渐变截面热声波导管内的声流解析模型

建立了二维渐变截面热声波导管内的声流模型,分别考虑了封闭直管和环形回路两种不同结构,获得了更为普适的解析结果。封闭直管结构的声流结果可应用于任意宽度的波导管,环路结构的结果考虑了渐变截面管段宽度远大于热、黏穿透深度的情形。研究结果表明,渐变截面热声波导管内的声流主要受声场结构、截面变化及轴向时均温度分布的影响,在其它参量不变时声流量值及分布随波导管特征尺度的不同而变化。该解析模型可应用于热声及其它物理背景下的声流分析。      

Analytic model of acoustic streaming in thermoacoustic waveguides with slowly varying cross-section

An analytic model of acoustic streaming generated in two-dimensional thermoa-coustic waveguides with slowly varying cross-section was developed for more general applications. The analytical solutions of acoustic streaming characteristics in the closed straight tube and the annular tube are given based on the model.The solution for the closed straight tube can be applied to the case with any transverse scale.The solution for the annular tube is obtained under the assumption that the width of the varying cross-section part is much larger than the viscous and thermal penetration depths.The effects of cross-section variation,time-averaged temperature distribution and components of sound field are reflected in the analytic solutions. The magnitude and distribution of acoustic streaming velocity vary with the characteristic scale of the waveguides.The analytic model of acoustic streaming can be applied in research under thermoacoustic and other physical backgrounds.     

Influence of stack geometry and resonator length on the performance of thermoacoustic engine

Thermoacoustic engines convert heat energy into high amplitude sound waves, which is used to drive thermoacoustic refrigerator or pulse tube cryocoolers by replacing the mechanical pistons such as compressors. The increasing interest in thermoacoustic technology is of its potentiality of no exotic materials, low cost and high reliability compared to vapor compression refrigeration systems. The experimental setup has been built based on the linear thermoacoustic model and some simple design parameters. The engines produce acoustic energy at the temperature difference of 325–450 K imposed along the stack of the system. This work illustrates the influence of stack parameters such as plate thickness (PT) and plate spacing (PS) with resonator length on the performance of thermoacoustic engine, which are measured in terms of onset temperature difference, resonance frequency and pressure amplitude using air as a working fluid. The results obtained from the experiments are in good agreement with the theoretical results from DeltaEc.     

驻波热声系统的自激振荡机理

热声发动机的起振过程是一个产生并维持自激振荡的过程, 研究热声自激振荡机理有助于进一步了解热声效应的实质. 根据热声网络理论, 建立了驻波热声发动机的整机网络. 将热声网络比拟成电网络, 利用厄米特式计算了输入热声网络的视在功流, 功流平衡对应自激, 在角频率虚部为零的情况下计算了热声发动机的阈值温度和运行频率. 结果表明, 计算值与实验值符合得较好, 充气压力与阈值温度和运行频率的耦合关系大致相同. 所得结论有助于进一步探究热声效应机理以及热声发动机系统的优化设计.     

高效室温行波热声制冷的研究 第一部分 方案及热力分析

文中对简化的热声网络法、T型传输线网络法以及传输矩阵法进行了比较讨论。采用简化的热声网络法对几种可能的制冷流程进行了分析 ,并确定出了可能高效工作的制冷方案。最后基于传输矩阵法对一种行波热声制冷机进行了分析和热力设计 ,得到该制冷机较优的结构参数。当制冷温度为 - 2 3℃时 ,其 COP可达 2 .86 ,相对卡诺热效率为 5 7%。     

40K温区的热驱动低温热声制冷机

热声驱动脉管制冷机主要由热声发动机和脉管制冷机组成,是一种完全无运动部件的新型低温制冷机。本文在实验室现有行波热声发动机的基础上,运用线性热声理论对两级脉管制冷机进行了设计,并用声学放大器对热声发动机和脉管制冷机进行耦合,提高脉管制冷机的驱动压比,从而获得了41 K的低温,这是目前热声驱动脉管制冷机所获得的最低制冷温度。正因为本热声驱动脉管制冷机系统的热驱动特性及其主要部件都是按照热声理论进行设计,所以我们将其称为热驱动低温热声制冷机。     

Heat transport by acoustic streaming within a cylindrical resonator

Several experiments on heat transport within a cylindrical resonance tube, mediated by acoustic streaming, are described. The amplitude dependence of the heat transfer coefficient, h, from a hot object located inside the tube depends on the size of the object. For an object short compared to the acoustic displacement amplitude, h is proportional to the square root of amplitude; for a long object, h is linear in amplitude. For an empty resonator with a heated wall segment, the radial heat flux varies with position in a manner consistent with the global streaming pattern within the tube. The magnitude of heat transport from the heated wall segment is increased by inserting an object into the tube because the localized streaming velocity induced by the object is larger than the global streaming velocity in the empty tube. These effects could find application in the cooling of hot objects like electronic components or in thermoacoustic engines.     

演示用Sondhauss管的研制及理论分析

介绍了演示用 Sondhauss管的结构与制作过程 ,它具有直观、简单、成本低等突出优点 ,是一种比较理想的热声效应演示器件。通过初步实验 ,文中对热声管发声机制进行了理论分析 ,有助于更好地理解热声效应 ,并为进一步研究热声机理奠定了基础     

Dynamic analysis and optimal design of a passive and an active piezo-electrical dynamic vibration absorber

This paper is concerned with the dynamic analysis and parameter optimization of both passive and active piezo-electrical dynamic vibration absorbers that are strongly coupled with a single degree of freedom vibrating structure. The passive absorber is implemented by using an R_s∥L_s parallel shunt circuit while the active absorber is implemented by feeding back the acceleration of the structure through a second-order lowpass filter. An impedance-mobility approach is used for the electromechanical coupling analysis of both types of absorbers coupled with the structure. Using this approach it is demonstrated that the passive and active absorbers can be made exactly equivalent. A maximally flat frequency response strategy is used to find the optimal damping ratio of the passive absorber while a robust, optimal control theory is used to find that for the active absorber. It is found that the passive optimization strategy corresponds to an optimal, robust feedback control of 2 dB spillover. Simulations and experiments are conducted to support the theoretical findings.     

Analysis of Anomalous Swelling by a Rubber Elasticity Model for Entangled Networks

A complete equation of the swelling activity parameter (S) as a function of swelling deformation (λ_s ) is derived by using a non-Gaussian elastic network model, including a tube concept and the Flory–Rehner model, and by following McKenna's criterion that takes into account the disparity between the Flory–Huggins interaction parameters for cross-linked and uncross-linked polymers. However, only a part of tube at the network chain size scale is extended to that for a large-scale structure according to the “gel tensile blob” model for equilibrium swollen networks. This approach is basically best for the “ideal regular network + simple structured good-solvent” binary systems due to its model character. As a result, it reproduces well the literature data of S versus λ_s ² with a maximum/inflection measured for such actual systems.     

Concepts in high-frequency EPR — Applications to bio-inorganic systems

In this contribution we describe a high-frequency high-field EPR facility which has been developed at the University of Nijmegen. We present the design of a heterodyne quasi-optical bridge based on a millimeter-wave vector network analyzer as source and detection system. The mm-waves are transported in free-space through Gaussian beam optic elements and through a corrugated guide inside the resonator insert. The Fabri-Pérot (TEM_00n) resonator is coupled through a metallic mesh and because of its bimodal property it can be operated using orthogonal detection leading to substantial improvement in sensitivity. In the first stage of the project, a multifrequency CW-facility is realized covering the 100–500 GHz range. In our initial explorative experiments we demonstrate the advantages of HF-EPR of high-spin systems: Due to the large microwave quantum, transitions which would be undetectable at X-band due to the large zerofield splitting can now be observed in good sensitivity. As a model for biological high-spin systems a sample of metmyoglobin was measured at D-band (130 GHz). Theg = 5.9 perpendicular line from theS = 5/2 ferric heme was detected and its line-width was compared to data previously obtained at Q-, X-, S- and L-band. As a model for biological integer spin systems theS = 1 signal of Ni(II) in nickel Tutton salt (Ni(NH₄)₂(SO₄)₂) was studied at 35 and 130 GHz.     

80 K温区的小型行波低温热声制冷机

热声制冷机由于结构简单、无运动部件,具有广阔的应用前景。本文在已有的小型行波热声发动机的基础上,开展了热声制冷的工作。利用线性热声理论对制冷机进行数值模拟,并对制冷机的各热声元件优化。优化后,系统整体装配横向尺寸仅0.5 m,在充气压力3 MPa,发动机输入功率384 W的条件下,达到了80 K的无负载温度。由于本制冷机由行波型热声发动机驱动,并且是通过线性热声理论优化,因此称之为小型行波低温热声制冷机。     

Quasi-Conformal Actions,Quaternionic Discrete Series and Twistors: <Emphasis Type="Italic">SU</Emphasis>(2, 1) and <Emphasis Type="Italic">G</Emphasis><Subscript>2(2)</Subscript>

Quasi-conformal actions were introduced in the physics literature as a generalization of the familiar fractional linear action on the upper half plane, to Hermitian symmetric tube domains based on arbitrary Jordan algebras, and further to arbitrary Freudenthal triple systems. In the mathematics literature, quaternionic discrete series unitary representations of real reductive groups in their quaternionic real form were constructed as degree 1 cohomology on the twistor spaces of symmetric quaternionic-Kähler spaces. These two constructions are essentially identical, as we show explicitly for the two rank 2 cases SU(2, 1) and G ₂₍₂₎. We obtain explicit results for certain principal series, quaternionic discrete series and minimal representations of these groups, including formulas for the lowest K-types in various polarizations. We expect our results to have applications to topological strings, black hole micro-state counting and to the theory of automorphic forms.     

Amoeba-like motion of an oil droplet

In this paper, we demonstrate our recent attempt to construct a chemical model system of amoeboid motion. The system is intended to mimic biological motility based on the generation and collapse of an elastic aggregate; it is composed of oil, water, and surfactants. In this chemical system, the oil–water interface shows extension and retreat of spherical extrusions accompanied by the generation of aggregate on the interface. This instability of the oil–water interface can cause autonomous splitting and motion of a floating oil droplet. The current mathematical model based on the generation of a passive elastic gel is explained, as well as the discrepancy between the model and the experiments. We further describe recently observed microscopic characteristics of the aggregate formation process that might cause the interfacial instability. Finally, we discuss the disadvantage of a chemical model system compared with active colloid and in vitro biological systems, and also mention its potential advantages.     

脉冲管制冷机调相机构的研究 第二部分:惯性管有无气库的研究

基于线性热声理论,通过计算证明了在层流状态下,带气库的惯性管调相机构可以用不带气库的单纯惯性管结构取代,单纯的惯性管结构更加便于在实验中进行调节变化,并且在尺寸的选择上具有更大的灵活性。在一台脉冲管制冷机上分别采用单纯惯性管和带气库的惯性管作为调相机构获得了相同的温度。     

Solution to the paradox of the linear stability of the Hagen-Poiseuille flow and the viscous dissipative mechanism of the emergence of turbulence in a boundary layer

It has been shown that the conclusion of the linear instability of the Hagen-Poiseuille flow at finite Reynolds numbers requires the refusal of the use of the traditional “normal” form of the representation of disturbances, which implies the possibility of separation of variables describing disturbances as functions of the radial and longitudinal (along the axis of a tube) coordinates. In the absence of such separation of variables in the developed linear theory, it has been proposed to use a modification of the Bubnov-Galerkin theory that makes it possible to take into account the difference between the periods of the longitudinal variability for different radial modes preliminarily determined by the standard application of the Galerkin-Kantorovich method to the evolution equation of extremely small axisymmetric disturbances of the tangential component of the velocity field. It has been shown that the consideration of even two linearly interacting radial modes for the Hagen-Poiseuille flow can provide linear instability only in the presence of the mentioned conditionally periodic longitudinal variability of disturbances along the axis of the tube, when the threshold Reynolds number Re_th(p) is very sensitive to the ratio p of two longitudinal periods each describing longitudinal variability for its radial disturbance mode. In this case, the threshold Reynolds number can tend to infinity, Re_th(p) → ∞, only at p = p _k = k, p = p _1/k = 1/k, and \(p = p_{\sqrt k } = [k + 1 \pm \sqrt {(k + 1)^2 - 4} ]/2\) , where k = 1, 2, 3, …. The minimum Reynolds number Re_th(p) ≈ 448 (at which p ≈ 1.527) for the linear instability of the Hagen-Poiseuille flow quantitatively corresponds to the condition of the excitation of Tollmien-Schlichting waves in the boundary layer, where Re_th = 420. Similarity of the mechanisms of linear viscous dissipative instability for the Hagen-Poiseuille flow and Tollmien-Schlichting waves has been discussed. Good quantitative agreement has been obtained between the phase velocities of the vortex disturbances and the experimental data on the velocities of the leading and trailing edges of turbulent “puffs” propagating along the axis of the tube.     

渐变截面热声波导管内的声流影响因素分析

通过理论分析和数值仿真,对渐变截面热声波导管内声流各影响因素进行了具体的分析,并给出了不同情形下波导管内的声流速度分布特性曲线。研究表明,热物理参数对渐变截面导致的声流变化无影响,针对具体的声场设计合适的截面变化形式可以使得管内声流在整体上得到一定程度的抑制或加强。此外,当波导管截面尺度与热穿透深度同数量级时,轴向时均温度分布对声流的影响十分显著。当不存在非零时均温度梯度时,热传导效应对声流的影响在管截面尺度为黏性穿透深度约10至20倍量级时最大。      

Critical dynamics of dipolar ferromagnets

The dynamical scaling functions for ferromagnets with dipolar interactions are computed by mode coupling theory above the critical temperature T_c. On the basis of this theory we explain apparently conflicting features of neutron scattering experiments on EuO, EuS and Fe. The position of the crossover from isotropic to dipolar critical dynamics is determined and further experiments are proposed.     

The transverse acoustic impedance of an inhomogeneous viscous fluid

The transverse acoustic impedance Z of a fluid can be determined from measurements of the complex reflection coefficient of a transverse ultrasonic wave incident on a plane solid/fluid interface. Inhomogeneities in the fluid close to the solid surface may have a significant effect on the measured values of Z. We have derived the Riccati equation which determines Z in an inhomogeneous viscous fluid, using transmission line theory. This equation was integrated numerically to obtain the impedance of viscous films and for inhomogeneities due to healing lengths and van der Waals forces near the solid/fluid interface. The results show that the measurement of both the real and imaginary parts of Z can be a powerful technique for investigating any inhomogeneities which occur on a length scale comparable with the viscous penetration depth in the fluid.     

A Brinkman penalization method for compressible flows in complex geometries

To simulate flows around solid obstacles of complex geometries, various immersed boundary methods had been developed. Their main advantage is the efficient implementation for stationary or moving solid boundaries of arbitrary complexity on fixed non-body conformal Cartesian grids. The Brinkman penalization method was proposed for incompressible viscous flows by penalizing the momentum equations. Its main idea is to model solid obstacles as porous media with porosity, ϕ, and viscous permeability approaching zero. It has the pronounced advantages of mathematical proof of error bound, strong convergence, and ease of numerical implementation with the volume penalization technique. In this paper, it is extended to compressible flows. The straightforward extension of penalizing momentum and energy equations using Brinkman penalization with respective normalized viscous, η, and thermal, η_T, permeabilities produces unsatisfactory results, mostly due to nonphysical wave transmissions into obstacles, resulting in considerable energy and mass losses in reflected waves. The objective of this paper is to extend the Brinkman penalization technique to compressible flows based on a physically sound mathematical model for compressible flows through porous media. In addition to penalizing momentum and energy equations, the continuity equation for porous media is considered inside obstacles. In this model, the penalized porous region acts as a high impedance medium, resulting in negligible wave transmissions. The asymptotic analysis reveals that the proposed Brinkman penalization technique results in the amplitude and phase errors of order O((ηϕ)^1/2) and O((η/η_T)^1/4ϕ^3/4), when the boundary layer within the porous media is respectively resolved or unresolved. The proposed method is tested using 1- and 2-D benchmark problems. The results of direct numerical simulation are in excellent agreement with the analytical solutions. The numerical simulations verify the accuracy and convergence rates.