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engine.pipeline.thermal.wall_conduction Namespace Reference

Classes

class  Layer
class  WallModel

Functions

np.ndarray _graded (float L, int n, float first)
np.ndarray _thomas (np.ndarray a, np.ndarray b, np.ndarray c, np.ndarray d)

Detailed Description

One-dimensional transient conduction through a layered wall with a receding hot face.

Backward Euler on a graded grid (fine at the hot face), layer interfaces on nodes, back face
adiabatic -- the conservative bound when the backing is not declared. The hot-face flux is a
function of the surface temperature, closed exactly each step: the interior is linear in the
surface temperature, so the surface balance is a scalar root.

Two recession modes:
  * ablating (liner): the surface cannot exceed ``T_ablation``; once it gets there the flux
    it cannot conduct away consumes material at ``H_surface`` J/kg (Landau problem);
  * chemical (graphite): recession is the carbon mass flux the surface chemistry returns at
    the solved surface temperature, not an energy balance.

A receding face is handled by remapping the profile onto the shortened wall each step.

A layer may carry ``cp_of(T)``: its heat capacity is then taken at each cell's temperature at the
start of every step (lagged one step, as backward Euler does with a property). Without it the
wall is exactly the constant-property model.

Function Documentation

◆ _graded()

np.ndarray engine.pipeline.thermal.wall_conduction._graded ( float L,
int n,
float first )
protected
n+1 node positions on [0, L], geometric from a first cell of ``first`` (capped uniform).

Definition at line 40 of file wall_conduction.py.

Referenced by engine.pipeline.thermal.wall_conduction.WallModel._build_grid().

◆ _thomas()

np.ndarray engine.pipeline.thermal.wall_conduction._thomas ( np.ndarray a,
np.ndarray b,
np.ndarray c,
np.ndarray d )
protected