Simulation of evaporation and propulsion of small particles in a laser beam

Abstract

The technique of numerical simulation of laser surface evaporation of small particles ranging in size from tens to several millimeters falling into the field of laser radiation is developed. The interaction of a laser beam with solid or liquid particles freely flying in a gas-dispersed stream is accompanied by heating and evaporation of the material, which occurs only from the irradiated part of the particle surface. The result is a reactive force created by the laser, which depends on the characteristics of the radiation and the physical properties of the particle material. The technique allows describing the pre-threshold, near-threshold and super-threshold modes of evaporation and is designed to calculate the light propulsion force due to the vapor recoil pressure arising from the irradiated part of the particle surface in the range of Mach numbers to unity. The Meshcherskii equation is used to simulate the reactive acceleration of particles. It is shown that, in the case of a pulsed laser effect, the theory is in good agreement with experimental data on reactive acceleration of aluminum, corundum, and graphite particles. A distinctive feature of the technique is the ability to calculate the gas dynamic parameters of steam and recoil pressure in a wide range of the power density of the absorbed laser radiation from 10 to 10,000 $\hbox {GW}/\hbox {m}^{{2}}$.

Appendix: The drag coefficient of a solid streamlined

The Walsh [20] and Henderson [21] approximations are used to calculate the drag coefficient of a body moving in a gas depending on the Reynolds number and Mach number:

$$\begin{aligned}&C_{D} =\left\{ {\begin{array}{llll} C_{d1} \left( {{\mathrm{Re}}_{\mathrm{p}},M_{\mathrm{p}} } \right) ,&{}\quad 0\le M_{\mathrm{p}} <1; \\ C_{d1} \left( {{\mathrm{Re}}_{\mathrm{p}},M_{\mathrm{p}} } \right) +\frac{4}{3}\left( {M_{\mathrm{p}} -1} \right) \left( {C_{d2} \left( {{\mathrm{Re}}_{\mathrm{p}},1.75} \right) -C_{d1} \left( {{\mathrm{Re}}_{\mathrm{p}},1} \right) } \right) , &{}\quad {1\le M_{\mathrm{p}} \le 1.75}; \\ C_{d2} \left( {{\mathrm{Re}}_{\mathrm{p}},M_{\mathrm{p}} } \right) ,&{}\quad {M_{\mathrm{p}} >1.75;} \\ \end{array}} \right. \\&C_{d1} \left( {{\mathrm{Re}}_{\mathrm{p}},M_{\mathrm{p}} } \right) =\frac{24}{{\mathrm{Re}}_{\mathrm{p}} +M_{\mathrm{p}} \sqrt{0.5\gamma } A}+\exp \left( {-0.5\frac{M_{\mathrm{p}} }{\sqrt{{\mathrm{Re}}_{\mathrm{p}} } }} \right) \\&\quad {\times \,\left( {\frac{4.5+0.38\left( {0.03{\mathrm{Re}}_{\mathrm{p}} +0.48\sqrt{{\mathrm{Re}}_{\mathrm{p}} } } \right) }{1+0.03{\mathrm{Re}}_{\mathrm{p}} +0.48\sqrt{{\mathrm{Re}}_{\mathrm{p}} } }+0.1M_{\mathrm{p}}^{2} +0.2M_{\mathrm{p}}^{8} } \right) } +B; \\&A=4.33+\frac{3.65-1.53}{1+0.353}\exp \left( {-0.247\frac{{\mathrm{Re}}_{\mathrm{p}} }{M_{\mathrm{p}} \sqrt{0.5\gamma } }} \right) ; \quad B=0.6M_{\mathrm{p}} \sqrt{0.5\gamma } \left( {1-\exp \left( {-\frac{{\mathrm{Re}}_{\mathrm{p}} }{M_{\mathrm{p}} }} \right) } \right) ;\\&C_{d2} \left( {{\mathrm{Re}}_{\mathrm{p}},M_{\mathrm{p}} } \right) =\frac{0.9+{0.34} \big / {M_{\mathrm{p}}^{2} }}{1+1.86\sqrt{{M_{\mathrm{p}} } \big / {{\mathrm{Re}}_{\mathrm{p}} }} }+1.86\sqrt{{M_{\mathrm{p}} } \big / {{\mathrm{Re}}_{\mathrm{p}} }} \frac{A_{1} }{B_{1} };\\&A_{1} =2+\frac{2}{\left( {M_{\mathrm{p}} \sqrt{0.5\gamma } } \right) ^{2}}+\frac{1.058}{M_{\mathrm{p}} \sqrt{0.5\gamma } }-\frac{1}{\left( {M_{\mathrm{p}} \sqrt{0.5\gamma } } \right) ^{4}}; \quad B_{1} =1+1.86\sqrt{{M_{\mathrm{p}} } \big / {{\mathrm{Re}}_{\mathrm{p}}}}. \end{aligned}$$