Yanbao Ma

Receptivity of a supersonic boundary layer over a flat plate. Part 1. Wave structures and interactions

This paper is the first part of a two-part study on the mechanisms of the receptivity to disturbances of a Mach 4.5 flow over a flat plate by using both direct numerical simulations (DNS) and linear stability theory (LST). The main objective of the current paper is to study the linear stability characteristics of the boundary-layer wave modes and their mutual resonant interactions. The numerical solutions of both steady base flow and unsteady flow induced by forcing disturbances are obtained by using a fifth-order shock-fitting method. Meanwhile, the LST results are used to study the supersonic boundary-layer stability characteristics relevant to the receptivity study. It is found that, in addition to the conventional first and second modes, there exist a family of stable wave modes in the supersonic boundary layer. These modes play a very important role in the receptivity process of excitation of the unstable Mack modes, especially the second mode. These stable modes are termed mode I, mode II, etc., in this paper. Though mode I and mode II waves are linearly stable, they can have resonant (synchronization) interactions with both acoustic waves and the Mack-mode waves. Therefore, the stable wave modes such as mode I and mode II are critical in transferring wave energy between the acoustic waves and the unstable second mode. The effects of frequencies and wall boundary conditions for the temperature perturbations on the boundary-layer stability and receptivity are also studied.

Receptivity of a supersonic boundary layer over a flat plate. Part 2. Receptivity to free-stream sound

In this paper, we continue to study the mechanisms of the receptivity of the supersonic boundary layer to free-stream disturbances by using both direct numerical simulation and linear stability theory. Specifically, the receptivity of a Mach 4.5 flow over a flat plate to free-stream fast acoustic waves is studied. The receptivity to free-stream slow acoustic waves, entropy waves and vorticity waves will be studied in the future. The oblique shock wave induced by the boundary-layer displacement plays an important role in the receptivity because the free-stream disturbance waves first pass through the shock before entering the boundary layer. A high-order shock-fitting scheme is used in the numerical simulations in order to account for the effects of interactions between free-stream disturbance waves and the oblique shock wave. The results show that the receptivity of the flat-plate boundary layer to free-stream fast acoustic waves leads to the excitation of both Mack modes and a family of stable modes, i.e. mode I, mode II, etc. It is found that the forcing fast acoustic waves do not interact directly with the unstable Mack modes. Instead, the stable mode I waves play an important role in the receptivity process because they interact with both the forcing acoustic waves and the unstable Mack-mode waves. Through the interactions, the stable mode I waves transfer wave energy from the forcing fast acoustic waves to the second Mack-mode waves. The effects of incident wave angles, forcing wave frequencies, and wall temperature perturbation conditions on the receptivity are studied. The results show that the receptivity mechanisms of the second mode are very different from those of modes I and II, which leads to very different receptivity properties of these discrete wave modes to free-stream fast acoustic waves with different incident wave angles, frequencies, and different wall boundary conditions. The maximum receptivities of the second mode, mode I and mode II to planar free-stream fast acoustic waves are obtained when incident wave angles approximately equal 26 ◦ ,4 5 ◦ , and 18 ◦ ,r espectively. The results of receptivity to a beam of free-stream fast acoustic waves show that the leading edge is one of the most efficient regions for receptivity.

Receptivity of a supersonic boundary layer over a flat plate. Part 3. Effects of different types of free-stream disturbances

Supersonic boundary-layer receptivity to different types of free-stream disturbance is studied for a Mach 4.5 boundary-layer flow over a flat plate by using the approaches of both direct numerical simulation and linear stability theory. This paper is Part 3 of a three-part study of the receptivity of supersonic boundary layers to free-stream disturbances. The present paper investigates receptivity to four types of different free-stream disturbances, i.e. slow and fast acoustic waves, entropy waves, and vorticity waves. A high-order shock-fitting scheme is used in the numerical simulation in order to accurately account for the effects of interactions between free-stream disturbance waves and the oblique shock wave. Numerical results on the generation of fast acoustic waves by free-stream entropy waves or vorticity waves are compared with those of a linear theory. Good agreement is obtained in both wave angles and amplitudes immediately behind the bow shock. It is found that the second-mode receptivity to free-stream slow acoustic waves is several times stronger than that to free-stream fast acoustic waves. This is because free-stream slow acoustic waves can directly induce and interact with the first and second Mack modes, while free-stream fast acoustic waves cannot. Instead, the free-stream fast acoustic waves can only induce and interact with stable mode I waves, which in turn induce unstable Mack modes. In the cases of receptivity to free-stream entropy waves and vorticity waves, it is found that the oblique shock wave created by the displacement of the boundary layer plays an important role because boundary-layer disturbances are mainly induced by fast acoustic waves generated behind the shock by free-stream forcing waves. As a result, mechanisms of the receptivity to free-stream entropy and vorticity waves are very similar to those of the receptivity to free-stream fast acoustic waves.

Three dimensional flow structures in a moving droplet on substrate: A dissipative particle dynamics study

It is of both fundamental and practical interest to study the flow physics in the manipulation of droplets. In this paper, we investigate complex flow in liquid droplets actuated by a linear gradient of wettability using dissipative particle dynamics simulation. The wetting property of the substrate ranging from hydrophilic to hydrophobic is achieved by adjusting the conservative solid-liquid interactions which results in a variation of solid-liquid surface tension. The internal three-dimensional velocity field with transverse flow in droplet is revealed and analyzed in detail. When the substrate is hydrophobic, it is found that there is slight deformation but strong flow circulation inside the droplet, and the droplet rolling is the dominant mechanism for the movement. However, large deformation of the droplet is generated after the droplet reaches the hydrophilic surface, and a mechanism combining rolling and sliding dominates the transportation of the droplet. Another interesting finding is that the th...

An unsteady microfluidic T-form mixer perturbed by hydrodynamic pressure

An unsteady microfluidic T-form mixer driven by pressure disturbances was designed and investigated. The performance of the mixer was examined both through numerical simulation and experimentation. Linear Stokes equations were used for these low Reynolds number flows. Unsteady mixing in a micro-channel of two aqueous solutions differing in concentrations of chemical species was described using a convection-dominated diffusion equation. The task was greatly simplified by employing linear superimposition of a velocity field for solving a scalar species concentration equation. Low-order-based numerical codes were found not to be suitable for simulation of a convection-dominated mixing process due to erroneous computational dissipation. The convection-dominated diffusion problem was addressed by designing a numerical algorithm with high numerical accuracy and computational-cost effectiveness. This numerical scheme was validated by examining a test case prior to being applied to the mixing simulation. Parametric analysis was performed using this newly developed numerical algorithm to determine the best mixing conditions. Numerical simulation identified the best mixing condition to have a Strouhal number (St)of 0.42. For a T-junction mixer (with channel width = 196 μm), about 75% mixing can be finished within a mixing distance of less than 3 mm (i.e. 15 channel width) at St = 0.42 for flow with a Reynolds number less than 0.24. Numerical results were validated experimentally by mixing two aqueous solutions containing yellow and blue dyes. Visualization of the flow field under the microscope revealed a high level of agreement between numerical simulation and experimental results.

Numerical Simulations of the Digital Microfluidic Manipulation of Single Microparticles.

Single-cell analysis techniques have been developed as a valuable bioanalytical tool for elucidating cellular heterogeneity at genomic, proteomic, and cellular levels. Cell manipulation is an indispensable process for single-cell analysis. Digital microfluidics (DMF) is an important platform for conducting cell manipulation and single-cell analysis in a high-throughput fashion. However, the manipulation of single cells in DMF has not been quantitatively studied so far. In this article, we investigate the interaction of a single microparticle with a liquid droplet on a flat substrate using numerical simulations. The droplet is driven by capillary force generated from the wettability gradient of the substrate. Considering the Brownian motion of microparticles, we utilize many-body dissipative particle dynamics (MDPD), an off-lattice mesoscopic simulation technique, in this numerical study. The manipulation processes (including pickup, transport, and drop-off) of a single microparticle with a liquid droplet are simulated. Parametric studies are conducted to investigate the effects on the manipulation processes from the droplet size, wettability gradient, wetting properties of the microparticle, and particle-substrate friction coefficients. The numerical results show that the pickup, transport, and drop-off processes can be precisely controlled by these parameters. On the basis of the numerical results, a trap-free delivery of a hydrophobic microparticle to a destination on the substrate is demonstrated in the numerical simulations. The numerical results not only provide a fundamental understanding of interactions among the microparticle, the droplet, and the substrate but also demonstrate a new technique for the trap-free immobilization of single hydrophobic microparticles in the DMF design. Finally, our numerical method also provides a powerful design and optimization tool for the manipulation of microparticles in DMF systems.

New Treatment of Pressure Boundary Conditions for DSMC Method in Micro-Channel Flow Simulations

Using DSMC to simulate micro flows in micro-channels, the numerical treatment of boundary conditions is very important. In this paper, several previous numerical treatments of boundary conditions are discussed with their merits and demerits, and a new treatment method based on the assumption of certain pressure distribution in the cells for boundary conditions is proposed. As comparable validity tests, it is applied in the DSMC simulations for the Poiseuille micro flows in micro-channels with four types of classical pressure boundary conditions. The dimensionless velocity profiles are shown and compared with analytical solutions derived from the Navier-Stokes equations with slip boundary conditions. The pressure distributions along the centerline of the micro-channel with the different boundary conditions are presented, and the simulation solutions agree well with the slip analytical solutions. As the Knudsen number increased, a strong linearity of the pressure distribution can be evidently predicted by the new method. Compared with the inlet and outlet velocity distribution, it is shown that the new method has better efficiency than the previous methods in the convergence.© 2007 ASME

Effects of wall temperature on the heat and mass transfer in microchannels using the DSMC method

Micro-electro-mechanical systems (MEMS) and nano-electro-mechanical systems (NEMS) have become the research focuses which attract a great deal of attention in recent years. The fluidic and thermal behaviors are usually different from those of the macro devices. In this paper, the heat and mass transfer characteristics of the rarefied nitrogen gas flows in microchannels are investigated using DSMC method. In order to study the effects of the wall temperature (Tw) on the mass flux and wall heat flux in the microchannels, the temperature of the incoming gas flow (T∞) is set constant at 300 K, and the wall temperature varies from 200 K to 800 K. For all of the simulated cases, majority of wall heat flux stays within the channel entrance region and drops to nearly zero when it reaches the middle region of the channel. When Tw ≪ T∞, with the restriction of the pressure driven condition and continuity of pressure, the number density of the flow has to decrease along the flow direction eventually after a short increase at the entrance region. When Tw ≫ T∞, the number density of the flow drops rapidly near the inlet, and the temperature of the gas flow increases. As the Tw increases, the flow becomes more rarefied, the mass flux decreases, and the resistance at the entrance region increases. Furthermore, when Tw ≫ T∞, sudden jump in heat transfer flux and temperature are observed at the exit region of the channel.

Improving DSMC with New Pressure Boundary Conditions for Heat and Mass Transfer of Microchannel Flows

A new treatment of pressure boundary conditions for the DSMC method is proposed for flow prediction in microchannels. Validity and accuracy of the new method are verified by comparing to the analytical solutions of the micro-Poiseuille flow under slip condition. The new method shows better convergence compared with previous boundary treatments. This advantage becomes more remarkable as the geometry of the microchannel becomes more complex. A study on a microchannel with sudden expansion is demonstrated using the new DSMC method. Wall temperature in the expanded region of the microchannel independently varies from 200 to 800 K to study the effects on the pressure distribution, velocity, mass flow rate, and heat flux of the microchannel flow. The results show that the wall temperature in the expanded region significantly affects the microchannel flow. Some unique phenomena are observed to be quite different from those of the macroscopic flow and the mechanism of these interesting phenomena is discussed.

Symmetry boundary condition in dissipative particle dynamics

Dissipative particle dynamics (DPD) is a coarse-grained particle method for modeling mesoscopic hydrodynamics. Most of the DPD simulations are carried out in 3D requiring remarkable computation time. For symmetric systems, this time can be reduced significantly by simulating only one half or one quarter of the systems. However, such simulations are not yet possible due to a lack of schemes to treat symmetric boundaries in DPD. In this study, we propose a numerical scheme for the implementation of the symmetric boundary condition (SBC) in both dissipative particle dynamics (DPD) and multibody dissipative particle dynamics (MDPD) using a combined ghost particles and specular reflection (CGPSR) method. We validate our scheme in four different configurations. The results demonstrate that our scheme can accurately reproduce the system properties, such as velocity, density and meniscus shapes of a full system with numerical simulations of a subsystem. Using a symmetric boundary condition for one half of the system, we demonstrate about 50% computation time saving in both DPD and MDPD. This approach for symmetric boundary treatment can be also applied to other coarse-grained particle methods such as Brownian and Langevin Dynamics to significantly reduce computation time.