The mathematical connection of fusion power and aerospace … · 2014. 10. 16. · Fusion is the process that powers the Sun. Fusion releases energy as a result of two light atoms

Fusion Energy Aerospace Engineering

The mathematical connection of fusionpower and aerospace engineering

Minh-Binh TRAN

Basque Center for Applied Mathematics, Spain

October 14, 2014

Fusion Energy Aerospace Engineering

Outline

1 Fusion Energy

2 Aerospace Engineering

Fusion Energy Aerospace Engineering

What is fusion?

Figure: Is this the Ford Fusion?

Fusion Energy Aerospace Engineering

What is fusion?

Figure: Is this the Gillette Fusion?

Fusion Energy Aerospace Engineering

What is fusion?

Figure: Sun

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Fusion Energy

Fusion is the process that powers the Sun.

Fusion releases energy as a result of two light atoms suchas hydrogen joining together to form a helium atom.

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It is fusion energy that makes all life on Earth possible.

Fusion Energy Aerospace Engineering

Fusion and Fission

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Fusion: the advantages

On Earth, the fuel for fusion reactors will be two forms(isotopes) of hydrogen gas: deuterium and tritium.If all the deuterium in one litre of water was fused withtritium it could produce as much electricity as burning 340litres of petrol!No transport of radioactive materials is needed for theday-to-day running of a fusion power plant.Fusion process will not create greenhouse gases orlong-lasting radioactive waste.

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How do we get controlled nuclear fusion?

Figure: Mr. Fusion Home Energy Reactor - Back to the Future(1985)?

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How do we get controlled nuclear fusion?

Figure: Terminator Skynet Global Digital Defense Network?

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Tokamak : a plasma heart

To produce fusion, tritium and deuterium must be heatedaround 100 million degree Celcius.At this high temperature −→ a plasma.Plasma is an ionised gas in which electrons are removedfrom gas atoms.The high-temperature plasma should be controlled in atokamak.

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Tokamak, a plasma heart

Figure: The Joint European Torus (JET), in the United Kingdom

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Landau kinetic equation

A kinetic equation for a weakly interacting gas: the transferequation of charged particles in a plasma with Coulombcollisions taken into account.Obtained by L.D. Landau.

Plasma spreads out and approaches an equilibrium state.People believed that this happened only because of thecollisions between atoms. However Landau argued thatthe plasma would converge toward equilibrium. Villanifinally proved Landau right.

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Hypersonic Aerodynamics

Hypersonic vehicles are commonplace: missiles, launchvehicles, etc.Technical problems of designing hypersonic vehicles

Temperature and aerodynamic heatingPressureBlunt shapesControl and stability issues lead to different shapesEngine-airframe Integration

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Temperature and aerodynamic heating

The X-15, the only real manned hypersonic airplane flown.The first flight, by Scott Crossfield, in June 1959.Crackling sounds in the airframe as it heated up.The shock interference heating was so severe that theshocks acted as a blowtorch.Internal damage to the airplane from the heating.

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Surface pressure

In many cases surface pressures are relatively easy to estimateat hypersonic speeds.

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Blunt shapes

Since round shapes have lots of drag, why do we see suchhighly rounded shapes? Answer: the heat transfer.We need the tip not to melt.

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Control and stability

The thick trailing edge on the vertical tail of the X-15.

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Engine-airframe Integration

Any air-breathing hypersonic vehicle will have a highlyintegrated engine and airframe.

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Roles of mathematics

Understanding rarefied gas effects in aerospace applications isimportant for an accurate calculation of the aerodynamiccoefficients during the early phase of the entry of a spacecapsule into a planetary atmosphere, prediction of the heat fluxduring entry and descent, and also a correct interpretation ofexperimental measurements.

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Boltzmann and Landau equations

Boltzmann equation

Landau equation

Fusion Energy Aerospace Engineering

THANK YOU FOR YOUR ATTENTION!