A Small Wobble in Mixture Fraction Drops the Mean Flame Temperature by 964 K — Presumed β-PDF and the Infinity at Z=0
At stoichiometric mean Z, the β-PDF mean temperature sits 964 K below T(Z̄). When a<1, a 100-cell uniform-grid integral also overshoots by 115 K. Here is why, with code.
One χ=50, two temperatures: 1759 K and 818 K — where a flamelet library folds
One χ=50 returns 1759 K and 818 K because the S-curve folds. A 61-point flamelet shows why a progress variable C makes that table single-valued.
2.0000 in laminar flow, 1.0322 in turbulent — the coefficient in front of the velocity head
A mean-velocity head is not the kinetic energy a pipe actually carries. Alpha is 2.0000 for laminar Poiseuille flow and 1.0322 at Re = 10^6.
49.9% of the Dynamic Coefficients Came Out Negative — the Germano Identity and the Averaging Operator
The Germano identity puts the Smagorinsky coefficient negative at half the points. Where the average is taken decides whether the run stays stable.
Where Turbulence Stops Speeding Up a Flame — Damköhler's Wrinkling Hypothesis and Bending
At u'/S_L = 12 the large-scale wrinkling factor stays near 4.03, while the small scale drops to 2.00 once Ka passes 29.
Turbulence Runs Three Rulers at Once — The Kolmogorov Cascade and the -5/3 Law
A tenfold rise in Reynolds shrinks η/L to about 0.18 of its value, and a lab tunnel at Re=10^4 already asks a 3D DNS for about 10^9 cells.
When the Stream Breaks — Reynolds' Critical Number and the Layered Turbulent Boundary
Pipe transition is usually quoted near Re 2300, yet a quiet pipe can stay laminar to 50,000. The wall then splits into sublayer, buffer, and log layer.
[OpenFOAM Tutorial] Backward Facing Step Flow Analysis — Capturing Recirculation Zones with simpleFoam
Scale 0.1 makes the step 0.1 m, while the viscosity note builds Re 1000 with H = 0.01 m. A 6–8H bubble then has two physical lengths.