|
tration according to multiple regression analysis of field
measurements, Fig.1.In this work it is assumed that the
velocity at the height of 10 m is representative for the ver-
ticaldistributionofsnow.Thehighestsnowconcentra-
tion is confined to a narrow zone close to the surface and
the vertical size of computational mesh cells must there-
fore be carefully chosen in order to obtain acceptablereso-
lution of the ground drift.
|
snowdriftaroundaporousfenceisperformed usinga
one equationturbulent energy model.Turbulent quanti-
ties are linked to mean flow equations byassuming that
the dynamic viscosityis asumofmolecularand turbu-
lent viscosities,µ=r(nT +n).
Numerical simulations ofsnowdrift
A numerical simulation of snow drift around atypical 50%
porous snow fence is performed and the different stages
inthegrowthofsnowdriftareshowninfigure2.The
fence is similarto 2.74 mtall Wyoming fence with a bot-
tom gap at 14% except for being vertical instead of having
a slight inclination.A mean inlet wind profile typical for
flat ground conditions isgiven,where the velocityis 10
m/s, measured at the heightof 10 m and the surfacerough-
ness is 10 -3m. The snow qualityin this simulation isas-
sumed to be something in between snow coming froma
wind-hardenedsurface and very light dry snow, and con-
sequently the threshold friction velocityis chosen as 0.2
m/s (Male, 1980).Otherconstants used in the simulation
are chosen as follow:drag constant,K=25.8kg/m3 s,ter-
minal snowfall velocity=0.4 m/s and roughnessheight for
friction velocity calculations=10 -4m.
It isnot realistic toperformnumerical simulations of
snow drift with a simulation time as long as forreal con-
dition.Figure 2 shows a simulation of23 minutes snow
drift and this short simulation time is possible by using a
smallfreezingfraction at0.1forsolidification.Drifting
snow is deposited in a surface mesh cellby assuming that
30% of the incoming snow flux accumulates for each time
step,which is a value based on simulation tests.
The calculated snow deposition in figure 2 is in satis-
factory agreementwith the equilibrium drift profile which
ischaracteristicforlessthanhalfwayfilledWyoming
fences, placed on a flat ground. There is no point in going
fortheidenticalproflewhenfieldmeasurementsand
boundary conditions are not given.An example of snow
formation development around a similarfence is shown
in figure 3. Early stage depositions behind the fenceshows
tendencytowards formation of a cornice or an abrupt drop
off on the leeward side, whichis caused by a recirculating
zonebehindthe formation.Thesamephenomenon can
be detected on the numerical simulation in figure 2.
SUMMARY AND CONCLUDING REMARKS
Anumerical method forsimulation of snow drift based
on two-phase theory isproposed.Snow transport is ba-
sicallyconsideredbysolvingascalartransportequa-
tionforsuspensionbythemeanflowandthesnow
phase is allowed to drift with respect to the air phase. In
theabsenceofrigoroustheorythetransportbycreep
andsaltationismodelledbymeansofexperimental
knowledge.Thismethodhasbeensuccessfullyem-
ployed to simulate the development of two dimensional
snow accumulations around a 50% porous fence and, as
a furtherdevelopment,thismodelwillbe extended to
handle three dimensional cases.
It isnecessary toevaluate drift-heights orsnow accu-
mulations by sharp interface techniques in order to study
how they affect the wind velocityfield.
|
|
|
Figure 1. Concentration of snow as a function of height above the snow
surface, for drift situations with velocities at 10, 15, and 20 m/s,
measured at a reference height of 10 m (Mellor and Fellers, 1986).
Right outlet boundary condition
Continuativeoutflowwhereall normal derivativesvan-
ishes is selected as rightboundary condition.Upstream
effects are minimized through evaluating normal deriva-
tives afterthe momentum equations,only.
Top and Bottomboundary conditions
The bottom boundary condition is defined as a rigid wall
with no-slip conditionswhere wall shearstress is calcu-
lated. Snow accumulation is treated as a new surface hav-
ingazerovelocityboundaryconditionfortheflow
simulations. Topboundary is specified as a symmetry con-
dition where free-slipis considered. Possible contribution
from vertical snowfall is neglected due to the low concen-
trationcompared togrounddriftingsnow.Thereareno
wind velocities normal to the bottom boundary, the snow
surface orthe top boundary condition.
Turbulence modelling in snow drift
Turbulence and particle interactions can be divided into
two aspects.The first isconcerning how particles are af-
fectedbyturbulenceinthe carrierfluid.Thesecond is
how particle interaction affects the turbulence in the mix-
ture fluid.Hetsroni (1992) indicated that the presence of
particlesthataresmallcomparedtothe turbulentscale
was suppressing the turbulence in the mixture flow due
to additional energy dissipation.Larger particles seemed
to have an opposite effect byenhancing turbulence.The
fieldofturbulencemodellingoftwo-phase,gas-particle
flows are poorly understood and this analysis is confined
to treating turbulence in the air phase and neglecting tur-
bulence effects due to particle interactions. Simulation of
|
|
1
2
3
4
5
