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Analogue Methods
Published in Ethirajan Rathakrishnan, Instrumentation, Measurements, and Experiments in Fluids, 2020
The Hele-Shaw apparatus produces a flow pattern which is similar to that of potential flow. It is an analogy experiment known as Hele-Shaw analogy. The flow in the apparatus is actually a highly viscous flow between two parallel plates with a very small gap between them. In this flow the inertia force is negligible compared to the viscous force. Under this condition the flow equation has the same form as that of Euler’s potential flow, however it does not satisfy the no-slip wall boundary condition. There is slip at the wall. Many interesting phenomena pertaining to potential flow can be observed using this apparatus. The flow through Hele-Shaw apparatus is two-dimensional and incompressible. In Hele-Shaw apparatus, the viscous flow of a liquid between two closely spaced plates may be shown to simulate the streamlines in the flow of a frictionless inviscid fluid. The Hele-Shaw flow is a low Reynolds number flow which has wide application in flow visualization apparatus because of its surprising property of reproducing the streamlines of potential flows (i.e., infinite Reynolds number flows).
Analogue Methods
Published in Ethirajan Rathakrishnan, Instrumentation, Measurements, and Experiments in Fluids, 2016
The Hele-Shaw apparatus produces a flow pattern which is similar to that of potential flow. It is an analogy experiment known as Hele-Shaw analogy. The flow in the apparatus is actually a highly viscous flow between two parallel plates with a very small gap between them. In this flow the inertia force is negligible compared to the viscous force. Under this condition the flow equation has the same form as that of Euler’s potential flow, however it does not satisfy the no-slip wall boundary condition. There is slip at the wall. Many interesting phenomena pertaining to potential flow can be observed using this apparatus. The flow through Hele-Shaw apparatus is two-dimensional and incompressible. In Hele-Shaw apparatus, the viscous flow of a liquid between two closely spaced plates may be shown to simulate the streamlines in the flow of a frictionless inviscid fluid. The Hele-Shaw flow is a low Reynolds number flow which has wide application in flow visualization apparatus because of its surprising property of reproducing the streamlines of potential flows (i.e., infinite Reynolds number flows).
The Effect of Gap Width on Premixed Flame Propagation in Non-adiabatic Closed Hele–Shaw Cells
Published in Combustion Science and Technology, 2022
Jiepeng Huo, Hang Su, Liqiao Jiang, Daiqing Zhao, Xing Li, Xiaohan Wang
The laminar flame propagating behaviors in narrow channels are therefore of wide interest, where the flame scale is the same order of magnitude as the quenching distance and the Hele–Shaw flow is imposed. The Hele–Shaw flow is characterized by sufficient low Reynolds number, leading to a linear relation for the Navier-Stokes equations averaged over the gap. Significant flame wrinkles (Jang, Lee, Kim 2020; Sharif, Abid, Ronney 1999) and oscillating behaviors (Martínez-Ruiz, Veiga-López, Sánchez-Sanz 2019) were reported in experimental observation on the flame propagation in Hele–Shaw cells. Noticeable flame deceleration was found when the gap width is as small as 1 mm (Veiga-López et al. 2019). In a millimeter-scale tubular burner varied from 2 mm to 5 mm in diameter, Ju and Xu (Ju and Xu 2006) ignited a premixed gas at the open exit and found faster flame speed in the tubes with greater diameters. However, when the flame starts from a closed end or the middle of the configuration, it accelerates due to the thermal expansion of the trapped burned gas and exhibits greater acceleration in smaller channels (Akkerman et al. 2006; Wu and Kuo 2013; Wu and Wang 2011), probably due to the flame structure changed by the scale. These results indicate that the flame propagation velocity in a Hele–Shaw cell not only depends on the characteristic gap size but also the configurations. In a closed combustion chamber, the temperature and pressure of the gases continuously increase during the burning process, which dynamically couples with the induced flow field and heat exchange with walls. However, most of the experimental studies have been conducted in tubes or two parallel plates in which the narrow spaces were open to the atmospheric conditions and the propagating flame was considered isobaric. It is of practical importance to obtain the flame propagation velocity and the pressure rise profiles in a millimeter-scale chamber, as they are parameters related to the performance of a miniature engine. These data are not largely available yet.