The Computational Fluid Dynamics (CFD) code, ‘BlackJack,’ was created with a singular purpose: to generate extremely accurate numerical solutions of the Navier-Stokes equations in support of a broader program to develop new analytical solutions to those same equations. Unlike general-purpose CFD tools designed for industrial applications or engineering approximations, BlackJack CFD is a research code, …
Category Archives: Research
Framework for Analytical Solutions of the Navier-Stokes Equations for Hyperbolic Boundary Value Problems in the Aerodynamic Near-Field
Abstract: A framework to create new specific analytical solutions of the equations of motion for hyperbolic boundary value problems is presented. The method relies on a closed-form integral equation for mass density, involving a term that combines sources, geometry, ambient values, and radiation. Products of the density integral result in new more complicated solutions. The …
A Possible High-Re Liquid He Experiment
I wrote about this experiment and discussed it with funding agencies long ago and just wanted to post the idea. I am exploring the possibility of conducting high-Reynolds number turbulence experiments. One experiment would involve constructing a large isolated vessel filled with liquid helium to create fully developed, spatially localized high-Re flow through transient forcing …
Hypersonics History of Reentry
Lately, I have been examining the entire history of hypersonics research and technology, with a particular focus on the re-entry problem and ablation for small vehicles, such as those from ballistic missiles. While reviewing the writings of Wernher von Braun, I was amused to find that he joked about using frozen balsa wood as a …
Kelly Johnson on X-Plane Programs
Our present research airplanes have developed startling performance only by the use of rocket engines and flying essentially in a vacuum. Testing airplanes designed for transonic flight speeds at Mach numbers between 2 and 3 has proven, mainly, the bravery of the test pilots and the fact that where there is no drag, the rocket …
Navier-Stokes Equations and Practicality
Because an effort is likely impossible and impractical does not mean it is not worth attempting. The Navier-Stokes equations and turbulent flow represent the last great classical problem in physics. Since the time of Leonard Euler and Jean-Baptiste le Rond d’Alembert, many have devoted much of their lives to working on these problems. Although they …
Reflections on Spalart-Allmarus Turbulence Model, 2024
The Spalart-Allmaras turbulence model, a one-equation turbulence model, was a response to the inadequacies observed in zero-equation models, particularly their lack of predictive accuracy in complex flow scenarios such as wakes, shear layers, and shock wave boundary layer interactions. The creation of the Spalart-Allmaras model was influenced by multiple prior works, including the Baldwin Barth …
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AIAA Journal – Fully Parabolized Hypersonic Sonic Boom Prediction with Real Gas and Viscous Effects
https://doi.org/10.2514/1.J063425 Abstract: We present a methodology to predict the aerodynamic near-field and sonic boom signature from slender bodies and waveriders using a fully parabolized approach. We solve the parabolized Navier–Stokes equations, which are integrated via spatial marching in the streamwise direction. We find that unique physics must be accounted for in the hypersonic regime relative …
Additional Thoughts on Half-Equation Model of Johnson and King
The Johnson King turbulence model represented a significant advancement in the understanding and modeling of turbulent flows. Introduced amidst the exploration of first and second equation models, the Johnson King model distinguished itself through the innovative concept of a half-equation model, emphasizing the critical role of memory in turbulence phenomena. The early stages of turbulence …
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Analytical Closed-Form Solution of the Navier-Stokes Equations for the Aerodynamic Near-field and Sonic Boom from Axisymmetric Bodies
I completed my Acoustical Society work and returned to the United States. Abstract: An analytical closed-form solution is presented for the aerodynamic near-field and ground signature from an axisymmetric body with a low thickness ratio. The Navier-Stokes equations are formulated as a boundary value problem that incorporates the incoming ambient flow-field and the aerodynamic properties …