THERMO-MECHANICAL ANALYSIS OF A COPPER VAPOR LASER

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1 THERMO-MECHANICAL ANALYSIS OF A COPPER VAPOR LASER E.mail: rchaube@cat.ernet.in R. CHAUBE, B. SINGH Abstract The thermal properties of the laser head such as temperature distribution, thermal gradient and heat flux in thermal insulation are of considerable importance in analyzing and improving the performance of the laser system. In this paper we present thermal analysis of a high temperature Copper Vapor Laser. The laser with input power of 4 k. Watt is capable of generating 30 Watt optical power with efficiency of about 0.75%. It is shown that alumina bulk fiber is most suitable insulation for the requirements of the laser discussed here. It is also shown through the analysis that packing density of alumina bulk fiber as insulation does not play significant role in deciding input requirements. The finite element method is employed for steady state and transient analysis using a commercial thermal code Ansys Introduction Copper vapor lasers are gas discharge visible lasers operating at 510 nm and 578 nm wave length. These lasers require high electrical input power of 4 5 kw for maintaining the discharge tube temperature of about C. High quality thermal insulation is provided around the discharge tube to maintain the tube temperature. The electrical input power required to keep the Cooper Vapor Laser (C.V.L.) discharge tube within the operating temperature range depends in the thermal insulation used. The lay out of a C.V.L. is shown in fig. (1). Typically a temperature of C C is required to maintain the desired plasma conditions. Two mutually contradictory conditions are encountered while designing suitable insulation for high power CVL. Using low thermal conductivity material reduces heat flux thereby requiring less electrical input power to reach desired steady state temperature and results in less optical output. On other hand using higher thermal conductivity material demands higher input power which overheats the active medium that leads to disruption of lasing due to the thermal population of the lower working metastable level. Smaller the insulation thickness used, smaller will be the discharge circuit inductance to achieve faster rise time current pulse through cooper vapors. Also the other objective of insulation over discharge tube is to establish a temperature gradient acceptable to the efficient convective cooling in the cooling jacket. Different thermal insulation material are attempted for C.V.L. discharge tube earlier [1,2]. The conductivity of the insulation increases with the temperature and the mean conductivity may be approximated as follows: K m = 1 ΔT T1 T2 f ( T )dt The other factors responsible to increase thermal conductivity are Moisture, pressure and density. The bulk density of the insulating material varies inversely with porosity. The fibrous and powder insulation show minimum conductivity at some particular bulk density. However there is no mathematical relationship established between bulk conductivity and density of insulating material. This is understandably because of the reason that although the conductivity of the insulation reduces with increase in porosity, but beyond certain porosity at high temperature, the radiation heat transfer across the pores becomes predominant. Moreover with high porosity the cross stream convection currents are set up due to the density differences of the operating fluids subjected to different temperatures. The apparent thermal conductivity of an alumina fiber insulation was measured at nominal densities of 24, 48 and 96 kg/m 3 by Daryabeigi [3] with pressure varying from 10-4 torr to 760 torr and temperature up to 0 C. In their numerical and experimental studies it was seen that the thermal conductivity increased with temperatures and also with pressure above 10-1 torr. The same author[4] carried forward their studies on the effective thermal conductivity of an alumina fibrous insulations at densities of 24, 48, and 72 kg/m 3 and at thick nesses of 13.3, 26.6 and 39.9 mm measured over a pressure range of 1.33 x 10-5 to kpa, and subject to temperature differences of K 1

2 maintained across the sample thickness and concluded that for fibrous insulation samples at densities equal to or larger than 24kg/m 3 the natural convection was not present as a mode of heat transfer. The flow characteristics in thermally insulating porous media under vacuum using two different CFD codes is presented elsewhere [5]. In this paper we present thermal characteristics of insulating porous media used in Kinetically enhanced Copper Vapor Laser with the emphasis on conductive heat transfer calculations. Two different bulk densities of alumia fiber are studied separately for C.V.L. discharge tube insulation. 2.0 Governing Equations On assuming constant density and specific heat with no mass transport of heat the equation takes the following form [6]: ρ CP = K x + K t x x y Where, ρ is the density, C P is Specific heat, T is Temperature, t is time, y + K y z z z K, K, K are conductivity in the element in x, y, z directions respectively. x y z The heat flux vector may be obtained by using Fourier s law utilizing thermal gradient as follows [7,8]: {} q = [ D]{}T L Where, [ D ] = Conductivity matrix, {} L = Vector operator, and temperature T is allowed to vary in space and time. The integration outputs will be as follows: T Thermal gradient vector, { a} = {} L T = x y z From thermal gradients the heat flux vector is calculated as follows: {} q = [ D]{} a 3.0 Analysis and Discussions The measurement of the temperature and heat flux at the intermediate layers is quite difficult. However the temperatures at the alumia tube (about C), intermediate layer of the insulation blanket (about C) and outer most layer (about C) are taken with the help of an optical pyrometer for a bulk density of 500 Kg./m 3 and 150 Kg./m 3. Due to complexity of the system computational approach is taken to do the analysis. The finite element method is employed for finding the temperature gradient, temperature distribution, heat flux and transient time required to reach steady state conditions using commercial thermal code Ansys 9.0. The meshing is performed with SOLID70 element, which is having 8 nodes. SOLID70 was used to save the time of calculation and memory. SOLID70 has a 3-D thermal conduction capability. The element has eight nodes with a single degree of freedom, temperature, at each node. The element is applicable to a 3-D, steady state or transient thermal analysis. The element is defined by eight nodes and the orthotropic material properties. Orthotropic material directions correspond to the element coordinate directions. 2

3 The mesh for the system is produced using free meshing using SOLID70 element. Element sizing is used to mesh the system using Sizing Scale Factor of The entire model is meshed at once rather than Sizing area-by-area or volume-by-volume to utilize the opportunity to reduce element sizes near small features in adjacent regions. The meshed model which gave grid independent results is presented in fig. 2. Thermal transient analysis is performed on the model as the temperature of the system is changing with time. In regions of severe thermal gradients during a transient process there is a relationship between the largest element size in the direction of the heat flow and the smallest time step size that will yield good results. Using more elements for the same time step size will normally give better results, but using more sub steps for the same mesh will often give worse results. Controlling of the maximum time step size by the description of the loading input and defines the minimum time step size (or maximum element size) based on the following relationship: ITS = Δ 2 / 4 α The Δ value is the conducting length of an element (along the direction of heat flow) in the expected highest temperature gradient. The α value is the thermal diffusivity, given by k/ρc. Where, k is the thermal conductivity, ρ is the mass density, and C is the specific heat. The initial condition for model is, the temperature of whole system is 25 O C at t = 0 Dirichlet boundary conditions are specified at the cylindrical walls of the insulation. The temperature of the inner cylindrical wall is kept constant and equal to the 1500 O C and that on outer wall equal to C. For two independent bulk densities the radial heat flux distribution (Fig. 3) and the temperature distribution (Fig. 4) closely follow the same pattern and the bulk fiber density may not significantly affect these two parameters. The radial thermal gradient is steeper with high density packing when compared with low bulk density (Fig. 5) and the attempts may be made to reduce the radial thickness further. With reduced insulation thickness the requirement of the heat transfer coefficient increases which may be taken care by increasing the coolant flow rate (10 lpm for present case). From transient analysis it is clear that the time required to reach the steady state is also more with high bulk densities when compared with low bulk density (Fig. 6 and Fig. 7). 4.0 Conclusion In conclusion we have studied the thermo- mechanical properties with two extreme filling densities of alumina fiber on copper vapor laser discharge tube. It is seen that the packing density does not significantly affect the thermal parameters of the system. It is also seen that the radial thickness of insulation may be further reduced to make the system more compact. Fig. (1) Lay Out of C.V.L. 3

5000 High density Low density 4500 Heat Flux in W/m 2 4000 3500 3000 2500 Fig. (2) Meshed volume 2000 Radial distance in m Fig.

4 5000 High density Low density 4500 Heat Flux in W/m Fig. (2) Meshed volume 2000 Radial distance in m Fig. (3) Radial Heat Flux Temperature in 0 K 1 X Axis Title Low Density C High Density D Fig. (4) Radial Temperature Distribution Thermal Gradient in 0 K/m Radial distance in m High Density C Low Density D Fig. (5) Radial Thermal Gradiant Low density fibre High density fibre Temperatures in 0 K Inner most layer Outermost layer Transient time in sec. Temperature in 0 K Innermost layer Outermost layer Transient time in sec. Fig. (6) Temperature V/S time Fig. (7) Temperature V/S time 4

5 References 1. J.J. Kim and J.F. Convey, Review of Scientific Instruments, 53, 1623, B. Singh et. al., Review of Scientific Instruments, 55, 1542, Kamran Daryabeigi, Analysis and testing of high temperature fiborous insulation for reusable launch vehicles, 37 th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, AIAA , January 11-14, Kamran Daryabeigi, Heat Transfer in High-Temperature Fibrous Insulation, AIAA , 8th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, June 2002 / St. Louis, MO. 5. Rajeev Chaube, Numerical Analysis of Porous Media under Vacuum for Gas Discharge Laser, Indian Vacuum Society National Symposium IVSN 2005, Inst. Plasma Research Gandhi Nagar, IVSNS 05 - Nov Sadik Kakac, Heat Conduction 3 rd edition (1993), Taylor & Francis 7. Baker, A. J. and Pepper, D. W., Finite Elements 1-2-3, McGraw-Hill Publ., New York, 1992, 200 pp. 8. Ansys 9.0, Theory reference manual 5

International Journal of Scientific & Engineering Research, Volume 8, Issue 2, February-2017 ISSN

International Journal of Scientific & Engineering Research, Volume 8, Issue 2, February-2017 ISSN ISSN 2229-5518 916 Laser Damage Effect Studies with Hollow Metallic Targets Satyender Kumar, S Jain, K C Sati, S Goyal, R Malhotra, R Rajan, N R Das & A K Srivastava Laser Science & Technology Centre Metcalfe