Impact of a snow avalanche against an obstacle. Formation of shock waves

The paper is devoted to the effect of compressibility of the avalanche snow impacting an obstacle. Compression shocks generated by obstacle cause high pressure peaks at first instants of impact. That is why the account of compressibility is essential for the understanding of measurements and the design of structures. The main problem in calculation compression shocks in avalanches is to formulate an equation of state for moving snow in impact. Two different types of equations of state are proposed depending on the type of the avalanche (low-density and high-density flows). The approach is not totally new. It was earlier proposed mainly in Russian literature. Here a brief review of the previous work is given with discussion of some gaps in it. The theory is reformulated and further developed to account thermodynamical equations. The simplest case of a normal compression shock in an avalanche flow is studied. Examples of estimations of pressure and density behind a shock are given. It is important to emphasize that the Mach number plays an important role in the theory of compressible flows so it should be taken into account (together with the Froude number) in calculation and modelling an avalanche impact pressure.     

Influence of obstacles on rapid granular flows

Summary. One means of preventing areas from being hit by avalanches is to divert the flow by appropriately constituted obstacles. Thus, there arises the question how a given avalanche flow is modified by obstructions and how the diverted flow depth and direction emerge. In this paper rapid gravity-driven dense granular flows, partly blocked by obstacles with different shapes, sizes and positions, are numerically investigated by solving the hyperbolic Savage-Hutter equations with an appropriate integration technique. The influences of the obstructions on the granular flows are graphically demonstrated and discussed for a finite mass and a steady inflow of granular material down an inclined plane, respectively. These flows are accompanied by shocks induced by both the presence of the obstacles and the transition of granular flows from an inclined surface into a horizontal run-out zone when the velocity transits from its supercritical to its subcritical state. The numerical results show that the theory is capable of capturing key qualitative features, such as shocks wave and particle-free regions.     

Actions of snow avalanches on a protection gallery

Better knowledge of the actions of snow avalanches on slightly inclined protection galleries such as snow sheds is vital for improving the design of such structures. Experimental measurements on a plate equipped with force sensors were carried out on a full-scale avalanche test site at Col du Lautaret (French Alps). For each artificial release of an avalanche, the impact effect and the resulting temporal variations were measured. This real-scale experiment was completed by laboratory-scale experimental tests using granular flows in an inclined channel that identified the relation between load and slope change. These experiments allowed us to measure the granular temperature of the flow. Finally, to assess the dynamic effect of the avalanche loading on the structure, numerical simulations of a real gallery were conducted with a simplified multifiber model, taking into account the tempo-spatial evolutions of the impact pressure observed during experiments.     

Calculation of compression shocks at low pressure

A method of calculating compression shocks at low pressure is given, together with a nomogram for water vapor which permits rapid and quite accurate calculation of the basic parameters of the shock.     

Contribution of theoretical and experimental results to powder-snow avalanche dynamics

A powder-snow avalanche can be considered as the flow of a turbulent buoyant volume of heavy fluid (air-snow suspension) in an ambient fluid, the air. In the dynamics of such a flow, two mechanisms must be taken into account: the air entrainment and the snow entrainment inside the avalanche. From fluid mechanics equations (mass conservation and momentum equations) formulae were obtained giving velocity and density of the avalanche as a function of the slope path, the growth rate of the avalanche and fresh snow-cover characteristics. On the other hand, laboratory simulations gave (among others) experimental results about the growth rates of buoyant clouds. From these theoretical and experimental studies, practical examples are proposed with given path profiles and snow-cover characteristics. Such examples can be generalised to any other cases.     

Topographic curvature effects in applied avalanche modeling

This paper describes the implementation of topographic curvature effects within the RApid Mass MovementS (RAMMS) snow avalanche simulation toolbox. RAMMS is based on a model similar to shallow water equations with a Coulomb friction relation and the velocity dependent Voellmy drag. It is used for snow avalanche risk assessment in Switzerland. The snow avalanche simulation relies on back calculation of observed avalanches. The calibration of the friction parameters depends on characteristics of the avalanche track. The topographic curvature terms are not yet included in the above mentioned classical model. Here, we fundamentally improve this model by mathematically and physically including the topographic curvature effects. By decomposing the velocity dependent friction into a topography dependent term that accounts for a curvature enhancement in the Coulomb friction, and a topography independent contribution similar to the classical Voellmy drag, we construct a general curvature dependent frictional resistance, and thus propose new extended model equations. With three site-specific examples, we compare the apparent frictional resistance of the new approach, which includes topographic curvature effects, to the classical one. Our simulation results demonstrate substantial effects of the curvature on the flow dynamics e.g., the dynamic pressure distribution along the slope. The comparison of resistance coefficients between the two models demonstrates that the physically based extension presents an improvement to the classical approach. Furthermore a practical example highlights its influence on the pressure outline in the run out zone of the avalanche. Snow avalanche dynamics modeling natural terrain curvature centrifugal force friction coefficients.     

Increasing the force with which a shock wave discharged from the channel acts on an obstacle by way of converting a normal pressure shock to a system of oblique shocks

The results are given of experimental and numerical investigations of the effect produced on an obstacle by shock waves discharged from channels of different cross-sectional shapes (circle, square, cross). The pressure distribution on an obstacle mounted normally to the flow axis is measured. The experimental results are compared to the data of numerical calculation for determining the optimal modes as regards the duration of calculation and the cell size that produce the least difference between the experimental and numerical data. Calculations are performed of the gas flow behind a shock wave discharged from a channel of X-shaped cross section, and the distribution of pressure and temperature over the obstacle surface is plotted. It is found that the force with which a flow acts on an obstacle when discharged from a channel of X-shaped cross section is much greater than in the case of being discharged from a channel of round or square cross section. Shadow photographs show that this is due to the reduction of the loss of total pressure in the flow because of the conversion of the normal pressure shock to a system of oblique shocks.Translated from Teplofizika Vysokikh Temperatur, Vol. 42, No. 6, 2004, pp. 900–907.Original Russian Text Copyright © 2004 by T. V. Bazhenova, V. V. Golub, A. L. Kotelnikov, A. S. Chizhikov, M. V. Bragin, and S. B. Shcherbak.     

DEM simulation of oblique shocks in gravity-driven granular flows with wedge obstacles

Deflecting wedge obstacles are often built to divert hazardous flows away from residential areas that are in the way of harm. When a rapid avalanche flow is deflected by an obstacle, this usually causes abrupt changes in the flow thickness and velocity and exhibits characteristics like oblique shock waves in the aerodynamic system or oblique hydraulic jumps in the open channel flows. In this study, the Discrete Element Method (DEM) is employed to simulate the motion of granular materials impinging on a wedge obstacle in an adjustable inclination chute. We use chutes with four different inclined angles combined with wedge obstacles having different angles to investigate the overall flow behavior. Both the flow velocity and the flow depth are obtained by averaging the numerical simulation data, and then the granular temperature and the shock angle are calculated. The results of the DEM simulation are compared with that of the classical oblique shock theory. We find that there is good agreement between the classical oblique granular shock theoretical calculations and the DEM simulation results. Moreover, the microdynamic variables related to flow structure such as the packing density and the coordination number are also discussed in the present study.     

Shock adiabat,phase diagram,and viscosity of mercury at a pressure up to 50 GPa

The results of measurements of shear viscosity of mercury under shock compression, obtained in [1]by the method of decay of small perturbations preassigned at the shock wave front, are considered in the light of new data on the phase diagram, isothermal compressibility, and equation of state for mercury in the high-pressure region. It is demonstrated that the measured value of viscosity η = 0.8 kPa s at a shock compression pressure of 44 GPa (which differs from the initial state under normal conditions by a factor of 5 × 10⁵) corresponds to the transition of mercury under shock compression to the solid state..     

Fuzzy modelling of powder snow avalanches

This paper examines powder snow avalanches by introducing a predetermined degree of variation, or fuzziness, in model parameters. Given a value of vagueness in the parameters, fuzzy set theory makes it possible to evaluate the vagueness in the results. The use of a more complex stochastic analysis can be avoided. Six parameters of the model are taken to be affected by a certain amount of uncertainty; the response of the numerical model is calculated by solving the fuzzy equations. In this way, it is possible to evaluate how the results are affected by a given change in the model parameters.The paper first presents a well-known avalanche model and its solution considering the influence of friction. A brief introduction of the fuzzy set is given with regard to the avalanche model mentioned. Later, the fuzzy solution of the model in terms of velocity and average pressure is calculated for three different levels of imprecision in the data. At the end, the results are presented and commented.     

A semi-empirical re-evaluation of the influence of state on elastic stiffness in granular materials

Granular Matter - The calculation of the impact pressure on obstacles in granular flows is a fundamental issue of practical relevance, e.g. for snow avalanches impacting obstacles. Previous...     

Equation of State,Composition, and Conductivity of Supercritical Iron Vapor in the Plasma Fluid Model

The caloric and thermal equations of state, composition, and conductivity of supercritical iron vapor were calculated with the previously proposed chemical model 3+. This model considers atoms, electrons, ions, and jellium, taking into account interatomic and intercharge interactions. The introduction of jellium enables makes it possible to describe ionization via pressure and explain the increase in fluid conductivity under compression. The cohesive atom bonds due to jellium weakens the effect of intercharge interactions on the equation of state. Comparison with the experimental data makes it possible to recommend the proposed plasma model for calculation of the properties of plasma fluid, i.e., an unusual gas-plasma state of matter with the density of a liquid.     

水下爆炸荷载作用下圆柱结构反射压力解析计算方法研究

为助于桥梁、码头等近海结构的抗爆和防护设计,该文拟针对近海结构中常见的等截面圆柱结构,提出一种计算水下爆炸情况中冲击波作用下圆柱分布反射压力的高效解析算法。基于绕射波浪理论,该文根据水体状态方程和边界条件,在柱坐标系下通过分离变量法推导圆柱结构反射压力的时域解;通过数值模拟对比验证该文提出的反射压力时域解的计算精度,数值算例表明二者计算误差在工程允许范围内;基于考虑水体压缩性的时域子结构分析方法,通过对比该文提出的未考虑水体压缩性的解析方法,分析了水体压缩性对反射压力的影响。     

Ping-pong ball avalanche at a ski jump

Three dimensional granular flow experiments were carried out on a ski jump with 300,000 ping-pong balls. Since the air drag was a large effect, the flow arrived at a steady state within a short distance. The terminal velocities attained showed a remarkable increase with the number of released balls. In addition, the flow formed a distinct head and tail structure, which has often been observed in large-scale geophysical flows in nature. Similarity analysis is used to show that the experiment corresponds to a natural snow avalanche that runs for several kilometers. Video cameras positioned above the flow allowed the measurement of the location and the distance of a single ball, which finally led to the particle velocity profiles. The static pressure depression measurements in and above the flow showed the air velocity profiles and suggested the strong interaction between the balls and the surrounding fluid(air). Computer simulation of 3-dimensional, inhomogeneous two-phase flows that uses the DEM for the particles and the Reynolds-averaged Navier Stokes equations for the fluid are currently in progress.     

The use of microwave FMCW radar in snow and avalanche research

This paper describes a frequency modulated, continuous wave (FMCW) microwave radar system used for different types of investigations in snow and avalanche research. Different semi-empirical equations describing transmission and backscatter of electromagnetic energy in snow are compared and applied to analyse the frequency domain spectra of the backscattered radiation. The FMCW scatterometers are either buried in the ground looking upward into the snow cover or are towed on skis looking downward into the snow. The backscatter of electromagnetic radiation from avalanche snow moving perpendicular to the radar beam is analysed to estimate the height of dense flow in the avalanche. The geometrical layering, density, water equivalence, settlement, total snow height, percolation of water through the snow cover and moisture content of the snow are determined from the backscatter of the stratigraphy of a static snow pack.     

Parallel computing of high‐speed compressible flows using a node‐based finite‐element method

An efficient parallel computing method for high‐speed compressible flows is presented. The numerical analysis of flows with shocks requires very fine computational grids and grid generation requires a great deal of time. In the proposed method, all computational procedures, from the mesh generation to the solution of a system of equations, can be performed seamlessly in parallel in terms of nodes. Local finite‐element mesh is generated robustly around each node, even for severe boundary shapes such as cracks. The algorithm and the data structure of finite‐element calculation are based on nodes, and parallel computing is realized by dividing a system of equations by the row of the global coefficient matrix. The inter‐processor communication is minimized by renumbering the nodal identification number using ParMETIS. The numerical scheme for high‐speed compressible flows is based on the two‐step Taylor–Galerkin method. The proposed method is implemented on distributed memory systems, such as an Alpha PC cluster, and a parallel supercomputer, Hitachi SR8000. The performance of the method is illustrated by the computation of supersonic flows over a forward facing step. The numerical examples show that crisp shocks are effectively computed on multiprocessors at high efficiency. Copyright © 2003 John Wiley & Sons, Ltd.     

On the computation of steady‐state compressible flows using a discontinuous Galerkin method

Computation of compressible steady‐state flows using a high‐order discontinuous Galerkin finite element method is presented in this paper. An accurate representation of the boundary normals based on the definition of the geometries is used for imposing solid wall boundary conditions for curved geometries. Particular attention is given to the impact and importance of slope limiters on the solution accuracy for flows with strong discontinuities. A physics‐based shock detector is introduced to effectively make a distinction between a smooth extremum and a shock wave. A recently developed, fast, low‐storage p‐multigrid method is used for solving the governing compressible Euler equations to obtain steady‐state solutions. The method is applied to compute a variety of compressible flow problems on unstructured grids. Numerical experiments for a wide range of flow conditions in both 2D and 3D configurations are presented to demonstrate the accuracy of the developed discontinuous Galerkin method for computing compressible steady‐state flows. Copyright © 2007 John Wiley & Sons, Ltd.     

新型聚酯材料状态方程的研究

聚酯材料在航空航天领域有着较广泛的应用,其高压力学性能的研究逐渐受到人们的关注。针对一种新型聚酯材料通过轻气炮(LGG)实验开展其冲击压缩力学性能研究。采用非对称碰撞直接测量法测量并计算激波速度(D)与波后质点速度(u)的D-u型Hugoniot曲线,并由此推导出P-η型Hugoniot曲线。建立了该材料的Murnagham状态方程,求得了相应的材料参数。并对新型聚酯材料的Murnagham状态方程和P-η型Hugoniot状态方程进行了比较和分析。     

On forecasting large and infrequent snow avalanches

Snow avalanches that threaten a highway or a residential area are often large avalanches that have a return period > 1 year. Danger assessment strongly relies on precipitation data since these avalanches are typically triggered by major snow storms. Given the extensive protection work that is in place in the European Alps, the avalanche control service (also called avalanche commission) responsible for danger assessment will usually monitor the avalanche situation throughout the winter, but only become active in case of a major snow fall. Related safety concepts describing the procedures and measures to be taken in a given danger situation are therefore often based on threshold values for new snow. By analysing the avalanche occurrence of a major avalanche path, we show that forecasting based on new snow amounts involves high uncertainty. Whereas the return period of an avalanche to, for example, the road was about 5 years, the return period for the corresponding new snow depth was substantially smaller, in our case slightly less than 2 years. Similar proportions were found for a number of other avalanche paths with different snow climate. The return period of the critical new snow depth was about 2–5 times smaller than the return period of the avalanche. This proportion is expected to increase with increasing return period. Hence, based on the return period of an avalanche path a first estimate for the critical new snow depth can be made. With a return period of the critical new snow depth of 1–2 years, avalanche prediction for individual avalanche path becomes very challenging since the false alarm ratio is expected to be high.