Convective Mach Number Increases Research Articles

Interfaces of high- and low-speed large-scale structures in compressible turbulent mixing layers: compressibility effects and structures

Direct numerical simulations of temporally developing mixing layers have been performed to investigate the effects of compressibility on statistics and structures near the interfaces of high- and low-speed large-scale structures (LSSs), covering a range of convective Mach numbers from $M_c=0.2$ to $1.8$ and Taylor Reynolds numbers up to 290. The interfaces of LSSs are directly defined by the isosurface of zero fluctuating streamwise velocity. The characteristic velocity jump at the interfaces grows rapidly in the transition stage and then decreases until reaching a gradual self-similar stage. The evolution of velocity jump is evidently delayed as the convective Mach number increases. The interface layer is formed by the shearing motion of neighbouring LSSs. A small vortical motion characterized by the Kolmogorov scale is induced in the interface layer by shear-dominated outer regions. The strengths of outer shearing motion and central vortical motion are greater at the leading edge, but smaller at the trailing edge, which is also reflected in a larger velocity jump at the leading edge. As the convective Mach number increases, the small-scale vortical structure is obviously suppressed by compressibility. At high convective Mach number $M_c=1.8$ , the compressive shear-dominated outer regions are linked with a sheet-like structure passing through the centre of the expansion region corresponding to a small-scale vortical structure. The compressibility and shearing strength near the interface are highly dependent on the interface orientation.

Compressibility effects on statistics and coherent structures of compressible turbulent mixing layers

The effects of compressibility on the statistics and coherent structures of a temporally developing mixing layer are studied using numerical simulations at convective Mach numbers ranging from $M_c=0.2$ to $1.8$ and at Taylor Reynolds numbers up to 290. As the convective Mach number increases, the streamwise dissipation becomes more effective to suppress the turbulent kinetic energy. At $M_c=1.8$ , the streamwise dissipation increases much faster than the other two components in the transition region, even larger than pressure–strain redistribution, correlating with the streamwise elongated vortical structures at a higher level of compressibility. We confirm the existence of the large-scale high- and low-speed structures in the mixing layers, which accompany the spanwise Kelvin–Helmholtz rollers at low convective Mach number and dominate the mixing layer at higher convective Mach number. Conditional statistics demonstrate that the large-scale low-speed structures are lifted upwards by a pair of counter-rotating quasi-streamwise rollers flanking the structures. The small-scale vortical structures have an apparent preference for clustering into the top of the low-speed regions, which is directly associated with high-shearing motions on top of the low-speed structures. The high-speed structures statistically exhibit central symmetry with the low-speed structures. The statistics and dynamics of large-scale high- and low-speed structures in the compressible mixing layers resemble those in the outer region of the turbulent boundary layers, which reveals the universality of the large-scale structures in free shear and wall-bounded turbulence. A conceptual model is introduced for the large-scale high- and low-speed structures in turbulent mixing layers.

A Numerical Investigation of Mixing Models in LES-FMDF for Compressible Reactive Flows

The filtered mass density function (FMDF) model has been employed for large-eddy simulations (LES) of compressible high-speed turbulent mixing and reacting flows. However, the mixing model remains a pressing challenge for FMDF methods, especially for compressible reactive flows. In this work, a temporal development mixing layer with two different convective Mach numbers, Mc=0.4 and Mc=0.8, is used to investigate the mixing models. A simplified one-step reaction and a real hydrogen/air reaction are employed to study the mixing and turbulence-chemistry interaction. Two widely used mixing models, interaction by exchange with the mean (IEM) and Euclidean minimum spanning tree (EMST), are studied. Numerical results indicate that no difference is observed between the IEM and EMST models in simple reaction flows. However, for hydrogen/air reactions, the EMST model can predict the reaction more accurately in high-speed flow. For mixing models in compressible reactive flows, the requirement of localness preservation tends to be more essential as the convective Mach number increases. With the increase of compressibility, the sensitivity of the mixing model coefficient is reduced significantly. Therefore, the appropriate mixing model coefficient has a wider range. Results also indicate that a large error may result when using a fixed mixing model coefficient in compressible flows.

Direct numerical simulation of fine flow structures of subsonic-supersonic mixing layer

Subsonic-supersonic mixing flow is one of the important research fields in turbulence research. For example, in the combustion chamber of the rocket ramjet combination engine, the rocket jet flow and the air inflow is a typical shear mixing flow, which has the characteristics of high convection Mach number and large flow parameter gradient. It is of great significance to explore the development law and flow structure of subsonic-supersonic mixing layer to enhance the mixing and thus improve the performance of rocket ramjet engine.In this paper, in order to further study the evolution process and obtain the evolution mechanism and fine flow structure of subsonic-supersonic mixing layer, three groups of high-order format direct numerical simulations of typical working conditions are carried out. The convective Mach numbers are 0.69, 0.92 and 1.27, respectively. The direct numerical simulation results show that: (1) the large-scale structure in the subsonic-supersonic shear mixing flow formed the small-scale structure earlier, and the flow was dominated by the small-scale and broken eddy structure; (2) the development process of the subsonic-supersonic shear mixing flow was mainly divided into three stages: laminar flow zone, transition zone and development zone. The transition zone was a transition zone from two-dimensional to three-dimensional, which began to show three-dimensional flow characteristics. The vorticity shows a twisted-winding structure. The large-scale Coherent structure, the Λ eddy and hairpin eddy, can be observed, and the Λ eddy structure is gradually elongated with the increase of convective Mach number; (3) the shocklets structure mainly occurs in the stage when the mixing layer has not fully developed. The starting point of the shocklets structure is near the vortex core. With the increase of convective Mach number, the position of the shocklets generation moves to the front of the vortex core; (4) the dynamic mode decomposition results show that the eigenvalues of each mode are basically located in the unit circle, which indicates that the calculated modes are stable; in addition, it is found that there is a certain dominant frequency in the flow structure, which can provide a reference for the active mixing enhancement method.

Characterization of flow mixing and structural topology in supersonic planar mixing layer

The investigations on mixing process and structural topology properties of supersonic planar mixing layer with different inflow conditions are conducted by employing direct numerical simulation. First, the present high-order accuracy numerical methods are validated by comparing the simulation results with the data gained from previous well characterized experimental and numerical cases. Then the high-resolved three-dimensional numerical visualizations of supersonic mixing layer are presented by utilizing Q-criterion. The visualization results show the full development and evolution process of mixing layer, including the shear action, the transition process populated sequentially by Λ-vortices, hairpin vortices and braid structures and the establishment of self-similar turbulence. The effects of density ratio, velocity ratio and convective Mach number between the two parallel streams on mixing layer growth rate are evaluated by examining the indexes including velocity thickness and momentum thickness represented the mixing process. The results indicate that for the only variation of density ratio, the velocity thickness growth rates do not significantly vary, while the momentum thickness becomes larger when the upper and lower streams possess the same density. With the increase of only velocity ratio, the mixing layer becomes more stable and the velocity and momentum thickness are both drastically depressed in the whole flow field. As only convective Mach number increases, the mixing layer growth is inhibited in the near field through the transition delay of the flow, while in the far field, the growth rates are nearly the same for different convective Mach numbers. The spatial correlation analysis of structural topology indicates that the effects of each of the three main flow parameters on vortex topology lead to different mean structure sizes and shapes. The present research is useful for evaluating the effects of different flow parameters on mixing properties, which is important for the future scramjet combustor design and evaluation in engineering.

Detailed experimental investigations on flow behaviors and velocity field properties of a supersonic mixing layer

The flow behaviors and mixing characteristics of a supersonic mixing layer with a convective Mach number of 0.2 have been experimentally investigated utilizing nanoparticle-based planar laser scattering and particle image velocimetry techniques. The full development and evolution process, including the formation of Kelvin-Helmholtz vortices, breakdown of large-scale structures and establishment of self-similar turbulence, is exhibited clearly in the experiments, which can give a qualitative graphically comparing for the DNS and LES results. The shocklets are first captured at this low convective Mach number, and their generation mechanisms are elaborated and analyzed. The convective velocity derived from two images with space-time correlations is well consistent with the theoretical result. The pairing and merging process of large-scale vortices in transition region is clearly revealed in the velocity vector field. The analysis of turbulent statistics indicates that in weakly compressible mixing layers, with the increase of convective Mach number, the peak values of streamwise turbulence intensity and Reynolds shear stress experience a sharp decrease, while the anisotropy ratio seems to keep quasi unchanged. The normalized growth rate of the present experiments shows a well agreement with former experimental and DNS data. The validation of present experimental results is important for that in the future the present work can be a reference for assessing the accuracy of numerical data.

Entrainment in a compressible turbulent shear layer

Direct numerical simulations (DNS) of temporally evolving shear layers have been performed to study the entrainment of irrotational flow into the turbulent region across the turbulent/non-turbulent interface (TNTI). Four cases with convective Mach number from 0.2 to 1.8 are used. Entrainment is studied via two mechanisms; nibbling, considered as vorticity diffusion across the TNTI, and engulfment, the drawing of the pockets of the outside irrotational fluid into the turbulent region. The mass flow rate due to nibbling is calculated as the product of the entrained mass flux with the surface area of the TNTI. It is found that increasing the convective Mach number results in a decrease of the average entrained mass flux and the surface area of the TNTI. For the incompressible shear layer the local entrained mass flux is shown to be highly correlated with the viscous terms. However, as the convective Mach number increases, the mass fluxes due to the baroclinic and the dilatation terms play a more important role in the local entrainment process. It is observed that the entrained mass flux is dependent on the local dilatation and geometrical shape of the TNTI. For a compressible shear layer, most of the entrainment of the irrotational flow into the turbulent region due to nibbling is associated with the compressed regions on the TNTI. As the convective Mach number increases, the percentage of the compressed regions on the TNTI decreases, resulting in a reduction of the average entrained mass flux. It is also shown that the local shape of the interface, looking from the turbulent region, is dominated by concave shaped surfaces with radii of curvature of the order of the Taylor length scale. The average entrained mass flux is found to be larger on highly curved concave shaped surfaces regardless of the level of dilatation. The mass fluxes due to vortex stretching, baroclinic torque and the shear stress/density gradient terms are weak functions of the local curvatures on the TNTI, whereas the mass fluxes due to dilatation and viscous diffusion plus the viscous dissipation terms have a stronger dependency on the local curvatures. As the convective Mach number increases, the probability of finding highly curved concave shaped surfaces on the TNTI decreases, whereas the probability of finding flatter concave and convex shaped surfaces increases. This results in a decrease of the average entrained mass flux across the TNTI. Similar to the previous works on jets, the results show that the contribution of the engulfment to the total entrainment is small for both incompressible and compressible mixing layers. It is also shown that increasing the convective Mach number decreases the velocities associated with the entrainment, i.e. induced velocity, boundary entrainment velocity and local entrainment velocity.

Impact of Heat on the Pressure Skewness and Kurtosis in Supersonic Jets

Mach wave radiation and crackle are dominant noise components from high-speed jets, found in both high-power engines and scale nozzles. The statistics of the pressure signal and its time derivative () have been widely studied to identify and quantify crackle. In this paper, we investigate the impact of operating condition on the overall sound pressure level, skewness, and kurtosis of the pressure and signals of a jet issuing from an converging–diverging conical nozzle. The effect of temperature and nonideal expansion were independently investigated. An increase in convective Mach number , achieved by increasing either jet temperature or nozzle pressure ratio, proved to be related to elevated values of overall sound pressure level, skewness, and kurtosis, in both the near and far fields. The peak values of overall sound pressure level, skewness levels, and kurtosis levels were found to propagate at different angles for cold jets, but at elevated temperature, the directivity was more similar. From here, it was concluded that the intense levels of the high-order statistics appear to be generated at different locations in the shear layer of the jet and strengthen away from the jet by nonlinear propagation effects.

Investigation on thin distortion of small light beam at different convective Mach number

In order to investigate shape distortion of small light beam at different convective Mach number ( Mc ), the technique of CCD camera imaging has been used. The theoretical analysis presents the relation between growth rate of diameter of small beam light (passing through the compressible mixing layer) and flow characteristic parameters (such as convective Mach number, free stream velocity, free stream density ratio and so on). The experimental results show that Airy spark diameter increases fast with the increase of convective Mach number, which implies more indistinct image. In addition, the theoretical results also point out the direction of further experimental design.

Theoretical and experimental investigation on aero-optical effect for a compressible mixing layer

Using dimensional analysis and experimental technique, the aero-optical effect for a compressible mixing layer around optical side window is investigated. According to the theoretical analysis, we find that time-averaged boresight error increases with the increase of convective Mach number (Mc). Moreover, we also present the relations between time-averaged boresight error (BSE) and Reynolds number, shear stress at interface between mixing layer and free stream, free stream velocity ratio and density ratio. The experimental results from a thin beam light passing through compressible mixing layer verify the theoretical result between time-averaged BSE and Mc.

Analysis of flow structures in supersonic plane mixing layers using the POD method

The proper orthogonal decomposition (POD) method was applied to analyzing the database obtained from the direct numerical simulation (DNS) of supersonic plane mixing layers. The effect of different forms of the inner products in the POD method was investigated. It was observed that the mean flow contributes to a predominant part of the total flow energy, and the energy spectrum of the turbulence fluctuations covers a wide range of POD modes. The patterns of leading (high energy) POD modes reveal that the flow structures exhibit spanwise counter rotating rolls, as well as oblique vortices. These flow patterns are insensitive to the velocity of the observer. As the convective Mach number increases, the energy spectrum becomes wider, the leading POD modes contain more complicated structures, and the flow becomes more chaotic.

Interactions between compressibility and heat release in turbulent mixing layers

AbstractReduced turbulence activity and growth rate of a compressible mixing layer when the convective Mach number increases, are well‐known phenomena. Heat release due to combustion has similar effects and important implications for applications such as scramjet engines the efficiency of which depends on a proper mixing of oxidizer and fuel. To understand the underlying mechanisms, highly resolved DNS of inert and reacting, temporally evolving mixing layers at different convective Mach numbers and Reynolds numbers ensuring a self‐similar state are performed and analyzed with a particular focus on the pressure‐strain correlations in the Reynolds‐stress transport equations. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Nonlinear Development of Particle-Laden Mixing Layers at Low Mach Number

The two-phase coupling effects on the particle-laden compressible mixing layer are studied for low convective Mach numbers. A full Eulerian approach is used to obtain a set of conservative partial differential equations. The initial condition is provided by the solution of the solution of the linear problem. The numerical solutions show that the presence of particles in the flow does not alter the typical development of the mixing layer observed for one-phase flows: the amplification of linear instability waves, the formation of two-dimensional large-scale vortices, and the pairing of vortices. The shape of the vortical structures is modified compared to single-phase calculations. The particle density distribution is greatly dependant on their inertia that can lead to a particle-free zone in the vortex. The compressibility effects are clearly seen on the modal kinetic energy, which decreases when the convective Mach number increases

Sound Generation in Compressible Mixing Layers

Direct numerical simulations have been performed to clarify the sound generation mechanism in two-dimensional temporally evolving compressible mixing layers. The sound generation in mixing layer is governed by the variations of vorticity which are induced by the Kelvin-Helmholtz instability. The pressure fluctuations with high frequency are observed in the period of vortex roll-up, and the amplitude of pressure fluctuations increase on the occasion of vortex pairing. The acoustic source term is governed by the Reynolds stress component and the viscous component is negligible. The effects of convective Mach number Mc on sound generation are also investigated. Both the pressure fluctuations and acoustic source term increase with the increase of convective Mach number. For Mc=0.6, shock wave called 'eddy shocklet' is produced by the vortex pairing, which dominates the sound generation from the mixing layer at high Mc. The far field sound computed by DNS is compared with the predictions based on the acoustic analogies derived by Powell and Lighthill. The prediction by Powell's analogy shows a good agreement with DNS, while the pressure fluctuations predicted by Lighthill's analogy are low compared with the DNS results after the vortex pairing.

Sound Generation in Compressible Mixing Layers.

Direct numerical simulations have been performed to clarify the sound generation mechanism in a two-dimensional temporally evolving compressible mixing layers. The sound generation in mixing layer is governed by the variations of vorticity which are induced by the Kelvin-Helmholtz instability. The pressure fluctuations with high frequency are observed in the period of vortex roll-up, and the amplitude of pressure fluctuations increase on the occasion of vortex pairing. The acoustic source term is governed by the Reynolds stress component and the viscous component is negligible. The effects of convective Mach number Mc on sound generation are also investigated. Both the pressure fluctuations and acoustic source term increase with the increase of convective Mach number. For Mc=0.6, shock wave called'eddy shocklet, is produced by the vortex pairing, which dominates the sound generation from the mixing layer at high Mc. The far-field sound computed by DNS is compared with the predictions based on the acoustic analogies derived by Powell and Lighthill. The prediction by Powell's analogy shows a good agreement with DNS, while the pressure fluctuations predicted by Lighthill's analogy are low compared with the DNS results after the vortex pairing.

Absolute/convective transition of wake-dominated supersonic shear layers

The absolute and convective instability characteristics of supersonic wake dominated shear layers, described by a hyperbolic-tangent profile plus a wake component represented by a Gaussian distribution, are investigated. The effects of the Mach number, the freestream temperature ratio and the wake deficit on the boundary of the absolute/convective transition and the branch point parameters (such as frequency, wave number, and the spatial growth rate) are studied using linear stability theory. For supersonic mixing layers, it is found that at a given wake deficit the amount of backflow necessary to cause absolute instability decreases as the convective Mach number increases and that all the branch point parameters vary slowly as functions of the convective Mach number as opposed to subsonic mixing layers. As the wake deficit decreases, the curve separating the absolute and the convective regions moves down to the values of more negative freestream velocity ratio for both subsonic and supersonic mixing layers and the branch point spatial growth rate decreases for a given convective Mach number. The effect of decreasing the wake deficit on the absolute/convective transition boundary is similar to that of increasing the freestream temperature ratio.

Unstructured grid simulations of spatially evolving supersonic shear layers

This research employed an adaptive unstructured finite element grid with a nonlinear monotonic scheme to undertake high-resolution inviscid eddy simulations of spatially evolving supersonic free shear layers. The objectives were to both improve physical understanding and evaluate the simulation fidelity by direct comparisons with detailed experimental measurements. With a physically consistent perturbation model, the compressibility effects on the nature of the shear layer were investigated by testing three different convective Mach numbers, 0.35, 0.45, and 0.7, nonetheless holding velocity and density ratios fixed. Reduction in eddy coherency as compressibility increased was found to be related to modifications in the merging process (slapping vs rotational merges). Turbulence statistics of velocity and mixture fraction exhibited reductions in the peak values of turbulent intensities of transverse velocity and passive scalar as convective Mach number increases, whereas turbulent intensity of streamwise velocity peak values remain constant.

Velocity field characteristics in supersonic mixing layers

Several compressible mixing layers, with one supersonic and one subsonic streams, are experimentally analyzed by pressure measurements and laser anemometry. Detailed measurements of the mean and fluctuating velocity fields are provided and compared against data from incompressible flows. The effects of compressibility on the flows are observed. The spreading rate of the mixing layers decrease when the Mach number is increased, in good agreement with results found in the literature. Laser Doppler measurements are performed for three test cases. The compressibility effects on the fluctuation levels are discussed and compared with existing results. The evolution of the turbulence structure of the flow, when the convective Mach number increases, is considered in the analysis when separate LDA seeding regimens are employed on the two sides of the layers. Some modifications of the large scale organization are observed when supersonic and subsonic mixing layers are compared and the two sides of the supersonic mixing layers have different characteristics.

Mean and turbulent velocity measurements of supersonic mixing layers

The behavior of supersonic mixing layers under three conditions has been examined by schlieren photography and laser Doppler velocimetry. In the schlieren photographs, some largescale, repetitive patterns were observed within the mixing layer; however, these structures do not appear to dominate the mixing layer character under the present flow conditions. It was found that higher levels of secondary freestream turbulence did not increase the peak turbulence intensity observed within the mixing layer, but slightly increased the growth rate. Higher levels of freestream turbulence also reduced the axial distance required for development of the mean velocity. At higher convective Mach numbers, the mixing layer growth rate was found to be smaller than that of an incompressible mixing layer at the same velocity and freestream density ratio. The increase in convective Mach number also caused a decrease in the turbulence intensity (σ u /ΔU).

Numerical Simulation of Ignition in Supersonic Reactive Shear Layers.

This study is a direct numerical simulation of a spatially evolving reactive mixing layer of a hydrogen/air system. A second-order TVD scheme with full chemical mechanism was employed to observe the mixing and ignition process. Mixing efficiency and ignition location were investigated under different convection Mach numbers. Techniques for enhancing ignition are discussed, attention being given to the coupling of the shear layer growth rate and viscous dissipation. Results show that an increase of convective Mach number significantly decreases fuel-air mixing efficiency, but enhances the viscous dissipation. As a result, a decrease of shear layer thickness enhances the auto-ignition at high Mach numbers. It was also found that an increase of hydrogen velocity causes the shear layer to shift toward the air side, leading to a shorter ignition delay time. Furthermore, the effect of instability of the shear layer on ignition was also investigated. It was found that an improvement of ignition was-achieved by imposing a very small perturbation upstream.