Study of the role of dissipation in evolution of nonlinear sloshing waves in a rectangular channel

The influence of dissipation at the modular four segment wavemaker and at the solid walls, on the evolution of sloshing waves in the vicinity of the second cut-off frequency in a rectangular tank, was studied both experimentally and theoretically. Experiments were performed at two different geometries of the wavemaker with correspondingly different dissipation rates. The conclusions regarding the importance of the dissipation rate at the wavemaker could thus be drawn. A model which allows to incorporate dissipation in the governing equation and in the wavemaker boundary condition, is presented. The actual values of the dissipation coefficients at the wavemaker were chosen by realizing the importance of the vortex shedding at the edges of the solid surfaces of the modular wavemaker. Stationary and modulated regimes were obtained both experimentally and numerically by varying the value of the detuning parameter.     

湍流能量耗散率标度律实验研究

应用粒子图像测速(PIV)系统对平板湍流边界层内流向和法向的瞬时速度进行了测量。湍流的能量耗散率由轴对称假设得到,同时在研究湍流动能耗散率标度律的过程中采用传统的统计学方法。实验结果显示,对于不同尺度上和不同法向位置湍流耗散率标度律来说,湍流耗散主要发生在小尺度上,也就是说湍动能耗散率标度律在小尺度上具有普适性。另外,根据层次结构理论假设,通过PIV实验数据对最高激发态的标度指数进行了研究,结果发现,最高激发态存在绝对标度指数,并且绝对标度律是由信号中最强耗散涨落的局部结构产生的。     

Implementation of physical boundary conditions into computational domain in modelling of oscillatory bottom boundary layers

This paper discusses the importance of realistic implementation of the physical boundary conditions into computational domain for the simulation of the oscillatory turbulent boundary layer flow over smooth and rough flat beds. A mathematical model composed of the Reynolds averaged Navier–Stokes equation, turbulent kinetic energy (k) and dissipation rate of the turbulent kinetic energy (ε) has been developed. Control‐volume approach is used to discretize the governing equations to facilitate the numerical solution. Non‐slip condition is imposed on the bottom surface, and irrotational main flow properties are applied to the upper boundary. The turbulent kinetic energy is zero at the bottom, whereas the dissipation rate is approaching to a constant value, which is proportional to the kinematic viscosity times the second derivative of the turbulent kinetic energy. The output of the model is compared with the available experimental studies conducted in oscillatory tunnels and wave flume. It is observed that the irrotational flow assumption at the upper boundary is not realistic in case of water tunnels. Therefore, new upper boundary conditions are proposed for oscillatory tunnels. The data of wave flume show good agreement with the proposed numerical model. Additionally, several factors such as grid aspect ratio, staggered grid arrangement, time‐marching scheme and convergence criteria that are important to obtain a robust, realistic and stable code are discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Direct numerical simulation of stationary particles in homogeneous turbulence decay: Application of the k–ε model

This study focuses on understanding how the presence of particles, in homogeneous turbulence decay, affects the dissipation of dissipation coefficient within the volume averaged dissipation transport equation. In developing this equation, the coefficient for dissipation of dissipation was assumed to be the sum of the single phase coefficient and an additional coefficient that is related to the effects of the dispersed phase. Direct numerical simulation was used to isolate the effect of stationary particles in homogeneous turbulent decay at low Reynolds numbers (Re_L = 3.3 and 12.5). The particles were positioned at each grid point and modeled as point forces and a comparison was made between a 64³ and 128³ domain. The results show that the dissipation of dissipation coefficient correlates well with a dimensionless parameter called the momentum coupling factor.     

Turbulence Energy Distribution in the Stokes Layer

Using the method of matched asymptotic expansions, an analytical solution of the balance equation for turbulence energy is constructed for a shallow basin (sea) in which the fluid depth does not exceed the Stokes layer thickness. In this case, a gradient-viscous balance is established with the turbulent viscosity being balanced mainly by the pressure gradient. It is shown that nonlinear boundary layers attributable to turbulence energy diffusion are formed near the bottom and the free surface (or ice). In the neighborhood of the point of maximum flow velocity (if this maximum is attained inside the flow), a nonlinear internal boundary layer also develops. Outside these layers, the turbulence energy generation is in the first approximation balanced by the energy dissipation. Asymptotic solutions for the boundary layers are constructed.     

Waves generated by an inclined-plate wave generator

This paper describes the characteristics of small-amplitude waves generated by a sinusoidally oscillating, inclined paddle-type wavemaker operating in a constant-depth channel. Two-dimensional, linearized potential flow is assumed. A semi-analytical method, the boundary collocation method, is used to establish the relationship between wave amplitude and paddle stroke. The numerical results are compared with the numerical results of the boundary integral equation method. It is found that the boundary collocation method is simpler and more flexible to implement and faster to compute. In addition, the numerical results are in reasonably good agreement with the laboratory experimental data. For the vertical wavemaker, which is a special case of the inclined wavemaker, an analytical series solution can be found. By using the boundary collocation method and the boundary integral equation method to solve the vertical wavemaker problem and comparing the results with the analytical series solution, it is found that the boundary collocation method yields a solution which is much more accurate than that from the boundary integral equation method. Finally, the relationships between wave amplitude and paddle stroke are established for different inclinations of the paddle-type wavemaker, based on the boundary collocation method.     

A theoretical model of the coherent structure in the wall region of a turbulent boundary layer

In this paper,the formation of the coherent structures in the wall region of aturbulent boundary layer was studied,using the nonlinear theory of the hydrodynamicstability.The spanwise and streamwise wavelengths of the most amplified unstablewave obtained by this study were found in good agreement with the experiments,whichmakes the distinct feature of this study in the present paper,as the basis of thestability analysis,a more rational velocity profile has been used,which is different fromthat of the turbulent mean flow.And also,the new nonlinear theory was used.Theresult is useful in understanding of the quasi-periodicity of the coherent structure in theturbulent boundary layer.     

Implicit large eddy simulation of a supersonic flat-plate boundary layer flow by weighted compact nonlinear scheme

The performance of implicit large eddy simulation (ILES) of a supersonic flat-plate turbulent boundary layer flow by weighted compact nonlinear scheme (WCNS) has been investigated. In view of features of WCNS and ILES, it was expected that ILES by WCNS could be an efficient approach to perform LES of supersonic turbulent flows. The flowfield calculated by WCNS was of lower turbulent intensity compared with an explicit LES data obtained by a numerical scheme of the same order of accuracy on a computational grid of similar resolution. It was concluded that the numerical dissipation inherent in WCNS is so large that applying WCNS to ILES of this flowfield is inefficient compared with explicit LES.     

EXPERIMENTAL STUDY OF MEASUREMENT FOR DISSIPATION RATE SCALING EXPONENT IN HEATED WALL TURBULENCE

Experimental investigations have been devoted to the study of scaling law of coarse-grained dissipation rate structure function for velocity and temperature fluctuation of non-isotropic and inhomogeneous turbulent flows at moderate Reynolds number. Much attention has been paid to the case of turbulent boundary layer, which is typically the non-istropic and inhomogeneous trubulence because of the dynamically important existence of organized coherent structure burst process in the near wall region . Longitudinal velocity and temperature have been measured at different vertical positions in turbulent boundary layer over a heated and unheated flat plate in a wind tunnel using hot wire anemometer. The influence of non-isotropy and inhomogeneity and heating the wall on the scaling law of the dissipation rate structure function is studied because of the existence of organized coherent structure burst process in the near wall region . The scaling law of coarse-grained dissipation rate structure function is foun     

Continuation methods applied to the 2D Navier–Stokes equations at high Reynolds numbers

Nonlinearities arise in aerodynamic flows as a function of various parameters, such as angle of attack, Mach number and Reynolds number. These nonlinearities can cause the change from steady to unsteady flow or give rise to static hysteresis. Understanding these nonlinearities is important for safety validation and performance enhancement of modern aircraft. A continuation method has been developed to study nonlinear steady state solutions with respect to changes in parameters for two‐dimensional compressible turbulent flows at high Reynolds numbers. This is the first time that such flows have been analysed with this approach. Continuation methods allow the stable and unstable solutions to be traced as flow parameters are changed. Continuation has been carried out on two‐dimensional aerofoils for several parameters: angle of attack, Mach number, Reynolds number, aerofoil thickness and turbulent inflow as well as levels of dissipation applied to the models. A range of results are presented. Copyright © 2012 John Wiley & Sons, Ltd.     

Direct numerical simulation of a particle-laden flow in a flat plate boundary layer

In this paper, a direct numerical simulation of particle-laden flow in a flat plate boundary layer is performed, using the Eulerian–Lagrangian point-particle approach. This is, as far as we know, the first simulation of a particle-laden spatially-developing turbulent boundary layer with two-way coupling. A local minimum of the particle number density is observed in the close vicinity of the wall. The present simulation results indicate that the inertial particles displace the quasi-streamwise vortices towards the wall, which, in turn, enhance the mean streamwise fluid velocity. As a result, the skin-friction coefficient is increased whereas the boundary layer integral thicknesses are reduced. The presence of particles augments the streamwise fluctuating velocity in the near-wall region but attenuates it in the outer layer. Nevertheless, the wall-normal and spanwise velocity fluctuations are significantly damped, and so is the Reynolds stress. In addition, the combined effect of a reduced energy production and an increased viscous dissipation leads to the attenuation of the turbulent kinetic energy.     

An experimental study on the effects of uniform injection through one perforated surface of a square cylinder on some aerodynamic parameters

It is well known that injection/suction (transpiration) through a perforated surface is an efficient way of influencing the characteristics of a turbulent boundary layer. Injection application creates a thicker boundary layer on a flat plate and it thus decreases drag. In aeronautical applications, suction is frequently used to delay boundary layer separation. This paper presents an experimental study on the effects of uniform injection through one perforated surface of a square cylinder on the pressure distribution and drag coefficient in a two-dimensional turbulent flow. For this purpose, surface pressure measurements around a square cylinder have been performed at three different Reynolds numbers in a wind tunnel. The parameters taken into account were injection rate, position of perforated surface (i.e., front, top, and rear), and pressure coefficient and drag coefficient. The results show that variation in pressure coefficient around the square cylinder and drag coefficient were influenced by the position of perforated surface and by injection rate.     

Molecular transfer in turbulent flows

For modeling the molecular transfer of a passive scalar in a known turbulent field, the equations for the average scalar value and the correlation function for the scalar field are written in a form which makes it possible to examine the effect of molecular transfer on turbulent transfer and scalar dissipation. For the closure of the equation for the correlation function, the Prandtl hypothesis is used. The statistical reliability of this closure is demonstrated. The system proposed makes it possible to predict the dynamics of a decaying uniform scalar field and to explain why the effect of the real value of the molecular-transfer coefficient on the decaying scalar field is weak. Specific features of the transport process in a plane layer with prescribed scalar values on the layer boundaries are considered.     

A quasi-similarity analysis of the turbulent boundary layer on a flat plate

The partial differential equation of the boundary layer on a flat plate are simplified by using the universal variables for turbulent flow. For laminar flow this gives boundary layer having a finite thickness and a friction coefficient differing by a few percent from the Blasius value. For a turbulent flow a differential equation for the velocity distribution is obtained with a parameter which varies slowly with the streamwise coordinate. The numerical value of this parameter is determined as an eigenvalue of the differential equations giving a velocity profile which evolves as the boundary layer thickens. Numerical calculations using a simple eddy viscosity model gave results in very good agreement with experiment.     

Experimental characterization of non-premixed turbulent jet propane flames

This paper reports an experimental study conducted on turbulent jet propane flames aiming at further understanding of turbulent structure in non-premixed slow-chemistry combustion systems. Measurements of mean and fluctuating velocity and temperature fields, mean concentration of major chemical species, correlation between velocity and temperature fluctuations, and dissipation of temperature fluctuations are reported in a turbulent round jet non-premixed propane flame, Re=20 400 and 37 600, issuing vertically in still air. The experimental conditions were designed to provide a complete definition of the upstream boundary conditions in the measurement domain for the purpose of validating computational models. The measured data depicts useful flow field information for describing turbulent non-premixed slow-chemistry flames. Velocity–temperature correlation measurements show turbulent heat fluxes tended to be restricted to the mixing layer where large temperature gradients occurred. Observations of non-gradient diffusion of heat at x/D=10 were verified. Temperature fluctuation dissipation, χ, showed the highest values in the shear layer, where the variance of temperature fluctuations was maximum and combustion occurred. The isotropy between the temperature dissipation in the radial and tangential directions was confirmed. By contrast, the observed anisotropy between axial and radial directions of dissipation suggests the influence of large structures in the entrainment shear layer on the production of temperature fluctuations in the flame region. The value of the normalized scalar dissipation at the stoichiometric mixture fraction surface, χ_st, was calculated, and ranges between 2 and 4 s⁻¹. The measured data were used to estimate the budgets in the balance equations for turbulent kinetic energy, Reynolds shear stresses, turbulent heat flux and temperature variance, quantifying the mechanisms involved in the generation of turbulence as well as in the transport of the temperature.     

DNS of turbulent channel flow with conjugate heat transfer: Effect of thermal boundary conditions on the second moments and budgets

Budgets of turbulent heat fluxes and temperature variance obtained from the Direct Numerical Simulation of an incompressible periodic channel flow with a Reynolds number of 150 (based on friction velocity) and a Prandtl number of 0.71 are presented and analysed for four cases: locally imposed temperature at the wall (constant Dirichlet), locally imposed heat flux (constant Neumann), heat exchange coefficient (Robin) and 3D conjugate heat transfer. The dissipation rate associated with the temperature variance is strongly impacted by the thermal boundary condition. For non-conjugate cases, a straightforward analytical analysis establishes the connection between the boundary condition, the temperature variance and the wall-normal part of the thermal dissipation rate at the wall. For the conjugate case, the two-point correlations of the thermal field in the solid domain confirms the existence of very large scale thermal structures.     

Invariant submodels of the Westervelt model with dissipation

We study three-dimensional Westervelt model of nonlinear hydroacoustics with dissipation. We received all its invariant submodels. With the help of invariant solutions, we explored some wave processes, specifying their physical meaning. The boundary value problems describing these processes are reduced to the nonlinear integro-differential equations. We established the existence and uniqueness of the solutions of these boundary value problems under some additional conditions. Also we considered the invariant solutions of rank 2 and 3. Mechanical relevance of the obtained solutions is as follows: (1) these solutions describe nonlinear and diffraction effects in ultrasonic fields of a special kind, (2) these solutions can be used as a test solutions in the numerical calculations performed in studies of ultrasonic fields generated by powerful emitters.     

一类平衡大气边界层边界条件研究

基于标准k-ε湍流模型,首先利用湍流粘度方程和剪切应力在整个边界层内恒定的假设,推导出一类耗散率表达式,并根据常用的湍动能入口剖面方程以及平均风速剖面方程,计算获得相应的耗散率方程;然后在输运方程中添加自定义源项,通过已经确定的平均速度方程、湍动能方程、耗散率方程计算得到相应输运方程的自定义源项表达式,并进行空风洞数值模拟,从而得到了一类满足平衡大气边界层的来流边界条件．通过将这种边界条件与由湍流平衡条件得到的边界条件进行比较,表明本方法获得的边界条件更适用．并且,本方法无需考虑修正壁面函数和修正湍流模型常数,因而计算更为简单,可为平衡大气边界层的研究提供一种新的思路．     

波浪与新型双排开孔圆筒防波堤相互作用三维数值模拟

双排开孔圆筒防波堤是基于圆筒、板式结构的一种复合式新型结构型式;基于不可压缩两相流模型建立三维数值波浪水槽,通过RNG k-ε湍流模型进行湍流封闭,并采用TruVOF方法捕捉自由液面,开展波浪与双排开孔圆筒防波堤相互作用数值模拟,探究相对排间距、开孔率对新型双排开孔圆筒防波堤消浪性能的影响,分析了后排开孔圆筒防波堤附近的复杂水动力现象和流动特性.结果表明,在本文研究工况范围内,沿程平均波高随相对排间距的增大先增大后减小,随开孔率的增大而增大,周期对沿程平均波高的影响没有明显规律;当B/D=9, e=23.11%时,新型双排开孔圆筒防波堤消浪效果最优,反射系数在0.4～0.46之间,透射系数在0.3～0.35之间,耗散系数在0.8～0.85之间;自由液面破碎、水气掺混、环状涡运动演化是新型双排开孔圆筒防波堤紊动耗能消波的主要原因;相对排间距会引起后排防波堤附近涡量分布以及剪切层形态的变化,从而导致不同的紊动特性,影响双排开孔圆筒防波堤消浪特性.研究结果可以为新型双排开孔圆筒防波堤工程设计与消浪机理研究提供理论支撑.     

Boundary Layer for the Navier-Stokes-alpha Model of Fluid Turbulence

We study boundary-layer turbulence using the Navier-Stokes-alpha model obtaining an extension of the Prandtl equations for the averaged flow in a turbulent boundary layer. In the case of a zero pressure gradient flow along a flat plate, we derive a nonlinear fifth-order ordinary differential equation, which is an extension of the Blasius equation. We study it analytically and prove the existence of a two-parameter family of solutions satisfying physical boundary conditions. Matching these parameters with the skin-friction coefficient and the Reynolds number based on momentum thickness, we get an agreement of the solutions with experimental data in the laminar and transitional boundary layers, as well as in the turbulent boundary layer for moderately large Reynolds numbers.