A Two-Dimensional Analysis of Laser Heat Addition in a Constant Absorptivity Gas

The two-dimensional equations of motion describing the interaction between a laser beam and a flowing gas are considered. An implicit numerical scheme is used to solve these equations for unchoked flow through a converging-diverging nozzle. Separate grids are used for the fluid dynamics and the radiation equations. The ef- fects of beam focusing and cross-beam intensity profiles are included. The calculations are based upon real gas properties for all quantities except the gas absorptivity, which is taken as a constant. The solutions contain the expected hot central core region with cool gas near the walls. This results in steep temperature gradients in both the streamwise and cross-stream directions. The absorption zone acts as a blockage in the nozzle causing a nonuniform velocity profile at the inlet and an overall decrease in mass flow. The absorption region also forces the streamlines to move away from the axis of symmetry, although this effect is not strong. ASER thermal propulsion promises to deliver higher specific impulse from a rocket nozzle than can be at- tained with conventional chemical propellants. The laser thruster derives its energy by absorbing an incoming beam of electromagnetic radiation, rather than from the combustion process which is utilized in a conventional system. Because its energy supply is external to the working fluid, the heat added per unit mass in the laser engine is not rigidly limited. Instead, the temperature rise and hence, the specific impluse, depends upon the details of the radiation/gasdynamic in- teraction. This interaction is highly complex and strongly nonlinear. Improved understanding is required if this poten- tially attractive concept is to be developed. Experimental studies must certainly be undertaken (Refs. 1 and 2 describe experiments currently under way), but analytical results are also necessary to guide and interpret the experimental studies and to scale laboratory results to full-scale applications. The general picture of a laser thruster is similar to that depicted in Fig. 1. Both the laser beam and the cool unheated gas enter the nozzle from the upstream end. As the gas flows toward the throat, it is heated by absorption of ra- diant energy, causing it to accelerate. The converging nozzle walls also aid in accelerating the gas. For the space propul- sion application, the nozzle remains choked at all times and the flow becomes supersonic downstream of the throat. Although the mixing and recombination phenomena which take place in the supersonic portion of the nozzle are of im- portance to propulsive performance, they do not affect the absorption process and are considered to be secondary in the present discussion. In an attempt to focus on the radia- tion/gasdynamic interaction, the present analysis considers the unchoked nozzle where the Mach number remains sub- sonic throughout. The unchoked nozzle flowfield contains the essential physics of the absorption process and provides considerable insight into this complex interaction. The exten- sion to choked throat conditions is straightforwa rd and re- quires no additional computational advances. In a practical laser thruster, the absorption heating will probably be restricted to the region near the centerline of the nozzle, leaving a cool, unheated layer of gas near the wall3'4