Abstract
Numerical simulations of hotwire anemometers in low-speed, high-altitude conditions have been carried out using the direct simulation Monte Carlo (DSMC) method. Hotwire instruments are commonly used for in-situ turbulence measurements because of their ability to obtain high spatial and temporal resolution data. Fast time responses are achieved by the wires having small diameters (1–5 μm). Hotwire instruments are currently being used to make in-situ measurements of high-altitude turbulence (20–40 km). At these altitudes, hotwires experience Knudsen number values that lie in the transition-regime between slip-flow and free-molecular flow. This article expands the current knowledge of hotwire anemometers by investigating their behavior in the transition-regime. Challenges involved with simulating hotwires at high Knudsen number and low Reynolds number conditions are discussed. The ability of the DSMC method to simulate hotwires from the free-molecular to slip-flow regimes is demonstrated. Dependence of heat transfer on surface accommodation coefficient is explored and discussed. Simulation results of Nusselt number dependence on Reynolds number show good agreement with experimental data. Magnitude discrepancies are attributed to differences between simulation and experimental conditions, while discrepancies in trend are attributed to finite simulation domain size.
Highlights
Recent demand for hypersonic vehicles requires an increased understanding of turbulence in the stratosphere, the region of the atmosphere in which these vehicles will likely cruise
This value of Nu differs from the measured value, Num, because of the thermal slip at the wire surface when wire Kn is in the slip-flow regime
Continuum computational fluid dynamics (CFD) models fail in the transition-regime from slip-flow to rarefied-flow where 10−1 ≤ Kn ≤ 101 because particle collisions are infrequent enough that gases cannot be treated as a continuous media, but particle collisions are frequent enough that they cannot be ignored as is done in free-molecular theory
Summary
Recent demand for hypersonic vehicles requires an increased understanding of turbulence in the stratosphere, the region of the atmosphere in which these vehicles will likely cruise. Low air density in the stratosphere results in fine-wire Knudsen number values (Kn = λ/d, where λ is the mean free path) in the range 0.1 < Kn < 4 based on a wire diameter of d = 5 μm These values correspond to the transition-regime between slip-flow and free-molecular flow. Collis and Williams [2] experimentally investigate hotwires in low Reynolds number flows They propose a slightly different calibration law that includes an explicit dependence on the film and free-stream temperatures: Nu. Equation (6) is limited by the fact that its derivation depends on a first-order approximation of the thermal slip at the wire surface [8] This assumption degrades at higher Kn values because property gradients are no longer linear over a distance approximately equal to the mean free path.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
