Variation of the Frost Boundary below Road and Railway Embankments in Permafrost Regions in Response to Solar Irradiation and Winds

Transcription

1 Excerpt fro the Proceedings of the COMSOL Conference 009 Milan Variation of the Frost Boundary below Road and Railway Ebankents in Perafrost Regions in Response to Solar Irradiation and Winds N.I. Köle and Wenjie Feng ) Space Research Institute, Austrian Acadey of Sciences, Graz, Austria ) State Key Laboratory of Frozen Soil Engineering, CAREERI, CAS, Lanzhou, China *Corresponding author: N.I. Köle, Space Research Institute, Austrian Acadey of Sciences, Schiedlstrasse 6, A-804 Graz; Austria. Eail: norbert.koele@oeaw.ac.at Abstract: We present COMSOL solutions for a coupled gas flow and heat transfer proble, which occurs particularly when traffic pathways are constructed in high altitude and arctic regions, where the underground is frozen soil. To avoid elting of the frozen ground (which usually leads to echanical instability) one has to find suitable easures to keep the subsurface soil and the ebankent suitably cool. Here we study two ways to do this: (i) protection of the ebankent by awning constructions against unwanted heating by solar irradiation and (ii) cooling or heating by lateral gas flows, e.g. natural winds. To study these effects experientally, a lab setup has been established at CAREERI, Lanzhou, which allows to siulate both the solar irradiation and the winds. The COMSOL odel presented in this paper iics this laboratory setup and can therefore be used as a nuerical tool to predict and interpret the experiental results. We calculate the flow field and its influence on the teperature field in the ebankent and the subsurface soil for lainar flows, using the appropriate COMSOL application odes. Keywords: Railway ebankents, awnings, perafrost regions.. Introduction In arctic and high altitude regions, as for exaple the Qinghai Tibet high plateau in China, engineers dealing with the construction of road and railway routes are frequently faced with the proble that the natural ground is peranently frozen even in the suer season. This can cause serious probles for the safety of traffic routes, because the traffic load usually creates additional heat leading to uncontrolled elting of the soil. Together with natural sources as solar irradiation and teperate winds, serious daage can occur. An exaple is shown in Figure. Therefore it is very iportant for the planning of any new infrastructure project in these sensitive areas to predict the variation of the frost isother in response to various heat sources and surface winds. It will becoe even ore iportant in the future, since due to the global waring trend of the world's cliate gradual elting of the perafrost is observed in Figure. Exaple of the daage of a road ebankent in the high altitude Qinghai-Tibet region due to uncontrolled perafrost elting (source: arctic and high altitude regions (Wu et al., 008). For road construction engineers this eans that they have to find ways to protect the perafrost below the ebankent as good as possible by shielding the ground fro unnecessary heat input. One way to do this is to use awnings'' along the ebankents, which keep radiation off and channel cold winds near the ground. At the CAREERI soil laboratory an experiental setup has been established, where irradiation of a road ebankent as well as air flow with a controlled teperature can be siulated. This allows to study the reaction of the frozen soil and ebankent to a given radiation level and air flow, both for unprotected ebankents and for ebankents shielded by awning constructions. Copared to observations in the natural field environent, this allows to vary paraeters in a ore controlled way. Since there is a strong interaction between heat transfer and the hydrodynaic gas flow in this proble, nuerical odeling is an iportant tool both for the preparation of such indoor tests and for their evaluation. Previous work in this field, focusing on the effect of awnings in road construction work and on the theral conductivity of road

2 construction aterials have been published in the recent years (Feng et al., 006; Köle et al., 007; Köle et al., 008). They for the basis for the paraeter values used in this report.. Proble Forulation Figure shows the basic setup of the experient, indicating also the ain diensions. The lower part is the solid doain, representing the natural clay soil and two layers of the road ebankent. On the upper left boundary air with a defined teperature (either colder or warer than the original soil teperature) enters the doain with a given velocity. The upper right side is the free outflow boundary for the air. Inside the air doain a lap (solid doain) is positioned, which fors an obstacle in the air flow. Radiation is directed only downwards, the backside of the lap is assued to be therally isolated. In the setup with awning the awning construction is positioned 5 c above the soil. The flow is assued to be lainar, therefore only low inflow velocities (of the order of c/s, i.e. slow winds) can be used in the following odel ipleentation. u u pi u 0 T u ( u) ui 3 and couple the with the tie dependent heat transfer equation which has the for T C t kt Q Cu T. COMSOL Ipleentation These equations are ipleented in COMSOL as a Multiphysics proble using the Weakly Copressible Navier Stokes application ode and the General Heat Transfer application ode. The physical paraeters used for the different doains (solid and fluid as shown in Figure ) are listed in Table. Hereby it has to be kept in ind that the theral related aterial paraeters (ρ, C p, k) change with tie when the frozen soil elts or the war soil freezes. To allow for this variation we ipleent step functions depending on the actual local teperature and the elt teperature T as follows: C k clay clay clay arctanb T T C C C C arctanb T T k k k k arctanb T T Figure : Scheatics of the experiental setup in the soil laboratory and its ipleentation in the COMSOL odel geoetry. The geoetry used for the odels without awning are the sae, but without the part representing the awning. To solve the proble described above, the gas flow ust be cobined with the heat transfer. For this purpose we use the Weakly Copressible Navier-Stokes Equations in their quasi-stationary for In order to ipleent the possibility of elting and freezing of the soil and to allow the correct inclusion of the elting/freezing heat, one has to odify the soil's theral capacity accordingly as: C C clay D Q Hereby D (T) is a narrow Gauss function around the elting teperature T, which ensures that elting or freezing heat is only released or consued when the aterial is close to T = T. This is an analytical approxiation of a Dirac- Delta function around the point T = T :

3 D e T T / Tbound Tinit arctan T arctan b t t arctan b t t / 4 b t t / arctan b t t / / 4 To obtain a convergent solution with COMSOL, the proble has to be solved in several steps. First, a stationary solution for the gas flow across the ebankent is calculated, where no heating or cooling of the inflowing air and no radiative heating by the laps is assued. This solution results in a stationary flow field for the gas across the ebankent. Using the Stationary Segregated Solver (on the Solver Paraeters page) results in a convergent solution, where the teperature reains constant throughout. Convergence is, however, only reached for low wind velocities which guarantee largely lainar flow conditions. In our exaple we used a parabolic velocity profile at the inflow boundary according to the forula u( y) u with y y y ytop y ax y botto y top Here u ax is the axiu inflow velocity at the position y and y botto and y top are the lower and upper liits of the inflow region. There u = 0 because of the no-slip boundary condition for the gas flow along solid/gas boundaries. In the exaple shown here u ax = 0.05 /s was chosen. In the second step, the stationary solution obtained as a result of Step is used as the start solution for a tie dependent calculation: at t = 0 s warer or colder air starts to flow into the doain fro the left boundary and subsequently interacts with the solid ebankent and the top boundary ( ceiling of the lab setup). In this case the tie-dependent segregated solver is used. The tie dependent calculation is executed over a period of 60 s. To provide sooth boundary conditions for the heating or cooling of the gas at the inflow boundary we use the following algebraic function of t: Choosing appropriate values of b, b results in a sooth, but still reasonably sharp teperature variation at the inflow boundary. The teperature change takes place at tie t and t, respectively. In our exaple t is beyond the tie-dependent calculation liit, i.e. there is only one teperature step within the calculation tie (either heating or cooling, depending on the sign of ΔT). In the third step, the obtained solution after t = 60 s is used as the start solution for a long ter calculation: The lap above the ebankent is switched on and radiates with a power of 00 W towards the ebankent surfaces. The lower side of the lap is considered as an IRradiator, which can both eit and receive infrared radiation, while the backside of the lap reains therally isolated. The heating of the ebankent by the eitted radiation is ipleented by odifying the concerned internal boundaries. In the Boundary Settings enu they are changed fro Continuity into Heat Source/Sink which allows to activate the Surface-to-Surface radiation ode with appropriate eissivity values. This long ter calculation is run over days (48 hours) and saved every 900 s (5 in). 4. Results The following figures show the results of soe illustrative odel calculations perfored along the lines described above. The paraeter values and constants used in the odel calculations are listed in Table. In order to evaluate the influence of the gas flow teperature on the otion of the elting isother we have coputed two cases. First, a gas strea 0 K warer than the initial overall teperature of the syste flows across the surface and heats it in addition to the lap radiation. In the second case, the gas strea oving across the surface is 0 K colder than the initial overall teperature. Figure 3 shows the gas flow of the heated air across the doain in

4 the first 60 seconds for the case without awning, in Figure 4 the sae case including the awning is shown. The white arrows indicate the flow field, note the shadow zones with low velocities that develop behind the lap and on the road plateau. In Figure 4 the channeled flow between the awning and the ebankent can also be seen. The following figures show the influence of the irradiation for the no awning and the awning cases, respectively. The awning structure is assued to have a high IR eissivity on the upper side and a low eissivity on the lower side, which is directed towards the soil. This would axiize the protection effect for the frozen soil and can be realized by appropriate coatings of the awning surfaces. For the soil and the lap, which radiate against each other, the sae eissivity values are used in the awning and the no awning case, respectively. The developent of the elting isother in response to the irradiation by the lap with 00 W over a period of 48 hours is shown for four different cases in the following figures: Figure 5: no awning heated air Figure 6: awning heated air Figure 7: no awning cooled air Figure 8: awning cooled air In all figures the white line indicates the 0 C isother, which in the solid doain represents the elt/freeze boundary. Paraeter Value Description k.60 [W//K] soil heat conductivity (unfrozen) k.98[w//k] soil heat conductivity (frozen) ρ 800 [kg/ 3 ] soil density (unfrozen) ρ 800 [kg/ 3 ] soil density (frozen) C 66 [J/kg/K] soil heat capacity (unfrozen) C 977. [J/kg/K] soil heat capacity (frozen) k air 0.04[W//K] air heat conductivity varrho_{air}.69[kg/ 3 ] air density C air 005[J/kg/K] air heat capacity η 7.e-6[Pa s] air viscosity T init 73.5 [K]- initial teperature 5[K] p 0 e5[pa] air pressure T 73.5[K] ice elting teperature b 0[/K] sharpness paraeter for phase change σ 0.[K] Gauss paraeter for phase change b 0[/s] sharpness paraeter for lap on b 0[/s] sharpness paraeter for lap off ΔT ± 0[K] air teperature change watercontent 0. water content of soil Q HO 333e3[J/kg] ice elting heat Q watercontent* soil elting heat Q_{HO} k awning 38[W//K] awning theral conductivity ρ awning 700[kg/ 3 ] awning density C awning 945[J/kg/K] awning heat capacity k lap 38[W//K] lap heat conductivity ρ lap 700[kg/ 3 ] lap density C lap 945[J/kg/K] lap heat capacity ε lap.00 lap eissivity ε clay 0.75 soil eissivity ε awningt 0.80 awning top eissivity ε awningb 0.30 awning botto eissivity Table : Paraeters used in the odel.

5 Figure 3: Model results showing the inflow of war air at the left boundary into the gas doain within the first 60 seconds after the begin of the war gas inflow. Figure 4: Model results showing the inflow of cold air at the left boundary into the gas doain within the first 60 seconds after the begin of the cold gas inflow.

6 Figure 5: Model result for the long ter calculation, 48 hours after the begin of the irradiation by the lap, when the ebankent is not covered by the awning structure. The white line in the solid part (ebankent) represents the elting isother war air case. Figure 6: Model result for the long ter calculation, 48 hours after the begin of the irradiation by the lap, when the ebankent is covered by the awning structure. The white line in the solid part (ebankent) represents the elting isother war air case.

7 Figure 7: Model result for the long ter calculation, 48 hours after the begin of the irradiation by the lap, when the ebankent is not covered by the awning structure. The white line in the solid part (ebankent) represents the elting isother cold air case. Figure 8: Model result for the long ter calculation, 48 hours after the begin of the irradiation by the lap, when the ebankent is covered by the awning structure. The white line in the solid part (ebankent) represents the elting isother cold air case.

8 5. Discussion and Conclusions Coparison of the awning and no awning cases indicates that in the latter the frozen ground has retreated considerably farther. For no awning protection the soil below the lap has elted over about 30 c depth, while in the awning cases the ground reains frozen below about 5 c depth, even after 48 hours of constant irradiation. This is due to the protection effect of the awning against the lap radiation. On the other hand, the variation of the air teperature has very little influence on the position of the elt boundary after 48 h of irradiation by the laps. In the no awning case the depth difference is a few illietres, in the awning case it is even saller and practically not discernable on the figures. The odels presented can give valuable guidelines for the design of the awning protections, although several aspects have not yet been included. First we have assued that the irradiation coes fro an IR source, therefore only the eissivities of the surfaces enter the odel, but not optical paraeters like the albedo. When studying irradiation by the sun, this aspect should be included in order to evaluate the influence of albedo variations. Second, the odels presented include only lainar gas flow across the ebankent, and therefore are restricted to low wind velocities. We tried to build siilar odels for the turbulent flow cases, but did not succeed to ake the produce converging solutions till now, when using the available COMSOL application odes for turbulent gas flow. 6. References Köle N.I., Bing H., Feng W.J., Wawrzaszek R., Hütter E.S., He Ping, Marczewski W., Dabrowski B., Schröer K., Spohn T.: Theral conductivity easureents of road construction aterials in frozen and unfrozen state. Acta Geotechnica, 7 38 (007). DOI 0.007/s Köle N.I., Hütter E.S., Kargl G., Ju H.H., Gao Y., Grygorczuk J.: Developent of theral sensors and drilling systes for application on lunar lander issions. Earth Moon Planet 03, 9 4 (008). DOI 0.007/s (open access). Feng Wenjie, Ma Wei, Li Dongqing, Zhang Luxin: Application of awning to roadway engineering on the Quinghai Tibet plateau. Cold Regions Science and Technology 45, 5 58 (006). Wu Qingbai, Cheng Guodong, Ma Wei, Liu Yongzhi: Railway construction techniques adapting to cliate waring in perafrost regions. Advances in Cliate Change Research 4 (Suppl.), (008). 7. Acknowledgeents This work was supported in part by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung under project L37 N4. Our ain conclusion fro the presented calculations is that at these low flow speeds the teperature of the air flowing across the ebankent has very little influence on the depth of the elting isother in the soil and the use of awnings can be very effective in avoiding frost elt. However, one should keep in ind that this picture ay change when high velocity, turbulent winds are studied, which can easily occur in the high altitude regions of the Qinghai Tibet plateau.