A ramjet is a form of air-breathing jet engine that uses the engine’s forward motion to compress incoming air without a built-in compressor. The air is simply “rammed” in. A typical ramjet works most efficiently at supersonic speeds around Mach 3 (2,300 mph). A Scramjet is a variant of a ramjet. Ramjets and scramjets differentiate one another by the speed of airflow through combustion chamber – sub (ram) or supersonic (scram).
My desire to write about the Lippisch P13a was motivated by a fascination with the Supermarine Spitfire. The Spitfire’s principal designer, Beverley Strahan Shenstone was a former employee of the aircraft firm Junkers in Dessau, Germany. The company would in due time be known mostly for its “Stuka” (from Sturzkampfflugzeug, “dive bomber”). While in Dessau, Shenstone befriended Dr. Alexander Lippisch, a formidable aircraft wing designer. Lippisch would, after the war, move to the United States under Operation Paperclip. Operation Paperclip saw more than 1,600 German scientists, engineers, and technicians, such as Werner von Braun and his V-2 rocket team taken from Germany to America for U.S. government employment.
Dr. Lippisch never built his futuristic ramjet, but his work on wings inspired Shenstone who would return to England and build the Spitfire. The friendship between Lippisch and Shenstone was said to be lifelong. See The Spitfire Wing Planform: A Suggestion (read planform, not platform). The iconic wing design dates back to Professor Ludwig Prandtl.
German wing design, first in 1918 and later 1931 & 1934, by Ludwig Prandtl
The characteristic design is the two-half ellipse which subsequently emerged in the Spitfire.
The Spitfire would go on to win the Battle of Britain, while the Lippisch was never built. Intriguingly, the Lippisch was intended to be coal fired. This article documents the effort to bring the concept fighter to life in an OpenFOAM Computational Fluid Dynamics (CFD) simulation — without the coal. When we speak of “fluid” in this context, we mean air.
Because a pure ramjet relies on input airflow at high speed and is unable to generate thrust from standstill, the design relies on assisted takeoff as shown below.
We begin with a high quality “Wavefront” CAD rendering of the aircraft that has 130,834 vertices and 261,764 patch faces.
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.
Mesh generation is a science of its own. It is also idiomatically similar to modern machine learning. A neural network may be said to be a universal function approximator which takes a finite set of input vectors and tries to probabilistically approximate those data points in the domain which are as yet unseen. A mesh generator does something similar. It receives a finite set of input vectors and approximates a 3D surface – as might a neural network tensor of rank 3. Like the neural network, the mesh generator is subject to “hyper parameters” which are orthogonal to the training data. The mesh generator’s job: derive a continuous surface from data points — not unlike a neural network regressor might do.
In our simulation, there are in excess of 70 mesh parameters to produce a high fidelity simulation.
Our simulation was run at Mach 1.3. This gives rise to an astounding computational complexity. Consider that each cell shown in the block above is part of a calculation. In our case, the flow of air as a “fluid” must be tracked through each cell at Mach 1.3 — even cells not occupied by the aircraft. Air as a “fluid” is compressible but the flow itself is not — up to approximately Mach 0.3. In the vicinity of the aircraft cell resolution is increased in what is known as “a refinement region.”
The above shows the refinement region inscribed within the wind tunnel. At present, simulation has 659,658 cells; 2,146,768 faces; and 837,805 points. However, the Lippisch P13a has a wingspan of a mere 6 meters. The Stratolaunch, by contrast, has a wingspan of 117 meters…
… the appropriate compute power is network cluster.
Finally, computational fluid dynamic 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.
Knowing what is required to obtain the images below, gives rise to their appreciation.
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 (not shown here).
Besides visualising turbulence, pressure and other parameters, we can also undertake other interesting analyses. For instance, we might cross-cut the model in “pressure view” longitudinally – snip.
This reveals the pressure path through the combustion chamber:
We may also conduct analyses of lift and drag. These are constructed by extracting the surface normals of pressure in the relevant direction ( lift on the z-axis and drag on the x-axis ) and integrating over the entire surface of the aircraft.
Pressure here is expressed as “kinematic pressure” which is pressure normalised for the quantity “rho” (fluid density). We immediately note that lift is negative which is to say the craft would have generated no aerodynamic lift and therefore ostensibly had to rely solely on a combination of thrust and steering. Outside of that, she simply would not fly.
She never flew — except virtually here today!
Epilogue
And finally, this article would not be complete without the most elegant airplane to ever grace the skies: The Spitfire.
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