Damköhler numbers

The Damköhler numbers (Da) (developed by Gerhard Damköhler, 1908-1944 ) are dimensionless parameters of chemical reaction engineering. Known are four different Damköhler numbers ( DaI, dAII, DaIII, DAIV ), which are known as Damköhler number n- th order, and a turbulent Damköhler number ( Dat ).

Damköhler number of the first order

The Damköhler number of the first order DaI describes the ratio of the rate constants of the reaction rate constants of the convective mass transfer. It is defined as

,

With: k = rate constant, = residence time or reaction time = initial concentration, n = reaction order, L = characteristic length and w = flow velocity. For the description of a discontinuous reactor the residence time is replaced by the reaction time. Thus we obtain a significantly more concise representation of the dimensionless mass balance of the ideal stirred tank reactor.

Damköhler number of the second order

The Damköhler number of the second order dAII can be found in the description of internal mass transfer properties (pore diffusion) on surfaces, for example on catalyst spheres. It is defined as the ratio of reaction rate to diffusion rate

With: = mass transfer coefficient, a = specific exchange surface. Daii can be viewed as the ratio of the reaction rate to the surface conditions on the rate of diffusion through the outer surface of the catalyst pellets.

Damköhler number third-order and fourth-order

The Damköhler number DaIII third order and the fourth order Damköhler number DAIV be used for the estimation of operating conditions with polytropic operation of reactors.

Turbulent Damköhler number

Turbulent Damköhler number DAT ( in combustion research usually simply referred to as As ) describes the relationship between the macroscopic time scale turbulent flow and the time scale of a chemical reaction:

Stands for the respective length scale, where as macroscopic length scale usually an integral length scale is chosen. This serves as a measure of the diameter of the energy-rich (and therefore typically the largest) in the vortex flow. Its peripheral speed is approximately equal to the standard deviation of the flow velocity. As the characteristic velocity of propagation for the chemical reactions used in the combustion research mostly the laminar flame speed, ie the speed with which propagates the flame front in the laminar case: Similarly, it is in reference to combustion processes common to use the thickness of the laminar flame front, in response length scale:

Based on the turbulent Damköhler number statements can be made about the spatial structure and temporal behavior of the reaction zone in a turbulent reacting flow meet.