3D numerical simulations and full scale measurements of snow depositions on a curved roof

Transcription

1 EACWE 5 Florence, Italy 19 th 23 rd July 2009 Flying Sphere image Museo Ideale L. Da Vinci 3D numerical simulations and full scale measurements of snow depositions on a curved roof T. K. Thiis, J. Potac, J. F. Ramberg Norwegian University of Life Sciences, Department of Mathematical Sciences and Technology thomas.thiis@umb.no P.O. Box 5003, 1432 Ås, Norway Keywords: snow, deposition, CFD, curved roof. ABSTRACT A two phase CFD simulation with transient changing snow surface has been used to simulate snow deposition on a large curved roof. The results from the simulations have been compared with full scale measurements taken from short term snow precipitation episodes in low wind speeds. The simulations have captured the measurements quite well but some discrepancies have been seen on the edges of the roof. This was possibly caused by end effects, which are sensitive to the approaching wind direction. The simulations were run with one single wind direction whereas the measurements result from slightly fluctuating wind direction over some time. This indicates the importance of accuracy of the wind flow simulation and the inlet conditions for a successful outcome in the prediction of snow deposition. The simulations have shown that the snow accumulation initiates close to the leeward reattachment zone and develops further downwind. This observation has been confirmed by the full scale measurements. Since the small changes in the wind flow alter the deposition and erosion rates, the results also underlines the importance of considering the transient development of the snow drift when determining snow loads in different climates. Contact person: T. K. Thiis, Norwegian University of Life Sciences, Department of Mathematical Sciences and Technology, P.O. Box 5003, 1432 Ås, telephone: , FAX: thomas.thiis@umb.no

2 1.INTRODUCTION In many areas snow load is the largest load imposed on buildings. The snow load may vary substantially over a relatively small distance on the roof. Even if the phenomenon is well known, there are still buildings collapsing, sometimes with devastating effects. As building design increases in complexity, the need for more sophisticated design tools increases. Complex roof shapes might sometimes create surprising patterns of snow drifts on the roof. When establishing the design snow load on a roof, the use of building standards has been common. Usually the standards apply a coefficient based approach, where the characteristic ground snow load is multiplied by various coefficients. These coefficients shall, for instance, take in account the effect of wind exposure, thermal transmittance and the shape of the roof. The coefficients found in standards are usually coarse simplifications representing the worst appearing load arrangement, often with some degree of conservatism. This results in a design load, which is in many occasions over estimated and, as structural collapses might indicate, in some occasions under estimated. To establish more accurate design load for a particular building, wind tunnel, water flume or Computational Fluid Dynamics (CFD) have been used. However, no commonly agreed and verified method to simulate the snow load on roofs has not been introduced yet. The use of numerical simulation of snow accumulation to establish the design snow load on structures is dependent on comparison with full scale measurements. In this paper, the use of a CFD solver on a large curved roof was investigated for three dimensional and two phase transient simulations In the previous work, Thiis at al (2008) found that snow accumulation is initiated at the reattachment zone on the leeward side of the roof. The background of this investigation is based on observations of snow load arrangement differing from the building standards used in Norway. On the investigated building the snowdrift parallel to the roof ridge is formed on the leeward side only. In the Norwegian national snow load standard NS :2001 and also in the European Eurocode standard EN ) the drifted snow load arrangement on the curved roof is treated as a two sided snow load, where the load on the windward side is half of the leeward one. However, the one sided load arrangement is often more severe for a curved roof than a two sided load arrangement. A new Norwegian National Annex to the Eurocode will ensure that curved roofs in Norway will be calculated for a one sided load arrangement in the future. Based upon 20 years of full scale measurements on about 200 agricultural buildings with gable roof, Høibø (1988) reported that the ratio of snow load on the roof to the ground snow load, introduced as shape coefficient, decreases with increasing ground snow load. There might be several explanations for this. Following Tabler (1988) measurements of equilibrium shape of snowdrifts, one explanation might be that the roof load reaches maximum when the snowdrift on the top of the roof is at equilibrium. When the snowdrift reaches the equilibrium, the shape factor will decrease as the ground load increases. This is valid only if the snowdrift is developed in windy conditions, either consisting of redistributed snow particles, or during episodes of precipitating snow in combination with wind. Also, Thiis (2003) measured that the development rate of snowdrifts around buildings decreased during the accumulation. Using the simplified model where ground snow load is multiplied by a shape factor implies that the shape factor could be reduced in areas with a long winter where snow drifts on roofs would be at an equilibrium. On the other hand, it could also imply that the shape factor should be increased in areas with a short winter. This depends on the climate the shape factor in the standard is developed for. Another simplification in the standard is the usage of ground snow load in the definition of unbalanced snow load. The unbalanced load is defined as the product of ground snow load, shape factor and a poorly defined exposure factor. (Meløysund 2006).

3 2. METHODOLOGY 2.1Field measurements The investigated building is a sports hall located in Oslo, and oriented with the ridge pointing 11 degrees west of north. The building overall dimensions are 123 m long, 106 m wide and 25 m tall. The roof is formed as a quarter of a cylinder with a radius of 60.5 m. The curved roof is met by a flat roof on each side where the slope of the arch reaches 45 degrees, making the span of the roof about 85 m. A total of 20 ventilation hatches are placed 11 m from the roof ridge, ten of both sides. The hatch dimensions are 2 m long, 1 m wide and 0.3 m high. Meteorological data is taken from a meteorological weather station located approximately 200 m north of the building. The characteristic ground snow load with a 50 year return period for this site is 3.5 kn/m 2. The building site can be expected to have a normal exposure to the wind, the exposure coefficient, according to Eurocode, has the value 1.0. The snow deposition on the roof was measured twice, in February 2007 and in January The governing wind direction during snow falls was altering between 60 and 80 degrees. When the wind direction is 80 degrees, the wind approaches perpendicular to the long side of the building. A wind rose together with model geometry can be seen in Figure 1. Note that the building model in is not oriented correctly according to the wind rose. Figure 1: Wind statistics, and model of geometry The wind speed, temperature and cumulative snow depth for the immediate period before the measurements are plotted in Figure 2. For the 2007 data, although the measured snow depths were non-zero, the roof was not covered by any snow at 21 st February when the snow precipitation started due to previous melting. The snow accumulating periods were then from 20 th to 27 th February 2007 and from 2 nd to 7 th January The measured average wind speeds were 4.3 m/s and 4.6 m/s, respectively. The snow depth was measured in several sections perpendicular to the ridge. Snow density samples were taken from different places in the snowdrift. The contribution of snow drifting from the upwind areas of the building can be ignored due to the height of the investigated building and the surrounding topography. The climate at the site is relatively mild and with low wind speeds. Therefore, the driving force forming the drifts on the leeward side is believed to be the wind during snow fall and the effect of snow particles being relocated between snow falls is believed be of minor importance.

4 Figure 2: Weather data during snow fall 2007 and Numerical simulation To simulate the wind field and snow accumulation, the general purpose finite volume CFD code ANSYS CFX 11 was applied. The simulations were three dimensional with a transient developing snow surface. The model of the building was placed in a domain measuring 150 x 500 meters. The CFD code solves the incompressible, time averaged Navier-Stokes equations, using the k-ε RNG turbulence model to close the equations. This turbulence model includes terms for dissipation rate development that improves the accuracy compared to the standard k-ε turbulence model. It is widely used in simulations of wind around buildings and it is capable of producing realistic results, according to Kim et al (2000). The two phase fluid flow is solved with the Euler-Euler approach. Both the air and the snow phase possess its own flow field and the fluids interact via the drag force in equation (1). F d = 1 2 snow A C d U snow U air (1) Here snow is the density of snow particles, A is the projected area of the the particle, C d is the drag coefficient set to 0.44, and U snow U air is the relative air velocity. The diameter of the snow particle is set to 1 mm (Mason 1962). The roof in consideration is probably not affected by redistributed snow. The wind conditions and the fetch at the site do not imply that snow will be moved from the ground to the roof. The simulation boundary conditions are therefore assumed to be similar to precipitating snow and low wind velocity. The vertical wind speed distribution is assumed to be the logarithmic function in equation (2).

5 u z = u * ln z z 0 (2) Where u z is the wind speed at a given height z, u * is the friction velocity set to 0.4. is the von Karman's constant equal 0.41 and z 0 is the aerodynamical height of the roughness elements set to 0.1 m. To simulate a transient development of the snow surface, the mesh is deformed after each time step by applying the erosion flux and the deposition flux given by Naaim et al (1998). q ero =B u 2 * u * t if u * u * t u 2 *t u * q dep =C w f 2 u *t if u * u *t (3) Where B is a coefficient representing the intergranular bonding in the surface layer, u * is the friction velocity, is u *t the threshold friction velocity of snow, C is the snow concentration and w f is the terminal fall velocity of a snow particle. In the present simulation the value of B is set to , the value of w f is set to 0.5 m/s and u *t is set to 0.25 m/s. The resulting erosion and deposition flux is then calculated by q erodep =q dep q ero In this form, the effect of impinging particles on the surface erosion is ignored. Finally, the change in snow surface level is calculated and applied as a mesh deformation by h t = q erodep where h,t, represents the snow surface level, time and bulk snow density, respectively. In the present analysis, the snow particle is simulated with a density of 50 kg/m 3. This density value corresponds to soft new snow (Armstrong et al 2008). However, the snow pack density in the model is set to 150 kg/m 3. The density of the snow particles is described as loose fresh dry snow by Kind (1981). (4) (5) 3. RESULTS 3.1Field measurements As was mentioned above, the snow depth was measured in several sections parallely to the building gable 11 m, 29 m, 44 m, 70 m, 81 m, 93 and 110 m in 2007, and 52 m, 64 m and 74 m in The windward side of the roof was uniformly covered by snow with the depth of 0.02 m in The maximum snowdrift depth of 0.76 m was measured approximately 27 m downwind from the roof ridge. This distance was not uniform along the roof. Due to the wind direction, the drift further from the origin edge was developed more downwind from the ridge. Generally there are two regions close to the roof edges which are affected by the vortices forming there and causing the snow to blow off the roof. However, a small snowdrift is accumulated along the lateral edges of the roof. This pattern is possibly developed by trailing vortices. The measured snow depth contours of 2007 season can be seen in Figure 3.

6 F07 cm Figure 3: Snow depth contours in 2007 Together with snow depth measurements several snow density samples were taken on the roof and on the ground. The results for both years can be seen in Table 1. Table 1: Snow densities measured on the ground and roof in 2007 and Year Snow Density [kg/m3] Roof Ground The average density on the roof measured in 2007 and 2008 was 207 kg/m 3 and 167 kg/m 3, respectively. The ground snow density samples were taken at random positions in the flat and open area north of the building. The average ground snow depth measured in 2007 and 2008 is 0.17 m and 0.2 m, respectively. 3.2Numerical simulation The computational domain was meshed containing cells. Close to all the surfaces, the mesh consists of an inflation layer with gradually increasing cell size with a minimum height of 1.7 cm. The inlet logarithmic wind profile was set up based on meteorological data to 4.6 m/s and 4.3 m/s at 10 meters above the ground. The turbulence intensity set up in velocity inlet was 5 %. The inlet snow fraction was set to , which corresponds to 9 mm/h of water equivalent. The roof boundary condition was defined as wall using the displacement mesh deformation condition. The mesh deformation approach can introduce errors to the mesh in regions where the snow accumulates fast and the surface is irregular e.g. along ridges. One way to avoid this could be to remesh the domain after each time step. However, since the CFX code has not implemented such a feature yet, another solution was tried. The most critical locations on the simulated building appear close to the ventilation hatches. Since the accurate snow accumulation has not been the main

7 concern in this area, a small patch using unspecified mesh deformation was defined around each ventilation hatch. The numerical model uses two separate sets of time steps. The first set is involved in solving the mesh deformation, and the other one in the transient flow calculations. The time constants used for transient flow and mesh deformation are in order of minutes and seconds, respectively. The simulation results together with the 2007 measurements for all planes are plotted in Figure 4. Figure 4: Simulation results and measurements in 2007 In the results for section 11, two zones can be indentified. In the first zone, close to the ridge, the agreement between simulation and measurements is quite well. The snow depth on the remaining part of the section does not reproduce the measurements. The reason for this can be found in the wind pattern shown in Figure 5 a). In this section no reattachment of the flow appear, inhibiting the accumulation of snow. Figure 5: a) Wind patterns of section 11, and b) overall snow drift contours

8 Since this plane is located in the area relatively close to the roof edge, the wind pattern on the roof is affected by the the wind flow around the ends of the roof. Figure 5 b) shows the simulated overall snowdrift pattern on the roof. The location of the end effects can be seen close to section 11. In the next two sections 27 and 44, the simulated shape fits the measured values well. Note, the short discontinuity in simulated snow depth in section 44 represents a ventilation hatch. In section 70, the position of the simulated snowdrift is 5 m closer to the ridge than in the measurements. There is also difference in maximum height about 20 cm. In plane 81 the simulated snowdrift is displaced approximately 5 m compare to measurements. There is a good correlation between simulation and measurements in the section 93. In 2008 the measured sections were located in the central part of the roof. The comparison between measurements and simulation can be seen in Figure 6. The obtained simulation results represent the measurements relatively well. Although there appears just a small offset, which can be caused by many factors, such as fluctuating wind speed, friction velocity threshold, snow particle properties, etc., the main drift shape is conserved. Figure 6: Simulation results and measurements in 2008 Based on the calculation methodology in snow load standard, the appearing snow load can be transformed to shape factors. The measured snow loads on the ground and roof are used to find the appearing shape factors for 2007 and Figure 7 a) shows these shape factors in sections 70 and 74 in 2007 and 2008, respectively. The figure also shows the design shape factor obtained from snow load code. The design shape factor clearly represents the one obtained in 2008, while compared to 2007 the difference is more than significant. Even if the measurements were not taken in the same snow episode, the development of the geometry of the snow drift might be observed. Figure 7 a) shows that the top of the smaller snow drift is positioned closer to the ridge than the more developed snow drift. This development is also shown in the simulations in figure 7 b), where

9 the snow drift in section 70 is shown for different development stages. Close to the ridge, the accumulation rate is slow, while the accumulation rate in the reattachment zone is larger. The top of the snowdrift moving downwind indicates that the reattachment zone moves as the snow surface developes. Figure 7: a ) The shape factor comparison, and b) snowdrift development. 4.DISCUSSION AND CONCLUSIONS Generally, the simulations comply well with the measurements and suitable changes in boundary conditions produce changes in the simulation results that are in agreement with the measurements. The simulation results are closer to the measurements in central part of the roof than at the roof ends. The unbalanced snow accumulation caused by the wind is sensitive to wind properties. Fluctuations in wind direction affect the central part of the roof less than the end of the roof. This is possibly caused by end effects including trailing vortices, which are sensitive to the approaching wind direction. The simulations are run with one single wind direction whereas the measurements result from slightly fluctuating wind direction over some time. This indicates how important the accuracy of the wind flow simulation and the inlet conditions are for a successful outcome in the prediction of snow deposition. In the simulations, the average values of wind speed and wind direction were used. The usage of average values will probably affects the wind pattern and snow accumulation process. Thus, to simulate snow accumulation in time and space exactly, a transient simulation with fluctuating boundary conditions might be necessary. It might also be necessary to introduce a particle size distribution in the model to increase to quality of a simulation results. Together with the measurements, the appearing and design shape factors were derived from the European Eurocode standard EN While the design shape factor seems to be reasonably well fitted with the measurements from 2008, the measurement from 2007 shows that the appearing shape factor is more than doubled of was found in the Eurocode. The position of the maximum snow load is also offset from where the standard indicates it to be. The snow precipitation episode before the measurements from 2007 was a little longer with a little higher wind velocity. Thus the horizontal snow transport was larger in 2007 than in The difference in ground snow load from 2007 to 2008 was not very large, which leads us to believe that the horizontal snow transport is a key factor in the development of an unbalanced snow load on a roof. Further work in standardization of snow load should include an easy method to quantify the horizontal snow transport.

10 REFERENCES Thiis T. K., Ramberg J. F. (2008). Measurements and Numerical Simulation of Development of Snow Drifts on Curved Roofs, Snow Engineering IV, Whistler, BC, Canada, ECI. EN (2003). Eurocode 1, Action on structures - Part 1-3: General actions Snow Loads. Høibø H. (1988). Snow Load on Gable Roofs Results from Snow Load Measurements on Farm Buildings in Norway. First International Conference on Snow Engineering, Santa Barbara, CA, USA, CREL, Special Report 89-6, Tabler R. D. (1988). Snow Fence Handbook (Release 1.1), Tabler & Associates, Wyoming, USA Thiis T. K. (2003). Large scale studies of development of snowdrifts around building, Journal of Wind Engineering and Industrial Aerodynamics, 91 (6), Meløysund V., et al. (2006). Effects of wind exposure on roof snow loads, Building and Environment, 42, Kim H. G., Patel V. C. (2000). Test of turbulence models for wind flow over terrain with separation and recirculation, Boundary layer meteorology, 64 (1), Mason B. J. (1962). Clouds, rain and rainmaking. Cambridge, England: University Press. Naaim M., Naaim-Bouvet F., Martinez H. (1998). Numerical simulation of drifting snow: erosion and deposition models, Annals of Glaciology 26, Armstrong R. L., Brun E. (2008). Snow and Climate: Physical Processes, Surface Energy Exchange and Modeling, Cambridge University Press, England, ISBN , Kind R. J. (1981). Snow drifting, Handbook of snow. Pergamon Press, Canada, ISBN X,