def calc_qi(dmin, dmax, dgr, dcr, rhog, l, mu, fr):
norm = gp.gamma_pdf_norm(mu, l)
i1 = pisxth*rhoi*gp.gintegral_seg(mu+3, l, dmin, dth)
i2 = ava*gp.gintegral_seg(mu+bva, l, dth, dgr)
i3 = pisxth*rhog*gp.gintegral_seg(mu+3, l, dgr, dcr)
i4 = 1/(1-fr)*ava*gp.gintegral_seg(mu+bva, l, dcr)
return (i1+i2+i3+i4)*norm
def calc_qi_quad(dmin, dmax, dgr, dcr, rhog, l, mu, fr):
dmax = 100000.0
dgr = min(dgr, dmax)
dcr = min(dcr, dmax)
D = [dmin, dth, dgr, dcr, dmax]
a = b = np.zeros(4)
b[0] = 3.0
b[1] = bva
b[2] = 3.0
b[3] = bva
a[0] = pisxth*rhoi
a[1] = ava
a[2] = pisxth*rhog
a[3] = 1/(1-fr)*ava
gamma = pifrth
sigma = bva
norm = gp.gamma_pdf_norm(mu, l)
# f = lambda x, alpha, beta, gamma, sigma: tv.calc_vt_simple(x, alpha, beta, gamma, sigma)*gp.gammapdf(x, mu, l)*alpha*x**beta
f = lambda x, alpha, beta: alpha*x**(mu+beta)*np.exp(-l*x)
integral = 0
for i in range(4):
tmp, err = quad(f, D[i], D[i+1], args=(a[i], b[i]))
integral += tmp
return integral*norm
def collision_rate_pyt(dgr, dcr, rhog, fr, mu, l):
Ku = ((8*calc.g)/(np.pi*calc.cd*calc.rhoa))**0.5
Ke = calc.E_coll*calc.pifrth
Nnorm = gp.gamma_pdf_norm(mu,l)
D = [[0, calc.dth], [calc.dth, dgr], [dgr, dcr], [dcr, lg.dmax]]
gfb = np.zeros((4, 3))
gf = np.zeros((4, 3))
b = np.zeros(4)
a = np.zeros(4)
b[0] = 3.0
b[1] = calc.bva
b[2] = 3.0
b[3] = calc.bva
a[0] = calc.pisxth*calc.rhoi
a[1] = calc.ava
a[2] = calc.pisxth*rhog
a[3] = 1/(1-fr)*calc.ava
# use lower gamma function for integral
for i in range(3):
for k in range(3):
expb = mu+b[i]*0.5+k-1
exp = mu+k
gfb[i,k] = gp.gintegral_seg(expb, l, D[i][0], D[i][1])
gf[i,k] = gp.gintegral_seg(exp, l, D[i][0], D[i][1])
# use upper gamma function for integral
for k in range(3):
i = 3
expb = mu+b[i]*0.5+k-1
exp = mu+k
gfb[i,k] = gp.gintegral_seg(expb, l, D[i][0])
gf[i,k] = gp.gintegral_seg(exp, l, D[i][0])
integral = 0
for i in np.arange(1,4):
for j in np.arange(0,i):
tmp1 = np.sqrt(a[i])*(gfb[i,2]*gf[j,0] + 2*gfb[i,1]*gf[j,1] + gfb[i,0]*gf[j,2])
tmp2 = np.sqrt(a[j])*(gf[i,2]*gfb[j,0] + 2*gf[i,1]*gfb[j,1] + gf[i,0]*gfb[j,2])
integral += tmp1-tmp2
integral = Ku*Ke*integral*Nnorm**2
# for i in range(4):
# ID1D2, err = dblquad(collision_integrand, D[i][0], D[i][1], lambda x:D[i][0], lambda x:x, args=(dgr, dcr, rhog, fr, mu, l))
# integral += ID1D2
return integral