ISO 20414 Test 18: walking speed in smoke

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What is tested

Whether smoke slows an occupant by exactly the factor the smoke-speed law gives, and whether that slower speed really changes the egress time. A factor that is computed but never applied, applied to the wrong speed, or applied twice, changes the egress time. In the FDS case, a wrong slice, quantity, height or position lookup changes the K the occupant sees.

Equation

Frantzich and Nilsson fitted \(v = \alpha + \beta K\) to 32 walks in a lit smoke tunnel (Lund report 3126, Eq. 3, App. D, Table D2, model 1), with α = 0.706 m/s and β = −0.057 m²/s (standard errors 0.069 and 0.015); see Fundamentals › Walking speed. FDS+Evac divides by α to make it a factor of the unimpeded speed and adds a floor of 0.1. That is the default law (lund) of pyFDS-Evac (Models › Smoke-speed). It turns the extinction coefficient K [1/m] into a speed factor f [-]:

The walking speed is \(v = f(K)\,v_0\), with \(v_0\) [m/s] the unimpeded speed. In a corridor where K is the same everywhere, the occupant walks the same distance at \(f v_0\) instead of \(v_0\), so ISO 20414’s expected result is

Here the egress time t is the simulated time at which the occupant is removed at the exit (run.log, “Simulation finished in”).

For the FDS case the deck prescribes a soot mass fraction \(Y_s\), and FDS computes \(K = K_m\,\rho\,Y_s\) with the mass extinction coefficient \(K_m = 8700\) m²/kg and the gas density ρ [kg/m³].

Setup

• Corridor: ISO 20414 Table 21, 100 × 2 m, with an exit zone of 1 × 0.92 m at the far end. One occupant, \(v_0\) = 1.25 m/s, seed 420, so it starts at the same point in the clear and the smoky run. It starts at x = −49.53 m and is removed at x ≈ 49.0 m, once its centre comes within 0.03 m of the exit zone (direct_steering_runtime.py). So it walks about 98.5 m, not 100 m. The seed fixes the target point it heads for, so the path is the same in the clear and the smoky run. ISO’s absolute time depends on that distance, so the page predicts each smoky time from clear runs of the same layout. ISO leaves the quantitative method to the tester.
• Constant K (assets/ISO-table21, social force model): K = 0.5, 1, 3, 7.5 and 10 1/m, as in ISO’s Table 21, and at K = 1 also \(v_0\) = 1.0, 0.75, 0.5 and 0.25 m/s. Each smoky run has its own clear run.
• FDS (assets/iso_table21_coupled, collision-free speed model): the corridor filled with soot at \(Y_s = 9.546\times10^{-5}\), no fire, one mesh with 0.5 m cells. Slices of K at 2.0 m and at 1.6 m, which FDS writes at 1.5 m. The occupant reads the 1.5 m slice, nearest the default sampling height of 1.6 m.
• Runs: run.py with a smoke update every 0.1 s and a time step of 0.01 s. Rerouting is off; irritant slowing (FIC) and incapacitation are off (--disable-tenability), as ISO asks: visibility only. 16 runs in all.

Expected

A smoky run at K and \(v_0\) is a clear run at desired speed \(f v_0\): the law only scales the desired speed. So the clear runs of the \(v_0\) sweep give the expected smoky time, start-up included.

Our inference for the slices: FDS’s density falls with height by \(\rho g z / p\). That predicts 1.74 × 10⁻⁴ below the deck’s value at 1.5 m and 2.32 × 10⁻⁴ at 2.0 m; the slices lie 1.70 × 10⁻⁴ and 2.27 × 10⁻⁴ below. The deck aimed at K = 1.0 1/m with 1.2041 kg/m³, the density of dry air (28.96 g/mol). Its background has no argon, so its molar mass and density are 0.43 % lower. That, plus the hydrostatic drop, and not a coupling error, is the gap to 0.9955.

Result

Every run records the factor of the law, and the occupant walks at that speed. Over the middle 40 m of the corridor, the speed along its path matches \(f v_0\) to 9.8 × 10⁻⁶.

The simulated ratio is always a little below 1/f, by up to 0.59 % at K = 10. That is the start-up time a: it does not scale with 1/f, so \(t_{\mathrm{smoke}}/t_{\mathrm{clear}} \cdot f - 1 = -a(1-f)/t_{\mathrm{clear}}\), which predicts −0.60 % at K = 10. Once a is taken from the clear runs, each egress time matches to 22 ms. The collision-free model in the FDS case has no start-up and matches the ratio to 6 × 10⁻⁵.

Both laws on the standard’s grid

Table 21 asks for the correlation the model uses, repeated over a range of unimpeded speeds and extinction coefficients, with 1.0, 0.75, 0.5 and 0.25 m/s and K = 10, 7.5, 3.0 and 0.5 1/m as examples. pyFDS-Evac ships two laws, and Ronchi et al. (2013) showed that results depend on which smoke–speed data a model uses, so both are checked (#841).

The Fridolf law

speed_law="fridolf" (Python only) uses Fridolf, Ronchi, Nilsson and Frantzich (2019, Eq. 7; Fundamentals › Walking speed), with \(w\) [m/s] the walking speed, \(w_{\mathrm{free}}\) the unimpeded speed and x [m] the visibility:

The reduction is additive: 0.34 m/s per metre of visibility below 3 m, the same for everyone. The floor is an absolute 0.2 m/s, not a fraction of \(w_{\mathrm{free}}\); it never lifts a walker above \(w_{\mathrm{free}}\), so a 0.25 m/s walker in dense smoke has \(f = 0.2/0.25 = 0.8\). Unlike the Lund factor, this factor depends on \(w_{\mathrm{free}}\).

The visibility constant. K is turned into a visibility by Jin’s relation \(x = A/K\), the paper’s Eq. 1 (Fridolf et al. 2019). pyFDS-Evac uses \(A = 2\), the paper’s value for light-reflecting items: the walls, obstacles and surroundings a walker must see (SmokeSpeedConfig.visibility_factor_c, which holds the paper’s A). The paper uses \(A = 8\) for light-emitting items; set visibility_factor_c = 8 for those. The 2018 extended abstract gives no constant. Before, the FDS convention \(C = 3\) was the default, which is not the paper’s: the knee \(x = 3\) m was at \(K = 1\) 1/m, against 0.67 for \(A = 2\) and 2.67 for \(A = 8\), so agents slowed later and less than the calibration. The grid’s smallest K, 0.5 1/m, gives \(x = 4\) m and so no slowing at all under this law. The tests also check \(C = 3\) and \(A = 8\) as configured values.

Hand calculation

\(w\) with \(A = 2\), by hand from the equation above (\(x\) = 0.2, 0.2667, 0.6667 and 4 m for K = 10, 7.5, 3 and 0.5 1/m; the drop is 0.952, 0.9293, 0.7933 and 0 m/s). “floor” means the unfloored value is below 0.2 m/s. The Lund column is \(f(K) = 1 - 0.0807\,K\), the same for every \(w_{\mathrm{free}}\).

The Lund floor is not reached in the grid: \(f = 0.1\) starts at \(K = 0.9 \times 0.706 / 0.057 = 11.147\) 1/m, which the tests check separately at 11, 11.147, 12 and 100 1/m. In the Fridolf law the floor decides 11 of the 16 grid cells, 4 are unaffected (K = 0.5) and only one (\(w_{\mathrm{free}}\) = 1.0, K = 3) is on the slope, 0.0067 m/s above the floor. The 1.25 m/s column is added because it is the corridor’s own unimpeded speed and the only one where the slope shows at K = 7.5 and 10. For \(w_{\mathrm{free}}\) = 1.0 the unfloored values are 0.0707 and 0.048 m/s there.

What CI runs

tests/test_iso_test_18_speed_laws.py, marker iso20414, about 25 s:

• All 16 grid cells, both laws, on the model’s speed factor and speed. The expected values are the hand-written ones above, not the code’s own function (#259). It also checks the 1.25 m/s column, the floor edges of both laws, the knee at \(x = 3\) m, and \(C = 3\) and \(A = 8\).
• Ten corridor runs (100 × 2 m, 1 m exit, one occupant, social force model, seed 420, constant K, update every 0.1 s). The expected egress time is the clear time of the same occupant plus \(L\,(1/w - 1/w_{\mathrm{free}})\), with \(w\) by hand and \(L\) = 98.321 m, the walked length fitted on this page. Each run also checks the recorded K, the base speed, the desired speed and the factor at every update.

The three floored Fridolf runs at \(w_{\mathrm{free}}\) = 1.0, 0.5 and 0.25 m/s all reach the exit at 492.17 s: the floor is an absolute speed. The tolerance is 2 time steps of 0.01 s (the clear and the smoky time are each a whole number of steps), the clear-run fit’s largest residual of 0.016 s, and an assumed 0.01 m error in \(L\) times \(|1/w - 1/w_{\mathrm{free}}|\). The clear times are from runs of the same layout: 79.24, 98.91, 131.69, 197.25 and 393.87 s for 1.25 to 0.25 m/s.

The other grid cells are checked on the speed only. The Lund law’s K sweep at 1.25 m/s and its \(w_{\mathrm{free}}\) sweep at K = 1 are the runs earlier on this page. Lund at 0.25 m/s and K = 10 (0.048 m/s, about 2000 s) is not run in a corridor.

Pass criteria

1. Factor. The recorded factor equals f(K) by hand to round-off, ≤ 10⁻¹². For the FDS case, the recorded K lies within the 1.5 m slice’s range and outside the 2.0 m slice’s range, and the factor within f of the 1.5 m range. The two ranges are 4.5 × 10⁻⁵ apart, almost four times the spread within one.
2. Speed. The speed along the path over the middle 40 m equals \(f v_0\) within 10⁻⁵. This tolerance is a margin, not derived. The collision-free model walks exactly at \(f v_0\); the social force model walks 2.2 to 9.8 × 10⁻⁶ slower, a property of the movement model. The smallest error the check must catch, a factor not applied at K = 0.5, is 1 − f = 4 %, four orders of magnitude larger.
3. Egress time. Each egress time is a whole number of time steps Δt = 0.01 s. For the social force runs, \(|t_{\mathrm{smoke}} - t_{\mathrm{pred}}| \le r_{\max} + 2\,\Delta t\) = 0.036 s. The clear fit’s largest residual \(r_{\max}\) = 0.016 s covers the fit’s misfit; one Δt is the rounding of the smoky time, one the rounding in the fitted line. For the FDS case, \(|t_{\mathrm{smoke}} - t_{\mathrm{clear}}/f| \le (1 + 1/f)\,\Delta t\) = 0.021 s: the clear time’s rounding, scaled by 1/f, plus the smoky time’s. The expected time uses no smoky run. Two runs lie just outside the clear runs’ speed range (0.25 to 1.25 m/s): K = 10 at 1.25 m/s (\(f v_0\) = 0.241 m/s) and K = 1 at 0.25 m/s (0.230 m/s). Their predictions are small extrapolations; both pass.

The pytest tests ask for less: the ratio within 8 %, and the factor equal to six decimals (#259).

Run it yourself

The tests of the first two cases run in about 20 s. They are weaker than this page: the coupled test reads the 2.0 m slice, not the 1.5 m slice the default height picks; both compute the expected factor with the code’s own function; and the time ratio passes within 8 % (#259):

uv run pytest tests/test_smoke_speed.py -k iso_table21 tests/test_iso_table21_coupled.py tests/test_iso_test_18_speed_laws.py

For the figures, run the 16 cases with run.py. The FDS output is committed in assets/iso_table21_coupled/fds/; to rebuild it, run uv run python assets/iso_table21_coupled/build_geometry.py and then fds iso_table21_coupled.fds (about 10 s). assets/ISO-table21 stops at 300 s, too early for K = 10 and for \(v_0\) = 0.25 m/s, so the constant-K runs use a copy with 600 s:

OUT=<out>
run() {  # name scenario [extra options]
  name=$1 scen=$2; shift 2
  mkdir -p $OUT/evac/$name
  uv run python run.py --scenario $scen --seed 420 --smoke-update-interval 0.1 \
    --no-enable-rerouting --disable-tenability "$@" \
    --output-sqlite $OUT/evac/$name/run.sqlite \
    --output-smoke-history $OUT/evac/$name/smoke_history.csv > $OUT/evac/$name/run.log
}
for v in 1.25 1 0.75 0.5 0.25; do
  d=$OUT/scenarios/v0_$v; mkdir -p $d; cp assets/ISO-table21/geometry.wkt $d/
  uv run python -c "import json,sys; c=json.load(open('assets/ISO-table21/config.json')); \
c['config']['simulation_settings']['simulationParams']['max_simulation_time']=600; \
[d['parameters'].update(v0=float(sys.argv[1])) for d in c['distributions'].values()]; \
json.dump(c, open(sys.argv[2]+'/config.json','w'), indent=2)" $v $d
done
run clear $OUT/scenarios/v0_1.25
for K in 0.5 1 3 7.5 10; do run K$K $OUT/scenarios/v0_1.25 --constant-extinction $K; done
for v in 1 0.75 0.5 0.25; do
  run v0_${v}_clear $OUT/scenarios/v0_$v
  run v0_${v}_K1 $OUT/scenarios/v0_$v --constant-extinction 1
done
cp -R assets/iso_table21_coupled/fds $OUT/fds
run coupled_clear assets/iso_table21_coupled/config.json
run coupled_fds assets/iso_table21_coupled/config.json --fds-dir $OUT/fds
uv run python scripts/verification/iso_test_18_figures.py --data $OUT

The script prints the table above, writes the figures, and exits with an error if a pass criterion fails. The runs behind this page, made on the branch of #401 at 8fc26b1 with a clean tree, give this table. The same commands on main at 9c820e0f (Python 3.12.13) print the same table and figures.

Limits

• The Fridolf law is run in the same corridor (see above) with constant K only, not K from FDS. The S2 corridor test also checks it. The hand calculation checks the code against Eq. 7 as printed in the paper (p. 38): form, slope 0.34, threshold 3 m and floor 0.2 m/s match. It checks the equation, not the paper’s data. The paper converts extinction to visibility with \(A\) = 2 (light-reflecting) or 8 (light-emitting); the default is \(A\) = 2. The tests do not check which of the two a given scene needs.
• K = 0.5, 1 and 10 1/m lie outside the tunnel data (about 1.9 to 7.4 1/m, the range given on the Fundamentals page; the report’s text says about 2 to 7 1/m). Passing Test 18 verifies the code, not the law, there.
• The FDS case confirms that the slice nearest 1.6 m is read. The two slices differ by only 6 × 10⁻⁵ 1/m, from hydrostatics. The test cannot show sampling in a real vertical or horizontal gradient, or at the occupant’s current position and time (#24).
• No run reaches the floor f = 0.1 (K ≥ 11.15 1/m).
• In the social force runs the occupant spawns 0.47 m from the back wall. The wall push briefly takes it above \(f v_0\) at the start (0.34 m/s at K = 10, against 0.24 m/s). This is movement-model behaviour; the time criterion absorbs it through the start-up time a of the clear runs.
• One occupant per condition, one seed. The ISO test asks for no more, but it says nothing about crowds in smoke.
• The tight criteria on this page are checked by the figure script on stored output. CI checks the time ratio within 8 %, reads the 2.0 m slice in the coupled test, and takes the expected factor from the code under test (#259).
• assets/ISO-table21/ISO-table21.fds is a template deck with a fire; no test and no run on this page uses it.