Kinetic and thermal simulation of water droplets in icing wind tunnels

Abstract

Within the certification process of aircraft, tests under specific icing conditions are required. For such safety relevant tests—which are performed under defined and repeatable test conditions—specially equipped Icing Wind Tunnels (IWT) are required. In such IWTs, supercooled water droplets are created with the aid of a spray system injecting pre-tempered water droplets of specific diameters into the free stream air flow. Especially tests with a droplet size up to 2mm (Supercooled Large Droplets - SLDs) are of great importance. SLDs are difficult to generate under laboratory conditions in IWT since usually the available droplet flight time from the injection location to the impact position on the test object is insufficient to reliably cool down a droplet at least to freezing temperature. To investigate the limitations associated with the application of SLD, the current work provides a method to allow detailed insight into the behavior of droplets on the path from the injection spray nozzle to the test section. In this work a state space model of a single droplet is derived that combines the kinetic aspects, thermal properties as well as the governing differential equations for motion, convective heat transfer at the droplet surface and heat conduction inside the droplet. Beside the states for the droplet’s position and velocity in space, the state space vector comprises various fluid and thermodynamic parameters. The droplet-internal temperature distribution is modelled by a discrete one-dimensional spherical shell model that also incorporates the aggregate phase (freezing mass fraction) at each shell node. This approach allows, therefore, the simulation of potential droplet phase change processes (freezing/melting) as well. With the model at hand, the influence of various boundary conditions (initial droplet temperature, flow field, ambient air temperature, etc.) can be determined and evaluated. As a result, concrete measures to achieve a desired operating condition (e.g. droplet temperature at the test object) for various model assumptions can be derived. In addition, the simulation model facilitates the prediction of the droplet diameter threshold for ensuring a supercooled state upon the impact on the test object. The governing theoretical influences are described, and various simulation results for representative test conditions that occur at the Rail-Tec-Arsenal (RTA) in Vienna are presented.

Parameter Identification of the Fractional-Order Mathematical Model for Convective Mass Transfer in a Porous Medium

“…Successful attempts to advance solving the problem of convective mass transfer in porous membranes have gained more importance recently [3]. Differential equations that describe the convective mass transfer process present significant difficulties for their solution [4]. An analytical solution to these equations can be practically expedient only for cases with significant simplifications [5].…”