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 …

# Category Archives: Fluid Dynamics

## 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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## 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 …

## Pendulum, Time, and Stokes’

In 1582, an observation by Galileo Galilei at the Pisa Cathedral marked an important moment in understanding of oscillatory motion. Galileo, noting the constant period of a swinging lamp despite diminishing amplitude, laid the foundation for the study of pendulums. This led to his discovery that a pendulum’s oscillation period is directly proportional to the …