Three-dimensional thermal analysis for laser-structural interactions

Abstract

ATHREE-DIMENSIONAL thermal analysis method with direct application to laser-structural interactions has been developed. This robust, implicit finite-volume technique solves the enthalpic form of the heat conduction equation for laser radiation interacting with three-dimensional aerospace structures. It utilizes finite elements derived from the structural analysis and accommodates arbitrary beam profiles to compute the ablative material response. Computed results for a composite hat-stiffened panel are illustrated. This method has also treated laser-structural problems involving oblique beam incidence, complex structures, multiple materials, and beam slewing. Contents The vulnerability of aerospace structures to laser radiation depends upon the structural material response under thermal loads. The thermal loads on the vehicle consist of laser energy absorption and energy fluxes produced by the aerothermodynamic environment including external aerodynamic heating as well as internal heat transfer associated with structural cooling and cryogenic fuels. This synoptic emphasies the thermal damage of such structures to laser radiation. The structural part of the laser-structural interaction problem is not considered herein. The stress fields are modified by the elevated temperatures and loss of mass (structure) that the absorbed laser energy produces. This structural behavior can be analyzed using a component of a unique integrated analysis method entitled vulnerability analysis of aerospace structures exposed to lasers (VAASEL).14 This new code consists of a threat analysis to determine the incident radiation on the target, a nonlinear, time-dependent, thermal analysis to determine the thermal response of the target, a material and geometric nonlinear structure analysis to determine structural response, and a failure analysis to determine strength and stiffness degradation. The three-dimensional thermal analysis capability of VAASEL is highlighted in this synoptic. Three-dimensional thermal analysis is necessary for laser beams striking geometrically complex structural surfaces such as a wing-fuselage juncture at an angle of incidence to both components. Up to this time, no extensive analysis capability existed to treat such a laser-material interaction. Even though previous approaches to the thermal problem5 had full threedimensional capability, they lacked the geometrical flexibility needed for general aircraft or aerospace vehicle configurations. Consequently, the thermal model consists of three major parts: 1) geometry submodule, 2) laser ray specifications, and 3) the finite-volume methodology. We first consider the structural geometry. For the thermal analysis, the structural elements are categorized as being either four-node quadrilateral surface elements or eight-node solid elements. A surface element has at least one face exposed to a nonstructural environment; an interior solid element is wholly surrounded by other structural elements. Once this level of distinction has been made, then all the metric information associated with the elements such as grid locations, surface area, volume, etc., can be determined. The definition of the beam geometry is very important. Let us imagine that the center of the beam strikes one particular surface element at a known position. Neighboring beam strike nearby. In order to perform accurate simulations of the beam-target interactions, it is necessary to follow each ray as it propagates through the structure. This would not be very important if only a top surface of elements were intercepted by the beam, however, if elements are removed due to ablation during the engagement, then the beam interactions with the subsequent elements must also be known a priori. As such, the laser spot is divided up into a number of rays with individual power levels and path information associated with each ray. These rays can be defined once the spot location and size are provided. This procedure has been fully automated. Once an aim-point is specified, a random distribution of neighboring rays is selected to provide adequate exposure of all surface and subsurface elements. The three-dimensional thermal analysis method uses a modified version of the multidimensional ablation code used extensively5 and proven to perform accurately and reliably. This is a finite-volume code with a conservative formulation which maintains integrated energy. Since its uses a fixed grid structure, some zones become empty as material ablates. It is first-order accurate in time and second-order accurate in space with uniformly spaced grids; with nonuniform grids (which may be required for complex geometries) the results become first-order accurate in space as well. A fully coupled, fully implicit scheme using a sparse matrix solution is used for the thermal diffusion simulation. This is done to insure the proper performance of the method under the most adverse circumstances. The change in the thermal energy of a general three