A mathematical and experimental study of anchor ice
The existence of anchor ice in supercooled water can have a profound impact on the management of water resource infrastructures in cold regions. For example, it can raise a tailrace water level and cause significant losses in generation revenue. So far, there have been limited studies on anchor ice, therefore, many problems still exist and much more study is needed. In the present research, experimental and mathematical studies of anchor ice were carried out. Experiments were conducted in a counter-rotating flume, located in a cold room at the University of Manitoba. The experiments were mainly focused on anchor ice evolution around rocks and on gravel beds under different hydro-meteorological conditions. The results are compared to a mathematical model developed herein and some important parameters such as anchor ice porosity and frazil ice deposition coefficient are examined. The growth process of anchor ice was monitored by two CCD cameras. A digital processing program was developed to analyze anchor ice images and determine the growth rate of anchor ice. In addition, anchor ice density, an important factor when studying anchor ice, was estimated and the effect of air temperature, Froude number and Reynolds number is explored. By analyzing torque load signals from the counter-rotating flume, the variation of bed roughness with the growth of anchor ice is elucidated. The deposition coefficient of anchor ice growth was also determined from the experiments. A mathematical model was developed based on a two-stage method to simulate the process of frazil ice transportation and deposition. Both frazil ice attachment and heat transfer between the supercooled water and ice crystals are considered in the model. Four governing equations related to the distribution of velocity and frazil ice transportation and deposition inside and outside the roughness layers were built. A fourth-order Runge- Kutta numerical method was used and programmed in Matlab to solve the governing equations. The growth rate of anchor ice under different hydro-meteorological conditions can be simulated by this numerical model. The proposed experimental and mathematical studies of anchor ice are presented intuitively in this paper and the results from this study contribute to a better understanding of the anchor ice growth mechanism. This study will help to develop better management strategies to mitigate ice related complications associated with hydroelectric generating stations and other hydraulic structures in cold regions.
anchor ice, ice, cold regions, growth rate, frazil ice