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 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 test_dirichlet(self):
T0 = lambda x: np.sin(2 * np.pi * (x - self.r - self.t) / self.t)
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")
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)
# Correct solution: temperatures head towards zero
T = self.tube.results['temperature'][-1]
self.assertTrue(np.allclose(T, 0))
def valid_fixedtemp_bc(loc):
if loc == "outer":
r = outer_radius
else:
r = inner_radius
return receiver.FixedTempBC(r, height, nt, nz, times,
np.zeros((len(times), nt, nz)))
def test_neumann_right(self):
T0 = lambda x: np.sin(2 * np.pi * (x - self.r - self.t) / self.t)
q = 10.0
Tright = receiver.HeatFluxBC(self.r, self.h, self.nt, self.nz,
self.times,
np.ones(self.ttimes.shape) * q)
self.tube.set_bc(Tright, "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)
# Correct solution:
Tright = q * self.r / self.k * np.log(
self.rs) - q * self.r / self.k * np.log(self.r - self.t)
T = self.tube.results["temperature"][-1]
self.assertTrue(np.allclose(T, Tright, rtol=1e-2))
def test_wrong_size(self):
with self.assertRaises(ValueError):
bc = receiver.FixedTempBC(inner_radius, height, nt, nz, times,
np.zeros((1, )))