Experimental study of turbulence in isothermal and stably stratified homogeneous shear flows: Mean flow measurements

The evolution of freestream turbulence under the combined action of linear shear and stable linear temperature profile is investigated. The experiment is carried out in a small, open circuit, low-speed test cell that uses air as working fluid. The temperature gradient formed at the entrance to the test section by means of an array of 24 horizontal, differentially heated elements is varied to get a maximum Brunt-Vaisala frequency N_o[=({g/T_m}{∂T/∂y})^1/2] of 3.1⁻¹. Linear velocity profiles are produced using screens of variable mesh size. The Reynolds number Re_M based on centre-line velocity and mesh size is varied from 80 to 175. Isothermal studies are carried out in four different experiments with varying velocity gradients. The effect of inlet turbulence level on growth of turbulence is studied in these flows by keeping the shear parameter Sh (=(x/u)(∂u/∂y)) constant. The range of shear parameters considered is 2.5–7.0. Shear and stratification combined produce a maximum gradient Richardson number Ri_g (= N_o²/(∂u/∂y)²) of 0.0145. Results have been presented in terms of evolution of variance of velocity fluctuations, Reynolds shear stress and temperature fluctuations. Measurements show the following: In isothermal flows the growth rate of turbulence quantities depends on both shear parameter and inlet turbulence level. There are distinct stages in the evolution of the flow and that can be identified by the power-law exponent of growth of turbulence. Shear is seen to promote the growth of turbulence and accelerate it towards a fully developed equilibrium state. Stratification initially suppresses the growth of turbulence and, hence, enhances the degree of underdevelopment. Under these conditions shear becomes active and subsequently enhances the growth rate of turbulence quantities.     

Open channel turbulent flow over hemispherical ribs

This paper reports an experimental investigation of open channel turbulent flow over hemispherical ribs. A row of ribs consists of hemispheres closely placed to one another in the spanwise direction and cover the entire span of the channel. The pitch-to-height ratio is varied to achieve the so-called d-type, intermediate and k-type roughness. The Reynolds numbers based on water depth, h, and momentum thickness, θ, of the approach flow are respectively, Re_h = 28,100 and Re_θ = 1800. A particle image velocimetry is used to obtain detailed velocity measurements in and above the cavity. Streamlines, mean velocity and time-averaged turbulent statistics are used to study the effects of pitch-to-height ratio on the flow characteristics and also to document similarities and differences between the present work and prior studies over two-dimensional transverse rods. It was observed that interaction between the outer flow and the shear layers generated by ribs is strongest for k-type and least for d-type ribs. The results also show that hemispherical ribs are less effective in augmenting flow resistance compared to two-dimensional transverse ribs. The levels of the Reynolds stresses and budget terms increase with increasing pitch-to-height ratio inside the roughness sublayer.     

Simulation of wing-body junction flows with hybrid RANS/LES methods

In this paper, flows past two wing-body junctions, the Rood at zero angle of attack and NASA TN D-712 at 12.5° angle of attack, are investigated with two Reynolds-Averaged Navier-Stokes (RANS) and large eddy simulation (LES) hybrid methods. One is detached eddy simulation (DES) and the other is delayed-DES, both are based on a weakly nonlinear two-equation k–ω model. While the RANS method can predict the mean flow behaviours reasonably accurately, its performance for the turbulent kinetic energy and shear stress, as compared with available experimental data, is not satisfactory. DES, through introducing a length scale in the dissipation terms of the turbulent kinetic energy equation, delivers flow separation, a vortex or the onset of vortex breakdown too early. DDES, with its delayed effect, shows a great improvement in flow structures and turbulence characteristics, and agrees well with measurements.     

Non-linear oscillations with multiple forcing terms

The problem of determining the transient response of a non-linear oscillator of the form ü + u = εƒ(u,u) + E(t) is studied by the method of multiple time scales, using the symbolic computation system MACSYMA. when the excitation E(t) consists of a finite number of harmonic forcing terms. Here ε is a small parameter and ƒ(u,u) is a non-linear function of its arguments. In particular, the Van der Pol and Duffing oscillators are studied in detail. It is found that when the forcing frequencies are not close to each other or close to the primary resonance of the system, then the response of the system is analogous to the behavior when only one forcing term is present. However, when the forcing frequencies are close to each other or close to the primary resonance, then the behavior is quite different, exhibiting certain oscillations not observed in the case of one forcing term.     

Invariant analysis of the Reynolds stress tensor for a nuclear fuel assembly with spacer grid and split type vanes

Invariant analysis of the Reynolds stress tensor anisotropy can give an accurate and deep intuitive understanding of the turbulent structure of a turbulent flow. Lumley's triangle has proven to be a powerful representation of the invariant analysis of the second-order statistics collection provided by the Reynolds stress tensor. In the present work the spectral element code Nek5000 has been used to investigate the turbulent structure of the flow across a pressurized water reactor spacer grid with split type mixing vanes. Wall-resolved large eddy simulation of the flow in a prototypical rod bundle geometry at Re = 14,000 and P/D = 1.32 are performed and validated against particle image velocimetry data. The results are then used to perform an in-depth invariant analysis. The results show a reorganization of the Reynolds stresses components in the downstream region of the spacer grid. The mixing vanes orientation produces a symmetric behavior between sub-channels. The turbulent structure in the fully developed region has the typical behavior of fully-developed channel flow turbulence. When averaging the state across regions of the sub-channels, we observed a transition from disk-like turbulence in the mixing vanes region to rod-like turbulence in the fully developed region.     

Forced convection from an isolated heat source in a channel with porous medium

A numerical study is made of flow and heat transfer characteristics of forced convection in a channel that is partially filled with a porous medium. The flow geometry models convective cooling process in a printed circuit board system with a porous insert.The channel walls are assumed to be adiabatic. Comprehensive numerical solutions are acquired to the governing Navier-Stokes equations, using the Brinkman-Forchheimer-extended Darcy model for the regions of porous media. Details of flow and thermal fields are examined over ranges of the principal parameters; i.e., the Reynolds number Re, the Darcy number Da (≡K/H²), the thickness of the porous substrate S, and the ratio of thermal conductivities R_k (≡k_eff/k). Two types of the location of the porous block are considered. The maximum temperature at the heat source and the associated pressure drop are presented for varying Re, Da, S, and R_k. The results illustrate that as S increases or Da decreases, the fluid flow rate increases. Also, as R_k increases for fixed Da, heat transfer rates are augmented. Explicit influences of Re on the flow and heat transport characteristics are also scrutinized. Assessment is made of the utility of using a porous insert by cross comparing the gain in heat transport against the increase in pressure drop.     

Flow measurements inside a heated multiple rotating cavity with axial throughflow

This paper discusses experimental results from a multiple cavity test rig representative of a high pressure compressor internal air system. Measurements of the axial, tangential and radial velocity components are presented. These were made using a two component, laser doppler anemometry (LDA) system for a range of non-dimensional parameters representative of engine conditions (Re up to 4 × 10⁶ and Re_z up to 1.8 × 10⁵). Tests were carried out for two different sizes of annular gap between the (non-rotating) drive shaft and the disc bores.

The axial and radial velocities inside the cavities are virtually zero. The size of the annular gap between disc bore and shaft has a significant effect on the radial distribution of tangential velocity. For the narrow annular gap (d_h/b = 0.092), there is an increase of non-dimensional tangential velocity V/Ωr with radial location from V/Ωr < 1 at the lower radii to solid body rotation V/Ωr = 1 further into the cavity. For the wider annular gap (d_h/b = 0.164), there is a decrease from V/Ωr > 1 at the lower radii to solid body rotation further into the cavity. An analysis of the frequency spectrum obtained from the tangential velocity measurements is consistent with a flow structure in the r– plane consisting of pairs of contra rotating vortices.     

Numerical study of the parametric evolution of bifurcations in the three-dimensional ring problem of N bodies

We study the dynamics of a massless particle in an annular configuration of N bodies, N − 1 of which have equal masses m and are located in equal distances on a fictitious circle and one has mass βm and is located at the center of the circle. Our interest is focused on the bifurcation points from planar to three-dimensional families of symmetric periodic orbits in the above problem. We study numerically the evolution of these bifurcation points with respect to the variation of the mass parameter β. In particular we investigate the continuous evolution of bifurcation points for values of β from 2 up to 1000. The two distinct cases of the system’s behavior at β = 2 and 1000 are examined comparatively and various conclusions are drawn regarding the overall dynamical evolution of the three-dimensional system as the relative mass of the central body grows.     

Two-dimensional instabilities of generalized Korteweg-de Vries waves

Instabilities of the generalized Korteweg-de Vries ((u_t+₁u^mu_x+₂uⁿu_x+u_xxx)_x+₃u_yy = 0) waves wi th respect to two-dimensional infinitesimal longitudinal disturbances are investigated using the Infeld-Rowlands method. A linear dispersion relation expressed as a cubic equation in w₁ is derived and instabilities of waves are discussed.     

湍流边界层外区相干结构的三维波模型

根据流动稳定性理论,提出了一种三维波模型来描述湍流边界层外区大尺度相干结构。计算所得流线图和等涡量线图较罗纪生,周恒（1993）的二维波模型更符合实验结果。说明该三维模型能够较好地反映湍流边界层外区大尺度相干结构的物理特征。     

Reconstruction of a quasi-instantaneous image of coherent structures from hotwire signals obtained by a multi-point simultaneous measurement system

The turbulent velocity components (u, v) at 11 points in a reciprocating oscillatory turbulent flow have been measured simultaneously by a set of eleven X-type hotwire probes located in a plane perpendicular to the mean flow. Using a conditional sampling technique and a new method of data analysis for the inverse estimation of flow fields called the “virtual plate/load and MASCON model”, a quasi-instantaneous three-dimensional image of coherent structures of turbulence was first reconstructed directly from the experimental velocity data. The quasi-instantaneous image was expressed in terms of the velocity components u, v, w and the vorticity components ω_x ω_y, ω_z and we found that the large-scale coherent structure was composed of a pair of counter-rotating fluid motions with asymmetry which was quite different from that of the ensemble-averaged one. Flow patterns induced by the large-scale structure have been clarified by perspective representations visualized by computer simulations that produce timelines and streaklines of fluid particle traces. Results showed that the new experimental method was applicable for investigating the three-dimensional feature of coherent structures including asymmetry.     

A note on a new theory of turbulence

In this paper,the creation and annihilaton of turbulent eddies are described aselementary particles in the quantum field theory.An elementary particle may be consideredas a solid entity as it exists in quantum theory,but a turbulent eddy is often changed in sizeand shape with time due to its energy dissipation in a turbulent field.Therefore,in order toapply the method of the quantum field theory to the turbulent field by analogy,the entity ofthe same eddy should be defined firstly.According to the linearized theory,the turbulenteddies with the similarity character in lime duration may be considered as the entity of thesame eddy,and the creation and annihilation of turbulent eddies without the similarcharacters are related to the interaction term φ_2 in equation(2.6).Then,the creationoperator and annihilation operator similar to those in the quantum field theory are used todescribe the state of turbulent eddy field.Finally,a“Schrǒdinger”equation of turbulenteddies is formulated based upon the nonline     

KOLMOGOROV BEHAVIOR OF NEAR-WALL TURBULENCE AND ITS APPLICATION IN TURBULENCE MODELING

The near-wall behavior of turbulence is re-examined in a way different from that proposed by Hanjalic and Launder¹ and followers^2,3,4,5. It is shown that at a certain distance from the wall, all energetic large eddies will reduce to Kolmogorov eddies (the smallest eddies in turbulence). All the important wall parameters, such as friction velocity, viscous length scale, and mean strain rate at the wall, are characterised by Kolmogorov microscales. According t o this Kolmogorov behavior of near-wall turbulence, the turbulence quantities, such as turbulent kinetic energy, dissipation rate, etc. at the location where the large eddies become “Kolmogorov” eddies, can be estimated by using both direct numerical simulation (DNS) data and asymptotic analysis of near-wall turbulence. This information will provide useful boundary conditions for the turbulent transport equations. As a n example, the concept is incorporated in the standard κ - εmodel which is then applied t o channel and boundary layer flows. Using appropriate boundary conditions (based on Kolmogorov behaviour of near-wall turbulence), there is no need for any wall-modification to the κ - ε equations (including model constants). Results compare very well with the DNS and experimental data.     

An application of Nagumo''s lemma to some singularly perturbed systems

The existence and asymptotic behavior as ε → 0⁺ of periodic, almost periodic, and bounded solutions of the differential system x = f(t, x, y, ε), Ωy′ = g(t, x, y, ε), are considered where x, f; are n-vectors, y, g are m-vectors and Ω = diag{ε^h₁}…, ε^h_m for integral h_i, h₁ h₂ …, h_m. The principal tools are a lemma of Nagumo which allows the construction of appropriate upper and lower solutions and the asymptotic theory of singularly perturbed linear differential systems.     

提取壁湍流相干结构的数字滤波法

以三丝热线探头测得平板湍流边界层的数据为对象，提出用数字滤波技术将湍流信号分解为接近各向同性的小尺度涡和非各向同性的大尺度涡的方法。并用条件采样技术从大涡信号中提取相干结构。     

Numerical Simulations of the Sandia Flame D Using the Eddy Dissipation Concept

A turbulent piloted methane/air diffusion flame (Sandia Flame D) is calculated using both compressible Reynolds-averaged and large-eddy simulations (RAS and LES, respectively). The Eddy Dissipation Concept (EDC) is used for the turbulence-chemistry interaction, which assumes that molecular mixing and the subsequent combustion occur in the fine structures (smaller dissipative eddies, which are close to the Kolmogorov length scales). Assuming the full turbulence energy cascade, the characteristic length and velocity scales of the fine structures are evaluated using a standard k- ?? turbulence model for RAS and a one-equation eddy-viscosity sub-grid scale model for LES. Finite-rate chemical kinetics are taken into account by treating the fine structures as constant pressure and adiabatic homogeneous reactors (calculated as a system of ordinary-differential equations (ODEs)) described by a Perfectly Stirred Reactor (PSR) concept. A robust implicit Runge-Kutta method (RADAU5) is used for integrating stiff ODEs to evaluate reaction rates. The radiation heat transfer is treated by the P1-approximation. The assumed β-PDF approach is applied to assess the influence of modeling of the turbulence-chemistry interaction. Numerical results are compared with available experimental data. In general, there is good agreement between present simulations and measurements both for RAS and LES, which gives a good indication on the adequacy and accuracy of the method and its further application for turbulent combustion simulations.     

Computational and experimental study of annular photo-reactor hydrodynamics

The performance of ultraviolet (UV) reactors used for water treatment is greatly influenced by the reactor hydrodynamics due to the non-homogeneity of the radiation field. Reliable modeling of the reactor flow structures is therefore crucial for the design process. In this study, the turbulent flow through two characteristic annular UV-reactor configurations, with inlets concentric (L-shape) and normal (U-shape) to the reactor axis, was investigated through computational fluid dynamic (CFD). The modeling results were evaluated with the velocity profiles from particle image velocimetry (PIV) experiments. The influence of mesh structure and density, as well as three turbulence models: Standard κ–, Realizable κ–, and Reynolds stress model (RSM), on the simulation results were evaluated. Mesh-independent solutions were achieved at mean cell volumes of 5 × 10⁻⁹ m³. The Realizable κ– displayed the best overall match to the experimental PIV measurements. In general, the CFD models showed a close agreement with the experimental data for the majority of the reactor domain and captured the influences of reactor configuration and internal reactor structures on the flow distribution. The validated CFD hydrodynamic models could be integrated with kinetic and radiation distribution models for UV-reactor performance simulation.     

Solutions of some classes of second order non-linear ordinary differential equations

A second order non-linear ordinary differential equation satisfied by a homogeneous function of u and v where u is a solution of the linear equation ÿ + p(t)ÿ + r(t)y = 0 and v = ωu, ω being an arbitrary function of t, is obtained. Defining ω suitably in two specific cases, solutions are obtained for a non-linear equation of the form ÿ + p(t)ÿ + q(t)y = μÿ²y^{−1 +} f(t)yⁿ where μ ≠ 1, n≠ 1. Applying our results, some classes of equations of the above type possessing solutions involving two or one or no arbitrary constants are derived. Some illustrative examples are also discussed.     

A study of properties of vortex stretching and enstrophy generation in numerical and laboratory turbulence

Dynamically relevant alignments are used in order to show that regions with weak vorticity are not structureless, non-Gaussian and dynamically not passive. for example, the structure of vorticity in quasi-homogeneous/isotropic turbulent flows is associated with strong alignment between vorticity ω and the eigenvectors of the rate of strain tensor λ_i (especially — but not only — between ω and λ₂) rather than with intense vorticity only. Consequently, much larger regions of turbulent flow than just those with intense vorticity are spatially structured. The whole flow field — even with the weakest measurable enstrophy — is strongly non-Gaussian, which among other things is manifested in strong alignment between vorticity and the vortex stretching vector W_i ≡ ω_jS_ij. It is shown that the quasi-two-dimensional regions corresponding to large cos(ω, λ₂) are qualitatively different from purely two-dimensional ones, e.g. in that they possess essentially nonvanishing enstrophy generation, which is larger than its mean for the whole field.