Large Eddy Simulation (2D) of a Reacting Plane Mixing Layer Using Filtered Density Function Closure

The filtered density function (FDF) is implemented for a two-dimensional, large eddy simulation (LES) of a gas phase, spatially developing, reacting and non-reacting, constant-density, plane mixing layer in a flow regime prior to the mixing transition where the flow is mainly two-dimensional. The unresolved scalar fluctuations are taken into account by considering the probability density function (PDF) of subgrid scale (SGS) scalar quantities following the FDF approach. In the derived FDF transport equation, the effect of chemical reactions appears in a closed form. The Lagrangian Monte Carlo scheme is used to solve the FDF transport equation. The applicability and performance of the FDF for LES of a reacting plane mixing layer are assessed by comparisons with experimental measurements. In non-reacting flow, the calculated mean streamwise velocity profiles and mean mixture fraction profiles relax to self-similarity, which is in satisfactory agreement with the measurements. In reacting flow, the FDF calculation provided a satisfactory accuracy in comparison with measurements of mean reactant and product concentration. The increase in the total amount of product formation in the flip case demonstrates the asymmetric characteristics of the entrainment and mixing characteristics in the mixing layer. This revised version was published online in July 2006 with corrections to the Cover Date.     

Numerical simulation of supersonic reacting mixing layer

In this paper, the supersonic chemically reacting mixing layer is simulated with the third order ENN scheme, based on the Navier-Stokes equations, containing transport equations of all species. The numerical results show that the thickness of mixing layer increases gradually along the flow direction, and that the Kelvin-Helmholtz instabilities may not exist in mixing layer flows. The project supported by the National Natural Science Foundation of China     

可压缩燃烧反应转捩混合层直接数值模拟

针对三维时间发展可压缩氢/氧非预混燃烧反应平面自由剪切混合层,采用5阶迎风/6阶对称紧致混合差分格式以及3阶显式Runge-Kutta时间推进方法,直接数值模拟了伴随燃烧产物生成和反应能量释放, 流动受扰动激发失稳并转捩的演化过程. 在转捩初期, 获得了${\it\Lambda}$涡、马蹄涡等典型的大尺度拟序结构,观察到了流动失稳后发生双马蹄涡三维对并的现象, 大尺度结构呈较好的对称性.在流动演化后期, 大尺度结构逐次破碎形成小尺度结构, 混合层进入转捩末期,呈明显的不对称性.      

Approximate two-dimensional equations of vortex flow in a plane layer with solid boundaries

Approximate two-dimensional equations governing turbulent vortex flows in plane fluid layers are considered. The equations were derived by the author in his earlier studies using the shallow water approximation and neglecting circulatory flows in the layer cross-sections. It is shown that, due to the centrifugal effect in the vortex flow, return flows in the layer cross-sections have only a slight influence on the fluid flow in the plane layer and can be neglected.     

混合层强化混合的数值研究

受 Ｗａｎｇ ＆ Ｆｉｅｄｌｅｒ（１９９７）的实验的启发，采用高阶精度的差分格式，通过数值模拟的方法，研究了二维混合层及限于两平板间的二维混合层（二维受限混合层）入口处加振动对提高混合层混合效率的作用．计算结果表明：对二维混合层，振动的频率越低，在混合层中产生的大尺度涡结构的尺度越大，在频率很低时，涡具有相似性；对限于两平板间的二维混合层，在一定的振动频率下，混合层中产生的涡较大而且破碎得也较好，这将有利于混合．这一结论与 Ｗａｎｇ ＆ Ｆｉｅｄｌｅｒ（１９９７）的实验观测到的结果是一致的．     

Statistical theory applied to a vortex street generated from meander of a jet

Statistic features of a vortex street formed by instability of a jet are investigated by numerical calculation and statistic theory. A formation process of a vortex street is numerically calculated using a simple barotropic quasi-geostrophic system: a jet in the initial state begins to meander owing to its instability and vortices are formed in both flanks of the jet and become a steady vortex street. Statistic theory of vorticity mixing for two-dimensional fluid, which describes the statistically steady equilibrium state based on the maximum entropy assumption, is applied to the numerically obtained features of the steady vortex street. The theoretically derived relation between stream function and potential vorticity explains the results in the numerical calculation very well. However, in the numerical calculation, there remain regions where the fluid is not mixed well. By calculating mixing process of another scalar, the unmixed region is clearly shown on the physical plane.     

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.     

Characteristics of flow from an oxy-fuel burner with separated jets: influence of jet injection angle

This paper presents an experimental study of flow development and structure on a separated jet burner in reacting and non-reacting flows. Effects of deflection jets in an aligned configuration of three round jets are emphasized. The idea is based on the confinement of a central jet of fuel by two side jets of oxygen to improve mixing, to control flame stability, and to reduce pollutant emissions. The fields of mean velocity and fluctuation intensity were measured using Particle Image Velocimetry. The deflection of jets has a considerable effect on the dynamic behavior and on the flame characteristics. Results showed that the deflection of jets favors mixing and accelerates merging and combining of jets to a single one. Measurements in reacting flow showed a high influence of combustion on dynamic fields. Compared to non-reactive case, in combustion, larger radial expansion and higher velocity were observed, particularly, above the stabilization point of the flame.     

STUDY ON THE FUEL AIR MIXING INDUCED BY A SHOCK WAVE PROPAGATING INTO A H_2-AIR INTERFACE

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｆｕｅｌａｉｒｍｉｘｉｎｇｉｎａｓｈｅａｒｌａｙｅｒｆｌｏｗｉｓａｎｉｍｐｏｒｔａｎｔｐｒｏｂｌｅｍｉｎｓｔｕｄｙｉｎｇｃｏｍｐｒｅｓｓｉｂｌｅｆｌｏｗａｎｄｓｕｐｅｒｓｏｎｉｃｃｏｍｂｕｓｔｉｏｎ ,ｓｕｃｈａｓｆｕｅｌｄｉｆｆｕｓｉｏｎａｎｄｍｉｘｉｎｇｉｎａＳｃｒａｍｊｅｔ[1].Ｒｏｓｈｋｏ[2 ]ｓｔｕｄｉｅｄｅｘｐｅｒｉｍｅｎｔａｌｌｙｔｈｅｐｈｅｎｏｍｅｎｏｎｏｆｆｕｅｌａｉｒｍｉｘｉｎｇｉｎａｓｕｂｓｏｎｉｃｓｈｅａｒｆｌｏｗａｎｄｆｏｕｎｄｌａｒｇｅ ,ｃｏｈ…     

超声速边界层/混合层组合流动的稳定性分析

利用可压缩线性稳定性理论研究了超声速混合层考虑壁面影响流动时的失稳特性. 基本流场选取了具有不同速度特征的2 股均匀来流,进入存在上下壁面的流道中. 混合层与边界层的距离为1~3 个边界层厚度,其中壁面取为绝热壁. 分析了该流动在超声速情况下的稳定性特征,同时还讨论了不同波角下的三维扰动波的演化特点,并与二维扰动波进行了比较和分析. 研究结果表明,在此流动情况下,边界层流动和混合层流动的稳定性特征同时存在,并互有影响,其流动稳定性特征既有别于单纯的平板边界层,也有别于单纯的平面混合层,呈现出了新的稳定性特征.      

超声速边界层/混合层组合流动的稳定性分析简

利用可压缩线性稳定性理论研究了超声速混合层考虑壁面影响流动时的失稳特性. 基本流场选取了具有不同速度特征的2 股均匀来流,进入存在上下壁面的流道中. 混合层与边界层的距离为1~3 个边界层厚度,其中壁面取为绝热壁. 分析了该流动在超声速情况下的稳定性特征,同时还讨论了不同波角下的三维扰动波的演化特点,并与二维扰动波进行了比较和分析. 研究结果表明,在此流动情况下,边界层流动和混合层流动的稳定性特征同时存在,并互有影响,其流动稳定性特征既有别于单纯的平板边界层,也有别于单纯的平面混合层,呈现出了新的稳定性特征.     

Study on the instability in separating–reattaching flow over a surface-mounted rib

A numerical study on the flow structure and instability in the separated–reattached flow over a surface-mounted rib at Re = 1000 is performed using large eddy simulation. It is found that the phenomenon of vortex pairing, which has been extensively observed in similar flows, exists in the separation zone. Based on the spectral analysis, the Kelvin–Helmholtz (K-H) instability of shear layer at St ≈ 0.361 (St ≡ fh/U₀) and its subharmonic at St ≈ 0.18 are found. It is assumed that the K-H instability reduces to its subharmonic through the vortex pairing. This process is further confirmed by the flow visualisation. The two-dimensional (2D) structures are subjected to sinusoidal undulation along the spanwise and observed to undergo helical pairing process, which is attributed to the transformation of 2D structures into 3D. However, the low frequency due to flapping of the shear layer is not found.     

Topological visualisation of focal structures in free shear flows

This paper describes a method for identifying and visualising the three-dimensional geometry of focal (vortex) structures in complex flows. The method is based primarily on the classification of the local topology as it is identified from the values of the velocity gradient tensor invariants. The identification of the local topology is reference frame invariant. Therefore, focal (vortex) structures can be unambiguously identified in these flows. A novel flow visualisation method is introduced whereby focal structures are rendered using a solid model view of the local topology. This new approach is applied to the identification of focal structures in three-dimensional plane mixing layer and plane wake flows.     

Study on the Fuel Air Mixing Induced by a Shock Wave Propagating into a H2-Air Interface

2nd-order upwind TVD scheme was used to solve the laminar, fully Navier-Stokes equations. The numerical simulations were done on the propagation of a shock wave with Ma _S = 2 and 4 into a hydrogen and air mixture in a duct and a duct with a rearward step. The results indicate that a swirling vortex may be generated in the lopsided interface behind the moving shock. Meanwhile, the complex shock system is also formed in this shear flow region. A large swirling vortex is produced and the fuel mixing can be enhanced by a shock wave at low Mach number. But in a duct with a rearward step, the shock almost disappears in hydrogen for Ma _S = 2. The shock in hydrogen will become strong if Ma _S is large. Similar to the condition of a shock moving in a duct full of hydrogen and air, a large vortex can be formed in the shear flow region. The large swirling vortex even gets through the reflected shock and impacts on the lower wall. Then, the distribution of hydrogen behind the rearward step is divided into two regions. The transition from regular reflection to Mach reflection was observed as well in case Ma _S = 4.     

NUMERICAL RESEARCH ON THE COHERENT STRUCTURES IN A MIXING LAYER WITH CROSS-SHEAR

The evolution of a time-developing mixing layer with cross-shear is simulated numerically using a pseudo-spectral method. The results indicate that stretching by the rollers is responsible for the formation of the streamwise vortices in a mixing layer with cross-shear. When the cross-shear is relatively strong (such as θ=20°), the co-rotating streamwise vortices related to the early spanwise Kelvin–Helmholtz instability are intensified rapidly by stretching and collapse into rib-shaped vortices, which are very similar to the ribs in a plane mixing layer. Atθ =20°, the vortex corresponding to the “quadrupole” in a plane mixing layer is also observed in the core region, and a set of streamwise vortices with signs opposite to those of the vortices containing the ribs lie at the spanwise braid region. The counterparts of the ribs, however, are of flat shape and much weaker. When θ is up to 30°, the ribs are so strong that their counterparts cannot develop. When θ is down to 10°, the symmetry of the streamwise vortices is more obvious, but the ribs do not form. Additionally, it is revealed that the introduction of the strong cross-shear results in enhanced mixing compared to a two-dimensional mixing layer.     

Linear stability of two-dimensional steady flow in wavy-walled channels

Linear stability of fully developed two-dimensional periodic steady flows in sinusoidal wavy-walled channels is investigated numerically. Two types of channels are considered: the geometry of wavy walls is identical and the location of the crest of the lower and upper walls coincides (symmetric channel) or the crest of the lower wall corresponds to the furrow of the upper wall (sinuous channel). It is found that the critical Reynolds number is substantially lower than that for plane channel flow and that when the non-dimensionalized wall variation amplitude is smaller than a critical value (about 0.26 for symmetric channel, 0.28 for sinuous channel), critical modes are three-dimensional stationary and for larger , two-dimensional oscillatory instabilities set in. Critical Reynolds numbers of sinuous channel flows are smaller for three-dimensional disturbances and larger for two-dimensional disturbances than those of symmetric channel flows. The disturbance velocity distribution obtained by the linear stability analysis suggests that the three-dimensional stationary instability is mainly caused by local concavity of basic flows near the reattachment point, while the critical two-dimensional mode resembles closely the Tollmien–Schlichting wave for plane Poiseuille flow.     

Three-dimensional instability of two counter-rotating vortices in a rectangular cavity driven by parallel wall motion

The linear stability of two counter-rotating vortices driven by the parallel motion of two facing walls in a rectangular cavity is investigated by a finite volume method. Critical Reynolds and wave numbers are calculated for aspect ratios ranging from 0.1 to 5. This range is sufficient to find the asymptotic behavior of the critical parameters when the aspect ratio tends to zero and infinity, respectively. The critical curve is smooth for all aspect ratios and, hence, the character of the instability changes continuously. When the moving walls are far apart the mechanism is centrifugal, as in the classical lid-driven cavity. For aspect ratios near unity a combined mechanism, also involving strain near the vortex cores, leads to the instability which tends to asymmetrically displace the vortex cores, very similar to the cooperative short-wave instability of a free counter-rotating vortex pair. In the limit when plane Poiseuille flow is approached in the bulk, the three-dimensional perturbations are strongly localized near both downstream ends of the moving walls.     

Effect of a Thin Longitudinal Inviscid Vortex on a Two-Dimensional Pre-Separation Boundary Layer

For large Reynolds numbers, an asymptotic solution of the Navier-Stokes equations describing the effect of a thin longitudinal vortex with a constant circulation on the development of an incompressible steady two-dimensional laminar boundary layer on a flat plate is obtained. It is established that, in a narrow wall region extending along the vortex filament, the viscous flow is described by the 3-D boundary layer equations. A solution of these equations for small values of the vortex circulation is studied. It is found that the solution of the two-dimensional pre-separation boundary layer equations collapses. This is attributable to the singular behavior of the 3-D disturbances near the zero-longitudinal-friction points.     

混合层中的流向涡与Rayleigh离心不稳定

用有限差分方法求解三维Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程和连续性方程，对时间发展的平面混合层中流向涡的产生原因进行了分析．将Ｒａｙｌｅｉｇｈ的轴对称无粘离心不稳定理论推广应用于分析混合层的二维基本流，并导出一无量纲量Ｒａｙ＝－（ｒ／νθ）νθ／ｒ，其中νθ为一流体质点相对于平均速度的速度，ｒ为该质点迹线的曲率半径．当Ｒａｙ＞１．０时就会发生离心不稳定．采用这一判别式后发现混合层中展向涡的周围，尤其是在辫带区，的确存在离心不稳定区域，而过去的实验结果也表明三维不稳定产生于展向涡之间的辫带区．因此有理由认为，除非雷诺数特别小，离心不稳定是流向涡产生和发展的主要原因