An approach for analytical solution pertinent to lattice temperature variation due to laser short-pulse heating

Non-equilibrium energy transport in the surface region of the metallic substrate occurs due to a laser irradiation, which in turn results in thermal separation of electron and lattice sub-systems. As the heating period exceeds the thermal relaxation time, both sub-systems become thermally in equilibrium having the identical temperatures. When electron and lattice temperatures become identical the corresponding instant can be called thermal equilibrium time. In the present study, an analytical formulation of lattice site temperature distribution in the domain of thermal equilibrium time is obtained. Temperature differences and temperature distributions in electron and lattice sub-systems are computed for gold. It is found that electron and lattice temperatures become identical for the heating period beyond the thermal equilibrium time. Temperature distribution obtained from the analytical solution and numerical predictions agree well.     

Instationary conjugate optical-thermal fields in thin films due to pulsed laser heating: A comparison between back and front treatment

Manufacturing of multilayer thin films deposited on a glass substrate can be accomplished by means of pulsed laser sources. Thermal and optical nonlinearities are induced during transient heating, since the response of weakly absorbing thin films depends on the temperature. The heat source can either directly impinge the film surface,␣front treatment, or the glass substrate, back treatment. In this paper a one-dimensional conjugate non-linear thermal-optical time dependent problem is numerically analysed. The investigation is accomplished in order to compare the two processes. For a Nd-YAG laser with wavelength of 1064 nm, a a-Si/TCO and Al/a-Si/TCO multilayers are investigated. Results are presented in form of spatial and temporal temperature profiles as well as absorbed heat transfer rates inside the layers. The accomplished analysis clearly shows that the back treatment is more efficient in terms of manufacturing process, oriented to the production of photovoltaic cells. Received on 4 November 1997     

Entropy generation due to laser step input pulse heating

Laser heating of surfaces results in thermal expansion of the substrate material in the region irradiated by a laser beam. In this case, the thermodynamic irreversibility associated with the thermal process is involved with temperature and thermal stress fields. In the present study, entropy analysis is carried out to quantify the thermodynamic irreversibility pertinent to laser pulse heating process. The formulation of entropy generation due to temperature and stress fields is presented and entropy generation is simulated for steel substrate. It is found that the rapid rise of surface displacement in the early heating period results in high rate of entropy generation due to stress field in the surface region while entropy generation due to temperature field increases steadily with increasing depth from the surface. c ₁ Wave speed in the solid (m/s) - c ₁* Dimensionless wave speed - c ₂ Constant - C _p Specific heat (J/kg.K) - E Elastic modules (Pa) - I Power intensity (W/m²) - I ₁ Power intensity after surface reflection (W/m²) - I _o Laser peak power intensity (W/m²) - k Thermal conductivity (W/m.K) - r _f Reflection coefficient - s Laplace variable - S Entropy generation rate (W/m³K) - S* Dimensionless entropy generation rate - T(x, t) Temperature (K) - T*(x*, t*) Dimensionless temperature - Temperature in Laplace domain (K) - Dimensionless reference temperature - t Time (s) - t* Dimensionless time - U Displacement (m) - U* Dimensionless displacement (U) - W* _lost Dimensionless lost work - x Spatial coordinate (m) - x* Dimensionless distance (x) - Thermal diffusivity (m²/s) - _T Thermal expansion coefficient (1/K) - Poissons ratio - Absorption coefficient (1/m) - Density (kg/m³) - _x Thermal stress (Pa) - _x * Dimensionless thermal stress      

Entropy generation in laser heating in relation to machining

Entropy generation during laser evaporative heating of solid substrate in relation to machining is considered and entropy generation rate due to different pulse intensities is computed. Energy method is used when simulating the phase change process and mushy zone formation across solid–liquid and liquid–vapor interfaces are accommodated. Since the heating duration is greater than the electron relaxation time, the Fourier heating model based on the equilibrium transport is employed in the simulations. Entropy generation in the substrate material is formulated during laser heating pulse. It is found that entropy generation rate in the surface region of the substrate material attains high values. Increasing power intensity ratio enhances the total entropy generation rate in a non-linear fashion.     

Heat conduction in a semi-infinite solid when subjected to spatially decaying instantaneous laser source

A closed-form model for the computation of temperature and heat flux distribution in a semi-infinite solid when subjected to spatially decaying, instantaneous laser source is investigated. The appropriate dimensionless parameters are identified and the reduced temperature and heat flux as a function of these parameters are presented in the graphic form. Some special cases of practical interest are also discussed. It is demonstrated that the present analysis covers the classical case of no heat generation in the solid as well as some new solutions.

---

Wärmeleitung in einem halbunendlichen Körper, der plötzlich durch eine mit zunehmender Eindringtiefe abklingende Laser-Wärmequelle beaufschlagt wird

Zusammenfassung Es wird ein geschlossenes Rechenmodell zur Ermittlung der Temperatur- und Wärmeflußverteilung in einem halbunendlichen Körper untersucht, der plötzlich durch eine mit der Eindringtiefe abklingende Laserquelle beaufschlagt wird. Die normierten Temperaturen und Wärmeflüsse sind als Funktionen relevanter Kenngrößen graphisch dargestellt. Spezialfälle von praktischem Interesse werden diskutiert. Die vorliegende Untersuchung liefert neben einigen neuen Lösungen auch das Ergebnis für den klassischen Fall, daß keine Wärmequellen wirksam sind.

     

头部对称刻槽弹体侵彻半无限厚铝合金靶实验与理论模型

在综合考虑弹体结构稳定性及截面比动能的前提下, 提出一种介于尖卵形弹体及尖锥形弹体间的头部对称刻槽弹体, 以期达到提高侵彻深度的目的。以尖卵形弹体侵彻深度为基准, 开展头部对称刻槽弹体侵彻半无限厚铝合金靶实验。在此基础上, 推导得到可描述头部对称刻槽弹体侵彻2A12铝合金靶过程的局部相互作用模型。同时, 结合头部对称刻槽弹体侵彻后靶体破坏现象, 提出适用于头部对称刻槽弹体的靶体响应力, 进而确立头部对称刻槽弹体的侵彻深度模型。实验结果与理论计算表明, 头部对称刻槽弹体具有相对于尖卵形弹体更好的侵彻能力。头部对称刻槽弹体侵彻深度提高的原因是弹体头部结构截面比动能增加及其侵彻过程中的靶体弱化效应, 其中弱化效应是侵彻深度提高的主控因素。

     

Heat transfer analysis of a semi-infinite solid heated by a laser beam

Laser heating of semi-infinite solid substance is introduced and analytical solution appropriate to the laser machining power intensities is obtained. Both conduction limited and non-conduction limited cases are considered. The limiting cases in non-conduction limited equation are investigated and the equation governing the conduction limited heating is deduced. In the case of non-conduction limited heating process, the location of maximum temperature and its functional relation with the substance and laser properties are developed. Steady state analysis of the heating process is taken into account and limiting laser power intensity is concluded. In addition, the applicability of Fourier heat conduction equation in laser heating is discussed.     

Numerical simulation of forced convection in a duct subjected to microwave heating

In this paper, forced convection in a rectangular duct subjected to microwave heating is investigated. Three types of non-Newtonian liquids flowing through the duct are considered, specifically, apple sauce, skim milk, and tomato sauce. A finite difference time domain method is used to solve Maxwell’s equations simulating the electromagnetic field. The three-dimensional temperature field is determined by solving the coupled momentum, energy, and Maxwell’s equations. Numerical results show that the heating pattern strongly depends on the dielectric properties of the fluid in the duct and the geometry of the microwave heating system.     

Instability of a liquid surface with laser heating

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 28–34, May–June, 1991.     

Numerical study on the resistance of rigid projectiles penetrating into semi-infinite concrete targets

A study on the resistance of rigid projectiles penetrating into semi-infinite concrete targets is performed in this paper. Experimental data are analyzed to examine the penetration resistance during various stages of the penetration process. A numerical tool using AUTODYN hydrocode is applied in the study. The numerical results on both deceleration-time history and depth of penetration of projectiles are in good agreement with experimental data, which demonstrate the feasibility of the numerical model in these conditions. Based on the numerical model with a two-staged pre-drilled hole, the rigid projectile penetration in tunneling stage is studied for concrete targets with different strengths in a wide range of impact velocities. The results show that the penetration in tunnel stage can be divided into two different cases in terms of initial impact velocity. In the first case, when the impact velocity is approximately less than 600 m/s, the deceleration depends on initial impact velocity. In the second case, when the impact velocity is greater than 600 m/s, the effect of target inertia becomes apparent, which agrees with commonly used concrete penetration resistance equations based on cavity expansion model.

Graphic abstract

A two-staged pre-drilled hole model was developed and the results show that the depth of entrance stage tends to decrease with the increase of impact velocity. The influence of the inertial term at low velocity range (approximately close to 600 m/s) is inconspicuous. With further increase of the penetration velocity, the effect of the target inertia becomes apparent as proposed by Forrestal. The effect of mass abrasion of projectiles, entrance phase and strain effect of concrete materials on the tendency of deceleration was clarified.

     

高超声速非定常流动的数值模拟与气动热计算

高超声速飞行器研究中的一个重点问题是飞行器表面的气动加热,它对飞行器的气动、热特性及安全性有重要的影响.受到当前实验技术的限制,地面实验无法准确模拟真实飞行条件,所以采用数值模拟研究气动加热问题成为目前重要的研究手段.本文采用数值方法求解三维N-S方程,得到钝头体再入模型绕流的瞬态流场,驻点温度及表面热流沿轨道变化规律.计算中采用变边界条件模拟沿轨道飞行的非定常性.     

An energy approach to the link-up of multiple cracks in thin aluminum alloy sheets

An energy approach has been used in the study of the coalescence or linkage of multiple cracks in aluminum alloy sheets. The study was motivated by concern for the structural integrity of aging aircraft. Forty reported tests for 2024-T3 aluminum panels with a major crack and several multiple-site damage (MSD) cracks have been analyzed via a simple computational model with a Dugdale–Barenblatt [D.S. Dugdale, J. Mech. Phys. Solids 8 (1960) 100–104; G.I. Barenblatt, in: H.L. Dryden, Th. VonKarman (Eds.), Advances in Applied Mechanics, vol. II, 1962, pp. 55–130] type of plastic or inelastic deformation. For simplicity, the computational model considers only the plastic interaction between the major crack and two symmetrically adjacent MSD cracks in an infinite sheet under remote tensile stress. By following the approach given in [B. Cotterell, J. K. Reddel, Int. J. Fract. 13 (1977) 267–277], the specific work to cause ligament failure is found to be a linear function of the normal extent of the confined plastic region for most tests considered. A few exceptions to this linear relation are attributed to the limitation of the employed computational model. A new criterion and an engineering method to predict crack link-up in an MSD sheet are proposed based on this specific work concept, and they have been demonstrated through application to stiffened panels.