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.

Parameters:
  • model (Model)

  • alpha_n (float | float64 | ndarray)

  • wn (float | float64 | ndarray)

  • wn_guess (float)

  • wm_guess (float)

  • extra_output (bool)

  • analytical (bool)

  • error_on_invalid (bool)

  • nan_on_invalid (bool)

  • log_invalid (bool)

Return type:

float | Tuple[float, float, float] | ndarray

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 \(v_w \geq v_{CJ,\text{bag}}\).

Parameters:

alpha_plus (float | float64 | ndarray)

Return type:

float | float64 | ndarray

pttools.bubble.chapman_jouguet.v_chapman_jouguet_const_cs(model, alpha_theta_bar_plus)
Parameters:
pttools.bubble.chapman_jouguet.v_chapman_jouguet_const_cs_reference(alpha_n, model)
Parameters:
Return type:

ndarray

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

pttools.bubble.chapman_jouguet.wm_solvable_chapman_jouguet(params, model, wp)
Parameters: