Diatomite Filter Aid Kiln - 2D Rotary Kiln Section and Temperature Profiles

Controls

Live readouts

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Numerical check

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Performance graph

How to use

A longitudinal section through a rotary kiln that dries and heats a mineral powder (diatomite-type filter aid). Wet solids enter at the left and move toward the burner end on the right as the tilted drum turns; hot gas flows the opposite way. The shell colour shows the solid temperature, the dashed line marks where the moisture has gone and the graph below shows solid temperature (orange), gas temperature (blue) and the water still left (green).

Try: raise the feed moisture and watch the flat 100 C drying zone grow and push the heating zone toward the burner; increase the slope or the speed to cut residence time; reduce the gas flow until the solids no longer reach their target; increase the shell loss coefficient and see the efficiency fall.

The science

Counter-current heat exchange. For solids heat-capacity flow C_s, gas C_g and transfer coefficient U over the bed contact area per metre P, the steady equations along the kiln areC_s dT_s/dx = U P (T_g - T_s), C_g dT_g/dx = U P (T_g - T_s) + U_loss pi D (T_g - T_amb)(gas flows toward smaller x). With no losses and no water this has the closed epsilon-NTU solution epsilon = (1 - e^{-NTU(1-C_r)}) / (1 - C_r e^{-NTU(1-C_r)}), NTU = U P L / C_min, which the page checks against the numerical result.

Drying. While free water is present the solid stays at 100 C and all heat goes to evaporation, dm/dx = U P (T_g - 100)/h_fg with h_fg = 2.257 MJ/kg; the solid cannot heat further until it is dry, so wetter feed needs a longer drying zone.

Residence time. The empirical Friedman-Marshall correlation for a plain rotary kiln gives tau = 0.23 L / (S N^0.9 D) minutes, with L and D in metres, slope S as a fraction and speed N in rpm: halving the slope or speed doubles the time in the kiln.

Simplified: steady state only, a 1D plug-flow model, constant specific heats (950 J/kg/K solids, 1150 J/kg/K gas), a fixed contact area (55 percent of the circumference), no radiation, no dust entrainment, no chemical reactions of the mineral (organic burn-off and calcination are not modelled), and no air ingress. The numbers show how the heat is distributed, not the design of a particular kiln.

Keyboard, touch and accessibility

Space pauses or resumes the simulation.
R resets it to its initial state.
C re-runs the numerical check.
All sliders are native range inputs and work with arrow keys, Home and End; on touch devices drag on the canvas where the sim supports pointer input.
Rendering is capped at a device pixel ratio of 2 so phones stay smooth; the frame-time graph above shows the cost of the current settings (green line is 16.7 ms, i.e. 60 frames per second).

What is checked and why you can trust it

Every time the page loads, and whenever you press Re-run check, the simulation evaluates its own mathematics against an independent reference, such as a closed-form formula, a finite-difference derivative or an exhaustive count. Each line above reports PASS or FAIL together with the measured numbers, so you can see by how much it agrees. Results are also published on window.__msChecks for automated testing. The check never uses the same code path as the animation it validates, otherwise it would only confirm itself.

How to read a failure: a FAIL line means the measured discrepancy exceeded the stated tolerance for the current slider values. Try Reset, then move the sliders back toward their defaults; if a check still fails at the defaults it is a bug worth reporting. Tolerances are chosen from the numerical method itself, never tuned to make a test pass: round-off level (1e-9) for exact algebra, about 1e-3 for finite differences and Monte Carlo estimates with a few hundred thousand samples, and a documented margin for stochastic learning runs.

Reproducibility: the particle and pen simulations use the browser random generator for initial positions, so exact pixels differ between visits, but the checks depend only on mathematics and not on those positions. Fixed wave tables (curl noise) and fixed grammars (L-system) are deterministic.

This is an educational model. It shows the mechanism clearly, but it is deliberately simplified; the science panel lists what was left out.