Modeling Frazil And Anchor Ice
During cold weather, water may become supercooled. When the water body is well mixed, supercooling may penetrate to a significant depth, even all the way to the bottom in shallow water.
Supercooling of water eventually leads to the growth and accumulation of suspended frazil ice crystals, the growth of anchor ice, or both. Blockage by icing may cause serious problems for turbine intakes of hydroelectric power plants and for consumer water intakes. The most serious potential icing problem is with nuclear power plants that take their cooling water from a sea, lake, or river.
Moreover, frazil and anchor ice may cause flooding of a river. Ice formation and release of ice at the bottom affects sediment transport and bottom fauna. Supercooling and frazil crystals in water may even endanger fish that are cultivated in rivers and coastal areas since they are unable to escape such conditions.
Frazil and anchor ice have been studied for over a century, initially inspired by severe ice-related flooding events in rivers. However, many aspects of ice accumulation in water intakes, as well as the formation of frazil and anchor ice in general, have been still unclear. Theoretical models have confirmed empirical observations that frazil events typically arise suddenly and are intensive. This emphasizes the importance of correctly predicting these events.
Frazil and anchor ice models necessarily include descriptions and quantifications of many different physical mechanisms regarding, for example, nucleation of ice, coalescence and rise velocity of frazil crystals, and heat transfer from ice crystals to water. Some of these mechanisms are poorly understood, and their quantification is not straightforward.
Our emphasis was on the engineering aspects of the problem, particularly in understanding the mechanisms resulting in blockage of submerged water intakes. Our analysis suggests unorthodox views on the physics of frazil and anchor ice. These views were adopted when numerically modeling frazil and anchor ice.
Small particles of foreign materials in water may act as seeds for nucleation of the frazil ice crystals. Accordingly, it is has been assumed that ice crystals that enter the water column from the air initiate the nucleation. The settlement of ice crystals on water surface can be related to snowfall, blowing snow, sea spray, or crystals that sublimate in the moist air above the water.
This explanation of nucleation of ice in water is accepted quite generally but leaves room for questions. For example, it does not consider the fact that when supercooled water is mechanically disturbed, it will immediately nucleate and start to freeze, even when no ice particles can penetrate the water. This can be observed e.g. by cooling water in a closed bottle in a freezer, and then shaking the bottle. In a turbulent flow, large eddies transfer their energy into smaller ones and so forth, so that the turbulent energy eventually dissipates at the smallest scale of the turbulent eddies. We propose that this local dissipation of turbulent energy acts as an impulse on micro- or nanobubbles that initiate the nucleation.
When the growth has taken place for some time, the increased size and concentration of frazil crystals cause impacts between them, and they adhere to each other. This is called flocculation and results in particles of centimeter scale. Flocculation typically starts when the mass concentration of frazil increases to about 0.15%. Hence, it can be assumed that in the active phase of a frazil event, where the concentration is smaller than this, frazil particles are small and disk-like in shape. In natural conditions, the mean diameter of frazil ice crystals has been measured to be of the order of 1-2 mm. There is considerable variability in the observed characteristic size and, therefore, also the rise velocity of frazil ice particles in water.
Based on microscopic studies, we concluded that thickness-to-diameter ratio of the disk-like ice crystals of 1/30 is a reasonable estimate in frazil ice modeling, although this ratio may depend on the degree of supercooling and the size of the crystals. Such growing frazil ice crystals release latent heat of fusion into the water, which makes the temperature of the water increase and the growth rate of ice decrease. Thus, an active frazil event involves a negative feedback mechanism. This puts a limit on the amount of ice that can form, given the time and the heat flux from the water body. Therefore, for a laterally homogenous water body, the entire active frazil event can be modeled by considering the associated physical mechanisms.
The fundamental thermal balance of frazil growth is that the latent heat released in the solidification of the ice crystals equals the sum of the heat consumed in warming the water plus the heat transferred from the water column to air. The efficiency of heat transfer from an ice crystal to water, i.e. the heat transfer coefficient of a frazil particle, depends on the relative water flow velocity with respect to it. In the previous literature and models, this velocity is assumed to be determined by water turbulence.
However, the density difference of ice crystals and water is small, so that suspended crystals tend to follow the water flow. This situation is analogous to the living environment of plankton, which, for these small organisms, is very stable. Considering the typical size of frazil ice crystals, the boundary layer thickness at the edges can be estimated to be less than about 0.05 mm. This is much smaller than the typical scale of 0.5 -1.5 mm of smallest turbulent eddies in natural waters. This suggests that turbulence does not significantly affect the thermal boundary layer and heat transfer from frazil ice crystals.
Accordingly, we propose that the water flow velocity with respect to a frazil ice crystal, which determines the heat flux from the crystal, is not determined by turbulence. Instead, it is determined simply by the rise velocity of the crystals due to buoyancy. The rise velocity of frazil ice crystals is well known from previous studies and can thus be used as a part of our model that predicts the growth rate of the diameter of an ice crystal and the growth rate of the frazil concentration. The model then provides the rate of temperature change in water when its equations are solved simultaneously by time-dependent numerical iteration. The required input is the water depth and the heat flux from the water to the air.
Major limitations for the application of the model are that the number and the aspect ratio of ice crystals are poorly known in natural waters. On the other hand, the model input, the heat flux from the water surface to air, can be readily estimated by the wind speed, air temperature, and the radiation balance using the customary methods of boundary-layer meteorology. Based on comparisons with empirical data from nature and laboratory experiments, our model predicts the observed evolution of frazil ice concentration and water temperature well. The maximum supercooling in a frazil event predicted by the theory is also in good agreement with observations. In nature, the lowest temperature during frazil events is typically -0.02 ºC, and the lowest temperature observed has been -0.060 ºC.
In the literature, the blockage of water intake screens is assumed to happen when frazil ice crystals move with the water flow, collide with the rods of the screen, and stick to their surface. When this process continues, the ice accumulation on the surfaces also grows in width and eventually fills the slots between the rods. This involves the assumption that all ice crystals traveling with the water flow and aimed at an object not only collide with it but also stick to it upon collision.
However, our study showed that the collision and sticking processes are very sensitive to the size of the object and the flow velocity. The collision is incomplete because friction between a particle and a fluid makes the particle follow the streamlines around an object. Therefore, very small particles go around a large object without collision. Quantitatively, the collision efficiency can be modeled by calculating the trajectories of particles coming towards the object at random positions.
It appears from such calculations that the blockage of water intakes due to the accumulation of frazil ice crystals is possible only when the components of the screen are very small and when the flow velocity is very high. Frazil accumulation events documented on intakes of hydropower plants involve a flow velocity of less than 3 m/s. In these conditions, frazil ice theoretically accumulates rapidly on real-scale screen components only towards the end of a frazil event when the ice crystals are large or flocculated.
Even when an ice crystal collides with an object in the flow, it does not necessarily stick to it. The assumption that a bond of ice at the contact area forms upon impact is justified from the theoretical point of view, but it is less clear whether such a bond is persistent. We estimated that the contact area is typically not sufficiently large and strong to keep a disk-shaped ice crystal adhered in a strong water flow. We conclude from these arguments that the role of accumulating suspended frazil ice crystals in the blockage of water intakes is very small.
Anchor ice is ice that grows directly from surfaces under water. It may sometimes cover large areas of the bottom of water bodies, particularly in rivers. The occurrence of anchor ice at the bottom of lakes and the sea is poorly known and may be more common than believed. Based on laboratory experiments in very shallow and turbulent streams, anchor ice has been explained as forming by the accumulation of suspended frazil ice particles. However, frazil ice and anchor ice form by two distinctly different mechanisms. When water is supercooled, ice on submerged objects may grow not only by accretion of frazil ice crystals nucleated in water but also in-situ, i.e., directly from the surfaces. We call such anchor ice “platelet ice” because of its appearance.
The growth rate of platelet ice from submerged objects increases with increasing supercooling and nucleates under the same conditions as suspended frazil ice. Thus, platelet ice and frazil ice may form on submerged objects simultaneously. It is noteworthy that in-situ thermal growth of platelet ice can be much quicker than that of suspended frazil crystals, because of a higher relative velocity, and thus more effective heat transfer, between water and a stationary ice crystal. Possibly, the in-situ growth of ice crystals initiates from the few frazil ice crystals that have already collided with the object or from the remains of them after they have been broken off from the surface by the water flow. This may explain why platelet ice crystals appear rather randomly oriented.
In contrast to frazil, anchor ice may be quite persistent for several days or even weeks. We were interested in the local growth problem of platelet ice in a fast flow of supercooled water, due to the concern of blockage of a water intake. To estimate the growth rate of platelet ice in this situation, we considered the heat transfer from a single ice platelet. Based on this analysis we propose that platelet ice is the main cause of blockage of fully submerged water intakes. Fortunately, its growth rate is much easier to estimate than that of frazil ice. However, to do that, the degree of supercooling must be obtained through modeling. When modeling the supercooling, one must include the effect of simultaneous frazil ice growth on the water temperature. This can be done by our frazil ice model.
To summarize, the conclusions of our study are somewhat different from the views presented earlier:
- Ice crystals in water may originate from microbubbles and turbulence, so that nucleation may occur regardless of an external source.
- The number concentration of ice crystals may not necessarily increase much during an active frazil ice event.
- The heat transfer from a frazil ice crystal is controlled by its relative rise velocity, not by water turbulence.
- The collision efficiency of frazil ice crystals on grid components is so small that frazil typically causes no blockage of submerged water intakes.
- Blockage is largely caused by ice platelets that grow in-situ on the structural components.
These findings are described in the article entitled Modelling frazil and anchor ice on submerged objects, recently published in the journal Cold Regions Science and Technology Volume 151, July 2018, Pages 64-74.
This work was conducted by Lasse Makkonen and Maria Tikanmäki from the VTT Technical Research Centre of Finland.