Short-wave instabilities on a vortex pair of unequal strength circulation ratio

The creation of vortex pairs occurs in a range of industries, including mixing, transport, and plastic moulding. In particular, vortex pairs are observed in the wake of aircraft, and are the cause of a significant hazard in the aviation industry. Instabilities, which grow on vortex pairs, have the potential to lead to enhanced dissipation, thus limiting this safety concern, in addition to enhancing mixing in chemical engineering industries. To date research has mostly considered instabilities growing on a vortex pair where each vortex has the same magnitude of circulation. However, in practice it is unusual to have an equal-strength vortex pair. This investigation is the first to consider the instability modes that may develop on a Lamb–Oseen vortex pair of arbitrary circulation ratio. We find a significant change in the growth rates of all instability modes reported previously for an equal-strength vortex pair. All simulations employ an accurate spectral-element method to discretise the domain coupled with a three-step time splitting scheme. A wide range of instability wavelengths is considered to ensure that all instability modes are captured. By identifying and enhancing the leading instability modes, we are able to enhance the dissipation of the vortex pair.     

Parallel Simulation of a Compressible Jet Including Nozzle Modelling

Circular jet flows play an important role for many technical applications. Realistic simulations of such flows require modelling of the nozzle geometry to represent the turbulent state of the boundary layer at the nozzle exit. An available high-order finite-difference code for solving the compressible Navier-Stokes equations on a cylindrical grid was adapted to account for the nozzle geometry within the simulation domain. The code was parallelized using the message-passing interface MPI to be able to complete the simulations within acceptable turn-around times. Validation of the implementation was performed by checking the convergence behaviour of the spatial discretization schemes. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Vortex breakdown in turbulent pipe flows

In many technical applications turbulent flows with embedded slender vortices exist. Depending on the boundary conditions vortex breakdown can occur. The purpose of this work is to develop and implement a solution scheme for large‐eddy simulations of vortex breakdown in turbulent pipe flows. One of the main problems in this simulation is the formulation of the inflow boundary condition for a fully developed turbulent flow with an embedded vortex. For that purpose a rescaling technique is developed in which a solution at a downstream location is inserted at the inflow boundary after an appropriate rescaling. To determine rescaling laws for pipe flows with an embedded vortex, analytical velocity profiles of swirling flows are first prescribed in a laminar flow. From the spatial development of the vortex a scaling law is deduced. In a next step this procedure is to be transferred to turbulent flows.     

Existence and numerical modelling of vortex rings with elliptic boundaries

We revisit in this paper the theory of axisymmetric vortex rings in an ideal fluid. The boundary separating the vortex ring from the external (potential) flow is assumed of elliptic shape. For a given distribution of vorticity in the vortex core, we theoretically put into evidence the critical parameter for the existence of non-trivial solutions, thus confirming the numerical observation of Durst et al. [ZAMP 32 (1981) 156]. A sharp estimation of the critical threshold is analytically derived. Theoretical predictions are confirmed by numerical simulations using finite elements. A new numerical algorithm is presented and shown to display better performances compared to previous published algorithms using finite differences. The convergence of the iterative algorithm is proved using the theory of elliptic partial differential equations with discontinuous nonlinearities.     

三角翼大迎角流场结构和气动力特性的计算分析研究

采用数值计算方法对亚音速三角翼纵向及带有小侧滑和横侧小扰动情况下的流场结构进行了计算,利用数值计算所得到的大迎角流动流场数据,结合相关的实验研究结果,建立了对大迎角旋涡流场结构进行定量分析的方法．给出了三角翼大迎角情况下相应的气动力、力矩系数,以及机翼前缘分离涡轴线位置和旋涡破裂位置随迎角的变化规律,并对带有小侧滑和横侧小扰动情况下对横侧力矩的影响进行了计算与分析．计算结果表明,在前缘分离涡破裂前的上游旋涡区内,前缘分离涡轴线基本保持为直线,且随着迎角增加,前缘分离涡轴线位置愈靠近翼根,并远离翼面;在前缘分离涡破裂的初始阶段,于旋涡轴线处,压力系数会迅速增加,沿涡轴线方向速度迅速减小,在垂直于流向的截面内,愈靠近涡轴线处,沿涡轴线方向速度愈小,甚至出现负值,说明沿涡轴线方向出现回流．当绕机翼上表面前缘分离涡破裂后,将会导致横侧运动不稳定,如果受到小扰动,将产生横侧力矩发散．     

Nonlinear Dynamics of Non-uniform Current-Vortex Sheets in Magnetohydrodynamic Flows

A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in two-dimensional MHD flows based on an idea of non-uniform current-vortex sheet. Application of vortex sheet model to MHD flows has a crucial difficulty because of non-conservative nature of magnetic tension. However, it is shown that when a magnetic field is initially parallel to an interface, the concept of vortex sheet can be extended to MHD flows (current-vortex sheet). Two-dimensional MHD flows are then described only by a one-dimensional Lagrange parameter on the sheet. It is also shown that bulk magnetic field and velocity can be calculated from their values on the sheet. The model is tested by MHD Richtmyer–Meshkov instability with sinusoidal vortex sheet strength. Two-dimensional ideal MHD simulations show that the nonlinear dynamics of a shocked interface with density stratification agrees fairly well with that for its corresponding potential flow. Numerical solutions of the model reproduce properly the results of the ideal MHD simulations, such as the roll-up of spike, exponential growth of magnetic field, and its saturation and oscillation. Nonlinear evolution of the interface is found to be determined by the Alfvén and Atwood numbers. Some of their dependence on the sheet dynamics and magnetic field amplification are discussed. It is shown by the model that the magnetic field amplification occurs locally associated with the nonlinear dynamics of the current-vortex sheet. We expect that our model can be applicable to a wide variety of MHD shear flows.     

On the bidirectional vortex and other similarity solutions in spherical coordinates

The bidirectional vortex refers to the bipolar, coaxial swirling motion that can be triggered, for example, in cyclone separators and some liquid rocket engines with tangential aft-end injectors. In this study, we present an exact solution to describe the corresponding bulk motion in spherical coordinates. To do so, we examine both linear and nonlinear solutions of the momentum and vorticity transport equations in spherical coordinates. The assumption will be that of steady, incompressible, inviscid, rotational, and axisymmetric flow. We further relate the vorticity to some power of the stream function. At the outset, three possible types of similarity solutions are shown to fulfill the momentum equation. While the first type is incapable of satisfying the conditions for the bidirectional vortex, it can be used to accommodate other physical settings such as Hill’s vortex. This case is illustrated in the context of inviscid flow over a sphere. The second leads to a closed-form analytical expression that satisfies the boundary conditions for the bidirectional vortex in a straight cylinder. The third type is more general and provides multiple solutions. The spherical bidirectional vortex is derived using separation of variables and the method of variation of parameters. The three-pronged analysis presented here increases our repertoire of general mean flow solutions that rarely appear in spherical geometry. It is hoped that these special forms will permit extending the current approach to other complex fluid motions that are easier to capture using spherical coordinates.     

Finite-time Euler singularities: A Lagrangian perspective

We address the question of whether a singularity in a three-dimensional incompressible inviscid fluid flow can occur in finite time. Analytical considerations and numerical simulations suggest high-symmetry flows as promising candidates for finite-time blowup. Utilizing Lagrangian and geometric non-blowup criteria, we present numerical evidence against the formation of a finite-time singularity for the high-symmetry vortex dodecapole initial condition. We use data obtained from high-resolution adaptively refined numerical simulations and inject Lagrangian tracer particles to monitor geometric properties of vortex line segments. We then verify the assumptions made in the analytical non-blowup criteria introduced by Deng et al. [Commun. PDE 31 (2006)] connecting vortex line geometry (curvature, spreading) to velocity increase, to rule out singular behavior.     

Wakes and vortex streets behind a localized force: Numerical simulations

Two-dimensional wakes behind a body force acting inside a small circular area are investigated using direct numerical simulations. The flows induced by a single force are asymptotically related to the far-field wakes of a bluff body but belong to a wider class of flows because the problem contains an extra control parameter. Stable (almost parallel) wakes as well as regular vortex streets similar to those observed in the wakes of bluff bodies were obtained in our simulations. The behavior of the frequency of vortex shedding in the unstable wakes is described in detail for different values of the main control parameters of the flow, namely the amplitude of the forcing, the velocity of the stream, the size of the forcing area and the kinematic viscosity of fluid. Two different regimes of vortex shedding were observed in the space of these control parameters. Transition between the regimes is characterized by a rapid drop in frequency. The relation between the flows generated by a force and those past a circular cylinder is identified.     

Turbulent Flow with Embedded Vortical Structures Induced by Vortex Generators in a Cascade

Presented work is the next step after several experimental examinations of vortex generator influence on a flow separation occurring on a model of the NACA 63A421 airfoil with deflected simple flap. In this stage of research the vortices produced by vortex generators (VGs) were studied using Particle Image Velocimetry technique (PIV) and numerical simulations. Vane type VGs with two spacings among VGs pairs in straight channel with turbulent flow were tested. The average velocity flow field, peak of vorticity and circulation decay downstream of VGs were evaluated. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Large Eddy Simulations of Swirling Nozzle-Jet Flow Undergoing Vortex Breakdown

We developed a numerical setup to simulate swirling jet flow undergoing vortex breakdown. Our simulation code CONCYL solves the compressible Navier-Stokes equations in cylindrical coordinates using high-order numerical schemes. A nozzle is included in the computational domain to account for more realistic inflow boundary conditions. Preliminary results of a Re = 5000 compressible swirling jet at Mach number M a = 0.6 with an azimuthal velocity as high as the maximum axial velocity (swirl number S = 1.0 ) capture the fundamental characteristics of this flow type: At a certain point in time the jet spreads and develops into a conical vortex breakdown. A stagnation point-flow in the vicinity of the jet axis is clearly visible with the stagnation point located close to the nozzle exit. The stagnation point precesses in time around the jet axis, moving up- and downstream. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Smoothed particle hydrodynamics modeling of the thermal behavior of double skin facades in fires considering the effects of venetian blinds

At present, the fire safety of double skin facades (DSFs) is an important research area due to recent spikes in fires in high rise buildings involving glass DSF systems, and also due to our limited understanding of the thermal behavior of these systems. To overcome this lack of knowledge, a numerical framework is proposed for simulating the thermal performance of DSFs under fire conditions. The framework is based on the smoothed particle hydrodynamics technique and it can be used to compute numerical solutions and simulate the thermal degradation of DSFs under fire conditions. The numerical model was validated by comparing the predicted response parameters in a fire exposed DSF system with those measured in fire experiments. The validated numerical model was then employed to derive empirical equations linking temperature with both the time and location along the interior and exterior glass panes of DSFs. Finally, numerical simulations were conducted for the same DSF configuration but equipped with venetian blinds in order to examine the influence of the blinds on the fire performance of glass DSFs. An in-house MATLAB code was developed and implemented to conduct these numerical simulations. The results obtained from these numerical simulations clearly indicated that the “blind tilt angle” can significantly affect the fire spread characteristics and temperature distribution in DSFs, and thus it should be considered in the design of DSF systems for high rise buildings.     

Numerical exploration of new features on three-dimensional transition of a cylinder wake

The three-dimensional transition of the wake flow behind a circular cylinder is studied in detail by direct numerical simulations using 3D incompressible N-S equations for Reynolds number ranging from 200 to 300. New features and vortex dynamics of the 3D transition of the wake are found and investigated. At Re = 200, the flow pattern is characterized by mode A instability. However, the spanwise characteristic length of the cylinder determines the transition features. Particularly for the specific spanwise charac-     

An immersed boundary-lattice Boltzmann method combined with a robust lattice spring model for solving flow–structure interaction problems

An immersed boundary (IB)-lattice Boltzmann method (LBM) combined with a robust lattice spring model (LSM) was developed for modeling fluid–elastic body interactions. To include the effects of viscous flow forces on the deformation of a flexible body, rotational invariant springs were connected regularly inside the deformable body with square lattices. Fluid–solid interactions were due to an additional force density in the lattice Boltzmann equation enhanced by the split-forcing approach. To check the validity and accuracy of the numerical method, the flow over a rigid plate and the deformation of a cantilever beam were investigated. To demonstrate the capability of the new method, different test cases were examined. The deformation of a two-dimensional flexible vertical plate in a laminar cross-flow stream at different conditions was analyzed. The simulations were performed for different boundary conditions imposed on the elastic plate, namely, fixed-end corners and fixed middle point. Different flow conditions such as “steady flow regime”, “vortex shedding flow regime”, and the limit of “rigid body motion” were examined using the new IB-LBM-LSM approach. A general formulation for evaluating the deformation of the elastic body was also introduced, in which the position of the LSM nodes (inside the body) was updated implicitly at each time step. Two dimensionless groups, namely capillary number (Ca) and Reynolds number (Re), were used for parametric study of the behavior of the flow around the deformable plate. It was found that for low Reynolds numbers (Re < 50) and when the middle of the plate was fixed, decreasing the capillary number led to a decrease in the drag coefficient. The fluctuation of the plate during the vortex shedding flow regime was also explored. It was found that when the middle of the plate was fixed, the critical Reynolds number for the initiation of vortex shedding increased. For Re > 100, the Strouhal number was observed to increase with the decrease in capillary number.     

Numerical simulation of cavitation dynamics using a cavitation-induced-momentum-defect (CIMD) correction approach

A new unsteady cavitation event tracking model is developed for predicting vapor dynamics occurring in multi-dimensional incompressible flows. The procedure solves incompressible Navier–Stokes equations for the liquid phase supplemented with an additional vapor transport equation for the vapor phase. The novel cavitation-induced-momentum-defect (CIMD) correction methodology developed in this study accounts for cavitation inception and collapse events as relevant momentum-source terms in the liquid phase momentum equations. The model tracks cavitation zones and applies compressibility effects, employing homogeneous equilibrium model (HEM) assumptions, in constructing the source term of the vapor transport model. Effects of vapor phase accumulation and diffusion are incorporated by detailed relaxation models. A modified RNG k–ε model, including the effects of compressibility in the vapor regions, is employed for modeling turbulence effects. Numerical simulations are carried out using a finite volume methodology available within the framework of commercial CFD software code Fluent v.6.2. Simulation results are in good qualitative agreement with experiments for unsteady cloud cavitation behavior in planar nozzle flows. Multitude of mechanisms such as formation of vortex cavities, vapor cluster shedding and coalescence, cavity pinch off are sharply captured by the CIMD approach. Our results indicate the profound influence of re-entrant jet motion and adverse pressure gradients on the cavitation dynamics.     

翼涡干扰前缘开孔被动控制数值研究

开孔方法是一种简单的流动被动控制方法.为找到一种有效降低桨涡干扰效应的被动控制方法,以NACA 0012翼型作为研究对象,建立了4种前缘开孔的模型.在不同来流速度、涡的强度和干扰距离条件下,对4种前缘开孔模型和无孔的基准翼型进行了二维平行桨涡干扰（翼涡干扰）数值模拟,对比了升力系数的变化.结果表明:前缘开孔可以降低翼涡干扰效应,但对翼型升力系数有一定的影响;宽度为2.5%弦长的直孔能在翼型升力系数损失较小的情况下有效地降低翼涡干扰效应,且适用范围较广.     

Stability analysis of the flow past miniature vortex generators in a Blasius boundary layer

It is shown in the literature that Tollmien−Schlichting waves can be damped and transition delayed by a proper modulation of the streamwise velocity in a boundary layer (BL), which can be obtained using miniature vortex generators (MVGs). Experiments show that the amplitude of TS waves is not always monotonically damped past the MVGs. In this study, direct numerical simulations and local stability analysis have been performed in order to provide an interpretation of the experiments and to characterize further the stabilization mechanism induced by this type of control. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Assessment of high-order discretization schemes for the DNS of compressible swirling mixing layers

We report on results of highly accurate Direct Numerical Simulations (DNS) solving the Navier-Stokes equations in cylindrical coordinates. The DNS code computes a compressible swirling mixing layer at Mach number Ma = 0.8. We present two simulations differing in the spatial discretization schemes for the convective terms. On the same grid, comparisons of flow simulations using different discretization schemes for otherwise identical conditions can be performed quantitatively and improve the understanding of the effects of numerical errors and in particular numerical dissipation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical exploration of new features on three-dimensional transition of a cylinder wake

The three-dimensional transition of the wake flow behind a circular cylinder is studied in detail by direct numerical simulations using 3D incompressible N-S equations for Reynolds number ranging from 200 to 300. New features and vortex dynamics of the 3D transition of the wake are found and investigated. At Re = 200, the flow pattern is characterized by mode A instability. However, the spanwise characteristic length of the cylinder determines the transition features. Particularly for the specific spanwise characteristic length linear stable mode may dominate the wake in place of mode A and determine the spanwise phase difference of the primary vortices shedding. At Re = 250 and 300 it is found that the streamwise vortices evolve into a new type of mode’“dual vortex pair mode” downstream. The streamwise vortex structures switch among mode A, mode B and dual vortex pair mode from near wake to downstream wake. At Re = 250, an independent low frequency f _m in addition to the vortex shedding frequency f _s is identified. Frequency coupling between f _m and f _s occurs. These result in the irregularity of the temporal signals and become a key feature in the transition of the wake. Based on the formation analysis of the streamwise vorticity in the vicinity of cylinder, it is suggested that mode A is caused by the emergence of the spanwise velocity due to three dimensionality of the incoming flow past the cylinder. Energy distribution on various wave numbers and the frequency variation in the wake are also described.