Thermal Contact Problems Research Articles

Multigrid method for the solution of thermal elastohydrodynamic lubrication point contact problem with surface asperities

The paper presents, the numerical investigation of point contact thermal elasto-hydrodynamic lubrication (EHL) with surface asperities are analyzed. The effect of temperature and surface roughness on fluid film thickness is studied in detail. The governing equations comprises Reynolds, film thickness, load balance and energy equations with appropriate boundary conditions. The second order finite difference approximation is used to discretize the governing equations and the resultant nonlinear system of algebraic equations is solved using Multigrid V-cycle with full approximation scheme (FAS) technique. Multi level multi integration (MLMI) technique is employed to solve the film thickness equation. The obtained results are illustrated in the form of graphs and tables which are comparable with earlier findings. The film thickness profiles shows dimple near to the outlet region due to temperature-viscosity wedge mechanism. Isothermal minimum film thickness is higher than the thermal minimum film thickness. Minimum film thickness is much smaller due to slide to roll ratio is positive ascompared to negative, whereas the behavior of central film thickness is contrast as that of minimum film thickness.

Three-dimensional thermal-mechanical analytical solutions for the half-space pressed by an inclined rigid cylindrical structure

Three-dimensional thermal-mechanical analytical solutions to the elastic half-space pressed by an inclined rigid cylindrical structure are presented in this article for the first time, based on the recent thermo-elastic general solutions in terms of harmonic functions and potential theory method. The obtained solutions are proved to be closed. The adequate validations are provided by comparing contact displacement and contact pressure on the contact plane from the presented solutions with those without heat effect in literatures. The geometric distribution of temperature on the contact region is also in accordance with that by previous researcher for the composite material under uniform heat flux. In addition, for the purpose of engineering application, a numerical example which is thermal contact problem between an inclined rigid circular displacement restrictor and elastic half-space is given, and the distributions of key field variables and effects of heat flux on contact pressure and normal displacement are discussed in detail.

A highly efficient semi-implicit two-field modeling for thermal contact problems with non-Fourier effects

In this paper, we revisit the thermal interface condition of thermal contact prob- lems with a nonzero thermal resistance. We point out that continuity conditions of the flux at the interfaces, which usually adopt the form of temperature gradient, leads to a paradoxical result if one of the adjacent bodies has zero temperature gradient. Specifically, that using the temperature gradient instead of the real heat flux yields a nonphysical temperature profile and fails to depict the thermal jump in cases with zero temperature gradients. We then show that the two-field (tem- perature and flux) formalism, in lieu of the classical single-field (temperature) naturally resolves this paradox. We propose an easy-to-implement semi-implicit scheme for this two-field formulation. The thermal interface problem is formu- lated in the fashion of differential algebraic equations (DAEs), in which the inter- face conditions are treated as algebraic equations constraining the associated heat process governed by differential equations. Our method can precisely fulfill the interface condition with the magnitude of machine error (10−16) and is computationally more efficient (around 8 to 10× faster) since it only needs to solve a very small Poisson-like system. End-to-end 1D and 2D simulations are presented to demonstrate the versatility and efficacy of our new method.

An imperfect thermal contact problem for consolidation of bilayered saturated soil subjected to ramp-type heating

This study proposes a generalized imperfect thermal contact model to simulate the thermal contact resistance existing at the interface between the two adjacent soil layers. Based on the generalized imperfect thermal contact model, a thermo-hydro-mechanical (THM) coupled consolidation model for bilayered saturated soil under ramp-type heating load is established. By means of the Laplace transform, the semi-analytical solutions of temperature increment, excess pore water pressure and displacement of the bilayered saturated soil are obtained. Based on the present solutions, the THM coupled consolidation behaviors are investigated through comparative and parametric analysis. The results show that the generalized imperfect thermal contact model can realistically describe the imperfect thermal contact problem and can be degenerated into other commonly-used thermal contact models. Due to the existence of interfacial thermal contact resistance, only a portion of heat flux passes through the interface, weakening the influence of the thermal load on the consolidation behaviors of non-heated layer. With the decrease of contact transfer coefficient and the increase of partition coefficient, the interfacial thermal contact resistance increases, and the influence of the thermal conductivity of soil grains reduces.

Contact Interaction of Steam Turbine Inner Casing Elements During Plastic Deformation

A structure’s material plasticity influence on the pattern of contact interaction of its elements during operation is studied. The stress-strain state problem for the inner casing of a steam turbine high-pressure cylinder operating at supercritical steam parameters (over 240 atm and 565 °C) is solved. The problem is solved by using a finite-element software package. A model of thermoplasticity with kinematic and isotropic hardening is considered. In carrying out the study, experimental strain curves were used for the materials of the connection. The main dependencies used in solving the problem are given. The method of solving the thermal contact problem of interaction of flange connector elements in the conditions of plasticity is based on the application of a contact layer model. To be able to take into account changes in the load from the fastening in the process of combined strain of both the fastening and the casing, first proposed is a method of the three-dimensional modeling of the thermal tightening of the fastening of the horizontal casing connector by applying the linear coefficient of linear expansion of the material. The proposed approach allows modeling the stress of the initial tightening of studs by specifying a fictitious change (decrease) of the coefficient of linear expansion of a stud given as a separate body in the calculation scheme. The magnitude of the specified change in the coefficient of linear expansion is determined from the relationship between the stress of the initial tightening in the stud and the required, for its creation, elongation, which is implemented in the calculation scheme in the presence of different values of linear expansion of both the stud and the casing. To conduct the numerical experiment, an ordered finite-element grid of the casing design was constructed. A 20-node finite element was used in the construction of the casing grid and the fastening. The effect of force loads and the temperature field, in which the structural element under consideration is operated, is taken into account. An analysis of the results of distribution of equivalent stresses and contact pressure during operation is carried out. The difference between the obtained results and the results of solving the problem in the elastic formulation is noted.

Thermo-mechanical FDEM model for thermal cracking of rock and granular materials

A coupled thermo-mechanical (TM) model based on the combined finite-discrete element method (FDEM) was proposed to simulate the thermal cracking of rock and granular materials. For heat conduction, it links continuous and contact heat transfer simultaneously through the continuum and discrete thermal elements, and can handle thermal contacts explicitly. For thermally induced stresses, the new TM model uses the concept of multiplicative decomposition of deformation gradient, which is consistent with the finite strain theory used in FDEM – for handling large strains and rotations. For thermal cracking, the coupling of the new TM model occurs in two directions, such as cracking in mechanical calculation affects thermal conduction, and friction caused by contact interactions generates heat, thus can capture the dynamic process of thermally induced fracturing. Four verification examples were given to validate its performance in simulating the thermal expansion in the steady-state, thermal stress in transient states, thermal cracking, and complex-shaped multibody thermal contact. The new TM model exhibits attractive features: robust to capture heat transfer for multibody thermal contact problems; better handle large strains and thermal cracking; better capture the progressive process of fracturing affects thermal conductivity; applicable to not only the steady-state but also the transient TM response.

Numerical analysis of a thermal frictional contact problem with long memory

<p style='text-indent:20px;'>The objective in this paper is to study a thermal frictional contact model. The deformable body consists of a viscoelastic material and the process is assumed to be dynamic. It is assumed that the material behaves in accordance with Kelvin-Voigt constitutive law and the thermal effect is added. The variational formulation of the model leads to a coupled system including a history-dependent hemivariational inequality for the displacement field and an evolution equation for the temperature field. In study of this system, we first consider a fully discrete scheme of it and then focus on deriving error estimates for numerical solutions. Under appropriate assumptions of solution regularity, an optimal order error estimate is obtained. At the end of this manuscript, we report some numerical simulation results for the contact problem so as to verify the theoretical results.

A Highly Efficient Semi-Implicit Two-Field Modeling for Thermal Contact Problems with Non-Fourier Effects

A Highly Efficient Semi-Implicit Two-Field Modeling for Thermal Contact Problems with Non-Fourier Effects

Perfect thermal contact of hyperbolic conduction semispaces with an interfacial heat source

The problem of thermal contact between two bodies with a heat source at their interface presents great scientific and practical interest. On the time scale of a nanosecond or shorter, heat propagation should be considered in the form of thermal waves of finite speeds. This study investigated the thermal behaviour of hyperbolic conduction semispaces in perfect thermal contact subjected to the action of an interfacial heat source. An analytical solution was derived using the Laplace integral transform approach. The contact temperature and heat fluxes were analysed for different ratios of thermal conductivities K1 and K2, thermal diffusivities k1 and k2, and thermal relaxation times τ1 and τ2 of the semispaces. It was shown that the interfacial heat generation results in a step-wise change in the contact temperature. It was also found that the initial partition of heat between the semispaces occurs due to the ratio of K1/k1τ1 and K2/k2τ2. The applicability of the obtained solution and its particular expressions was illustrated on the example of microscopic problems of ultra-short laser pulse welding and sliding friction.

Transient thermal contact in gyro unit–platform assembly

Thermal contact conditions of parts change in time in the process of heating. Cases of thermal contact instability may occur even under constant boundary conditions. This is due to the combination of temperature and strain fields interdependence based on thermal expansion, the influence of shape of parts and the conditions of their connection in the assembly. In this paper, using the example of a model problem of thermal contact of a gyro unit–platform assembly, we study qualitative and quantitative aspects of the temporal behavior of thermal contact conductance. A significant qualitative difference between thermal contact conductance and its steady-state value has been obtained. Given that the magnitude of the deviation is within the acceptable engineering accuracy, it is of interest in terms of thermal contact model development.

Modeling of thermal contacts with heat generation: Application to electrothermal problems

When modeling thermal contacts with heat generation between two solids (e.g. electrothermal applications), we are often interested in evaluating the heat transfer rates and contact temperatures, and generally, it is difficult to evaluate these thermal characteristics due to interfacial conditions. In this work, a general representation of solid-solid thermal contact problems with heat generation is proposed. This representation is based on the thermal-electrical analogy and uses the notion of partition coefficient β. The resulting equivalent thermal circuits are presented and discussed. The pertinence of this analytical approach is demonstrated for the electrothermal application of Joule heating for different contact configurations (similar and dissimilar materials, with and without interstitial fluid). The analytical results for each configuration are compared to numerical results obtained using numerical simulations under similar conditions, both results are in very good agreement.

Symmetrical node-to-node formulation for thermal contact problems between non-conforming or non-matching meshes

The aim of this paper is to propose a symmetrical finite element formulation for the numerical treatment of thermal contact problems without any constraint on the shape, size and order of approximation of the meshes in contact. The new formulation implicitly ensures the heat balance through the contact and it is well adapted for the use of non-linear symmetric solvers minimizing the matrix storage. Examples are presented to show the relevance of the formulation developed.

Multiscale thermomechanical modeling of frictional contact problems considering wear – Application to a pin-on-disc system

This paper presents a multi-scale strategy for thermomechanical simulation of frictional systems, as brakes, taking into account the scale of the contact interface phenomena which is much lower than the macro scale of the system. At macro scale, a finite element model is considered to model the system components. At micro scale, the thermal and mechanical contact problems are solved considering surface roughness and wear. At this scale, semi analytic methods, accelerated with the Fast Fourier Transform, and optimization techniques are used. As regards wear, Archard's law is used with a wear rate coefficient depending on temperature. From these models, contact parameters such as stiffness and heat partition coefficient are integrated into the macroscale model, and this for each surface element. Moreover, the solving scheme is transient allowing to update the surface topography under thermomechanical and wear effects. As an example, this multi-scale strategy is used to study the thermomechanical behavior of a pin-on-disc system. Moreover, implications of the interface on friction induced vibrations are also investigated. With this model, the influence of the interface behavior and wear on the system response, are clearly shown. Conversely this strategy gives results locally, close to the physical mechanisms involved in the contact. A comparison is performed with a classical model considering a perfect flat contact.

Investigation of thermal inter-facial problems involving non-locality in space and time

The vastly disparate length and time scales existing in new devices and materials born out of micro-/nano- devices have made thermal modeling and simulation more important and more difficult. The heat transfer process in one certain micro-device is essentially a thermal contact problem that involves various scales of space and time in each of the sub-components. In this communication, we utilize a newly developed computational framework to investigate problems of thermal contact involving size-effects that span the ballistic, ballistic-diffusive, and diffusive heat transfer processes. The preliminary work regarding this generalized computational framework has been published in Xue, Zhang, and Tamma (2018) and has been proved to readily resolve the problem of thermal contact between Fourier-type and nonFourier-type sub-domains. The fashion of solving the thermal inter-facial problems from the perspective of differential-algebraic equations is extended to a broad range of thermal contact problems in the present work, including both the temporal and spatial non-locality. The numerical results demonstrate the prediction of thermal response of the bodies in contact at different scales. The proposed computational framework paves the way for investigating the thermal inter-facial problems in micro-/nano- devices.

A two-field state-based Peridynamic theory for thermal contact problems

Peridynamics is a non-local based method and an extension of classical continuum theory that has been proved to have the ability to solve problems involving discontinuities. This work extends the state-based Peridynamic formulation to describe heat transfer process in the adjacent regions via using the domain decomposition technique. The state-based Peridynamic heat conduction model is proposed to couple with a generalized thermal diffusion model in a two-field form, in which both the temperature and the thermal flux are treated as the primary variables. Coupled with thermal interface conditions, the proposed two-field state-based Peridynamic heat conduction naturally leads to a classical differential algebraic equation, which permits the numerical simulations of thermal contacts between various diffusion models. A unified time integration, termed as generalized single step single solve (GS4), is extended to solve the resulting differential algebraic equations. Numerical results of the simulations are reported and compared with those obtained by Finite Element Method which show that the method is promising for these applications in terms of accurately capturing the physics and preserving the interface conditions.

Numerical analysis of a thermal contact problem with adhesion

In this paper, we study a class of dynamic thermal problems involving a frictional normal compliance adhesive contact model and a non-clamped condition for visco-elastic materials. The variational formulation of the problem leads to a general system defined by a second-order quasi-variational evolution inequality on the displacement field coupled with the two first-order evolution equations describing the evolution of the temperature and adhesion. We establish an existence and uniqueness result of the solution on displacement, temperature and adhesion. Then we provide a fully discrete numerical scheme of approximation and derive an error estimate. Finally, various numerical computations are included.

Generalized heat conduction model involving imperfect thermal contact surface: Application of the GSSSS-1 differential-algebraic equation time integration

A number of contributions have been made to model thermal contact problems involving perfect/imperfect thermal interfaces. The Fourier-, Cattaneo-, and Jeffreys-types of thermal flux modes have been exploited to govern the heat transfer processes of adjacent regions. However, most of the existing studies consider using only one type of these thermal flux models to describe the thermal physics of the entire system such that the mathematical model may fail to precisely describe the physics within the multi-domain system, especially, when the mean free paths of different adjacent domains span in a large range with respect to the characteristic dimension of the material. To circumvent this issue, a generalized heat conduction model, termed C- and F-processes heat conduction model, with the consideration of perfect/imperfect thermal interface is proposed and formulated under the expression of a first-order time dependent differential-algebraic equation in which the interface conditions are treated as algebraic equations. The unified time integration of GSSSS-1 is extended to solve the resulting differential-algebraic system with Index 2 constraints. The numerical results illustrate that the proposed framework has a better capacity of describing the thermal contacts with/without the thermal resistance of Fourier-Fourier, Fourier-Cattaneo, and other general cases.

Review : Thermal contact problems at cryogenic temperature

This paper addresses technical problems of thermal contact conductance or resistance which inevitably occurs in most cryogenic engineering systems. The main focus of this paper is to examine what kind of physical factors primarily influences the thermal contact resistance and to suggest how it can be minimized. It is a good practical rule that the contact surface must have sub-micron roughness level with no oxide layer and be thinly covered by indium, gold, or Apiezon-N grease for securing sufficient direct contact area. The higher contact pressure, the lower the thermal contact resistance. The general description of this technique has been widely perceived and reasonable engineering results have been achieved in most applications. However, the detailed view of employing these techniques and their relative efficacies to reduce thermal contact resistances need to be thoroughly reviewed. We should consider specific thermal contact conditions, examine the engineering requirements, and execute each method with precautions to fulfil their maximum potentials.

Applying artificial neural networks (ANN) to the estimation of thermal contact conductance in the exhaust valve of internal combustion engine

Exhaust valve temperature increases significantly due exhaust hot gases obtained from combustion fuel-air mixture in combustion chamber of internal combustion engine. In order to avoid the damage of the combustion chamber and the engine itself, heat must be taken away from the valve. This can be done when the valve in contact with the seat and the periodic contact heat transfer takes place. Therefore study of heat transfer contact between the valve and its seat is important and necessary. In this study back propagation neural (BPN) network has been used to estimate two parameters to determine the heat transfer rate through the valve and its seat due the complexity of thermal contact problem between the valve and its seat. This thermal contact problem is solved to obtain the required information for design the neural network using inverse heat transfer method (conjugate gradient method using a two search step sizes). The results show that, between the different algorithms, Levenberg Marquardt algorithm is produced the best model for estimating the unknown parameters.

Numerical treatment of a class of thermal contact problems

A mathematical problem modeling dynamical behavior of viscoelastic materials is studied. The problem is related to highly nonlinear and non-smooth phenomena like contact, friction and a class of dynamic contact problems with friction and thermal effects. The applied approach leads to a system involving variational inequalities and a fully discrete scheme for numerical approximations and the analysis of error estimate order is provided. Numerical computations are given so as to illustrate the mathematical model.