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Research ArticleExperiment Investigation and Numerical Simulation ofSnowdrift on a Typical Large-Span Retractable Roof

Zhenggang Cao 12 Mengmeng Liu12 and Pengcheng Wu12

1Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education Harbin Institute of TechnologyHarbin 150090 China2Key Lab of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of Industryand Information Technology Harbin Institute of Technology Harbin 150090 China

Correspondence should be addressed to Zhenggang Cao caozg75163com

Received 5 September 2019 Revised 26 November 2019 Accepted 2 December 2019 Published 26 December 2019

Academic Editor Toshikazu Kuniya

Copyright copy 2019 Zhenggang Cao et al is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Retractable roofs are commonly used in designing large-span stadiums because of their versatility However retractable roofs aresubject to sudden changes in shape and thus factors in addition to those considered for conventional roofs need to be taken intoaccount In particular retractable roofs are considerably more sensitive to snow loads because their shapes are complex andsnowdrift on roofs may lead to diculties for the operating of retractable roofs To investigate the distribution of snow onretractable roofs this study proposes a method based on a numerical simulation of snowdrift obtained using the EulerndashEulermethod in multiphase ow theory is numerical model employs a mixture model by using the commercial computational uiddynamics (CFD) software FLUENT A suitable turbulence model is selected for the simulation through verication against two-dimensional (2D) data obtained from eld measurements reported in previous studies However the snow load on retractableroofs cannot be determined by a 2D distribution easily e accuracy of predicting the overall distribution of snow load on roofswas veried by experiments conducted on a horizontally retractable roof e results show that a nonuniform snow distributionon such roofs is distinct and should be considered

1 Introduction

Frequent snow and ice storms occur all over the world andthe partial structural overload and collapse of the roofs ofbuildings owing to the unbalanced distribution of snow onthem are common Research on the snow load on roofs isthus important for the safety of structures particularly long-span spatial structures

ree methods are commonly used to investigate wind-induced snowdrift eld measurements wind tunnel ex-periments and numerical simulations ese methodssupplement one another and each oers its own advantagesand disadvantages Field observations are essential instudies on wind-induced snowdrift and are known toprovide the bulk of relevant data However the resultsobtained are often aected by various external factors and

the accumulation of data from eld observations is a time-consuming process Wind tunnel experiments are based onthe motion mechanism of snow particles reasonablesimilarity relations and appropriate granular materialssimulating snow particles to carry out rapid predictions ofsnowdrift [1] However it is dicult at present to satisfy allsimilarity criteria and several of them may be ignoreddepending on the situation Numerical simulations arepopular and have been widely adopted in recent yearsbecause they are cost eective highly ecient and easilycontrollable [2] Moreover no similarity problems occurwhen studying large-scale buildings using simulationsHowever many methods based on numerical simulationsare available and in the absence of a uniform standardselecting a suitable method is challenging is is thereforeone of the goals of this study

HindawiComplexityVolume 2019 Article ID 5984804 14 pageshttpsdoiorg10115520195984804

Two methods based on numerical simulations aremainly used to implement two-phase flow theory theEulerndashLagrange method and the EulerndashEuler method

-e EulerndashLagrange method assumes that the snowphase is discrete in the air Newtonrsquos law of motion is used toobtain the trajectory of a single snow particle and the volumeof snow is then distributed by integration Alhajraf [3]applied the EulerndashLagrange method to establish a FLOW-3Dmodel to investigate snowdrift around a snow fence andfound that the results were in agreement with those ofmeasurements Okaze et al [4] proposed a simulationmethod based on the coupling of large eddymodel (LES) andLagrangian method and applied this method to simulate thedevelopment of snow particle migration process under lowwind speed -is study found that at the initial stage thesnow particle transport mainly relies on the airflow to keepthe saltation of particles with the development of time theparticle splash and rebound caused by the collision occupythe dominant position of the particle transport Zhou et al[5] applied the CFD-DEMmethod to simulate the snowdrifton a typical stepped roof in 2D both considering the co-hesion and collision between snow particles and the snowdistribution was verified to be similar to that in fieldmeasurement and wind tunnel test

-e EulerndashEuler method assumes that both the air andthe snow phases are continuous and it is solved by addingthe governing equation of the snow phase to the controlequation of the air phase and most current numericalsimulations of wind-induced snowdrift use the EulerndashEulermethod

Uematsu et al [6] conducted a numerical simulation ofthe distribution of snowdrift around a snow fence -eyconsidered the saltation and suspension processes in thesimulation and proposed a three-dimensional (3D) simu-lation to yield results close to those of field observationsHowever the method only considers the rate of snow masstransfer and ignores the influence of wind turbulence Inprevious studies researchers were more concerned withsnowdrift on the ground Beyers et al [7] used FLOW-3D tosimulate snowdrift around a cube with a length of 2m -eyused the standard kndashεmodel and an improved turbulent wallfunction to consider the effect of the drift of the snowparticles on the effective length of roughness of the snowsurface and compared the results with those of measurementat the SANAE IV scientific research station in Antarctica-ey concluded that the results of snowdrift were in goodagreement with the measured values in terms of both shapeand magnitude Beyers and Waechter [8] used Fluent tosimulate snowdrift around two side-by-side cubic buildingsthree side-by-side overhead buildings and dormitorycomplex of the Antarctic scientific research base Embeddeduser-defined functions and mesh deformation were used tomodel changes in snowdrift over time owing to snow de-position or erosion Although the results of the numericalsimulation were in good agreement with measurementsbecause the authors had used the k-ε turbulencemodel in thesimulation where this model has inherent deficiencies theyalso opined that better results can be obtained when usingimproved two-equation models Tominaga et al [9] pointed

out that the governing equations used in previous studiescould not describe the changes of flow field around thebuilding accurately -e boundary conditions such asthreshold velocity and snow phase concentration have greatinfluence on the simulation results and a new method isproposed based on the Renault Time-Rate Method (RANS)and the reliability of the new method is verified by com-paring the simulation result of snow distribution around thecube with the measured results

Recent years researchers have witnessed more researchon the snow load on roofs -iis et al [10] conducted fieldmeasurements and numerical simulations on the curvedroof of a sports hall located in Oslo Sun et al [11] simulatedthe snowdrift on a long-span membrane roof and me-chanical performance of the membrane structure undernonuniform snow load was also studied However moststudies have focused on specific buildings and research onthe general rules of patterns of snow distribution on large-span roofs has rarely been reported Considering the di-versity of the shapes of large-span roofs many scholars havesuggested that for such structures with complex roof shapesboth numerical simulations and wind tunnel tests should becarried out to determine the coefficient of snow distribution

As the name implies the retractable roof is a type of roofstructure that allows the building to be used with an ldquoopenrdquoor ldquoclosedrdquo roof As a type of large-span structure with astrong comprehensive function the retractable roof savesenergy and is environmentally friendly in line with currentdevelopments in architectural technologies Retractableroofs are widely used however owing to their discontinuousshape more complex snow distribution occurs on themMoreover unlike the typical large-span roof snowdrift onretractable roofs may cause serious operational issues

Research relating to snow loads on retractable roofs isscant no specific provisions for this type of structure areavailable and only certain introductory articles are availablefor reference

-is study focuses on snow loads on a typical hori-zontally retractable roof which was widely used in long-spanroof structures as shown in Figure 1 and only the ldquoclosedrdquostate of the retractable roof is considered because buildingsshould be generally covered when it is snowing To validatethe accuracy of the numerical simulation of snow loaddistribution experiments on a horizontally retractable roofmodel were carried out to determine the accuracy of pre-dicting the overall snow load distribution and the regularityof snowdrift on such a roof Finally distributions of snow ontwo other typical retractable roofs were investigated usingthe CFD method

2 Numerical Method and Validation

21 Governing Equations EulerndashEuler description in mul-tiphase flow theory is used for the simulation in this study inwhich both snow and air are treated as continuous phases-ere are three EulerndashEuler-based multiphase models inFLUENT the VOF mixture and Eulerian models Amongthem the mixture model exhibits superior stability and lowcomputation requirements while delivering nearly the same

2 Complexity

precision as the Euler model [12] thus the mixture model isused in this study

In the mixture model mixture phases including air andsnow share the same equations of mass continuity andconservation of momentum as per equations (1) and (2) Itis assumed that only one-way coupling exists between the airand the snow phases and equations of the momentum andturbulence of air can be regarded as unaffected by the air-borne snow

Moreover the continuity equation for the snow phase isprovided by equation (3) [13]

z

ztρm( 1113857 + nabla middot ρm v

m1113872 1113873 0 (1)

z ρm vm1113872 1113873

zt+ nabla middot ρmvm v

m1113872 1113873 minus nabla middotp + nabla middot μm nablav

m + nablav

T

m1113874 11138751113876 1113877

+ ρmg

+ F

(2)

z ρsf2( 1113857

zt+ nabla middot ρsf2 v

m1113872 1113873 0 (3)

where ρm 11139362k1fkρk is the density of the air and snow

mixture ]m 11139362k1fkρk ]

kρm is the average velocity of the

mixture phase fk is the volume fraction of the air phase(k 1) and snow phase (k 2) p is the pressure of the airfield and μm 1113936

2k1αkμk represents hybrid viscosity

-e governing equations selected for the simulation donot consider the effect of slip velocity and mass exchangebetween the phases in their source terms -ere is nocredible evidence for the determination of the slip velocitybetween the phases and Hao et al [14] found no significantdifference in the results without considering the relative slipvelocity Moreover it is difficult to guarantee its convergencewhen considering mass exchange between phases and thusits effect was ignored in the simulation

22Deposition andErosionModel Wall shear stress whichis used to determine the state of movement of snowparticles is an important parameter in snowdrift Snowparticles begin moving when the wall shear stress τ on the

snow surface exceeds the threshold wall shear stress τtotherwise the snow particles remain stationary In thenumerical simulation the wall shear stress τ is replacedby frictional velocity ulowast and defined as the followingrelation

ulowast

τρ

1113971

κu(z)

ln zzs( 1113857 (4)

where κ refers to the Von Karman constant that is equal to04 and zs is the height of aerodynamic roughness over thesnow surface which was set to 30times10minus 5m -e snow massflux of erosion qero is simplified as a function of the frictionalvelocity and bonding strength of the snowdrift -e depo-sition flux qdep is calculated as a function of the snow fractionf and snowfall velocity wf ([15])

qero Aero u2lowastt minus u

2lowast1113872 1113873

qdep ρsfwf

u2lowastt minus u2

lowastu2lowastt

(5)

where Aero is a proportionality coefficient set to 70times10 minus 4ulowastt is the threshold frictional velocity set to 02ms [9] andwf is snowfall velocity assumed to be 02ms

-e thickness of snow distribution changes with erosionor deposition In this case qs is uniformly used to replaceqdep or qero and the change in the thickness of snow dis-tribution over time is calculated as follows

dh minusqs

ρscdt (6)

where c is the maximum volume fraction of the snow phase-e steady method simplifies the snowdrift process and

is only valid for relatively small snowdrifts however theresults of prediction of the steady method have been shownto reasonably reproduce field observations or wind tunneltest data [9] In the steady simulation the erosiondepositionof snow is regarded as in a steady state and the rate of changeof snow depth per unit time qsρs remains constant-us thetime integration in equation (6) becomes

h(t) h0 +qs

ρsΔt (7)

where h0 is the initial depth of snow

(a) (b)

Figure 1 Typical horizontally retractable roof (a) Sky Dome Canada (b) Ocean Dome Japan

Complexity 3

23 Inflow Boundary Conditions -e fully developed inletwind velocity profile is determined from the power lawprofile

v(z) v0z

z01113888 1113889

α

(8)

where v0 and z0 are the reference velocity and referenceheight respectively

Furthermore the turbulent kinetic energy k and tur-bulent kinetic dissipation rate ε were also provided for theturbulence characteristic

k 32(vI)

2

ε C34μ

k32

l

(9)

where C is the empirical coefficient that is selected as 009and l and I are the turbulence length scale and turbulenceintensity respectively which are determined by the fol-lowing equations[16]

l

100z

301113874 1113875

05 30mlt zltZG

100 zle 30m

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(10)

l

01z

zG

1113888 1113889

minus αprimeminus 005

zb lt zltZG

01zb

zG

1113888 1113889


zle zb

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(11)

On the assumption of unidirectional coupling the inletvelocities of the snow and air phases were considered to bethe same -e spatial distribution of the snow phase isdivided into creep saltation and suspension in which thetransport volume of the slow-moving layer is relativelysmall -us only the saltation and suspension of thesnowdrift are considered -e snow mass transfer rates inthe saltation (zle hs) and suspension (z le hs) layers areexpressed as equations (12) and (13) according to actualmeasurements taken by Pomeroy and Gray and Pomeroyand Male [17 18]

f

068ρupulowastghsρs

ulowastt u2lowast minus u

2lowastt1113872 1113873 zle hs

08 exp minus 155 478uminus 0544lowast minus zminus 0544( 11138571113876 1113877

ρs zgt hs

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(12)

where up is the average velocity of the snow particle in thesaltation layer and is set as 28 ulowastt and hs is the average heightof the saltation layer which is determined by the followingequation [17]

hs 16u2lowast

2g (13)

Note that the friction velocity ulowast at the inflow boundaryshould exceed the threshold friction velocity to initiatesnowdrift

24 Optimization and Validation of the Turbulence ModelIn previous studies various turbulence models have beenemployed in snowdrift simulation Tominaga and Mochida[19] used a modified version of the k-ε model in a snowdriftsimulation and compared the results with those of thestandard k-ε model Beyers et al [7] adopted the standard k-εmodel and indicated that it is necessary to perform a criticalexamination of the influence of inaccuracies in the isotropicturbulence assumption on snow accumulation and erosionOkaze [20] developed a new k-ε model that incorporates theeffects of snow particles on a flow field and verified the ac-curacy of the new model by comparison with the wind tunneltest Although many different turbulence models have beenemployed in the literature the results obtained by thesemodels are in strong agreement with field observations or testdata

In this study in order to select a suitable turbulencemodel different turbulence models were used to simulatethe snow load on a stepped flat roof -e stepped flat roofmodel adopted was a 1 1 model by Tsuchiya et al [21] usedin field observations carried out on the ground of theHokkaido Institute of Technology (Sapporo Japan) Asketch of the model is illustrated in Figure 2 and the pa-rameters used in the CFD simulation are listed in Table 1-e snow density is 150 kgm3 the snow particle terminalvelocity wf is 02ms and the threshold friction velocity is02ms and considering that the snowing duration is un-available and to get a relatively stable fully developedsnowdrift result an assumed snowing duration Δt 24 h isadopted in the simulation

Figure 3 compares the normalized snow depth obtainedby different turbulence models along the line of mea-surement and gives the distribution of ratio of frictionvelocity above the lower roof to threshold friction velocity-e snowdrift obtained by field observations was dividedinto four sections according to its features to clarify theassessment -e x-axis represents the relative position onthe roof and H was 09m -e y-axis represents thenormalized snow depth at any point and S and Sd are themeasured snow depths at any point and the averagesnowfall respectively Drifting sections I and II show thatall three turbulence models underestimated the effect oferosion and the results of the realizable k-ε and k-kl-wmodels were closer to the snowdrift reported by fieldobservations in terms of shape SST k minus wwas not accurateat estimating the location of extreme points in the erosionzone Comparing the models in sections III and IV theresults obtained by the realizable k-ε model yielded theclosest distribution to field observations and the result wasmore conservative -e other two methods were inade-quately estimated for snow accumulation From the above

4 Complexity

20 200

175

150

125

100

075

050

025

000

18

16

14

12

10

08

06

04

02

0000 05 10 15 20 25 30

Nor

mal

ized

snow

dep

ths S

Sd

xH

u lowastu

lowastt

SST k-wk-kl-wRealizable k-ε

ulowastu

lowastt

Tsuchiya et al

I II III IV

Figure 3 Normalized snow depth obtained by different turbulence models along the line of measurement

Coordinate axis

Lower roof on the windward side

6H

3H2H

H

H

XY

Z

H = 09m

Wind

Measurement line

Figure 2 Sketch of model [2]

Table 1 Computation conditions

Conditions SettingsComputational domain 220m (x)times 40m (y)times 24m (z)Number of elements Approximately 1500000Minimum mesh size 004m

Inflow boundaryWind velocity profile (see equation (8)) where v0 and

z0 are 74ms and 09m respectivelySnow fraction profile (see equation (12))

Outflow boundaryZero gradient condition the wind velocity gradientzuzn and snow fraction gradient zfzn are set to zero

(outflow)

Upper face and sideZero gradient condition for all variables the normalcomponents of the wind velocity with respect to the

boundaries are set to zero (symmetry)

Building and ground surface No-slip boundary condition (wall) except that thewall roughness z0 50times10minus 5 for the snow surface

Turbulence model SST k-w model k-kl-w model realizable k-ε modelMultiphase model Mixture model

Complexity 5

analysis the results obtained by the realizable k-ε modelexhibited stronger agreement with field observations -usthe realizable k-ε model was selected as turbulence modelfor the subsequent CFD simulation

3 Experimental Validation of Snowdrift onHorizontally Retractable Roofs

Although CFD simulations have been shown to providerelatively effective reductions of the snow depth along theline of measurement snow distribution on certain large-span or complex roofs such as retractable roofs cannot bedescribed using only a simple 2D distribution-erefore todetermine whether the CFD simulation method can ac-curately predict snow distribution on such roofs bothexperiments and numerical simulations were conducted onsnow distribution using a small-scale horizontally re-tractable roof model

31 Experimental System

311 Experimental Facility Amajority of scholars use windtunnels to conduct wind-induced snowdrift tests -esimulation of snowdrift in a building wind tunnel isimplemented by diverting precovered snow using an in-coming wind field -e experimental subjects are generallyflat surface models and thus it is reasonable to apply auniformly distributed layer of snow ahead of time Howeverwhen the subject is nonplanar its curved surface makes itdifficult to uniformly distribute snow on the large-span roof

-e Harbin Institute of Technology has independentlyproposed the Snow-Wind Combined Experimental Facilitycomposed of six assembled fans in a ldquopowerrdquo section asshown in Figure 4 It forms a stable wind field through aldquodiversionrdquo section A snowfall simulator is set up in thewind field to provide a stable snow environment and sim-ulate the natural snowfall process Moreover the structure ofthe equipment is assembly type which is convenient fordisassembly removal and transformation A stable windspeed range of 05 to 115ms was used in the test section andnatural snow particles were used in the experiments [22]

312 Model Information No confirmed prototype of thearchitecture and related conditions was available for the testinvestigation According to a typical form of a horizontallyretractable roof the prototype roof span was 30mtimes 60mthe rise-to-span ratio was 1 10 the specific length of thefixed roof on both sides was 21m the two retractable roofs inthe middle were 9mtimes 30m and the span ratio was 1 10

-e geometric scale ratio of the test was 1 30-emodelwas constructed from plywood and timber framing and hadsufficient strength and rigidity As illustrated in Figure 5 thefixed roof was 110th of the cylindrical shell surface and thecentral part formed the retractable roof Moreover to obtainan accurate snow distribution measurement points were setevery 5 cm in the horizontal projection area

313 Similarity Criterion and Operating ConditionsReliable experimental modeling at scale depends on anappropriate similarity criterion Several similarity criteriaare available that are however incompatible -us thesimilarity criterion must be selected according to itsrelevance

According to the test scheme of the French Jules VerneClimatic Wind Tunnel [3] the equation for the number ofsimilarities was determined based on the Froude numberaccording to the number of migrating particles in the jumplayer Furthermore the wind speed and simulation time ofthe test were established on the basis of parameters similar tothose of equations (14)ndash(19) such as the Reynoldsrsquo numberlimit [23ndash29]

1 minusU0

U1113874 1113875

U2

Lg1113888 1113889

p 1 minus

U0

U1113874 1113875

U2

Lg1113888 1113889

m (14)

UT

L1113874 1113875

p

UT

L1113874 1113875

m (15)

u3lowastt

2g]1113888 1113889

mge 30 (16)

u2lowastt

Dpgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

p

u2lowastt

Dpgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

m

(17)

ρpρ

1113888 1113889mge 600 (18)

u2lowastt

Lgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

p

u2lowastt

Lgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

m

(19)

where L is the reference length of the structureDP is particlediameter T is the time needed for the experiment ρp is thedensity of the particles ρ is air density and U and U0 are thereference wind speed and threshold reference wind speedrespectively-e air density was set to 1341 kgm3 (when thetemperature minus 10degC) particle density for the model was setto 910 kgm3 and that for the prototype was set to 300 kgm3

(the subscript p represents the prototype and m representsmodel) Furthermore ulowastt is the threshold frictional velocityg is gravitational acceleration and υ is kinematic viscositywhich varies from 132times10minus 5 to 167times10minus 5m2 sminus 1 and wasset to 15times10minus 5m2 sminus 1 in this study

Fan matrixSnowfallsimulator

Wind speedmonitoring

Snowtrapper

Model

Figure 4 Snow-wind combined experimental facility

6 Complexity

Artificial snow was used in the experiments To eliminatethe differences in particle properties snow particles used in theexperiments were all produced on the same day (01202017)by a single snowmaker Fresh snow produced by a snowmakeris unsuitable for experiments because of its high moisturecontent It also needs to be stored in a sheltered area for at leastfive days prior to the experiments -e physical properties ofthe artificial snow particles were measured before the exper-iments In particular the diameter and shape of the particleswere observed by an optical microscope and the repose angle asdetermined by accumulated experiments was 45deg All buildingmodels were constructed from wood and the friction anglebetween wood and artificial snow was approximately 50deg -eshape of the snow particles is illustrated in Figure 6 and acomparison of the physical parameters of the real and artificialsnow particles is provided in Table 2

Taking the Harbin facility as a reference a type-B landformof the atmospheric boundary layer was adopted-e basic windpressure in the 50-year recurrence interval was 05 kNm2 andthe wind speed of the test prototype was determined to be 045times that of the 50-year recurrence interval according to thehistorical data [30] -e monitoring point for the referencewind speed point was located 02m above the ground (cor-responding to the height of 6m of the prototypical buildingroof) According to the similarity criteria the experimentalwind speed was 25ms (at a height of 02m) and the ex-perimental parameters are shown in Table 3 As indicated inTable 4 all similarity ratios were satisfied after each parameterwas reduced by the scale ratio except the value ρpρ Kind [25]has noted that this ratio need not be the same in the prototypeand the model but the ratio ρp(ρp minus ρ) should always be closeto one In this section the value of this ratio for prototype andmodel were approximately 101 and 1002 respectively

314 Information on Experimental Conditions To obtainwind speed data near the model during the test a thermalanemometer with a long probe was used to monitor theexperimental wind speed prior to the experiments -eaccuracy of measurement of wind speed was 001ms -eprofiles of the normalized mean wind speed (the ratio of themeasured wind speed U(z) to the reference wind speed U(R)and turbulence intensity at the front middle and rear abovethe experiment platform are illustrated in Figure 7 -e y-axis represents the cross-sectional height and the x-axis thenormalized wind velocity or turbulence intensity -ere is alittle difference between the test wind profile and the

normalized wind profile however Anno [23] indicated thatthe shape of the wind profile did not play a major role incontrolling the characteristic of the snowdrift by the windtunnel test on snow fences for the snowdrift pattern of themodel with abrupt height changes the small distortion of thewind profile is allowed -e box-type snow flux trapperdraws on the design experience summarized by Kimura [31]and snow flux along the height in the vertical plane wasmeasured by additional experiments with only the snow fluxtrapper on the test ground Snow flux along the verticaldirection in the experiments is illustrated in Figure 8 -e y-axis represents the height above the platform and the x-axisthe volume of snow flowing past in one second per squaremeter In these conditions it was challenging to consider thesimilarity of snow flux Considering that the experimentsfocused on snowdrift on the roof (02m above the ground) itcould not have had a large and unexpected impact on snowdistribution on the roof even though a snow flux rate below02m is high -us this similarity was ignored

Figure 6 Shape of the artificial snow particles

Table 2 Comparison of physical parameters of snow particles

Kind of particles Naturalsnow

Artificialsnow

Diameter Dp (mm) 015sim050 02sim050Particle density ρp (kgm3) 126sim294 540sim575Bulk density ρb (kgm3) 90sim210 386sim411-reshold friction velocity ulowastt(mmiddotsminus 1) 020 035

Angle of repose θ (deg) 30sim50 45

Table 3 Experimental parameters of prototype and experiments

Description Prototype ModelGeometrical scale ratio 1 1 1 30Wind velocity at height of reference point 114ms 25msWind duration 6 h 54min

Retractable roof Fixed roof

(a)

100m

020m

030m030m

012m200m

(b)

Figure 5 Schematic of size and shape of the test model (a) Photograph of the test model (b) ldquoClosedrdquo state

Complexity 7

Snow depth was measured using a steel ruler by hand toaccurately record the distribution of snow in the experi-ments According to the horizontal projection area of themodel a measurement point was arranged every 5 cm for atotal of 945 measurement points During the test the TC-4automatic weather station was used to monitor externalnatural conditions such as the natural wind environmenttemperature and humidity in real time

Wind direction is shown in Figure 9 -ree experimentswere designed to study the effect of wind direction when the

retractable roof was ldquoclosedrdquo -e experimental conditionsare listed in Table 5

32 CFD Simulation of Snowdrift on Horizontally RetractableRoof -e steady method was used to simulate the drift ofsnow particles on the surface of the roof and the transportequations of the air and snow phases were respectivelyestablished It was assumed that the relationship between thetwo phases was one-way coupledmdashthat is snowdriftedunder the action of wind (the air phase)mdashand the effects ofthe transport process and particle collision in the air wereignored

-e horizontally retractable roof model adopted for theCFD simulation is illustrated in Figure 10 and the meshscheme is presented in Figure 11 -e computation con-ditions are provided in Table 6 and the simulation conditionsare outlined in Table 7 -e initial snow depth is set as 03m

Table 4 Similarity parameters of prototype and scale model

Dimensionless parameters Prototype value Model value (110 scale)(1 minus (U0U))(U2Lg) 0163 0166UTL 4104 4050u3lowastt2g]ge 30 mdash 146

(u2lowasttDpg) middot (ρ(ρp minus ρ)) 0050sim0068 0054sim0065

ρpρ 974sim2274 4176sim4448(u2lowasttLg) middot (ρ(ρp minus ρ)) 0321times 10minus 6sim105times10minus 5 0216times10minus 5sim167times10minus 5

FrontMiddle

RearNormalized wind profile

00020406081012141618

H (m

)

06 07 08 09 10 11 12 1305U(z)U(R)

(a)

FrontMiddleRear

000 005 010 0151

00020406081012141618

H (m

)

(b)

Figure 7 Variations in normalized mean (a) wind speed and (b) intensity of turbulence with height

Experiment with U = 25ms

Roof level

100 2000V (cm3middotmndash2middotsndash1)

00

02

04

06

08

10

H (m

)

Figure 8 Snow flux along the vertical direction

Retractable roof

Fixed roof I Fixed roof II

0deg

45deg90deg

Figure 9 Sketch of the incidence angle of wind

8 Complexity

corresponding to the snow load of 045 kNm2 (snow densityequals 150 kgm3)

33 Comparison between Experimental Results and CFDSimulation Figure 12 illustrates the results of the simulationof the distribution of snow -e snow load coefficient is theratio of the depth of snow on the roof to the average snowfallSd (for the experiments Sd was determined by an additionalexperiment conducted for the same duration but withoutany obstacles in the test section and at least 10 points withan interval greater than 10 cm in the experimental modelarea should be selected to calculate the average)

When the wind direction was 0deg there were threemain snowdrifts on the roof I was at the front of the fixedroof I II was near the bottom of the retractable roof andIV was in the middle of fixed roof II -e snowdriftobtained by the CFD method was in good agreement withthat from the experiment in terms of both shape andvalue except that the snow accumulated in area III wasoverestimated

-e above overestimation can be explained according tothe wind field shown in Figure 13 Owing to the large lengthof the fixed roof on the windward side the wind reattachedat the front and this caused wind speed in the nearby area tobe low because of which a small amount of snow was de-posited at the front of the roof Near the junction with themovable roof the wind had a small vortex scale and lowwind speed because of which snow deposition occurred Onthe leeward side due to the reattachment of the wind to thecentral region and low wind speed there occurred

remarkable snowdrift -e difference in snow accumulationat the leeward junction might have obtained because in thenumerical simulation the accumulation of snow was rep-resented by the time integral according to the rate of snowdepositionerosion However although the wind speed waslow enough to make the snow particles settle at the leewardjunction the source of snow particles in this area was mainlythe reverse flow on the leeward roof and fewer snow par-ticles could enter this low-speed zone in snowfall -us alarge amount of snow was not accumulated

When the wind direction was 45deg although there wasconsiderable snowdrift in area I snow mainly accumulatedin area II and was distributed in a triangular shape -ereason for the difference at the junction on the leeward roofmight have been identical to that in the case when winddirection was 0deg

When the wind direction was 90deg snow mainly accu-mulated on the leeward side of the arched roof and its shapeand magnitude as obtained through the numerical simu-lation and the experiment were in good agreement -is canbe explained according to the wind field shown in Figure 14-e windward side of the roof is the acceleration zone andwind speed is relatively large therefore there is almost nosnow accumulation -e wind field is separated at the rearend of the leeward side and a standing vortex is formed onthe roof so that large snow accumulation occurs A dif-ference occurred at the windward side of the roof and thereason for it might be that wind speed in the experiment wasreduced according to the similarity criterion so thatsnowdrift occurred in the reverse area at the front of thewindward side of roof

In particular a significant change was evident insnow distribution on the roof -e area in which heavyaccumulation occurred changed and this indicatesthat wind direction had a significant effect on snowdistribution

Figures 15 and 16 illustrate snow distributions alongthe red line when the wind directions were 0deg and 90degrespectively -e x-axis represents the relative position onthe roof the y-axis represents the normalized snow depthat any point and S and Sd are the measured snow depth atany point and the average snowfall respectively It isevident that the snow distributions of the experiment andthe CFD simulation on the windward side exhibited thesame features in terms of distribution but their extremawere slightly different and the maximum snow depth inthe CFD simulation was 10 smaller than that in theexperiments Moreover by comparing snow depth on theleeward side the two results were observed to be inagreement with each other except when the snow depthwas overestimated near the border between the retractableand fixed roofs However considering that this

Table 5 Details of experimental conditions

Experiments Wind direction Wind speed Temperature Humidity Testing time State of retractable roof(a) 0deg 25ms minus 6degC 61 36min Closed(b) 45deg 25ms minus 10degC 55 36min Closed(c) 90deg 25ms minus 9degC 55 36min Closed

Retractable roof

Fixed roof

0deg

90deg h

fl1

l2

l1 = 30ml2 = 60m

fl2 = 60mh = 3m

Figure 10 Horizontally retractable roof model

Figure 11 Mesh scheme of model

Complexity 9


Conditions Settings

Computational domain 850m(x)lowast 250m(y)lowast 60m(z) (the building waslocated at 13 away from the entrance of airflow)

Number of elements Approximately 4800000Minimum mesh size 035m




(outflow)

Upper face and sideZero gradient condition for all variables and the

normal components of the wind velocity with respectto the boundaries are set to zero (symmetry)


Turbulence model Realizable k-ε modelMultiphase model Mixture modelResidual 10ndash7

Table 7 Simulation conditions

Experiments Wind direction (deg) Wind speed (at 6m height) (ms) State of retractable roof(a) 0 114 Closed(b) 45 114 Closed(c) 90 114 Closed

Movableroof

Movableroof

141312

091

0806

urWind

1612

20

0804

0

I II

Volume fraction

27E ndash 0528E ndash 0526E ndash 0525E ndash 0524E ndash 0523E ndash 0522E ndash 0521E ndash 052E ndash 0519E ndash 0518E ndash 0517E ndash 0516E ndash 0515E ndash 05

II III IVI II III IVI(A) (B)

(a)

Figure 12 Continued

10 Complexity

1716151413121110987654321

Reverse flow Reattachment point

XY

Z

ms

Figure 13 Wind speed vector at midsection when wind direction 0deg

Movableroof

Movableroof

12

10

08

05

03

01

urWind15

12

09

06

03

0

III

Volume fraction26E ndash 0725E ndash 0724E ndash 0723E ndash 0722E ndash 0721E ndash 0719E ndash 0718E ndash 0717E ndash 0716E ndash 0715E ndash 0714E ndash 0713E ndash 0712E ndash 0711E ndash 07

III III(A) (B)

(b)

Movableroof

Movableroof

1513110907050301

urWind1512090603

0

I II

Volume fraction27E ndash 0726E ndash 0725E ndash 0724E ndash 0723E ndash 0722E ndash 0721E ndash 072E ndash 0719E ndash 0718E ndash 0717E ndash 0716E ndash 0715E ndash 0714E ndash 07

II IIII II IIII(A) (B)

(c)

Figure 12 Comparison of results of experiments and simulations with different wind directions (A) Measurement (B) CFD simulation(a) When wind direction is 0deg (b) When wind direction is 45deg (c) When wind direction is 90deg

Complexity 11

overestimation was conservative the result obtained bythe CFD simulation is acceptable

Figure 16 shows that the results of the numericalsimulation along the windward side show severe erosionand snow accumulation here had a coecient of 06 in thetest on the leeward side the numerical simulation showsthat the extreme value of snow deposition was 5 greaterthan that in the experiment and the positions of theextrema were all in the range xl1 09sim10 e results onthe leeward side agreed well with the experimentalresults

e above analysis indicates that some dierencespersisted in the shape of the snow accumulated but con-sidering that the CFDmethod is reasonable at estimating theshape andmagnitude of the accumulating snow in general itis feasible and reliable for simulating snow distribution onretractable roofs

0

Wind

01 02 03 04 05 06 07 08 09 1000xl1

ExperimentCFD simulation

00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd

Figure 16 Comparison of results by means of experiments andCFD simulation along the central line when wind direction 90deg

Standing vortex

ms

X Y

Z

1716151413121110987654321


0

Wind


00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd

005000 015 020 025010 030 035xl2

(a)

0

Wind


00

05

10

15

20N

orm

aliz

ed sn

ow d

epth

SS

d

005000 015 020 025010 030 035xl2

(b)

Figure 15 Comparison of results by means of experiments and CFD simulation along the central line when wind direction 0deg(a) Windward side (b) Leeward side

12 Complexity

4 Conclusions

In this paper the accuracy of the CFD method in predictingsnow distribution was analyzed according to a snowdriftsimulation on a stepped roof model Snow distribution on atypical retractable roof was investigated both by experimentsand CFD simulations and the conclusions drawn from thestudy are as follows

(i) According to the results of the snowdrift simulationon a stepped roof with different turbulence modelsthe result obtained by the realizable k-ε modelexhibited better agreement with field observationsin terms of 2D distribution than other models

(ii) A typical horizontally retractable roof model wasselected to verify the accuracy of the CFD model inpredicting the 3D distribution of snow loads oncomplex roofs -e results obtained from the ex-periments and numerical simulations were in goodagreement for most snow accumulated whichfurther proves that numerical simulations can beused to estimate the distribution of snow load on theroofs of buildings

(iii) Under different wind directions snow accumula-tion always occurred at the boundary between themovable roof and the fixed roof and the leewardside-e distribution of snow in the retractable roofcan be determined by using directions of wind of 0degand 90deg as unfavorable angles We recommendinstalling snow removal equipment near theboundary of the movable roof

(iv) -e numerical simulations and the experimentsreflect the same law of snow deposition anderosion and the extrema of the obtained snowdistribution were similar but differences per-sisted in the specific area of deposition -is re-quires further study

Nonuniform snow loads on retractable roofs are com-plex and significant to safety Based on this study severalconclusions can be drawn using a simplified CFD methodwith dependent verification However this study has certainlimitations which will form the focus of future work

(i) When verifying the accuracy of the CFD method inpredicting 3D distributions of snow loads on com-plex roofs field observations of full-scale structuresor large-scale models are required

(ii) Only the ldquoclosedrdquo state of retractable roofs wasconsidered However in the event of a suddensnowstorm the retractable roof in its ldquoopenrdquo stateshould also be taken into account

Data Availability

-e data used to support the findings of this study are in-cluded within the article Previously reported data were usedto support this study and are available at (DOI 101016jjweia201712010) -ese prior studies (and datasets) arecited at relevant places within the text as references

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is work was conducted through the financial support ofthe National Natural Science Foundation of China (Projectdesignation 51878218 and 51378147)

References

[1] X Zhou J Hu andM Gu ldquoWind tunnel test of snow loads ona stepped flat roof using different granular materialsrdquo NaturalHazards vol 74 no 3 pp 1629ndash1648 2014

[2] Y Tominaga ldquoComputational fluid dynamics simulation ofsnowdrift around buildings past achievements and futureperspectivesrdquo Cold Regions Science and Technology vol 150pp 2ndash14 2018

[3] S Alhajraf ldquoComputational fluid dynamic modeling ofdrifting particles at porous fencesrdquo Environmental Modellingamp Software vol 19 no 2 pp 163ndash170 2004

[4] T Okaze H Niiya and K Nishimura ldquoDevelopment of alarge-eddy simulation coupled with Lagrangian snow trans-port modelrdquo Journal of Wind Engineering and IndustrialAerodynamics vol 183 pp 35ndash43 2018

[5] X Zhou L Kang M Gu L Qiu and J Hu ldquoNumericalsimulation and wind tunnel test for redistribution of snow ona flat roofrdquo Journal of Wind Engineering and IndustrialAerodynamics vol 153 pp 92ndash105 2016

[6] T Uematsu T Nakata K Takeuchi Y Arisawa andY Kaneda ldquo-ree-dimensional numerical simulation ofsnowdriftrdquo Cold Regions Science and Technology vol 20 no 1pp 65ndash73 1991

[7] J H M Beyers P A Sundsboslash and T M Harms ldquoNumericalsimulation of three-dimensional transient snow driftingaround a cuberdquo Journal of Wind Engineering and IndustrialAerodynamics vol 92 no 9 pp 725ndash747 2004

[8] M Beyers and B Waechter ldquoModeling transient snowdriftdevelopment around complex three-dimensional structuresrdquoJournal of Wind Engineering and Industrial vol 96 no 10-11pp 1603ndash1615 2008

[9] Y Tominaga T Okaze and A Mochida ldquoCFD modeling ofsnowdrift around a building an overview of models andevaluation of a new approachrdquo Building and Environmentvol 46 no 4 pp 899ndash910 2011

[10] T K -iis J Potac and J F Ramberg ldquo3D numericalsimulations and full scale measurements of snow depositionson a curved roofrdquo in Proceedings of the 5th European ampAfrican Conference on Wind Engineering Florence Italy July2009

[11] X Sun R He and YWu ldquoNumerical simulation of snowdrifton a membrane roof and the mechanical performance undersnow loadsrdquo Cold Regions Science and Technology vol 150pp 15ndash24 2018

[12] S J Wakes ldquoUse of CFD in the initial design of a snow fencerdquoin Proceedings of the 7th International Congress on Environ-mental Modelling and Software San Diego CA USA June2014

[13] ANSYSANSYS FLUENTHeory Guide ANSYS CanonsburgPA USA 2011

[14] Y Hao H Liu and Z Chen ldquoStudy on non-uniform snowload on single layer reticulated shell in Yujiapurdquo International

Complexity 13

Journal of Space Structures vol 22 no 02 pp 22ndash27 2016 inChinese

[15] M Naaim F Naaim-Bouvet and H Martinez ldquoNumericalsimulation of drifting snow erosion and deposition modelsrdquoAnnals of Glaciology vol 26 pp 191ndash196 1998

[16] AIJ AIJ Recommendations for Loads on Buildings AIJ TokyoJapan 2004

[17] J W Pomeroy and D M Gray ldquoSaltation of snowrdquo WaterResources Research vol 26 no 7 pp 1583ndash1594 1990

[18] J W Pomeroy and D H Male ldquoSteady-state suspension ofsnowrdquo Journal of Hydrology vol 1ndash4 no 136 pp 275ndash3011992

[19] Y Tominaga and A Mochida ldquoCFD prediction of flowfieldand snowdrift around a building complex in a snowy regionrdquoJournal of Wind Engineering and Industrial Aerodynamicsvol 81 no 1ndash3 pp 273ndash282 1999

[20] T Okaze Y Takano A Mochida and Y Tominaga ldquoDe-velopment of a new k-ε model to reproduce the aerodynamiceffects of snow particles on a flow fieldrdquo Journal of WindEngineering and Industrial Aerodynamics vol 144 pp 118ndash124 2015

[21] M Tsuchiya T Tomabechi T Hongo and H Ueda ldquoWindeffects on snowdrift on stepped flat roofsrdquo Journal of WindEngineering and Industrial Aerodynamics vol 90 no 12ndash15pp 1881ndash1892 2002

[22] M Liu Q Zhang F Fan and S Shen ldquoExperiments onnatural snow distribution around simplified building modelsbased on open air snow-wind combined experimental facil-ityrdquo Journal of Wind Engineering and Industrial Aerody-namics vol 173 pp 1ndash13 2018

[23] Y Anno ldquoRequirements for modeling of a snowdriftrdquo ColdRegions Science and Technology vol 8 no 3 pp 241ndash2521984

[24] J D Iversen ldquoComparison of wind-tunnel model and full-scale snow fence driftsrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 8 no 3 pp 231ndash249 1981

[25] R J Kind ldquoA critical examination of the requirements formodel simulation of wind-induced erosiondeposition phe-nomena such as snow driftingrdquo Atmospheric Environmentvol 10 no 3 pp 219ndash227 1976

[26] R J Kind ldquoSnowdrifting a review of modelling methodsrdquoCold Regions Science and Technology vol 12 no 3 pp 217ndash228 1986

[27] R J Kind and S B Murray ldquoSaltation flow measurementsrelating to modeling of snow driftingrdquo Journal of WindEngineering and Industrial Aerodynamics vol 10 no 1pp 89ndash102 1982

[28] F Naaim-Bouvet ldquoComparison of requirements for modelingsnowdrift in the case of outdoor and wind tunnel experi-mentsrdquo Surveys in Geophysics vol 16 no 5-6 pp 711ndash7271995

[29] R D Tabler ldquoSelf-similarity of wind profiles in blowing snowallows outdoor modelingrdquo Journal of Glaciology vol 26no 94 pp 421ndash434 1980

[30] H Mo F Fan and H Hong ldquoEvaluation of input wind speedused in wind tunnel test and numerical simulation to estimatedrifting snow profilerdquo Journal of Building Structures vol 36no 7 pp 75ndash80 2015 in Chinese

[31] T Kimura ldquoMeasurements of drifting snow particlesrdquoJournal of Geography (Chigaku Zasshi) vol 100 no 2pp 250ndash263 1991

14 Complexity

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of


Mathematical Problems in Engineering

Applied MathematicsJournal of


Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of



Engineering Mathematics

International Journal of


Operations ResearchAdvances in

Journal of


Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences


Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018


Decision SciencesAdvances in


AnalysisInternational Journal of


Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Two methods based on numerical simulations aremainly used to implement two-phase flow theory theEulerndashLagrange method and the EulerndashEuler method

-e EulerndashLagrange method assumes that the snowphase is discrete in the air Newtonrsquos law of motion is used toobtain the trajectory of a single snow particle and the volumeof snow is then distributed by integration Alhajraf [3]applied the EulerndashLagrange method to establish a FLOW-3Dmodel to investigate snowdrift around a snow fence andfound that the results were in agreement with those ofmeasurements Okaze et al [4] proposed a simulationmethod based on the coupling of large eddymodel (LES) andLagrangian method and applied this method to simulate thedevelopment of snow particle migration process under lowwind speed -is study found that at the initial stage thesnow particle transport mainly relies on the airflow to keepthe saltation of particles with the development of time theparticle splash and rebound caused by the collision occupythe dominant position of the particle transport Zhou et al[5] applied the CFD-DEMmethod to simulate the snowdrifton a typical stepped roof in 2D both considering the co-hesion and collision between snow particles and the snowdistribution was verified to be similar to that in fieldmeasurement and wind tunnel test

-e EulerndashEuler method assumes that both the air andthe snow phases are continuous and it is solved by addingthe governing equation of the snow phase to the controlequation of the air phase and most current numericalsimulations of wind-induced snowdrift use the EulerndashEulermethod

Uematsu et al [6] conducted a numerical simulation ofthe distribution of snowdrift around a snow fence -eyconsidered the saltation and suspension processes in thesimulation and proposed a three-dimensional (3D) simu-lation to yield results close to those of field observationsHowever the method only considers the rate of snow masstransfer and ignores the influence of wind turbulence Inprevious studies researchers were more concerned withsnowdrift on the ground Beyers et al [7] used FLOW-3D tosimulate snowdrift around a cube with a length of 2m -eyused the standard kndashεmodel and an improved turbulent wallfunction to consider the effect of the drift of the snowparticles on the effective length of roughness of the snowsurface and compared the results with those of measurementat the SANAE IV scientific research station in Antarctica-ey concluded that the results of snowdrift were in goodagreement with the measured values in terms of both shapeand magnitude Beyers and Waechter [8] used Fluent tosimulate snowdrift around two side-by-side cubic buildingsthree side-by-side overhead buildings and dormitorycomplex of the Antarctic scientific research base Embeddeduser-defined functions and mesh deformation were used tomodel changes in snowdrift over time owing to snow de-position or erosion Although the results of the numericalsimulation were in good agreement with measurementsbecause the authors had used the k-ε turbulencemodel in thesimulation where this model has inherent deficiencies theyalso opined that better results can be obtained when usingimproved two-equation models Tominaga et al [9] pointed

out that the governing equations used in previous studiescould not describe the changes of flow field around thebuilding accurately -e boundary conditions such asthreshold velocity and snow phase concentration have greatinfluence on the simulation results and a new method isproposed based on the Renault Time-Rate Method (RANS)and the reliability of the new method is verified by com-paring the simulation result of snow distribution around thecube with the measured results

Recent years researchers have witnessed more researchon the snow load on roofs -iis et al [10] conducted fieldmeasurements and numerical simulations on the curvedroof of a sports hall located in Oslo Sun et al [11] simulatedthe snowdrift on a long-span membrane roof and me-chanical performance of the membrane structure undernonuniform snow load was also studied However moststudies have focused on specific buildings and research onthe general rules of patterns of snow distribution on large-span roofs has rarely been reported Considering the di-versity of the shapes of large-span roofs many scholars havesuggested that for such structures with complex roof shapesboth numerical simulations and wind tunnel tests should becarried out to determine the coefficient of snow distribution

As the name implies the retractable roof is a type of roofstructure that allows the building to be used with an ldquoopenrdquoor ldquoclosedrdquo roof As a type of large-span structure with astrong comprehensive function the retractable roof savesenergy and is environmentally friendly in line with currentdevelopments in architectural technologies Retractableroofs are widely used however owing to their discontinuousshape more complex snow distribution occurs on themMoreover unlike the typical large-span roof snowdrift onretractable roofs may cause serious operational issues

Research relating to snow loads on retractable roofs isscant no specific provisions for this type of structure areavailable and only certain introductory articles are availablefor reference

-is study focuses on snow loads on a typical hori-zontally retractable roof which was widely used in long-spanroof structures as shown in Figure 1 and only the ldquoclosedrdquostate of the retractable roof is considered because buildingsshould be generally covered when it is snowing To validatethe accuracy of the numerical simulation of snow loaddistribution experiments on a horizontally retractable roofmodel were carried out to determine the accuracy of pre-dicting the overall snow load distribution and the regularityof snowdrift on such a roof Finally distributions of snow ontwo other typical retractable roofs were investigated usingthe CFD method

2 Numerical Method and Validation

21 Governing Equations EulerndashEuler description in mul-tiphase flow theory is used for the simulation in this study inwhich both snow and air are treated as continuous phases-ere are three EulerndashEuler-based multiphase models inFLUENT the VOF mixture and Eulerian models Amongthem the mixture model exhibits superior stability and lowcomputation requirements while delivering nearly the same

2 Complexity




z


m1113872 1113873 0 (1)

z ρm vm1113872 1113873



m + nablav

T

m1113874 11138751113876 1113877

+ ρmg

+ F

(2)

z ρsf2( 1113857


m1113872 1113873 0 (3)









ulowast

τρ

1113971

κu(z)

ln zzs( 1113857 (4)



2lowast1113872 1113873

qdep ρsfwf

u2lowastt minus u2

lowastu2lowastt

(5)



dh minusqs

ρscdt (6)



h(t) h0 +qs

ρsΔt (7)


(a) (b)


Complexity 3


v(z) v0z

z01113888 1113889

α

(8)



k 32(vI)

2

ε C34μ

k32

l

(9)


l

100z

301113874 1113875

05 30mlt zltZG

100 zle 30m

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(10)

l

01z

zG

1113888 1113889


zb lt zltZG

01zb

zG

1113888 1113889


zle zb

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(11)


f





ρs zgt hs

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(12)


hs 16u2lowast

2g (13)





4 Complexity

20 200

175

150

125

100

075

050

025

000

18

16

14

12

10

08

06

04

02

0000 05 10 15 20 25 30

Nor

mal

ized

snow

dep

ths S

Sd

xH

u lowastu

lowastt


ulowastu

lowastt

Tsuchiya et al

I II III IV


Coordinate axis


6H

3H2H

H

H

XY

Z

H = 09m

Wind

Measurement line







(outflow)





Complexity 5











1 minusU0

U1113874 1113875

U2

Lg1113888 1113889

p 1 minus

U0

U1113874 1113875

U2

Lg1113888 1113889

m (14)

UT

L1113874 1113875

p

UT

L1113874 1113875

m (15)

u3lowastt

2g]1113888 1113889

mge 30 (16)

u2lowastt

Dpgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

p

u2lowastt

Dpgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

m

(17)

ρpρ

1113888 1113889mge 600 (18)

u2lowastt

Lgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

p

u2lowastt

Lgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

m

(19)





Snowtrapper

Model


6 Complexity








Artificialsnow






(a)

100m

020m

030m030m

012m200m

(b)


Complexity 7










FrontMiddle


00020406081012141618

H (m

)

06 07 08 09 10 11 12 1305U(z)U(R)

(a)

FrontMiddleRear

000 005 010 0151

00020406081012141618

H (m

)

(b)



Roof level


00

02

04

06

08

10

H (m

)


Retractable roof


0deg

45deg90deg


8 Complexity












Retractable roof

Fixed roof

0deg

90deg h

fl1

l2

l1 = 30ml2 = 60m

fl2 = 60mh = 3m



Complexity 9


Conditions Settings






(outflow)







Movableroof

Movableroof

141312

091

0806

urWind

1612

20

0804

0

I II

Volume fraction



(a)

Figure 12 Continued

10 Complexity

1716151413121110987654321


XY

Z

ms


Movableroof

Movableroof

12

10

08

05

03

01

urWind15

12

09

06

03

0

III


III III(A) (B)

(b)

Movableroof

Movableroof

1513110907050301

urWind1512090603

0

I II



(c)


Complexity 11




0

Wind

01 02 03 04 05 06 07 08 09 1000xl1


00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd


Standing vortex

ms

X Y

Z

1716151413121110987654321


0

Wind


00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd

005000 015 020 025010 030 035xl2

(a)

0

Wind


00

05

10

15

20N

orm

aliz

ed sn

ow d

epth

SS

d

005000 015 020 025010 030 035xl2

(b)


12 Complexity

4 Conclusions









Data Availability




Acknowledgments


References















Complexity 13



















14 Complexity








Journal of












Journal of







Volume 2018






Volume 2018











z


m1113872 1113873 0 (1)

z ρm vm1113872 1113873



m + nablav

T

m1113874 11138751113876 1113877

+ ρmg

+ F

(2)

z ρsf2( 1113857


m1113872 1113873 0 (3)









ulowast

τρ

1113971

κu(z)

ln zzs( 1113857 (4)



2lowast1113872 1113873

qdep ρsfwf

u2lowastt minus u2

lowastu2lowastt

(5)



dh minusqs

ρscdt (6)



h(t) h0 +qs

ρsΔt (7)


(a) (b)


Complexity 3


v(z) v0z

z01113888 1113889

α

(8)



k 32(vI)

2

ε C34μ

k32

l

(9)


l

100z

301113874 1113875

05 30mlt zltZG

100 zle 30m

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(10)

l

01z

zG

1113888 1113889


zb lt zltZG

01zb

zG

1113888 1113889


zle zb

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(11)


f





ρs zgt hs

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(12)


hs 16u2lowast

2g (13)





4 Complexity

20 200

175

150

125

100

075

050

025

000

18

16

14

12

10

08

06

04

02

0000 05 10 15 20 25 30

Nor

mal

ized

snow

dep

ths S

Sd

xH

u lowastu

lowastt


ulowastu

lowastt

Tsuchiya et al

I II III IV


Coordinate axis


6H

3H2H

H

H

XY

Z

H = 09m

Wind

Measurement line







(outflow)





Complexity 5











1 minusU0

U1113874 1113875

U2

Lg1113888 1113889

p 1 minus

U0

U1113874 1113875

U2

Lg1113888 1113889

m (14)

UT

L1113874 1113875

p

UT

L1113874 1113875

m (15)

u3lowastt

2g]1113888 1113889

mge 30 (16)

u2lowastt

Dpgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

p

u2lowastt

Dpgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

m

(17)

ρpρ

1113888 1113889mge 600 (18)

u2lowastt

Lgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

p

u2lowastt

Lgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

m

(19)





Snowtrapper

Model


6 Complexity








Artificialsnow






(a)

100m

020m

030m030m

012m200m

(b)


Complexity 7










FrontMiddle


00020406081012141618

H (m

)

06 07 08 09 10 11 12 1305U(z)U(R)

(a)

FrontMiddleRear

000 005 010 0151

00020406081012141618

H (m

)

(b)



Roof level


00

02

04

06

08

10

H (m

)


Retractable roof


0deg

45deg90deg


8 Complexity












Retractable roof

Fixed roof

0deg

90deg h

fl1

l2

l1 = 30ml2 = 60m

fl2 = 60mh = 3m



Complexity 9


Conditions Settings






(outflow)







Movableroof

Movableroof

141312

091

0806

urWind

1612

20

0804

0

I II

Volume fraction



(a)

Figure 12 Continued

10 Complexity

1716151413121110987654321


XY

Z

ms


Movableroof

Movableroof

12

10

08

05

03

01

urWind15

12

09

06

03

0

III


III III(A) (B)

(b)

Movableroof

Movableroof

1513110907050301

urWind1512090603

0

I II



(c)


Complexity 11




0

Wind

01 02 03 04 05 06 07 08 09 1000xl1


00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd


Standing vortex

ms

X Y

Z

1716151413121110987654321


0

Wind


00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd

005000 015 020 025010 030 035xl2

(a)

0

Wind


00

05

10

15

20N

orm

aliz

ed sn

ow d

epth

SS

d

005000 015 020 025010 030 035xl2

(b)


12 Complexity

4 Conclusions









Data Availability




Acknowledgments


References















Complexity 13



















14 Complexity








Journal of












Journal of







Volume 2018






Volume 2018









v(z) v0z

z01113888 1113889

α

(8)



k 32(vI)

2

ε C34μ

k32

l

(9)


l

100z

301113874 1113875

05 30mlt zltZG

100 zle 30m

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(10)

l

01z

zG

1113888 1113889


zb lt zltZG

01zb

zG

1113888 1113889


zle zb

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(11)


f





ρs zgt hs

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(12)


hs 16u2lowast

2g (13)





4 Complexity

20 200

175

150

125

100

075

050

025

000

18

16

14

12

10

08

06

04

02

0000 05 10 15 20 25 30

Nor

mal

ized

snow

dep

ths S

Sd

xH

u lowastu

lowastt


ulowastu

lowastt

Tsuchiya et al

I II III IV


Coordinate axis


6H

3H2H

H

H

XY

Z

H = 09m

Wind

Measurement line







(outflow)





Complexity 5











1 minusU0

U1113874 1113875

U2

Lg1113888 1113889

p 1 minus

U0

U1113874 1113875

U2

Lg1113888 1113889

m (14)

UT

L1113874 1113875

p

UT

L1113874 1113875

m (15)

u3lowastt

2g]1113888 1113889

mge 30 (16)

u2lowastt

Dpgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

p

u2lowastt

Dpgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

m

(17)

ρpρ

1113888 1113889mge 600 (18)

u2lowastt

Lgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

p

u2lowastt

Lgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

m

(19)





Snowtrapper

Model


6 Complexity








Artificialsnow






(a)

100m

020m

030m030m

012m200m

(b)


Complexity 7










FrontMiddle


00020406081012141618

H (m

)

06 07 08 09 10 11 12 1305U(z)U(R)

(a)

FrontMiddleRear

000 005 010 0151

00020406081012141618

H (m

)

(b)



Roof level


00

02

04

06

08

10

H (m

)


Retractable roof


0deg

45deg90deg


8 Complexity












Retractable roof

Fixed roof

0deg

90deg h

fl1

l2

l1 = 30ml2 = 60m

fl2 = 60mh = 3m



Complexity 9


Conditions Settings






(outflow)







Movableroof

Movableroof

141312

091

0806

urWind

1612

20

0804

0

I II

Volume fraction



(a)

Figure 12 Continued

10 Complexity

1716151413121110987654321


XY

Z

ms


Movableroof

Movableroof

12

10

08

05

03

01

urWind15

12

09

06

03

0

III


III III(A) (B)

(b)

Movableroof

Movableroof

1513110907050301

urWind1512090603

0

I II



(c)


Complexity 11




0

Wind

01 02 03 04 05 06 07 08 09 1000xl1


00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd


Standing vortex

ms

X Y

Z

1716151413121110987654321


0

Wind


00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd

005000 015 020 025010 030 035xl2

(a)

0

Wind


00

05

10

15

20N

orm

aliz

ed sn

ow d

epth

SS

d

005000 015 020 025010 030 035xl2

(b)


12 Complexity

4 Conclusions









Data Availability




Acknowledgments


References















Complexity 13



















14 Complexity








Journal of












Journal of







Volume 2018






Volume 2018








20 200

175

150

125

100

075

050

025

000

18

16

14

12

10

08

06

04

02

0000 05 10 15 20 25 30

Nor

mal

ized

snow

dep

ths S

Sd

xH

u lowastu

lowastt


ulowastu

lowastt

Tsuchiya et al

I II III IV


Coordinate axis


6H

3H2H

H

H

XY

Z

H = 09m

Wind

Measurement line







(outflow)





Complexity 5











1 minusU0

U1113874 1113875

U2

Lg1113888 1113889

p 1 minus

U0

U1113874 1113875

U2

Lg1113888 1113889

m (14)

UT

L1113874 1113875

p

UT

L1113874 1113875

m (15)

u3lowastt

2g]1113888 1113889

mge 30 (16)

u2lowastt

Dpgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

p

u2lowastt

Dpgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

m

(17)

ρpρ

1113888 1113889mge 600 (18)

u2lowastt

Lgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

p

u2lowastt

Lgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

m

(19)





Snowtrapper

Model


6 Complexity








Artificialsnow






(a)

100m

020m

030m030m

012m200m

(b)


Complexity 7










FrontMiddle


00020406081012141618

H (m

)

06 07 08 09 10 11 12 1305U(z)U(R)

(a)

FrontMiddleRear

000 005 010 0151

00020406081012141618

H (m

)

(b)



Roof level


00

02

04

06

08

10

H (m

)


Retractable roof


0deg

45deg90deg


8 Complexity












Retractable roof

Fixed roof

0deg

90deg h

fl1

l2

l1 = 30ml2 = 60m

fl2 = 60mh = 3m



Complexity 9


Conditions Settings






(outflow)







Movableroof

Movableroof

141312

091

0806

urWind

1612

20

0804

0

I II

Volume fraction



(a)

Figure 12 Continued

10 Complexity

1716151413121110987654321


XY

Z

ms


Movableroof

Movableroof

12

10

08

05

03

01

urWind15

12

09

06

03

0

III


III III(A) (B)

(b)

Movableroof

Movableroof

1513110907050301

urWind1512090603

0

I II



(c)


Complexity 11




0

Wind

01 02 03 04 05 06 07 08 09 1000xl1


00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd


Standing vortex

ms

X Y

Z

1716151413121110987654321


0

Wind


00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd

005000 015 020 025010 030 035xl2

(a)

0

Wind


00

05

10

15

20N

orm

aliz

ed sn

ow d

epth

SS

d

005000 015 020 025010 030 035xl2

(b)


12 Complexity

4 Conclusions









Data Availability




Acknowledgments


References















Complexity 13



















14 Complexity








Journal of












Journal of







Volume 2018






Volume 2018


















1 minusU0

U1113874 1113875

U2

Lg1113888 1113889

p 1 minus

U0

U1113874 1113875

U2

Lg1113888 1113889

m (14)

UT

L1113874 1113875

p

UT

L1113874 1113875

m (15)

u3lowastt

2g]1113888 1113889

mge 30 (16)

u2lowastt

Dpgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

p

u2lowastt

Dpgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

m

(17)

ρpρ

1113888 1113889mge 600 (18)

u2lowastt

Lgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

p

u2lowastt

Lgmiddot

ρρp minus ρ1113872 1113873

⎛⎝ ⎞⎠

m

(19)





Snowtrapper

Model


6 Complexity








Artificialsnow






(a)

100m

020m

030m030m

012m200m

(b)


Complexity 7










FrontMiddle


00020406081012141618

H (m

)

06 07 08 09 10 11 12 1305U(z)U(R)

(a)

FrontMiddleRear

000 005 010 0151

00020406081012141618

H (m

)

(b)



Roof level


00

02

04

06

08

10

H (m

)


Retractable roof


0deg

45deg90deg


8 Complexity












Retractable roof

Fixed roof

0deg

90deg h

fl1

l2

l1 = 30ml2 = 60m

fl2 = 60mh = 3m



Complexity 9


Conditions Settings






(outflow)







Movableroof

Movableroof

141312

091

0806

urWind

1612

20

0804

0

I II

Volume fraction



(a)

Figure 12 Continued

10 Complexity

1716151413121110987654321


XY

Z

ms


Movableroof

Movableroof

12

10

08

05

03

01

urWind15

12

09

06

03

0

III


III III(A) (B)

(b)

Movableroof

Movableroof

1513110907050301

urWind1512090603

0

I II



(c)


Complexity 11




0

Wind

01 02 03 04 05 06 07 08 09 1000xl1


00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd


Standing vortex

ms

X Y

Z

1716151413121110987654321


0

Wind


00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd

005000 015 020 025010 030 035xl2

(a)

0

Wind


00

05

10

15

20N

orm

aliz

ed sn

ow d

epth

SS

d

005000 015 020 025010 030 035xl2

(b)


12 Complexity

4 Conclusions









Data Availability




Acknowledgments


References















Complexity 13



















14 Complexity








Journal of












Journal of







Volume 2018






Volume 2018















Artificialsnow






(a)

100m

020m

030m030m

012m200m

(b)


Complexity 7










FrontMiddle


00020406081012141618

H (m

)

06 07 08 09 10 11 12 1305U(z)U(R)

(a)

FrontMiddleRear

000 005 010 0151

00020406081012141618

H (m

)

(b)



Roof level


00

02

04

06

08

10

H (m

)


Retractable roof


0deg

45deg90deg


8 Complexity












Retractable roof

Fixed roof

0deg

90deg h

fl1

l2

l1 = 30ml2 = 60m

fl2 = 60mh = 3m



Complexity 9


Conditions Settings






(outflow)







Movableroof

Movableroof

141312

091

0806

urWind

1612

20

0804

0

I II

Volume fraction



(a)

Figure 12 Continued

10 Complexity

1716151413121110987654321


XY

Z

ms


Movableroof

Movableroof

12

10

08

05

03

01

urWind15

12

09

06

03

0

III


III III(A) (B)

(b)

Movableroof

Movableroof

1513110907050301

urWind1512090603

0

I II



(c)


Complexity 11




0

Wind

01 02 03 04 05 06 07 08 09 1000xl1


00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd


Standing vortex

ms

X Y

Z

1716151413121110987654321


0

Wind


00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd

005000 015 020 025010 030 035xl2

(a)

0

Wind


00

05

10

15

20N

orm

aliz

ed sn

ow d

epth

SS

d

005000 015 020 025010 030 035xl2

(b)


12 Complexity

4 Conclusions









Data Availability




Acknowledgments


References















Complexity 13



















14 Complexity








Journal of












Journal of







Volume 2018






Volume 2018

















FrontMiddle


00020406081012141618

H (m

)

06 07 08 09 10 11 12 1305U(z)U(R)

(a)

FrontMiddleRear

000 005 010 0151

00020406081012141618

H (m

)

(b)



Roof level


00

02

04

06

08

10

H (m

)


Retractable roof


0deg

45deg90deg


8 Complexity












Retractable roof

Fixed roof

0deg

90deg h

fl1

l2

l1 = 30ml2 = 60m

fl2 = 60mh = 3m



Complexity 9


Conditions Settings






(outflow)







Movableroof

Movableroof

141312

091

0806

urWind

1612

20

0804

0

I II

Volume fraction



(a)

Figure 12 Continued

10 Complexity

1716151413121110987654321


XY

Z

ms


Movableroof

Movableroof

12

10

08

05

03

01

urWind15

12

09

06

03

0

III


III III(A) (B)

(b)

Movableroof

Movableroof

1513110907050301

urWind1512090603

0

I II



(c)


Complexity 11




0

Wind

01 02 03 04 05 06 07 08 09 1000xl1


00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd


Standing vortex

ms

X Y

Z

1716151413121110987654321


0

Wind


00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd

005000 015 020 025010 030 035xl2

(a)

0

Wind


00

05

10

15

20N

orm

aliz

ed sn

ow d

epth

SS

d

005000 015 020 025010 030 035xl2

(b)


12 Complexity

4 Conclusions









Data Availability




Acknowledgments


References















Complexity 13



















14 Complexity








Journal of












Journal of







Volume 2018






Volume 2018



















Retractable roof

Fixed roof

0deg

90deg h

fl1

l2

l1 = 30ml2 = 60m

fl2 = 60mh = 3m



Complexity 9


Conditions Settings






(outflow)







Movableroof

Movableroof

141312

091

0806

urWind

1612

20

0804

0

I II

Volume fraction



(a)

Figure 12 Continued

10 Complexity

1716151413121110987654321


XY

Z

ms


Movableroof

Movableroof

12

10

08

05

03

01

urWind15

12

09

06

03

0

III


III III(A) (B)

(b)

Movableroof

Movableroof

1513110907050301

urWind1512090603

0

I II



(c)


Complexity 11




0

Wind

01 02 03 04 05 06 07 08 09 1000xl1


00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd


Standing vortex

ms

X Y

Z

1716151413121110987654321


0

Wind


00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd

005000 015 020 025010 030 035xl2

(a)

0

Wind


00

05

10

15

20N

orm

aliz

ed sn

ow d

epth

SS

d

005000 015 020 025010 030 035xl2

(b)


12 Complexity

4 Conclusions









Data Availability




Acknowledgments


References















Complexity 13



















14 Complexity








Journal of












Journal of







Volume 2018






Volume 2018









Conditions Settings






(outflow)







Movableroof

Movableroof

141312

091

0806

urWind

1612

20

0804

0

I II

Volume fraction



(a)

Figure 12 Continued

10 Complexity

1716151413121110987654321


XY

Z

ms


Movableroof

Movableroof

12

10

08

05

03

01

urWind15

12

09

06

03

0

III


III III(A) (B)

(b)

Movableroof

Movableroof

1513110907050301

urWind1512090603

0

I II



(c)


Complexity 11




0

Wind

01 02 03 04 05 06 07 08 09 1000xl1


00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd


Standing vortex

ms

X Y

Z

1716151413121110987654321


0

Wind


00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd

005000 015 020 025010 030 035xl2

(a)

0

Wind


00

05

10

15

20N

orm

aliz

ed sn

ow d

epth

SS

d

005000 015 020 025010 030 035xl2

(b)


12 Complexity

4 Conclusions









Data Availability




Acknowledgments


References















Complexity 13



















14 Complexity








Journal of












Journal of







Volume 2018






Volume 2018








1716151413121110987654321


XY

Z

ms


Movableroof

Movableroof

12

10

08

05

03

01

urWind15

12

09

06

03

0

III


III III(A) (B)

(b)

Movableroof

Movableroof

1513110907050301

urWind1512090603

0

I II



(c)


Complexity 11




0

Wind

01 02 03 04 05 06 07 08 09 1000xl1


00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd


Standing vortex

ms

X Y

Z

1716151413121110987654321


0

Wind


00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd

005000 015 020 025010 030 035xl2

(a)

0

Wind


00

05

10

15

20N

orm

aliz

ed sn

ow d

epth

SS

d

005000 015 020 025010 030 035xl2

(b)


12 Complexity

4 Conclusions









Data Availability




Acknowledgments


References















Complexity 13



















14 Complexity








Journal of












Journal of







Volume 2018






Volume 2018











0

Wind

01 02 03 04 05 06 07 08 09 1000xl1


00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd


Standing vortex

ms

X Y

Z

1716151413121110987654321


0

Wind


00

05

10

15

20

Nor

mal

ized

snow

dep

th S

Sd

005000 015 020 025010 030 035xl2

(a)

0

Wind


00

05

10

15

20N

orm

aliz

ed sn

ow d

epth

SS

d

005000 015 020 025010 030 035xl2

(b)


12 Complexity

4 Conclusions









Data Availability




Acknowledgments


References















Complexity 13



















14 Complexity








Journal of












Journal of







Volume 2018






Volume 2018








4 Conclusions









Data Availability




Acknowledgments


References















Complexity 13



















14 Complexity








Journal of












Journal of







Volume 2018






Volume 2018


























14 Complexity








Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








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