Near-wall Vortices Research Articles

Direct Numerical Simulation of Solid Propellant Combustion in Crossflow

A direct numerical simulation (DNS) of a homogeneous ammonium perchlorate/hydroxyl-terminated polybutadiene solid propellant in crossflow was carried out to provide proper boundary conditions to an interior ballistics model. A two-step global finite-rate chemistry model for ammonium perchlorate decomposition and decomposition gas-binder gas reactions was used. An Arrhenius pyrolysis model was used to describe the propellant regression rate. Using strand burn rate data, the DNS model was calibrated by modeling an environment with no crossflow and adjusting thermodynamic properties in the gas/solid to match the measured regression rate. Crossflow Mach numbers were then induced, ranging from At = 0.0 to 0.8, where the calculated regression rates are compared to the base regression rate at M = 0.0. The analysis shows that near-wall vorticity increases with Mach number, but does not significantly reduce the flame to wall stand-off distance. Temperature gradients due to boundary layer compression are shown to dominate the regression rate. The validity of the results was tested by incorporating them into an interior ballistics model to simulate the performance of an actual rocket motor and compare to static test data. A simplified DNS heat-transfer-based analysis is presented and shown to produce similar conclusions.

On the coherent drag-reducing and turbulence-enhancing behaviour of polymers in wall flows

Numerical simulations of turbulent polymer solutions using the FENE-P model are used to characterize the action of polymers on turbulence in drag-reduced flows. The energetics of turbulence is investigated by correlating the work done by polymers on the flow with turbulent structures. Polymers are found to store and to release energy to the flow in a well-organized manner. The storage of energy occurs around near-wall vortices as has been anticipated for a long time. Quite unexpectedly, coherent release of energy is observed in the very near-wall region. Large fluctuations of polymer work are shown to re-energize decaying streamwise velocity fluctuations in high-speed streaks just above the viscous sublayer. These distinct behaviours are used to propose an autonomous regeneration cycle of polymer wall turbulence, in the spirit of Jiménez & Pinelli (1999).

A visual study on complex flow structures and flow breakdown in a boundary layer transition

A visualization study is conducted on the excited laminar-turbulent transition within a flat plate boundary layer flow in a water tunnel. The hydrogen bubble technique is employed to investigate the complex characteristics of the flow structure and its breakdown in the later stages of the transition. A new flow structure is observed, which involves two secondary hairpin vortices outboard of both legs of a primary hairpin vortex. This complex structure is argued to be a precursor of a turbulent spot in this K-type transition. Also reported in the paper is the evolution of the flow structure and its subsequent breakdown, manifested by the emergence of dark spots, low-speed fluid bumps, and near-wall hairpin vortex groups. The results indicate that the near-wall flow breakdown is the result of instability of a local three-dimensional high-shear layer between the low-speed fluid bump and the outer higher-speed region.

Numerical Investigation on Large-Scale Structure and Statistics in Turbulent Flow in a Rotating Channel

Fully-developed flow in a channel subjected to the spanwise rotation was investigated by means of the direct numerical simulation (DNS). Two steps of rotation number, Roτ=1 and Roτ=2.5, and stationary condition were mainly calculated. The turbulence was enhanced in the pressure side and attenuated in the suction side by increasing the rotation number, but the change was not monotonic.Notable feature was found for the case of Roτ≈ 1 : the flow rate takes its maximum ; it fluctuated in time ; the shift of Reynolds shear stress almost teminated. For higher rotation rate, roll-cell vortices and, as a consequence, the constant-gradient in the mean velocity profile were observed. Furthermore, the log profile was evident only in the region blown from the pressure side by the roll-cell vortices. Due to these observations, it was found that the rotation number 'unity' was a turning point of the change of dominant structures : the near-wall vortices in lower rotation and the large-scale roll-cell vortices in higher.

1325 境界層ヘアピン渦を制御するための機構の研究

Control of near-wall large-scale vortices is significant for a skin frication reduction in the turbulent boundary layers. From this viewpoint, the mechanism to control hairpin vortices in the transitional boundary layers developing on a flat plate is studied. Using a pair of wings, which is designed so that each wing generates a circulation opposite to longitudinal hairpin vorticity, hairpin vortices have been manipulated. This configuration of the wings results in as much as 35% turbulent fluctuation reduction. This technique will be applied to manipulation of many hairpin vortices generated by acoustic excitation with a loudspeaker.

Mechanisms for particle transfer and segregation in a turbulent boundary layer

Particle transfer in the wall region of turbulent boundary layers is dominated by the coherent structures which control the turbulence regeneration cycle. Coherent structures bring particles toward and away from the wall and favour particle segregation in the viscous region, giving rise to non-uniform particle distribution profiles which peak close to the wall. The object of this work is to understand the reasons for higher particle concentration in the wall region by examining turbulent transfer of heavy particles to and away from the wall in connection with the coherent structures of the boundary layer. We will examine the behaviour of a dilute dispersion of heavy particles – flyashes in air – in a vertical channel flow, using pseudo-spectral direct numerical simulation to calculate the turbulent flow field at a shear Reynolds number Reτ = 150, and Lagrangian tracking to describe the dynamics of particles. Drag force, gravity and Saffman lift are used in the equation of motion for the particles, which are assumed to have no influence on the flow field. Particle interaction with the wall is fully elastic. As reported in several previous investigations, we found that particles are transferred by sweeps – Q2 type events – in the wall region, where they preferentially accumulate in the low-speed streak environments, whereas ejections – Q4 type events – transfer particles from the wall region to the outer flow. We quantify the efficiency of the instantaneous realizations of the Reynolds stresses events in transferring different size particles to the wall and away from the wall, respectively. Our findings confirm that sweeps and ejections are efficient transfer mechanisms for particles. In particular, we find that only those sweep and ejection events with substantial spatial coherence are effective in transferring particles. However, the efficiency of the transfer mechanisms is conditioned by the presence of particles to be transferred. In the case of ejections, particles are more rarely available since, when in the viscous wall layer, they are concentrated under the low-speed streaks. Even though the low-speed streaks are ejection-like environments, particles remain trapped for a long time. This phenomenon, which causes accumulation of particles in the near-wall region, can be interpreted in terms of overall fluxes toward and away from the wall by the theory of turbophoresis. This theory, proposed initially by Caporaloni et al. (1975) and re-examined later by Reeks (1983), can help to explain the existence of net particle fluxes toward the wall as a manifestation of the skewness in the velocity distribution of the particles (Reeks 1983). To understand the local and instantaneous mechanisms which give rise to the phenomenon of turbophoresis, we focus on the near-wall region of the turbulent boundary layer. We examine the role of the rear-end of a quasistreamwise vortex very near to the wall in preventing particles in the proximity of the wall from being re-entrained by the pumping action of the large, farther from the wall, forward-end of a following quasi-streamwise vortex. We examine several mechanisms for turbulence structures near the wall and we find that the mechanism based on the archetypal quasi-streamwise structures identified by Schoppa & Hussain (1997), the parent–offspring regeneration cycle for near-wall quasi-streamwise vortices discussed by Brooke & Hanratty (1993), and the mechanism based on coherent packets of hairpin vortices, the fundamental super-structure characterized by Adrian, Meinhart & Tomkins (2000), all depict the same characteristic pattern which is responsible for particle trapping very near to the wall.

Navier–Stokes solutions of unsteady separation induced by a vortex

Numerical solutions of the unsteady Navier–Stokes equations are considered for the flow induced by a thick-core vortex convecting along a surface in a two-dimensional incompressible flow. The presence of the vortex induces an adverse streamwise pressure gradient along the surface that leads to the formation of a secondary recirculation region followed by a narrow eruption of near-wall fluid in solutions of the unsteady boundary-layer equations. The locally thickening boundary layer in the vicinity of the eruption provokes an interaction between the viscous boundary layer and the outer inviscid flow. Numerical solutions of the Navier–Stokes equations show that the interaction occurs on two distinct streamwise length scales depending upon which of three Reynolds-number regimes is being considered. At high Reynolds numbers, the spike leads to a small-scale interaction; at moderate Reynolds numbers, the flow experiences a large-scale interaction followed by the small-scale interaction due to the spike; at low Reynolds numbers, large-scale interaction occurs, but there is no spike or subsequent small-scale interaction. The large-scale interaction is found to play an essential role in determining the overall evolution of unsteady separation in the moderate-Reynolds-number regime; it accelerates the spike formation process and leads to formation of secondary recirculation regions, splitting of the primary recirculation region into multiple corotating eddies and ejections of near-wall vorticity. These eddies later merge prior to being lifted away from the surface and causing detachment of the thick-core vortex.

Reynolds number effect on wall turbulence: toward effective feedback control

Direct numerical simulation of turbulent channel flow at Re τ =110–650 is made in order to assess the feedback control algorithms which have been proposed for reducing skin friction. The effectiveness of the existing control schemes is decreased with increasing the Reynolds number from Re τ =110 to 300. It is found, through the Karhunen–Loeve (KL) decomposition of turbulent fluctuations, that the KL modes at 15< y +<30, which correspond to longitudinal vortices and near-wall streaky structures, play a dominant role in the production of turbulence and wall shear stress at Re τ =110. At Re τ =300, however, the KL modes at 30< y +<75 also make appreciable contribution to the wall shear stress generation. The regeneration mechanism of the near-wall vortices is related to the nonlinear interaction between the KL modes at 15< y +<30 and those at 30< y +<75.

Assessment of Local Blowing and Suction in a Turbulent Boundary Layer

Effects of local blowing or suction from a spanwise slot on a turbulent boundary layer flow are investigated using the direct numerical simulation technique. Three different blowing or suction velocities are imposed on the slot keeping blowing or suction flow rate constant. The recoveries of mean wall pressure for the different blowing velocities collapse well on the same recovery line. However, each wall pressure recovers just after the slot for suction. In the blowing case, the relaxation of rms wall pressure fluctuations and pressure gradient after the slot is seen and the relaxation distance from the slot center is nearly constant for three different blowing velocities. In the suction case, the flow recovers from the immediate rear of the slot. These features are also observed in three-dimensional views of the near-wall vortices.

Assessment of local blowing and suction in a turbulent boundary layer

Effects of local blowing or suction from a spanwise slot on a turbulent boundary layer flow are investigated using the direct numerical simulation technique. Three different blowing or suction velocities are imposed on the slot keeping blowing or suction flow rate constant. The recoveries of mean wall pressure for the different blowing velocities collapse well on the same recovery line. However, each wall pressure recovers just after the slot for suction. In the blowing case, the relaxation of rms wall pressure fluctuations and pressure gradient after the slot is seen and the relaxation distance from the slot center is nearly constant for three different blowing velocities. In the suction case, the flow recovers from the immediate rear of the slot. These features are also observed in three-dimensional views of the near-wall vortices.

Reynolds Number Effect on Wall Turbulence. Toward Effective Feedback Control.

Direct numerical simulation of turbulent channel flow at Reτ=110∼650 is made in order to assess the feedback control algorithms which have been proposed for reducing skin friction. The effectiveness of the existing control schemes is decreased with increasing the Reynolds number from Reτ=110 to 300. It is found, through the Karhunen-Loeve (KL) decomposition of turbulent fluctuations, that the KL modes at 15<y+<30, which correspond to longitudinal vortices and near-wall streaky structures, play a dominant role in the production of turbulence and wall shear stress at Reτ=110. At Reτ=300, however, the KL modes at 30<y+<75 also make appreciable contribution to the wall shear stress generation. The regeneration mechanism of the near-wall vortices is related to the nonlinear interaction between the KL modes at 15<y+<30 and those at 30<y+<75.

Physical Analysis and Scaling of a Jet and Vortex Actuator

Our previous studies have shown that the Jet and Vortex Actuator generates free-jet, wall-jet, and near-wall vortex flow fields. That is, the actuator can be operated in different modes by simply varying the driving frequency and/or amplitude. For this study, variations are made in the actuator plate and wide-slot widths and sine/asymmetrical actuator plate input forcing (drivers) to further study the actuator induced flow fields. Laser sheet flow visualization, particle-image velocimetry, and laser velocimetry are used to measure and charactrerize the actuator induced flow fields. Laser velocimetry measurements indicate that the vortex strength increases with the driver reptition rate for a fixed actuator geometry (wide slot and plate width). For a given driver repetition rate, the vortex strength increases as the plate width decreases provided the wide-slot to plate-width ratio is fixed. Using an asymmetric plate driver, a stronger vortex is generated for the same actuator geometry and a given driver repetition rate. The nondimensional scaling provides the approximate ranges for operating the actuator in the free jet, wall jet, or vortex flow regimes. Finally, phase-locked velocity measurements from particle image velocimetry indicate that the vortex structure is stationary, confirming previous computations. Both the computations and the particle image velocimetry measurements (expectantly) show unsteadiness near the wide-slot opening, which is indicative of mass ejection from the actuator.

Transport and deposition of flexible fibers in turbulent duct flows

Transport, dispersion, and deposition of flexible fibrous particles in the near-wall coherent vortices in a turbulent duct flow are studied. The vortical flow field is modeled as a sequence of plane stagnation point flows. Fibers are assumed to be inextensible but completely flexible. That is, fibers have no stiffness and offer no resistance to bending. In the simulation, a flexible fiber is divided into many segments. Interactions of each element with the adjacent elements are through interfacial forces that are evaluated as part of the solution. For different fiber diameters, aspect ratios, and initial configurations, deposition velocities are evaluated, and the fiber dispersion is analyzed. An empirical equation for the deposition velocity of flexible fibers is also developed. The results for flexible fiber deposition rate are compared with those for rigid straight fibers and the empirical equation predictions.

Three-dimensional calculations of the flow field around a turbine blade with film cooling injection near the leading edge

Injection of coolant air from a showerhead injection system at the leading edge of a high pressure turbine blade is investigated using a fully implicit three-dimensional finite-volume method on multi-block grids. For various blowing rates, the calculation results for the velocity and pressure fields and turbulence intensity are compared with available experimental data. The present method yields excellent agreement with the experiments for the isentropic Mach number distributions on the blade surface. The standardk–e turbulence model with wall functions is already capable of capturing the major details of the flow field including the injection-induced secondary-flow vortices, particularly so on the suction side. On the pressure side, however, the lateral jet spreading is under-predicted somewhat together with an exaggeration of the near-wall sink-flow vortices. On this side with convex walls, where turbulence anisotropy is appreciable according to the experiments, overall better predictions were obtained with the anisotropy correction of Bergeles et al. [23] promoting the Reynolds stress in the lateral direction. The correction has no beneficial effect on the suction side with concave walls where the turbulence anisotropy was observed to be much smaller.

Aerosol Particle Removal and Re-entrainment in Turbulent Channel Flows – A Direct Numerical Simulation Approach

Aerosol particle removal and re-entrainment in turbulent channel flows are studied. The instantaneous fluid velocity field is generated by the direct numerical simulation (DNS) of the Navier – Stokes equation via a pseudospectral method. Particle removal mechanisms in turbulent channel flows are examined and the effects of hydrodynamic forces, torques and the near-wall coherent vorticity are discussed. The particle resuspension rates are evaluated, and the results are compared with the model of Reeks. The particle equation of motion used includes the hydrodynamic, the Brownian, the shearinduced lift and the gravitational forces. An ensemble of 8192 particles is used for particle resuspension and the subsequent trajectory analyses. It is found that large-size particles move away roughly perpendicular to the wall due to the action of the lift force. Small particles, however, follow the upward flows formed by the near-wall eddies in the low-speed streak regions. Thus, turbulent near-wall vortical structures play an important role in small particle resuspension, while the lift is an important factor for reentrainment of large particles. The simulation results suggests that small particles (with τ p + ≤ 0.023) primarily move away from the wall in the low-speed streaks, while larger particles (with τ p + ≥ 780) are mostly removed in the high-speed streaks.

WALL DEPOSITION OF SMALL ELLIPSOIDS FROM TURBULENT AIR FLOWS—A BROWNIAN DYNAMICS SIMULATION

Brownian dynamics simulations of the motions of ellipsoidal particles in the turbulence near-wall coherent vortices are carried out. The kinematics and the dynamics of an ellipsoidal particle moving in shear flows are outlined. Euler's four parameters (quaternions) are used for describing the particle orientation. The particle equation of motion includes the hydrodynamic forces and torques, the shear-induced lift force, and the Brownian forces and torques. The near-wall coherent structures are simulated using vortical flow models. A turbulence mean flow is used in the streamwise direction, and the spanwise direction is assumed to be periodic. The wall is modeled as an absorbing (a sticky surface) boundary condition. Ensembles of particle trajectories are evaluated and statistically analyzed. For various particle sizes, aspect ratios, and densities, the deposition velocities of elongated particles in turbulent air streams are evaluated. An empirical equation for the turbulent deposition rate of ellipsoidal particles is also developed. The results are compared with earlier studies and the available experimental data.

Nonlinear RDT theory of near-wall turbulence

A WKB method was recently used to extend rapid distortion theory (RDT) to initially inhomogeneous turbulence strained by irrotational mean flows [S.V. Nazarenko, N. Kevlahan, B. Dubrulle, J. Fluid Mech. 390 (1999) 325]. This theory takes into account the feedback of turbulence on the mean flow, and it was used by Nazarenko et al. to explain the effect of strain reduction caused by turbulence observed by Andreotti et al. [B. Andreotti, S. Douady,Y. Couder, in: O. Boratav, A. Eden, A. Erzan (Eds.), Turbulence Modeling and Vortex Dynamics, Proceedings of a Workshop held at Istanbul, Turkey, 2–6 September 1996, pp. 92–108]. In this paper, we develop a similar WKB RDT approach for shear flows. We restrict ourselves to problems where the turbulence is small-scale with respect to the mean flow length-scale and turbulence vorticity is weak compared to the mean shear. We show that the celebrated log-law of the wall exists as an exact analytical solution in our model if the initial turbulence vorticity (debris of the near-wall vortices penetrating into the outer regions) is statistically homogeneous in space and shortly correlated in time. We demonstrate that the main contribution to the shear stress comes from very small turbulent scales which are close to the viscous cut-off and which are elongated in the stream-wise direction (streaks). We also find that anisotropy of the initial turbulent vorticity changes the scaling of the shear stress, but leaves the log-law essentially unchanged.

Coherent structure dynamics in near-wall turbulence

The regeneration and dynamics of near-wall longitudinal vortices – which dominate turbulence production, drag, and heat transfer – are analyzed using direct numerical simulation of turbulent channel flow. These dominant streamwise vortices are shown to result from nonlinear saturation of an instability of lifted low-speed streaks near a single wall, free from any initial vortex. The newly-found instability mechanism initiates streak waviness in the ( x, z) plane, generating streamwise vorticity sheets. Streak waviness in turn induces positive ∂u/ ∂x (i.e. positive VISA), which causes these sheets’ vorticity to then concentrate via stretching (rather than roll up) into new streamwise vortices. The instability requires sufficiently strong streaks ( y circulation per unit x>7.6 wall units) and is inviscid in nature, despite the close proximity of the no-slip wall. We find that self-annihilation of streaks due to viscous cross-diffusion of opposite-signed wall normal vorticity across each streak causes the instability amplification to scale in wall units, suggesting the relevance of our results to high Re as well. Significantly, the strongly 3D vortices generated by streak instability agree well with the CS educed from fully turbulent flow, suggesting the prevalence of this streak instability-based vortex formation mechanism. Simultaneous to vortex generation, an internal shear layer is generated across the streak from each streamwise vortex by stretching of spanwise vorticity. Such a shear layer eventually rolls up at the downstream end of a streamwise vortex, and the two link up and propagate outward to form a spanwise “arch” vortex. The newly generated streamwise vortices act to sustain/strengthen the preexisting streak which spawned them through localized lifting of near-wall fluid by induction. We develop a new spatiotemporal vortex generation mechanism, in which vortices leave behind “vortex-less” streaks, whose instability, due to the mechanism explained herein, initiates streamwise vortex formation.

Relationship between wall pressure and velocity-field sources

The objective of this investigation is to study the velocity-field sources for the fluctuating wall pressure, determine their locations in the boundary layer, and investigate their physics. The velocity-field sources and partial wall pressures were computed from a database generated by a direct numerical simulation of a low Reynolds number, fully developed, turbulent channel flow. Results show that the mean-shear (MS) and turbulence-turbulence (TT) partial pressures (πMS and πTT, respectively) are the same order of magnitude. The buffer region dominates most of the wave number range; the viscous shear layer is significant at the highest wavenumbers; the buffer and logarithmic regions are important at low wavenumbers. Over most of the wavenumber range, the contribution from the buffer region is the dominant TT component; in the low-wavenumber range, the viscous shear layer, buffer region, and logarithmic region are significant; in the medium and high wavenumbers the viscous shear layer and buffer region dominate. The most important TT partial pressures are π23TT, π13TT and π12TT from the buffer region. It is conjectured that π23TT and π13TT may be generated by quasi-streamwise vortices. π12TT may be due to near-wall shear layers and spanwise vortices. π23TT, π22TT and π33TT from the viscous shear layer are the dominant high-wavenumber partial pressures.

The turbulent boundary layer over transverse square cavities

Laser-induced uorescence (LIF) and laser Doppler velocimetry (LDV) are used to explore the structure of a turbulent boundary layer over a wall made up of two-dimensional square cavities placed transversely to the flow direction. There is strong evidence of occurrence of outflows of fluid from the cavities as well as inflows into the cavities. These events occur in a pseudo-random manner and are closely associated with the passage of near-wall quasi-streamwise vortices. These vortices and the associated low-speed streaks are similar to those found in a turbulent boundary layer over a smooth wall. It is conjectured that outflows play an important role in maintaining the level of turbulent energy in the layer and enhancing the approach towards self-preservation. Relative to a smooth wall layer, there is a discernible increase in the magnitudes of all the Reynolds stresses and a smaller streamwise variation of the local skin friction coefficient. A local maximum in the Reynolds shear stress is observed in the shear layers over the cavities.