Heat Transfer Between Colliding Surfaces and Particles

2011 ◽  
Author(s):  
Like Li ◽  
Renwei Mei ◽  
James F. Klausner ◽  
David W. Hahn
Keyword(s):  
Heat Transfer ◽  
Contact Area ◽  
Initial Period ◽  
Asymptotic Methods ◽  
Theory Of Elasticity ◽  
Hertzian Contact ◽  
Contact Radius ◽  
Asymptotic Result ◽  
Fourier Number ◽  
Entire Duration

Collisional heat transfer between two contacting curved surfaces is investigated computationally using the finite difference method and analytically using various asymptotic methods. Transformed coordinates that scale with the contact radius and the diffusion length are used for the computations. Hertzian contact theory of elasticity is used to characterize the contact area as a function of time. For an axisymmetric contact area, a two-dimensional self-similar solution for the thermal field during the initial period of contact is obtained and it serves as an initial condition for the heat transfer simulation throughout the entire duration of collision. A modified 2-D asymptotic result of heat transfer at small Fourier number is obtained. For finite Fourier numbers the heat transfer during the collision has been determined computationally. A closed-form formula is developed to predict the heat transfer as a function of the Fourier number, the thermal diffusivity ratio and conductivity ratio of the impacting particles.

Heat Transfer Between Colliding Surfaces and Particles

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Like Li ◽  
Renwei Mei ◽  
James F. Klausner ◽  
David W. Hahn
Keyword(s):  
Heat Transfer ◽  
Contact Area ◽  
Thermal Field ◽  
Initial Period ◽  
Asymptotic Methods ◽  
Hertzian Contact ◽  
Thermal Conductivity Ratio ◽  
Contact Radius ◽  
Two Dimensional ◽  
Fourier Number

Collisional heat transfer between two contacting curved surfaces is investigated computationally using a finite difference method and analytically using various asymptotic methods. Transformed coordinates that scale with the contact radius and the diffusion length are used for the computations. Hertzian contact theory of elasticity is used to characterize the contact area as a function of time. For an axisymmetric contact area, a two-dimensional self-similar solution for the thermal field during the initial period of contact is obtained, and it serves as an initial condition for the heat transfer simulation throughout the entire duration of collision. A two-dimensional asymptotic heat transfer result is obtained for small Fourier number. For finite Fourier numbers, local analytical solutions are presented to elucidate the nature of the singularity of the thermal field and heat flux near the contact point. From the computationally determined heat transfer during the collision, a closed-form formula is developed to predict the heat transfer as a function of the Fourier number, the thermal diffusivity ratio, and the thermal conductivity ratio of the impacting particles.

scholarly journals The Elastic Contact of Rough Spheres Investigated Using a Deterministic Multi-Asperity Model

2019 ◽  
Vol 10 (01) ◽  
pp. 1841002 ◽  
Author(s):  
Vladislav A. Yastrebov
Keyword(s):  
Contact Area ◽  
Rough Surfaces ◽  
Contact Problems ◽  
Hertzian Contact ◽  
Contact Radius ◽  
Geometrical Shape ◽  
Elastic Contact ◽  
Deterministic Analysis ◽  
Asperity Model ◽  
Deformation Modes

In this paper, we use a deterministic multi-asperity model to investigate the elastic contact of rough spheres. Synthetic rough surfaces with controllable spectra were used to identify individual asperities, their locations and curvatures. The deterministic analysis enables to capture both particular deformation modes of individual rough surfaces and also statistical deformation regimes, which involve averaging over a big number of roughness realizations. Two regimes of contact area growth were identified: the Hertzian regime at light loads at the scale of a single asperity, and the linear regime at higher loads involving multiple contacting asperities. The transition between the regimes occurs at the load which depends on the second and the fourth spectral moments. It is shown that at light indentation the radius of circumference delimiting the contact area is always considerably larger than Hertzian contact radius. Therefore, it suggests that there is no scale separation in contact problems at light loads. In particular, the geometrical shape cannot be considered separately from the surface roughness at least for approaching greater than one standard roughness deviation.

scholarly journals Improved design criterion for frictionally engaged contacts in overrunning clutches

2021 ◽  
Author(s):  
Nadine Nagler ◽  
Armin Lohrengel
Keyword(s):  
Design Process ◽  
Contact Area ◽  
Axial Load ◽  
State Of The Art ◽  
Tangential Force ◽  
Design Criterion ◽  
Hertzian Contact ◽  
Loss Of Function ◽  
Axial Loads ◽  
Improved Design

AbstractOverrunning clutches, also known as freewheel clutches, are frictionally engaged, directional clutches; they transmit torque depending on the Freewheel clutch rings’ rotation directions. The torque causes a tangential force in the Hertzian contact area. The hitherto “state-of-the-art design criterion” bases on this load situation. In practice, axial loads additionally act on the frictionally engaged Hertzian contact area. This additional axial load can cause the loss of the friction connection and so the freewheel clutch slips. This publication presents an improved design criterion for frictionally engaged contacts in freewheel clutches. It allows to consider tangential as well as axial loads during the design process. Additionally, it offers the possibility to estimate the probability of frictional engagement loss and gross slip based on the freewheel clutch’s application scenario. This publication points out how to use the improved design criterion to design freewheel clutches that are more robust against a loss of function.

A simplified formulation of adhesion problems with elastic plates

2009 ◽  
Vol 465 (2107) ◽  
pp. 2217-2230 ◽  
Author(s):  
Carmel Majidi ◽  
George G. Adams
Keyword(s):  
Potential Energy ◽  
Contact Area ◽  
Contact Region ◽  
Bending Moment ◽  
Total Potential Energy ◽  
Work Of Adhesion ◽  
Contact Radius ◽  
Algebraic Complexity ◽  
Elastic Plates ◽  
Total Potential

The solution of adhesion problems with elastic plates generally involves solving a boundary-value problem with an assumed contact area. The contact region is then found by minimizing the total potential energy with respect to the contact area (i.e. the contact radius for the axisymmetric case). Such a procedure can be extremely long and tedious. Here, we show that the inclusion of adhesion is equivalent to specifying a discontinuous internal bending moment at the contact region boundary. The magnitude of this moment discontinuity is related to the work of adhesion and flexural rigidity of the plate. Such a formulation can greatly reduce the algebraic complexity of solving these problems. It is noted that the related plate contact problems without adhesion can also be solved by minimizing the total potential energy. However, it has long been recognized that it is mathematically more efficient to find the contact area by specifying a continuous internal bending moment at the boundary of the contact region. Thus, our moment discontinuity method can be considered to be a generalization of that procedure which is applicable for problems with adhesion.

Experimental and numerical study on cavitation under elastohydrodynamic lubrication point contact

2021 ◽  
pp. 135065012110527
Author(s):  
Mingfei Ma ◽  
Wen Wang ◽  
Wenxun Jiang
Keyword(s):  
Contact Area ◽  
Numerical Study ◽  
Ambient Pressure ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Hertzian Contact ◽  
Pressure Area ◽  
Cavitation Pressure ◽  
Experimental Researches ◽  
State 1

As a common phenomenon in elastohydrodynamic lubrication, cavitation has an effect on the completeness of the oil film in the contact area. Many studies have therefore been conducted on cavitation. Experimental researches on cavitation usually rely on optical interference observation, which offers a limited resolution and observation range. In this paper, an infrared thermal camera is used to observe the cavity bubbles on a ball-on-disc setup under sliding/rolling conditions. The results show that the cavity length increases with an increases of the entrainment speed and the viscosity of the lubricants. These observations are explained by a numerical model based on Elrod's algorithm. Effects of entrainment speed and lubricant viscosity on the breakup of cavitation bubbles and the cavitation states are investigated. Both the simulation and experimental results show that a negative pressure area is present behind the Hertzian contact area. The ambient pressure plays a role in maintaining cavitation state 1. The cavitation pressure is close to the vacuum pressure when the entrainment speed is low and to the ambient pressure instead when the entrainment speed is high.

Phase Change Process Inside a Small-radii Cylinder Subjected to Cyclic Convective Boundary Conditions: a Numerical Study

2021 ◽  
Author(s):  
Yousef Kanani ◽  
Avijit Karmakar ◽  
Sumanta Acharya
Keyword(s):  
Heat Transfer ◽  
Surface Temperature ◽  
Phase Change ◽  
Phase Change Materials ◽  
Numerical Study ◽  
Convective Boundary Condition ◽  
Freezing Process ◽  
Fourier Number ◽  
Two Phase ◽  
Convective Boundary

Abstract We numerically investigate the melting and solidi?cation behavior of phase change materials encapsulated in a small-radii cylinder subjected to a cyclic convective boundary condition (square wave). Initially, we explore the effect of the Stefan and Biot numbers on the non-dimensionalized time required (i.e. reference Fourier number Tref ) for a PCM initially held at Tcold to melt and reach the cross?ow temperature Thot. The increase in either Stefan or Biot number decreases Tref and can be predicted accurately using a correlation developed in this work. The variations of the PCM melt fraction, surface temperature, and heat transfer rate as a function of Fourier number are reported and analyzed for the above process. We further study the effect of the cyclic Fourier number on the periodic melting and freezing process. The melting or freezing front initiates at the outer periphery of the PCM and propagates towards the center. At higher frequencies, multiple two-phase interfaces are generated (propagating inward), and higher overall heat transfer is achieved as the surface temperature oscillates in the vicinity of the melting temperature, which increases the effective temperature difference driving the convective heat transfer.

scholarly journals Coaxial Thermocouples for Heat Transfer Measurements in Long-Duration High Enthalpy Flows

Sensors ◽  
2020 ◽  
Vol 20 (18) ◽  
pp. 5254
Author(s):  
Shizhong Zhang ◽  
Qiu Wang ◽  
Jinping Li ◽  
Xiaoyuan Zhang ◽  
Hong Chen
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Surface Temperature ◽  
Thermal Effusivity ◽  
Fast Response ◽  
Test Time ◽  
Physical Parameters ◽  
Fourier Number ◽  
High Enthalpy ◽  
Long Duration

Coaxial thermocouples have the advantages of fast response and good durability. They are widely used for heat transfer measurements in transient facilities, and researchers have also considered their use for long-duration heat transfer measurements. However, the model thickness, transverse heat transfer, and changes in the physical parameters of the materials with increasing temperature influence the accuracy of heat transfer measurements. A numerical analysis of coaxial thermocouples is conducted to determine the above influences on the measurement deviation. The minimum deviation is obtained if the thermal effusivity of chromel that changes with the surface temperature is used to derive the heat flux from the surface temperature. The deviation of the heat flux is less than 5.5% when the Fourier number is smaller than 0.255 and 10% when the Fourier number is smaller than 0.520. The results provide guidance for the design of test models and coaxial thermocouples in long-duration heat transfer measurements. The numerical calculation results are verified by a laser radiation heating experiment, and heat transfer measurements using coaxial thermocouples in an arc tunnel with a test time of several seconds are performed.

Hertzian Contact and Adhesion of Elastomers

1969 ◽  
Vol 91 (4) ◽  
pp. 732-737 ◽  
Author(s):  
Richard C. Drutowski
Keyword(s):  
Stress Distribution ◽  
Tensile Stress ◽  
Contact Area ◽  
Hard Sphere ◽  
Continuous Measurement ◽  
Hertzian Contact ◽  
Initial Contact ◽  
Circular Zone ◽  
Outer Annulus ◽  
Contact Size

The contact of a hard sphere with a flat elastomer is examined both analytically and experimentally when adhesive stresses are present. Use of a transparent spherical indenter enables continuous measurement of contact size while the samples are pulled apart. For any combination of load and contact area, the superposition of a Hertz and a Boussinesq stress distribution separates the contact into a circular zone under compression and an outer annulus under tension. During separation, while the contact size decreases and the tensile annulus becomes a larger percentage of the total contact, the average tensile stress remains constant. This average adhesive is a material property which is easily measured and is shown to be invariant with respect to indenter radius and initial contact pressure. An application of this analysis to opaque indenters is described.

Nano-Meter Film Rheology and Asperity Lubrication

2002 ◽  
Vol 124 (3) ◽  
pp. 595-599 ◽  
Author(s):  
Bo Jacobson
Keyword(s):  
Contact Area ◽  
Pressure Fluctuations ◽  
Slip Rate ◽  
Hertzian Contact ◽  
Metal Contact ◽  
Rolling Motion ◽  
Oil Film ◽  
Pure Rolling ◽  
Total Separation ◽  
Molecular Dimensions

It is today possible to manufacture so smooth surfaces that they can elastically conform totally to each other over the whole Hertzian contact area. For pure rolling lubrication such surfaces only need an oil film of molecular dimensions to get total separation. When the rolling motion is combined with sliding, the pressure fluctuations inside the Hertzian contact redistribute the oil and make metal-to-metal contact possible. The redistribution velocity is a function of the slip rate S and the number of asperities N from the inlet to the outlet of the Hertzian contact area. The asperity top oil film thickness decreases with a factor of the order 2NS going from the inlet to the outlet of the Hertzian contact.

A Study of the Effect of m and n Coefficients of the Hertzian Contact Theory on Railroad Vehicle Dynamics

2007 ◽  
Author(s):  
J. P. Pascal ◽  
Khaled E. Zaazaa
Keyword(s):  
Contact Area ◽  
Contact Region ◽  
Local Deformation ◽  
Hertzian Contact ◽  
Vehicle Dynamic ◽  
Railroad Vehicle Dynamics ◽  
Original Table ◽  
Data Points ◽  
Railroad Vehicle ◽  
Contact Ellipse

For the wheel/rail contact problem, the Hertz theory for two elastic bodies in contact is commonly used to determine the shape and dimensions of the contact area and the local deformation of the wheel and rail surfaces at the contact region. The shape of the contact area is assumed to be elliptical. The ratio of the contact ellipse semi-axes is equal to the ratio of two non-dimensional contact area coefficients, known as m and n coefficients. Hertz presented a table of these two coefficients, determined as a function of an angular parameter, θ. Most railroad vehicle dynamic codes use this table with online interpolation to determine the contact ellipse semi-axes. Recently, it was found that this original table may be too coarse, and that more data points are needed within the table for solving the wheel/rail contact accurately. This paper discusses the effect of the accuracy of the m and n coefficients in solving for wheel/rail contact, and demonstrates this effect with two numerical examples that show the resulting differences in the dynamic behavior of railroad vehicles dependent on this accuracy. A new table with more data points is presented that is recommended for use in railroad vehicle dynamic codes that employ the Hertzian contact for solving the wheel/rail contact interaction. This modified table was originally derived by Jean-Pierre Pascal as a part of collaborative research between the Federal Railroad Administration (FRA) and the French Ministry of Transportation.

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