I finally published my compressible flow notes online. They are under classes – comp. flow. They are the result of teaching the course over nine years at University of Florida. I compressed the file a bit to conserve my website bandwidth. Enjoy!
Category Archives: Fluid Dynamics
High-Order CFD for Validating Analytical Solution of the Navier-Stokes Equations – ‘BlackJack’
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, …
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 …
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 …
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 …
Madame Rousseau on d’Alembert
You will never be anything but a philosopher – and what is that but an ass who plagues himself all his life, that he may be talked about after he is dead. ~ Madame Rousseau on d’Alembert
Fechner-Weber
The Fechner-Weber law states that for a sensation’s intensity to increase in an arithmetic progression, the stimulus must increase in a geometric progression. This relation describes sensory perceptions and physical stimuli for hearing. Human hearing can detect noise so quiet that the eardrum moves less than an atom’s width, and noise 10 trillion times more …
Rodi and Algebraic Stress Models
Rodi examined nonlinear algebraic stress models by approximating the convective transport terms of the Reynolds stress tensor and normalizing Reynolds stress with turbulent kinetic energy, coupled with a transport equation for turbulent kinetic energy. This approach simplifies the Reynolds stress transport terms, resulting in an algebraic equation essential for determining the Reynolds stress tensor. This …
Saffman \(k-\omega^2\)
Saffman’s \(k-\omega^2\) turbulence model, initiated by Saffman’s research, plays a role in the two-equation models dedicated to turbulence research since the time of Kolmogorov in the 1940’s. The basics of Saffman’s model is shown in the portrayal of a statistically steady or ‘slowly varying’ inhomogeneous turbulence field alongside the mean velocity distribution. This model states …
Baldwin Barth One-Equation Model Reviewed
During the present semester, I reexamined the Baldwin-Barth one-equation turbulence model. This model constitutes a reformulation of the $k$ and $\epsilon$ equations, culminating in a single partial differential equation for the turbulent eddy viscosity, denoted as $\nu_t$, multiplied by the turbulent Reynolds number, $Re_t$. The model’s closure for the Reynolds-averaged Navier-Stokes (RANS) equations was a …
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