An orifice flow model for laminar and turbulent conditions

The square root characteristic commonly used to model the flow through hydraulic orifices may cause numerical problems because the derivative of the flow with respect to the pressure drop tends to infinity when the pressure drop approaches zero. Moreover, for small values of the pressure drop it is more reasonable to assume that the flow depends linearly on the pressure drop.The paper starts from an approximation of the measured characteristic of the discharge coefficient versus the square root of the Reynolds number given by Merritt and proposes a single empirical flow formula that provides a linear relation for small pressure differences and the conventional square root law for turbulent conditions. The transition from the laminar to the turbulent region is smooth. Since the slope of the characteristic is finite at zero pressure difference, numerical difficulties are avoided. The formula comprises physical meaningful terms and employs parameters which have a physical meaning. The proposed orifice model has been used in a bond graph model of a hydraulic sample circuit. Simulation results have proved to be accurate. The orifice model is easily implemented as a library model in a modern modeling language. Ultimately, the model can be adapted to approximate pipe flow losses as well.     

Investigations of laminar flow in a pipe with sudden contraction of cross sectional area

The present paper summarizes results of experimental and numerical investigations of laminar flow in a pipe with a sudden contraction in its cross sectional area. Investigations were carried out in order to gain an insight into the flow structure near the sudden contraction and an understanding of the increased pressure losses generated in this region. In addition, the detailed experimental velocity profile measurements permit comparison with numerical predictions. To yield reliable data, a laser-Doppler anemometer together with a test section containing a liquid with the same refractive index as the test section wall material was employed. In this way, reliable measurements close to the wall could be carried out in a Reynolds number range: 23 ? Re ? 1213. Examples of measurements are given in this paper in the form of diagrams and tables. Numerical predictions of the flow employing a finite difference computer code were also undertaken. This code was carefully checked and optimized to yield reliable predictions for pipe flows with a sudden contraction in cross sectional area. Computational results are presented and compared with experiments. Good agreement is achieved over most parts of the flow field. Small discrepancies in some parts of the flow domain are explained in the paper and measures to overcome these are given.     

利用层流分布测量微流控芯片压力的方法研究

针对微流控芯片中压力相关测量的问题,提出了一种利用微尺度层流分布测量微流控芯片中的压力(流速)的方法。主要研究内容包括微汇合层流结构的设计(Y型结构),微尺度层流分布的压力(流速)关系的推导和利用显微图像处理进行测量的方法等,并通过计算机仿真和实际芯片实验对Y型测压结构进行了分析,结果证实了提出方法的有效性。     

高压管汇冲蚀磨损的多相流仿真

建立试验弯管和节流管汇2个高压管汇实体模型.基于CFD方法,采用离散相模型计算不同半径粒子的轨道和岩屑对高压管壁的冲蚀.计算结果与试验数据较为吻合,能预测节流管汇磨损严重部位,为指导节流管汇的设计和定期检测提供参考.     

Effect of sidewall boundary conditions on unsteady high speed cavity flow and acoustics

The effect of sidewall boundary conditions on the computed unsteady flow and sound pressure level is investigated in a transonic open cavity. The hybrid approach used for modeling turbulence combines a Reynolds averaged mode in the boundary layer, and a large eddy simulation mode in the massively separated flow region within the cavity to resolve the wide dynamic range involved. Computational results are presented for the instantaneous vorticity and for the sound pressure level spectra. Comparison of the results obtained using inviscid and periodic sidewall boundary conditions show the sensitivity of the computed SPL spectra and autocorrelation to the conditions enforced at the sidewalls. The computed SPL spectra are also compared with available experimental results, with LES computational results, and with prior investigations based on the same hybrid turbulence model without the wall function used in the current investigation. The comparisons show that the current results obtained using inviscid sidewall boundary conditions are closest to the experimental sound pressure level spectra and that agreement is achieved at considerable saving in required computational resources.     

Interactive visualization and analysis of transitional flow

A stand-alone visualization application has been developed by a multi-disciplinary, collaborative team with the sole purpose of creating an interactive exploration environment allowing turbulent flow researchers to experiment and validate hypotheses using visualization. This system has specific optimizations made in data management, caching computations, and visualization allowing for the interactive exploration of datasets on the order of 1TB in size. Using this application, the user (co-author Calo) is able to interactively visualize and analyze all regions of a transitional flow volume, including the laminar, transitional and fully turbulent regions. The underlying goal of the visualizations produced from these transitional flow simulations is to localize turbulent spots in the laminar region of the boundary layer, determine under which conditions they form, and follow their evolution. The initiation of turbulent spots, which ultimately lead to full turbulence, was located via a proposed feature detection condition and verified by experimental results. The conditions under which these turbulent spots form and coalesce are validated and presented.     

基于ZnO传感器的高流速气体压力测试

针对机械系统中气体轴承间气膜压力的分布检测,提出并研发了一种基于ZnO传感器的检测方法。ZnO纳米颗粒敏感材料采用化学沉淀法制备;用X射线衍射和扫描电镜对其进行了表征。利用ZnO传感器的响应电压与动态气体压力的关系,成功测试出高压动态气体的压力。分析了氧气吸附、压电效应和热传导对响应电压的影响,拟合出对应的气体压力-响应电压关系曲线,本研究为高流速气体压力的测试提供了一种新途径。     

Direct numerical simulation of transitional flow at high Mach number coupled with a thermal wall model

In transitional and turbulent high speed boundary-layer flows the wall thermal boundary conditions play an important role and in many cases an assumption of a constant temperature or a specified heat flux may not be appropriate for numerical simulations. In this paper we extend a formulation for direct numerical simulation of compressible flows to include a thin plate that is thermally fully coupled to the flow. Even without such thermal coupling compressible flows with shock waves and turbulence represent a challenge for numerical methods. In this paper we review the scaling properties of algorithms, based on explicit high-order finite differencing combined with shock capturing, that are suitable for dealing with such flows. An application is then considered in which an isolated roughness element is of sufficient height to trigger transition in the presence of acoustic forcing. With the thermal wall model included it is observed that the plate heats up sufficiently during the simulation for the transition process to be halted and the flow consequently re-laminarises.     

Design optimization of laminar flow machine rotors based on the topological derivative concept

Flow machines are very important to industry, being widely used on various processes. Thus, performance improvements are relevant and can be achieved by using topology optimization methods. In particular, this work aims to develop a topological derivative formulation to design radial flow machine rotors by considering laminar flow. Based on the concept of traditional topology optimization approaches, in the adopted topological derivative formulation, solid or fluid material is distributed at each point of the domain. This is achieved by combining Navier–Stokes equations on a rotary referential with Darcy’s law equations. This strategy allows for working in a fixed computational domain, which leads to a topology design algorithm of remarkably simple computational implementation. In the optimization problem formulation, a multi-objective function is defined, aiming to minimize the energy dissipation, vorticity and power considering a volume constraint. The constrained optimization problem is rewritten in the form of an unconstrained optimization problem by using the Augmented Lagrangian formalism. The resulting multi-objective shape functional is then minimized with help of the topological derivative concept. In the context of this article, the topological derivative represents the exact sensitivity with respect to the nucleation of an inclusion within the design domain and the obtained analytical (closed) formula can be evaluated through a simple post processing of the solutions to the direct and adjoints problems. Both mentioned features allow for obtaining the optimized designs in few iterations by using a minimal number of user defined algorithm parameters. All equations and the derived continuous adjoint equations are solved through finite element method. As a result, two-dimensional designs of flow machine rotors are obtained by using this methodology. Their performance is analyzed by evaluating velocity and pressure distributions inside rotor.     

基于FINE/Turbo的高压涡轮叶片流热耦合分析

为验证FINE/Turbo软件对高压涡轮流热耦合求解问题的准确性,将Mark Ⅱ型燃气涡轮叶片作为分析对象,选用不同的湍流模型和转捩模型进行数值模拟,得到叶片表面压力分布,B2B面的压力、温度、马赫数和湍流动能分布,叶片内部温度分布以及叶片表面传热系数分布,并与试验数据进行比较.结果表明:对于流热耦合问题,FINE/T...     

Application of multiscale elastic homogenization based on nanoindentation for high performance concrete

The paper aims at developing a simple two-step homogenization scheme for prediction of elastic properties of a high performance concrete (HPC) in which microstructural heterogeneities are distinguished with the help of nanoindentation. The main components of the analyzed material include blended cement, fly-ash and fine aggregate. The material heterogeneity appears on several length scales as well as porosity that is accounted for in the model. Grid nanoindentation is applied as a fundamental source of elastic properties of individual microstructural phases in which subsequent statistical evaluation and deconvolution of phase properties are employed. The multilevel porosity is evaluated from combined sources, namely mercury intrusion porosimetry and optical image analyses. Micromechanical data serve as input parameters for analytical (Mori–Tanaka) and numerical FFT-based elastic homogenizations at microscale. Both schemes give similar results and justify the isotropic character of the material. The elastic stiffness matrices are derived from individual phase properties and directly from the grid nanoindentation data with very good agreement. The second material level, which accounts for large air porosity and aggregate, is treated with analytical homogenization to predict the overall composite properties. The results are compared with macroscopic experimental measurements received from static and dynamic tests. Also here, good agreement was achieved within the experimental error, which includes microscale phase interactions in a very dense heterogeneous composite matrix. The methodology applied in this paper gives promising results for the better prediction of HPC elastic properties and for further reduction of expensive experimental works that must be, otherwise, performed on macroscopic level.     

Role of interface shape on the laminar flow through an array of superhydrophobic pillars

In this study, measurements of the pressure drop and the velocity vector fields through a regular array of superhydrophobic pillars were systematically taken to investigate the role of air–water interface shape on laminar drag reduction. A polydimethylsiloxane microfluidic channel was created with a regular array of apple-core-shaped and circular pillars bridging across the entire channel. Due to the shape and hydrophobicity of the apple-core-shaped pillars, air was trapped on the side of the pillars after filling the microchannel with water. The measurements were taken at a capillary number of Ca = 6.6 × 10^?5. The shape of the air–water interface trapped within the superhydrophobic apple-core-shaped pillars was systematically modified from concave to convex by changing the static pressure within the microchannel. The pressure drop through the microchannel containing the superhydrophobic apple-core-shaped pillars was found to be sensitive to the shape of the air–water interface. For static pressures which resulted in the apple-core-shaped superhydrophobic pillars having a circular cross section, D/D ₀ = 1, a drag reduction of 7% was measured as a result of slip along the air–water interface. At large static pressures, the interface was driven into the apple-core-shaped pillars, resulting in decrease in the effective size of the pillars and an increase in the effective spacing between pillars. When combined with a slip velocity measured to be 10% of the average velocity between the pillars, the result was a pressure drop reduction of 18% compared to the circular pillars at a non-dimensional interface diameter of D/D ₀ = 0.8. At low static pressures, the pressure drop increased significantly as the expanded air–water interface constricted flow through the array of pillars even as large interfacial slip velocity was maintained. At D/D ₀ = 1.1, for example, the pressure drop increased by 17% compared to the circular pillar. This drag increase was the result of an increased form drag due to a decrease in porosity and permeability of the pillar array and a decrease in the skin friction drag due to the presence of the air–water interface. For D/D ₀ = 1.1, the slip velocity was measured to be 45% of the average streamwise velocity between the pillars. When compared to no-slip pillars of similar shape, the drag reduction was found to increase from 6 to 9% with increasing convex curvature of the air–water interface.     

High Knudsen number fluid flow at near-standard temperature and pressure conditions using precision nanochannels

Gas flows over a wide range of Knudsen numbers (~0.5–10) are studied using silicon nanochannel arrays with slit-shaped pores. The pore sizes of the silicon nanochannel arrays range from micrometer to sub-10-nm scales. The flows are generated under conditions of room temperature and near-atmospheric pressure (~22°C and ~101–115 kPa) and span the continuum flow, continuum-slip flow, transition flow and free-molecular flow regimes. The measured flow rates of helium, argon and carbon dioxide are in good agreement with a theoretical model (Unified Slip Model) proposed by Beskok and Karniadakis (Nanoscale Microscale Thermophys Eng 3:43–77, 1999).     

Numerical prediction of a laminar boundary layer flow on a rotating sphere

Numerical solutions to a laminar boundary layer flow past a sphere are considered. The solutions are presented using the procedure of Gosman et al. [1] with appropriate modifications. Successful numerical solution procedures have been devised for the solution of flow problems, see [5]. The SOR method is chosen as a method of solution. Although it looks like a simple method, application of such a method to nonlinear Navier-Stokes equations is highly nontrivial. The matrix method is not used because convergence was not a problem for the type of flow considered in this paper. The governing nonlinear differential equations are converted into finite difference equations by integrating the equations over a control volume and are then solved by an iterative procedure. The numerical results predict that the transverse velocity v_θ is positive in the upper hemisphere, goes to zero in the equitorial plane and becomes negative in the lower hemisphere.     

Numerical simulations of the laminar flow in pipes with wire coil inserts

Helical wire coils fitted inside a round pipe is a simple and well-known heat transfer enhancement technique in order to improve the overall performance of heat exchangers. Three-dimensional numerical simulations of the incompressible laminar flow that develops into smooth round pipes of diameter, d, with wire coil inserts of helical pitch, p, and diameter, e, have been accomplished with the finite volume method. In particular, we describe the behaviour of the Fanning friction factor, f, as a function of the Reynolds number, Re = ρUd/μ, where, U = 4Q/πd², is the mean velocity based in the flow rate, Q, and ρ and μ the density and dynamic viscosity of the fluid, respectively. For a wire coil of 40 pitches in length with dimensionless pitch p/d = 2.5 and dimensionless wire diameter e/d = 0.074, both pitch-periodic and full domain numerical results have been validated with experiments. We have found an excellent agreement with both numerical models and experimental results for Re < 500, showing the friction factor a quasi-linear dependence on Re when is plotted in log–log axes. For 500 < Re < 600 both experimental and full domain numerical results of the values for the friction factor leave the quasi-linear trend observed for Re < 500. Our full domain numerical calculations reveal the onset of a linear instability into the range 500 < Re < 550 that becomes the flow unsteady and breaks the periodic axial pattern of the flow. The friction factor becomes constant in the range, 600 < Re < 850, and only the full numerical model shows a good agreement with the experimental results, but periodic numerical simulations fail. For 850 < Re, even the full domain laminar model fails due to the onset of turbulent outbreaks. Finally, the effect of the pitch on the friction factor has been addressed by performing a parametrical study with a pitch-periodic computational domain for wire coils within the dimensionless pitch range, 1.50 ? p/d ? 4.50, and dimensionless wire diameter, e/d = 0.074, showing that the increase of the nondimensional pitch, p/d, decreases the friction factor.     

The specification and numerical solution of a benchmark swirling laminar flow problem

A primitive variable finite element method for solving swirling incompressible flow problems is presented. A flow problem of physical importance is analysed and the results are critically compared with an earlier solution. The numerical solution of a problem characterized by a particular choice of Reynolds number and swirl ratio is discussed in detail; this problem is proposed as a benchmark for general swirling flow calculations.     

Investigations on possibilities of inline inspection of high aspect ratio microstructures

LIGA is the basic idea of promising developments for the manufacturing of microelectromechanical system parts containing high aspect ratio microstructures. Aim of the work is a brief discussion of the starting-points for inline process inspection within a direct LIGA technology using deep X-ray lithography for the production of micromechanical gear wheels with critical dimensions of ∼35 μm width at ∼1 mm height as well as to show methodic and technical measuring possibilities. Firstly, results of the determination of residual solvent content distribution within ultra-thick SU-8 films are shown obtained from refracted near field optical measurements. Furthermore, the capability of X-ray computer tomographic imaging is discussed and measurements for the determination of the three-dimensional shape of high aspect ratio microstructures are practically demonstrated with microscopic and interferometric optical methods. Finally, first results demonstrate the potential of the optical coherence tomography for several further important measurement tasks, among others, e.g. for the imaging of the distribution of mechanical stress at the resist–substrate interface. The results show that much information which is essential in the LIGA process can be achieved with recently available measurement methods. However, further development of non-destructive measurement techniques would be desirable for an effective inline process control of mass production of micromechanical parts. This work is a summary of the poster “Residual Solvent Content Distribution in Ultra-Thick SU-8 Films and Its Influence on the Imaging Quality” and of the presentation “Possibilities of Inline Process Inspection of High Aspect Ratio LIGA Micro Structures” to the High Aspect Ratio Micro Structure Technology workshop HARMST 2005 held in Gyeongju (Republic of Korea), June 10–13, 2005.