def process_one_slice(flow, grd, i):
"""
Returns ...
Use cell-average flow quantities and areas from the EAST boundary faces.
This is a little dodgy, in general, but we gat away with it here
because the cells have right angles.
"""
TOL = 5.0e-2
rho_f1_z_dA = 0.0
rho_z_dA = 0.0
m_flux = 0.0
H_flux = 0.0
A_f0 = 0.0
A_f1 = 0.0
A_mix = 0.0
A_tot = 0.0
nj = flow.nj
nk = flow.nk
for j in range(nj):
for k in range(nk):
vtx = grd.get_vertex_list_for_cell(i, j, k)
# The EAST cell face has 1, 2, 6, 5 as corners (unit normal out).
face_centroid = quad_centroid(vtx[1], vtx[2], vtx[6], vtx[5])
face_normal = quad_normal(vtx[1], vtx[2], vtx[6], vtx[5])
face_area = quad_area(vtx[1], vtx[2], vtx[6], vtx[5])
# average conditions in cell
z = flow.data['pos.z'][i, j, k]
pressure = flow.data['p'][i, j, k]
rho = flow.data['rho'][i, j, k]
e = flow.data['e[0]'][i, j, k]
f0 = flow.data['massf[0]'][i, j, k]
f1 = flow.data['massf[1]'][i, j, k]
rho_z_dA += rho * face_area * z
rho_f1_z_dA += rho * f1 * face_area * z
A_tot += face_area
if f0 > 1.0 - TOL:
A_f0 += face_area
elif f0 < TOL:
A_f1 += face_area
else:
A_mix += face_area
v_x = flow.data['vel.x'][i, j, k]
v_y = flow.data['vel.y'][i, j, k]
v_z = flow.data['vel.z'][i, j, k]
vel_abs = Vector(v_x, v_y, v_z)
df = face_area * pressure * face_normal
dm_flux = rho * dot(vel_abs, face_normal) * face_area
m_flux += dm_flux
H_flux += dm_flux * (e + pressure / rho + 0.5 *
(v_x * v_x + v_y * v_y + v_z * v_z))
return m_flux, H_flux, A_f0, A_f1, A_mix, A_tot, rho_z_dA, rho_f1_z_dA
def objective(alpha, x_s=x_s, y_s=y_s):
"""
Objective function for the optimizer.
"""
from libprep3 import Bezier, Vector
bx, by = define_bezier_points(alpha, x_s, y_s)
bpath = Bezier([Vector(bx[0],by[0]),Vector(bx[1],by[1]),
Vector(bx[2],by[2]),Vector(bx[3],by[3])])
nbez = 1000
pbez = []
for i in range(nbez):
t = 1.0/nbez * i
pbez.append(bpath.eval(t))
n = len(x_s)
sum_sq_err = 0.0
for j in range(n):
min_dist = (x_s[j]-pbez[0].x)**2 + (y_s[j]-pbez[0].y)**2
for i in range(1,nbez):
dist = (x_s[j]-pbez[i].x)**2 + (y_s[j]-pbez[i].y)**2
if dist < min_dist: min_dist = dist
sum_sq_err += min_dist
# print "alpha=", alpha, "sum_sq_err=", sum_sq_err
return sum_sq_err
print "Begin: Pick up data for tindx=", tindx
from libprep3 import Vector, cross, dot, vabs
from e3_flow import read_all_blocks
from math import sqrt
#
nb = 28
pick_list = [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26] # surface
rho_inf = 6.081e-4 # kg/m**3
p_inf = 18.55 # Pa
u_inf = 2576.0 # m/s
T_inf = 102.2 # K
T_wall = 295.8 # K
from cfpylib.gasdyn import sutherland
mu_inf = sutherland.mu(T_inf, 'N2')
mm = 0.001 # metres
corner1 = Vector(92.08, 42.94) * mm
corner2 = Vector(153.69, 130.925) * mm
#
grid, flow, dim = read_all_blocks(job, nb, tindx, zipFiles=True)
print "Compute properties for cell-centres along the surface"
outfile = open("surface.data", "w")
outfile.write(
"# x(m) s(m) tau_w(Pa) Cf Cf_blasius y_plus p(Pa) Cp q(W/m**2) Ch\n")
for ib in pick_list:
j = 0 # surface is along the South boundary
k = 0 # of a 2D grid
print "# start of block"
for i in range(flow[ib].ni):
# Cell closest to surface
x = flow[ib].data['pos.x'][i, j, k]
y = flow[ib].data['pos.y'][i, j, k]
from e3_flow import read_all_blocks
from math import sqrt
#
nb = 24
pick_list = [0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22] # blocks against surface
rho_inf = 8.81e-4 # kg/m**3
p_inf = 31.88 # Pa
u_inf = 2304.0 # m/s
T_inf = 120.4 # K
T_wall = 295.2 # K
from cfpylib.gasdyn import sutherland
mu_inf = sutherland.mu(T_inf, 'N2')
mm = 0.001 # metres
R = 32.5*mm
xcorner = 101.7*mm
corner = Vector(xcorner,R)
#
grid, flow, dim = read_all_blocks(job, nb, tindx, zipFiles=True)
print "Compute shear stress for cell-centres along the surface"
outfile = open("surface.data", "w")
outfile.write("# x(m) s(m) tau_w(Pa) Cf Cf_blasius y_plus p(Pa) Cp q(W/m**2) Ch\n")
for ib in pick_list:
j = 0 # surface is along the South boundary
k = 0 # of a 2D grid
print "# start of block"
for i in range(flow[ib].ni):
# Cell closest to surface
x = flow[ib].data['pos.x'][i,j,k]
y = flow[ib].data['pos.y'][i,j,k]
ctr = Vector(x, y)
# Get vertices on surface, for this cell.
def print_stats_MoA(sliceFileName,jobName,coreRfraction,weight):
"""
(MoA = Mass- or Area-weighted)
Display either the mass-weighted or area-weighted statistics
of flow properties at the nozzle exit.
"""
print weight.capitalize()+"-Weighted Nozzle-exit statistics:"
variable_list, data = get_slice_data(sliceFileName)
#
# Identify edge of core flow.
ys = data['pos.y']
xs = data['pos.x']
y_edge = ys[-1] * coreRfraction
#
# Compute and print area-weighted-average core flow values.
exclude_list = ['pos.x', 'pos.y', 'pos.z', 'volume', 'vel.z', 'S']
#
fout = open(jobName+'-exit.stats'+weight.capitalize(),'w')
fout.write('CoreRadiusFraction: %10.6f\n' % coreRfraction)
fout.write('%15s %12s %10s %10s %10s\n' %
("variable","mean-value","minus","plus","std-dev"))
fout.write(65*'-'+'\n')
#
print "%15s %12s %10s %10s %10s" % \
("variable", "mean-value", "minus", "plus","std-dev")
print 65*'-'
u = data['vel.x']; v = data['vel.y']; rho = data['rho']
for var in variable_list:
if var in exclude_list: continue
MassFlux = 0.0; F = 0.0;
for j in range(len(ys)):
if ys[j] > y_edge: break
y1 = 0.5*(ys[j]+ys[j+1])
x1 = 0.5*(xs[j]+xs[j+1])
if j == 0:
y0 = 0.0
dx = xs[j]-x1
x0 = xs[j]+dx
else:
y0 = 0.5*(ys[j-1]+ys[j])
x0 = 0.5*(xs[j-1]+xs[j])
# Area element...
#d_Area = y1**2 - y0**2
d_Area = pi*(y0+y1)*sqrt((y1-y0)**2+(x0-x1)**2)
# Unit normal vector...
edge = Vector(x0,y0,0.0)-Vector(x1,y1,0.0)
nhat = Vector(-edge.y, edge.x, 0.0)/vabs(edge)
# Velocity vector...
vel = Vector(u[j],v[j],0.0)
# Weighting factor...
if weight in ['area']:
weighting = 1.0
elif weight in ['mass']:
weighting = rho[j]*dot(vel,nhat)
else:
print "Unknown weighting option given"
break
# Accumulate total...
F += data[var][j] * weighting * d_Area
MassFlux += weighting * d_Area
mean = F/MassFlux
# Identify low and high values.
diff_minus = 0.0
diff_plus = 0.0
count = 0.0
stddev = 0.0
for j in range(len(ys)):
if ys[j] > y_edge: break
diff = data[var][j] - mean
diff_minus = min(diff, diff_minus)
diff_plus = max(diff, diff_plus)
count += 1
stddev += diff**2
# Calculate the sample standard deviation
stddev = (stddev/(count-1))**0.5
print "%15s %12.5g %10.3g %10.3g %10.3g" % \
(var, mean, diff_minus, diff_plus, stddev)
fout.write('%15s %12.5g %10.3g %10.3g %10.3g\n' % \
(var, mean, diff_minus, diff_plus, stddev))
#
print 65*'-'
fout.write(65*'-'+'\n')
fout.close()
return
def print_stats_CMME(sliceFileName,jobName,coreRfraction,gmodelFile):
"""
Display statistics of flow properties at the nozzle exit using
conservation of mass, momentum and energy (CMME) method.
The implementation is loosely based on the paper:
Baurle, R.A. and Gaffney, R.L. (2008)
"Extraction of One-Dimensional Flow Properties from Multidimensional Data Sets",
Journal of Propulsion and Power, vol. 24, no. 4, pg. 704
Equations numbers given in the comments of the code refer to the paper.
PJ, 22-Aug-2012: Use brute-force to get the effective 1D flow properties.
Assumptions: Geometry is axisymmetric. The fluxes are calculated normal to
the curve (which may not be straight) over which we are integrating. The
returned averaged velocity vector is parallel to the averaged unit normal
over the curve.
"""
print "Nozzle-exit statistics (CMME):"
variable_list, data = get_slice_data(sliceFileName)
#
# Identify edge of core flow.
ys = data['pos.y']
xs = data['pos.x']
y_edge = ys[-1] * coreRfraction
#
# Over the core region of interest we now want to calculate:
# (1) total area;
# (2) the unit normal;
# (3) total mass flux for each species;
# (4) total momentum flux; and
# (5) total energy flux.
#
# First, we need to do a bit of fiddling with variable names in order
# to get the species names.
speciesKeys = [k for k in variable_list if k.startswith("mass")]
# Get a list of just the species names (without the "massf[i]-" prefix)...
speciesNames = [name.split('-')[1] for name in speciesKeys]
nsp = len(speciesKeys)
#
# Initialise the totals across the slice:
Area = 0.0 #...area
nhatTotal = Vector(0.0) #...unit normal
speciesMassFluxes = zeros((nsp,))
massFlux = 0.0
momentumFlux = Vector(0.0)
energyFlux = 0.0
# We also need to calculate the mass-weighted Mach number for later use.
mach = 0.0
# Mass-weighted turbulent parameters will also be reported in the stats file.
tke = 0.0
omega = 0.0
dt_chem = 0.0
#
# Define the following for ease of use in the integration process below.
rho = data['rho']
u = data['vel.x']
v = data['vel.y']
p = data['p']
h0 = data['total_h'] # this includes tke
a = data['a']
M = data['M_local']
#
# Integrate the conserved properties across the slice.
for j in range(len(ys)):
if ys[j] > y_edge: break
y1 = 0.5*(ys[j]+ys[j+1])
x1 = 0.5*(xs[j]+xs[j+1])
if j == 0:
y0 = 0.0
dx = xs[j]-x1
x0 = xs[j]+dx
else:
y0 = 0.5*(ys[j-1]+ys[j])
x0 = 0.5*(xs[j-1]+xs[j])
# We assume the data is axi-symmetric but no
# assumption is made about the straightness
# of the plane over which we are integrating.
# Hence we use a truncated cone for the area.
d_Area = pi*(y0+y1)*sqrt((y1-y0)**2+(x0-x1)**2)
Area += d_Area
# Calculate the outward pointing unit
# normal vector to the differential area
# element...
edge = Vector(x0,y0,0)-Vector(x1,y1,0)
nhat = Vector(-edge.y, edge.x, 0)/vabs(edge)
nhatTotal += nhat*d_Area
# Velocity vector and weighting function...
vel = Vector(u[j],v[j],0.0)
weighting = rho[j]*dot(vel,nhat)
# Total mass, momentum and energy fluxes...
# Eq'ns (2a), (2b), and (2c) in paper.
momentumFlux += (weighting*vel + p[j]*nhat)*d_Area
#h0 = e0[j] + p[j]/rho[j] + 0.5*dot(vel,vel)
#energyFlux += weighting*h0*d_Area
energyFlux += weighting*h0[j]*d_Area
speciesFractions = array([data[species][j] for species in speciesKeys])
speciesMassFluxes += weighting*speciesFractions*d_Area
massFlux += weighting*d_Area
#
# Mass-weighted parameters...
mach += M[j]*weighting*d_Area
if 'tke' in data.keys():
tke += data['tke'][j]*weighting*d_Area
if 'omega' in data.keys():
omega += data['omega'][j]*weighting*d_Area
if 'dt_chem' in data.keys():
dt_chem += data['dt_chem'][j]*weighting*d_Area
# Check the total mass flux...Eq'n (A2)
assert abs(massFlux - sum(speciesMassFluxes)) <= 1e-7
#
# Now, compute the effective 1D flow properties
# to have the same integral properties.
#
# Calculate the overall unit normal vector using Eq'n (10)
g_nhat = nhatTotal/Area
# and a scalar momentum flux of the effective 1D flow, Eq'n (A8)
momentumFluxScalar = dot(momentumFlux,g_nhat)
# 1D species mass fractions...Eq'n (A4)
massFrac = speciesMassFluxes/massFlux
# Mass-weighted Mach number
aveMach = mach/massFlux
# and mass-weighted turbulent parameters.
ave_tke = tke/massFlux #...Eq'n (20) and (A2)
ave_omega = omega/massFlux
ave_dt_chem = dt_chem/massFlux
# and reconstruct the gas state
gmodel = create_gas_model(gmodelFile)
gdata = Gas_data(gmodel)
massfDict = dict([(k,v) for k,v in zip(speciesNames,massFrac)])
set_massf(gdata,gmodel,massfDict)
gdata.rho = data['rho'][0]
gdata.T[0] = data['T[0]'][0]
gmodel.eval_thermo_state_rhoT(gdata)
vx = massFlux/(gdata.rho*Area)
#print "Before optimizer, vx=", vx, "p=", gdata.p, "T=", gdata.T[0], "rho=", gdata.rho
#
#print "fm=",massFlux,"fp=",momentumFluxScalar,"fe=",energyFlux
def error_estimate(params,
gasData=gdata, gasModel=gmodel,
fm=massFlux, fp=momentumFluxScalar, fe=energyFlux,
tke=ave_tke, Area=Area, mach=aveMach):
"""
Estimate the badness the current guess for 1D flow properties.
params : [rho, T, v] 1D flow properties to be evaluated
"""
rho, T, vx = params
gasData.T[0] = T
gasData.rho = rho
gmodel.eval_thermo_state_rhoT(gasData)
p = gasData.p
h = gasModel.mixture_enthalpy(gasData) #...1D static enthalpy
M = vx/gasData.a
# Relative errors in each conserved quantity.
# The "+1.0" items are to avoid (unlikely) problems with zero values
# for the given quantities.
fm_err = abs(fm - rho*vx*Area)/(abs(fm)+1.0)
fp_err = abs(fp - (rho*vx*vx*Area + p*Area))/(abs(fp)+1.0)
fe_err = abs(fe - rho*vx*Area*(h+0.5*vx*vx+tke))/(abs(fe)+1.0)
mach_err = abs(M - mach)/(abs(mach)+1.0)
# The overall error estimate is a weighted sum.
return fm_err + fp_err + fe_err + 0.1*mach_err
#
print "Optimize estimate of 1D flow properties"
flow_params, fx, conv_flag, nfe, nres = minimize(error_estimate,
[gdata.rho, gdata.T[0], vx],
[0.01, 10.0, 10.0], maxfe=1000)
rho, T, vx = flow_params
#print "fx=", fx
#print "convergence-flag=", conv_flag
#print "number-of-fn-evaluations=", nfe
#print "number-of-restarts=", nres
if conv_flag != 1:
print "WARNING! Optimizer did not converge properly."
gdata.T[0] = T
gdata.rho = rho
gmodel.eval_thermo_state_rhoT(gdata)
p = gdata.p
#print "After optimizer, vx=", vx, "p=", p, "T=", T, "rho=", rho
g = gmodel.gamma(gdata)
R = gmodel.R(gdata)
M = vx/gdata.a
total_h = energyFlux/massFlux
#
gmodel.eval_transport_coefficients(gdata)
properties = {}
properties['rho'] = rho
properties['vel.x'] = vx
properties['vel.y'] = 0.0
properties['p'] = p
properties['a'] = gdata.a
properties['mu'] = gdata.mu
properties['k[0]'] = gdata.k[0]
properties['e[0]'] = gdata.e[0]
properties['T[0]'] = T
properties['M_local'] = M
properties['total_h'] = total_h
properties['gamma'] = g
properties['R'] = R
for k in range(nsp):
properties[speciesKeys[k]] = massFrac[k]
# Calculate Pitot pressure using Rayleigh formula...
if M > 1.0:
t1 = (g+1)*M*M/2
t2 = (g+1)/(2*g*M*M - (g-1));
pitot_p = p * pow(t1,(g/(g-1))) * pow(t2,(1/(g-1)));
else:
t1 = 1 + 0.5*(g-1)*M*M
pitot_p = p * pow(t1,(g/(g-1)))
properties['pitot_p'] = pitot_p
# Calculate total pressure (as isentropic process)...
t1 = 1 + 0.5*(g-1)*M*M
total_p = p * pow(t1,(g/(g-1)))
properties['total_p'] = total_p
#
# Calculate the turbulent viscosity and thermal
# conductivity using definitions given in:
# Chan, W.Y.K., Jacobs, P.A., Nap, J.P., Mee, D.J.,
# Kirchhartz, R.M. (2011)
# "The k-w turbulence model in Eilmer3: User guide
# test cases", Research Report Number 2010/11
properties['mu_t'] = properties['rho']*ave_tke/ave_omega
Pr_t = 8.0/9.0 #...turbulent Prandtl number.
Cp = gmodel.Cp(gdata)
properties['k_t'] = Cp*properties['mu_t']/Pr_t
# Finally, add the remaining mass-weighted turbulent
# and chemistry parameters...
properties['tke'] = ave_tke
properties['omega'] = ave_omega
properties['dt_chem'] = ave_dt_chem
#
# Now we have all the one-dimensionalised flow properties,
# calculate the statistics and write a summary.
#
fout = open(jobName+'-exit.stats','w')
if conv_flag != 1:
fout.write('WARNING! Optimizer did not converge properly\n')
fout.write('CoreRadiusFraction: %10.6f\n' % coreRfraction)
fout.write('%15s %12s %10s %10s %10s\n' % \
("variable","mean-value","minus","plus","std-dev"))
fout.write(65*'-')
fout.write('\n')
print "%15s %12s %10s %10s %10s" % \
("variable", "mean-value", "minus", "plus","std-dev")
print 65*'-'
#
exclude_list = ['pos.x', 'pos.y', 'pos.z', 'volume', 'vel.z', 'S']
for var in variable_list:
if var in exclude_list: continue
# Identify the low and high values
diff_minus = 0.0
diff_plus = 0.0
count = 0.0
stddev = 0.0
for j in range(len(ys)):
if ys[j] > y_edge: break
diff = data[var][j] - properties[var]
diff_minus = min(diff, diff_minus)
diff_plus = max(diff, diff_plus)
count += 1
stddev += diff**2
# Calculate the sample standard deviation
stddev = (stddev/(count-1))**0.5
print "%15s %12.5g %10.3g %10.3g %10.3g" % \
(var, properties[var], diff_minus, diff_plus, stddev)
fout.write('%15s %12.5g %10.3g %10.3g %10.3g\n' % \
(var, properties[var], diff_minus, diff_plus, stddev))
#
print 65*'-'
fout.write(65*'-'+'\n')
fout.close()
return
def process_one_slice(flow, grd, i):
"""
Returns ...
Use cell-average flow quantities and areas from the EAST boundary faces.
"""
m_flux = 0.0
mf_flux = 0.0
mfR_flux = 0.0
H_flux = 0.0
Circ = 0.0
prec = 0.0
z_pen = 0.0
nj = flow.nj
nk = flow.nk
f0stoic = 0.02876
f0lim = 0.1 * f0stoic # limiting mass fraction defining edge of jet
for j in range(nj):
for k in range(nk):
vtx = grd.get_vertex_list_for_cell(i, j, k)
# The EAST cell face has 1, 2, 6, 5 as corners (unit normal out).
face_centroid = quad_centroid(vtx[1], vtx[2], vtx[6], vtx[5])
face_normal = quad_normal(vtx[1], vtx[2], vtx[6], vtx[5])
face_area = quad_area(vtx[1], vtx[2], vtx[6], vtx[5])
# average conditions in cell
y = flow.data['pos.y'][i, j, k]
z = flow.data['pos.z'][i, j, k]
pressure = flow.data['p'][i, j, k]
rho = flow.data['rho'][i, j, k]
e = flow.data['e[0]'][i, j, k]
a = flow.data['a'][i, j, k]
v_x = flow.data['vel.x'][i, j, k]
v_y = flow.data['vel.y'][i, j, k]
v_z = flow.data['vel.z'][i, j, k]
if j == 0:
if k == 0:
yp = flow.data['pos.y'][i, j + 1, k]
zp = flow.data['pos.z'][i, j, k + 1]
v_yp = flow.data['vel.y'][i, j, k + 1]
v_zp = flow.data['vel.z'][i, j + 1, k]
vort_x = (v_zp - v_z) / (yp - y) - (v_yp - v_y) / (zp - z)
elif k == nk - 1:
yp = flow.data['pos.y'][i, j + 1, k]
zm = flow.data['pos.z'][i, j, k - 1]
v_zp = flow.data['vel.z'][i, j + 1, k]
v_ym = flow.data['vel.y'][i, j, k - 1]
vort_x = (v_zp - v_z) / (yp - y) - (v_y - v_ym) / (z - zm)
else:
yp = flow.data['pos.y'][i, j + 1, k]
zp = flow.data['pos.z'][i, j, k + 1]
zm = flow.data['pos.z'][i, j, k - 1]
v_zp = flow.data['vel.z'][i, j + 1, k]
v_yp = flow.data['vel.y'][i, j, k + 1]
v_ym = flow.data['vel.y'][i, j, k - 1]
vort_x = 0.5 * (2.0 * (v_zp - v_z) / (yp - y) -
(v_yp - v_y) / (zp - z) - (v_y - v_ym) /
(z - zm))
elif j == nj - 1:
if k == 0:
ym = flow.data['pos.y'][i, j - 1, k]
zp = flow.data['pos.z'][i, j, k + 1]
v_yp = flow.data['vel.y'][i, j, k + 1]
v_zm = flow.data['vel.z'][i, j - 1, k]
vort_x = (v_zm - v_z) / (ym - y) - (v_yp - v_y) / (zp - z)
elif k == nk - 1:
ym = flow.data['pos.y'][i, j - 1, k]
zm = flow.data['pos.z'][i, j, k - 1]
v_zm = flow.data['vel.z'][i, j - 1, k]
v_ym = flow.data['vel.y'][i, j, k - 1]
vort_x = (v_zm - v_z) / (ym - y) - (v_y - v_ym) / (z - zm)
else:
ym = flow.data['pos.y'][i, j - 1, k]
zp = flow.data['pos.z'][i, j, k + 1]
zm = flow.data['pos.z'][i, j, k - 1]
v_zm = flow.data['vel.z'][i, j - 1, k]
v_yp = flow.data['vel.y'][i, j, k + 1]
v_ym = flow.data['vel.y'][i, j, k - 1]
vort_x = 0.5 * (2.0 * (v_zm - v_z) / (ym - y) -
(v_yp - v_y) / (zp - z) - (v_y - v_ym) /
(z - zm))
elif k == 0:
yp = flow.data['pos.y'][i, j + 1, k]
zp = flow.data['pos.z'][i, j, k + 1]
ym = flow.data['pos.y'][i, j - 1, k]
v_yp = flow.data['vel.y'][i, j, k + 1]
v_zp = flow.data['vel.z'][i, j + 1, k]
v_zm = flow.data['vel.z'][i, j - 1, k]
vort_x = 0.5 * ((v_zp - v_z) / (yp - y) + (v_z - v_zm) /
(y - ym) - 2.0 * (v_yp - v_y) / (zp - z))
elif k == nk - 1:
yp = flow.data['pos.y'][i, j + 1, k]
ym = flow.data['pos.y'][i, j - 1, k]
zm = flow.data['pos.z'][i, j, k - 1]
v_zp = flow.data['vel.z'][i, j + 1, k]
v_ym = flow.data['vel.y'][i, j, k - 1]
v_zm = flow.data['vel.z'][i, j - 1, k]
vort_x = 0.5 * ((v_zp - v_z) / (yp - y) + (v_z - v_zm) /
(y - ym) - 2.0 * (v_y - v_ym) / (z - zm))
else:
yp = flow.data['pos.y'][i, j + 1, k]
zp = flow.data['pos.z'][i, j, k + 1]
ym = flow.data['pos.y'][i, j - 1, k]
zm = flow.data['pos.z'][i, j, k - 1]
v_yp = flow.data['vel.y'][i, j, k + 1]
v_zp = flow.data['vel.z'][i, j + 1, k]
v_ym = flow.data['vel.y'][i, j, k - 1]
v_zm = flow.data['vel.z'][i, j - 1, k]
vort_x = 0.5 * ((v_zp - v_z) / (yp - y) + (v_z - v_zm) /
(y - ym) - (v_yp - v_y) / (zp - z) -
(v_y - v_ym) / (z - zm))
Circ += math.fabs(vort_x) * face_area
vel_abs = Vector(v_x, v_y, v_z)
M = math.sqrt(v_x * v_x + v_y * v_y + v_z * v_z) / a
gam = 1.4
p0 = pressure * math.pow(1.0 + 0.5 * (gam - 1.0) * M * M, gam /
(gam - 1.0))
df = face_area * pressure * face_normal
dm_flux = rho * dot(vel_abs, face_normal) * face_area
m_flux += dm_flux
f0 = flow.data['massf[0]-H2'][i, j, k]
f1 = flow.data['massf[1]-air'][i, j, k]
mf_flux += f0 * dm_flux
if f0 < 0.02961 * f1:
mfR_flux += f0 * dm_flux
else:
mfR_flux += 0.02961 * f1 * dm_flux
if f0 > f0lim:
if z > z_pen:
z_pen = z
zp = flow.data['pos.z'][i, j, k + 1]
f0p = flow.data['massf[0]-H2'][i, j, k + 1]
if f0p < f0lim:
z_pen = (f0lim - f0) / (f0p - f0) * (zp - z) + z
prec += p0 * dm_flux
H_flux += dm_flux * (e + pressure / rho + 0.5 *
math.sqrt(v_x * v_x + v_y * v_y + v_z * v_z))
return m_flux, H_flux, mf_flux, mfR_flux, prec, Circ, z_pen