Instability and Receptivity of Laminar Wall Jets

Results of eigenvalue analysis based on global and local eigenvalue considerations are presented. A collocation method with the Chebyshev polynomial approximation has been used for the global eigenvalue analysis. The results explain the appearance of a second unstable mode. In the case of real frequencies with Reynolds number R < 381 there is only one unstable mode. This mode coalesces at R≈ 381 with a stable mode. At R > 381 they become separated by interchannging their branches, then the second unstable mode occurs. The receptivity problem has been considered with respect to perturbations emanating from a wall. The results illustrate that high-frequency modes have a stronger response than low-frequency modes. It is shown that the method of expansion in a biorthogonal eigenfunction system and the method used by Ashpis and Reshotko are equivalent with regard to the receptivity problem solution. Received: 29 March 1996 and accepted 26 November 1996     

Mathematical and Physical Constraints on Large-Eddy Simulations

We examine the mathematical constraints on the filtering operation in large-eddy simulation (LES), and the physical constraints on the formulation of subgrid scale (SGS) models. The mathematical constraints on filtering arise from the assumption of commutativity between the filtering operation and the differential operators: this breaks down for finite domains and for non-uniform filter kernels. The physical constraints on the modelling are twofold; invariance principles require any model to be invariant under a group of transformations: the most stringent of these being the principle of frame indifference. In addition, realizability requires that the SGS model should have the same mathematical properties as the term it replaces, which leads to further constraints on the modelling. Finally, we investigate the effects of commutation and realizability for two simulated cases: forced homogeneous isotropic turbulence in a box and fully developed channel flow. In particular, we look for correlations between the commutation errors and the non-realizable regions, and the large-scale resolved flow structures in the simulations. Received: 17 June 1996 and accepted 3 April 1997     

Backscatter Models for Large-Eddy Simulations

Using previously established properties of nonlinear subgrid-scale interactions we derive deterministic models of backscatter for large-eddy simulations. The models provide approximately equal amounts of forward and inverse transfer and consequently affect only weakly the total kinetic energy of turbulence. The modeling procedures are tested on a simple case of forced isotropic turbulence with the inertial range and in turbulent channel flow. The presence of backscatter increases the physical realism of large-eddy simulations. Received: 24 January 1997 and accepted 20 March 1997     

Large-Eddy Simulation of Transition to Turbulence in Boundary Layers

Large-eddy simulation (LES) results for laminar-to-turbulent transition in a spatially developing boundary layer are presented. The disturbances are ingested into a laminar flow through an unsteady suction-and-blowing strip. The filtered, three-dimensional time-dependent Navier–Stokes equations are integrated numerically using spectral, high-order finite-differences, and a three-stage low-storage Runge–Kutta/Crank–Nicolson time-advancement method. The buffer-domain technique is used for the outflow boundary condition. The localized dynamic model used to parametrize the subgrid-scale (SGS) stresses begins to have a significant impact at the beginning of the nonlinear transition (or intermittency) region. The flow structures commonly found in experiments are also observed in the present simulation; the computed linear instability modes and secondary instability $\Lambda$-vortex structures are in agreement with the experiments, and the streak-like structures and turbulent statistics compare with both the experiments and the theory. The physics captured in the present LES are consistent with the experiments and the full Navier–Stokes simulation (DNS), at a significant fraction of the DNS cost. A comparison of the results obtained with several SGS models shows that the localized model gives accurate results both in a statistical sense and in terms of predicting the dynamics of the energy-carrying eddies, while requiring fewer ad hoc adjustments than the other models. Received: 5 April 1996 and accepted 27 March     

Statistics of Particle Accumulation in Spatially Developing Turbulent Boundary Layers

We present the results of a Direct Numerical Simulation of a particle-laden spatially developing turbulent boundary layer up to Re _θ ?=?2500. Two main features differentiate the behavior of inertial particles in a zero-pressure-gradient turbulent boundary layer from the more commonly studied case of a parallel channel flow. The first is the variation along the streamwise direction of the local dimensionless parameters defining the fluid-particle interactions. The second is the coexistence of an irrotational free-stream and a near-wall rotational turbulent flow. As concerns the first issue, an inner and an outer Stokes number can be defined using inner and outer flow units. The inner Stokes number governs the near-wall behavior similarly to the case of channel flow. To understand the effect of a laminar-turbulent interface, we examine the behavior of particles initially released in the free stream and show that they present a distinct behavior with respect to those directly injected inside the boundary layer. A region of minimum concentration occurs inside the turbulent boundary layer at about one displacement thickness from the wall. Its formation is due to the competition between two transport mechanisms: a relatively slow turbulent diffusion towards the buffer layer and a fast turbophoretic drift towards the wall.     

On the Distribution and Scaling of Convective Wavespeeds in the Shear Layers of Heated Supersonic Jets

The noise generated by supersonic plumes is of growing concern given the enormous peak noise intensity radiated by tactical aircraft engines. A key component of this noise is the enhanced radiation of mixing noise caused by large scale eddies convecting supersonically relative to the surrounding quiescent medium. As very little data exist for eddy convection in high Reynolds number, supersonic plumes, our current ability to develop concepts that alter compressible eddy convection is limited. Herein we present new experimental data of eddy convective wavespeeds in the developing shear layer of supersonic heated jets. A new scaling of the wavespeed in radial similarity coordinates is proposed which takes into account the influence of the ratio of static densities between the jet and ambient streams. In particular, we observe a structural change in wavespeed spectra at the end of the potential core—in addition to high turbulence levels, the potential core breakdown region can have enhanced eddy wavespeeds, increasing noise radiation efficiency. The results provide a first examination of the interplay of density ratio effects and the dynamic breakdown process of the potential core in supersonic jets—physics integral to the noise generation process.     

Large-Eddy Simulations of Forced Three-Dimensional Impinging Jets

Large-eddy simulations of the flow field around twin three-dimensional impinging jets were carried out to simulate the near-ground hover configuration of a vertical takeoff and landing (VTOL) aircraft. Both the impinging jet and the upwash caused by the collision of the wall jets are modeled in this study. The evolution of the vortical structures in the impinging jet flow field, due to the introduction of axisymmetric and azimuthal perturbations at the jet exit, has been investigated. The vortical structures formed in the jet shear layer due to azimuthal forcing, show significant three-dimensional vortex stretching effects when compared to the structures formed during axisymmetric forcing. Breakdown of the large-scale structures into smaller vortices also occurs much earlier during azimuthal forcing. When compared to the upwash formed during axisymmetric forcing, the azimuthally perturbed jet forms an upwash that is less coherent and results in a weaker upload or lift-off force on the aircraft undersurface. Comparison with available experimental data indicates good agreement for the centerline velocity decay, the wall pressure variation and the phase speed of the vortical structures.     

Large Eddy Simulations of Unconfined Non-reacting and Reacting Turbulent Low Swirl Jets

The low swirl flow is a novel method for stabilizing lean premixed combustion to achieve low emissions of nitrogen oxides. Understanding the characteristics of low swirl flows is of both practical and fundamental interest. In this paper, in order to gain better insight into low swirl stabilized combustion, large eddy simulation and dynamically thickened flame combustion modeling are used to characterize various features of non-reacting and reacting low swirl flows including vortex breakdown, shear layers’ instability, and coherent structures. Furthermore, four test cases with different equivalence ratios are studied to evaluate the effects of equivalence ratio on the flame and flow characteristics. A finite volume scheme on a Cartesian grid with a dynamic one equation eddy viscosity subgrid model is used for large eddy simulations. The obtained results show that the combustion heat release and increase in equivalence ratio toward the stoichiometric value decrease the local swirl number of the flow field, while increasing the flow spreading at the burner outlet. Results show that the flame becomes W shaped as the equivalence ratio increases. Moreover, the combination of the swirling motion and combustion heat release temporally imposes a vortex breakdown in the post-flame region, which leads to occurrence of a transient recirculation zone. The temporal recirculation zone disappears downstream of the burner outlet due to merging of the inner shear layer from all sides at the centerline. Also, various analyses of shear layers’ wavy and vortical structures show that combustion heat release has the effect of decreasing the instability amplitude and vortex shedding frequency.     

A Dissipation Rate Equation for Low-Reynolds-Number and Near-Wall Turbulence

Two-equation turbulence models are usually formulated for specific flow types and are seldom validated against a variety of flows to account for near-wall and low-Reynolds-number effects simultaneously. In addition to low-Reynolds-number effects, near-wall flows also experience wall blocking, which is absent in free flows. Consequently, near-wall modifications to two-equation models could be quite different from low-Reynolds-number corrections. Besides, it is known that existing two-equation models perform poorly when used to calculate plane wall jets and two-dimensional backstep flows. These problems could be traced to the modeling of the dissipation rate equation. In this paper an attempt is made to improve the modeling of the dissipation rate equation so that it could successfully predict both free and wall-bounded shear flows including plane wall jets and backstep flows. The predictions are compared with experimental and direct numerical simulation data whenever available. Most of the data used are obtained at low Reynolds numbers. Good correlation with data is obtained. Therefore, for the first time, a model capable of correctly predicting free and wall-bounded shear flows, backstep flows, and plane wall jets is available. Received: 12 December 1995 and accepted 12 November 1996     

Large Eddy Simulations of Turbulent Mixing Layers Excited with Two Frequencies

In this study, we investigate the energy transfer during the pairing and merging process of two vortices into one in an excited turbulent mixing layer using Large Eddy Simulations. We present simulations of natural and periodically excited mixing layers for validation purposes and study the vortex pairing dynamics by exciting the mixing layer by two frequencies. The results help in understanding the effects of the energy transfer in the long-wave turbulent spectrum and assessing the role of backscatter.     

Interaction of Two-Dimensional Trailing Vortex Pair with a Shear Layer

The basic laws governing the interaction of a two-dimensional vortex pair with a shear layer of constant thickness are considered. The main idea of the study is to develop and adapt a simplified representation of a hydrodynamic flow based on a point-vortex model simulating the actual interaction of full-scale vortex patterns over the ground surface. It is shown that vortices with vorticity opposite in sign to the shear layer may stop or even ricochet from this layer, while the other vortex may penetrate through the layer. Numerical results are presented as plots and analyzed     

On the Interaction of Turbulent Shear Layers with Harmonic Perturbations

The problem of coherent perturbations in a turbulent shear layer is considered for the purpose of developing a mathematical model based on a triple decomposition that extracts the coherent components of random fluctuations. The governing equations for the mean and the coherent parts of flow are derived, assuming the eddy-viscosity equivalence for the random part of flow, and solved by iterations to provide a coupled solution of the problem as a whole. Calculations agree well with experimental data in the upstream part of the layer where the mean–coherent flow interaction is the most important. In this region, the interaction changes the mean flow velocity distribution in such a manner that the neutral stability curve is shifted upstream relative to its position in the undisturbed layer and the perturbation intensity decreases further downstream. Experiments show that the coherent waves suppress the turbulent Reynolds stress production downstream of this region, but the model fails to predict the layer spreading correctly probably due to an inadequate turbulence closure of the mean flow. For the case of a turbulent mixing layer, we suggest a new closure relation that takes into account this coherent-random interaction.     

斜向自由剪切层流动特性的实验研究

本文用恒温热线风速仪对斜向自由剪切层流场进行了测量,得到了流场动量厚度、平均速度和二阶脉动速度相关统计量的变化规律;给出了不同位置处纵、展方向上速度信号随时间变化的波形、概率密度分布、自相关和互相关函数以及功率谱;表明斜向自由剪切层流场中有螺旋形涡存在的特征.     

Localization of Shear Waves Near Layers Separating Two Regularly Laminated Half-Spaces

The existence conditions for surface and normal shear waves in finite and infinite periodically laminated structures with broken translational symmetry are studied theoretically and numerically. The problems posed are reduced to systems of linear algebraic equations. The existence condition for their nontrivial solutions yield dispersion relations. Conditions for the existence of surface and normal shear waves are established. Some results are plotted. The dependence of the dispersion spectrum on the physical and geometrical properties of the symmetry breaker is studied__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 128–134, January 2005.     

Shear Testing of Polypropylene Materials Analysed by Digital Image Correlation and Numerical Simulations

Distributions of shear strains and strain states (triaxiality) were analysed for two in-plane shear test fixtures (Iosipescu and V-notched rail), using digital image correlation and numerical simulations. Three different polypropylene-based materials (two talc-filled compounds and one unfilled homopolymer) were tested. The three materials behaved differently in the shear tests. Most notably, cracks developed in tension near the notches for the particle-filled materials, while the unfilled homopolymer did not fracture. There were also differences between the materials regarding strain localisation between the notches, strain rates vs. strain level (for a given cross-head speed), thickness change in the sheared section, and triaxiality. The yield stresses in shear, uniaxial tension and uniaxial compression showed pressure sensitivity. At least for equivalent strain rates below 1?s^?1, the strain rate sensitivity of the yield stress was approximately the same in these three stress states. The stress?Cstrain curves obtained with the two methods were quite similar for these materials. There were some differences between the methods regarding the ease of mounting and aligning specimens, the complexity of specimen deformation patterns, and the uniformity of the shear strain distribution between the notches.     

Numerical Simulation of Particle Dispersion in a Spatially Developing Mixing Layer

Although there have been several numerical studies on particle dispersion in mixing layers, most of them have been conducted for temporally evolving mixing layers. In this study, numerical simulations of a spatially developing mixing layer are performed to investigate particle dispersion under various conditions. The full compressible Navier--Stokes equations are solved with a high-order compact finite difference scheme, along with high-order time-integration. Accurate non-reflecting boundary conditions for the fluid flow are used, and several methods for introducing particles into the computational domain are tested. The particles are traced using a Lagrangian approach assuming one-way coupling between the continuous and the dispersed phases. The study focuses on the roles of the large-scale vortex structures in particle dispersion at low, medium and high Stokes numbers, which highlights the important effects of interacting vortex structures in nearby regions in the spatially developing mixing layer. The effects of particles with randomly distributed sizes (or Stokes numbers) are also investigated. Both instantaneous flow fields and statistical quantities are analyzed, which reveals essential features of particle dispersion in spatially developing free shear flows, which are different from those observed in temporally developing flows. The inclusion of the gravity not only modifies the overall dispersion patterns, but also enhances stream-crossing by particles. Received 7 June 2001 and accepted 19 February 2002     

Effects of Localized Micro-blowing on a Spatially Developing Flat Turbulent Boundary Layer

Flow, Turbulence and Combustion - Direct numerical simulation (DNS) is used to investigate the turbulent flat-plate boundary layer with localized micro-blowing. The 32?×?32 array...     

Large Eddy Simulation of Turbulent Reacting Shear Layers Including Finite-Rate Chemistry and Detailed Diffusion Processes

Large eddy simulations (LES) of turbulent temporal shear layers with hydrogen chemistry are performed. In these simulations, approximate deconvolution is applied as an implicit subgrid-scale modeling approach to a reacting flow in combination with a steady flamelet model for the filtered heat release term. No additional heuristical or physical subgrid models are used. The formulation of the flamelet equations in physical space does not only allow to consider a detailed reaction scheme and the extinguished phase but also to take into account detailed diffusion mechanisms (Soret and Dufour effects, multicomponent diffusion coefficients). Two different levels of diffusion approximations are investigated in this work, the aim of which is twofold: Firstly, to verify approximate deconvolution as a tool for convective transport of mass, momentum and energy in gas flow, by comparing the LES results with those of a direct numerical simulation and secondly, to investigate the influence of detailed diffusion on the laminar flamelets and the LES results.