Analysis of Particle Behavior in High-Velocity Oxy-Fuel Thermal Spraying Process

This paper analyzes the behavior of coating particle as Well as the gas flow both of inside and outside the High-Velocity Oxy-Fuel (HVOF) thermal spraying gun by using quasi-one-dimensional analysis and numerical simulation. The HVOF gun in the present analysis is an axisymmetric convergent-divergent nozzle with the design Mach number of 2.0 followed by a straight passage called barrel. In the present analysis it is assumed that the influence of the particles injected in the gas flow is neglected, and the interaction between the particles is also neglected. The gas flow in the gun is assumed to be quasi-one-dimensional adiabatic flow. The velocity, temperature and density of gas in the jet discharged from the barrel exit are predicted by solving Navier-Stokes equations numerically. The particle equation of motion is numerically integrated using three-step Runge-Kutta method. The drag coefficient of the particle is calculated by linear interpolation of the experimental data obtained in the past. Particle     

TRANSIENT THERMOELASTIC ANALYSIS OF AN ANNULAR FIN WITH COUPLING EFFECT AND VARIABLE HEAT TRANSFER COEFFICIENT

A hybrid numerical method of the Laplace transformation and the finite difference method is applied to solve the transient thermoelastic problem of an annular fin, in which the thermomechanical coupling effect is taken into account in the governing equation of heat conduction and the heat transfer coefficient is a function of the radius of the fin. The general solutions of the governing equations are first solved in the transform domain. Then the inversion to the real domain is completed via the method of matrix similarity transformation and Fourier series technique. The transient distributions of temperature increment and thermal stresses of the fin in the real domain are calculated numerically. The presented method is more efficient in computing time and is applicable to other types of boundary conditions.     

Aerodynamic study on supersonic flows in high-velocity oxy-fuel thermal spray process

To clarify the characteristics of gas flow in high velocity oxy-fuel (HVOF) thermal spray gun, aerodynamic research is performed using a special gun. The gun has rectangular cross-sectional area and sidewalls of optical glass to visualize the internal flow. The gun consists of a supersonic nozzle with the design Mach number of 2.0 followed by a straight passage called barrel. Compressed dry air up to 0.78 MPa is used as a process gas instead of combustion gas which is used in a commercial HVOF gun. The high-speed gas flows with shock waves in the gun and jets are visualized by schlieren technique. Complicated internal and external flow-fields containing various types of shock wave as well as expansion wave are visualized.     

DQM-Based Thermal Stresses Analysis of a Functionally Graded Cylindrical Shell Under Thermal Shock

The transient thermal stresses of a functionally graded (FG) cylindrical shell subjected to a thermal shock are investigated. The dynamic temperature fields of FG shells are obtained by using the Laplace transform and power series method. The differential quadrature method is developed to obtain the transient thermal stresses by solving dynamic governing equations in terms of displacements. The effects of the material constitutions on the transient temperature and the thermal stresses are analyzed in the cases of obverse thermal shock and reverse thermal shock. It turns out that the thermal stresses could be alleviated by means of changing the volume fractions of the constituents.     

Transient coupled thermoelastic analysis of an annular fin

This work is to investigate the transient coupled thermoelasticity of an annular fin with its base suddenly subjected to a heat flux of a decayed exponential function of time. While neglecting the effect of the inertia term in the governing equation of motion, the thermomechanical coupling effect is taken into account in the governing equation of heat conduction. By taking the Laplace transform with respect to time, the governing equations are decoupled and general solutions for temperature increments and displacements are obtained in the transform domain. A Fourier series technique is taken to achieve the inversion to the real domain. The transient distributions of temperature increments and thermal stresses in the real domain are presented numerically. It is found that the coupling parameter can lead to an obvious lagging effect in both the temperature and the stress distributions of the fin. Moreover, the present method also can be applied to cases with different types of boundary conditions, such as time-dependent changes in boundary temperatures.     

Experimental and Numerical Evaluation of the Performance of Supersonic Two-Stage High-Velocity Oxy-Fuel Thermal Spray （Warm Spray） Gun

The water-cooled supersonic two-stage high-velocity oxy-fuel (HVOF) thermal spray gun was developed to make a coating of temperature-sensitive material,such as titanium,on a substrate.The gun has a combustion chamber (CC) followed by a mixing chamber (MC),in which the combustion gas is mixed with the nitrogen gas at room temperature.The mixed gas is accelerated to supersonic speed through a converging-diverging (C-D) nozzle followed by a straight passage called the barrel.This paper proposes an experimental procedure to estimate the cooling rate of CC,MC and barrel separately.Then,the mathematical model is presented to predict the pressure and temperature in the MC for the specific mass flow rates of fuel,oxygen and nitrogen by assuming chemical equilibrium with water-cooling in the CC and MC,and frozen flow with constant specific heat from stagnant condition to the throat in the CC and MC.Finally,the present mathematical model was validated by comparing the calculated and measured stagnant pressures of the CC of the two-stage HVOF gun.     

In-Situ Thermal Resistance Evaluation of Walls Using an Iterative Dynamic Model

This paper proposes and validates, numerically and experimentally, an iterative model to evaluate the thermal resistance of multilayer walls in a dynamic state.

The paper first presents the analytical solution for simulating heat conduction in the frequency domain. The model is then modified by assuming a single-layer wall with unknown thermal properties. A nonlinear system is obtained by imposing temperatures and fluxes on the external surfaces. This is solved using an iterative approach based on the Newton–Raphson method. Finally, the model is applied to evaluate the thermal resistance of a wall in real conditions.     

TRANSIENT THERMOELASTIC ANALYSIS FOR TWO-DIMENSIONAL DISSIMILAR MATERIALS BY THE BOUNDARY ELEMENT METHOD

This article deals with the transient thermoelastic analysis for dissimilar materials under the plane strain condition. In the process of the boundary element formulation, the time-dependent fundamental solution for the transient heat conduction problem and the thermoelastic displacement potential for the transient thermal stress problem are introduced. Consequently, domain integrals are completely eliminated. The discretization based on the domain combination method for these boundary integral equations is implemented, and the transient temperature and stress fields are analyzed numerically. The transient temperature at the lateral surface and the transient thermal stress at the interface are investigated for the three categories that have been determined according to the characteristic equation expressed by Dundurs parameters.     

Advances in Studying Phonon Mean Free Path Dependent Contributions to Thermal Conductivity

The thermal conductivity of a material or device is dependent on its characteristic dimension. When the characteristic dimension is commensurate to the mean free paths of thermal energy carriers, the thermal conductivity decreases. The precise relationship between characteristic size and thermal conductivity, which depends on the distribution of energy carrier mean free paths in the material, is not straightforward to determine experimentally. The utility of this relationship has led many researchers to study the mean free path dependent contributions of thermal energy carriers to the thermal conductivity of materials, known as the thermal conductivity accumulation function. This review highlights a number of recent experimental results and techniques used to study the thermal conductivity accumulation function, including transient thermal grating, time domain thermoreflectance, and broadband frequency domain thermoreflectance. In these techniques, nondiffusive thermal transport is induced (i.e., thermal gradients occur over length scales comparable to energy carrier mean free paths) and an effective thermal conductivity of the material is determined. We conclude with our outlook on future directions for the field focused on improved interpretations of the experiments and new materials with unique mean free path distributions.     

Hybrid numerical method applied to transient hygrothermal analysis in an annular cylinder

A hybrid numerical method of the Laplace transformation and the finite difference is applied to solve the transient hygrothermal problem of an infinitely long annular cylinder, in which the temperature and moisture coupling at the inner and outer surfaces is taken into account in the boundary conditions. By a combining method of the Laplace transformation and the finite difference, the general solutions of the governing equations are first solved in the transform domain. Then the inversion to the real domain is completed by the method of matrix operation and Fourier series technique. The transient distributions of temperature, moisture, displacement, stresses of the annular cylinder in the real domain are calculated numerically. The presented method is also applicable to multiplayer annular cylinders and to other types of boundary conditions.     

光学热带法测量固态材料热物性研究

针对接触式瞬态热带法测量导热系数时,加热丝和样品间接触热阻,会影响实验测量结果以及对固体样品形状大小要求较高的现状,根据瞬态热带法原理,本文提出了一种光学瞬态热带法来测量固体材料的导热系数。采用连续激光为加热源,通过透镜将光斑放大并聚焦照射在样品表面,实现样品非接触式测量。构建二维导热模型,采用红外热像仪记录样品表面温升随时间的变化关系,根据导热理论模型求出待测样品的热扩散系数及导热系数。以K9和石英玻璃为样品对本套测量方法进行验证,制备并测量了纯石蜡、0.5%和1%石墨烯-石蜡的固态复合相变材料的导热系数,探讨了影响实验结果的潜在因素。     

Analysis of conduction – natural convection conjugate heat transfer in the gap between concentric cylinders under solar irradiation

Although, in general, most of concentric cylinders used in engineering applications are heated non-uniformly, studies on the natural convection in the air layer between the cylinders have been performed only for the uniform heating so that it is difficult to apply the results to the real cases. In the present study, the effects of material property of outer cylinder and the air gap thickness between cylinders on the natural convection are investigated by computational fluid dynamics and experimental means. Namely, conduction-natural convection conjugated heat transfer in the concentric cylinders, gun and shield tube, under solar irradiation, is analyzed numerically and the various predictions on the resultant thermal deformations of gun are compared to the experimental data with variation of the gap thickness of cylinders and material properties of shield tube. Results show that larger the thermal conductivity of shield tube, smaller the Nusselt number variations of gun and shield tube surfaces. This is due to that balance of conduction in the cylinders and natural convection in the gap between inner and outer cylinders may increase the uniformity of the air layer temperature. High thermal conductivity of shield tube inhibits the natural convection in the air layer and there exists a gap thickness that exerts an influence critically on the thermal deformation of gun.     

Analytical solution of the parabolic and hyperbolic heat transfer equations with constant and transient heat flux conditions on skin tissue

In this article, the parabolic (Pennes bioheat equation) and hyperbolic (thermal wave) bioheat transfer models for constant, periodic and pulse train heat flux boundary conditions are solved analytically by applying the Laplace transform method for skin as a semi-infinite and finite domain. The bioheat transfer analysis with transient heat flux on skin tissue has only been studied by Pennes equation for a semi-infinite domain. For modeling heat transfer in short duration of an initial transient, or when the propagation speed of the thermal wave is finite, there are major differences between the results of parabolic and hyperbolic heat transfer equations. The non-Fourier bioheat transfer equation describes the thermal behavior in the biological tissues better than Fourier equation. The outcome of transient heat flux condition shows that by penetrating into the depths beneath the skin subjected to heat, the amplitude of temperature response decreases significantly. The blood perfusion rate can be predicted using the phase shift between the surface temperature and transient surface heat flux. The thermal damage of the skin is studied by applying both the parabolic and hyperbolic bioheat transfer equations.     

Thermal Fracture Analysis Of Nonhomogeneous Plate with Interfaces Under Uniform Heat Flow

The mixed-mode thermomechanical fracture problem in a nonhomogeneous material plate with two interfaces is studied in this research. Uniform heat flow conditions are considered. The interaction energy integral method for the thermal fracture problem is developed to calculate the thermal stress intensity factors (TSIFs) in nonhomogeneous materials. This method is proved to be domain independent for nonhomogeneous materials even when the integral domain is cut by one interface or many interfaces. Combining the interaction energy integral method with the extended Finite Element Method (XFEM), the temperature fields, the displacement fields, the thermal stress fields, and the TSIFs are calculated. In this article, both the edge crack and the internal crack are considered. Some examples are presented to study the influence of the material properties on the TSIFs. It can be found that the mismatch of the elastic modulus and thermal expansion coefficient can affect the TSIFs dramatically; however, the thermal conductivity interface will not arouse a kinking behavior of the TSIFs. It can be concluded that the existence of an interface (especially for elastic modulus and thermal expansion coefficient) affects the TSIFs greatly.     

Thermal Behavior of Insulated Electric Wires Producing Pulsating Signals

A model describing the transient thermal behavior of an insulated electric wire is presented. The transient temperatures in both conductor and insulator result from the energy generated in the conductor by means of an alternating electric current that fluctuates in any specified manner. The mathematical model is solved analytically using Green's function method. The effect of many parameters on the transient thermal behavior of the insulated wire is described. The cooling rate from the wire is evaluated at different values of the insulation thickness, and then the effect of different parameters on the critical thickness of insulation is investigated.     

Investigation Methods for Thermal Shock Crack Problems of Functionally Graded Materials–Part II: Combined Analytical-Numerical Method

Fractures phenomena can be often found in functionally graded materials (FGMs) subjected to thermal shock loadings. This paper aims to develop a set of analytical-numerical methods for analyzing the mixed-mode thermal shock crack problems of a functionally graded plate (FGP). First, a domain-independent interaction energy integral method is developed for obtaining the mixed-mode transient thermal stress intensity factors (TSIFs). A perturbation method is adopted to obtain the transient temperature field. Then an analytical-numerical method combining the interaction energy integral method, a perturbation method, and the finite element method is developed to solve the present crack problem. Particularly, the influences of the materials parameters, crack length, and crack angle on the TSIFs and the crack growth angle are investigated. The results show that the present analytical-numerical method can be used to solve the thermal shock crack problem with high efficiency. The present work will be significant for the fracture mechanics analysis and design of FGM structures.     

Assessment of Thermal Properties via Nanosecond Thermoreflectance Method

Nanosecond time-domain thermoreflectance (ns-TDTR) is an all optical method of determining independently a variety of thermal parameters of both homogeneous and layered materials. Despite its relative experimental simplicity, the sensitivity of the temperature decay (measured by the transient reflectivity signal) to the relevant thermal properties has yet to be fully characterized. In principle, it is possible to simultaneously extract multiple thermal parameters from a single measurement. In practice, however, changes to several of these parameters may result in experimentally indistinguishable variations to the transient reflectivity signal. In this work, we focus on investigating thermal properties of bulk material and the contact resistance between the thin-film coating that is needed for the ns-TDTR method and the bulk substrate. To extract multiple properties from one temperature decay trace, we divide the data into temporal sub-regions known to be influenced to different degrees by each individual thermal parameter and iteratively fit with a 1-D heat conduction model to independently determine the contact resistance and cross-plane thermal conductivity.     

Thermoviscoelastic Dynamic Behavior of a Double-Layered Hollow Cylinder Under Thermal Shocking

In this article, thermoviscoelastic dynamic behavior of a double-layered cylinder with a thermal barrier coating under radially symmetric mechanic and thermal loadings is investigated. The double-layered hollow cylinder is constructed of a viscoelastic layer and a homogenous layer, and the cylinder is subjected to thermal shocking. The material parameters of the cylinder are assumed to be temperature-dependent. The governing equation of the motion of the double-layered hollow cylinder under both dynamic mechanical and thermal loads is obtained based on the plane-stain theory, meanwhile, the transient heat transfer problems are solved by the finite difference method (FDM), Newmark method (NM), and iterative method. Numerical results show that mechanical load, boundary conditions, temperature field and whether considering the viscoelasticity of the inner layer each have a great influence on the dynamic behavior of the double-layered hollow cylinder.     

Application of Transient Analysis Methodology to Quantify Thermal Performance of Heat Exchangers

A transient testing technique is developed to evaluate the thermal performance of industrial-scale heat exchangers. A Galerkin-based numerical method with a choice of spectral basis elements to account for spatial temperature variations in heat exchangers is developed to solve the transient heat exchanger model equations.

Testing a heat exchanger in the transient state may be the only viable alternative where conventional steady-state testing procedures are impossible or infeasible. For example, this methodology is particularly suited to the determination of apparent fouling levels in component cooling water system heat exchangers in nuclear power plants. The head load on these so-called component coolers under steady-state conditions is too small to permit meaningful testing. An adequate heat load develops immediately after a reactor shutdown when the exchanger inlet temperatures are highly time-dependent. The application of the analysis methodology is illustrated herein with reference to an in-situ transient testing carried out at a nuclear power plant. The method, however, is applicable to any transient testing application.     

A Precise Time-Domain Expanding Boundary-Element Method for Solving Three-Dimensional Transient Heat Conduction Problems with Variable Thermal Conductivity

A combined approach of the radial integration boundary-element method (RIBEM) and the precise algorithm in the time domain is presented for solving three-dimensional transient heat conduction problems with variable thermal conductivity. First, by expanding physical quantities at discrete time intervals, the recursive formulation of the governing equation is derived. Then, the recursive equation is solved by the RIBEM, and a self-adaptive check technique is carried out to estimate how many expansion terms are needed in a time step. Finally, three numerical examples show that the present approach can obtain very stable and accurate results for different time-step size.