Supercooled large droplets, also known as SLD, are typically found in freezing drizzle and rain where water droplets retained liquid form although water temperature is below freezing temperatures. In general, droplets greater than 40 microns (thickness of human hair is approximately 100 to 200 microns) are considered SLD. Icing on aircraft due to SLD occurs more frequently than first thought but it was not recognized as a threat to aviation safety until the fatal accident at Roselawn, Indiana (source: NTSB). In that accident, the aircraft was instrumented with ice protection system and certified to operate in icing conditions. However, post-accident investigations which involved in-flight tests behind an icing air tanker had revealed ice accretions forming in areas beyond the limits of the ice protection systems, which rendered them ineffective. As a result of this and a number of other icing related incidents involving SLD, the FAA and the icing branch of NASA Glenn has developed a roadmap for generating database and fundamental knowledge on SLD. A number of research establishments and universities were invited to participate in the program, and WSU is one of the universities involved in the effort.
The following topics have received particular focus of attention:
Reference Probe for measuring LWC in Supercooled Large Droplet (SLD) and Appendix C icing clouds
The measurement of the liquid water concentration (LWC) in icing clouds with supercooled large droplets (SLD) presents a challenge for conventional hotwire based probes. It is known that measurement errors in these LWC probes could vary by as much as 50%. Therefore a research program, funded by the FAA and supported by NASA Glenn, was conceived to develop a proof-of-concept probe for measuring in Appendix C and SLD icing conditions. This probe is different to other existing LWC instruments due to its ability to measure SLD cloud and mixed phase icing conditions. It is also relatively insensitivity to droplet splashing, a common phenomenon with large droplets when they impinge on solid surfaces. The present design creates iso-kinetic flow at the probe inlet so that droplets within a suction cone (yellow colored stream in figure shown below), which is equivalent to the probe inlet area, are caught inside the probe. The captured water mass is then used to compute for the cloud concentration. Unlike the hot-wire design of existing LWC instruments, which rely on the vaporization of water droplets that impinge on the wire directly hence splashing loss, the present design philosophy adopted here does not involve water impingement at all therefore droplet splashing is not an issue. Tests conducted in a laboratory shows that the measurement range of the probe is between 0.5 and 4 g/m3. Measurement resolution is less than ±10% compared to about ±25% in existing LWC instruments. Limited tests had also been conducted in a dry-air wind tunnel to demonstrate the operation of the iso-kinetic flow control system. This was successful but further tests are still being planned to determine its performance in an icing tunnel before it can be used to measure LWC in SLD icing clouds.
DOT/FAA/AR-05/23 Development of a Reference Liquid Water Content Probe
Droplet Breakup due to Viscous Aerodynamic Forces
This research investigates the potential for large water droplets to distort and break up when they are subjected to strong viscous aerodynamic forces (figure shown right) such as those found at the leading edge of an airfoil or behind an ice ridge. Large droplets are more susceptible these dynamic effects due to the greater surface area that interacts with the external forces. Depending on the prevailing adverse pressure gradients and droplet properties (such as viscosity, surface tension, density), the type of breakup mode could take many different forms e.g. when droplets encounter a shockwave, an explosive type of breakup is more likely to occur rather than a vibrational or bag type breakup. In general, droplet Weber numbers have been used to characterize the breakup process e.g. Pilch has defined the following five distinct breakup modes: We ≤ 12, vibrational breakup; 12 < We ≤ 50, bag breakup; 50 < We ≤ 100, bag and stamen breakup; 100 < We ≤ 350, sheet stripping; We > 350, wave crest stripping, where D is the droplet diameter, ρg is the gas density, σd is the droplet surface tension and Vr is the relative velocity between the droplet and surrounding gas. The critical droplet Weber numbers where break-up occurs are between 12 and 14.
Effect of Droplet Splashing on Droplet Impingement Characteristics
Droplet splashing commonly occurs when droplets collide with solid surfaces as shown in the figure on the right. The amount of splashed-back droplets depends on the droplet sizes, impact speeds and angles, wall surface roughness, presence of a water film, and depth of film.
In terms of ice accretion modeling, all icing computer programs assumed no droplet splashing because the droplet sizes considered for icing certification purposes are quite small. The FAA document Part 25, Appendix C suggests using droplet median volumetric diameter (MVD) between 15 and 20 microns (actual sizes could range from 4 to 100 microns) in icing wind tunnel and in-flight testing with airborne icing tankers. In reality, large droplets within the Appendix C size range do splash but the mass loss is negligible due to the small number of large droplets in the spray cloud (i.e. low mass fraction). However for a large MVD cloud, where a majority of droplet population is consisted of large droplets (>40 microns), mass loss due droplet splashing can be significant. Figure on the left shows the comparison between experimental droplet impingement values measured on the NACA 652415 airfoil and values predicted with LEWICE. The distribution is directly related to the amount of water mass flux that would be deposited on the airfoil surface therefore it has a major impact on the final shape of the ice. The figure shows an over-prediction of the water mass flux on the airfoil surface. There are evidences [Papadakis,Tan, Mundo, Potucpzuk] to suggest that droplet splashing is the main cause of the differences. In order to account for the mass loss due to splashing, WSU has developed an empirical mass loss model to compute the splashed mass given a cloud MVD and discrete droplet impact parameter. In simple terms, a splash function is added to the algorithms to account for the mass loss during the computation of the droplet impingement efficiency. Figure on right shows vast improvement to the predicted droplet impingement values (in red) with the application of the mass loss model.
Numerical Modeling of Droplet Splashing and Re-impingement with VOF Technique
Droplet impingement and splashing commonly occurs when aircrafts encounter inclement weathers such as freezing drizzle and rain. In order to develop the mathematical models to simulate the physical processes and generate the appropriate formulations, it may be necessary to conduct experiments with a range of droplet sizes and impact velocities representative of those found in-flights. However it may not be possible to perform tests for all possible scenarios, for example, droplet coalescence, droplet-droplet interactions, droplet-water film interactions or interactions between incoming and splashed droplets. In addition, droplet interactions usually occur in a fraction of a second (~ 1 to 50ms) thus extremely high-speed systems and high-intensity illuminations are needed to capture and record the transient events. An alternative to this is to apply direct numerical simulation techniques such as the volume of fluid (VOF) methodology to study droplet interactions such as splashing, re-impingement, distortion, or even droplet-droplet interactions. Figure above and on the left shows an example of a VOF simulation of a droplet impinging on a stationary water film (130 microns diameter, 50 microns depth, impact velocity of 60m/s). The VOF formulation relies on the fact that two or more fluids (or phases) are not interpenetrating. For each additional phase that is added to the model, a variable is introduced: the volume fraction of the phase in the computational cell. In each control volume, the volume fractions of all phases sum to unity. The fields for all variables and properties are shared by the phases and represent volume-averaged values, as long as the volume fraction of each of the phases is known at each location. Thus the variables and properties in any given cell are either purely representative of one of the phases, or representative of a mixture of the phases, depending upon the volume fraction values.
Supercooling of Large Water Droplet
It is known that larger droplets take longer to reach equilibrium temperature with the surrounding medium than smaller ones due to their greater thermal mass. In order to demonstrate the time taken to reach local flow temperature (i.e. thermal residence times), a 1-D analysis was carried out with a range of droplet sizes varying from 20 to 500 microns. The results show that a 180 microns droplet require more than 30 times longer to reach the same local flow temperatures as a 20 microns droplet. The thermal residence time is less critical for Appendix C droplet sizes because most icing wind tunnels have been optimized for these smaller sizes. However, tunnels with insufficient length may not be able to achieve SLD icing condition due to the longer thermal residence times required for large droplets to reach reached local static temperatures at the test section. As a result, the ice shapes generated in these kinds of facility may not be representative of the true SLD icings.