Experimental and numerical study of weak shock wave transmissions through minitubes
Résumé
The aim of this letter is to present an original experimental technique to study weak shock wave in a minitube. Thus, we designed an apparatus that can be connected to any classical shock tube in order to characterize high speed flows induced by the shock wave transmission in minitubes. We proposed appropriated measurements based on high speed strioscopy coupled with pressure sensors. Two minitube diameters are considered: 1.020 0.010 and 0.480 0.010 mm. We realized preliminary experimental and numerical campaigns with an incident shock wave Mach number at 1.12 0.01. The generation of a microshock wave was observable in the two minitubes. For the smallest minitube, we found an attenuation of the strength of the shock wave with a decrease of 1.8% of the Mach number. The recent researches in the fluids mechanics of micro-systems let us foresee the advances that may allow the min-iaturization of microvalves, micronozzles, or micropumps. 1 In these microdevices the ratio between lateral surfaces and volume could be extremely greater than that in macrodevices and, as a consequence, increases the energy exchanges. If we focus on the domain of the microflows of gas, many studies have been proposed by the scientific community since the past two decades. 2,3 Previous studies were carried in our team to treat microfluidic flows with low velocity regime. The aim of these studies was to characterize the gas/wall interactions through the slip velocity in the slip regime and the estimation of accommodation coefficients from hydrody-namics to free molecular regime Knudsen number 0.001,50. 4,5 Moreover, these studies allowed us to develop experimental techniques to deal with microflows at low speed. 6 However, the applications in high speed regime are numerous, for example, in microwave rotors where shock waves are efficiently used to transfer energy. 7 Nevertheless, the shock propagation in microchannel is not yet well studied and need to be better understood to increase microsystem efficiency. Even if we can note recent analytical modeliza-tion study, such as Mirshekari and Brouillette's one, 8 there is an important lack of experiments dealing with the high speed flows, with or without shock wave. To our knowledge, the only working device devoted to the high speed gaseous flows in microchannels is that developed by Udagawa, Garen, and their co-workers in Refs. 9 and 10. Their apparatus is based on the use of a quickly deformable opening valve that initially separates the microchannel from the high pressure chamber. In previous studies, we numerically investigated the possibility to transmit a shock wave into a microchannel. 11 In this work, several simulations have been realized to consider the influence of the microchannel dimensions. Besides, we designed an original apparatus based on the use of a generic microvalve to generate microshock waves. 12 However, before building this whole device, we decided to use our classical shock tube facilities in order to study weaker microshock waves and to bring additional validations for our code CARBUR Ref. 13 IUSTI, Marseille, France to deal with microfluidics phenomena. Thus, the present letter is dedicated to the presentation of the new experimental technique and the results we obtained both experimentally and numerically. First of all, we describe how we adapted a minitube to our classical shock tube T80 Ref. 14 and what types of measures have been done. Then, we present the results of experiments and simulations and we conclude and give the main perspectives of this work. As the simplest device to generate shock wave is a shock tube, our idea is to connect a minitube to the end of a classical shock tube. A shock tube allows one to study compress-ible flows with a good repeatability and with an easy control of the shock strength. With this principle, one can deal with the shock wave transmission and high speed flow generation in a microsystem. In this context, we use our T80 facility with a high speed shadowgraph video recording diagnostic. We use mirrors with a diameter equals to 0.3 m and a focal length of 3 m. The video is recorded with the digital camera fastcam SA1 of Photron, San Diego, CA. All the experiments were made with air, and because the minitube makes a connection between the shock tube and the ambient air, the pressure P 1 was atmospheric pressure, 1 0.01 10 5 Pa, and the temperature was the ambient temperature, 300 2 K. In these conditions, the maximum of incident shock strength we can reach with our facility is equal to M s = 1.5 0.01. One can note that it is smaller than shock wave strength expected by the other device we designed in Ref. 12. Minitubes' overall dimensions are given by Fig. 1. The minitubes are realized with commercial microsyringes. We only keep the cylindrical glass tube of the microsyringes, cut at the required dimensions. The main dimensions of minitubes are, for mini-tube 1, its length is equal to 81.24 0.05 mm and its diameter was measured at 1.020 0.010 mm. For the minitube 2, its length is equal to 46.44 0.05 mm and its diameter is a Electronic