# Damkohler number

The Damkohler number is used in turbulent combustion and corresponds to the ratio of chemical time scale $\tau_c$ and turbulent time scale $\tau_t$. This turbulent scale is usually taken as the integral scale.

$Da \equiv \frac{\tau_t}{\tau_c}$

Damkohler number measures how important is the interaction between chemistry and turbulence. Most combustion models are placed in the extremes of Damkohler.

If $Da << 1$ the turbulence is much faster than the chemistry. This regime is the "well-stirred reactor", where products and reactants are rapidly mixed. The Karlovitz number is linked to the Damkholer number.

The Damkohler number is also defined in a chemical non-equilibrium process at very high velocities of the fluid or vehicles (with reference to fluid). There are two ratios of Damkohler number that can be defined and are as follows:

1. First Damkohler Number or DAM 1

$DAM 1 = \frac{t_{res}}{\tau}$

Where $t_{res}$ is the residence time of the flow, where $\frac{L_{ref}}{U_{ref}}$ where $L_{ref}$ is the reference length of the vehicle and $U_{ref}$ is the reference velocity of fluid or vehicle with respect to fluid

2. Second Damkohler Number or DAM 2

$DAM 2 = \frac{q_{ne}}{h_o}$

Where $q_{ne}$ is the energy involved in a non-equilibrium process and $h_o$ is the total enthalpy of the flow