Numerical study on the turbulent mixing of planar shock-accelerated triangular heavy gases interface

The interaction of a planar shock wave with a triangle-shaped sulfur hexafluoride (\(\mathrm{SF_6}\)) cylinder surrounded by air is numerically studied using a high resolution finite volume method with minimum dispersion and controllable dissipation reconstruction. The vortex dynamics of the Richtmyer–Meshkov instability and the turbulent mixing induced by the Kelvin–Helmholtz instability are discussed. A modified reconstruction model is proposed to predict the circulation for the shock triangular gas–cylinder interaction flow. Several typical stages leading the shock-driven inhomogeneity flow to turbulent mixing transition are demonstrated. Both the decoupled length scales and the broadened inertial range of the turbulent kinetic energy spectrum in late time manifest the turbulent mixing transition for the present case. The analysis of variable-density energy transfer indicates that the flow structures with high wavenumbers inside the Kelvin–Helmholtz vortices can gain energy from the mean flow in total. Consequently, small scale flow structures are generated therein by means of nonlinear interactions. Furthermore, the occasional “pairing” between a vortex and its neighboring vortex will trigger the merging process of vortices and, finally, create a large turbulent mixing zone.     

Bifurcation mechanism of interfacial electrohydrodynamic gravity-capillary waves near the minimum phase speed under a horizontal electric field

We investigate the evolution of interfacial gravity-capillary waves propagating along the interface between two dielectric fluids under the action of a horizontal electric field. There is a uniform background flow in each layer, and the relative motion tends to induce Kelvin–Helmholtz(KH) instability. The combined effects of gravity, surface tension and electrically induced forces are all taken into account. Under the short-wave assumption, the expansion and truncation method of Dirichlet-Neumann(DN) operators is applied to derive a reduced dynamical model. When KH instability is suppressed linearly by a considerably large electric field, our numerical results reveal that in certain regions of parameter space, nonlinear symmetric traveling wave solutions can be found near the minimum phase speed. Additionally, the detailed bifurcation structures are presented together with typical wave profiles.     

Statistical analysis of the hydrodynamic pressure in the near field of compressible jets

This paper is devoted to the statistical characterization of the pressure fluctuations measured in the near field of a compressible jet at two subsonic Mach numbers, 0.6 and 0.9. The analysis is focused on the hydrodynamic pressure measured at different distances from the jet exit and analyzed at the typical frequency associated to the Kelvin–Helmholtz instability. Statistical properties are retrieved by the application of the wavelet transform to the experimental data and the computation of the wavelet scalogram around that frequency. This procedure highlights traces of events that appear intermittently in time and have variable strength. A wavelet-based event tracking procedure has been applied providing a statistical characterization of the time delay between successive events and of their energy level. On this basis, two stochastic models are proposed and validated against the experimental data in the different flow conditions     

Acceleration and wall pressure fluctuations generated by an incompressible jet in installed configuration

In this work, the cross-statistics of acceleration and wall pressure fluctuations generated by an incompressible jet interacting with a tangential flat-plate are presented. The results are derived from an experimental test campaign on a laboratory-scale model involving simultaneous velocity and wall pressure measurements. The pressure footprint of the jet on the surface was measured through a cavity-mounted microphone array, whereas pointwise velocity measurements were carried out by a hot wire anemometer. The time derivative of the velocity signal has been taken as an estimation of the local acceleration of the jet. The multivariate statistics between acceleration and wall pressure are achieved through cross-correlations and cross-spectra, highlighting that the causality relation is more significant in the potential core where the Kelvin–Helmholtz instability is dominant. The application of a conditional sampling procedure based on wavelet transform allowed us to educe the acceleration flow structures related to the energetic wall-pressure events. The analysis revealed that, unlike the velocity, the acceleration signatures were detected only for positions where the jet had not yet impinged on the plate, their shape being related to a convected wavepacket structure.     

Impact of density stratification on the global mode in a swirling jet: Stochastic modelling and Lagrangian coherent structures

In an experimental investigation, the stochastic dynamics of the global mode in a turbulent swirling jet are considered. From the application of the swirling jet in gas turbine combustors, it was observed that a specific density gradient in the flow leads to a suppression of the global mode. This phenomenon was replicated in a generic swirling jet using an electrical heating coil placed inside the breakdown bubble. In the present investigation, the dynamics of the global mode obtained from PIV and pressure measurements are analysed using a stochastic reduced-order model to describe the instability. The stochastic model is necessary to explain the interaction between the deterministic dynamics of the global mode and the perturbations by the background turbulence. The calibration of the stochastic model provides the amplification rate of the global mode that defines the transition of the flow, dependent on the swirling strength and the density difference. The spatial structure of the global mode is further investigated from Lagrangian coherent structures of the flow field which are computed from the 3D time-resolved velocity field reconstruction based on planar PIV measurements. The Lagrangian visualisations and schlieren visualisations are used to explain the absence of the density effects on the global mode at larger Reynolds numbers. The analysis gives a detailed view of the stochastic dynamics of a hydrodynamic instability in a turbulent flow.     

Numerical investigation of a perturbed swirling annular two-phase jet

A swirling annular gas–liquid two-phase jet flow system has been investigated by solving the compressible, time-dependent, non-dimensional Navier–Stokes equations using highly accurate numerical methods. The mathematical formulation for the flow system is based on an Eulerian approach with mixed-fluid treatment while an adjusted volume of fluid method is utilised to account for the gas compressibility. Surface tension effects are captured by a continuum surface force model. Swirling motion is applied at the inlet while a small helical perturbation is also applied to initiate the instability. Three-dimensional spatial direct numerical simulation has been performed with parallelisation of the code based on domain decomposition. The results show that the flow is characterised by a geometrical recirculation zone adjacent to the nozzle exit and by a central recirculation zone further downstream. Swirl enhances the flow instability and vorticity and promotes liquid dispersion in the cross-streamwise directions. A dynamic precessing vortex core is developed demonstrating that the growth of such a vortex in annular configurations can be initiated even at low swirl numbers, in agreement with experimental findings. Analysis of the averaged results revealed the existence of a geometrical recirculation zone and a swirl induced central recirculation zone in the flow field.     

An experimental study of the under-expanded swirling jet with secondary coaxial stream

The present study addresses experimental results for investigating the details of the near field flow characteristics produced in an under-expanded, dual, coaxial, swirling jet. The under-expanded swirling jet is discharged from a sonic inner nozzle. An outer annular nozzle produces co- and counter-swirling streams relative to the inner primary swirling jet. The interaction between both the outer annular swirling stream and inner under-expanded swirling jet is quantified by impact and static pressure measurements, and visualized by using the shadowgraph method. Experiments are performed for several different pressure ratios. The results show that the outer secondary co-swirling jet significantly changes the structure of the inner under-expanded swirling jet, such as the shock structures and the recirculation region generated at the jet axis. The effect of the outer secondary stream on the major structures of the inner primary swirling jet is strongly dependent on the pressure ratio of the inner swirling jet, regardless of the swirl direction of the outer stream.Received: 17 May 2004, Accepted: 27 September 2004, Published online: 26 November 2004[/PUBLISHED]H.D. Kim: Correspondence to     

An Experimental Investigation of the Separated-Flow Transition Under High-Lift Turbine Blade Pressure Gradients

Laminar boundary layer separation, shear layer transition and reattachment have been experimentally investigated on a flat plate installed within a double contoured test section designed to produce an adverse pressure gradient typical of Ultra-High-Lift turbine profiles. Measurements have been performed for the Reynolds number range 70,000 < Re < 200,000, typical of real engine operation. Profile aerodynamic loadings as well as boundary layer velocity profiles have been measured to survey the separation and transition processes. Particle Image Velocimetry measurements allowed the visualization of vortical structures induced by the shear layer instability. Spectral analysis of hot-wire velocity data has been adopted to identify the characteristic frequencies of the phenomena. Distinct energy peaks, associated with the Kelvin–Helmholtz waves generated in the shear layer over the separation bubble, appear in the spectra. In particular the evolution along the shear layer of the energy contents at the characteristic frequencies of the phenomenon has been analyzed. Two frequency ranges have been identified in which the instability waves are amplified within the shear layer over the stagnation area. The inviscid Kelvin–Helmholtz instability is the main mechanism that drives transition, but it starts to be relevant only after that lower frequency oscillations are amplified and reach the saturation.     

Hybrid LES-RANS study of an effusion cooling array with circular holes

A multi-row effusion cooling configuration with scaled gas turbine combustor conditions is studied numerically, using a novel wall-proximity-based hybrid LES-RANS approach. The distribution of the coolant film is examined by surface adiabatic cooling effectiveness (ACE). Simulation results have shown that the accuracy of cooling effectiveness prediction is closely related to the resolution of turbulent flow structures involved in hot-cold flow mixing, especially those close to the plate surface. The formation of the coolant film in the streamwise direction is investigated. It is shown that the plate surface directly downstream the coolant holes are covered well by the coolant jets, while surface regions in between the two columns of the coolant holes could not be protected until the coolant film is developed sufficiently in the spanwise direction in the downstream region. More detailed study has also been carried out to study the time-averaged and time-dependent flow fields. The relation between the turbulent flow structures and coolant film distribution are also examined. The Kelvin–Helmholtz instability in the upper and lower coolant jet shear layer, is found to have the same frequency of around 8000 Hz, and is independent of the coolant hole position. Additionally, it is suggested by the spectral coherence analysis that those unsteady flow structures from the lower shear layer are closely related to the near wall flow temperature, and such effect is also independent of the coolant hole position.     

Instability of the interface in two-layer flows with large viscosity contrast at small Reynolds numbers

The Kelvin–Helmholtz instability is believed to be the dominant instability mechanism for free shear flows at large Reynolds numbers. At small Reynolds numbers, a new instability mode is identified when the temporal instability of parallel viscous two fluid mixing layers is extended to current-fluid mud systems by considering a composite error function velocity profile. The new mode is caused by the large viscosity difference between the two fluids. This interfacial mode exists when the fluid mud boundary layer is sufficiently thin. Its performance is different from that of the Kelvin–Helmholtz mode. This mode has not yet been reported for interface instability problems with large viscosity contrasts.These results are essential for further stability analysis of flows relevant to the breaking up of this type of interface.     

Swirling and Impinging Effects in an Annular Nonpremixed Jet Flame

The effects of swirl and downstream wall confinement on an annular nonpremixed flame were investigated using direct numerical simulation (DNS). Fully three-dimensional parallel DNS was performed employing high-order numerical methods and high-fidelity boundary conditions to solve governing equations for variable-density flow and finite-rate Arrhenius chemistry. Three swirl numbers have been examined: 0 (without swirl), 0.4 and 0.8, while the effects of downstream wall confinement have been examined for swirl numbers 0 and 0.4. Results have been presented in terms of instantaneous and time-averaged flow quantities, which have also been analysed using energy spectra and proper orthogonal decomposition (POD). Effects of swirl on the fluid dynamic behaviour of the annular nonpremixed flame were found to be significant. The fluid dynamic behaviour of the flame is greatly affected by the interaction between the geometrical recirculation zone (GRZ) near the jet nozzle exit due to the annular configuration, the central recirculation zone (CRZ) associated with swirl, the unsteady vortical structures in the jet column due to the shear instability, and the downstream wall confinement. Depending on the degree of swirl, the GRZ near the burner mouth and the CRZ may co-exist or one zone may be overwhelmed by another. At a moderate swirl number, the co-existence leads to a flame with strong reaction attached to the burner mouth; while at a high swirl number, the CRZ dominates over the GRZ. The precessing vortex core was observed to exist in the swirling flow fields. The Nusselt number distribution of the annular impinging flames differs from that of round impinging jets. The POD analysis revealed that wall effects on the flow field are mainly associated with the higher mode numbers.     

Viscous solution of the triple-shock reflection problem

The reflection of a triple-shock configuration was studied numerically in two dimensions using the Navier–Stokes equations. The flow field was initialized using three shock theory, and the reflection of the triple point on a plane of symmetry was studied. The conditions simulated a stoichiometric methane-oxygen detonation cell at low pressure on time scales preceding ignition when the gas was assumed to be inert. Viscosity was found to play an important role on some shock reflection mechanisms believed to accelerate reaction rates in detonations when time scales are small. A small wall jet was present in the double Mach reflection and increased in size with Reynolds number, eventually forming a small vortex. Kelvin–Helmholtz instabilities were absent, and there was no Mach stem bifurcation at Reynolds numbers corresponding to when the Mach stem had travelled distances on the scale of the induction length. Kelvin–Helmholtz instabilities are found to not likely be a source of rapid reactions in detonations at time scales commensurate with the ignition delay behind the Mach stem.     

A numerical study of an annular liquid jet in a compressible gas medium

An annular liquid jet in a compressible gas medium has been examined using an Eulerian approach with mixed-fluid treatment. The governing equations have been solved by using highly accurate numerical methods. An adapted volume of fluid method combined with a continuum surface force model was used to capture the gas–liquid interface dynamics. The numerical simulations showed the existence of a recirculation zone adjacent to the nozzle exit and unsteady large vortical structures at downstream locations, which lead to significant velocity reversals in the flow field. It was found that the annular jet flow is highly unstable because of the existence of two adjacent shear layers in the annular configuration. The large vortical structures developed naturally in the flow field without external perturbations. Surface tension tends to promote the Kelvin–Helmholtz instability and the development of vortical structures that leads to an increased liquid dispersion. A decrease in the liquid sheet thickness resulted in a reduced liquid dispersion. It was identified that the liquid-to-gas density and viscosity ratios have opposite effects on the flow field with the reduced liquid-to-gas density ratio demoting the instability and the reduced liquid-to-gas viscosity ratio promoting the instability characteristics.     

Experimental investigation of jets from rectangular six-lobed and round orifices at very low Reynolds number

This article presents an experimental study conducted on a six-lobed rectangular jet at a very low Reynolds number of 800. The near-exit flow dynamics is compared to the reference counterpart circular jet with same initial conditions. Flow dynamics is analyzed using time-resolved flow-visualizations, hot-wire anemometry and laser Doppler velocimetry. In the round jet, flow motion is dominated by large primary Kelvin–Helmholtz (K–H) structures. In the six-lobed rectangular jet, the K–H vortices are very thin compared to the large secondary vortices generated by the high shear at the lobed nozzle lip. The inspection of mean-velocity profiles and streamwise evolutions of the spreading rates in the major and the minor planes of the lobed jet confirm the absence of the switching-over phenomenon not observed on flow images. The streamwise structures that develop in orifice troughs render the volumetric flow rate significantly higher than that of the reference circular jet. Comparison of the obtained results to available data of the literature of similar rectangular six-lobed jets investigated at very high Reynolds numbers reinforces the notion that the three-dimensional flowfields at very low and very high Reynolds numbers are similar if the geometry of the lobed nozzle is conserved. However, important variations in flow dynamics might occur if one or several geometric parameters of the lobed nozzle are modified.     

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.     

Comparison between Kelvin–Helmholtz instability experiments on OMEGA and simulation results using the CRASH code

The Center for Radiative Shock Hydrodynamics (CRASH) at the University of Michigan has developed a Eulerian radiation-hydrodynamics code with dynamic adaptive mesh refinement, CRASH, which can model high-energy-density laser-driven experiments. One of these experiments, performed previously on the OMEGA laser facility, was designed to produce and observe the Kelvin–Helmholtz instability. The target design included low-density carbonized-resorcinol-formaldehyde (CRF) foam layered on top of polyamide–imide plastic, with a sinusoidal perturbation on the interface and with the assembled materials encased in beryllium. The results of a series of CRASH simulations of these Kelvin–Helmholtz instability experiments are presented. These simulation results show good agreement both quantitatively and qualitatively with the experimental data.     

IMPLEMENTATION OF VORTEX FILAMENT METHODS ON PARALLEL MACHINES WITH DISTRIBUTED ADAPTIVE DATA STRUCTURE

This paper addressed the implementation of vortex filament methods on parallel machines with distributed memory to simulate a three-dimensionally evolving jet. Vortical structure developments due to Kelvin–Helmholtz instability of the axially perturbed jet are also examined. The implementation is conducted in a single-programme multiple-data (SPMD) environment and the parallelism is focused on issues of data distribution, efficient support of parallel I/O and overlapping of communications with computations. In addition, since the number of segment markers in a filament is dynamically growing according to the requirement of numerical accuracy, a novel packet-oriented data structure is proposed not only to partition filament segment markers among distributed processors but also to support dynamical load balancing at run time. This work is the first to apply packet-oriented structures to implement a parallel vortex filament method. Experimental results indicate performance improvement from 1·5 to 2·6 times over static schemes on nCUBE2, DEC Alpha and IBM SP2 by incorporating the proposed scheme with packet-oriented structures. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 939–951, 1997.     

Numerical study of hysteresis in annular swirling jets with a stepped‐conical nozzle

This study investigates the experimentally observed hysteresis in the mean flow field of an annular swirling jet with a stepped‐conical nozzle. The flow is simulated using the Reynolds‐averaged Navier–Stokes (RANS) approach for incompressible flow with a k–ε and a Reynolds stress transport (RSTM) turbulence model. Four different flow structures are observed depending on the swirl number: ‘closed jet flow’, ‘open jet flow low swirl’, ‘open jet flow high swirl’ and ‘coanda jet flow’. These flow patterns change with varying swirl number and hysteresis at low and intermediate swirl numbers is revealed when increasing and subsequently decreasing the swirl. The influence of the inlet velocity profile on the transitional swirl numbers is investigated. When comparing computational fluid dynamics with experiments, the results show that both turbulence models predict the four different flow structures and the associated hysteresis and multiple solutions at low and intermediate swirl numbers. Therefore, a good agreement exists between experiments and numerics. Copyright © 2006 John Wiley & Sons, Ltd.     

LES study of global instability in annular jets

The paper presents results of numerical investigations of annular non–swirling jets. The research is performed with the use of large eddy simulations (LES) and a high–order code based on the compact differences and the Fourier approximation combined with a projection method for pressure–velocity coupling. We consider various Reynolds numbers and inner shear layer thicknesses and observe that both parameters affect the dynamics of the flow in such a way that the formation of the turbulent structures follows two different scenarios. For the particular group of the inlet conditions the flow pattern is found to be similar to low–swirling jets. The instantaneous flow–fields reveal the formation of the spiral structures located in the inner and outer mixing layers. The analysis shows that the structures are the result of the instability that leads to the precession of the recirculation region formed in the near–field. The winding sense of the spirals are clockwise or counterclockwise depending on the case and azimuthal distribution of perturbations.     

On coherent structures and mixing characteristics in the near field of a rotating-pipe jet

Mixing characteristics and coherent structures populating the near-nozzle area of a rotating-pipe jet at the Reynolds number of 5300 were studied by Large-eddy simulation (LES). The swirl rate, defined as the ratio of the tangential velocity of the inner pipe wall to the bulk axial velocity, varied from 0 to 1, corresponding to a weak-to-moderate swirl intensity, insufficient to induce reverse flow near the nozzle. The visualization shows that for the non-swirling jet the near-wall streaky structures generated in the pipe interact with the shear layer, evolving into hairpin-like structures that become tilted at low rotation rates. For higher swirl, they cannot be recognized as they are destroyed at the nozzle exit. No large-scale coherent structures akin to Kelvin–Helmholtz vortical rings in the ‘top-hat’ jets are identifiable close to the nozzle. Using the single and joint probability density functions of velocity and passive scalar (temperature) fields we quantify the events responsible for the intensive entrainment at various swirl numbers. The isosurface of the temperature field indicates the meandering and precessing motion of the rotating jet core at the axial distance of 6D downstream, where D is the diameter of the pipe. The Fourier analysis with respect to the azimuthal angle and time reveals an interplay between the co- and counter-rotating modes. These findings explain the previously detected but not fully clarified phenomenon of the weakly counter-rotating jet core at low swirl rates.