Study of jet precession, recirculation and vortex breakdown in turbulent swirling jets using LES

Large eddy simulations (LES) are used to investigate turbulent isothermal swirling flows with a strong emphasis on vortex breakdown, recirculation and instability behaviour. The Sydney swirl burner configuration is used for all simulated test cases from low to high swirl and Reynolds numbers. The governing equations for continuity and momentum are solved on a structured Cartesian grid, and a Smagorinsky eddy viscosity model with the localised dynamic procedure is used as the sub-grid scale turbulence model. The LES successfully predicts both the upstream first recirculation zone generated by the bluff body and the downstream vortex breakdown bubble. The frequency spectrum indicates the presence of low frequency oscillations and the existence of a central jet precession as observed in experiments. The LES calculations well captured the distinct precession frequencies. The results also highlight the precession mode of instability in the center jet and the oscillations of the central jet precession, which forms a precessing vortex core. The study further highlights the predictive capabilities of LES on unsteady oscillations of turbulent swirling flow fields and provides a good framework for complex instability investigations.     

Large-eddy simulations of film cooling flows

Large-eddy simulations (LES) of a jet in a cross-flow (JICF) problem are carried out to investigate the turbulent flow structure and the vortex dynamics in gas turbine blade film cooling. A turbulent flat plate boundary layer at a Reynolds number of Re_∞ = 400,000 interacts with a jet issued from a pipe. To study the effect of the jet inclination angle α on the flow field, two angles are chosen, the perpendicular injection at 90° and the streamwise inclined injection at 30°. For the normal injection case a small blowing ratio of the jet velocity to the cross-stream velocity R = 0.1 is examined. For the streamwise inclined injection case two blowing ratios R = 0.1 and R = 0.48 are investigated to check the impact of the jet velocity on the cooling performance. The time-dependent turbulent inflow information for the cross-flow is provided by a simultaneously performed LES of a spatially developing turbulent boundary layer. Whereas in the perpendicular injection case a rather large separation region is found at the leading edge of the jet hole, in the streamwise inclined injection cases no separation is observed. Compared with the normal injection case at the same blowing ratio, the streamwise inclination weakens the jet-cross-flow interaction significantly. Thus, the first appearance of the counter-rotating vortex pair (CVP) is shifted downstream and its strength is reduced. The increase of the blowing ratio leads to a stronger penetration of the jet into the cross-flow, resulting in a more upstream located and more pronounced CVP. Downstream of the jet exit the streamwise vortices are so large that besides the jet fluid also the cross-stream is partially entrained into this zone, which yields the worst cooling performance.     

Nature of sensitive high-order resonant modes in piezoelectric excited millimeter sized cantilever (PEMC) sensors

High-order resonant modes of piezoelectric-excited cantilever (PEMC) sensors were previously shown to be very highly sensitive at 0.3-2 fg/Hz for in-liquid applications. The purpose of this work is to show experimentally and with finite element model (FEM) simulations that such sensitive modes are strongly influenced by the sensor width, suggesting that the sensitive modes are torsional or buckling modes. From experimental observations the resonant frequency of high-order modes had a strong dependence on width, where a sensor with a smaller width had resonant modes at a higher frequency. Also the FEM simulations indicate that in this frequency range there are resonant modes with a buckling nature that change for a decrease in width, consistent with experimental observations. In order to establish that the width-dependent modes are mass-sensitive in liquids, resonant frequency change to density changes in flow experiments under fully liquid-immersed conditions were determined. Average frequency shifts of 475 ± 49 Hz (n = 5), 533 ± 31 Hz (n = 5), 715 ± 103 Hz (n = 5) and 725 ± 37 Hz (n = 5) were obtained for the four designs investigated in response to a density change of 0.0118 g/cm³. The results show that the resonant frequency response to variations in the geometry provides insightful data on the role of width in PEMC sensor design.     

Simulations of confined turbulent vortex flow

Large-eddy simulations (LES) of the turbulent flow in a swirl tube with a tangential inlet have been performed. The geometry, and flow conditions were chosen according to an experimental study by [Escudier MP, Bornstein J, Zehnder N. Observations and LDA measurements of confined turbulent vortex flow. J Fluid Mech 1980;98:49-63]. Lattice-Boltzmann discretization was used to numerically solve the Navier-Stokes equations in the incompressible limit. Effects of spatial resolution and choices in subgrid-scale modeling were explicitly investigated with the experimental data set as the testing ground. Experimentally observed flow features, such as vortex breakdown and laminarization of the vortex core were well represented by the LES. The simulations confirmed the experimental observations that the average velocity profiles in the entire vortex tube are extremely sensitivity to the exit pipe diameter. For the narrowest exit pipe considered in the simulations, very high average velocity gradients are encountered. In this situation, the LES shows the most pronounced effects of spatial resolution and subgrid-scale modeling.     

LES of synthetic jets in boundary layer with laminar separation caused by adverse pressure gradient

In the development of synthetic jet actuators (SJAs) for active flow control, numerical simulation has played an important role. In controlling the boundary layer flow separation, an integrated numerical model which includes both the baseline flow and the SJA is still in its initial stage of development. This paper reports preliminary results of simulating the interaction between a synthetic jet and a laminar separation bubble caused by adverse pressure gradient in a boundary layer. The computational domain was three-dimensional and Large-eddy simulation (LES) was adopted. The initial and boundary conditions were defined using or referring to our wind tunnel experimental results. Prior to numerically simulating the interaction between the synthetic jets and the baseline flow, a numerical model for simulating the separation bubble was developed and verified. In the numerical model including the SJA, the synthetic jet velocity at the exit of the SJA was defined as an input. The numerical model was further verified by comparing the simulation with experimental results. Based on reasonable agreement between the numerical and experimental results, simulations were carried out to investigate the dependency of flow control using synthetic jets on the forcing frequency, focused on the lower frequency range of the Tollmien-Schlichting (T-S) instability, and on the forcing amplitude which was represented by the maximum jet velocity at the exit of the SJA. Supporting the hypothesis based on the experiment, LES results showed that the forcing frequency had stronger influence on SJA’s effective elimination of the separation bubble than the forcing amplitude did.     

Large eddy simulation of pulsating flow over a circular cylinder at subcritical Reynolds number

The pulsating cross-flow over a single circular cylinder at the subcritical Reynolds number Re_D = 2580 is studied with the large eddy simulation (LES) technique using the standard Smagorinsky model as well as a dynamic model in which the test filtered quantities are evaluated through a truncated Taylor series expansion. The filtered equations are discretised using the finite volume method in an unstructured, collocated grid arrangement with a second-order accurate method, in both space and time. The predictions are compared against very detailed experiments for mean velocities and Reynolds stresses that were performed in a duct of cross-section 72 mm × 72 mm using the PIV technique. The effects of mesh refinement close to the cylinder as well as of subgrid scale model are also examined. The numerical predictions are in very good agreement with the measurements in terms of mean as well as turbulence quantities. The instantaneous flow patterns of the flow field are examined and the effect of the external flow pulsation on the wake characteristics such as vortex formation length, vortex strength, Strouhal number as well as the lift and drag coefficients is quantified. The vortex formation length is decreased while the mean drag, as well as the rms values of the drag and lift coefficients increase significantly under pulsating flow conditions. The performance of the LES technique is analysed in the light of the wake characteristics.     

Direct numerical simulation of turbulent channel flows using a stabilized finite element method

Direct numerical simulations (DNS) of incompressible turbulent channel flows at Re_τ = 180 and 395 (i.e., Reynolds number, based on the friction velocity and channel half-width) were performed using a stabilized finite element method (FEM). These simulations have been motivated by the fact that the use of stabilized finite element methods for DNS and LES is fairly recent and thus the question of how accurately these methods capture the wide range of scales in a turbulent flow remains open. To help address this question, we present converged results of turbulent channel flows under statistical equilibrium in terms of mean velocity, mean shear stresses, root mean square velocity fluctuations, autocorrelation coefficients, one-dimensional energy spectra and balances of the transport equation for turbulent kinetic energy. These results are consistent with previously published DNS results based on a pseudo-spectral method, thereby demonstrating the accuracy of the stabilized FEM for turbulence simulations.     

Linear and nonlinear model large-eddy simulations of a plane jet

The mixed-nonlinear Kosovi?, Leray and LANS-α subgrid scale models are contrasted with linear Smagorinsky and Yoshizawa large-eddy simulations for a Re = 4000 plane jet simulation. Comparisons are made with direct numerical simulation data and reliable measurements. Global properties of the jet such as the spreading and centerline velocity decay rates are investigated. The mean-flow and turbulence parameters in the self-similar region are also studied. Mixed models developed for boundary layers compare well with the benchmark jet data and the linear model predictions. Differences between the models are minor and none showed any clear advantage in all the data comparisons.     

Two-step simulation of slat noise

The flow field and the acoustic field of a high-lift configuration consisting of a slat and a main wing are numerically investigated by a hybrid method. In a first step, the unsteady flow field is computed via a large-eddy simulation (LES) and in a second step, the acoustic field is determined by solving the acoustic perturbation equations (APE). The mean flow field is compared to experimental findings followed by an investigation of the turbulent structures which are visualized by λ₂ contours. The analysis of the acoustic field shows that at the main wing trailing edge acoustic pressure fluctuations of approximately 5 kHz are generated. Correlations between the noise sources and the acoustic pressure identify the slat-gap region to be responsible for the mixture of broadband and tonal noise between 1 and 3 kHz. The decay of the pressure spectrum is found to be approximately f⁻² which is in agreement with the literature.     

Computation of a high Reynolds number jet and its radiated noise using large eddy simulation based on explicit filtering

An isothermal circular jet with a Mach number of M = 0.9 and a Reynolds number of Re_D = 4 × 10⁵ is computed by compressible large eddy simulation (LES). The LES is carried out using an explicit filtering to damp the scales discretized by less than four grid points without affecting the resolved large scales. The jet features are thus found not to appreciably depend on the filtering procedure. The flow development is also shown from simulations on different grids to be independent of the location of the grid boundaries. The flow and the sound field obtained directly by LES are compared to measurements of the literature. The acoustic radiation especially displays spectra and azimuthal correlation functions which behave according to the observation angle as expected for a high Reynolds number. Furthermore the two components of jet noise usually associated to large structures and to fine-scale turbulence, respectively, are apparently found.     

Frequency characteristics of coherent structures and their excitations in small aspect-ratio rectangular jets using large eddy simulation

Large eddy simulations of air jets from small aspect-ratio (AR) rectangular nozzles are performed with the dynamic subgrid-scale closure. Mean streamwise velocity profiles are in good agreement with experimental data. Results indicate that vortices originating from the longer side of the rectangular jet are dominant compared with that from the shorter side. Furthermore, entrainment is slight in the potential core, and significantly increases in the following vortex roll-up region. However, the jet entrains more with smaller AR. Power spectral density of the streamwise velocity indicates that the oscillations consist of a series of sub-harmonic frequencies, with the predominant frequencies reducing along the axial direction. Analysis shows that among multiple frequencies, there is a characteristic one at f = 0.22 which dominates the near field of the rectangular jet. The characteristic frequency is independent of velocity components, aspect ratios of the jet and locations. Based on this characteristic frequency, calculations with different forced frequencies imposed on the inlet nozzle are carried out. Results indicate that when the forced frequency is approximately equal to the characteristic frequency, development of the coherent structures is the most intense in the near field, and exhibits the strongest entrainment.     

Large-eddy simulation of streamwise-rotating turbulent channel flow

In many engineering and industrial applications the investigation of rotating turbulent flow is of great interest. Whereas some research has been done concerning channel flows with a spanwise rotation axis, only few investigations have been performed on channel flows with a rotation about the streamwise axis. In the present study an LES of a turbulent streamwise-rotating channel flow at Re_τ = 180 is performed using a moving grid method. The three-dimensional structures and the details of the secondary flow distribution are analyzed and compared with experimental data. The numerical-experimental comparison shows a convincing agreement as to the overall flow features. The results confirm the development of a secondary flow in the spanwise direction, which has been found to be correlated to the rotational speed. Furthermore, the findings show the distortion of the main flow velocity profile, the slight decrease of the streamwise Reynolds stresses in the vicinity of the walls, and the pronounced increase of the spanwise Reynolds stresses at higher rotation rates near the walls and particularly in the symmetry region. As to the numerical set-up it is shown that periodic boundary conditions in the spanwise direction suffice if the spanwise extent of the computational domain is larger than 10 times the channel half width.     

Simulation of the effect of geometric parameters on tangentially injected swirling pipe airflow

A realizable k–ε turbulence model is employed to study compressible tangentially injected swirling flow in the nozzle of air–jet spinning. The effects of the nozzle geometric parameters (the injection angle, the diameter, number and position of the injector, nozzle length and chamber diameter) on both the flow and yarn properties are investigated. The simulation results show that some factors, such as velocity distribution, reverse flow in the upstream of the injector and vortex breakdown in the downstream caused by the nozzle geometric variation, are significantly related to fluid flow, and consequently to yarn properties. With increase in the injection angle or injector diameter or injector number, in the downstream of the injector, velocities will increase somewhat, and the locations of vortex breakdown move downward. As injector number increase with the total injection area being kept constant, the strength of vortex breakdown in the downstream of the injector will slightly increase. A larger reverse flow will be not helpful to draw the fibers into nozzle, as the injector position is closer to the nozzle inlet. The flow is more turbulent for a larger chamber diameter.     

Two-dimensional side-by-side circular cylinders at moderate Reynolds numbers

In a companion article [1], we described computer simulations of the flow around 2 two-dimensional, tandem circular cylinders in a flow for 1?Re?20. In this article we adopt a similar approach to characterize the flow around side-by-side cylinders with surface-to-surface separation/diameter in the range 0.1 < s/D < 30. The results revealed some distinct and interesting features of the flow, which are completely different than those observed at higher Reynolds numbers.At low Reynolds numbers, 1?Re?5, for all gap spacings, the flow contains no regions of flow separation. At higher Re, four distinct flow behaviors were observed. For very small gap spacings, e.g. 0.1 < s/D < 0.6 at Re = 20, two elongated “detached vortices” form downstream of the cylinders. The drag coefficient increases sharply with the gap spacing. For gap spacings 0.6 < s/D < 0.7 at Re = 20, no vortices form anywhere in the flow. For gap spacings around s/D ≈ 1 separation regions form only on the inside portions of the cylinders. For larger gap spacings s/D > 1 the flow reverts to something similar to that around an isolated cylinder in the flow, i.e. two attached vortices on the rear side of each cylinder. In general, the drag coefficient increases as the gap spacing increases. At higher Reynolds number it is known that the cylinder lift coefficients decrease monotonically with gap spacing. In contrast, at these lower Reynolds number the lift coefficient curves rise to a maximum for 0.3 < s/D < 3 and then decrease monotonically for larger s/D.     

A zonal RANS-LES method to determine the flow over a high-lift configuration

High Reynolds number flows are particularly challenging problems for large-eddy simulations (LES) since small-scale structures in thin and often transitional boundary layers are to be resolved. The range of the turbulent scales is enormous, especially when high-lift configuration flows are considered. For this reason, the prediction of high Reynolds number flow over the entire airfoil using LES requires huge computer resources. To remedy this problem a zonal RANS-LES method for the flow over an airfoil in high-lift configuration at Re_c=1.0×10⁶ is presented. In a first step, a 2D RANS solution is sought, from which boundary conditions are formulated for an embedded LES domain, which comprises the flap and a sub-part of the main airfoil. The turbulent fluctuations in the boundary layers at the inflow region of the LES domain are generated by controlled forcing terms, which use the turbulent shear stress profiles obtained from the RANS solution. The comparison with an LES solution for the full domain and with experimental data shows likewise results for the velocity profiles and wall pressure distributions. The zonal RANS-LES method reduces the computational effort of a full domain LES by approx. 50%.     

Lattice Boltzmann simulation of lid-driven swirling flow in confined cylindrical cavity

Lid-driven swirling flow in a confined cylindrical cavity is investigated using lattice Boltzmann equation (LBE) method. The steady, 3-dimensional flow is examined at different aspect (height-to-radius) ratios and Reynolds numbers. The LBE simulations are carried out using the multiple-relaxation-time method. The LBE simulation results are compared with the results of a finite volume solution of Navier-Stokes equations and with published experimental data. Numerical results are presented for cylindrical cavities with two aspect ratios of 1.5 and 2.5, and three Reynolds numbers of 990, 1010 and 1290. Effects of the aspect ratio and Reynolds number on the size, position and breakdown of the central recirculation bubble, together with the flow pattern in the cavity, are determined. Detailed topological features of the flow, such as, (1) structure and breakdown of the vortex along the axis, (2) azimuthal component of vorticity, and (3) circulation strength of flow about the axis are investigated and compared with previous findings from experiments and theory.The predicted results from LBE simulations are consistent with experiments and theory. Steady results reveal the occurrence of a breakdown bubble in agreement with the regime diagram due to Escudier. The vortex breakdown around a region may be characterized by a change in sign of the azimuthal vorticity near such locations. Investigations are carried out on the characteristics of angular momentum when the vortex breakdown occurs. The theoretical criterion for vortex breakdown to occur, as proposed by Brown and Lopez is verified using the numerical data obtained from the simulations.     

Eduction of near wall flow structures responsible for large deviations of the momentum-heat transfer analogy and fluctuations of wall transfer rates in turbulent channel flow

In this paper we analyze the flow structures responsible for large local instantaneous deviations of the conventional momentum-heat transfer analogy and large fluctuations of the wall shear stress and the wall heat flux in a forced convection turbulent channel flow at low-Reynolds numbers (Re = 4570, Pr = 0.7). The analysis was carried out using a database obtained from a direct numerical simulation performed with a second-order finite volume code. The ensemble averaged velocity and temperature profiles and profiles of the turbulence intensities and turbulent heat fluxes agree well with direct numerical simulations available in the literature. When the flow was statistically fully developed, we recorded the time evolution of the velocities and temperatures near one wall of the channel. The near wall structures responsible for the extreme values of the deviations were educed by a conditional sampling technique. Results show that extreme values of the wall shear stress and wall heat transfer rates, as well as departures from the conventional analogy between momentum and heat transfer, occur within the high-speed streaks on the wall and are associated with fluctuations of the streamwise pressure gradient. These large fluctuations on the wall are produced by the combined effect of two quasi-parallel counterrotating streamwise vortices.     

Optimization of a synthetic jet actuator for aerodynamic stall control

The numerical simulation of aerodynamic stall control using a synthetic jet actuator is presented and the automatic optimization of the control parameters is investigated. Unsteady Reynolds-averaged Navier-Stokes equations are solved on unstructured grids using a near-wall low-Reynolds number turbulence closure to simulate the effects of a synthetic jet, located at 12% of the chord from the leading edge of a NACA 0015 airfoil, for a Reynolds number Re = 8.96 × 10⁵ and incidences between 12° and 24°. Then, an automatic optimization procedure coupled with the flow solver is employed to optimize the parameters of the actuator (momentum coefficient, frequency, angle with respect to the wall) at each incidence in order to increase the time-averaged lift. A significant increase of the maximum lift is obtained (+52% with respect to the baseline airfoil) and the stall delayed from 16° to 22° for optimal parameters. The flow characteristics and the influence of the respective control parameters are analysed.     

DNS of a plane mixing layer for the investigation of sound generation mechanisms

Direct numerical simulations in two and three dimensions have been performed to investigate the sound generation by vortex pairing in a compressible plane mixing layer with Ma₁ = 0.5 being the upper and Ma₂ = 0.25 being the lower stream Mach number. The Reynolds number based on the vorticity thickness at the inflow and the velocity of the upper stream is Re=500. The flow is forced at the inflow with eigenfunctions obtained from viscous linear stability theory including three-dimensional disturbances. The results are verified with linear stability theory and the two-dimensional simulations performed by Colonius et al. [Colonius T, Lele SK, Moin P. Sound generation in a mixing layer. J Fluid Mech 1997;330:375-409]. The excitation of a steady longitudinal vortex mode leads to an early three-dimensional deformation of the travelling spanwise vortices and reduced sound emission to the slower fluid stream side.     

Lattice Boltzmann simulations to determine drag, lift and torque acting on non-spherical particles

The drag, lift and moment coefficients of differently shaped single particles have been determined as a function of the angle of incidence at particle Reynolds numbers between Re = 0.3 and 240 under different conditions. For this purpose simulations of the flow around these particles have been performed using the three-dimensional Lattice Boltzmann method. In the first case studied a particle is fixed in a uniform flow, in the second case the particle is rotating in a uniform flow to determine, among others, the Magnus lift force and in the third case the particle is fixed in a linear shear flow. In the first case six particle shapes are considered, i.e. a sphere, a spheroid, a cube, a cuboid and two cylinders with an axis ratio of 1 and 1.5, respectively. In the second and third case the sphere and the spheroid are considered. At the higher Re considered, the drag depends strongly on particle shape, the angle of incidence and particle rotation. The lift and the torque of both the sphere and the spheroid are strongly affected by particle rotation and fluid shear. For approximately Re ? 1, the shear induced lift for unbounded flow could not be simulated as the top and bottom wall have a significant influence in the current flow configuration. The shear induced lift of the sphere changes direction at approximately Re = 50 and the mean (over the orientation) shear induced lift of the spheroid changes direction at approximately Re = 90.