Splitter silencer designer

What this calculates

This implements the actual VDI 2081 Blatt 1 (2001-07) splitter-silencer correlation, Section 7.2.3.2 — an earlier version of this page used a general fluid-mechanics approximation instead, because the formula couldn't be verified against a source at the time. It's now checked against the fully worked numeric example in VDI 2081 Blatt 2 (2005-05), Table 1: for a splitter silencer with s=100 mm, d_k=200 mm, L=2.000 m, duct velocity v=4.94 m/s, the standard's own published result is Δp_t=145 Pa; this calculator reproduces 145.6 Pa (0.4% difference, within the rounding VDI 2081 itself documents for its tabulated examples) — and the flow-noise result below reproduces the standard's published 52 dB(A) to 0.02 dB.

v is the duct (approach) velocity, not the gap velocity — Equation 42's own symbol list defines it that way, and Section 7.2.3.2 doesn't redefine it, so it carries over unchanged. Using the gap velocity here instead was the exact mistake behind the earlier, abandoned reconstruction attempt. Coefficients a₁, a₂, b₁, b₂ are tabulated in VDI 2081-1 for exactly three curtain thicknesses (100/200/300 mm); this calculator linearly interpolates between the two bracketing rows for any other thickness you enter, and flags it when your thickness falls outside that 100–300 mm range entirely (the standard doesn't define coefficients beyond it).

The gap width is calculated automatically from duct width, splitter count and splitter thickness, following VDI 2081-1's own Bild 32 arrangement (half-width gaps at each duct wall, full-width gaps between interior splitters): for N splitters of thickness d_k, s = W/N − d_k — or you can override it directly. The "Technical drawing" panel in the results draws this arrangement to scale — a plan view and a cross-section looking along the flow, both dimensioned — so it's a schematic for checking the arrangement makes sense, not a fabrication/shop drawing. The "3D model" panel below it renders the same geometry with the casing semi-transparent so the splitters (and, if enabled, the end flanges with their bolt positions) are visible — drag to rotate, scroll to zoom. It's a visualization aid, not a CAD model: no gauge-accurate profiles, welds, gaskets or real bolt threads.

Self-generated flow noise

The L_WA result is the A-weighted sound power the silencer itself generates from air rushing past the curtains — VDI 2081-1 Equation (49), L_WA = 56.6 lg(v_gap) − 0.5 lg(Δp_t) + 10 lg(S) − 12.7, using the VDI pressure drop above and the duct cross-section area S. This is a different quantity from the silencer's insertion loss (how much it attenuates noise passing through it) — VDI 2081 does not give a formula for that. Section 7.2.2 of the standard is explicit that insertion loss depends on the specific curtain construction and is manufacturer-tested data (its own worked example labels those octave values "Herstellerangaben" — manufacturer's data — not a calculation); typical shapes are shown only as illustrative example curves, not general design equations. VDI 2081-1 gives no formula for it at all, so use your silencer manufacturer's tested octave-band data as the design value.

VDI 2081-1 also gives a polynomial approximation (Eq. 46, 50, 51, using a Strouhal number) for how that total flow noise splits across octave bands. We could not get this specific piece to reproduce the worked example's own numbers with confidence (a consistent ~24% mismatch in the calculated Strouhal numbers we haven't traced to its source), so — consistent with this site's policy of not shipping unverified precision — it isn't implemented here; only the verified total L_WA is shown.

Insertion loss — ASHRAE lined-duct estimate (unverified)

Since VDI 2081 gives no formula for insertion loss, the octave-band table below borrows a different, real published source instead: the 2019 ASHRAE Handbook — HVAC Applications, Chapter 49, Tables 17 & 18 — measured insertion loss for a straight rectangular sheet-metal duct lined with 25 mm or 50 mm fiberglass, for five square duct sizes (300–1220 mm) at four tested lengths each. The values were extracted from the source PDF's own text layer, not read off a scan, so they're exact — but everything about how they're used here is an approximation with real limits, disclosed up front rather than hidden:

• These tables describe a single lined duct, not a multi-curtain silencer. This calculator treats one gap between two curtains as if it were its own small lined duct, matched to the table by P/A (perimeter/area) ratio — the same parameter ASHRAE's own Table 16 organizes duct attenuation by, so it's a reasonable acoustic-engineering analogy, but it is not a citable method for splitter silencers specifically and has no worked example here to check it against.
• The smallest duct size ASHRAE tabulates (300×300 mm, P/A = 13.3 /m) already has less absorptive surface per unit area than a typical splitter gap (e.g. the VDI 2081 worked example's own gap has P/A = 23.3 /m) — so most real splitter gaps fall outside this table's own tabulated range, requiring extrapolation rather than interpolation. Whenever that happens, the result is flagged explicitly above the table with the nearest reference size used.
• Length is interpolated between the four tested lengths (2/3/6/12 m) where possible; outside that range it's scaled proportionally with length and capped at 50 dB, matching the cap ASHRAE itself applies.

Treat this table as a rough order-of-magnitude guide for early sizing decisions, not a design value — and definitely not a substitute for a manufacturer's own tested octave-band insertion loss for the actual curtain construction you specify. The table's "Sum" column is a plain arithmetic total of the eight band values, the same shorthand most silencer catalogs quote — it is not an energy- or A-weighted single number.

Outlet noise estimate

If you enter a fan's octave-band inlet sound power spectrum (optional, under "Fan inlet noise spectrum" in the inputs), this calculator estimates what comes out the other end: each band is reduced by the ASHRAE insertion-loss estimate above, the resulting spectrum is A-weighted and logarithmically summed to one overall level, and the silencer's own self-generated flow noise (Eq. 49) is then added to that as an independent broadband source (10 log₁₀[10^(L_attenuated/10) + 10^(L_self-noise/10)]) — it is not distributed across bands, because no verified octave shape exists for it (see above). This chains two approximations end to end (the ASHRAE estimate, and at low velocities the self-noise floor), so use it to compare design options, not as a substitute for a manufacturer's tested acoustic submittal.

Cross-check — general engineering model

Kept alongside the VDI result as an independent sanity check, not because it replaces it: air entering the silencer contracts from the full duct area into the gaps between splitters, runs through the gaps as a straight rectangular duct, then expands back to the full duct area on the way out, using formulas already verified elsewhere on this site — Darcy-Weisbach + Colebrook-White against Moody-chart reference points, and the Borda-Carnot contraction/enlargement coefficients against basic momentum conservation.

The two methods agreeing reasonably closely is itself a useful check; a large divergence between them is worth a second look at your inputs.