Trans RINA, Vol 156, Part B2, Intl J Small Craft Tech, Jul-Dec 2014
eventually of energy. In this case it is necessary to accurately control the scaling of the emissions, ensuring the similarity of the mixing conditions of the released exhausts. Dimensional analysis of the parameters which mainly affect the behaviour of the exhausts discharged from a stack requires the conservation of a series of dimensionless parameters involving both the properties of the emission and those of the flow itself. In particular, the complete scaling is based on the following equation:
CU L2 ref ref QUf
s,, 2 a ref U
W gL ref
where W is the outlet speed of the gas released from the model, ρa and ρs represent, respectively, the density of the ambient air and of the emission, C is the volume
concentration and Q is the volumetric flow‐rate of the contaminant emitted by the source, at standard conditions of temperature and
pressure. The above equation
expresses the dimensionless concentration field as a function of three dimensionless parameters that relate the physical properties of the emission with those of the flow field in which it is dispersed. This implies that in order to have a perfect similarity between the full scale and the
lab‐scale model the following parameters should be kept constant:
Speed ratio: W Uref
Density ratio:
Froude Number: 2
s a
Fr U gL
2
ref ref
The Froude number which can be also expressed as: 22
Fr UL gL
2 3
represents the ratio between the inertia and gravity forces in the considered flow. This type of scaling (complete scaling) cannot be easily obtained due to speed or temperature conditions required in the wind tunnel for
the small‐scale model. For this reason, the complete scaling, is often not used.
In order to be able to simulate a real scenario with a good representation of the main physical aspect of the problem, in a way that is consistent
with the
requirements of the complete scaling, some restrictions must be eliminated using what are called "enhanced scaling relationships".
This is how it is possible to combine different process variables in several dimensionless parameters which are
ref
not necessarily a complete set of parameters allowing for the definition of new scaling rules.
A parameter which is not essential is the ratio of density between the gas emitted and the surrounding air, α. It is not important by itself but it can affect the momentum of the emission and its buoyancy. The non-conservation of α results in several possible scaling rules, based on the consideration that the trajectory of the plume that is transported from the local wind is mainly determined by the ratio between the inertial and buoyancy forces. Therefore, this can lead to the following approximated equation:
CU L2 sW sa gL
ref ref f
Q UUa ref
2 () 22,
ref ref
in which ρref is a reference density which can be that of air, or that of the gas emitted.
In the wind tunnel experiments the choice is to follow a conservative approach by performing a scaling of the ratio between the emission and wind momentum, so as to reproduce consistently the interaction and the dilution/mixing conditions between flue gas and the external flow field, without obtaining a complete scaling of the buoyancy contribution. In practice, the density of the emission, which in the real case is less than that of air (given the high temperature of the flue gas), in the experiments is considered substantially equal to that of the air. This leads to a negative buoyancy of the plume, with the aim to better highlight the potential entrainment of the exhausts in areas of interest of the model. In fact the effect of a higher temperature of the fumes at full scale would
be to facilitate the dispersion in the
atmosphere of the fumes themselves, thereby reducing the chances of having re-ingestion phenomena or of discomfort in the areas of relevance of the vessel and its superstructure. Accordingly, the scaling of the gas discharge conditions is carried out as follows:
WW UU m
stack m stack
00
()
where W0 is the exhaust speed at the stack tip, Ustack the wind speed at the actual stack height above the sea surface and α the density ratio. The subscript m indicates the parameters related to the small‐scale model.
During the wind tunnel tests tracer gas dispersion measurements are then performed using wind speed scaled accordingly to Froude number similarity law (i.e. maintaining the ratio between the inertia forces and the weight force).
ref
B-76
© 2014: The Royal Institution of Naval Architects
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