Kelvin-Helmholtz-like instabilities in turbulent flows over complex surfaces

Riblets are small surface protrusions aligned with the flow direction, which confer an anisotropic roughness to the surface [6]. We have recently reported that the transitional-roughness effect in riblets, which limits their performance, is due to a Kelvin–Helmholtz-like instability of the overlying mean flow [7]. According to our DNSs, the instability sets on as the Reynolds number based on the roughness size of the riblets increases, and coherent, elongated spanwise vortices begin to develop immediately above the riblet tips, causing the degradation of the drag-reduction effect. This is a very novel concept, since prior studies had proposed that the degradation was due to the interaction of riblets with the flow as independent units, either to the lodging of quasi-streamwise vortices in the surface grooves [2] or to the shedding of secondary streamwise vorticity at the riblet peaks [9]. We have proposed an approximate inviscid analysis for the instability, in which the presence of riblets is modelled through an average boundary condition for an overlying, spanwise-independent mean flow. This simplification lacks the accuracy of an exact analysis [4], but in turn applies to riblet surfaces in general. Our analysis succeeds in predicting the riblet size for the onset of the instability, while qualitatively reproducing the wavelengths and shapes of the spanwise structures observed in the DNSs. The analysis also connects the observations with the Kelvin–Helmholtz instability of mixing layers. The fundamental riblet length scale for the onset of the instability is a ‘penetration length,’ which reflects how easily the perturbation flow moves through the riblet grooves. This result is in excellent agreement with the available experimental evidence, and has enabled the identification of the key geometric parameters to delay the breakdown. Although the appearance of elongated spanwise vortices was unexpected in the case of riblets, similar phenomena had already been observed over other rough [3], porous [1] and permeable [11] surfaces, as well as over plant [5,14] and urban [12] canopies, both in the transitional and in the fully-rough regimes. However, the theoretical analyses that support the connection of these observations with the Kelvin–Helmholtz instability are somewhat scarce [7, 11, 13]. It has been recently proposed that Kelvin–Helmholtz-like instabilities are a dominant feature common to “obstructed” shear flows [8]. It is interesting that the instability does not require an inflection point to develop, as is often claimed in the literature. The Kelvin-Helmholtz rollers are rather triggered by the apparent wall-normal-transpiration ability of the flow at the plane immediately above the obstructing elements [7,11]. Although both conditions are generally complementary, if wall-normal transpiration is not present the spanwise vortices may not develop, even if an inflection point exists within the roughness [10]. REFERENCES [1] Breugem, W. P., Boersma, B. J. & Uittenbogaard, R. E. 2006 J. Fluid Mech. 562, 35–72. [2] Choi, H., Moin, P. & Kim, J. 1993 J. Fluid Mech. 255, 503–539. [3] Coceal, O., Dobre, A., Thomas, T. G. & Belcher, S. E. 2007 J. Fluid Mech. 589, 375–409. [4] Ehrenstein, U. 2009 Phys. Fluids 8, 3194–3196. [5] Finnigan, J. 2000 Ann. Rev. Fluid Mech. 32, 519–571. [6] Garcia-Mayoral, R. & Jimenez, J. 2011 Phil. Trans. R. Soc. A 369, 1412–1427. [7] Garcia-Mayoral, R. & Jimenez, J. 2011 J. Fluid Mech. doi: 10.1017/jfm.2011.114. [8] Ghisalberti, M. 2009 J. Fluid Mech. 641, 51–61. [9] Goldstein, D. B. & Tuan, T. C. 1998 J. Fluid Mech. 363, 115–151. [10] Hahn, S., Je, J. & Choi, H. 2002 J. Fluid Mech. 450, 259–285. [11] Jimenez, J., Uhlman, M., Pinelli, A. & G., K. 2001 J. Fluid Mech. 442, 89–117. [12] Letzel, M. O., Krane, M. & Raasch, S. 2008 Atmos. Environ. 42, 8770–8784. [13] Py, C., de Langre, E. & Moulia, B. 2006 J. Fluid Mech. 568, 425–449. [14] Raupach, M. R., Finnigan, J. & Brunet, Y. 1996 Boundary-Layer Meteorol. 78, 351–382.

Effects of the biodiesel fuel physical properties on the swirl stabilised spray combustion characteristics

An increasin g interest in biofuel applications in modern engines requires a better understanding of biodiesel combustion behaviour. Many numerical studies have been carried out on unsteady combustion of biodiesel in situations similar to diesel engines, but very few studies have been done on the steady combustion of biodiesel in situations similar to a gas turbine combustor environment. The study of biodiesel spray combustion in gas turbine applications is of special interest due to the possible use of biodiesel in the power generation and aviation industries. In modelling spray combustion, an accurate representation of the physical properties of the fuel is a first important step, since spray formation is largely influenced by fuel properties such as viscosity, density, surface tension and vapour pressure. In the present work, a calculated biodiesel properties database based on the measured composition of Fatty Acid Methyl Esters (FAME) has been implemented in a multi-dimensional Computational Fluid Dynamics (CFD) spray simulation code. Simulations of non-reacting and reacting atmospheric-pressure sprays of both diesel and biodiesel have been carried out using a spray burner configuration for which experimental data is available. A pre-defined droplet size probability density function (pdf) has been implemented together with droplet dynamics based on phase Doppler anemometry (PDA) measurements in the near-nozzle region. The gas phase boundary condition for the reacting spray cases is similar to that of the experiment which employs a plain air-blast atomiser and a straight-vane axial swirler for flame stabilisation. A reaction mechanism for heptane has been used to represent the chemistry for both diesel and biodiesel. Simulated flame heights, spray characteristics and gas phase velocities have been found to compare well with the experimental results. In the reacting spray cases, biodiesel shows a smaller mean droplet size compared to that of diesel at a constant fuel mass flow rate. A lack of sensitivity towards different fuel properties has been observed based on the non-reacting spray simulations, which indicates a need for improved models of secondary breakup. By comparing the results of the non-reacting and reacting spray simulations, an improvement in the complexity of the physical modelling is achieved which is necessary in the understanding of the complex physical processes involved in spray combustion simulation. Copyright © 2012 SAE International.

Semiconductor laser with a biconical waveguide

The propagation losses in the fundamental mode of a bicone made of highly reflecting metal or a dielectric of large refraction were approximately estimated using Leontovich's boundary condition. A 400-fold concentration of the energy flux density lias been obtained in a cross section which is much smaller than λ. Here, the losses are 2.5% at λ = 550 nm in an Ag bicone and 12% in a semiconductor bicone with a band gap of ≈1 eV for hv larger than the band gap. The excitation efficiency of a bicone has been estimated. While not too large, it can be increased significantly using the method proposed in the present paper. The application of the optical bicone for the multiplication of a semiconductor-laser frequency is discussed. The results obtained are also of use in scanning near-field optical microscopy and in experiments on focusing laser pulses of ultrahigh power. © 2000 Plenum/Kluwer Publishing Corporation.

Rashba electron transport in one-dimensional quantum waveguides

The properties of Rashba wave function in the planar one-dimensional waveguide are studied, and the following results are obtained. Due to the Rashba effect, the plane waves of electron with the energy E divide into two kinds of waves with the wave vectors k(1)=k(0)+k(delta) and k(2)=k(0)-k(delta), where k(delta) is proportional to the Rashba coefficient, and their spin orientations are +pi/2 (spin up) and -pi/2 (spin down) with respect to the circuit, respectively. If there is gate or ferromagnetic contact in the circuit, the Rashba wave function becomes standing wave form exp(+/- ik(delta)l)sin[k(0)(l-L)], where L is the position coordinate of the gate or contact. Unlike the electron without considering the spin, the phase of the Rashba plane or standing wave function depends on the direction angle theta of the circuit. The travel velocity of the Rashba waves with the wave vector k(1) or k(2) are the same hk(0)/m*. The boundary conditions of the Rashba wave functions at the intersection of circuits are given from the continuity of wave functions and the conservation of current density. Using the boundary conditions of Rashba wave functions we study the transmission and reflection probabilities of Rashba electron moving in several structures, and find the interference effects of the two Rashba waves with different wave vectors caused by ferromagnetic contact or the gate. Lastly we derive the general theory of multiple branches structure. The theory can be used to design various spin polarized devices.

Partially coherent tunneling through a series of barriers: Inelastic scattering versus pure dephasing

Within the Buttiker dephasing model, the backscattering in the dephasing process is eliminated by setting a proper boundary condition. Explicit expression is carried out for the effective total tunneling probability in the presence of multiple pure dephasing scatterers with partial coherence. The derived formula is illustrated analytically by various limiting cases, and numerically for its application in tunneling through multibarrier systems.

Linear and nonlinear intersubband optical properties in a step quantum well with an applied electric field

Within the framework of the effective-mass envelope-function theory, the field-dependent intersubband optical properties of a Al0.4Ga0.6As/Al0.2Ga0.8As/GaAs step quantum well are investigated theoretically based on the periodic boundary condition. A very large Stark shift occurs when the lowest subband electron remains confined to the small well while the higher subband electron confined to the big well. The optical nonlinearity in a step well due to resonant intersubband transition (ISBT) is analyzed using a density-matrix approach. The second-harmonic generation coefficient chi(2 omega)((2)) and nonlinear optical rectification chi(0)((2)) have also been investigated theoretically. The results show that the ISBT in a step well can generate very large second order optical nonlinearities, chi(0)((2)) and chi(2 omega)((2)) can be tuned by the electric field over a wide range.

SOME ASPECTS ON INTERFACE MODES AND LO EIGENMODES IN GAAS/ALAS QUANTUM-WELLS

The interface modes and LO phonon modes in GaAs/AlAs quantum wells is investigated within the isotropic dispersionless dielectric continuum with nodes in displacement u at the interfaces as boundary condition. The interface modes are found to be purely interface polarization charge effect while LO eigenmodes induce only bulk polarization charges. Analytical expression is determined for LO eigenmodes and is found in good agreement with realistic model calculation, and its labeling index is interpreted as the helicity of electric field as it travels from one side to the other side of the slab.

Electronic structures of T-shaped quantum wires

In this paper, we propose the periodic boundary condition which can be applied to a variety of semiconductor nanostructures to overcome che difficulty of solving Schrodinger equation under the natural boundary condition. When the barrier width is large enough. the average of the maximum and minimum of energy band under the periodic boundary condition is very close to the energy level obtained under the natural boundary condition. As an example, we take the GaAs/Ga1-xAlxAs system, If the width of the Ga1-xAlxAs barrier is 200 Angstrom, the average of the maximum and minimum of energy band of the GaAs/Ga1-xAlxAs superlattices is very close to the energy level of the GaAs/Ga1-xAlxAs quantum wells (QWs). We give the electronic structure effective mass calculation of T-shaped quantum wires (T-QWRs) under the periodic boundary condition, The lateral confinement energies E1D-2D of electrons and holes, the energy difference between T-QWRs and QWs, are precisely determined.

耗散粒子动力学处理复杂固体壁面的一种有效方法

耗散粒子动力学(dissipative particle dynamics,DPD)作为一种介观尺度拉格朗日型粒子方法,已经成功地应用于微纳米流动和生化科技的研究中. 复杂固体壁面的处理和壁面边界条件的实施一直是DPD方法发展及应用的一个障碍. 提出了处理复杂固体壁面的一种新的方法. 复杂固体区域通过冻结随机分布并且达到平衡状态的DPD粒子代表;所冻结的DPD粒子位于临近流动区域的一个截距内;在靠近固体壁面的流动区域中设置流动反弹层,当流动DPD粒子进入此流动层后反弹回流动区域. 应用这种固体壁面处理方法.

Holographic dual of linear dilaton black hole in Einstein-Maxwell-dilaton-axion gravity

Motivated by the recently proposed Kerr/CFT correspondence, we investigate the holographic dual of the extremal and non-extremal rotating linear dilaton black hole in Einstein-Maxwell-Dilaton-Axion Gravity. For the case of extremal black hole, by imposing the appropriate boundary condition at spatial infinity of the near horizon extremal geometry, the Virasoro algebra of conserved charges associated with the asymptotic symmetry group is obtained. It is shown that the microscopic entropy of the dual conformal field given by Cardy formula exactly agrees with Bekenstein-Hawking entropy of extremal black hole. Then, by rewriting the wave equation of massless scalar field with sufficient low energy as the SLL(2, R) x SLR(2, R) Casimir operator, we find the hidden conformal symmetry of the non-extremal linear dilaton black hole, which implies that the non-extremal rotating linear dilaton black hole is holographically dual to a two dimensional conformal field theory with the non-zero left and right temperatures. Furthermore, it is shown that the entropy of non-extremal black hole can be reproduced by using Cardy formula.

Rashba electron transport in 1D quantum waveguides

City Univ Hong Kong

NONLINEAR GRAVITY-WAVES IN DEEP-WATER

In consideration of the problem on the boundary condition of nonlinear free water wave, coordinate transform is used to handle the free boundary. Supposing the solution form be the traveling wave, the ordinary differential equations of the one-order autonomous system with two variables are caused, then expanding the nonlinear terms at the equilibrium point with the Taylor expansion, we obtained the solution to traveling wave. The linear approximate equation near the equilibrium point is the small amplitude wave. A new nonlinear periodic traveling wave and nonlinear dispersion relation are shown when expanding to the second-order terms. A conclusion that the expansion of dispersion relation does not contain any odd-power terms of wave steepness and because of the nonlinear effort an oscillate structure is produced in the vertical direction is drawn.

Wave breaking on turbulent energy budget in the ocean surface mixed layer

As an important physical process at the air-sea interface, wave movement and breaking have a significant effect on the ocean surface mixed layer (OSML). When breaking waves occur at the ocean surface, turbulent kinetic energy (TKE) is input downwards, and a sublayer is formed near the surface and turbulence vertical mixing is intensively enhanced. A one-dimensional ocean model including the Mellor-Yamada level 2.5 turbulence closure equations was employed in our research on variations in turbulent energy budget within OSML. The influence of wave breaking could be introduced into the model by modifying an existing surface boundary condition of the TKE equation and specifying its input. The vertical diffusion and dissipation of TKE were effectively enhanced in the sublayer when wave breaking was considered. Turbulent energy dissipated in the sublayer was about 92.0% of the total depth-integrated dissipated TKE, which is twice higher than that of non-wave breaking. The shear production of TKE decreased by 3.5% because the mean flow fields tended to be uniform due to wave-enhanced turbulent mixing. As a result, a new local equilibrium between diffusion and dissipation of TKE was reached in the wave-enhanced layer. Below the sublayer, the local equilibrium between shear production and dissipation of TKE agreed with the conclusion drawn from the classical law-of-the-wall (Craig and Banner, 1994).

Traveling wave front for the Fisher equation on an infinite band region

Instead of discussing the existence of a one-dimensional traveling wave front solution which connects two constant steady states, the present work deals with the case connecting a constant and a nonhomogeneous steady state on an infinite band region. The corresponding model is the well-known Fisher equation with variational coefficient and Dirichlet boundary condition. (c) 2006 Elsevier Ltd. All rights reserved.

潮波模型的优化开边界方法研究

数值模式是潮波研究的一种有利手段，但在研究中会面临各种具体问题，包括开边界条件的确定、底摩擦系数和耗散系数的选取等。数据同化是解决这些问题的一种途径，即利用有限数量的潮汐观测资料对潮波进行最优估计，其根本目的是迫使模型预报值逼近观测值，使模式不要偏离实际情况太远。本文采用了一种优化开边界方法，沿着数值模型的开边界优化潮汐水位信息，目的是设法使数值解在动力约束的意义下接近观测值，获得研究区域的潮汐结果。边界值由指定优化问题的解来定，以提高模拟区域的潮汐精度，最优问题的解是基于通过开边界的能量通量的变化，处理开边界处的观测值与计算值之差的最小化。这里提供了辐射型边界条件，由Reid 和Bodine（本文简称为RB）推导，我们将采用的优化后的RB方法（称为ORB）是优化开边界的特殊情况。 本文对理想矩形海域（ E- E， N- N， 分辨率 ）进行了潮波模拟，有东部开边界，模式采用ECOM3D模式。对数据结果的误差分析采用，振幅平均偏差，平均绝对偏差，平均相对误差和均方根偏差四个值来衡量模拟结果的好坏程度。 需要优化入开边界的解析潮汐值本文采用的解析解由方国洪《海湾的潮汐与潮流》（1966年）方法提供，为验证本文所做的解析解和方文的一致，本文做了其第一个例子的关键值a,b,z,结果与其结果吻合的相当好。但略有差别，分析的可能原因是两法在具体迭代方案和计算机保留小数上有区别造成微小误差。另外，我们取m=20，得到更精确的数值，我们发现对前十项的各项参数值，取m=10,m=20各项参数略有改进。当然我们可以获得m更大的各项参数值。 同时为了检验解析解的正确性讨论m和l变化对边界值的影响，结果指出，增大m，m=20时，u的模最大在本身u1或u2的模的6%；m=100时，u的模最大在本身u1或u2的模的4%；m再增大，m=1000时，u的模最大在本身u1或u2的模的4%，改变不大。当l<1时， =0处u的模最大为2。当l=1时， =0处u的模最大为0.1，当l>1时，l越大，u的模越小，当l=10时，u的模最大为0.001，可以认为为0。 为检验该优化方法的应用情况，我们对理想矩形区域进行模拟，首先将本文所采用的优化开边界方法应用于30m的情况，在开边界优化入开边界得出模式解，所得模拟结果与解析解吻合得相当好，该模式解和解析解在整个区域上，振幅平均绝对偏差为9.9cm,相位平均绝对偏差只有4.0 ，均方根偏差只有13.3cm，说明该优化方法在潮波模型中有效。 为验证该优化方法在各种条件下的模拟结果情况，在下面我们做了三类敏感性试验： 第一类试验：为证明在开边界上使用优化方法相比于没有采用优化方法的模拟解更接近于解析解，我们来比较ORB条件与RB条件的优劣，我们模拟用了两个不同的摩擦系数，k分别为：0,0.00006。 结果显示，针对不同摩擦系数，显示在开边界上使用ORB条件的解比使用RB条件的解无论是振幅还是相位都有显著改善，两个试验均方根偏差优化程度分别为84.3%，83.7%。说明在开边界上使用优化方法相比于没有采用优化方法的模拟解更接近于解析解，大大提高了模拟水平。上述的两个试验得出， k=0.00006优化结果比k=0的好。 第二类试验，使用ORB条件确定优化开边界情况下，在东西边界加入出入流的情况，流考虑线性和非线性情况，结果显示，加入流的情况，潮汐模拟的效果降低不少，流为1Sv的情况要比5Sv的情况均方根偏差相差20cm,而不加流的情况只有0.2cm。线性流和非线性流情况两者模式解相差不大，振幅，相位各项指数都相近, 说明流的线性与否对结果影响不大。 第三类试验，不仅在开边界使用ORB条件，在模式内部也使用ORB条件，比较了内部优化和不优化情况与解析解的偏差。结果显示，选用不同的k,振幅都能得到很好的模拟，而相位相对较差。另外，在内部优化的情况下，考虑不同的k的模式解， 我们选用了与解析解相近的6个模式解的k,结果显示，不同的k,振幅都能得到很好的模拟，而相位较差。 总之，在开边界使用ORB条件比使用RB条件好，振幅相位都有大幅度改进，在加入出入流情况下，流的大小对模拟结果有影响，但线形流和非线性流差别不大。内部优化的结果显示，模式采用不同的k都能很好模拟解析解的振幅。