Propagation of Continuum Damage in a Viscoelastic Ice Bar

1994 ◽  
Vol 116 (2) ◽  
pp. 109-113
Author(s):  
J. G. Shin ◽  
D. G. Karr
Keyword(s):  
Method Of Characteristics ◽  
Stable Solution ◽  
Continuum Damage ◽  
Governing Equations ◽  
Initial Value ◽  
Nonlinear Viscoelastic ◽  
Characteristic Lines ◽  
Polycrystalline Ice ◽  
Speed Of Propagation ◽  
The Continuum

An initial value problem of a semi-infinite nonlinear viscoelastic bar is solved with continuum damage evolution. The evolution law of the continuum damage for a viscoelastic material is used in order to explore the propagation of two crushing mechanisms: grain boundary cracking and transgranular cracking. Using the method of characteristics, the speed of propagation is found to be dependent on the continuum damage. On the wave front, the delayed elastic strain is zero, and only the continuum damage due to the transgranular cracking evolves. A finite difference method is developed to solve the governing equations on the obtained characteristic lines, and gives a stable solution of the propagation of the stress, strain, and damage. Numerical results are obtained and discussed using the material properties of polycrystalline ice.

scholarly journals Triple Solutions and Stability Analysis of Micropolar Fluid Flow on an Exponentially Shrinking Surface

Crystals ◽  
2020 ◽  
Vol 10 (4) ◽  
pp. 283 ◽  
Author(s):  
Liaquat Ali Lund ◽  
Zurni Omar ◽  
Ilyas Khan ◽  
Dumitru Baleanu ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Stability Analysis ◽  
Shooting Method ◽  
Stable Solution ◽  
Governing Equations ◽  
Initial Value ◽  
Suction Parameter ◽  
Linear Ordinary Differential Equations ◽  
Runge Kutta Method ◽  
Micropolar Fluid Flow ◽  
Shrinking Surface

In this article, we reconsidered the problem of Aurangzaib et al., and reproduced the results for triple solutions. The system of governing equations has been transformed into the system of non-linear ordinary differential equations (ODEs) by using exponential similarity transformation. The system of ODEs is reduced to initial value problems (IVPs) by employing the shooting method before solving IVPs by the Runge Kutta method. The results reveal that there are ranges of multiple solutions, triple solutions, and a single solution. However, Aurangzaib et al., only found dual solutions. The effect of the micropolar parameter, suction parameter, and Prandtl number on velocity, angular velocity, and temperature profiles have been taken into account. Stability analysis of triple solutions is performed and found that a physically possible stable solution is the first one, while all leftover solutions are not stable and cannot be experimentally seen.

Heat Transfer Analysis of Room-Temperature Finned-Tube Evaporator for Cryogenic Nitrogen

2011 ◽  
Vol 133 (9) ◽  
Author(s):  
Shun Ching Lee ◽  
Tzu-Min Chen
Keyword(s):  
Heat Flux ◽  
Room Temperature ◽  
Integrated Model ◽  
Finned Tube ◽  
Heat Transfer Analysis ◽  
Outlet Temperature ◽  
Ambient Conditions ◽  
Governing Equations ◽  
Initial Value ◽  
Two Phase

Abstract The behavior of cryogenic nitrogen in a room-temperature evaporator six meters long is analyzed. Trapezoid fins are employed to enhance the heat flux supplied by the environment. The steady-state governing equations specified by the mixed parameters are derived from the conservations of momentum and energy. The initial value problem is solved by space integration. The fixed ambient conditions are confirmed by way of the meltback effect. An integrated model is utilized to analyze the convective effect of two-phase flow, which dominates the evaporation behavior. Another integrated model is employed to determine the total heat flux from the environment to the wet surface of the evaporator. The foundation of the formation of an ice layer surrounding the evaporator is presented. If the fin height is shorter than 0.5 m, the whole evaporator is surrounded by ice layer. If the fin height is longer than 0.5 m, the total pressure drop of nitrogen in the tube is negligible. The outlet temperature is always within the range between −12 °C and 16 °C for the evaporator with the fin height of 1.0 m. For the evaporator with dry surface, the nitrogen has the outlet temperature less than the ambient temperature at least by 5 °C.

Predicting the wear coefficient and friction coefficient in dry point contact using continuum damage mechanics

2018 ◽  
Vol 233 (3) ◽  
pp. 447-455 ◽  
Author(s):  
Sahar Ghatrehsamani ◽  
Saleh Akbarzadeh
Keyword(s):  
Friction Coefficient ◽  
Damage Mechanics ◽  
Point Contact ◽  
Continuum Damage Mechanics ◽  
Continuum Damage ◽  
Wear Coefficient ◽  
Mechanics Model ◽  
Pin On Disk ◽  
Disk Test ◽  
The Continuum

Wear coefficient and friction coefficient are two of the key parameters in the performance of any tribo-system. The main purpose of the present research is to use continuum damage mechanics to predict wear coefficient. Thus, a contact model is utilized that can be used to obtain the friction coefficient between the contacting surfaces. By applying this model to the continuum damage mechanics model, the wear coefficient between dry surfaces is predicted. One of the advantages of using this model is that the wear coefficient can be numerically predicted unlike other methods which highly rely on experimental data. In order to verify the results predicted by this model, tests were performed using pin-on-disk test rig for several ST37 samples. The results indicated that the wear coefficient increases with increasing the friction coefficient.

On the Motion of Granular Materials Due to Shear

2000 ◽  
Author(s):  
Mehrdad Massoudi ◽  
Tran X. Phuoc
Keyword(s):  
Finite Difference ◽  
Granular Materials ◽  
Continuum Model ◽  
Theory Model ◽  
Governing Equations ◽  
Flat Plates ◽  
Material Parameters ◽  
Finite Difference Technique ◽  
Linear Differential ◽  
The Continuum

Abstract In this paper we study the flow of granular materials between two horisontal flat plates where the top plate is moving with a constant speed. The constitutive relation used for the stress is based on the continuum model proposed by Rajagopal and Massoudi (1990), where the material parameters are derived using the kinetic theory model proposed by Boyle and Massoudi (1990). The governing equations are non-dimensionalized and the resulting system of non-linear differential equations is solved numerically using finite difference technique.

scholarly journals A Framework and Numerical Solution of the Drying Process in Porous Media by Using a Continuous Model

2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Hong Thai Vu ◽  
Evangelos Tsotsas
Keyword(s):  
Porous Media ◽  
Control Volume ◽  
Continuous Model ◽  
Control Volume Method ◽  
Drying Process ◽  
Transport Parameters ◽  
Governing Equations ◽  
Numerical Tools ◽  
Volume Method ◽  
The Continuum

The modelling and numerical simulation of the drying process in porous media are discussed in this work with the objective of presenting the drying problem as the system of governing equations, which is ready to be solved by many of the now widely available control-volume-based numerical tools. By reviewing the connection between the transport equations at the pore level and their up-scaled ones at the continuum level and then by transforming these equations into a format that can be solved by the control volume method, we would like to present an easy-to-use framework for studying the drying process in porous media. In order to take into account the microstructure of porous media in the format of pore-size distribution, the concept of bundle of capillaries is used to derive the needed transport parameters. Some numerical examples are presented to demonstrate the use of the presented formulas.

scholarly journals Study of Unsteady Flow in a Heat Exchanger by the Method of Characteristics

1992 ◽  
Vol 114 (4) ◽  
pp. 459-463 ◽  
Author(s):  
Yuan Mao Huang
Keyword(s):  
Heat Exchanger ◽  
Unsteady Flow ◽  
Transfer Rate ◽  
Method Of Characteristics ◽  
Governing Equations ◽  
One Dimensional ◽  
The Method Of Characteristics ◽  
Improvement Factor ◽  
The One ◽  
Good Agreement

The one-dimensional, unsteady flow in an air-to-air heat exchanger is studied. The governing equations are derived and the method of characteristics with the uniform interval scheme is used in the analysis. The effect of the fin improvement factor on the air temperature in the heat exchanger and the heat transfer rate of the heat exchanger, and air properties in the heat exchanger are analyzed. The numerical results are compared and show good agreement with the available data.

Three Dimensional Fully Localized Waves on Ice-Covered Ocean

2013 ◽  
Author(s):  
Yong Liang ◽  
M.-Reza Alam
Keyword(s):  
Numerical Scheme ◽  
Perturbation Technique ◽  
Three Dimensional ◽  
Multiple Scale ◽  
Governing Equations ◽  
Weakly Nonlinear ◽  
Scale Perturbation ◽  
Speed Of Propagation ◽  
Localized Waves ◽  
Mean Current

We have recently shown [1] that fully-localized three-dimensional wave envelopes (so-called dromions) can exist and propagate on the surface of ice-covered waters. Here we show that the inertia of the ice can play an important role in the size, direction and speed of propagation of these structures. We use multiple-scale perturbation technique to derive governing equations for the weakly nonlinear envelope of monochromatic waves propagating over the ice-covered seas. We show that the governing equations simplify to a coupled set of one equation for the envelope amplitude and one equation for the underlying mean current. This set of nonlinear equations can be further simplified to fall in the category of Davey-Stewartson equations [2]. We then use a numerical scheme initialized with the analytical dromion solution of DSI (i.e. shallow-water and surface-tension dominated regimes of Davey-Stewartson equation) to look for dromion solution of our equations. Dromions can travel over long distances and can transport mass, momentum and energy from the ice-edge deep into the solid ice-cover that can result in the ice cracking/breaking and also in posing dangers to icebreaker ships.

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