2-D and 3-D numerical modelling of a dynamic resonant shear stress sensor

Despite the importance of wall shear stress measurements in both fundamental and applied fluid dynamic problems, sensors for this application suffer from several shortcomings. A new class of wall shear stress sensor concept that addresses these shortcomings is studied numerically. The properties of a dynamic resonant shear stress sensor are determined using a specially-developed two-dimensional unsteady boundary layer code and a commercially available three-dimensional fluid model. Several characteristics of the sensors are determined using these models including: static sensitivities with and without pressure gradients, sensor design parameter effects. These results indicate that low amplitude, high resonant frequency operation associated with small sensors will have optimum performance. These results also suggest that a MEMS implementation of this sensor should provide the capability of measuring wall shear stress fluctuations in turbulent flows.     

A parametrized three-dimensional model for MEMS thermal shear-stress sensors

This paper presents an accurate and efficient model of MEMS thermal shear-stress sensors featuring a thin-film hotwire on a vacuum-isolated dielectric diaphragm. We consider three-dimensional (3-D) heat transfer in sensors operating in constant-temperature mode, and describe sensor response with a functional relationship between dimensionless forms of hotwire power and shear stress. This relationship is parametrized by the diaphragm aspect ratio and two additional dimensionless parameters that represent heat conduction in the hotwire and diaphragm. Closed-form correlations are obtained to represent this relationship, yielding a MEMS sensor model that is highly efficient while retaining the accuracy of three-dimensional heat transfer analysis. The model is compared with experimental data, and the agreement in the total and net hotwire power, the latter being a small second-order quantity induced by the applied shear stress, is respectively within 0.5% and 11% when uncertainties in sensor geometry and material properties are taken into account. The model is then used to elucidate thermal boundary layer characteristics for MEMS sensors, and in particular, quantitatively show that the relatively thick thermal boundary layer renders classical shear-stress sensor theory invalid for MEMS sensors operating in air. The model is also used to systematically study the effects of geometry and material properties on MEMS sensor behavior, yielding insights useful as practical design guidelines.     

微致动器在流动控制中的应用研究

基于MEMS技术,研制了一种微气泡型致动器.对前缘布置有微致动器的三角翼进行了数值模拟和风洞实验,结果表明:微致动器可以改变三角翼前缘的旋涡流状态,扰动边界层,改变三角翼前缘分离涡位置,合理布置微致动器可以获得一定的滚转力矩,利用微致动器可以进行流动控制,进而改变飞行器的动力性能.     

Normal shock boundary layer control with various vortex generator geometries

Various vortex generators which include ramp, split-ramp and a new hybrid concept “ramped-vane” are investigated under normal shock conditions with a diffuser at Mach number of 1.3. The dimensions of the computational domain were designed using Reynolds Average Navier–Stokes studies to be representative of the flow in an external-compression supersonic inlet. Using this flow geometry, various vortex generator concepts were studied with Implicit Large Eddy Simulation. In general, the ramped-vane provided increased vorticity compared to the other devices and reduced the separation length downstream of the device centerline. In addition, the size, edge gap and streamwise position respect to the shock were studied for the ramped-vane and it was found that a height of about half the boundary thickness and a large trailing edge gap yielded a fully attached flow downstream of the device. This ramped-vane also provided the largest reduction in the turbulent kinetic energy and pressure fluctuations. Additional benefits include negligible drag while the reductions in boundary layer displacement thickness and shape factor were seen compared to other devices.     

On the discontinuous Galerkin method for the simulation of compressible flow with wide range of Mach numbers

The paper is concerned with the numerical simulation of compressible flow with wide range of Mach numbers. We present a new technique which combines the discontinuous Galerkin space discretization, a semi-implicit time discretization and a special treatment of boundary conditions in inviscid convective terms. It is applicable to the solution of steady and unsteady compressible flow with high Mach numbers as well as low Mach number flow at incompressible limit without any modification of the Euler or Navier–Stokes equations.     

Implementation of synthetic turbulence inlet for turbomachinery LES

Large eddy simulation (LES) has the potential to model complex separated flows, where Reynolds Averaged Navier–Stokes (RANS) based methods often fail. An important aspect of LES is specifying correlated turbulent fluctuations at the inlet boundary. This is particularly important in turbomachines, where turbulence length scale and intensity play a key role in the correct prediction of component performance.In this work, a method is implemented into an unstructured Computational Fluid Dynamics (CFD) solver to impose correlated turbulent fluctuations in a compressible form. It is shown that compressibility effects are particularly important in turbomachinery and must be taken into account. The method uses a pre-processing method to generate a cube of isotropic, homogeneous turbulence. The velocity fluctuations so obtained are used to determine a fluctuating Mach number in order to evaluate the instantaneous total pressure and temperature fluctuations at domain inlet. In the authors knowledge this is one of the first attempts to define correlated fluctuations in a compressible form.The method is successfully applied to two turbomachinery related flows. Firstly, the jet flow from a propelling nozzle is investigated. Following this, the flow over a low pressure (LP) turbine blade is predicted. Results from the LES simulations show that modifications to the inlet conditions can significantly affect flow development. For the jet, changes in the shear layer and peak shear stress are shown, important in the context of high frequency sideline noise generated by the jet. Despite what is suggested in the literature the differences in shear stresses are important also in a non-swirling jet.For the LP turbine, incoming turbulent fluctuations modify the onset of transition and the extent of separation bubble. Without imposed turbulence fluctuations, loss is overpredicted by up to 50%. Moreover it is important to use a compressible solver. Despite the fact that the majority of the results proposed in literature on LP turbine is using incompressible solvers, the difference in terms of pressure coefficient, Cp, is comparable to turbulence contribution.     

Fabrication and flow-sensor application of flexible thermal MEMS device based on Cu on polyimide substrate

A Cu on polyimide (COP) substrate was proposed as a MEMS material, and the fabrication process for a flexible thermal MEMS sensor was developed. The COP substrate application to MEMS devices has the advantage that typical MEMS structures fabricated in a SOI wafer in the past—such as a diaphragm, a beam, a heater formed on a diaphragm—can also be easily produced in the COP substrate in the flexible fashion. These structures can be used as the sensing element in various physical sensors, such as flow, acceleration, and shear stress sensors. A flexible thermal MEMS sensor was produced by using a lift-off process and sacrificial etching of a copper layer on the COP substrate. A metal film working as a flow sensing element was formed on a thin polyimide membrane produced by the sacrificial etching. The fabricated flexible thermal MEMS sensor was used as a flow sensor, and its characteristics were evaluated. The obtained sensor output versus the flow rate curve closely matched the approximate curve derived using King’s law. The rising and falling response times obtained were 0.50 and 0.67 s, respectively.

     

Solution of viscous transonic flow over wings

Knowledge of the viscous flow about wings is very important in 3-D wing design. In transonic flow about a typical supercritical wing, the viscous effect results in a sizable reduction of the lift-to-drag ratio. The Reynolds number dependence of the flow is not clearly defined, and no known similitude exists that can be used to scale the experimental data for a particular design. Recent advances in computer technology and numerical technique have relieved the difficulty of obtaining a theoretical solution somewhat, but the lack of a proper reliable method of treating the turbulence in a time-averaged Navier-Stokes solution remains the major stumbling block.For this paper, a “zonal” approach has been used for a viscid-inviscid interaction analysis to yield an iterative solution for the viscous flow about wings in the transonic flow regime. The chord Reynolds number considered was of the order of 10⁶ and above so that the flow was predominantly turbulent. The inviscid flow field was obtained by solving the 3-D potential flow equation. A parabolic coordinate mapping was used in the computation, in conjunction with a finite volume formulation. A new approximate factorization scheme has been developed for the iterative solution of the inviscid flow. A special far field asymptotic boundary condition that improves the accuracy and convergence of the method was derived. For the 3-D boundary layer calculation, the integral method of Myring-Smith-Stock was extensively modified to make it suitable for the interaction calculation. The effect of wing thickness was taken into account and the 3-D viscous wake was computed. The interaction calculation was formulated with a set of coupling conditions that includes the source flux distribution due to the surface boundary layer on the wing, the flux jump distribution due to the viscous wake, and the effect of the viscous wake curvature. The transpiration boundary conditions have been used for the inviscid flow in the coupled calculation. In addition, a method was devised so that the results of an analysis of the trailing edge strong interaction solution for a 2-D viscous airfoil could be adapted for the normal pressure correction near the trailing edge. The theory has been applied to supercritical wing geometries of practical interest. The converged viscous flow results compare favorably with experimental pressure data.     

Flexible hot-film anemometer arrays on curved structures for active flow control on airplane wings

A set of flexible MEMS sensor arrays for flow measurements in boundary layers is presented. The sensor principle of these anemometers is based on convective heat transfer from a hot-film into the fluid. Each sensor consists of a nickel sensing element between copper supply tracks. The functional layers are attached either on a ready-made polyimide foil or on a spin-on polyimide layer. These variants are designed to meet the requirements of measurements in different environments. Spin-on technology enables the use of very thin polyimide layers, ideally suited for measurements in transient flows. It is a unique characteristic of the presented arrays that their total thickness can be scaled from 7 to 52 μm. This is essential, because the sensor thickness has to be adapted to the varying thickness of the boundary layers in different aerodynamic tests. With these sensors we meet the special requirements of a wide range of fluid mechanic experiments but in particular those of future active flow control on airplane wings. For less critical flow conditions with much thicker boundary layers, thicker sensors might be sufficient and cheaper, so that sensors fabricated on ready-made foils are perfect for these applications. Since the presented sensors are flexible, they can be attached on curved aerodynamic structures without any geometric mismatches. The entire development, starting from theoretical investigations, is described. Further, the micro-fabrication is discussed, including photolithography, sputtering and wet-etching. In particular the wet-etching of the sensing element is found to be critical for the functional characteristics.     

On a method for direct numerical simulation of shear layer/compression wave interaction for aeroacoustic investigations

Direct numerical simulation (DNS) of a spatially developing mixing layer was performed. The compressible three-dimensional Navier-Stokes equations were solved for pressure, velocities and entropy for this flow using a compact finite-difference scheme of sixth-order accuracy in space, combined with Runge-Kutta three-step time advancement. On one of the transverse boundaries of the box-shaped domain, a compression wave profile was imposed in pressure and velocity components via a wave decomposition of the governing equations, in order to study the interaction of an isolated weak shock wave entering the domain with the mixed subsonic/supersonic shear layer. This flow situation is found along the shear layer of supersonic, imperfectly expanded jets containing a shock cell structure. In the present work, an isolated compression-expansion structure constitutes the model problem. The domain setup and the boundary conditions were chosen such as to allow analysis of the sound field generated by the turbulent flow and the shock-turbulence interaction. The numerical method used to impose the boundary conditions and solve the compressible Navier-Stokes equations, and the choice of numerical parameters, are described in detail. Some results on the two-dimensional and three-dimensional flow field computed are presented as well.     

MEMS壁剪应力传感器热效应的数值模拟

借助计算流体动力学(CFD)商业软件FLUENT,采用数值模拟的方法,对基于MEMS的壁剪应力传感器热交换效应进行了分析。计算结果表明:在壁剪应力传感器的热膜下方加入真空腔或者空气腔是十分必要的。针对水流中测量的计算结果显示,真空腔和空气腔在整个计算区域的温度场分布以及对流体的传热效率的差别不大,而空腔可以明显地减小底层的热损失,这对提高剪应力传感器的灵敏度是十分有利的。此外,MEMS壁剪应力传感器的尺寸效应对传热效率也存在影响。     

Stability enhancement by boundary control in 2-D channel flow

In this paper, we stabilize the parabolic equilibrium profile in a two-dimensional (2-D) channel flow using actuators and sensors only at the wall. The control of channel flow was previously considered by Speyer and coworkers, and Bewley and coworkers, who derived feedback laws based on linear optimal control, and implemented by wall-normal actuation. With an objective to achieve global Lyapunov stabilization, we arrive at a feedback law using tangential actuation (using teamed pairs of synthetic jets or rotating disks) and only local measurements of wall shear stress, allowing to embed the feedback in microelectromechanical systems (MEMS) hardware, without need for wiring. This feedback is shown to guarantee global stability in at least H² norm, which by Sobolev's embedding theorem implies continuity in space and time of both the flow field and the control (as well as their convergence to the desired steady state). The theoretical results are limited to low values of Reynolds number, however, we present simulations that demonstrate the effectiveness of the proposed feedback for values five order of magnitude higher     

Numerical simulation of a compressible turbulent boundary layer over a conductive wall with line heat source

A conjugated problem of supersonic turbulent flow over a conductive solid wall with an embedded line heat source has been investigated as a model of a separation detector and skin friction gage. The 2-D Navier-Stokes equations for compressible fluid, including a two layer eddy viscosity model, are solved simultaneously with the heat transfer equation for the solid, written in general coordinates. The effect of the interface boundary condition on the stability of the implicit scheme of the flow field has been checked. A careful investigation of the effect of heat source strength, solid and fluid conductivity and Mach and Reynolds numbers on flow and temperature fields has been performed. The results of this investigation may be used to design an optimal gage with a minimum influence on the flow field.     

Study of subsonic�Csupersonic gas flow through micro/nanoscale nozzles using unstructured DSMC solver

We use an extended direct simulation Monte Carlo (DSMC) method, applicable to unstructured meshes, to numerically simulate a wide range of rarefaction regimes from subsonic to supersonic flows through micro/nanoscale converging–diverging nozzles. Our unstructured DSMC method considers a uniform distribution of particles, employs proper subcell geometry, and follows an appropriate particle tracking algorithm. Using the unstructured DSMC, we study the effects of back pressure, gas/surface interactions (diffuse/specular reflections), and Knudsen number on the flow field in micro/nanoscale nozzles. If we apply the back pressure at the nozzle outlet, a boundary layer separation occurs before the outlet and a region with reverse flow appears inside the boundary layer. Meanwhile, the core region of inviscid flow experiences multiple shock-expansion waves. In order to accurately simulate the outflow, we extend a buffer zone at the nozzle outlet. We show that a high viscous force creation in the wall boundary layer prevents any supersonic flow formation in the divergent part of the nozzle if the Knudsen number exceeds a moderate magnitude. We also show that the wall boundary layer prevents forming any normal shock in the divergent part. In reality, Mach cores would appear at the nozzle center followed by bow shocks and expansion region. We compare the current DSMC results with the solution of the Navier–Stokes equations subject to the velocity slip and temperature jump boundary conditions. We use OpenFOAM as a compressible flow solver to treat the Navier–Stokes equations.     

The interaction between membrane structure and wind based on the discontinuous boundary element

Small disturbance potential theory is widely used in solving aerodynamic problems with low Mach numbers, and it plays an important role in engineering design. Concerning structure wind engineering, the body of the structure is in a low velocity wind field, with a low viscosity of air and thin boundary layer, therefore, the tiny shear stress caused by the boundary layer can be ignored, only wind pressure being considered. In this paper, based on small disturbance potential theory, the fluid-structure interac...     

Numerical simulation of high-speed planar mixing layer

In this paper gas-kinetic BGK scheme is applied to simulate 2-D supersonic mixing layer with free-stream Mach numbers ranging from 1.1 to 1.9 on one side and 2.3 to 3.1 on the other. The convective Mach number M_c falls in the range 0.2–1.0. The numerical results provide the flow-field structure, the characteristic of velocity fluctuation, the self-similarity profiles of the mean velocity, Reynolds stresses and high-order moments of velocity fluctuation. The mean velocity field and the normalized growth rate agree well with experimental results. Due to 2-D limitations the velocity fluctuation intensities and shear stress are overpredicted, especially in cases with high M_c. The pairings of large structures in high M_c mixing layers still exist, although compressibility restrains their development. Present study reveals the good property of the BGK scheme in the simulation of compressible flows that ensures its wide applications.     

An unstructured finite elements method for solving the compressible RANS equations and the Spalart-Allmaras turbulence model

This paper deals with a stabilized finite element method for solving the compressible Navier-Stokes equations combined with the Spalart-Allmaras turbulence model. The aim is to assess the ability of this formulation to solve high Reynolds number turbulent flows over anisotropic meshes. This formulation lies in the framework of the Stream-Line-Upwind-Petrove-galerkin method. We propose a simple and efficient formulation for the stabilization τ matrix and develop a shock-capturing operator. Numerical tests on the 3D boundary layer over a flat plate and on the ONERA-M6 wing show the stability and robustness of the proposed method.     

A large-eddy simulation method for low Mach number flows using preconditioning and multigrid

Large-eddy simulation (LES) has become one of the major tools to investigate the physics of turbulent compressible and incompressible flows. At low Mach numbers the performance of LES codes developed for the conservation equations of compressible fluids deteriorates due to the presence of two different time scales associated with acoustic and convective waves. In many subsonic turbulent flows low Mach number regions exist, which require large integration times until a fully developed flow is established. In such cases, the efficiency of algorithms for compressible flows can be improved considerably by low Mach number preconditioning methods. In this paper an efficient method of solution for low subsonic flows is developed based on an implicit dual time stepping scheme combined with low Mach number preconditioning and a multigrid acceleration technique. To validate the efficiency and the accuracy of the method, large-eddy simulations of turbulent channel flow at Re_τ = 590 and cylinder flow at Re = 3900 are performed for several Mach numbers and the data are compared with numerical and experimental findings from the literature. The speedup compared to a purely explicit approach is in the range of 6–40.     

Adaptive boundary layer meshing for viscous flow simulations

A procedure for anisotropic mesh adaptation accounting for mixed element types and boundary layer meshes is presented. The method allows to automatically construct meshes on domains of interest to accurately and efficiently compute key flow quantities, especially near wall quantities like wall shear stress. The new adaptive approach uses local mesh modification procedures in a manner that maintains layered and graded elements near the walls, which are popularly known as boundary layer or semi-structured meshes, with highly anisotropic elements of mixed topologies. The technique developed is well suited for viscous flow applications where exact knowledge of the mesh resolution over the computational domain required to accurately resolve flow features of interest is unknown a priori. We apply the method to two types of problem cases; the first type, which lies in the field of hemodynamics, involves pulsatile flow in blood vessels including a porcine aorta case with a stenosis bypassed by a graft whereas the other involves high-speed flow through a double throat nozzle encountered in the field of aerodynamics.     

Numerical study on mechanisms of second sweep and positive spikes in transitional flow on a flat plate

Ring-like vortex is a flow structure at late stages of a transitional boundary layer. Independent to the initial disturbance conditions corresponding to K- and N-scenarios of transition, the vortical structure shows some universal features. The nonlinear evolution of the ring-like vortices, detail flow structures around ring-like vortex and their effects on the surrounding flow were studied by direct numerical simulation with high order accuracy. A detailed enforced spatial transition on a flat-plate boundary layer in the compressible flow was studied. This study reveals the mechanism of the second sweep generation, mechanism of the positive spike formation and mechanism of high shear layer distribution.