_coeff = linkp.start_node.emitter_coeff + linkp.start_node.demand_coeff
H[i], V[i] = add_leakage(emitter_coeff, link1, linkp, elev,
H1, V1, H2, V2, dt, g, i,
np.sign(links1), [-1])
elif utype[0] == 'Pump':
pumpc = pump[0]
H[i], V[i] = pump_node(pumpc, link1, linkp, H1, V1, H2, V2, dt,
g, i, np.sign(links1), [-1])
elif utype[0] == 'Valve':
valvec = valve[0]
H[i], V[i] = valve_node(valvec, link1, linkp, H1, V1, H2, V2,
dt, g, i, np.sign(links1), [-1])
# Pipe end
if i == n:
V1 = V0[i - 1]
H1 = H0[i - 1]
V2 = V20
H2 = H20
if dtype[0] == 'Pipe':
elev = linkp.end_node.elevation
emitter_coeff = linkp.end_node.emitter_coeff + linkp.end_node.demand_coeff
H[i], V[i] = add_leakage(emitter_coeff, linkp, link2, elev, H1,
V1, H2, V2, dt, g, i, [1],
np.sign(links2))
elif dtype[0] == 'Pump':
pumpc = pump[1]
H[i], V[i] = pump_node(pumpc, linkp, link2, H1, V1, H2, V2, dt,
g, i, [1], np.sign(links2))
elif dtype[0] == 'Valve':
valvec = valve[1]
H[i], V[i] = valve_node(valvec, linkp, link2, H1, V1, H2, V2,
dt, g, i, [1], np.sign(links2))
# Interior points
if (i > 0) and (i < n):
V1 = V0[i - 1]
H1 = H0[i - 1]
V2 = V0[i + 1]
H2 = H0[i + 1]
H[i], V[i] = inner_node(linkp, linkp, 0, H1, V1, H2, V2, dt, g, i,
[1], [-1])
return H, V
def inner_pipe (linkp, pn, dt, links1, links2, utype, dtype, p,
H0, V0, H, V, H10, V10, H20, V20, pump, valve,
friction, dVdt, dVdx,
dVdt10, dVdx10, dVdt20, dVdx20):
"""MOC solution for an individual inner pipe.
Parameters
----------
linkp : object
Current pipe object
pn : int
Current pipe ID
dt : float
Time step
H : numpy.ndarray
Head of current pipe at current time step [m]
V : numpy.ndarray
Velocity of current pipe at current time step [m/s]
links1 : list
Upstream adjacent pipes
links2 : list
Downstream adjacent pipes
utype : list
Upstream adjacent link type, and if not pipe, their name
dtype : list
Downstream adjacent link type, and if not pipe, their name
p : list
pipe list
H0 : numpy.ndarray
Head of current pipe at previous time step [m]
V0 : numpy.ndarray
Velocity of current pipe at previous time step [m/s]
H10 : list
Head of left adjacent nodes at previous time step [m]
V10 : list
Velocity of left adjacent nodes at previous time step [m/s]
H20 : list
Head of right adjacent nodes at previous time step [m]
V20 : list
Velocity of right adjacent nodes at previous time step [m/s]
pump : list
Characteristics of the pump
valve : list
Characteristics of the valve
friction: str
friction model, e.g., 'steady', 'quasi-steady', 'unsteady',
by default 'steady'
dVdt: numpy.ndarray
local instantaneous acceleration approximation to be used
for unsteady friction calculation, 0 if not
in unsteady friction mode [m/s^2]
dVdx: numpy.ndarray
convective instantaneous acceleration approximation to be used
for unsteady friction calculation, 0 if not
in unsteady friction mode [m/s^2]
dVdt10 : list
local instantaneous acceleration of left adjacent nodes at previous time step [m]
dVdx10 : list
convective instantaneous acceleration of left adjacent nodes at previous time step [m/s]
dVdt20 : list
local instantaneous acceleration of right adjacent nodes at previous time step [m]
dVdx20 : list
convective instantaneous acceleration of right adjacent nodes at previous time step [m/s]
Returns
-------
H : numpy.ndarray
Head results of the current pipe at current time step. [m]
V : numpy.ndarray
Velocity results of the current pipe at current time step. [m/s]
"""
# Properties of current pipe
g = 9.8 # m/s^2
link1 = [p[abs(i)-1] for i in links1]
link2 = [p[abs(i)-1] for i in links2]
n = linkp.number_of_segments # spatial discretization
# inner nodes
if friction == 'steady':
H[1:-1], V[1:-1] = inner_node_steady(linkp, H0, V0, dt, g)
elif friction == 'quasi-steady':
H[1:-1], V[1:-1] = inner_node_quasisteady(linkp, H0, V0, dt, g)
else:
H[1:-1], V[1:-1] = inner_node_unsteady(linkp, H0, V0, dt, g,
dVdx, dVdt)
# Pipe start
V1 = V10; H1 = H10 #list
V2 = V0[1]; H2 = H0[1]
dVdx1 = dVdx10 ; dVdt1 = dVdt10
dVdx2 = dVdx[0]; dVdt2 = dVdt[1]
if utype[0] == 'Pipe':
if linkp.start_node.transient_node_type == 'SurgeTank':
shape = linkp.start_node.tank_shape
H[0], V[0], Qs = surge_tank(shape, link1, linkp,
H1, V1, H2, V2, dt, g, 0, np.sign(links1), [-1],
friction, dVdx1, dVdx2, dVdt1, dVdt2)
linkp.start_node.water_level = H[0]
linkp.start_node.tank_flow = Qs
elif linkp.start_node.transient_node_type == 'Chamber':
shape = linkp.start_node.tank_shape
H[0], V[0], Qs, zp = air_chamber(shape, link1, linkp,
H1, V1, H2, V2, dt, g, 0, np.sign(links1), [-1],
friction, dVdx1, dVdx2, dVdt1, dVdt2)
linkp.start_node.water_level = zp
linkp.start_node.tank_flow = Qs
else:
elev = linkp.start_node.elevation
emitter_coeff = linkp.start_node.emitter_coeff + linkp.start_node.demand_coeff
block_per = linkp.start_node.block_per
H[0], V[0] = add_leakage(emitter_coeff, block_per, link1, linkp, elev,
H1, V1, H2, V2, dt, g, 0, np.sign(links1), [-1],
friction, dVdx1, dVdx2, dVdt1, dVdt2)
elif utype[0] == 'Pump':
pumpc = pump[0]
H[0], V[0] = pump_node(pumpc, link1, linkp,
H1, V1, H2, V2, dt, g, 0, np.sign(links1), [-1],
friction, dVdx1, dVdx2, dVdt1, dVdt2)
elif utype[0] == 'Valve':
valvec = valve[0]
H[0], V[0] = valve_node(valvec, link1, linkp,
H1, V1, H2, V2, dt, g, 0, np.sign(links1), [-1],
friction, dVdx1, dVdx2, dVdt1, dVdt2)
# Pipe end
V1 = V0[n-1]; H1 = H0[n-1]
V2 = V20; H2 = H20
dVdx1 = dVdx[n-1] ; dVdt1 = dVdt[n-1]
dVdx2 = dVdx20; dVdt2 = dVdt20
if dtype[0] == 'Pipe':
if linkp.end_node.transient_node_type == 'SurgeTank':
shape = linkp.end_node.tank_shape
H[n], V[n], Qs = surge_tank(shape, linkp, link2,
H1, V1, H2, V2, dt, g, n, [1], np.sign(links2),
friction, dVdx1, dVdx2, dVdt1, dVdt2)
linkp.end_node.water_level = H[n]
linkp.end_node.tank_flow = Qs
elif linkp.end_node.transient_node_type == 'Chamber':
shape = linkp.end_node.tank_shape
H[n], V[n], Qs,zp = air_chamber(shape, linkp, link2,
H1, V1, H2, V2, dt, g, n, [1], np.sign(links2),
friction, dVdx1, dVdx2, dVdt1, dVdt2)
linkp.end_node.water_level = zp
linkp.end_node.tank_flow = Qs
else:
elev = linkp.end_node.elevation
emitter_coeff = linkp.end_node.emitter_coeff + linkp.end_node.demand_coeff
block_per = linkp.end_node.block_per
H[n], V[n] = add_leakage(emitter_coeff, block_per,linkp, link2, elev,
H1, V1, H2, V2, dt, g, n, [1], np.sign(links2),
friction, dVdx1, dVdx2, dVdt1, dVdt2)
elif dtype[0] == 'Pump':
pumpc = pump[1]
H[n], V[n] = pump_node(pumpc, linkp, link2,
H1, V1, H2, V2, dt, g, n, [1], np.sign(links2),
friction, dVdx1, dVdx2, dVdt1, dVdt2)
elif dtype[0] == 'Valve':
valvec = valve[1]
H[n], V[n] = valve_node(valvec, linkp, link2,
H1, V1, H2, V2, dt, g, n, [1], np.sign(links2),
friction, dVdx1, dVdx2, dVdt1, dVdt2)
return H, V