PySDM_examples.Srivastava_1982.equations

 1import numpy as np
 2
 3
 4class Equations:
 5    """Equations from Srivastava 1982: "A Simple Model of Particle Coalescence and Breakup"
 6    (https://doi.org/10.1175/1520-0469(1982)039%3C1317:ASMOPC%3E2.0.CO;2)
 7    note: all equations assume constant fragment mass"""
 8
 9    @property
10    def alpha_star(self):
11        """see eq. 6"""
12        return self._alpha_star or self.alpha / self.c / self.M
13
14    @property
15    def beta_star(self):
16        """see eq. 6"""
17        return self._beta_star or self.beta / self.c
18
19    def tau(self, t):
20        """see eq. 6"""
21        return self.c * self.M * t
22
23    def __init__(
24        self, *, M=None, c=None, alpha=None, beta=None, alpha_star=None, beta_star=None
25    ):
26        if alpha_star and (alpha or M or c):
27            raise ValueError("conflicting parameter")
28        self.M = M
29        self.c = c
30        self.alpha = alpha
31        self.beta = beta
32
33        self._beta_star = beta_star
34        self._alpha_star = alpha_star
35
36        if alpha_star and beta_star:
37            amb = alpha_star - beta_star
38            self._A = amb / 2 / alpha_star
39            self._B = 1 / np.sqrt(
40                (0.5 / alpha_star + beta_star / alpha_star)
41                + amb**2 / (4 * alpha_star**2)
42            )
43
44    def eq12(self):
45        """equilibrium (τ→∞) mean mass under collisions and spontaneous breakup
46        (no collisional breakup)
47        expressed as a ratio to fragment mass (i.e., dimensionless)"""
48        equilibrium_mean_mass_to_frag_mass_ratio = (
49            0.5 + (0.25 + 0.5 / self.alpha_star) ** 0.5
50        )
51        return equilibrium_mean_mass_to_frag_mass_ratio
52
53    def eq13(self, m0, tau):
54        """mean mass expressed as a ratio to fragment mass as a function of
55        dimensionless scaled time (τ) under coalescence and collisional breakup
56        (no spontaneous breakup)"""
57        mean_mass_to_frag_mass_ratio = self._eq13(m0, tau)
58        return mean_mass_to_frag_mass_ratio
59
60    def _eq13(self, m0, tau):
61        ebt = np.exp(-self.beta_star * tau)
62        return m0 * ebt + (1 + 0.5 / self.beta_star) * (1 - ebt)
63
64    def eq14(self):
65        """equilibrium (τ→∞) mean mass expressed as a ratio to fragment mass for
66        under collisional merging and breakup (no spontaneous breakup)"""
67        equilibrium_mean_mass_to_frag_mass_ratio = 1 + 0.5 / self.beta_star
68        return equilibrium_mean_mass_to_frag_mass_ratio
69
70    def eq15(self, m):
71        return (m - self._A) * self._B
72
73    def eq15_m_of_y(self, y):
74        return (y / self._B) + self._A
75
76    def eq16(self, tau):
77        return tau * self.alpha_star / self._B
78
79    def eq10(self, m0, tau):
80        """ratio of mean mass to fragment size mass as a function of scaled time
81        for the case of coalescence only"""
82        mean_mass_to_frag_mass_ratio = m0 + tau / 2
83        return mean_mass_to_frag_mass_ratio
84
85
86class EquationsHelpers:
87    def __init__(self, total_volume, total_number_0, rho, frag_mass):
88        self.total_volume = total_volume
89        self.total_number_0 = total_number_0
90        self.rho = rho
91        self.frag_mass = frag_mass
92
93    def m0(self):
94        mean_volume_0 = self.total_volume / self.total_number_0
95        m0 = self.rho * mean_volume_0 / self.frag_mass
96        return m0