Figure 5.5 Effective PAT Reduction by Reingestion
20 40
60 80
100 120
140
20 40
60 80
100 120
MPAT Ef
fect ive PA
T
Deck 1 Bottom Deck 2 Middle
Deck 3 Top
5.4 Deck and Crosswind Scaling
This section describes the mathematical modelling and similarity rules used to extrapolate CFD results to other geometries.
5.4.1 A Model of Reingestion
In very still conditions, heated air leaving one open deck at the sides will be partially reingested at the sides of the deck above. This obviously reduces the effective PAT on the
higher deck. The amount of this reingestion depends on the mechanically supplied airflow and the deck width and height. The severity of the effect also increases with successive
decks higher up the ship. The mathematics of the model are documented in Appendix D. The result is a description for the PAT on deck ‘N’ based on the PAT for the lowest open
deck deck ‘1’ and a ‘reingestion fraction’;
=
1 -
N
R -
1 R
- 1
1 PAT
N PAT
where the reingestion fraction is given by;
× =
H W
MPAT 0.000294
- 0.405
R
Where: MPAT
is the deck mechanical pen air turnover mhr W
is the deck width m H
is the deck height m
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Figure 5.6 shows the reingestion fraction interpreted from CFD runs on cattle decks and the correlation applied equation above to consolidate the information to allow calculation of
conditions. Figure C.37 and Figure C.38 indicate that crosswinds of 1ms are sufficient to prevent reingestion.
Figure 5.6 Reingestion Fraction Interpreted from CFD and Correlated to PAT, Deck Width and Deck Height
0.05 0.1
0.15 0.2
0.25 0.3
0.35 0.4
0.45
200 400
600 800
1000 1200
1400 1600
PATWH Re
inge s
tion Fra c
tion R
CFD Results Reingestion Correlation
5.4.2 Natural Convection
As implicitly stated in the reingestion scaling above, the thermal buoyancy of air heated by the animals drives some air turnover even without any crosswind or supply air. The strength
of this effect obviously depends on the deck height and width. Appendix D goes through the scaling arguments to conclude that PAT driven by natural convection ignoring reingestion is
proportional to deck height and inversely proportional to the two-thirds power of deck width. Based on the CFD results, the natural convection PAT for a 24m wide, 2.4m high cattle deck
was taken as 72mhr with the figures for other decks scaled from that. For the ‘standard’ 24m wide sheep deck with 1.3m high double tiers, the natural convection PAT was taken as
42mhr, with other decks scaled from that. The effect of the scaling can be seen in the equations in the flowsheets, Figure 5.7 and Figure 5.8.
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Figure 5.7 Crosswind Assessment Flowsheet for Cattle Decks
Calculate required closed-deck equivalent PAT RPAT for a given level of risk, ship location, time
and stocking level.
Calculate reingestion factor R = 0.405-0.00294 MPAT x WH
Is RPAT 72 24W
23
H2.41-R1-R
N-1
Is RPAT below the natural convection level with re-ingestion from decks below?
Is RPAT MPAT 1-R1-R
N-1
including re-ingestion scaling for zero xwind?
Does MPAT mechanical PAT provide RPAT, still accounting
for re-ingestion from tiers below? Any Crosswind is OK
MPAT not required for heat but possibly for ammonia
Any Crosswind is OK 100 MPAT will suffice
Calculate crosswind to give RPAT AND ensure no significant reingestion Cross Wind {W24 x 2.4H}
1.5
x [RPAT + 234] x 1.5250 ms AND
Cross Wind 2 x {W24 x 2.4H}
1.5
ms MPAT not required for heat but possibly for ammonia
Notes: 1. Reingestion scaling not required in first expression as crosswind has
ensured essentially zero reingestion. 2. As crosswind climbs above about 1ms, crosswind ventilation also
overwhelms most mechanical effort.
Step 1
Step 2
Step 3
Step 4
No Yes
Yes
No
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Figure 5.8 Crosswind Assessment Flowsheet for Double-tiered Sheep Decks
Calculate required closed-deck equivalent PAT RPAT for a given level of risk, ship location, time
and stocking level.
Calculate reingestion factor R = 0.405-0.000294 MPAT x WH
Is RPAT 42 24W
23
H1.31-R1-R
N-1
Is RPAT below the natural convection level with re- ingestion from decks below?
Is RPAT MPAT60110+181-R1-R
N-1
including re-ingestion scaling for zero xwind Does MPAT provide RPAT, still accounting for
re-ingestion from tiers below? Any Crosswind is OK
MPAT not required for heat but possibly for ammonia
Any Crosswind is OK 100 MPAT will suffice
Calculate crosswind to give RPAT AND ensure no significant reingestion Cross Wind {W241.3H}
1.5
[RPAT-10]260 ms AND
Cross Wind 2 {W241.3H}
1.5
ms MPAT not required for heat but possibly for ammonia
Notes: 1. Reingestion scaling not required in first expression as crosswind has ensured
essentially zero reingestion.
2.
As crosswind climbs above about 1ms, crosswind ventilation also overwhelms most mechanical effort.
Step 1
Step 2
Step 3
Step 4
No Yes
Yes
No
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5.4.3 Crosswind Scaling
