DSMC study of the radiometric force acting on a thin plate with surface temperatures much higher than the environment temperature
Graphical abstract
An expression is proposed for quick estimation of the radiometric force by introducing an effective Knudsen number Kne, which incorporates the expansion effect caused by the very high surface temperature. It is found out that the radiometric force is proportional to for small Knudsen numbers.
Introduction
Radiometric flow is one of the most important subjects in vacuum environments as well as in micro- and nano-scale systems. The pioneering application of radiometric phenomena was in the Crookes radiometer, which was invented in the 1870s by Sir William Crookes [1,2]. The Crookes radiometer consists of a partially evacuated glass bulb containing a set of thin vanes mounted on a spindle. The vanes are black on one side and white on the other side. When the vane is exposed to the sunlight, the black side is hotter than the white side, which results in a radiometric force directed from the hot side to the cold side and drives the vane to rotate around the spindle. Many prominent scientists investigated the mechanism underlying the radiometric force in late 19th and early 20th centuries [3], [4], [5], [6], [7]. It has been widely accepted that the force is induced by a kinetic effect of the gas molecules in the rarefied flow regime, which was the explanation proposed by Tait and Dewar [8].
With the development of micro-electromechanical systems (MEMS) and outer space exploration, there is a growing interest in radiometric phenomena. Radiometric phenomena can be used for gas transport in microscale devices [9], [10], [11], [12], [13], [14], [15], [16], [17], [18] and for gas detection in MEMS sensors [19], [20], [21], [22], [23], [24]. In contrast, the radiometric force can be employed to control or propel high-altitude aircraft and spacecraft with large area to mass ratios, such as solar sails [25], [26], [27], [28], [29], [30]. For example, Nallapu et al. proposed the concept of a radiometric actuator recently [29], and they suggested that the radiometric actuators are free of jitter and could help small satellites achieve precision pointing of a few arc-seconds or less. Benford et al. proposed a vane like aero-spacecraft for the far upper atmosphere supported by a radiometric force with the bottom surface heated by microwave [27]. The bottom surface of the vane was designed to be heated by microwaves to a temperature higher than 1000 K, and the vane was envisioned to be made of an ultralight carbon material that could sustain a large temperature difference between the two sides. In 2012, Cornella et al. analyzed the propulsion that could be provided by multi-vane radiometer arrays, which were mounted on a near-space vehicle to withstand wind disturbances [31]. They further studied the impact of the separation distance and vane thickness on the force experimentally and numerically [32,33]. It was demonstrated that the propulsion system could produce a thrust of 0.0156 N/m2 at an altitude of 60 km and at a temperature difference of 20 K, and this thrust is too small for engineering applications [31]. Therefore, a large temperature difference is one of the essential conditions to produce a macroscale force for controlling the attitude of a spacecraft or to lift it. However, there have been few studies on the radiometric forces under conditions of very high surface temperatures.
Together with the growing interest in applications of radiometric phenomena in aerospace technology, there is a growing number of studies on the gas–surface interaction dynamics and the variation behaviors of the radiometric force in the transition and slip regimes [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48]. The quantitative estimation of the radimetric force dates back to 1920s. By assuming that the force is produced in an area within the mean free path to the edge, Einstein proposed a formulation describing the radiometric force for very small Knudsen numbers [6]. Einstein's theory was then modified by Sexl [49]. Recently, Scandurra et al. tried to develop a more precise quantitative formulation to estimate the radiometric force for small Knudsen numbers [39], and it was then proven that the formulation over-predicted the force perhaps due to some improper assumptions used in the model [36]. Selden et al. [35,36] discussed the area and edge effects in the radiometric force under conditions with different Knudsen numbers, and they proposed a formulation [36] that described the influence of Kn on the radiometric force qualitatively in regimes from free molecular flow to continuum flow. However, none of these models provided a sufficiently accurate estimate of the radiometric force for small Knudsen numbers, which was partly due to the paucity of radiometric force data and the ambiguous understanding of the dynamics underlying the gas–surface interactions for small Knudsen numbers.
In this work, we studied the radiometric flow around a thin circular plate with a direct simulation Monte Carlo method. The surface temperatures of the plate were much higher than that of the environment, and the temperature difference was set to be large, which could be sustained with an advanced material, such as an aerogel. The main objectives of this work were to analyze the molecular and momentum fluxes to the plate and numerically study the variation behaviors of the radiometric force for a wide range of surface temperatures and Knudsen numbers. We hope that the presented analysis on the dynamics of the gas–plate interactions will be useful for studying the radiometric force theoretically and to obtain a general formulation for estimating the radiometric force quickly.
Section snippets
Dimensional analysis
We consider a circular plate with radius R that is immersed in an open gas with temperature T0, pressure p0, mean free path λ0, and molecule mass mg. The plate is very thin, and the thickness is set to zero. The temperatures of the cold upper side and the hot lower side of the plate were denoted by Tc and Th, respectively. The surface of the plate is assumed to be completely diffusive. The dependence of the gaseous viscosity μ0 with temperature T0 can be described as follows: . μ0can be
Flow field structure
We ran a total of 99 thermal radiometric simulations for various values of Kn, Th/T0, and Tc/T0. The radius-based Kn ranged from 0.05 to 20. The dimensionless temperatures of the hot and cold sides of the vane, which were respectively denoted as Th/T0 and Tc/T0, had ranges of 1.47–8.12 and 1–3.05, respectively. A total of nine temperature conditions were used, as listed in Table 2. We assigned temperatures much higher than the environment temperature to obtain a larger radiometric force. A Th/T0
Conclusions
We studied the radiometric flow around a circular thin plate that was immersed in an open gas for a wide range of surface temperatures and Knudsen numbers. Dimensional analysis showed that the scaled radiometric force depended on the scaled surface temperatures and Knudsen number.
Statistical analysis of the gas–plate interactions showed that the gas around the plate was in a strong thermal non-equilibrium state. On the cold side, the incident pressure was larger and the outgoing pressure was
CRediT authorship contribution statement
Dandan Zeng: Conceptualization, Methodology, Writing - original draft. Rong Cai: Funding acquisition. Yanchu Yang: Supervision.
Declaration of Competing Interest
There is no conflict of interest.
Acknowledgments
This work was supported by the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDA17020101).
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