COMPUTATIONAL ENGINEERING

Academic year 2008-2009; Class: 4th block, Friday 9:15 - 11:00

In this course an impression will be given of the use of mathematical and computational methodsin engineering problems. As a specific example, the dynamic behaviour of liquids with a freesurface, and its influence on its surroundings, is studied. Sloshing liquids can have a negativeinfluence on stability and control of vehicles1, but they can also be used in a positive sense todampen unwanted oscillations. In the course, several models (at various levels of sophistication)will be investigated to describe and predict sloshing dynamics.

The course will be carried out in the form of projects, where students will be asked to investigatepractical engineering problems. Weekly project meetings will monitor progress and providebackground information.

Description

In the 2008-2009 course in Computational Engineering a number of engineering applicationswhere free-surface flow plays a dominant role will be studied. The case studies (projects) comefrom various engineering disciplines, such as– Marine Engineering: influence of liquid sloshing in cargo tanks onboard LNG tank ships;– Spacecraft Technology: influence of liquid sloshing on the dynamics of spacecraft;– Earthquake Engineering: oscillation suppression in tall buildings through tuned liquid dampers

(TLD);– Vehicle Dynamics: liquid sloshing in road and railway containers.

Each project consists of several aspects:

• Literature studyWhat is the engineering relevance of the case study? Which type of approaches are in use(modelling at various levels of sophistication)?

• Selection of testcasesSearch in the literature for (simple) cases that can be used for either analytical investigationor for numerical simulation. I.e. they should be simple enough, sufficiently documented,and validation material (either through experiments or numerical simulation) should beavailable.

• Investigation by analytical and numerical toolsCarry out the investigation on various modelling levels. Formulate the equations of mo-tion (e.g. pendulum analogy, potential theory or Navier-Stokes) and boundary conditions.Identify simplified situations where analytical theory (‘pencil and paper’) can be used;distinguish between sloshing on earth and sloshing in space. Describe numerical methods(CFD) to solve the equations of motion.

• Verification and validation of simulation resultsMake sure that the numerical simulation results may be looked at with a physical eye, i.e.numerical errors should be sufficiently small. In other words: Have I done the job right?

1A Dutch truck driver once said during a radio interview: “Als je met vloeistoffen rijdt, moet je flink gasterugnemen.”

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Compare the outcome of the analytical and numerical studies with results of analysis,experiments or other numerical simulations. In other words: Have I done the right job?

• Preparation of deliverablesPrepare oral and written reports, at several moments during the project: projectplan,intermediate progress reports, final report and presentation.

Project organisation

The projects are to be carried out in groups of 3-5 students: the project teams. Identify subtasksand divide them between the project team members. Several subtasks can be imagined, suchas:– literature study on engineering background;– literature study on analytical approaches;– literature study on mechanical models;– literature study on numerical approaches;– slosh predictions from analytical theory;– application of mechanical models;– familiarisation with the simulation tool ComFlo (see below);– preparation of the input for the simulations;– slosh predictions by numerical means;– validation of the various models used;– writing of subreports for the above subtasks;– combining subreports into one overall report.

Many other aspects should be taken into account, such as:– Who takes care of the coordination within a projectteam?– Who is responsible for subtasks?– Is there any knowledge to share with other projectteams?

The largest challenge in the project will be ‘time’. The project should be finished within thecurrent teaching block: “design to cost”. Keep track of the amount of hours you are spendingon the project.

Final deliverable

At the end of the project a document should be prepared that contains the following informa-tion:– problem description, engineering relevance;– available expertise and data (from experiments or simulations);– description of various levels of modeling;– theoretical predictions (various levels);– discussion of results;– recommendations for further research.

Further, an oral presentation has to be held by each project team.

Available material

• Flyers (obtained from internet) introducing the case studies will be handed out.

• For analytical info on sloshing see e.g.

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– A.R. Paterson. A first course in fluid dynamics. Cambridge University Press, 1983.Chapter XIII.

• A general review paper is:

– R.A. Ibrahim, V.N. Pilipchuk and T. Ikeda. Recent advances in liquid sloshing dy-namics. Appl. Mech. Rev. 54(2), 2001, pp. 133–199. In particular Chapter III,“Equivalent mechanical models,” pp. 147–150. Cannot be downloaded; copy avail-able from the docent.

• More specific information including testcases can be found in the following papers.

– For LNG tanks:A. Cariou and G. Casella. Liquid sloshing in ship tanks: a comparative study ofnumerical simulation. Marine Structures 12 (3), 1999, pp. 183–198.V. Armenio and M. La Rocca. On the analysis of sloshing of water in rectangularcontainers: numerical study and experimental evaluation. Ocean Engineering 23 (8),1996, pp. 705–739.M. Serdar Celebi and H. Akyildiz. Nonlinear modeling of liquid sloshing in a movingrectangular tank. Ocean Engineering 29, 2002, pp. 1527–1553.

– For sloshing in space:W. Teichert and M. Klein. The dynamic behaviour of fluids in microgravity. ESABulletin 85, February 1996. Available at:http://esapub.esrin.esa.it/bulletin/bullet85/klein85.htm

P.J. Enright and E.C. Wong. Propellant slosh models for the Cassini spacecraft.Paper AIAA-94-3730-C, 1994. Copy available from the docent.H.N. Abramson. The dynamic behaviour of liquids in moving containers, NASA SP-106, 1966. In particular Chapter 11.4 “Low-g sloshing and some related problems.”Copy (of reprinted version) available from the docent.A.E.P. Veldman, J. Gerrits, R. Luppes, J.A. Helder and J.P.B Vreeburg. The numer-ical simulation of liquid sloshing on board spacecraft. J. Comput. Phys. 224, 2007,pp. 82–99.

– For tuned liquid dampers (TLD):D. Reed, J. Yu, H. Yeh and S. Gardarsson. Investigation of tuned liquid dampersunder large amplitude excitation. J. Engineering Mechanics 124 (4), 1998, pp. 405–413.S. Gardarsson, H. Yeh and D. Reed. Behaviour of sloped-bottom tuned liquiddampers. J. Engineering Mechanics 127 (3), 2001, pp. 266–271.D.E. Olson and D.A. Reed. A nonlinear numerical model of the sloped bottom tunedliquid damper. In: 8th ASCE Speciality Conference of Probabilistic Mechanics andStructural Reliability, paper PMC2000-030. Downloadable from:www.usc.edu/dept/civil eng/johnsone/pmc2000/sessions/papers/p030.pdf

– For road/railway vehicle dynamics:University of Michigan Transportation Research Institute (UMTRI). Rollover of heavycommercial vehicles. UMTRI Research Review 31 (4), October-December 2000, pp.1–20. Downloadable from: www.umtri.umich.edu/content/rr31 4.pdf.

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I.M. Ibrahim, M.A. El-Nashar and Y.K. Younes. Ride behaviour of trucks transport-ing liquids. Int. J. Vehicle Design 5 (3/4), 1998, pp. 261–276. Copy available fromthe docent.S. Aliabadi, A. Johnson and J. Abedi. Comparison of finite element and pendulummodels for simulation of sloshing. Computers and Fluids 32, 2003, pp. 535–545.

The referred journals (and many more) are on-line available throughwww.rug.nl/bibliotheek/catalogibestanden/elektijdschr/ejournalsoverzichtalf.

• A global theoretical background on simulation methods for free-surface flow can be foundin chapter 5 of the outdated (Dutch) lecture notes “Numerieke Stromingsleer”. As thesenotes are no longer available, this chapter will be handed out.

• The in-house-developed computation method ComFlo for the simulation of free-surfaceflow, including documentation, will be made available. The input file provided correspondswith Test 1.1 of Cariou and Casella (1999).

• Examples of calculations with ComFlo, and its two-dimensional predecessor Savof96,can be found at our website www.math.rug.nl/∼veldman/cfd-gallery.html

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