Investigation on choking behavior of gas flow in microducts

In continuum regime, the large surface-to-volume ratio in microscale flow indicates stronger influence of boundary layer on internal flow, which is confirmed by the present study through quantitatively analyzing the in-duct choking and profile of boundary layer in a series of straight rectangular microducts with convergent entrances. The exit height and width of the microducts are 500 µm and 2500 µm. The number density distribution along the duct centerline is measured using a laser-induced fluorescence technique in underexpanded conditions for Reynolds numbers ranging from 745 to 6710. The experimental results show that an unexpected drop in number density emerges upstream of the duct exits. By numerically solving the 3-D Navier–Stokes equations, the computational results reveal that the build-up of boundary layer forms a virtual throat upstream of the duct exit, thus turns the straight duct into a convergent–divergent micronozzle. The location of Mach-number unity (choking) and the boundary-layer thickness are found affected by both duct configuration and Reynolds number at choking. In addition, location of the farthest in-duct choking from duct exit is found corresponding to a certain range of transition from laminar to turbulent at Re?～?2000. The 1-D analysis confirms that the in-duct choking phenomenon is related to the boundary-layer blockage rather than friction. The results of the present survey indicate the significance of reckoning boundary-layer blockage in micronozzle or microduct design.     

Incompressible and compressible flows through rectangular microorifices entrenched in silicon microchannels

Incompressible and compressible flows through indispensable configurations such as rectangular microorifices entrenched in microchannels have been experimentally investigated. The current endeavor evaluates the effects of microorifice and microchannel size, estimates the discharge coefficients associated with both compressible and incompressible flows, examines the contraction coefficients, probes subsonic and supercritical gas flows, and explores the presence of any anomalous effects such as those reported for microchannels. The discharge coefficient in incompressible flow, using deionized (DI) water as the working fluid, rises and peaks at a critical Reynolds number, (200/spl les/Re/sub Crit//spl les/500). The reported range of the transitional Reynolds number compares favorably with the values observed in conventional scale studies and suggests the absence of any irregular scaling effects. Furthermore, nitrogen flows through various microorifices suggests that the constriction element rather than the microchannel area determines the flow rate. Additionally, the critical pressure ratio at choking is close to the isentropic value (0.47/spl les/(P/sub 2//P/sub 1/)/sub Crit//spl les/0.64) and no anomalous scale or slip effects have been observed. Unlike macroscale compressible flows through an orifice, the losses seem minimal and the discharge coefficients are close to unity. The geometry acts as a smooth converging-diverging nozzle and the mass flow rate trends appear similar to the data obtained in micronozzle flows.     

Investigation of the structure of supersonic nitrogen microjets

Results of research on microjets escaping into an ambient space from nozzles with diameters of 341–10.4 μm are described. A special Pitot microtube is used for studying the structure of supersonic microjets. The main feature of this microtube is a small diameter of the intake hole (12 μm). The main parameters of supersonic underexpanded microjets are identified, including the size of shock cells and the supersonic core length of the microjet. The results show a significant increase in the supersonic core length of microjets compared to macrojets. The Reynolds numbers of the laminar–turbulent transition in microjets are found to be in the range of 1,100–2,100. In addition, a classification of supersonic underexpanded axisymmetric microjets escaping into the ambient space is proposed.     

Computational method for turbulent supersonic flows

The calculation features of the turbulent flows described by the Reynolds equations and the two-equation model of turbulence are examined for an explicit high-order accurate Godunov method. Under these features, a new version of a high order of Godunov’s method is developed for calculating the compressible turbulent flows. To illustrate the capability of the new method, some results of the calculation are shown for a supersonic turbulent jet with a complex shock-wave structure and for a separate flow in a plane nozzle.     

Variational sensitivity analysis and design optimization

Variational method (VM) is employed to derive the co-state equations, boundary (transversality) conditions, and functional sensitivity derivatives. The converged solutions of the state equations together with the steady state solution of the co-state equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The application of the variational method to aerodynamic shape optimization problems is demonstrated on internal flow problems at supersonic Mach number range of 1.5. Optimization results for flows with and without shock phenomena are presented. The study shows that while maintaining the accuracy of aerodynamical objective function and constraint within the reasonable range for engineering prediction purposes, variational method provides a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference computations.     

An experimental and numerical study of the structure and stability of laminar opposed-jet flows

Experiments, simulations, and numerical bifurcation analysis are used to study the incompressible flow between two opposed tubes with disks mounted at their exits. The experiments in this axisymmetric geometry show that for low and equal Reynolds numbers, Re, at both nozzles, the flow remains symmetric about the plane halfway through the nozzle exits and the stagnation plane is located halfway between the two jets. When Re is increased past a critical value, asymmetric flow fields are obtained even when the momentum fluxes of the two opposed streams are equal. For unequal Re at the jet exits, when the fixed velocity (and the corresponding Reynolds number, Re₁) of one stream is low, the stagnation plane location, SPL, changes smoothly with the Re₂. For high enough Re₁, a hysteretic jump of SPL is observed. Particle Image Velocimetry and flow visualization demonstrate that within the hysteretic range, the two stable flow fields are anti-symmetric. The experimental setup is also studied with transient incompressible flow simulations using a spectral element solver. It is found that to accurately model the flow, we either need to extend the domain into the nozzles, or impose experimental velocity profiles at the nozzle exits. As in the experiments asymmetric flows are obtained past a critical Re. Finally, bifurcation analysis using a Newton-Picard method shows that the transition from symmetric to asymmetric flows results from the loss of stability of the symmetric flows at a pitchfork bifurcation.     

A fine grid finite element computation of two-dimensional high Reynolds number flows

A velocity—pressure integrated, mixed interpolation, Galerkin finite element computation of the Navier-Stokes equations using fine grids, is presented. In the method, the velocity variables were interpolated using complete quadratic shape functions: and the pressure was interpolated using linear shape functions defined on a triangular element, which is contained inside the quadratic element for velocity variables. Comprehensive computational results for a cavity flow for Reynolds number of 400 through 10,000 and a laminar backward-facing step flow for Reynolds number of 100 through 900 are presented in this paper. Many high Reynolds number flows involve convection dominated motion as well as diffusion dominated motion (such as the fluid motion inside the subtle pressure driven recirculation zones where the local Reynolds number may become vanishingly small) in the flow domain. The computational results for both of the fluid motions compared favorably with the high accuracy finite difference computational results and/or experimental data available.     

Numerical simulation for gas microflows using Boltzmann equation

A computational method based on a kinetic model Boltzmann equation has been developed for microscale low speed flows. The results obtained with the method are compared with those of the direct simulation Monte Carlo method and experiments for supersonic flows. Numerical results for low speed flows over a microcircular cylinder and a microsphere are also obtained with the method, while it is difficult to obtain the low speed flow results with the direct simulation Monte Carlo method. Results of the Navier–Stokes equations with slip boundary conditions generally agree with those of the kinetic model Boltzmann equation if the Knudsen number is less than 0.1. A kinetic/continuum hybrid method has also been developed. The hybrid method may be a promising tool for analyzing whole flow regimes from free molecule to continuum flows.     

Low Reynolds number turbulent flows around a dynamically shaped airfoil

A computational investigation for flows surrounding a dynamically shaped airfoil, at a chord Reynolds number of 78,800, is conducted along with a parallel experimental effort. A piezo-actuated flap on the upper surface of a fixed airfoil is adopted for active control. The actuation frequency focused on is 500 Hz. The computational framework consists of a multi-block, moving grid technique, the eⁿ-based laminar-turbulent transition model, the two-equation turbulence closure, and a pressure-based flow solver. The moving grid technique, which handles the geometric variations in time, employs the transfinite interpolation scheme with a spring network approach. Comparing the experimental and computational results for pressure and velocity fields, implications of the detailed flap geometry, the flapping amplitude, turbulence modeling, and grid distributions on the flow structure are assessed. The effect of the flap movement on the separation location and vortex dynamics is also investigated.     

A Numerical Method for Simulation of Microflows by Solving Directly Kinetic Equations with WENO Schemes

A numerical method for simulation of transitional-regime gas flows in microdevices is presented. The method is based on solving relaxation-type kinetic equations using high-order shock capturing weighted essentially non-oscillatory (WENO) schemes in the coordinate space and the discrete ordinate techniques in the velocity space. In contrast to the direct simulation Monte Carlo (DSMC) method, this approach is not subject to statistical scattering and is equally efficient when simulating both steady and unsteady flows. The presented numerical method is used to simulate some classical problems of rarefied gas dynamics as well as some microflows of practical interest, namely shock wave propagation in a microchannel and steady and unsteady flows in a supersonic micronozzle. Computational results are compared with Navier–Stokes and DSMC solutions.     

The gas flow rate increase obtained by an oscillating piezoelectric actuator on a micronozzle

Micronozzles with piezoelectric actuator were fabricated and investigated. The micronozzles were fabricated in glass substrates using a powder-blasting technique, and the actuator is a bimorph structure made from a piezoelectric polymer. The actuator was located at the nozzle outlet, and was driven in an oscillating mode by applying an alternating voltage across the actuator electrodes. With a pressure difference between inlet and outlet, the gas flow rate through the device was increased. This effect was quantified, and compared to a similar micronozzle with no actuator. The increase in the flow rate was defined as the gas flow through the micronozzle with actuator oscillating minus the gas flow without actuator, was found to depend on the inlet pressure, the pressure ratio, and the nozzle throat diameter.     

An immersed-boundary method for compressible viscous flows

This paper combines a state-of-the-art method for solving the preconditioned compressible Navier-Stokes equations accurately and efficiently for a wide range of the Mach number with an immersed-boundary approach which allows one to use Cartesian grids for arbitrarily complex geometries. The method is validated versus well documented test problems for a wide range of the Reynolds and Mach numbers. The numerical results demonstrate the efficiency and versatility of the proposed approach as well as its accuracy, from incompressible to supersonic flow conditions, for moderate values of the Reynolds number. Further improvements, obtained via local grid refinement or non-linear wall functions, can render the proposed approach a formidable tool for studying complex three-dimensional flows of industrial interest.     

Comparative study between computational and experimental results for binary rarefied gas flows through long microchannels

A comparative study between computational and experimental results for pressure-driven binary gas flows through long microchannels is performed. The theoretical formulation is based on the McCormack kinetic model and the computational results are valid in the whole range of the Knudsen number. Diffusion effects are taken into consideration. The experimental work is based on the Constant Volume Method, and the results are in the slip and transition regime. Using both approaches, the molar flow rates of the He–Ar gas mixture flowing through a rectangular microchannel are estimated for a wide range of pressure drops between the upstream and downstream reservoirs and several mixture concentrations varying from pure He to pure Ar. In all cases, a very good agreement is found, within the margins of the introduced modeling and measurement uncertainties. In addition, computational results for the pressure and concentration distributions along the channel are provided. As far as the authors are aware of, this is the first detailed and complete comparative study between theory and experiment for gaseous flows through long microchannels in the case of binary mixtures.     

Numerical studies in high Reynolds number aerodynamics

Two numerical approaches are presented for the computation of viscous compressible flows at high Reynolds' numbers. In the first approach, named global approach, the whole flow field, which includes viscous and inviscid regions, is determined as the solution of a single set of equations, which may be the full Navier-Stokes equations, or some approximate form of these equations. The second approach, named coupling approach, consists in solving two different sets of equations in their respective domains simultaneously; one of the two sets governs an inviscid flow whose boundary conditions are provided by the viscous effects, determined by the other set.The discussion of the global approach is centred on two particular features of the finite-difference method used: a discretization technique, directly in the physical plane with arbitrary meshes: and a mesh adaptation technique, which combines a coordinate transformation to fit the mesh system to particular lines in the flow, and a technique of dichotomy for mesh refinement. Numerical results are presented for an axisymmetric compression corner and a shock-boundary layer interaction on a flat plate, both in supersonic regime, and for a transonic nozzle flow.For the coupling approach, emphasis is given firstly to the improvement resulting from an interacting analysis where the viscous and inviscid computations are matched, and not only patched. It is shown that the parabolic problems associated with simple viscous theories are always replaced by elliptic problems, even for supersonic flows, and that “supercritical interactions” or “critical points”, as defined by Crocco-Lees, are removed. Secondly, a new coupling method, fully automatized and capable of solving directly a well-posed problem for supersonic flow, is illustrated by examples involving shock wave-boundary layer interactions and reverse flow bubbles; they concern flows over symmetrical transonic airfoils and supersonic compression ramps.     

Numerical simulation of vortical flows in the near field of jets from notched circular nozzles

The vortex dominated flows in the near field of jets from notched circular nozzles are investigated using direct numerical simulation. The nozzles studied include a normal circular nozzle, a V-shaped notched nozzle, and an A-shaped notched nozzle, all with the same circular cross-section. The vortical structures resulting from these different circular nozzles are visualized by using a numerical dye visualization technique. Results for the V-shaped notched nozzle are compared with available experimental measurements using laser-induced fluorescence techniques. In addition to azimuthal vortex rings created because of the shear-layer between the jet and the ambient fluid, the computations also reveal streamwise vortex pairs both inside and outside the vortex rings that spread outward as the vortex rings move downstream. Comparisons of the three different nozzles show that, unlike in the case of the circular nozzle where the streamwise vortex pairs emerge evenly along the nozzle lip, streamwise vortex pairs for the notched circular nozzles are produced only at peak and trough locations. Analysis of the mixing characteristics of the three types of nozzles shows that the notches in the nozzle exit significantly enhance jet mixing.     

Lattice Boltzmann large eddy simulation of subcritical flows around a sphere on non-uniform grids

In this work, the suitability of the lattice Boltzmann method is evaluated for the simulation of subcritical turbulent flows around a sphere. Special measures are taken to reduce the computational cost without sacrificing the accuracy of the method. A large eddy simulation turbulence model is employed to allow efficient simulation of resolved flow structures on non-uniform computational meshes. In the vicinity of solid walls, where the flow is governed by the presence of a thin boundary layer, local grid-refinement is employed in order to capture the fine structures of the flow. In the test case considered, reference values for the drag force in the Reynolds number range from 2000 to 10 000 and for the surface pressure distribution and the angle of separation at a Reynolds number of 10 000 could be quantitatively reproduced. A parallel efficiency of 80% was obtained on an Opteron cluster.     

Numerical Simulation of a Hypersonic Flow over an Aircraft in a High-Altitude Active Movement Area

A hypersonic flow over an axisymmetric aircraft is numerically simulated in the case of a highly underexpanded exhaust plume (jet) of the main engine. The characteristics of the boundary layer separation occurring on the aircraft’s side surface are investigated for several successive points of its takeoff path. The Mach number at the nozzle exit is 6.5. The Mach number of the incoming flow varies from 4 to 7. In this case, the Reynolds number ranges from 2.5 × 10⁵ to 3 × 10³ and the ratio of the nozzle’s exit pressure to the ambient pressure, from 350 to 5 × 10⁴. In the case of the Mach number of the incoming flow M_∞ = 4, the variation range of the pressure ratio extends to 106. Replacement of the exhaust plume with a rigid simulator is considered. Data are obtained on the pressure ratios for which a separation flow begins to form on the side surface, the recirculation zone length, and the level of pressure in it in comparison with the available empirical dependences. A significant increase of the recirculation zone in front of the exhaust plume is shown when it is replaced by a rigid simulator of the same dimensions.     

小型聚焦纹影实验台的设计与搭建

聚焦纹影系统能对垂直于光轴的特定平面内的流场细节进行显示,避免了视场范围内其余非均匀流场对背景成像的干扰。为实现对收缩喷管出口超声速流场的观测,设计并搭建了小型聚焦纹影实验台和超声速流动实验台。超声速流动实验台由2组收缩喷管组成,相距15 cm,垂直摆放,利用高压气源供气,使喷管出口继续膨胀产生超声速气流。首次利用CAD设计胶片上格栅间距尺寸,验证了在胶片纸上进行源光栅、刀口栅改造的正确性。综合考虑超声速流动区域的大小,选取了锐利聚焦深度和非锐利聚焦深度等设计指标。完成了对小型超声速流动实验台流场的拍摄,获得了其流场结构图。通过对比聚焦纹影、计算流体力学(CFD)仿真和传统纹影的流场图,说明此聚焦纹影实验台原理正确,可以达到预期的显示效果。同时,针对聚焦纹影系统高速流场的显示,提出合理的建议。     

Simulation of liquid micro-jet in free expanding high-speed co-flowing gas streams

We present the development of an experimentally validated computational fluid dynamics model for liquid micro jets. Such jets are produced by focusing hydrodynamic momentum from a co-flowing sheath of gas on a liquid stream in a nozzle. The numerical model based on laminar two-phase, Newtonian, compressible Navier–Stokes equations is solved with finite volume method, where the phase interface is treated by the volume of fluid approach. A mixture model of the two-phase system is solved in axisymmetry using?~?300,000 finite volumes, while ensuring mesh independence with the finite volumes of the size 0.25 µm in the vicinity of the jet and drops. The numerical model is evaluated by comparing jet diameters and jet lengths obtained experimentally and from scaling analysis. They are not affected by the strong temperature and viscosity changes in the focusing gas while expanding at nozzle outlet. A range of gas and liquid-operating parameters is investigated numerically to understand their influence on the jet performance. The study is performed for gas and liquid Reynolds numbers in the range 17–1222 and 110–215, and Weber numbers in the range 3–320, respectively. A reasonably good agreement between experimental and scaling results is found for the range of operating parameters never tackled before. This study provides a basis for further computational designs as well as adjustments of the operating conditions for specific liquids and gases.     

Computational study of flow in a rocket-based combined cycle (RBCC) engine inlet

A two-dimensional axisymmetric viscous flow analysis of a rocket-based combined cycle (RBCC) engine inlet is performed using a time-marching numerical scheme to solve the Reynolds-averaged Navier-Stokes equations. The flow configuration is a subscale model of the engine inlet which was previously tested in the 1X1 supersonic wind tunnel at NASA Glenn Research Center. The computed results are compared with the experimental data which include static pressure profiles along the centerbody and the cowl surface of the inlet. The computational results show a reasonably good agreement with the experimental data.