(heatsim2.boundary_thininsulatinglayer,
composite_rho * composite_c * thininsulatinglayerdepth / np.sqrt(np.pi)))
volumetric = ( # on material grid
# 0: nothing
(
heatsim2.NO_SOURCE, ),
#1: impulse source @ t=0
(heatsim2.IMPULSE_SOURCE, 0.0, flash_energy / (dz / dz_refinement)
), # t (sec), Energy J/m^2
)
# initialize all elements to zero
(material_elements, boundary_z_elements, boundary_y_elements,
boundary_x_elements,
volumetric_elements) = heatsim2.zero_elements(nz * dz_refinement, ny, nx)
# define nonzero material elements
material_elements[(zgrid_refine >= barrier_min_z) & (ygrid >= barrier_min_y) &
(ygrid <= barrier_max_y) & (xgrid >= barrier_min_x) &
(xgrid <= barrier_max_x)] = 1 # material 1: barrier
volumetric_elements[0, :, :] = 1 # set flash source (for heatsim2)
# set edges to insulating
boundary_x_elements[:, :, 0] = 1 # insulating
boundary_x_elements[:, :, -1] = 1 # insulating
boundary_y_elements[:, 0, :] = 1 # insulating
boundary_y_elements[:, -1, :] = 1 # insulating
boundary_z_elements[0, :, :] = 1 # insulating
)
volumetric = ( # on material grid
# 0: nothing
(
heatsim2.NO_SOURCE, ),
##1: impulse source @ t=0
(heatsim2.IMPULSE_SOURCE, 0.0, 10e3 / dz), # t (sec), Energy J/m^2
#1: stepped source
#(heatsim2.STEPPED_SOURCE,0.0-dt/2.0,1.0-dt/2.0,10e3/dz), # t0 (sec), t1 (sec), Power W/m^2
)
# initialize all elements to zero
(material_elements, boundary_z_elements, boundary_y_elements,
boundary_x_elements,
volumetric_elements) = heatsim2.zero_elements(nz, ny, nx)
# place water in hole and on back surface
material_elements[(xgrid > hole_min_x) & (xgrid < hole_max_x) &
(ygrid > hole_min_y) & (ygrid < hole_max_y) &
(zgrid > hole_depth)] = 1
# set x and y and z=0 edges to insulating
boundary_x_elements[:, :, 0] = 1 # insulating
boundary_x_elements[:, :, -1] = 1 # insulating
boundary_y_elements[:, 0, :] = 1 # insulating
boundary_y_elements[:, -1, :] = 1 # insulating
boundary_z_elements[0, :, :] = 1 # insulating
# zero temperature BC at back end of model
boundary_z_elements[-1, :, :] = 1 # insulating
def heatsim_calc(ny, nx, dz, dx, dy, z, y, x, zgrid, ygrid, xgrid, z_bnd,
y_bnd, x_bnd, kz, ky, kx, rho, c, trange, dt, hole_min_z,
hole_min_y, hole_max_y, hole_min_x, hole_max_x,
thininsulatinglayerdepth, thininsulatinglayer_min_y,
thininsulatinglayer_max_y, thininsulatinglayer_min_x,
thininsulatinglayer_max_x):
flash_energy = 10e3 # J/m^2
#
dz_refinement = 3.0
nz = z.shape[0]
nz_refine = int(nz * dz_refinement)
z_bnd_refine = np.arange(
nz_refine + 1,
dtype='d') * dz / dz_refinement # z boundary starts at zero
z_refine = z_bnd_refine[:-1] + dz / (dz_refinement * 2.0)
(zgrid_refine, ygrid, xgrid) = np.meshgrid(z_refine, y, x, indexing='ij')
#
(z_bnd_z, z_bnd_y, z_bnd_x) = np.meshgrid(z_bnd_refine,
y,
x,
indexing='ij')
#
(y_bnd_z, y_bnd_y, y_bnd_x) = np.meshgrid(z_refine,
y_bnd,
x,
indexing='ij')
#
(x_bnd_z, x_bnd_y, x_bnd_x) = np.meshgrid(z_refine,
y,
x_bnd,
indexing='ij')
#
#hole_min_z=2.5e-3; # 0.8e-3
##hole_min_z=z_thick
#hole_min_x=3e-3
#hole_max_x=20e-3
#hole_min_y=12.e-3
#hole_max_y=24.e-3
#
hole_k = 0 # W/m/deg K
hole_rho = rho # W/m/deg K
hole_c = c # J/kg/deg K
#
# thininsulatinglayerdepth=2*dz
# thininsulatinglayer_min_x=16e-3
# thininsulatinglayer_max_x=32e-3
# thininsulatinglayer_min_y=15e-3
# thininsulatinglayer_max_y=30e-3
materials = (
# material 0: composite
(heatsim2.TEMPERATURE_COMPUTE,
np.diag(np.array((kz, ky, kx), dtype='d')), rho, c),
#(heatsim2.TEMPERATURE_COMPUTE,kz,rho,c),
# material 1: hole
(heatsim2.TEMPERATURE_COMPUTE,
np.diag(np.array((hole_k, hole_k, hole_k),
dtype='d')), hole_rho, hole_c),
#(heatsim2.TEMPERATURE_COMPUTE,hole_k,hole_rho,hole_c),
# material 2: composite (so we can use same material matrix as heatsim)
(heatsim2.TEMPERATURE_COMPUTE,
np.diag(np.array((kz, ky, kx), dtype='d')), rho, c),
#(heatsim2.TEMPERATURE_COMPUTE,kz,rho,c),
# material 3: Fixed temperature (Dirichlet boundary condition)
(
heatsim2.TEMPERATURE_FIXED, ),
)
boundaries = (
# boundary 0: conducting
(
heatsim2.boundary_conducting_anisotropic, ),
#(heatsim2.boundary_conducting,),
# boundary 1: insulating
(
heatsim2.boundary_insulating, ),
# boundary 2: thininsulatinglayer
# We want a thin insulating layer that halves
# the effective thermal effusivity of the remainder of the
# material
# e=sqrt(k rho c) has units of Joules/(m^2*deg K*sqrt(s))
# effusivities are probably e1e2/(e1+e2) form
# so we want e1e2/(e1+e2)=e2/2
# e1/(e1+e2)=1/2
# e1=e2
# thin insulating layer coefficient is Joules/(m^2*deg K)
# so we get this from effusivity * sqrt(characteristic time/2.0)
# sqrt(kz*rho*c)*sqrt(thininsulatinglayerdepth**2/(2*np.pi*(kz/(rho*c))))
# Simplifying:
# rho*c*thininsulatinglayerdepth/np.sqrt(2.0*np.pi)
(heatsim2.boundary_thininsulatinglayer,
rho * c * thininsulatinglayerdepth / np.sqrt(2.0 * np.pi)))
volumetric = ( # on material grid
# 0: nothing
(
heatsim2.NO_SOURCE, ),
#1: impulse source @ t=0
(heatsim2.IMPULSE_SOURCE, 0.0, flash_energy / (dz / dz_refinement)
), # t (sec), Energy J/m^2
)
#
# initialize all elements to zero
(material_elements, boundary_z_elements, boundary_y_elements,
boundary_x_elements,
volumetric_elements) = heatsim2.zero_elements(nz_refine, ny, nx)
#
# define nonzero material elements
#
material_elements[(zgrid_refine >= hole_min_z) & (ygrid >= hole_min_y) &
(ygrid <= hole_max_y) & (xgrid >= hole_min_x) &
(xgrid <= hole_max_x)] = 1 # material 1: hole
#
volumetric_elements[0, :, :] = 1 # set flash source (for heatsim2)
#
#
# set edges to insulating
boundary_x_elements[:, :, 0] = 1 # insulating
boundary_x_elements[:, :, -1] = 1 # insulating
boundary_y_elements[:, 0, :] = 1 # insulating
boundary_y_elements[:, -1, :] = 1 # insulating
boundary_z_elements[0, :, :] = 1 # insulating
boundary_z_elements[-1, :, :] = 1 # insulating
#
# add thin insulating layer
if thininsulatinglayerdepth < z_bnd[-1]:
boundary_z_elements[(z_bnd_x > thininsulatinglayer_min_x)
& (z_bnd_x < thininsulatinglayer_max_x) &
(z_bnd_y > thininsulatinglayer_min_y) &
(z_bnd_y < thininsulatinglayer_max_y) &
(z_bnd_z == z_bnd_refine[(np.abs(
z_bnd_refine -
thininsulatinglayerdepth)).argmin()])] = 2
pass
#
# set boundaries of hole to insulating
if hole_min_z < z_bnd[-1]:
boundary_z_elements[(z_bnd_x > hole_min_x) & (z_bnd_x < hole_max_x) &
(z_bnd_y > hole_min_y) & (z_bnd_y < hole_max_y) &
(z_bnd_z == z_bnd_refine[(np.abs(
z_bnd_refine - hole_min_z)).argmin()])] = 1 #
pass
#
boundary_x_elements[(
(x_bnd_x == x_bnd[np.abs(x_bnd - hole_min_x).argmin()])
| (x_bnd_x == x_bnd[np.abs(x_bnd - hole_max_x).argmin()]))
& (x_bnd_y > hole_min_y) & (x_bnd_y < hole_max_y) &
(x_bnd_z > hole_min_z)] = 1
#
boundary_y_elements[(
(y_bnd_y == y_bnd[np.abs(y_bnd - hole_min_y).argmin()])
| (y_bnd_y == y_bnd[np.abs(y_bnd - hole_max_y).argmin()]))
& (y_bnd_x > hole_min_x) & (y_bnd_x < hole_max_x) &
(y_bnd_z > hole_min_z)] = 1
#
(ADI_params,
ADI_steps) = heatsim2.setup(z[0], y[0], x[0], dz / dz_refinement, dy, dx,
nz_refine, ny, nx, dt, materials, boundaries,
volumetric, material_elements,
boundary_z_elements, boundary_y_elements,
boundary_x_elements, volumetric_elements)
hs2trange = dt / 2.0 + np.arange(trange[-1] // dt + 1) * dt
#
T = np.zeros((hs2trange.shape[0], ny, nx), dtype='d')
fullstate = np.zeros((nz_refine, ny, nx), dtype='d')
for tcnt in range(hs2trange.shape[0]):
curt = hs2trange[tcnt] - dt / 2.0
print "t=%f" % (curt)
fullstate = heatsim2.run_adi_steps(ADI_params, ADI_steps, curt, dt,
fullstate, volumetric_elements,
volumetric)
T[tcnt, :, :] = fullstate[0, :, :] # extract top layer
pass
#
return T[(T.shape[0] - trange.shape[0]):T.shape[0], :, :]
(heatsim.BOUNDARY_NONE, composite_k, composite_rho, composite_c, 0.0, 0.0,
0.0, 0.0),
# material 1: barrier
(heatsim.BOUNDARY_NONE, barrier_k, barrier_rho, barrier_c, 0.0, 0.0, 0.0,
0.0),
# material 2: flash source
(heatsim.BOUNDARY_IMPULSE, composite_k, composite_rho, composite_c, 0.0,
0.0, 0.0, 0.0),
# material 3: insulator
(heatsim.BOUNDARY_INSULATING, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0),
)
# initialize all elements to zero
(material_elements, boundary_z_elements, boundary_y_elements,
boundary_x_elements,
volumetric_elements) = heatsim2.zero_elements(nz, ny, nx)
(material_elements_fine, boundary_z_elements_fine, boundary_y_elements_fine,
boundary_x_elements_fine,
volumetric_elements_fine) = heatsim2.zero_elements(nz_fine, ny_fine, nx_fine)
# define nonzero material elements
material_elements[0, :, :] = 2 # material 2: flash source (for heatsim)
material_elements_fine[0, :, :] = 2 # material 2: flash source (for heatsim)
if enable_barrier:
material_elements[(zgrid >= barrier_min_z) & (zgrid <= barrier_max_z) &
(ygrid >= barrier_min_y) & (ygrid <= barrier_max_y) &
(xgrid >= barrier_min_x) &
(xgrid <= barrier_max_x)] = 1 # material 1: barrier