A novel method to realize a non-uniform heat flux distribution through the variable-speed scanning of an electron beam

Abstract

Quartz lamp heaters and hypersonic wind tunnel are currently applied in thermal assessment of heat resistant materials and surface of aircraft. However, it is difficult to achieve precise heat flux distribution by quartz lamp heaters, while enormous energy is required by a large scale hypersonic wind tunnel. Electron beam can be focused into a beam spot of millimeter scale by an electromagnetic lens and electron-magnetically deflected to achieve a rapid scanning over a workpiece. Moreover, it is of high energy utilization efficiency when applying an electron beam to heat a metal workpiece. Therefore, we propose to apply an electron beam with a variable speed to establish a novel method to realize various non-uniform heat flux boundary conditions. Besides, an electron beam thermal assessment equipment is devised. To analyze the feasibility of this method, an approach to calculate the heat flux distribution formed by an electron beam with variable-speed scanning is constructed with beam power, diameter of the beam spot and dwell duration of the electron beam at various locations as the key parameters. To realize a desired non-uniform heat flux distribution of the maximum gradient of 1.1 MW/m3, a variable-speed scanning strategy is constructed on basis of the conservation of energy. Compared with the desired heat flux, the maximum deviation of the scanned heat flux is 4.5% and the deviation in the main thermal assessment area is less than 3%. To verify the method, taking the time-average scanned heat flux as the boundary condition, a heat transfer model is constructed and temperature results are calculated. The experiment of variable-speed scanning of an electron beam according to the scanning strategy has been carried out. The measured temperatures are in good agreement with the predicted results at various locations. Temperature fluctuation during the scanning process is analyzed, and it is found to be proportional to the scanned heat flux divided by volumetric heat capacity, which is applicable for different materials up to 3.35 MW/m2. This study provides a novel and effective method for precise realization of various non-uniform heat flux boundary conditions.

A voltage waveform design method for shortening current response time of a coil

“…Therefore, according to Equation ( 2), Δt is on the scale of 0.1 ns and thus negligible compared with the period of current in the thermal assessment experiment, which is on the scale of microseconds. [11][12][13] Furthermore, the electric field that generates the current is of a low frequency, and the proportionality factor between the magnetic flux through coil turns and the coil current can be defined as the inductance (H) 23 : By combining Equations ( 1) and ( 3), the relationship between the voltage and current of the Helmholtz coil can be expressed as…”

“…5,6 Electron guns are used in applications of electron-beam evaporation, 7 electron-beam welding, [8][9][10] and electron-beam thermal assessment. [11][12][13] Among them, electron-beam thermal assessment is a novel aerodynamic heating simulation method for testing the thermal protective materials of hypersonic vehicles that has the advantages of high resolution, high energy density, and high energy utilization efficiency in comparison with the hypersonic wind tunnel and quartz lamp heaters. [11][12][13] However, periodic scanning is used in the electron-beam thermal assessment, which results in a temperature fluctuation on the surface of the workpiece and may cause thermal shock and thermal fatigue.…”

“…[11][12][13] However, periodic scanning is used in the electron-beam thermal assessment, which results in a temperature fluctuation on the surface of the workpiece and may cause thermal shock and thermal fatigue. 14 The amplitude of the temperature fluctuation can be reduced by increasing the scanning frequency, 11 which is usually assessed by the number of times per second that the magnetic induction changes. A fast-changing magnetic induction is significant in MR dampers, solenoid valves, and electron guns, and a good following performance of the magnetic induction to the excitation voltage is the premise of the fast change of the magnetic induction.…”

“…[11][12][13] Among them, electron-beam thermal assessment is a novel aerodynamic heating simulation method for testing the thermal protective materials of hypersonic vehicles that has the advantages of high resolution, high energy density, and high energy utilization efficiency in comparison with the hypersonic wind tunnel and quartz lamp heaters. [11][12][13] However, periodic scanning is used in the electron-beam thermal assessment, which results in a temperature fluctuation on the surface of the workpiece and may cause thermal shock and thermal fatigue. 14 The amplitude of the temperature fluctuation can be reduced by increasing the scanning frequency, 11 which is usually assessed by the number of times per second that the magnetic induction changes.…”

“…4,[16][17][18][19] Among them, the period for the current to reach 95% of the expected value from the initial value is widely adopted 17,18 and is used in this research. For a coil without an iron core, such as the deflection coil used in electron-beam thermal assessment equipment, 11 the current response time can account for approximately 100% of the total response time. The effect of the hysteresis on the response time of the magnetic induction relative to the current (the magnetic induction response time) is considered only for the coils with iron cores, such as the coils of MR dampers and solenoid valves.…”