Short communicationPressure-sensitive paint measurements for microscale supersonic flow with wedge models
Introduction
Recent advances in space technology have enabled the extensive use of small satellites for weather monitoring, signal relay, signal transmission, and Global Positioning System services. These satellites are tens of centimeters in size and typically weigh under 10 kg; they are often referred to as cube satellites. The satellites require a small propulsion system with a thrust of approximately a few mN or less for precise attitude control [1], [2]. To design and fabricate these small propulsion systems, supersonic nozzles of between a few hundred micrometers and a few millimeters are used [3]. The flow physics involved in microscale supersonic flow is dramatically different than that in macroscale supersonic flow. Macroscale supersonic flow analysis is performed under the assumption of inviscid flow because the Reynolds number is on the order of 107; however, the Reynolds number in microscale supersonic flow is on the order of 103 because of the small characteristic length of the device and causes viscous effects to influence the flow behavior. For example, a thick viscous layer grows quickly on the sidewall in microscale supersonic flow; this viscous layer is ignored for macroscale supersonic flow with the inviscid assumption. Alexeenko et al. used numerical simulations with the Navier–Stokes equation and direct simulation Monte Carlo (DSMC) to study flow patterns in axis-symmetrical, two-dimensional, and three-dimensional micronozzles [4]. They observed a boundary layer quickly growing from the sidewall and a consequent decrease in thrust. Xu et al. applied two-dimensional numerical simulation with the Navier–Stokes equation and the slip boundary condition and discussed the flow behavior in supersonic micronozzles under various backpressure conditions [5]. Patterns different from the normal shock pattern expected under the inviscid flow assumption, namely bow shock and shock diamonds, have been observed from these supersonic micronozzles. These patterns occurred due to viscous effects in the micronozzles and boundary layer separation. Darbandi et al. simulated a supersonic micronozzle by using DSMC with various backpressure settings [6]. They reported that boundary layer separation occurred inside the nozzle under backpressure and series compression, and expansion waves (instead of a normal shock wave) formed in the divergent section of the nozzle.
Due to the difficulty of fabricating supersonic micronozzles as well as the challenges of performing experiments, few experimental data have been reported. An experimental method of using luminescent molecules to measure surface pressure, known as pressure-sensitive paint (PSP), has been used in a low-speed experiment in a U bend with strong curvature and high-speed experiments in wind tunnel tests since 1980 [7], [8], [9], [10], [11], [12], [13], [14], [15]. The background and applications of PSP for macroscale experiments can be found in the references [16], [17]. PSP was adapted for microscale experiments in 2002, and further applications on the microscale have been made, including various microfluidic devices such as microchannels, microjets, micronozzles, and micromixers [18], [19], [20], [21]. Huang et al. used PSP and a modified schlieren technique to observe flow fields inside supersonic micronozzles [18], [22]. Early deceleration in the nozzles was identified and was attributed to the fast-growing boundary layer in the microscale supersonic flow. Nagai et al. used both numerical simulations and PSP experiments to investigate viscous effects in two-dimensional and three-dimensional nozzles [23]. The two-dimensional nozzle simulation deviated from the experimental data acquired through the PSP measurements, whereas the three-dimensional nozzle simulation was consistent with the experiment. Matsuda et al. adapted PSP technique in microscale experiments and proposed a pressure-sensitive molecular film for micro gas flow investigation [24]. The pressure distribution inside a convergent-divergent nozzle was measured and showed a good agreement compared with numerical simulation with DSMC. Huang et al. designed and fabricated submillimeter supersonic wind tunnels and studied the pressure distribution around a circular cylinder with a diameter of 50 μm by using the PSP technique [25]. The detailed pressure profiles inside the wind tunnel as well as the pressure variation around the circular cylinder model were successfully acquired at Mach 1.6. A substantial pressure increase in front of the circular cylinder model was identified; a pressure increase with the extended bow shock was not observed. This result was attributed to the reduced strength of bow shocks at the microscale and the location of PSP coating at the bottom of the supersonic wind tunnel. The PSP measurements have been applied to the macroscale experiments in wind tunnel tests and successfully retrieved detailed pressure data on the model surface [26], [27], [28], [29], [30]. In this study, the PSP measurement was applied to the microscale experiment to acquire the pressure profiles around wedge models. Different than the previous research work on the microscale PSP measurements [18], [23], [24], two wedge models with different vertex angles have been installed in the micro-supersonic flow for analyzing the flow fields, especially with the information retrieved at the lateral direction of the wedge models, which can be used for the future design of wedge-type flame holders in micro-supersonic propulsion system.
Section snippets
Research methods
In this study, the PSP technique was applied to determine the detailed pressure distribution around wedge models in microscale supersonic flow. The experimental arrangement is identical to the submillimeter supersonic wind tunnel of our previous study [25]. A de Laval nozzle with a 500-μm throat was designed and connected to a test section with a 4° divergent angle. The depth of the submillimeter supersonic wind tunnel was 150 μm. The test section with the 4° divergent angle was selected to
Results and discussion
Pressure distributions around two wedge models with vertex angles of 20° and 30°, respectively, in microscale supersonic flow were examined using PSP. Inlet and outlet pressures of 100 and 20 kPa, respectively, were applied across the submillimeter supersonic wind tunnel to achieve Mach 1.6 flow. The Reynolds number of the flow was estimated as 3100 with the characteristic length selected as the hydraulic diameter at the exit of the test section. Fig. 3 presents the pressure profiles inside the
Conclusion
The PSP technique was used to measure pressure inside a MEMS-fabricated submillimeter supersonic wind tunnel with two wedge models. The pressure distributions inside the wind tunnel with 20° and 30° wedge models were successfully acquired and showed favorable agreement with the results of numerical simulation performed with ANSYS Fluent. The pressure distribution around the wedge models was examined. A large pressure rise was observed at the front tip of the wedge model, and a low-pressure
Declaration of Competing Interest
The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Chih-Yung Huang reports financial support was provided by The Ministry of Science and Technology, Taiwan (grant number MOST 108-2221-E-007-030-MY3).
Acknowledgements
The authors thank the Ministry of Science and Technology, Taiwan, for its financial support under project no. MOST 108-2221-E-007-030-MY3.
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