UCT researcher takes cryogenic breakthrough to NASA Glenn

When aerospace engineers talk about the future of flight, liquid hydrogen (LH₂) is often part of the conversation. It is lightweight, energy-dense and carbon-free at the point of use. But storing and controlling it inside aircraft and spacecraft tanks is anything but simple.

However, designing the next generation LH₂ tanks and control system requires accurate computer-based modelling. Though computational fluid dynamics (CFD) software has the potential to offer this, existing codes are computationally very slow.

On 24 February, a team of 12 CFD experts and users at the NASA Glenn Research Center heard how a team led by Professor Arnaud Malan of the University of Cape Town (UCT) is tackling that complexity head-on. Their new CFD software, AlphaFlow, now models LH2 tanks up to 40 times faster than conventional approaches, which is a gamechanger for the industry. AlphaFlow is the result of the public–private partnership between Professor Malan’s SARChI Chair in Industrial CFD and the UCT spin-off company Elemental Numerics.

The seminar was organised by Professor Mohammad Kassemi, who is the director of the National Center for Space Exploration Research (NCSER) at the NASA Glenn Research Center & Case Western Reserve University. It focused on recent advances in high-fidelity modelling of heat and mass transfer in cryogenic tanks – the ultra-cold vessels used to store LH₂.

“You’ve got these equations fighting each other all the time.”

“It’s a huge privilege for me to represent my team here,” Malan told the online audience. “We’ve learned a lot from your work with your colleagues at Glenn Research Center.”

Inside a liquid hydrogen tank, physics unfolds at multiple scales at once. The liquid and vapour phases interact across a constantly moving interface. Pressure and temperature are tightly coupled. Turbulence can be extreme. Phase change – evaporation and condensation – alters mass and energy in real time.

“So, in our case, we do need to know precisely where the interface is,” Malan explained. Unlike many other engineering applications, where small positional errors may be tolerable, here even minor inaccuracies can distort pressure predictions and heat transfer.

Traditional CFD tools often struggle with this coupling. “You’ve got these equations fighting each other all the time,” he said, referring to standard formulations where gas energy and pressure equations can compete numerically.

His team’s response has been to rethink the governing equations themselves.

Separating thermodynamics from rate

One of the key conceptual paradigm shifts in their framework is separating global thermodynamic behaviour from local rate processes.

As part of the CFD simulation, the software automatically creates pressure–temperature (P–T) diagrams using semi-analytical thermodynamic relations. These diagrams predict the direction the system will move – toward evaporation, condensation, or equilibrium. These semi-analytical models were the result of Dr Francesco Gambioli’s PhD research, with Malan and Professor Franco Mastroddi at Sapienza University in Rome serving as supervisors.

“We know already a priori, before the solving starts, what is actually going to happen,” Malan said. “We know: Are we going to have dominant evaporation? Condensation? Where are we going to go?”

The P–T paths, he noted, are often deceptively simple. “They don’t just appear to be straight lines. They are straight lines. Nature is trying to go from superheated to saturated in the shortest possible path. Our CFD is then used to compute how fast the system follows that thermodynamic path. And this is done with speed.”

“If you’re making a small error at every time step, within a million-time steps, it adds up.”

Cryogenic simulations can require hundreds of thousands – even millions – of time steps. Small numerical errors, if not limited, accumulate.

“If you’re making a small error at every time step, within a million-time steps, it adds up,” Malan warned.

His team strives to enforce both mass and energy conservation to machine precision – not only in space but in time. “Most people are only worried about the spatial term,” he said. “But you need to be worried about the temporal term as well.”

Without strict conservation, predicted pressure–temperature relationships drift away from physical reality.

Reformulating the equations

Rather than solving the liquid and gas energy equations directly, the team reformulated the problem around a nonlinear total-energy based equation that embeds thermodynamic consistency. When asked whether the energy equation was still being solved, Malan replied: “Everything. Everything is wrapped up and wrapped in.” This new governing equation was the result of the research of one of Malan’s PhD students, Yusufali Oomar, who has just submitted this thesis for examination and is already employed as a senior CFD engineer at Elemental Numerics.

The payoff of the new governing equation is computational speed.

In one active pressurisation case, modelling 423 seconds of tank behaviour took just 14 minutes. “That’s almost real-time computing right here,” he said. “If we had a factor of two, we’d be doing this in real time.”

Across benchmark cases, the solver achieved speedups of up to 40 times compared to established commercial tools.

“Once you’ve reconstructed your interfacial facet, it’s mass conservative.”

A major technical hurdle lies at the liquid–vapour interface, where phase change occurs. The team uses a sharp, mass-conservative reconstruction method to ensure that the interface is both geometrically accurate and thermodynamically consistent.

“Once you’ve reconstructed your interfacial facet, it’s mass conservative,” Malan explained. “That gives you a lot of robustness and accuracy.”

Saturation temperature is enforced at the interface – but not naively. “We never impose at a node,” he clarified. “We only impose at the interface facet.”

Simply forcing saturation everywhere would violate energy balance. “From an energy point of view, you can’t just impose a saturated condition at the interface. If you do that, you can start sucking out more energy than is there.”

Instead, saturation is embedded within a nonlinear implicit solve that ensures consistency between heat flux and phase change.

Validation tests, including a growing vapour bubble in a superheated liquid, showed second-order accuracy, with interface position errors dropping to about 1% under mesh refinement.

Turbulence, slosh and calibrated caps

The AlphaFlow software was also tested against NASA pressurisation and violent slosh experiments. In 3D slosh cases lasting 2.5 minutes, pressure evolution was predicted to 98% accuracy within 48 hours of compute time.

Turbulence modelling proved crucial. The team favours Large Eddy Simulation (LES) over RANS for multiphase flows.

“When it comes to volume-of-fluid and multiphase, don’t use RANS. RANS just hurts,” Malan said. “LES is far gentler – but you need to treat it with care.”

Although high-performance computing often focuses on GPUs, Malan emphasised algorithmic design.

“We don’t do any acceleration at the moment,” he said. “The pen is mightier than the sword. We’ve focused on the governing equations.”

“The pen is mightier than the sword. We’ve focused on the governing equations.”

Their solver uses provably stable discretisation rather than conventional CFD schemes to avoid artificial damping terms that distort energy spectra. “Our numerical discretisation scheme is provably stable,” he said.

Solid wall heat capacity is integrated analytically over time to avoid cumulative discretisation errors. “Discretisation adds little errors that are small at one time step, but a thousand-time steps later, they add up.”

The session closed with enthusiasm from NASA Glenn researchers, many of whom have worked on cryogenic modelling for decades.

“All of us are intrigued by the numerical efficiency,” one participant said. “We hope that we can learn from what you have done.”

Malan returned the compliment. “You guys are the stars internationally in this realm,” he said. “We come with a little different angle. But I’m hoping that we can join forces going forward.”

Professor Kassemi closed the seminar, expressing a keen interest in collaborating in future.

This work was supported by the DSI-NRF of South Africa, the European Union HASTA and by the Department of Trade and Industry.