Introduction
Wet snowflakes containing much free water easily accrete on electric wires; this often causes serious damage such as the breakage of power lines and crashing down of high-voltage power-transmission towers.
Extensive studies concerning snow accretion and sleet jump on power lines have been made by many workers in Japan since the 1930's. Among them was Shōda, the first person who studied in detail the growth processes and mechanisms of snow accretion on wires. He found that snow accretion takes place at an air temperature between –1° and +1.5°C when the wind speed is less than 3 m/s (Shōda, 1953). He emphasized that when the wind speed exceeds 3 m/s snow accumulated on a wire is easily blown from the wire by wind action. These earlier works were, however, restricted to the Hokuriku district in coastal regions in central Honshu facing the Sea of Japan. Snow accretions there derived mainly from monsoon-type heavy wet snowfalls in winter. (Snow accretions derived from monsoon-type snowfalls are referred to as “monsoon-induced snow accretion” for convenience.)
In Hokkaido, the northernmost island of Japan, incidents of serious damage to power lines and transmission towers due to heavy wet snow accretions have been frequently reported in the last 15 years; these took place when a strong cyclone passed this area in winter or early spring. (Snow accretions derived from a cyclone are referred to as “cyclone-induced snow accretion” for convenience.) The wind speed of such a cyclone was 10, 15 or 20 m/s at times, very different from the wind speed observed and reported by Shōda for the monsoon-induced snow accretion. Attention has been drawn to the fact that damage of this nature is not unique to Hokkaido but has been reported from other parts of Japan.
Summarized in Table IA are available data of such snowfalls that resulted in heavy damage to power lines and transmission towers, i.e. the date of occurrence, location, the degree of damage and certain meteorological factors. Similar information on damage reported from Canada and the U.S.A. is given in Table IB, where the cause of the damage includes mountain icing and freezing rain.
Table IA. Selected data for heavy snow accretions, causing serious damage to power lines or transmission towers, reported recently from Japan
Table IB. Snow or ice accretions reported from Canada and the U.S.A. (compiled by K. Koike, Hokkaido Electric Company)
In order to clarify the detailed processes and mechanisms of snow accretion in a strong wind on wires, as often observed in Hokkaido, a series of experiments was conducted on artificial snow accretion in a wind tunnel installed in a cold laboratory. On the basis of the results obtained from the experiments and field observations, effective devices against snow accretion have been developed in the Technical Research Institute of the Hokkaido Electric Company (Reference Nakano and T.Nakano and others, 1974, p. 1–32; Reference Gotō and KuroiwaGotō and Kuroiwa, 1975).
Wind-tunnel experiments
A wind tunnel installed with a device to produce artificial wet snow particles was used to study the growth processes and mechanisms of snow accretion on electric wires. A lump of snow collected from a natural snow-pack was crushed by three-layered vibrating metallic sieves; a supply of these disaggregated snow particles was fed continuously into the wind tunnel; they were wetted by spraying water at one before they impinged on the wires stretched horizontally in the tunnel and perpendicular to the direction of the wind. The air temperature in the tunnel was controlled between + 1.0° and 2.0°C. Two types of wire were used: a single wire with a circular cross-section and a stranded wire.
Time-lapse and slow-motion pictures were taken on 16 mm film to observe the growth processes of snow accretion and the trajectories of the snow particles impinging on or passing by the wire. The adhesive force of wet snow to the wire was also measured. Snow accreted on the wire was carefully removed from it, so that the structure, density, free-water content of snow and the microscopic texture, including the grain-size, shape and crystallographic orientations, could be measured and observed.
Experimental results
Growth processes if snow accretion on wires
When wet snow was continuously blown on to a single wire in the wind tunnel, it began to accrete in the windward direction (Fig. 1a). When the snow accretion reached a thickness similar to the diameter of the wire, it began to rotate slowly around the wire by its own weight, hanging down from the wire (Fig. 1b), without being blown away by the wind. A continuous accumulation of snow took place on the windward face of the wire; the whole snow mass rotated again and this process was repeated (Fig. 1c and d). The wire was soon entirely enveloped by wet snow.
Fig. 1. Schematic representations of growth processes of snow accretion on a wire in a weak wind.
The snow deposit thereafter was rarely blown away by the wind and it grew to a thick cylindrical snow body. Though the free-water content (mass of water/mass of wet snow, in %) of the falling snow fed into the wind tunnel was 3–8%, that of the snow deposit on the wire increased with time due to an effective heat transfer from the moving air to the snow mass. The snow deposit gradually became semi-transparent during its growth, and the excess of free water was removed from the leeward of the snow deposit. The free-water content of the snow deposit on the wire was measured immediately after the end of each experiment by a calorimetric method; its value ranged from 18 to 37%.
There is a possibility that freezing of free water in the snow deposit may take place during its growth due to evaporation in a strong wind. In order to investigate this possibility, the temperature distribution within the snow deposit was measured by using eight thermocouples embedded in it at a wind speed of 10 m/s and a relative humidity in the wind tunnel of 70%, but no evidence indicating the freezing of water was obtained.
As for snow accretion on a stranded wire, its growth process was different from that on a single wire; namely, snow accreted slowly and slid down along the strands of the wire. Rotating around the wire, it also grew to form a cylindrical snow deposit.
Effect of wind speed on snow accretion
A series of experiments was carried out to clarify the effect of wind speeds in the tunnel from 0 to 20 m/so In these experiments it was found that a heavy snow accretion took place at any wind speed up to 20 m/s, though the modes of snow accretion were somewhat different from one another. For instance, when the wind speed was less than 10 m/s, the snow deposit tended to rotate around the wire under gravitation but, when the wind speed exceeded 10 m/s, the rotation of snow was sometimes upwards due to aerodynamic lift. It was also found that the snow deposit fell from the wire when the wind speed was suddenly reduced from 10 to 0 m/s in the initial stage of snow accretion. These facts suggest that a high wind speed such as 10 m/s plays an important role in the development of snow accretion on wires; that is, a strong wind produces aerodynamic lift which acts on the snow deposit in equilibrium with the gravitational force, thus preventing the snow deposit from falling off the wire. This experimental fact is clearly contrary to earlier workers' results which emphasized that a strong wind easily removes a growing snow deposit from the wire.
Adhesive force of snow accretion to wires
If the snow deposit falls from the wire after the initial rotation around it in the early stage of snow accretion, it cannot develop to a thick cylindrical snow body. The adhesive force by which the snow deposit hangs down from the wire, is therefore very important in the study of practical problems. The adhesive force between the snow deposit and the wire was measured as follows.
Wet snow was deposited continuously on to the upper surface of a wire 40 and 20 mm in diameter under no wind conditions. When the weigh t of snow accumulated on a unit length of the wire exceeded approximately 1.2 g/mm, the mound-like deposit of snow became unstable and began to rotate around the wire by the action of gravity and then fell off the wire. If the weight of the deposit was less than 1.2 g/mm, the snow rarely began to rotate by itself. Then, a very slow rotation was given to the wire such as to allow the snow to start turning around the wire. When the deposited snow was turned over, it sometimes fell from the wire, but sometimes not, hanging down from the bottom surface of the wire. The shear stress σs, which prevents the snow turning around the wire, could be estimated from the critical angle at which the rotation began; the value of σs thus obtained was approximately 0.2 × 10-3 bar.
It may be assumed that the negative pressure induced in water existing at the interface between the wet snow and the wire allows the snow to adhere to the wire. The pressure, p, is given by the formula p = – (σ/r), where σ is the surface tension of water and r is the radius of curvature of the concave water surface at the interface. The value of r may be of the order of the radius of the snow grains, e.g. 0.3–0.5 mm. When the negative pressure is overcome by the gravitational force, the snow should fall from the wire; when the negative pressure exceeds the gravitational force, it never falls off but hangs down from the wire. Hence the negative pressure gives us the adhesive stress. The adhesive stress thus obtained was approximately (1.9 ± 0.1) × 10-3 bar when the free-water content was greater than 20%, or when air voids among the snow grains at the interface were saturated with water. Substituting the adhesive stress thus obtained into p of the above formula, the derived radius of curvature r of the water surface at the interface is 0.4 mm, which agrees well with that estimated from the grain-size of the snow. The adhesive force becomes smaller when the free-water content of snow is lower than 20%, because the air voids are not saturated with water.
Density, structure and texture of snow accretion
The density of an artificially made snow accretion ranged from 0.7 to 0.9 Mg/mJ, which agreed well with the densities observed for natural cyclone-type snow accretions. This is in remarkable contrast to the monsoon-type snow accretion with a density of approximately 0.2 Mg/m3.
Natural snow accretions of the cyclone type were sliced to a thickness of 10 mm and diluted ink was sprayed on to the sliced surface to reveal the internal structure of the snow. A continuous helical structure was found in the sections as illustrated in Figure 2a. This strongly suggests that the snow accretion had grown by turning around the wire many times, and that the wire itself was twisted in such a way that the middle part of a long span between the transmission towers rotated freely around the axis, thus allowing the helical growth of the snow accretion around the wire as shown schematically in Figure 2b. It has been actually observed in situ that most of the catenaries were twisted by rotation of as much as several times 2π radians by the torque induced by an irregular accumulation of snow on the windward surface of the line during the growth of a heavy snow accretion. Snow accretions were, however, easily broken down and fell from both of the end parts of a line close to the towers where only slight twisting was allowable, and where a thick cylindrical snow accretion never developed. These facts show that the torsional twist of the wires and catenaries may play an important role in the development of a snow accretion. Results similar to those obtained in situ were obtained in the wind-tunnel experiments; if the wire was fixed firmly to a rigid framework, the snow deposit frequently fell from the wire during its growth but, when the wire was not fixed and allowed to rotate, it readily grew into a thick cylindrical snow deposit without falling off the wire. In the unfixed condition, when the wind speed was less than 10 m/s, the snow deposit moved downwards to some extent as it grew, causing the wire to rotate around its axis discontinuously, whereas when the wind speed exceeded 10 m/s, the snow deposit moved continuously either upwards or downwards as it grew, causing the wire to rotate around its axis continuously. This continuous rotation was frequently observed when the wind speed varied between 12 and 17 m/s. Immediately after the experiment was completed, the accumulated snow was carefully removed from the wire and cut into 10 mm thick slices to study its internal structure. Sector-shaped structures were observed in the thin sections of the snow deposit formed in a comparatively weak wind as illustrated in Figure 2d. A number of conformable circular structures were observed in the sections of the snow accumulated at a wind speed greater than 10 m/s (Fig. 2c). These structures of sector or circular patterns seen in the sections of the deposited snow are therefore a good reflection of the rotational growth of snow accretion on wires.
Fig. 2. Cross-sections showing growth processes of snow accretion on wires. (a) A cross-section of a natural snow accretion. Diluted ink was sprayed on the section to reveal its internal structure. Diameter of the snow accretion was approximately 300 mm. (b) Schematic representation of a snow accretion on a long-spanned power line due to the rotations of the wire. (c) Artificial snow accretions on wires in a wind tunnel. (d) and (e) Thin sections of artificial snow accretions showing discontinuous rotational growth in a weak wind (d) and continuous rotational growth in a strong wind (e).
Coefficient if collision and coefficient of collection of snow particles on the wire
Though the coefficients of collision and collection of snow particles on a wire are very important factors in the understanding of snow accretion, they are not yet well known. In order to determine these factors, the trajectories of snow particles were studied by photographing them when they were just impinging on or rebounding from the wire (Fig. 3a). A technique of narrow-banded lighting and stroboscopic lighting was used to distinguish the traces of individual snow particles colliding with or rebounding from the wire. 16 mm slow-motion pictures were taken to observe continuously the paths of the particles just impinging on or passing by the wire.
Fig. 3. Trajectories of snow particles impinging on and passing by a wire. A large number of snow particles are rebounding from the snow deposit on the wire.
It was found from an analysis of these photographs and films that the trajectories of snow particles just passing by a wire were very straight, as seen in Figure 3, which means that the coefficient of collision defined by Reference Langmuir and BlodgettLangmuir and Blodgett (1946) is 100%. Though it had been believed that wet snow particles impinging on a wire may easily adhere to its surface, these experiments showed that the number of snow particles which rebounded from the surface of the wire or the snow deposit was unexpectedly large (Fig. 3). The coefficient of rebound exceeded 80% for a wire 4 cm in diameter; hence, the coefficient of collection of snow particles was less than 20%. It was frequently observed that a snow particle which collided with the surface of the snow expelled several snow particles each time from the surface. It should be noted that, with a decrease in the radius of the wire, the coefficient of collection of snow particles increased. These facts are very important in order to estimate the growth rate of snow accretion on power lines in computer simulations.
New techniques for preventing lines from accreting snow
As described above, a lump of wet snow accumulated on a stranded wire slowly slides along the strands of the wire, and then develops into a large cylindrical snow accumulation. Therefore, if the sliding rotation along the strands is stopped, the cylindrical growth of snow accretion may be interrupted. When plastic rings 2–4 mm in thickness were attached to the surface of a stranded wire at an interval 1.5–2 times the length of the stranding pitch (Fig. 4a), the rotational sliding of the snow along the strands was arrested; hence, the cylindrical growth of the snow accretion could be stopped. This new technique was developed by the Snow Accretion Prevention Research Group of the Hokkaido Electric Company; it has been proved that this was very effective for a short-span catenary, less than 100 m, of the transmission lines with ACSR (Aluminum Conductor Steel Reinforced) 13.5–18 mm in diameter, but the de-icing effect of the plastic rings was reduced for long spans of transmission lines because of the twists of the wires themselves. In the latter case, 0.8 kg m anti-torsion weights were attached to the wire at intervals of less than 100 m to prevent the wires from twisting. It has been proved in situ that this method is also very effective for the prevention of snow accretion on a long-spanned transmission line.
Fig. 4. New techniques for the prevention of snow accretion on a stranded wire (a) and a single vinyl wire (b).
In the case of vinyl-covered single wires with a circular cross-section, which are mainly used in towns and streets in urban areas, a lump of snow accumulated on them slides down along the cross-section, and then develops into a large cylindrical snow accretion. If the rotation is interrupted by an obstacle, the growth of the snow accretion may be stopped. A pair of tiny fins was attached to both sides of the vinyl wire as schematic ally shown in Figure 4b. This new technique which was also developed by the Hokkaido Electric Company Group has proved to be very effective for these kinds of wires.
Concluding remarks
It has been confirmed that there are two types of snow accretion: “monsoon-induced snow accretion”, which often occurs in Honshu in the middle of winter when a heavy wet snowfall 4–5 mm/h in intensity continues all day long at an air temperature between —1 and + 1.5°C in a wind of less than 3 m/s; “cyclone-induced snow accretion”, which often occurs in Hokkaido when a heavier wet snowfall 20–30 mm/h in intensity accompanied by a strong cyclone passing by this island continues all day long at an air temperature between 0 and +2°C in a strong wind of more than 10 m/s. There is a great contrast between the growth conditions for these two types of snow accretion, in spite of the wind speed in which snow accretion develops. The reason why the cyclone-induced snow accretion can develop even in a strong wind may be explained as follows: the free-water content of cyclone-induced snow accretion is much larger than that of the monsoon-type accretion. The great difference between the density of snow accretions of these two types, i.e. 0.7–0.9 Mg/m3 for the cyclone-induced type and 0.2 Mg/m3 for the monsoon-induced type, is due to the difference in free-water content of snow between the two. In general, the adhesive force of snow to a wire increases with an increase in the free-water content. The cyclone-induced snow accretion therefore, adheres much more to a wire than the monsoon-induced one, and it can grow to a cylindrical accretion as thick as 30 cm in diameter without falling from the wire even when the wind speed exceeds 10 m/s. The monsoon-induced snow accretion is, on the contrary, easily blown off in a strong wind because of the smaller adhesive force to the wire due to a smaller free-water content.
A series of wind-tunnel experiments for cyclone-induced snow accretions was conducted at a controlled temperature ranging from + 1 to + 3°C, and it was confirmed that artificially wetted snow can accumulate on wires at any wind speed between 0 and 20 m/s. Studied in these experiments were the growth processes of snow accumulation, the adhesive force of snow to wires, the structure and texture of snow accumulated on wires, coefficients of both collision and collection of snow particles on wires, and the trajectories of snow particles passing near a wire. New techniques for the prevention of snow accretion both on stranded and single wires have been developed, and these have proved to be very effective for de-icing any type of electric line or wire in snowy areas.
Acknowledgements
The authors wish to express their deep appreciation to the members of the Snow and Ice Accretion Study Group in the Institute of Low Temperature Science, Hokkaido University, and to the members of the Snow Accretion Prevention Research Group in the Hokkaido Electric Company, for their kind co-operation and stimulating discussions throughout the work. This study was partly supported by the Ministry of Education and partly by the Hokkaido Electric Company.
Discussion
A. Frolov: Your experiments and measurements are very interesting and important. However, I should like to know whether you have any data on the qualitative dependence between thickness of ice formation per unit of time and the different thermodynamic conditions of the experiments.
G. Wakahama: No. We have no quantitative relations between rate of accretion of snow and thermodynamic conditions at present. However, we are currently analysing our films and hope soon to be able to determine growth rate as a function of wind speed, air temperature, etc.
