def test_substep(self):
T0 = lambda x: np.sin(2*np.pi*(x-self.r-self.t)/self.t)
T_outer = 250
Tout = receiver.ConvectiveBC(self.r, self.h, self.nz,
self.times, np.ones((self.ntime+1,self.nz))*T_outer)
self.tube.set_bc(Tout, "outer")
Tleft = receiver.FixedTempBC(self.r-self.t, self.h, self.nt, self.nz,
self.times, np.zeros(self.ttimes.shape))
self.tube.set_bc(Tleft, "inner")
self.solver.solve(self.tube, self.material, self.fluid,
T0 = T0, substep = 10)
T = self.tube.results['temperature'][-1]
ri = self.r - self.t
C1 = self.hcoef * T_outer / (self.k/self.r + self.hcoef * np.log(self.r) - self.hcoef * np.log(ri))
C2 = -C1 * np.log(ri)
Texact = C1 * np.log(self.rs) + C2
self.assertTrue(np.allclose(T,Texact, rtol = 1.0e-2))
def setUp(self):
self.k = 15.0
self.a = 5.0
self.hcoef = 1.0
self.solver = thermal.FiniteDifferenceImplicitThermalSolver()
self.material = materials.ConstantThermalMaterial("Test", self.k, self.a)
self.fluid = materials.ConstantFluidMaterial({"Test": self.hcoef})
self.t = 0.2
self.r = 2.0
self.h = 1.0
self.nr = 5
self.nt = 10
self.nz = 5
self.tmax = 10.0
self.ntime = 10
self.tube = receiver.Tube(self.r, self.t, self.h, self.nr, self.nt, self.nz, 0)
self.times = np.linspace(0, self.tmax, self.ntime+1)
self.tube.set_times(self.times)
self.T_inner = 100
Tin = receiver.ConvectiveBC(self.r-self.t, self.h, self.nz,
self.times, np.ones((self.ntime+1,self.nz))*self.T_inner)
self.tube.set_bc(Tin, "inner")
Tright = receiver.HeatFluxBC(self.r, self.h, self.nt, self.nz,
self.times, np.zeros((self.ntime+1,self.nt,self.nz)))
self.tube.set_bc(Tright, "outer")
def test_convection_left(self):
T0 = lambda x: np.sin(2*np.pi*(x-self.r-self.t)/self.t)
T_inner = 25
Tin = receiver.ConvectiveBC(self.r-self.t, self.h, self.nz,
self.times, np.ones((self.ntime+1,self.nz))*T_inner)
self.tube.set_bc(Tin, "inner")
Tright = receiver.FixedTempBC(self.r, self.h, self.nt, self.nz,
self.times, np.zeros(self.ttimes.shape))
self.tube.set_bc(Tright, "outer")
self.solver.solve(self.tube, self.material, self.fluid,
T0 = T0)
T = self.tube.results['temperature'][-1]
ri = self.r - self.t
C1 = T_inner * self.hcoef / (self.hcoef*np.log(ri) - self.hcoef*np.log(self.r) - self.k/ri)
C2 = -C1 * np.log(self.r)
Texact = C1 * np.log(self.rs) + C2
self.assertTrue(np.allclose(T,Texact, rtol = 1.0e-2))
def valid_convective_bc(loc):
if loc == "outer":
r = outer_radius
else:
r = inner_radius
return receiver.ConvectiveBC(r, height, nz, times,
np.zeros((len(times), nz)))
def make_tube(D, period):
R = 1.0
t = 0.1
h = 10.0
nr = 10
nt = 20
nz = 10
T0 = 50
tmax = period
ntime = 10
T0 = 300
tube = receiver.Tube(R, t, h, nr, nt, nz, T0=T0)
if D == 1:
tube.make_1D(h / 2, 1)
elif D == 2:
tube.make_2D(h / 2)
times = np.linspace(0, tmax, ntime)
tube.set_times(times)
Tf_0 = 300
Tf_m = 600
def fluid_T(t):
if t < tmax / 2.0:
return Tf_0 + (Tf_m - Tf_0) / (tmax / 2.0) * t
else:
return Tf_m - (Tf_m - Tf_0) / (tmax / 2.0) * (t - tmax / 2.0)
ftemps = np.array([fluid_T(t) * np.ones((nz, )) for t in times])
inner_convection = receiver.ConvectiveBC(R - t, h, nz, times, ftemps)
tube.set_bc(inner_convection, "inner")
hflux = receiver.HeatFluxBC(R, h, nt, nz, times,
np.zeros((ntime, nt, nz)) + 2.0)
tube.set_bc(hflux, "outer")
solver = thermal.FiniteDifferenceImplicitThermalSolver()
tmat = materials.ConstantThermalMaterial("dummy", 20.0e-3, 4.8)
fmat = materials.ConstantFluidMaterial({"dummy": 8.1e-3})
solver.solve(tube, tmat, fmat)
return tube
def test_wrong_size(self):
with self.assertRaises(ValueError):
bc = receiver.ConvectiveBC(inner_radius, height, nz, times,
np.zeros((1, )))
# Time increments throughout the 24 hour day
times = np.linspace(0,24,24*2+1)
# Various meshes needed to define the boundary conditions
# 1) A mesh over the times and height (for the fluid temperatures)
time_h, z_h = np.meshgrid(times, np.linspace(0,height,nz), indexing='ij')
# 2) A surface mesh over the outer surface (for the flux)
time_s, theta_s, z_s = np.meshgrid(times, np.linspace(0,2*np.pi,nt+1)[:nt],
np.linspace(0,height,nz), indexing = 'ij')
# Setup each tube in turn and assign it to the correct panel
# Tube 0
tube_0 = receiver.Tube(r_outer, thickness, height, nr, nt, nz, T0 = T_base)
tube_0.set_times(times)
tube_0.set_bc(receiver.ConvectiveBC(r_outer-thickness,
height, nz, times, fluid_temp(time_h,z_h)), "inner")
tube_0.set_bc(receiver.HeatFluxBC(r_outer, height,
nt, nz, times, h_flux(time_s, theta_s, z_s) * h_tube_0), "outer")
tube_0.set_pressure_bc(receiver.PressureBC(times, pressure(times)))
# Tube 1
tube_1 = receiver.Tube(r_outer, thickness, height, nr, nt, nz, T0 = T_base)
tube_1.set_times(times)
tube_1.set_bc(receiver.ConvectiveBC(r_outer-thickness,
height, nz, times, fluid_temp(time_h,z_h)), "inner")
tube_1.set_bc(receiver.HeatFluxBC(r_outer, height,
nt, nz, times, h_flux(time_s, theta_s, z_s) * h_tube_1), "outer")
tube_1.set_pressure_bc(receiver.PressureBC(times, pressure(times)))
# Tube 2
tube_2 = receiver.Tube(r_outer, thickness, height, nr, nt, nz, T0 = T_base)