“Alice showed initiative in her approach to research and was diligent in her work. She was resourceful and innovative. Alice's work helped us to gain a better appreciation of water condensation and run-off in fuel tanks as part of a wider research project.” Joseph Lam

IP09-025(April 2012) Exploi�ng the power of mathema�cs www.innovateuk.org/mathsktn

WATER CONDENSATION AND RUNOFF IN AIRCRAFT FUEL TANKS

Airbus Operations Ltd / University of Nottingham

Aircraft fuel tanks operate over a wide range of atmos-pheric temperatures and pres-sures, which vary with altitude. During descent, the increasing atmospheric pressure causes a net flow of air into the vent-ed fuel tank. Depending on the local weather, this air can be warm and humid, in con-trast to the cold tank and fuel from cruising altitude.

When warm humid air comes into contact with cold surfaces within the tank, water conden-sation can form. Water is a fuel contaminant with strict regulations regarding maxi-mum permissible concentra-tions. Frequent drainage of the tank sump poses a maintenance burden to air-lines.

This project aimed to predict the effect of hydrophobic fuel tank coatings on the drainage rate of condensed water.

Two factors that affect the drain-age rate of condensed water on a sloping surface are the maxi-mum size of water drops pinned to the surface by surface tension and the speed at which larger drops slide down the surface. This critical drop size and speed depend on physical and chemi-cal properties of the surface coating. Simple mathematical models were developed to relate the critical size and drop speed for each surface to the surface slope angle. It was found that there is a signif-icant difference in performance, in both runoff size and speed, between different surface coat-

ings. The use of hydrophobic coatings can greatly reduce the total volume of condensed water retained on the tank walls. It was also observed that upon striking the fuel surface, most droplets rapidly moved away from the tank wall. The implica-tion of this is that once droplets have reached the fuel surface, their migration through the fuel should be independent of the tank wall coating. This collaboration gave the stu-dent an opportunity to apply the skills she developed in her PhD research to a practical and cur-rent fluid mechanical problem which the company faced.

All systems go

The outcomes The need

IP09-025(April 2012)

Project Details

Partners

Airbus Operations Ltd University of Nottingham

Project investment

£15,000

Intern

Alice Thompson

For further details on the technology:

Joseph Lam Airbus Operations Ltd

Joseph.Lam@airbus.com

For information on internships and

other collaborations: Lorcán Mac Manus

Industrial Mathematics KTN lbmm@industrialmaths.net

+44 (0) 1483 565252

“This internship was an excellent opportunity to apply mathe-matical modelling to a variety of interesting fluid dynamical prob-lems. I greatly enjoyed being based in an engineering team for six months, and gained new perspectives on the importance of surface tension in industrial design.”

Alice Thompson, University of Nottingham

“Alice’s PhD project, on surface tension driven recoil of fluid wedges, is very theoretical, so I am very pleased that she was able to apply her skills in a more practical, but closely related, research situation. It was also interesting to see how Airbus study and solve the fluid mechanical problems they encounter in their fuel tanks.”

John Billingham, University of Nottingham

Exploi�ng the power of mathema�cs www.innovateuk.org/mathsktn

This project was part of the programme of industrial mathematics internships managed by the Knowledge Transfer Network (KTN) for Industrial Mathematics. The KTN works to exploit mathematics as an engine for innovation. It is sup-ported by the Technology Strategy Board, in its role as the UK’s national inno-vation agency, and the Engineering and Physical Sciences Research Council, in its role as the main UK government agency for funding research and training in engineering and the physical sciences.

Technical summary

A number of experiments were carried out to complement the mathematical modelling. We measured the critical size of pinned drops on dif-ferent surfaces and the runoff speed for different drop volumes and slope angles, using motion tracking algorithms.

Drop displacement vs time for a hydrophobic surface. The legend shows the drop volume in microliters. Note the distinct period of acceleration, perhaps caused by deformation of the contact line to a narrower shape.

The migration rate of water through the tank also depends on how droplets interact with the air/fuel surface, where the surface tension coefficients can (just) support a three-phase contact line. It is therefore theoretically possible for very small

droplets to float just beneath the fuel surface as in Fig 3(b) or to become trapped at the contact line between the wall/air/fuel surfaces as in Fig 3(a). Our experiments demonstrated very small ax-isymmetric floating droplets. However, high speed filming indicated that drops are not usually trapped at the wall/air/fuel surface as shown in Fig 3(a). Instead, upon reaching the fuel layer,

water drops rapidly gained a horizontal velocity component away from the wall, sometimes form-ing satellite droplets in the process. This was ob-served even for the most hydrophilic surface coat-ings tested, implying that the migration of water droplets below the fuel surface should be inde-pendent of the tank wall coating.