def mixing(flmlname):
print("\n********** Calculating the mixing diagnostics\n")
# warn user about assumptions
print(
"Background potential energy calculations makes two assumptions: \n i) domain height = 0.1m \n ii) initial temperature difference is 1.0 degC"
)
domainheight = 0.1
rho_zero, T_zero, alpha, g = le_tools.Getconstantsfromflml(flmlname)
# get mixing bin bounds and remove lower bound (=-\infty)
bounds = le_tools.Getmixingbinboundsfromflml(flmlname)[1:]
# find indicies of selected bounds for plotting
index_plot = []
for b in [-0.5, -0.25, 0.0, 0.25, 0.5]:
index_plot.append(
numpy.where(numpy.array([abs(val - b)
for val in bounds]) < 1E-6)[0])
time = []
volume_fraction = []
reference_state = []
bpe = []
# get stat files
# time_index_end used to ensure don't repeat values
stat_files, time_index_end = le_tools.GetstatFiles('./')
for i in range(len(stat_files)):
stat = stat_parser(stat_files[i])
for j in range(time_index_end[i]):
time.append(stat['ElapsedTime']['value'][j])
bins = stat['fluid']['Temperature']['mixing_bins%cv_normalised'][:,
j]
# rearrange bins so have nobins = nobounds -1
# amounts to including any undershoot or overshoots in lower/upper most bin
# for discussion of impacts see H. Hiester, PhD thesis (2011), chapter 4.
bins[1] = bins[0] + bins[1]
bins[-2] = bins[-2] + bins[-1]
bins = bins[1:-1]
# sum up bins for plot
volume_fraction.append(
tuple([
sum(bins[index_plot[k]:index_plot[k + 1]])
for k in range(len(index_plot) - 1)
]))
# get reference state using method of Tseng and Ferziger 2001
Abins = sum([
bins[k] * (bounds[k + 1] - bounds[k]) for k in range(len(bins))
])
pdf = [val / Abins for val in bins]
rs = [0]
for k in range(len(pdf)):
rs.append(rs[-1] + (domainheight * pdf[k] *
(bounds[k + 1] - bounds[k])))
reference_state.append(tuple(rs))
# get background potential energy,
# noting \rho = \rho_zero(1-\alpha(T-T_zero))
# and reference state is based on temperature
# bpe_bckgd = 0.5*(g*rho_zero*(1.0+(alpha*T_zero)))*(domainheight**2)
# but don't include this as will look at difference over time
bpe.append(-rho_zero * alpha * g * scipy.integrate.trapz(
x=reference_state[-1],
y=[
bounds[j] * reference_state[-1][j]
for j in range(len(reference_state[-1]))
]))
volume_fraction = numpy.array(volume_fraction)
reference_state = numpy.array(reference_state)
bpe_zero = bpe[0]
bpe = [val - bpe_zero for val in bpe]
# plot
fs = 18
pylab.figure(num=2, figsize=(16.5, 11.5))
pylab.suptitle('Mixing', fontsize=fs)
# volume fraction
pylab.subplot(221)
pylab.plot(time, volume_fraction[:, 0], label='$T < -0.25$', color='k')
pylab.plot(time,
volume_fraction[:, 1],
label='$-0.25 < T < 0.0$',
color='g')
pylab.plot(time,
volume_fraction[:, 2],
label='$0.0 < T < 0.25$',
color='b')
pylab.plot(time, volume_fraction[:, 3], label='$0.25 < T$', color='0.5')
pylab.axis([0, time[-1], 0, 0.5])
pylab.legend(loc=0)
pylab.grid('on')
pylab.xlabel('$t$ (s)', fontsize=fs)
pylab.ylabel('$V/|\\Omega|$', fontsize=fs)
pylab.title('Volume fraction', fontsize=fs)
# reference state contours
pylab.subplot(222)
for i in index_plot:
pylab.plot(time, reference_state[:, i], color='k')
pylab.text(
time[-1] / 100,
1.5E-3,
'From bottom to top contours correspond to values \n $T = -0.5, \, -0.25, \, 0.0, \, 0.25, \, 0.5$ \nwhere the values for $T=-0.5$ and $0.5$ take the values\n$z_* = 0.0$ and $0.1$ respectively',
bbox=dict(facecolor='white', edgecolor='black'))
pylab.axis([0, time[-1], 0, domainheight])
pylab.grid('on')
pylab.xlabel('$t$ (s)', fontsize=fs)
pylab.ylabel('$z_*$ (m)', fontsize=fs)
pylab.title('Reference state', fontsize=fs)
pylab.subplot(223)
pylab.plot(bounds, reference_state[-1], color='k')
pylab.grid('on')
pylab.axis([-0.5, 0.5, 0, domainheight])
pylab.xlabel('$T$ ($^\\circ$C)', fontsize=fs)
pylab.ylabel('$z_*$ (m)', fontsize=fs)
pylab.title('Reference state at $t=' + str(time[-1]) + '\\,$s',
fontsize=fs)
pylab.subplot(224)
pylab.plot(time, bpe, color='k')
pylab.grid('on')
pylab.gca().get_xaxis().get_axes().set_xlim(0.0, time[-1])
pylab.xlabel('$t$ (s)', fontsize=fs)
pylab.ylabel('$\\Delta E_b$', fontsize=fs - 2)
pylab.gca().get_yaxis().set_major_formatter(
pylab.FormatStrFormatter('%1.1e'))
pylab.title('Background potential energy', fontsize=fs)
pylab.savefig('diagnostics/plots/mixing.png')
return
def Froudenumber(flmlname):
print("\n********** Calculating the Froude number\n")
# warn user about assumptions
print(
"Froude number calculations makes three assumptions: \n i) domain height = 0.1m \n ii) mid point domain is at x = 0.4 \n iii) initial temperature difference is 1.0 degC"
)
domainheight = 0.1
domainmid = 0.4
rho_zero, T_zero, alpha, g = le_tools.Getconstantsfromflml(flmlname)
gprime = rho_zero * alpha * g * 1.0 # this has assumed the initial temperature difference is 1.0 degC
# get list of vtus
filelist = le_tools.GetFiles('./')
logs = [
'diagnostics/logs/time.log', 'diagnostics/logs/X_ns.log',
'diagnostics/logs/X_fs.log'
]
try:
# if have extracted information already just use that
os.stat('diagnostics/logs/time.log')
os.stat('diagnostics/logs/X_ns.log')
os.stat('diagnostics/logs/X_fs.log')
time = le_tools.ReadLog('diagnostics/logs/time.log')
X_ns = [
x - domainmid
for x in le_tools.ReadLog('diagnostics/logs/X_ns.log')
]
X_fs = [
domainmid - x
for x in le_tools.ReadLog('diagnostics/logs/X_fs.log')
]
except OSError:
# otherwise get X_ns and X_fs and t from vtus
time, X_ns, X_fs = le_tools.GetXandt(filelist)
f_time = open('./diagnostics/logs/time.log', 'w')
for t in time:
f_time.write(str(t) + '\n')
f_time.close()
f_X_ns = open('./diagnostics/logs/X_ns.log', 'w')
for X in X_ns:
f_X_ns.write(str(X) + '\n')
f_X_ns.close()
f_X_fs = open('./diagnostics/logs/X_fs.log', 'w')
for X in X_fs:
f_X_fs.write(str(X) + '\n')
f_X_fs.close()
# shift so bot X_ns and X_fs are
# distance of front from
#initial position (mid point of domain)
X_ns = [x - domainmid for x in X_ns]
X_fs = [domainmid - x for x in X_fs]
# Calculate U_ns and U_fs from X_ns, X_fs and t
U_ns = le_tools.GetU(time, X_ns)
U_fs = le_tools.GetU(time, X_fs)
U_average = [[], []]
# If possible average
# (if fronts have not travelled far enough then will not average)
start_val, end_val, average_flag_ns = le_tools.GetAverageRange(
X_ns, 0.2, domainheight)
if average_flag_ns == True:
U_average[0].append(pylab.average(U_ns[start_val:end_val]))
start_val, end_val, average_flag_fs = le_tools.GetAverageRange(
X_fs, 0.25, domainheight)
if average_flag_fs == True:
U_average[1].append(pylab.average(U_fs[start_val:end_val]))
# plot
fs = 18
pylab.figure(num=1, figsize=(16.5, 11.5))
pylab.suptitle('Front speed', fontsize=fs)
pylab.subplot(221)
pylab.plot(time, X_ns, color='k')
pylab.axis([0, 45, 0, 0.4])
pylab.grid('on')
pylab.xlabel('$t$ (s)', fontsize=fs)
pylab.ylabel('$X$ (m)', fontsize=fs)
pylab.title('no-slip', fontsize=fs)
pylab.subplot(222)
pylab.plot([x / domainheight for x in X_ns],
[U / math.sqrt(gprime * domainheight) for U in U_ns],
color='k')
pylab.axis([0, 4, 0, 0.6])
pylab.grid('on')
pylab.axhline(0.406, color='k')
pylab.axhline(0.432, color='k')
pylab.text(3.95,
0.396,
'Hartel 2000',
bbox=dict(facecolor='white', edgecolor='black'),
va='top',
ha='right')
pylab.text(3.95,
0.442,
'Simpson 1979',
bbox=dict(facecolor='white', edgecolor='black'),
ha='right')
pylab.xlabel('$X/H$', fontsize=fs)
pylab.ylabel('$Fr$', fontsize=fs)
pylab.title('no-slip', fontsize=fs)
if average_flag_ns == True:
pylab.axvline(2.0, color='k')
pylab.axvline(3.0, color='k')
pylab.text(
0.05,
0.01,
'Average Fr = ' + '{0:.2f}'.format(
U_average[0][0] / math.sqrt(gprime * domainheight)) +
'\nvertical lines indicate the range \nover which the average is taken',
bbox=dict(facecolor='white', edgecolor='black'))
pylab.subplot(223)
pylab.plot(time, X_fs, color='k')
pylab.axis([0, 45, 0, 0.4])
pylab.grid('on')
pylab.xlabel('$t$ (s)', fontsize=fs)
pylab.ylabel('$X$ (m)', fontsize=fs)
pylab.title('free-slip', fontsize=fs)
pylab.subplot(224)
pylab.plot([x / domainheight for x in X_fs],
[U / math.sqrt(gprime * domainheight) for U in U_fs],
color='k')
pylab.axis([0, 4, 0, 0.6])
pylab.grid('on')
pylab.axhline(0.477, color='k')
pylab.text(3.95,
0.467,
'Hartel 2000',
va='top',
bbox=dict(facecolor='white', edgecolor='black'),
ha='right')
pylab.xlabel('$X/H$', fontsize=fs)
pylab.ylabel('$Fr$', fontsize=fs)
pylab.title('free-slip', fontsize=fs)
if average_flag_fs == True:
pylab.text(
0.05,
0.01,
'Average Fr = ' + '{0:.2f}'.format(
U_average[1][0] / math.sqrt(gprime * domainheight)) +
'\nvertical lines indicate the range \nover which the average is taken',
bbox=dict(facecolor='white', edgecolor='black'))
pylab.axvline(2.5, color='k')
pylab.axvline(3.0, color='k')
pylab.savefig('diagnostics/plots/front_speed.png')
return