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 = 10
self.nt = 200
self.nz = 2
self.tmax = 1000.0
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.tube.make_1D(self.tube.h/2, 0)
self.ttimes, self.thetas, self.zs = np.meshgrid(
self.times, np.linspace(0, 2*np.pi, self.nt + 1)[:-1],
np.linspace(0, self.h, self.nz), indexing = 'ij')
self.rs = np.linspace(self.r - self.t, self.r, self.nr)
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 setUp(self):
self.solver = thermal.FiniteDifferenceImplicitThermalSolver()
self.material = materials.ConstantThermalMaterial("Test", 10.0, 5.0)
self.fluid = materials.ConstantFluidMaterial({"Test": 7.5})
self.tol = 1e-2
self.atol = 1e-3
def setUp(self):
self.problems = [
ManufacturedSolution("1D: no spatial", 1,
lambda t, r: t,
lambda t, k, alpha, r: k/alpha * (r*0.0+1)),
ManufacturedSolution("1D: spatial and time", 1,
lambda t, r: np.sin(t)*np.log(r),
lambda t, k, alpha, r: k/alpha * np.log(r) * np.cos(t)),
ManufacturedSolution("1D: just spatial", 1,
lambda t, r: np.sin(r),
lambda t, k, alpha, r: k * np.sin(r) - k/r*np.cos(r)),
ManufacturedSolution("2D: just time", 2,
lambda t, r, th: t,
lambda t, k, alpha, r, th: k/alpha * (r*0.0+1)),
ManufacturedSolution("2D: just r", 2,
lambda t, r, th: np.sin(r),
lambda t, k, alpha, r, th: k * np.sin(r) - k/r * np.cos(r)),
ManufacturedSolution("2D: just theta", 2,
lambda t, r, th: np.cos(th),
lambda t, k, alpha, r, th: k * np.cos(th) / r**2.0),
ManufacturedSolution("2D: theta and r", 2,
lambda t, r, th: np.cos(th) / r,
lambda t, k, alpha, r, th: -k*np.cos(th) / r**3.0),
ManufacturedSolution("2D: all three", 2,
lambda t, r, th: np.log(r) * np.sin(th) / (t+1),
lambda t, k, alpha, r, th: k*np.log(r)*np.sin(th)/((t+1)*r**2.0) - k/alpha * np.log(r) * np.sin(th) / (t+1)**2.0),
ManufacturedSolution("3D: just t", 3,
lambda t, r, th, z: t,
lambda t, k, alpha, r, th, z: k/alpha * (r*0.0+1)),
ManufacturedSolution("3D: just r", 3,
lambda t, r, th, z: np.sin(r),
lambda t, k, alpha, r, th, z: k * np.sin(r) - k/r * np.cos(r)),
ManufacturedSolution("3D: just theta", 3,
lambda t, r, th, z: np.cos(th),
lambda t, k, alpha, r, th, z: k * np.cos(th) / r**2.0),
ManufacturedSolution("3D: just z", 3,
lambda t, r, th, z: np.sin(z),
lambda t, k, alpha, r, th, z: k * np.sin(z)),
ManufacturedSolution("3D: all spatial", 3,
lambda t, r, th, z: z**2.0*np.cos(th)/r,
lambda t, k, alpha, r, th, z: -k*np.cos(th)/r*((z/r)**2.0+2)),
ManufacturedSolution("3D: everything", 3,
lambda t, r, th, z: np.log(r)*np.sin(th)*np.cos(z)/(t+1.0),
lambda t, k, alpha, r, th, z: k*np.log(r) * np.sin(th) * np.cos(z) / (t+1) * (1.0 + 1/r**2.0 - 1.0/(alpha*(t+1)))),
]
self.solver = thermal.FiniteDifferenceImplicitThermalSolver()
self.material = materials.ConstantThermalMaterial("Test", 10.0, 5.0)
self.fluid = materials.ConstantFluidMaterial({"Test": 7.5})
self.tol = 1e-2
self.atol = 1e-3
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
import numpy as np
problem = ManufacturedSolution(
"test", 1, lambda t, r: np.sin(r),
lambda t, k, alpha, r: k * np.sin(r) - k / r * np.cos(r))
def run_with(solver, material, fluid):
"""
Run the standard problems with the provided solver and material
"""
for problem in problems:
res = problem.solve(solver, material, fluid)
problem.plot_comparison(res)
plt.show()
if __name__ == "__main__":
solver = thermal.FiniteDifferenceImplicitThermalSolver()
tmat = materials.ConstantThermalMaterial("Test", 10.0, 5.0)
fmat = materials.ConstantFluidMaterial({"Test": 7.5})
if len(sys.argv) == 2:
n = int(sys.argv[1])
else:
n = 1
for i in range(n):
res = problem.solve(solver, tmat, fmat)