Thermal jet drilling of granite rock: a numerical 3D finite-element study

This paper presents a numerical study on thermal jet drilling of granite rock that is based on a thermal spallation phenomenon. For this end, a numerical method based on finite elements and a damage–viscoplasticity model are developed for solving the underlying coupled thermo-mechanical problem. An explicit time-stepping scheme is applied in solving the global problem, which in the present case is amenable to extreme mass scaling. Rock heterogeneity is accounted for as random clusters of finite elements representing rock constituent minerals. The numerical approach is validated based on experiments on thermal shock weakening effect of granite in a dynamic Brazilian disc test. The validated model is applied in three-dimensional simulations of thermal jet drilling with a short duration (0.2 s) and high intensity (approx. 3 MW m −2 ) thermal flux. The present numerical approach predicts the spalling as highly (tensile) damaged rock. Finally, it was shown that thermal drilling exploiting heating-forced cooling cycles is a viable method when drilling in hot rock mass. This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe’.

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A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers

Journal of Fluid Mechanics ◽

10.1017/s0022112070000691 ◽

1970 ◽

Vol 41 (2) ◽

pp. 453-480 ◽

Cited By ~ 1098

Author(s):

James W. Deardorff

Keyword(s):

Scale Effects ◽

Numerical Study ◽

Equations Of Motion ◽

Three Dimensional ◽

Turbulent Channel Flow ◽

Reynolds Numbers ◽

Numerical Approach ◽

Uniform Grid ◽

Turbulence Energy ◽

Vertical Diffusion

The three-dimensional, primitive equations of motion have been integrated numerically in time for the case of turbulent, plane Poiseuille flow at very large Reynolds numbers. A total of 6720 uniform grid intervals were used, with sub-grid scale effects simulated with eddy coefficients proportional to the local velocity deformation. The agreement of calculated statistics against those measured by Laufer ranges from good to marginal. The eddy shapes are examined, and only theu-component, longitudinal eddies are found to be elongated in the downstream direction. However, the lateralveddies have distinct downstream tilts. The turbulence energy balance is examined, including the separate effects of vertical diffusion of pressure and local kinetic energy.It is concluded that the numerical approach to the problem of turbulence at large Reynolds numbers is already profitable, with increased accuracy to be expected with modest increase of numerical resolution.

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Numerical study of single bubble mobility in triangular and deltoid microchannels using the boundary element method

Journal of Physics Conference Series ◽

10.1088/1742-6596/2057/1/012042 ◽

2021 ◽

Vol 2057 (1) ◽

pp. 012042

Author(s):

A Z Bulatova ◽

O A Solnyshkina ◽

N B Fatkullina

Keyword(s):

Boundary Element Method ◽

Boundary Element ◽

Complex Geometry ◽

Numerical Study ◽

Center Of Mass ◽

Three Dimensional ◽

Numerical Approach ◽

Variable Pressure ◽

Bubbly Liquid ◽

Element Method

Abstract The study of bubbly liquid dynamics in microchannels of unconventional shapes is of great importance for different fields of science and industry. This work investigates the dynamics of the incompressible single bubbles in the slow periodic flow of viscous liquid in a triangular channel with a variable pressure gradient. The numerical approach used in this research is based on the boundary element method (BEM). This method is widely used for solving three-dimensional problems and problems in areas with complex geometry. The influence of the bubble’s initial position relative to the channel centerline on the bubble deformation, the relative velocity of the bubble, and its center of mass displacement in the channel are considered.

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Investigation of Flutter Mechanisms of a Contra-Rotating Open Rotor

Volume 7B: Structures and Dynamics ◽

10.1115/gt2015-42159 ◽

2015 ◽

Author(s):

Sina C. Stapelfeldt ◽

Mehdi Vahdati ◽

Anthony B. Parry

Keyword(s):

Numerical Study ◽

Three Dimensional ◽

Suction Side ◽

Numerical Approach ◽

Torsional Mode ◽

Aerodynamic Damping ◽

Initial Validation ◽

Pressure Profiles ◽

Open Rotor ◽

State Mixing

The growing pressure to reduce fuel consumption and cut emissions has triggered renewed interest in contra-rotating open rotor technologies. One of their potential issues is self-excited or forced vibration of the unducted, light-weight, highly swept blades. This paper presents a numerical study into the flutter behaviour of a contra-rotating open rotor rig at take-off conditions. The study presented in this paper aimed to validate the numerical approach and provide insights into the flutter mechanisms of the open rotor under investigation. For the initial validation, pressure profiles and thrust coefficients from steady state mixing plane calculations were compared against rig measurements. A full domain unsteady analysis predicted front rotor instability at low advance ratios. Flutter occured in the first torsional mode in 0ND and 1ND which agreed with experimental observations. Subsequent unsteady computations focussed on the isolated front rotor and first torsional mode. The flow field and aerodynamic damping over a range of advance ratios was studied. It was found that minimum aerodynamic damping occured at low advance ratios when the flow was highly three-dimensional on the suction side. A correlation between the quasi-steady loading on the blade and aeroelastic stability was made and related to the numerical results. The effects of variations in frequency were then investigated by linking local aerodynamic damping to the unsteady pressure on the blade surface.

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Numerical Study of Large Diameter Butterfly Valve on Flow Characteristics

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.236-238.1653 ◽

2011 ◽

Vol 236-238 ◽

pp. 1653-1657 ◽

Cited By ~ 1

Author(s):

Xiao Dong Wang ◽

Jing Liang Dong ◽

Tian Wang

Keyword(s):

Pressure Drop ◽

Flow Resistance ◽

Numerical Study ◽

Large Diameter ◽

Three Dimensional ◽

Flow Characteristics ◽

Numerical Approach ◽

Resistance Coefficient ◽

Butterfly Valve ◽

Dimensional Simulation

A numerical approach was used to investigate the flow characteristics around a butterfly valve with the diameter of 2108 mm by the commercial computational fluid dynamics (CFD) code FLUENT6.3. The simulation was carried out to predict flow field structure, flow resistance coefficient, hydrodynamics torque and so on, when the large diameter butterfly valve operated at various opening degrees. The three-dimensional simulation results shown that there are vortexes presented near valve back region as the opening degree smaller than 40 degree; the flow resistance coefficient reduces rapidly with the increasing of opening degree and the resistance coefficient is quite small as the angle larger than 50 degree; the hydrodynamic torque reduces with the increasing of opening degree and the hydrodynamic torque is smaller than 20% of maximum torque; the torque ratio and the pressure drop ratio are reduce with the increasing of opening degree, the pressure drop ratio reduces rapidly as the opening degree is smaller than 50 degree.

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Investigation of Flutter Mechanisms of a Contra-Rotating Open Rotor

Journal of Turbomachinery ◽

10.1115/1.4032186 ◽

2016 ◽

Vol 138 (5) ◽

Cited By ~ 4

Author(s):

Sina C. Stapelfeldt ◽

Anthony B. Parry ◽

Mehdi Vahdati

Keyword(s):

Numerical Study ◽

Three Dimensional ◽

Suction Side ◽

Numerical Approach ◽

Torsional Mode ◽

Nodal Diameter ◽

Aerodynamic Damping ◽

Pressure Profiles ◽

Open Rotor ◽

State Mixing

The growing pressure to reduce fuel consumption and cut emissions has triggered renewed interest in contra-rotating open rotor (CROR) technologies. One of their potential issues is self-excited or forced vibration of the unducted, light-weight, highly swept blades. This paper presents a numerical study into the flutter behavior of a CROR rig at take-off conditions. The study presented in this paper aimed to validate the numerical approach and provide insights into the flutter mechanisms of the open rotor under investigation. For the initial validation, pressure profiles and thrust coefficients from steady-state mixing plane calculations were compared against rig measurements. A full domain unsteady analysis predicted front rotor instability at low advance ratios. Flutter occurred in the first torsional mode in 0 and 1 nodal diameter (ND) which agreed with experimental observations. Subsequent unsteady computations focused on the isolated front rotor and first torsional mode. The flow field and aerodynamic damping over a range of advance ratios were studied. It was found that minimum aerodynamic damping occurred at low advance ratios when the flow was highly three-dimensional on the suction side. A correlation between the quasi-steady loading on the blade and aeroelastic stability was made and related to the numerical results. The effects of variations in frequency were then investigated by linking local aerodynamic damping to the unsteady pressure on the blade surface.

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Nonlinear Dynamics of Rigid and Flexible Multibody Systems

Volume 7A: 17th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc99/vib-8248 ◽

1999 ◽

Author(s):

Evtim V. Zakhariev

Keyword(s):

Finite Elements ◽

Multibody Systems ◽

Virtual Work ◽

Space Station ◽

Three Dimensional ◽

Numerical Procedure ◽

Numerical Approach ◽

Dynamic Equations ◽

Dynamics Modeling ◽

Lagrange Equations

Abstract In the present paper a unified numerical approach for dynamics modeling of multibody systems with rigid and flexible bodies is suggested. The dynamic equations are second order ordinary differential equations (without constraints) with respect to a minimal set of generalized coordinates that describe the parameters of gross relative motion of the adjacent bodies and their small elastic deformations. The numerical procedure consists of the following stages: structural decomposition of elastic links into fictitious rigid points and/or bodies connected by joints in which small force dependent relative displacements are achieved; kinematic analysis; deriving explicit form dynamic equations. The algorithm is developed in case of elastic slender beams and finite elements achieving spatial motion with three translations and three rotations of nodes. The beam elements are basic design units in many mechanical devices as space station antennae and manipulators, cranes and etc. doing three dimensional motion which large elastic deflections could not be neglected or linearised. The stiffness coefficients and inertia mass parameters of the fictitious joints and links are calculated using the numerical procedures of the finite element theory. The method is called finite elements in relative coordinates. Its equivalence with the procedures of recently developed finite segment approaches is shown, while in the treatment different results are obtained. The approach is used for solution of some nonlinear static problems and for deriving the explicit configuration space dynamic equations of spatial flexible system using the principle of virtual work and Euler-Lagrange equations.

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Numerical modeling of the contact between three-dimensional regions with the use of FEM

MATEC Web of Conferences ◽

10.1051/matecconf/201815708009 ◽

2018 ◽

Vol 157 ◽

pp. 08009

Author(s):

Tomasz Skrzypczak ◽

Ewa Węgrzyn-Skrzypczak ◽

Leszek Sowa

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Numerical Modeling ◽

Finite Elements ◽

Three Dimensional ◽

Numerical Approach ◽

Mechanical Interaction ◽

The Finite Element Method ◽

Three Dimensional Objects ◽

Original Program

The numerical approach based on the finite element method (FEM) for modeling of mechanical interaction between three-dimensional objects is presented in the paper. The model of contact is based on the assumption that the nodes of the region which is the source of contact cannot overlap with the nodes of the region being the target. The procedure of the detection of collision between surfaces of the source and the target is discussed in details. The behaviour of surfaces being in contact depends on their rigidity and is numerically modeled in the case of perfectly rigid source and deformable target. Each modeled object has an independent mesh of finite elements. These meshes can be freely moved relative to each other. Example of calculation using original program written in C++ is presented and discussed.

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