Computational Fluid Dynamics of the World's Largest Airplane: Stratolaunch

For some time now, I have been fascinated with Computational Fluid Dynamics (CFD) in Physics. Some of the concepts underpinning CFD are not unlike modern machine learning (ML). Both seek solutions to problems which are intractable in analytic form, so called NP-Complete problems. NP-complete problems are often addressed through approximation, heuristics and convergence. Indeed, the list of problem domains of the leading open source CFD tool (OpenFoam) is incredible diverse and ranges from modelling how fires spread through buildings, how wind flows through a city-scape, how to price financial options and modelling the effects of supersonic flight.

When it was announced that Stratolaunch, the plane with the largest wingspan in the world, had taken flight in the Mojave desert of California, a plane wider than a football field, and whose purpose it is to deliver payloads to space, I was wondering what kind of stresses, turbulence and pressures would be created by taking a behemoth such as this to the skies. After all, the Stratolaunch is designed to take 250-ton rocket ships at a height of 35,000 feet into the stratosphere. The plane might best be described as an airborne launchpad for spaceflight, a sort of "Cape Canaveral in the Sky."

Stratolaunch was founded by the late Microsoft co-founder Paul G. Allen. The company is impressive in other ways: it builds jet engines which are 85% 3D printed.

Not being able to witness the maiden flight personally, I had to simulate this. To this end, I obtained a 3 dimensional CAD model from the internet. Included in the model is a simulated payload.

The first step in preparing a CAD model for CFD simulation is to create a watertight "manifold geometry." 3D printing and CFD have this requirement in common. A non-manifold geometry would be a geometry which cannot exist in the real world, e.g. one with unsupported parts. The geometry is then rendered into a mesh, imported into OpenFoam where it is placed into a wind tunnel and the appropriate solvers are run to determine turbulence, surface pressure and flow velocities. Optionally, streamlines are added for visualisation which depict the flow of air around the body of the aircraft.

Below are the results obtained by running OpenFoam on the resulting Stratolaunch geometry. Simulation speed was 198 MPH.

The above visualisation depicts pressure P across the surface of the aircraft.

The above visualisation depicts turbulence kinematic energy across the surface of the aircraft.

The above visualisation depicts flow velocity across the surface of the aircraft. Force coefficients such as lift and drag are modelled in a like manner (elided here).

Up Next: Resurrecting the Lippisch P13a, an experimental ramjet-powered delta wing interceptor aircraft designed in late 1944 by Dr. Alexander Martin Lippisch.

The Lippisch P13a never made it past the drawing board, but testing of wind tunnel models showed that the design had extraordinary stability into the Mach 2.6 range. Dr. Lippisch was a "wing specialist." Indeed, his designs were said to be little more than wings and anticipated both the delta shaped wing designs used by modern aircraft such as the B2 stealth bomber as well as modern hypersonic glide vehicles. Crucially, Lippisch was the mentor and friend of Beverley Shenstone, the designer of the most elegant airplane to ever grace the skies: The Spitfire. What set the Spitfire apart was it's elliptical wing design.

German wing design, 1918, by Ludwig Prandtl with the characteristic two-half ellipse design which subsequently emerged in the Supermarine Spitfire.

Stay tuned for: "Resurrecting a Ramjet."