Assessment and improvement of the 2019 ASHRAE handbook model for exhaust-to-intake dilution calculations for rooftop exhaust systems (ASHRAE 1823-RP)

Figures & data

Fig. 1 Flow recirculation zones and other geometrical exhaust parameters (ASHRAE 2019-Modified).

Fig. 2 Observed and predicted dilutions for Hajra, Stathopoulos, and Bahloul (2011) (Points are measured observations and curves are model predictions).

Fig. 3 Observed and predicted dilutions from Gupta, Stathopoulos, and Saathoff (2012) (Points are measured observations and curves are model predictions).

Fig. 4 Observed and predicted dilutions from Petersen, Carter, and Ratcliff (1997) (Points are measured observations and curves are model predictions).

Fig. 5 Observed and predicted dilutions from Schulman and Scire (1991) (Points are measured observations and curves are model predictions).

Fig. 6 Observed and predicted dilutions from Wilson and Chui (1994) (Points are measured observations and curves are model predictions).

Fig. 7 Observed and predicted dilutions from Wilson and Lamb (1994) (Points are measured observations and curves are model predictions).

Table 1 Progressive improvement of model through addition of variables and effect on objective function.

Case	α	γ	iself	P	δ	Number of Failings	F
Original	1	0.35	0	0	0	10	439,477
Optimized γ	1	1.7	0	0	0	10	90,750 (21%)
Optimized α & γ	0.6	1	0	0	0	10	21,062 (4.8%)
Optimized α, γ, iself , p, and δ	0.6	1	0.9	0.5	0.6	9	7,987 (1.8%)

Table 2 Physical meaning of defined parameters.

Parameter	Previous value	Optimal value	Physical meaning
α	1	0.6	Active portion of recirculation zone can be assumed to 40% below height of recirculation zone, avoiding difficulties cited above
γ	0.35	1	Initial source size can be assumed to be equal to the width of the exhaust stack
iself	0	0.9	Plume spread immediately leaving stack behaves as if there were initial turbulence intensity of 90% in lateral and vertical directions. This is likely due to several mechanisms.
p	0	0.5	Parameter defining the distance from the stack at which plume spread is dominated by atmospheric turbulence rather than self-induced turbulence in the plume.
δ	0	0.6	Plume trajectory in near-field is assumed to be 60% between previously assumed plume trajectory and final plume rise.

Table 3 Optimized values checked on other data sets results.

Case	α	γ	iself	p	δ	F (original)	F (optimized)	Number of failings (original)	Number of failings (optimized)
Wilson and Lamb 1994	0.6	1	0	0	0	155794	122313	9	14
Wilson and Chui 1994	0.6	1	0	0	0	301049	181162	0	0
RP 805 (tests with screens)	0.6	1	0	0	0	1486477	647931	60	60
Schulman and Scire 1991 (Hidden intakes)	0.6	1	0	0	0	119	76	11	21
Wilson and Lamb 1994	0.6	1	0.9	0.5	0.6	155794	45902	9	4
Wilson and Chui 1994	0.6	1	0.9	0.5	0.6	301049	122378	0	0
RP 805 (tests with screens)	0.6	1	0.9	0.5	0.6	1486477	460478	60	60
Schulman and Scire 1991 (Hidden intakes)	0.6	1	0.9	0.5	0.6	119	16	11	3

Fig. A1 Relationship between htop and hplume for three different scenarios.

Fig. B1 Log of dilution ratio versus distance from the stack (Original).

Fig. B2 Log of dilution ratio versus distance from the stack (With cutoff).

Fig. B3 Log of dilution ratio versus distance from the stack (Optimized with the variable γ).

Fig. B4 Log of dilution ratio versus distance from the stack (Optimized with the variables α and γ).

Fig. B5 Log of dilution ratio versus distance from the stack (Optimized with the variables α, γ, iself, p and δ).

Fig. B6 Original and optimized dilution predictions for Wilson and Chui (1994).

Fig. B7 Original and optimized dilution predictions for Wilson and Lamb (1994).

Fig. B8 Original and optimized dilution predictions for ASHRAE RP 805 (Tests with Screen).

Fig. B9 Original and optimized dilution predictions for Schulman & Scire (Hidden Intakes).

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