Sound Radiation from Chimneys or Stacks

Directivity correction for chimney stacks according to ISO 9613-2 (2024) Annex B

ISO 9613-2 (2024) Annex B describes the directivity correction of chimneys or other vertical and upwardly directed open pipes based on parameters like e.g. the exhaust temperature and the radius of the opening.

In CadnaA, the following formula B.1, which deviates from ISO 9613-2 (2024), is used to correctly calculate the angle theta where zR > zS. A correction to the standard has not yet been made..

\(\vartheta=90°+\arctan (\frac{z_S-z_R}{d_p})-\arcsin(\frac{d}{2r})\)

Radiation Characteristicsof Chimneys according to VDI 3733 (1996)

The VDI 3733 (1996) references a method developed in a research project funded by th German Environmental Protection Agency (UBA) from 1981 UBA-17-81 for the directional sound radiation of chimney outlets.

Range of Application

The simplified approach to determine the radiation characteristics of chimneys and cooling towers is valid with the following conditions:

diameter of the chimney opening d = 5 to 7 m
wind speed WL ≅ 3 ms-1
emitted medium: CO2, temperature range TF = 473 to 773 K
emitted medium: steam, temperature TF = 308 K

Directivity Correction

The following figure shows the geometrical situation:

Radiation by chimneys and stacks

The angle δ calculates from:

\(\delta=90°+\arctan(h*s^{-1})-\arcsin(\sqrt{h^2+s^2}*10^{-4})-\arctan((W_L*T_F)(W_F*T_L)^{-1})\)

with

h source height (relative to the receiver) [m]
s distance receiver-source (z coordinate) [m]
WL downwind velocity [ms-2]
TF temperature of the exhaust gas/medium [K]
WF velocity of the exhaust gas/medium [ms-2]
TL ambient temperature [K]

Directivity Index Kδ (in dB):

δ	f in Hz
δ	63	125	250	500	1000	2000	4000	8000
30°	2,0	2,5	2,5	3,6	3,0	2,0	2,0	2,0
45°-60°	4,0	4,8	3,2	4,1	4,8	4,8	4,8	4,8
75°	1,0	1,5	1,5	1,5	0,8	0,5	0,5	0,5
90°	-2,0	-2,5	-3,0	-3,5	-4,8	-5,6	-5,6	-5,6
105°	-4,0	-5,5	-7,0	-9,0	-10,0	-10,6	-10,0	-10,0
120°	-5,0	-7,5	-9,2	-11,5	-15,2	-19,8	-20,0	-20,0

Example

see Radiation from Stacks and Chimneys in the manual „Introduction to CadnaA“