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 …
Category Archives: Turbulence
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 …
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 …
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 …
Continue reading “Baldwin Barth One-Equation Model Reviewed”
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 …
Continue reading “Reflections on Spalart-Allmarus Turbulence Model, 2024”
Returning to Ludwig Prandtl’s One-Equation Model
In my turbulence class this semester, I recently reviewed Prandtl’s one-equation model, which was developed over 20 years since the time of boundary theory in the early 1900s. The major paper by Ludwig Prandtl was published in the early 1940s. He presented the first one-equation turbulence model for the closure of the boundary layer equations, …
Continue reading “Returning to Ludwig Prandtl’s One-Equation Model”
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 …
Continue reading “Additional Thoughts on Half-Equation Model of Johnson and King”