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.
Dividing the Reverse Rate by Kp Split 99.6% of AlO at 2500 K — The (p°/RT)^Δn Hidden in the Equilibrium Constant
Plugging Kp into kr = kf/K skews the equilibrium of any reaction with Δn≠0 by (p°/RT)^Δn. An AlO dissociation reactor reproduces the SI and CGS versions of the mistake.
A 1 μm Aluminum Particle Heated 4.6× Slower Than the Continuum Formula — Sherman Interpolation in the Knudsen Transition Regime
At 1500 K and 1 atm a 1 μm aluminum particle sits at Kn = 0.67. Nu = 2 shortens heat-up by 4.58; Sherman's harmonic mean puts that time back.
Cutting Distance Checks 574x Lost 104 Contacts — One Grain Sets the DEM Sector Size
Sector pruning in DEM neighbor search is only safe when shell·s exceeds d_max, and 2400 agglomerating grains show exactly what a shorter reach costs.
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.
Giving every species its own tau threw the total mass off by 16.8% — correction velocity in multicomponent LBM
Different taus make Fick fluxes miss zero. Over 2000 steps a three-species LBM drops the worst mass defect from 0.168 to 0.0005.
202x More Scalar Dissipation, 13% Less Temperature — Where a Laminar Flamelet Quenches
Scalar dissipation rose 202-fold while peak temperature fell only 13%, then the burning solution vanished. Python pins that quench limit.
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.