Fluiddynamik in der Cigarette und deren Einfluß auf den Zugwiderstand

The objective of the theoretical study is to present a model that simulates the instationary flow characteristics within cigarettes which are adjusted to a routine smoking machine. By assuming laminar fluid flow the well knownKozeny-Carman equation is used to evaluate the flow impedance of cigarettes. The model parameters are determined by five variations of routine pressure-drop measurements yielding the entire set of flow impedances, which are necessary for describing a steady state Fluid-Network. Using this relation further elements of the fluid dynamics, e.g. the Fluid-Inductor, a storage element of kinetic energy (fluid inertor), and the Fluid-Capacitor, a storage element of potential energy (fluid volume), are evaluated. In addition, the electrical and fluid dynamical analogies are demonstrated. The model uses a set of distributed parameters including pneumatic impedances, capacitors and inductors, to represent filtered cigarettes and a second order linear partial differential equation to describe the fluid flow within the cigarettes. A simple presentation of the Fluid-Network with lumped parameters is analysed and its significant time constants are determined. A characteristical value for the time constant of the cigarette fluid-inertor is given by T_L ≈ 0.02 ms and depending on the fluid volume of cigarette their dominant time parameter is given by T_C ≈ 2 ms. Finally the transient fluid flow within cigarettes in a conventional smoking machine is considered including a simulation of their fluid dynamics. A simple estimation gives the time response of the system (consisting of cigarettes and routine smoking machine) with T_cR ≈ 70 ms as a product of dead and sweep volume times the pressure drop of unencapsulated cigarettes. Variation of parameters caused by cigarette pressure drops and dead volumes of the smoking machine are simulated and discussed.