我正在尝试求解以下 dB 方程(为简单起见,我在问题标题中将 dB 表示为 x):
方程中的所有其他项都是已知的。我尝试使用 SymPy 象征性地求解 dB,但我不断收到超时错误。我也尝试过使用fminbound
from scipy.optimize
但 dB 的答案是错误的(请参阅下面的 Python 代码,使用fminbound
方法)。
有谁知道使用Python求解dB方程的方法吗?
import numpy as np
from scipy.optimize import fminbound
#------------------------------------------------------------------------------
# parameters
umf = 0.063 # minimum fluidization velocity, m/s
dbed = 0.055 # bed diameter, m
z0 = 0 # position bubbles are generated, m
z = 0.117 # bed vertical position, m
g = 9.81 # gravity, m/s^2
#------------------------------------------------------------------------------
# calculations
m = 3 # multiplier for Umf
u = m*umf # gas superficial velocity, m/s
abed = (np.pi*dbed**2)/4.0 # bed cross-sectional area, m^2
# calculate parameters used in equation
dbmax = 2.59*(g**-0.2)*(abed*(u-umf))**0.4
dbmin = 3.77*(u-umf)**2/g
c1 = 2.56*10**-2*((dbed / g)**0.5/umf)
c2 = (c1**2 + (4*dbmax)/dbed)**0.5
c3 = 0.25*dbed*(c1 + c2)**2
dbeq = 0.25*dbed*(-c1 + (c1**2 + 4*(dbmax/dbed))**0.5 )**2
# general form of equation ... (term1)^power1 * (term2)^power2 = term3
power1 = 1 - c1/c2
power2 = 1 + c1/c2
term3 = np.exp(-0.3*(z - z0)/dbed)
def dB(d):
term1 = (np.sqrt(d) - np.sqrt(dbeq)) / (np.sqrt(dbmin) - np.sqrt(dbeq))
term2 = (np.sqrt(d) + np.sqrt(c3)) / (np.sqrt(dbmin) + np.sqrt(c3))
return term1**power1 * term2**power2 - term3
# solve main equation for dB
dbub = fminbound(dB, 0.01, dbed)
print 'dbub = ', dbub
以下是四种单维根方法:
from scipy.optimize import brentq, brenth, ridder, bisect
for rootMth in [brentq, brenth, ridder, bisect]:
dbub = rootMth(dB, 0.01, dbed)
print 'dbub = ', dbub, '; sanity check (is it a root?):', dB(dbub)
还有牛顿-拉夫森(割线/海利)方法:
from scipy.optimize import newton
dbub = newton(dB, dbed)
print 'dbub = ', dbub, '; sanity check (is it a root?):', dB(dbub)
如果您有括号间隔,scipy 文档建议使用 brentq。
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