pttools.bubble.chapman_jouguet
Chapman-Jouguet speed
Functions
- pttools.bubble.chapman_jouguet.v_chapman_jouguet(model, alpha_n, wn=None, wn_guess=None, wm_guess=None, extra_output=False, analytical=True, error_on_invalid=True, nan_on_invalid=True, log_invalid=True)
Chapman-Jouguet speed
This is the minimum wall speed for detonations.
- pttools.bubble.chapman_jouguet.v_chapman_jouguet_bag(alpha_plus)
Chapman-Jouguet speed for the bag model
\(\alpha_n\) can be given instead of \(\alpha_+\), as “The two definitions of the transition strength coincide only in the case of detonations within the bag model.” Hindmarsh et al., 2021 p. 40
\[v_{CJ}(\alpha_+) = \frac{1}{\sqrt{3}} \frac{1 + \sqrt{2\alpha_+ + 3 \alpha_+^2}}{1 + \alpha_+}\]This differs from :notes:` ` eq. 7.34 and eq. B.19 and Giombi & Hindmarsh, 2024 eq. 2.23 by a factor of 2. Other sources: Gowling & Hindmarsh, 2021 eq. 2.4 It should be noted that \(v_{CJ} \in [0, 1] \forall \alpha_+ >= 0\).The Chapman-Jouguet speed can be different for other models, but for all detonations \(v_w \geq v_{CJ,\text{bag}}\).
- pttools.bubble.chapman_jouguet.v_chapman_jouguet_const_cs(model, alpha_theta_bar_plus)
- Parameters:
model (ConstCSModel)
alpha_theta_bar_plus (float | float64 | ndarray)
- pttools.bubble.chapman_jouguet.v_chapman_jouguet_const_cs_reference(alpha_n, model)
- Parameters:
alpha_n (ndarray)
model (ConstCSModel)
- Return type:
- pttools.bubble.chapman_jouguet.wm_chapman_jouguet(model, wp, wm_guess=None, error_on_invalid=True, nan_on_invalid=True, log_invalid=True)
Get \({w}_-\) for a transition that has $ ilde{v}_-=c_{{s},-}({w}_-)$ such as a Chapman-Jouguet detonation or a Chapman-Jouguet deflagration.
- Parameters:
model (Model)
wp (float)
wm_guess (float)
error_on_invalid (bool)
nan_on_invalid (bool)
log_invalid (bool)
- Return type:
float