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• 101.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
Department of Engineering, University of Cambridge, Cambridge, UK. DIIN, University of Salerno, Fisciano, Italy. Department of Engineering, Univerisyt of Cambridge, Cambridge, UK. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
The planar X-junction flow: stability analysis and control2014In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 753, p. 1-28Article in journal (Refereed)

The bifurcations and control of the flow in a planar X-junction are studied via linear stability analysis and direct numerical simulations. This study reveals the instability mechanisms in a symmetric channel junction and shows how these can be stabilized or destabilized by boundary modification. We observe two bifurcations as the Reynolds number increases. They both scale with the inlet speed of the two side channels and are almost independent of the inlet speed of the main channel. Equivalently, both bifurcations appear when the recirculation zones reach a critical length. A two-dimensional stationary global mode becomes unstable first, changing the flow from a steady symmetric state to a steady asymmetric state via a pitchfork bifurcation. The core of this instability, whether defined by the structural sensitivity or by the disturbance energy production, is at the edges of the recirculation bubbles, which are located symmetrically along the walls of the downstream channel. The energy analysis shows that the first bifurcation is due to a lift-up mechanism. We develop an adjustable control strategy for the first bifurcation with distributed suction or blowing at the walls. The linearly optimal wall-normal velocity distribution is computed through a sensitivity analysis and is shown to delay the first bifurcation from Re = 82.5 to Re = 150. This stabilizing effect arises because blowing at the walls weakens the wall-normal gradient of the streamwise velocity around the recirculation zone and hinders the lift-up. At the second bifurcation, a three-dimensional stationary global mode with a spanwise wavenumber of order unity becomes unstable around the asymmetric steady state. Nonlinear three-dimensional simulations at the second bifurcation display transition to a nonlinear cycle involving growth of a three-dimensional steady structure, time-periodic secondary instability and nonlinear breakdown restoring a two-dimensional flow. Finally, we show that the sensitivity to wall suction at the second bifurcation is as large as it is at the first bifurcation, providing a possible mechanism for destabilization.

• 102.
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
An explicit algebraic Reynolds-stress and scalar-flux model for stably stratified flows2013In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 723, p. 91-125Article in journal (Refereed)

This work describes the derivation of an algebraic model for the Reynolds stresses and turbulent heat flux in stably stratified turbulent flows, which are mutually coupled for this type of flow. For general two-dimensional mean flows, we present a correct way of expressing the Reynolds-stress anisotropy and the (normalized) turbulent heat flux as tensorial combinations of the mean strain rate, the mean rotation rate, the mean temperature gradient and gravity. A system of linear equations is derived for the coefficients in these expansions, which can easily be solved with computer algebra software for a specific choice of the model constants. The general model is simplified in the case of parallel mean shear flows where the temperature gradient is aligned with gravity. For this case, fully explicit and coupled expressions for the Reynolds-stress tensor and heat-flux vector are given. A self-consistent derivation of this model would, however, require finding a root of a polynomial equation of sixth-order, for which no simple analytical expression exists. Therefore, the nonlinear part of the algebraic equations is modelled through an approximation that is close to the consistent formulation. By using the framework of a K-omega model (where K is turbulent kinetic energy and omega an inverse time scale) and, where needed, near-wall corrections, the model is applied to homogeneous shear flow and turbulent channel flow, both with stable stratification. For the case of homogeneous shear flow, the model predicts a critical Richardson number of 0.25 above which the turbulent kinetic energy decays to zero. The channel-flow results agree well with DNS data. Furthermore, the model is shown to be robust and approximately self-consistent. It also fulfils the requirements of realizability.

• 103.
KTH, School of Engineering Sciences (SCI), Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics.
A study of the Blasius wall jet2005In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 539, p. 313-347Article in journal (Refereed)

A plane wall-jet flow is numerically investigated and compared to experiments. The measured base flow is matched to a boundary-layer solution developing from a coupled Blasius boundary layer and Blasius shear layer. Linear stability analysis is performed, revealing high instability of two-dimensional eigenmodes and non-modal streaks. The nonlinear stage of laminar-flow breakdown is studied with three-dimensional direct numerical simulations and experimentally visualized. In the direct numerical simulation, an investigation of the nonlinear interaction between two-dimensional waves and streaks is made. The role of subharmonic waves and pairing of vortex rollers is also investigated. It is demonstrated that the streaks play an important role in the breakdown process, where their growth is transformed from algebraic to exponential as they become part of the secondary instability of the two-dimensional waves. In the presence of streaks, pairing is suppressed and breakdown to turbulence is enhanced.

• 104.
KTH, School of Engineering Sciences (SCI), Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics.
Turbulent spots in the asymptotic suction boundary layer2007In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 584, p. 397-413Article in journal (Refereed)

Amplitude thresholds for transition of localized disturbances, their breakdown to turbulence and the development of turbulent spots in the asymptotic suction boundary layer are studied using direct numerical simulations. A parametric study of the horizontal scales of the initial disturbance is performed and the disturbances that lead to the highest growth under the conditions investigated are used in the simulations. The Reynolds-number dependence of the threshold amplitude of a localized disturbance is investigated for 500 <= Re <= 1200, based on the free-stream velocity and the displacement thickness. It is found that the threshold amplitude scales as Re-1.5 for the considered Reynolds numbers. For Re <= 367, the localized disturbance does not lead to a turbulent spot and this provides an estimate of the critical Reynolds number for the onset of turbulence. When the localized disturbance breaks down to a turbulent spot, it happens through the development of hairpin and spiral vortices. The shape and spreading rate of the turbulent spot are determined for Re = 500, 800 and 1200. Flow visualizations reveal that the turbulent spot takes a bullet-shaped form that becomes more distinct for higher Reynolds numbers. Long streaks extend in front of the spot and in its wake a calm region exists. The spreading rate of the turbulent spot is found to increase with increasing Reynolds number.

• 105.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
A Helmholtz decomposition of structure functions and spectra calculated from aircraft data2015In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 762, p. R4-Article in journal (Refereed)

Longitudinal and transverse structure functions, D-ll = <delta u(l)delta u(l)> and D-tt = delta u(t)delta u(t), can be calculated from aircraft data. Here, d denotes the increment between two points separated by a distance r, u(l) and u(t) the velocity components parallel and perpendicular to the aircraft track respectively and < > an average. Assuming statistical axisymmetry and making a Helmholtz decomposition of the horizontal velocity, u = u(r) + u(d), where u(r) is the rotational and u(d) the divergent component of the velocity, we derive expressions relating the structure functions D-rr = delta u(r). delta u(r) and D-dd = delta u(d). delta u(d) to D-ll and D-tt. Corresponding expressions are also derived in spectral space. The decomposition is applied to structure functions calculated from aircraft data. In the lower stratosphere, D-rr and D-dd both show a nice r(2/3)-dependence for r epsilon [2, 20] km. In this range, the ratio between rotational and divergent energy is a little larger than unity, excluding gravity waves as the principal agent behind the observations. In the upper troposphere, D-rr and D-dd show no clean r(2/3)-dependence, although the overall slope of D-dd is close to 2/3 for r epsilon [2, 400] km. The ratio between rotational and divergent energy is approximately three for r < 100 km, excluding gravity waves also in this case. We argue that the possible errors in the decomposition at scales of the order of 10 km are marginal.

• 106.
KTH, School of Engineering Sciences (SCI), Mechanics.
A note on acoustic turbulence2019In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 874, article id R2Article in journal (Refereed)

We consider a three-dimensional acoustic field of an ideal gas in which all entropy production is confined to weak shocks and show that similar scaling relations hold for such a field as for forced Burgers turbulence, where the shock amplitude scales as (epsilon d)(1/3) and the pth-order structure function scales as (epsilon d)(p/3)3r/d, epsilon being the mean energy dissipation per unit mass, d the mean distance between the shocks and r the separation distance. However, for the acoustic field, epsilon should be replaced by epsilon + chi, where chi is associated with entropy production due to heat conduction. In particular, the third-order longitudinal structure function scales as <delta u(r)(3)> = -C(epsilon + chi)r, where C takes the value 12/5 (gamma + 1) in the weak shock limit, gamma = c(p)/c(v) being the ratio between the specific heats at constant pressure and constant volume.

• 107.
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence.
The energy cascade in a strongly stratified fluid2006In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 550, p. 207-242Article in journal (Refereed)

A cascade hypothesis for a strongly stratified fluid is developed on the basis of the Boussinesq equations. According to this hypothesis, kinetic and potential energy are transferred from large to small scales in a highly anisotropic turbulent cascade. A relation for the ratio, l(v)/l(h), between the vertical and horizontal length scale is derived, showing how this ratio decreases with increased stratification. Similarity expressions are formulated for the horizontal and vertical spectra of kinetic and potential energy. A series of box simulations of the Boussinesq equations are carried out and a good agreement between the proposed hypothesis and the simulations is seen. The simulations with strongest stratification give horizontal kinetic and potential energy spectra of the form EKh = C1 is an element of E-K(2/3) k(h)(-5/3) and E-Ph = C-2 is an element of(P)k(h)(-5/3)/is an element of(1/3)(k), where k(h) is the horizontal wavenumber, EK and ep are the dissipation of kinetic and potential energy, respectively, and C-1 and C-2 are two constants. Within the given numerical accuracy, it is found that these two constants have the same value: C-1 approximate to C-2 = 0.51 +/- 0.02.

• 108.
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence.
Third-order structure function relations for quasi-geostrophic turbulence2007In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 572, p. 255-260Article in journal (Refereed)

We derive two third-order structure function relations for quasi-geostrophic turbulence, one for the forward cascade of potential enstrophy and one for the inverse cascade of energy. These relations are the counterparts of Kolmovorov's (1941) four-fifths law for the third-order longitudinal structure functions of three-dimensional turbulence.

• 109.
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence.
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence.
Stratified turbulence forced in rotational and divergent modes2007In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 586, p. 83-108Article in journal (Refereed)

We perform numerical box simulations of strongly stratified turbulence. The equations solved are the Boussinesq equations with constant Brunt-Vaisala frequency and forcing either in rotational or divergent modes, or, with another terminology, in vortical or wave modes. In both cases, we observe a forward energy cascade and inertial-range scaling of the horizontal kinetic and potential energy spectra. With forcing in rotational modes, there is approximate equipartition of kinetic energy between rotational and divergent modes in the inertial range. With forcing in divergent modes the results are sensitive to the vertical forcing wavenumber K-v(f) If k(v)(f) is sufficiently large the dynamics is very similar to the dynamics of the V V simulations which are forced in rotational modes, with approximate equipartition of kinetic energy in rotational and divergent modes in the inertial range. Frequency spectra of rotational, divergent and potential energy are calculated for individual Fourier modes. Waves are present at low horizontal wavenumbers corresponding to the largest scales in the boxes. In the inertial range, the frequency spectra exhibit no distinctive peaks in the internal wave frequency. In modes for which the vertical wavenumber is considerably larger than the horizontal wavenumber, the frequency spectra of rotational and divergent modes fall on top of each other. The simulation results indicate that the dynamics of rotational and divergent modes develop on the same time scale in stratified turbulence. We discuss the relevance of our results to atmospheric and oceanic dynamics. In particular, we review a number of observational reports indicating that stratified turbulence may be a prevalent dynamic process in the ocean at horizontal scales of the order of 10 or 100m up to several kilometres.

• 110.
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence.
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence.
Vertical dispersion by stratified turbulence2008In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 614, p. 303-314Article in journal (Refereed)

We derive a relation for the growth of the mean square of vertical displacements, delta z, of fluid particles of stratified turbulence. In the case of freely decaying turbulence, we find that for large times (delta z(2)) goes to a constant value 2(E-P(0) + aE(0))/N-2, where E-P(0) and E(0) are the initial mean potential and total turbulent energy per unit mass, respectively, a < 1 and N is the Brunt-Vaisala frequency. In the case of stationary turbulence, we find that (delta z(2)) = /N-2 + 2 epsilon(P)t/N-2, where epsilon(P) is the mean dissipation of turbulent potential energy per unit mass and is the Lagrangian structure function of normalized buoyancy fluctuations. The first term is the same as that obtained in the case of adiabatic fluid particle dispersion. This term goes to the finite limit 4E(P)/N-2 as t -> infinity. Assuming that the second term represents irreversible mixing, we show that the Osborn & Cox model for vertical diffusion is retained. In the case where the motion is dominated by a turbulent cascade with an eddy turnover time T >> N-1, rather than linear gravity waves, we suggest that there is a range of time scales, t, between N-1 and T, where = 2 pi C-PL epsilon(P)t, where C-PL is a constant of the order of unity. This means that for such motion the ratio between the adiabatic and the diabatic mean-square displacement is universal and equal to pi C-PL in this range. Comparing this result with observations, we make the estimate C-PL approximate to 3.

• 111.
KTH, Superseded Departments, Mechanics.
KTH, Superseded Departments, Mechanics.
Evaluation of scaling laws derived from Lie group symmetry methods in zero-pressure-gradient turbulent boundary layers2004In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 502, p. 127-152Article in journal (Refereed)

New scaling laws for turbulent boundary layers recently derived (see Oberlack 2000) using Lie group symmetry methods have been tested against experimental data from the KTH database for zero-pressure-gradient turbulent boundary layers. The most significant new law predicts an exponential variation of the mean velocity defect in the outer (wake) region. It was shown to fit the experimental data very well over a large part of the boundary layer, from the outer part of the overlap region to about half the boundary layer thickness (699). In the outermost part of the boundary layer the velocity defect falls more rapidly than predicted by the exponential law. This can partly be attributed to intermittency in that region but the main cause stems from non-parallel effects that are not accounted for in the derivation of the exponential law. The two-point correlation function behaviour in the outer region, where an exponential velocity defect law is observed, was found to be very different from that derived under the assumption of parallel flow. It is found to be plausible that this indeed can be attributed to non-parallel effects. A small modification of the innermost part of the log-layer in the form of an additive constant within the log-function is predicted by the Lie group symmetry method. A qualitative agreement with such a behaviour just below the overlap region was found. The derived scaling law behaviour in the overlap region for the two-point correlation functions was also verified by the experimental data.

• 112.
KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Physics.
Reactive control of transition induced by free-stream turbulence: an experimental demonstration2007In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 585, p. 41-71Article in journal (Refereed)

The present wind-tunnel experiment demonstrates that a reactive control system is able to decrease the amplitude of random disturbances in a flat-plate boundary layer. The disturbances were induced in a laminar boundary layer by a turbulent free stream. The control system consisted of upstream wall-shear-stress sensors (wall wires) and downstream actuators (suction through holes). An ad hoe threshold-and-delay control algorithm is evaluated and parameter variations were performed in order to find a suitable working point of the control system. Detailed measurements of the flow field show how the control influences the disturbances in the boundary layer, whereas the effect on the mean flow owing to the control is minute. The control system manages to inhibit the growth of the fluctuations of the streamwise velocity component for a considerable distance downstream of the two actuator positions. Further downstream, however, the amplitudes of the fluctuations grow again. The flow rate used to obtain the control effect is one sixth of that necessary if continuous distributed suction is used to reach the same control objective. Finally, correlations and spectra show that the elongation of the structures in the streamwise direction is eliminated in the regions where the control has the largest effect. The spanwise scale of the disturbances is not affected by the control.

• 113.
KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics.
KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics.
Streamwise evolution of longitudinal vortices in a turbulent boundary layer2009In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 623, p. 27-58Article in journal (Refereed)

In this experimental study both smoke visualisation and three component hotwire measurements have been performed in order to characterize the streamwise evolution of longitudinal counter-rotating vortices in a turbulent boundary layer. The vortices were generated by means of vortex generators (VGs) in different configurations. Both single pairs and arrays in a natural setting as well as in yaw have been considered. Moreover three different vortex blade heights h, with the spacing d and the distance to the neighbouring vortex pair D for the array con guration, were studied keeping the same d / h and D / h ratios. It is shown that the vortex core paths scale with h in the streamwise direction and with D and h in the spanwise and wall-normal directions, respectively. A new peculiar "hooklike" vortex core motion, seen in the cross-ow plane, has been identi ed in the far region, starting around 200h and 50h for the pair and the array con guration, respectively. This behaviour is explained in the paper. Furthermore the experimental data indicate that the vortex paths asymptote to a prescribed location in the cross-ow plane, which rst was stated as a hypothesis and later veri ed. This observation goes against previously reported numerical results based on inviscid theory. An account for the important viscous e ects is taken in a pseudo-viscous vortex model which is able to capture the streamwise core evolution throughout the measurement region down to 450h. Finally, the e ect of yawing is reported, and it is shown that spanwiseaveraged quantities such as the shape factor and the circulation are hardly perceptible. However, the evolution of the vortex cores are di erent both between the pair and the array con guration and in the natural setting versus the case with yaw. From a general point of view the present paper reports on fundamental results concerning the vortex evolution in a fully developed turbulent boundary layer.

• 114.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
Mixing efficiency in stratified turbulence2016In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 794, article id R3Article in journal (Refereed)

We consider mixing of the density field in stratified turbulence and argue that, at sufficiently high Reynolds numbers, stationary turbulence will have a mixing efficiency and closely related mixing coefficient described solely by the turbulent Froude number (Formula presented.), where (Formula presented.) is the kinetic energy dissipation, (Formula presented.) is a turbulent horizontal velocity scale and (Formula presented.) is the Brunt–Väisälä frequency. For (Formula presented.), in the limit of weakly stratified turbulence, we show through a simple scaling analysis that the mixing coefficient scales as (Formula presented.), where (Formula presented.) and (Formula presented.) is the potential energy dissipation. In the opposite limit of strongly stratified turbulence with (Formula presented.), we argue that (Formula presented.) should reach a constant value of order unity. We carry out direct numerical simulations of forced stratified turbulence across a range of (Formula presented.) and confirm that at high (Formula presented.), (Formula presented.), while at low (Formula presented.) it approaches a constant value close to (Formula presented.). The parametrization of (Formula presented.) based on (Formula presented.) due to Shih et al. (J. Fluid Mech., vol. 525, 2005, pp. 193–214) can be reinterpreted in this light because the observed variation of (Formula presented.) in their study as well as in datasets from recent oceanic and atmospheric measurements occurs at a Froude number of order unity, close to the transition value (Formula presented.) found in our simulations.

• 115. Magaletti, F.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
The sharp-interface limit of the Cahn-Hilliard/Navier-Stokes model for binary fluids2013In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 714, p. 95-126Article in journal (Refereed)

The Cahn-Hilliard model is increasingly often being used in combination with the incompressible Navier-Stokes equation to describe unsteady binary fluids in a variety of applications ranging from turbulent two-phase flows to microfluidics. The thickness of the interface between the two bulk fluids and the mobility are the main parameters of the model. For real fluids they are usually too small to be directly used in numerical simulations. Several authors proposed criteria for the proper choice of interface thickness and mobility in order to reach the so-called 'sharp-interface limit'. In this paper the problem is approached by a formal asymptotic expansion of the governing equations. It is shown that the mobility is an effective parameter to be chosen proportional to the square of the interface thickness. The theoretical results are confirmed by numerical simulations for two prototypal flows, namely capillary waves riding the interface and droplets coalescence. The numerical analysis of two different physical problems confirms the theoretical findings and establishes an optimal relationship between the effective parameters of the model.

• 116.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
Coherent structures and dominant frequencies in a turbulent three-dimensional diffuser2012In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 699, p. 320-351Article in journal (Refereed)
• 117.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
Explicit algebraic subgrid stress models with application to rotating channel flow2009In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 639, p. 403-432Article in journal (Refereed)

New explicit subgrid stress models are proposed involving the strain rate and rotation rate tensor, which can account for rotation in a natural way. The new models are based on the same methodology that leads to the explicit algebraic Reynolds stress model formulation for Reynolds-averaged Navier-Stokes simulations. One dynamic model and one non-dynamic model are proposed. The non-dynamic model represents a computationally efficient subgrid scale (SGS) stress model, whereas the dynamic model is the most accurate. The models are validated through large eddy simulations (LESs) of spanwise and streamwise rotating channel flow and are compared with the standard and dynamic Smagorinsky models. The proposed explicit dependence on the system rotation improves the description of the mean velocity profiles and the turbulent kinetic energy at high rotation rates. Comparison with the dynamic Smagorinsky model shows that not using the eddy-viscosity assumption improves the description of both the Reynolds stress anisotropy and the SGS stress anisotropy. LESs of rotating channel flow at Re-tau = 950 have been carried out as well. These reveal some significant Reynolds number influences on the turbulence statistics. LESs of non-rotating turbulent channel flow at Re-tau = 950 show that the new explicit model especially at coarse resolutions significantly better predicts the mean velocity, wall shear and Reynolds stresses than the dynamic Smagorinsky model, which is probably the result of a better prediction of the anisotropy of the subgrid dissipation.

• 118.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
The effect of small-amplitude convective disturbances on the size and bursting of a laminar separation bubble2011In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 671, p. 1-33Article in journal (Refereed)

Short laminar separation bubbles can develop on a flat plate due to an externally imposed pressure gradient. Here, these bubbles are computed by means of direct numerical simulations. Laminar-turbulent transition occurs in the bubble, triggered by small disturbance input with fixed frequency, but varying amplitude, to keep the bubbles short. The forcing amplitudes span a range of two orders of magnitude. All resulting bubbles differ with respect to their mean flow, linear-stability characteristics and distance between transition and mean reattachment locations. Mechanisms responsible for these differences are analysed in detail. Switching off the disturbance input or reducing it below a certain, very small threshold causes the short bubble to grow continuously. Eventually, it no longer exhibits typical characteristics of a short laminar separation bubble. Instead, it is argued that bursting has occurred and the bubble displays characteristics of a long-bubble state, even though this state was not a statistically steady state. This hypothesis is backed by a comparison of numerical results with measurements. For long bubbles, the transition to turbulence is not able to reattach the flow immediately. This effect can lead to the bursting of a short bubble, which remains short only when sufficiently large disturbances are convected into the bubble. Large-scale spanwise-oriented vortices at transition are observed for short but not for long bubbles. The failure of the transition process to reattach the flow in the long-bubble case is ascribed to this difference in transitional vortical structures.

• 119.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
Mechanisms for spatial steady three-dimensional disturbance growth in a non-parallel and separating boundary layer2009In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 634, p. 165-189Article in journal (Refereed)

Steady linear three-dimensional disturbances are investigated in a two-dimensional laminar boundary layer. The boundary layer is Subject to a streamwise favourable-to-adverse pressure gradient and eventually undergoes separation. The separating flow corresponds to the first part of a pressure-induced laminar-separation bubble on a flat plate. Streamwise disturbance development in such a flow is studied by means of direct numerical simulation, a water-tunnel experiment and an adjoint-based parabolic theory suited to study spatial optimal growth. A complete overview of the disturbance evolution in various areas of the Favourable-to-adverse pressure gradient laminar boundary layer is given. Results from all investigation methods show overall good agreement with respect to disturbance growth and shape within the entire domain. In the favourable pressure-gradient region and, again, slightly downstream of separation, transient growth caused by the lift-Up effect dominates disturbance behaviour. In the adverse pressure-gradient region, a modal instability is observed. Evidence is presented that this instability is of Gortler type.

• 120. Matsubara, M.
KTH, Superseded Departments, Mechanics.
Disturbance growth in boundary layers subjected to free-stream turbulence2001In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 430, p. 149-168Article in journal (Refereed)

This paper aims at a description of boundary-layer flow which is subjected to freestream turbulence in the range from 1-6% and is based on both flow visualization results and extensive hot-wire measurements. Such flows develop streamwise elongated regions of high and low streamwise velocity which seem to lead to secondary instability and breakdown to turbulence. The initial growth of the streaky structures is found to be closely related to algebraic or transient growth theory. The data have been used to determine streamwise and spanwise scales of the streaky structures. Both the flow visualization and the hot-wire measurements show that close to the leading edge the spanwise scale is large as compared to the boundary-layer thickness, but further downstream the spanwise scale approaches the boundary-layer thickness. Wavenumber spectra in both the streamwise and the spanwise directions were calculated. A scaling for the streamwise structure of the disturbance was found, which allows us to collapse the spectra from different downstream positions. The scaling combines the facts that the streaky structures increase their streamwise length in the downstream direction which becomes proportional to the boundary-layer thickness and that the energy growth is algebraic, close to proportional to the downstream distance.

• 121.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
Global three-dimensional optimal disturbances in the Blasius boundary-layer flow using time-steppers2010In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 650, p. 181-214Article in journal (Refereed)

The global linear stability of the flat-plate boundary-layer flow to three-dimensional disturbances is studied by means of an optimization technique. We consider both the optimal initial condition leading to the largest growth at finite times and the optimal time-periodic forcing leading to the largest asymptotic response. Both optimization problems are solved using a Lagrange multiplier technique, where the objective function is the kinetic energy of the flow perturbations and the constraints involve the linearized Navier-Stokes equations. The approach proposed here is particularly suited to examine convectively unstable flows, where single global eigenmodes of the system do not capture the downstream growth of the disturbances. In addition, the use of matrix-free methods enables us to extend the present framework to any geometrical configuration. The optimal initial condition for spanwise wavelengths of the order of the boundary-layer thickness are finite-length streamwise vortices exploiting the lift-up mechanism to create streaks. For long spanwise wavelengths, it is the Orr mechanism combined with the amplification of oblique wave packets that is responsible for the disturbance growth. This mechanism is dominant for the long computational domain and thus for the relatively high Reynolds number considered here. Three-dimensional localized optimal initial conditions are also computed and the corresponding wave packets examined. For short optimization times, the optimal disturbances consist of streaky structures propagating and elongating in the downstream direction without significant spreading in the lateral direction. For long optimization times, we find the optimal disturbances with the largest energy amplification. These are wave packets of Tollmien-Schlichting waves with low streamwise propagation speed and faster spreading in the spanwise direction. The pseudo-spectrum of the system for real frequencies is also computed with matrix-free methods. The spatial structure of the optimal forcing is similar to that of the optimal initial condition, and the largest response to forcing is also associated with the Orr/oblique wave mechanism, however less so than in the case of the optimal initial condition. The lift-up mechanism is most efficient at zero frequency and degrades slowly for increasing frequencies. The response to localized upstream forcing is also discussed.

• 122.
KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
Univ Paris Saclay, LIMSI, UPR 3251 CNRS, F-91400 Orsay, France.. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. Cent Nantes, LHEEA, UMR 6598, CNRS, F-44300 Nantes, France..
On the relevance of Reynolds stresses in resolvent analyses of turbulent wall-bounded flows2019In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 867, p. 969-984, article id PII S0022112019001964Article in journal (Refereed)

The ability of linear stochastic response analysis to estimate coherent motions is investigated in turbulent channel flow at the friction Reynolds number Re-r = 1007. The analysis is performed for spatial scales characteristic of buffer-layer and large-scale motions by separating the contributions of different temporal frequencies. Good agreement between the measured spatio-temporal power spectral densities and those estimated by means of the resolvent is found when the effect of turbulent Reynolds stresses, modelled with an eddy-viscosity associate with the turbulent mean flow, is included in the resolvent operator. The agreement is further improved when the flat forcing power spectrum (white noise) is replaced with a power spectrum matching the measures. Such a good agreement is not observed when the eddy-viscosity terms are not included in the resolvent operator. In this case, the estimation based on the resolvent is unable to select the right peak frequency and wall-normal location of buffer-layer motions. Similar results are found when comparing truncated expansions of measured streamwise velocity power spectral densities based on a spectral proper orthogonal decomposition to those obtained with optimal resolvent modes.

• 123.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. School of Mechanical Engineering, Shiraz University. University of Padova, Department of Industrial Engineering. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
Heat transfer in laminar Couette flow laden with rigid spherical particles2018In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 834, p. 308-334Article in journal (Refereed)

We study heat transfer in plane Couette flow laden with rigid spherical particles by means of direct numerical simulations. In the simulations we use a direct-forcing immersed boundary method to account for the dispersed phase together with a volume-of-fluid approach to solve the temperature field inside and outside the particles. We focus on the variation of the heat transfer with the particle Reynolds number, total volume fraction (number of particles) and the ratio between the particle and fluid thermal diffusivity, quantified in terms of an effective suspension diffusivity. We show that, when inertia at the particle scale is negligible, the heat transfer increases with respect to the unladen case following an empirical correlation recently proposed in the literature. In addition, an average composite diffusivity can be used to approximate the effective diffusivity of the suspension in the inertialess regime when varying the molecular diffusion in the two phases. At finite particle inertia, however, the heat transfer increase is significantly larger, smoothly saturating at higher volume fractions. By phase-ensemble-averaging we identify the different mechanisms contributing to the total heat transfer and show that the increase of the effective conductivity observed at finite inertia is due to the increase of the transport associated with fluid and particle velocity. We also show that the contribution of the heat conduction in the solid phase to the total wall-normal heat flux reduces when increasing the particle Reynolds number, so that particles of low thermal diffusivity weakly alter the total heat flux in the suspension at finite particle Reynolds numbers. On the other hand, a higher particle thermal diffusivity significantly increases the total heat transfer.

• 124.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
Turbulence modulation in channel flow of finite-size spheroidal particles2018In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 859, p. 887-901Article in journal (Refereed)

Finite-size particles modulate wall-bounded turbulence, leading, for the case of spherical particles, to increased drag also owing to the formation of a particle wall layer. Here, we study the effect of particle shape on the turbulence in suspensions of spheroidal particles at volume fraction phi = 10 % and show how the near-wall particle dynamics deeply changes with the particle aspect ratio and how this affects the global suspension behaviour. Direct numerical simulations are performed using a direct-forcing immersed boundary method to account for the dispersed phase, combined with a soft-sphere collision model and lubrication corrections for short-range particle-particle and particle-wall interactions. The turbulence reduces with the aspect ratio of oblate particles, leading to drag reduction with respect to the single-phase flow for particles with aspect ratio AR <= 1/3, when the significant reduction in Reynolds shear stress is more than the compensation by the additional stresses, induced by the solid phase. Oblate particles are found to avoid the region close to the wall, travelling parallel to it with small angular velocities, while preferentially sampling high-speed fluid in the wall region. Prolate particles also tend to orient parallel to the wall and avoid its vicinity. Their reluctance to rotate around the spanwise axis reduces the wall-normal velocity fluctuation of the flow and therefore the turbulence Reynolds stress, similar to oblates; however, they undergo rotations in wall-parallel planes which increase the additional solid stresses due to their relatively larger angular velocities compared to the oblates. These larger additional stresses compensate for the reduction in turbulence activity and lead to a wall drag similar to that of single-phase flows. Spheres on the other hand, form a layer close to the wall with large angular velocities in the spanwise direction, which increases the turbulence activity in addition to exerting the largest solid stresses on the suspension, in comparison to the other studied shapes. Spherical particles therefore increase the wall drag with respect to the single-phase flow.

• 125.
KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
University of Padova, Department of Industrial Engineering. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
Drag reduction in turbulent channel flow laden with finite-size oblate spheroids2017In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 816, p. 43-70Article in journal (Refereed)

We study suspensions of oblate rigid particles in a viscous fluid for different values of the particle volume fractions.Direct numerical simulations have been performed using a direct-forcing immersed boundary method to account for the dispersed phase, combined with a soft-sphere collision model and lubrication corrections for short-range particle-particle and particle-wall interactions. With respect to the single phase flow, we show that in flows laden with oblate spheroids the drag is reduced and the turbulent fluctuations attenuated.In particular, the turbulence activity decreases to lower values than those obtained by only accounting for the effective suspension viscosity.To explain the observed drag reduction we consider the particle dynamics and the interactions of the particles with the turbulent velocity field and show that the particle wall layer, previously observed and found to be responsible for the increased dissipation in suspensions of spheres, disappears in the case of oblate particles.These rotate significantly slower than spheres near the wall and tend to stay with their major axes parallel to the wall, which leads to a decrease of the Reynolds stresses and turbulence production and so to the overall drag reduction.

• 126.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics.
Turbulent  flow of finite-size spherical particles with viscous hyper-elastic walls2018In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645Article in journal (Other academic)
• 127.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
Turbulent flow of finite-size spherical particles in channels with viscous hyper-elastic walls2019In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 873, p. 410-440, article id PII S0022112019004130Article in journal (Refereed)

We study single-phase and particle-laden turbulent channel flows bounded by two incompressible hyper-elastic walls with different deformability at bulk Reynolds number $5600$ . The solid volume fraction of finite-size neutrally buoyant rigid spherical particles considered is $10\,\%$ . The elastic walls are assumed to be of a neo-Hookean material. A fully Eulerian formulation is employed to model the elastic walls together with a direct-forcing immersed boundary method for the coupling between the fluid and the particles. The data show a significant drag increase and the enhancement of the turbulence activity with growing wall elasticity for both the single-phase and particle-laden flows when compared with the single-phase flow over rigid walls. Drag reduction and turbulence attenuation is obtained, on the other hand, with highly elastic walls when comparing the particle-laden flow with the single-phase flow for the same wall properties; the opposite effect, drag increase, is observed upon adding particles to the flow over less elastic walls. This is explained by investigating the near-wall turbulence, where the strong asymmetry in the magnitude of the wall-normal velocity fluctuations (favouring positive $v<^>{\prime }$ ), is found to push the particles towards the channel centre. The particle layer close to the wall contributes to turbulence production by increasing the wall-normal velocity fluctuations, so that in the absence of this layer, smaller wall deformations and in turn turbulence attenuation is observed. For a moderate wall elasticity, we increase the particle volume fraction up to $20\,\%$ and find that particle migration away from the wall is the cause of turbulence attenuation with respect to the flow over rigid walls. However, for this higher volume fractions, the particle induced stress compensates for the decreasing Reynolds shear stress, resulting in a higher overall drag for the case with elastic walls. The effect of the wall elasticity on the overall drag reduces significantly with increasing particle volume fraction.

• 128.
KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. School of Marine Sciences, University of Maine. Department of Mathematical Sciences, University of Liverpool. Department of Civil and Environmental Engineering, University of California.
Sedimentation of inertia-less prolate spheroids in homogenous isotropic turbulence with application to non-motile phytoplankton2017In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 831, p. 655-674Article in journal (Refereed)

Phytoplankton are the foundation of aquatic food webs. Through photosynthesis, phytoplankton draw down $CO_2$ at magnitudes equivalent to forests and other terrestrial plants and convert it to organic material that is then consumed by other organisms of phytoplankton in higher trophic levels. Mechanisms that affect local concentrations and velocities are of primary significance to many encounter-based processes in the plankton including prey-predator interactions, fertilization and aggregate formation. We report results from simulations of sinking phytoplankton, considered as elongated spheroids, in homogenous isotropic turbulence to answer the question of whether trajectories and velocities of sinking phytoplankton are altered by turbulence. We show in particular that settling spheroids with physical characteristics similar to those of diatoms weakly cluster and preferentially sample regions of down-welling flow, corresponding to an increase of the mean settling speed with respect to the mean settling speed in quiescent fluid.  We explain how different parameters can affect the settling speed and what underlying mechanisms might be involved.  Interestingly, we observe that the increase in the aspect ratio of the prolate spheroids can affect the clustering and the average settling speed of particles by two mechanisms: first is the effect of aspect ratio on the rotation rate of the particles, which saturates faster than the second mechanism of increasing drag anisotropy.

• 129.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
Particle transport in turbulent curved pipe flow2016In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 793, p. 248-279Article in journal (Refereed)

Direct numerical simulations (DNS) of particle-laden turbulent flow in straight, mildly curved and strongly bent pipes are performed in which the solid phase is modelled as small heavy spherical particles. A total of seven populations of dilute particles with different Stokes numbers, one-way coupled with their carrier phase, are simulated. The objective is to examine the effect of the curvature on micro-particle transport and accumulation. It is shown that even a slight non-zero curvature in the flow configuration strongly impact the particle concentration map such that the concentration of inertial particles with hulk Stokes number 0.45 (based on hulk velocity and pipe radius) at the inner bend wall of mildly curved pipe becomes 12.8 times larger than that in the viscous sublayer of the straight pipe. Near-wall helicoidal particle streaks are observed in the curved configurations with their inclination varying with the strength of the secondary motion of the carrier phase. A reflection layer, as previously observed in particle laden turbulent S-shaped channels, is also apparent in the strongly curved pipe with heavy particles. In addition, depending on the curvature, the central regions of the mean Dean vortices appear to he completely depleted of particles, as observed also in the partially relaminarised region at the inner bend. The turbophoretic drift of the particles is shown to he affected by weak and strong secondary motions of the carrier phase and geometry-induced centrifugal forces. The first- and second-order moments of the velocity and acceleration of the particulate phase in the same configurations are addressed in a companion paper by the same authors. The current data set will be useful for modelling particles advected in wall-bounded turbulent flows where the effects of the curvature are not negligible.

• 130. Nowbahar, Arash
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
Turbophoresis attenuation in a turbulent channel flow with polymer additives2013In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 732, p. 706-719Article in journal (Refereed)

Turbophoresis occurs in wall-bounded turbulent flows where it induces a preferential accumulation of inertial particles towards the wall and is related to the spatial gradients of the turbulent velocity fluctuations. In this work, we address the effects of drag-reducing polymer additives on turbophoresis in a channel flow. The analysis is based on data from a direct numerical simulation of the turbulent flow of a viscoelastic fluid modelled with the FENE-P closure and laden with particles of different inertia. We show that polymer additives decrease the particle preferential wall accumulation and demonstrate with an analytical model that the turbophoretic drift is reduced because the wall-normal variation of the wall-normal fluid velocity fluctuations decreases. As this is a typical feature of drag reduction in turbulent flows, an attenuation of turbophoresis and a corresponding increase in the particle streamwise flux are expected to be observed in all of these flows, e. g. fibre or bubble suspensions and magnetohydrodynamics.

• 131.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
Direct numerical simulation of separated flow in a three-dimensional diffuser2010In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 650, p. 307-318Article in journal (Refereed)

A direct numerical simulation (DNS) of turbulent flow in a three-dimensional diffuser at Re = 10 000 (based on bulk velocity and inflow-duct height) was performed with a massively parallel high-order spectral element method running on up to 32 768 processors. Accurate inflow condition is ensured through unsteady trip forcing and a long development section. Mean flow results are in good agreement with experimental data by Cherry et al. (Intl J. Heat Fluid Flow, vol. 29, 2008, pp. 803-811), in particular the separated region starting from one corner and gradually spreading to the top expanding diffuser wall. It is found that the corner vortices induced by the secondary flow in the duct persist into the diffuser, where they give rise to a dominant low-speed streak, due to a similar mechanism as the 'lift-up effect' in transitional shear flows, thus governing the separation behaviour. Well-resolved simulations of complex turbulent flows are thus possible even at realistic Reynolds numbers, providing accurate and detailed information about the flow physics. The available Reynolds stress budgets provide valuable references for future development of turbulence models.

• 132. Parsheh, Mehran
KTH, School of Engineering Sciences (SCI), Mechanics.
Evolution of flat-plate wakes in sink flow2009In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 626, p. 241-262Article in journal (Refereed)

Evolution of flat-plate wakes in sink flow has been studied both analytically and experimentally. For such wakes, a similarity solution is derived which considers simultaneous presence of both laminar and turbulent stresses inside the wake. This solution utilizes an additional Reynolds-stress term which represents the fluctuations similar to those in wall-bounded flows, accounting for the fluctuations originating from the plate boundary layer. In this solution, it is shown that the total stress, the sum of laminar and Reynolds shear stresses, becomes self-similar. To investigate the accuracy of the analytical results, the wake of a flat plate located at the centreline of a planar contraction is studied using hot-wire anemometry. Wakes of both tapered and blunt edges are considered. The length of the plates and the flow acceleration number K = 6.25 x 10(-6) are chosen such that the boundary-layer profiles at the plate edge approach the self-similar laminar solution of Pohlhausen (Z. Angew. Math. Mech., vol. 1, 1921, p. 252). A short plate in which the boundary layer at the edge does not fully relaminarize is also considered. The development of the turbulent diffusivity used in the analysis is determined empirically for each experimental case. We have shown that the obtained similarity solutions, accounting also for the initial conditions in each case, generally agree well with the experimental results even in the near field. The results also show that the mean velocity of the transitional wake behind a tapered edge becomes self-similar almost immediately downstream of the edge.

• 133.
KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
Turbulent channel flow of dense suspensions of neutrally buoyant spheres2015In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 764, p. 463-487Article in journal (Refereed)

Dense particle suspensions are widely encountered in many applications and in environmental flows. While many previous studies investigate their rheological properties in laminar flows, little is known on the behaviour of these suspensions in the turbulent/inertial regime. The present study aims to fill this gap by investigating the turbulent flow of a Newtonian fluid laden with solid neutrally-buoyant spheres at relatively high volume fractions in a plane channel. Direct numerical simulation (DNS) are performed in the range of volume fractions Phi=0-0.2 with an immersed boundary method (IBM) used to account for the dispersed phase. The results show that the mean velocity profiles are significantly altered by the presence of a solid phase with a decrease of the von Karman constant in the log-law. The overall drag is found to increase with the volume fraction, more than one would expect if just considering the increase of the system viscosity due to the presence of the particles. At the highest volume fraction investigated here, Phi = 0.2, the velocity fluctuation intensities and the Reynolds shear stress are found to decrease. The analysis of the mean momentum balance shows that the particle-induced stresses govern the dynamics at high Phi and are the main responsible of the overall drag increase. In the dense limit, we therefore find a decrease of the turbulence activity and a growth of the particle induced stress, where the latter dominates for the Reynolds numbers considered here.

• 134.
Eindhoven University of Technology, Netherlands .
Formation of coherent structures by fluid inertia in three-dimensional laminar flows2010In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 654, p. 5-34Article in journal (Refereed)

Mixing under laminar flow conditions is key to a wide variety of industrial fluid systems of size extending from micrometres to metres. Profound insight into three-dimensional laminar mixing mechanisms is essential for better understanding of the behaviour of such systems and is in fact imperative for further advancement of (in particular, microscopic) mixing technology. This insight remains limited to date, however. The present study concentrates on a fundamental transport phenomenon relevant to laminar mixing: the formation and interaction of coherent structures in the web of three-dimensional paths of passive tracers due to fluid inertia. Such coherent structures geometrically determine the transport properties of the flow and thus their formation and topological structure are essential to three-dimensional mixing phenomena. The formation of coherent structures, its universal character and its impact upon three-dimensional transport properties is demonstrated by way of experimentally realizable time-periodic model flows. Key result is that fluid inertia induces partial disintegration of coherent structures of the non-inertial limit into chaotic regions and merger of surviving parts into intricate three-dimensional structures. This response to inertial perturbations, though exhibiting great diversity, follows a universal scenario and is therefore believed to reflect an essentially three-dimensional route to chaos. Furthermore, a first outlook towards experimental validation and investigation of the observed dynamics is made. Press.

• 135. Pralits, J. O.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
Three-dimensional instability of the flow around a rotating circular cylinder2013In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 730, p. 5-18Article in journal (Refereed)

The two-dimensional stationary flow past a rotating cylinder is investigated for both two- and three-dimensional perturbations. The instability mechanisms are analysed using linear stability analysis and the complete neutral curve is presented. It is shown that the first bifurcation in the case of the rotating cylinder occurs for stationary three-dimensional perturbations, confirming recent experiments. Interestingly, the critical Reynolds number at high rotation rates is lower than that for the stationary circular cylinder. The spatial characteristics of the disturbance and a qualitative comparison with the results obtained for linear flows suggest that the stationary unstable three-dimensional mode could be of hyperbolic nature.

• 136. Pralits, J. O.
Adjoint-based optimization of steady suction for disturbance control in incompressible flows2002In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 467, p. 129-161Article in journal (Refereed)

• 137. Pralits, Jan O.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
Instability and sensitivity of the flow around a rotating circular cylinder2010In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 650, p. 513-536Article in journal (Refereed)

The two-dimensional flow around a rotating circular cylinder is studied at Re = 100. The instability mechanisms for the first and second shedding modes are analysed. The region in the flow with a role of 'wavemaker' in the excitation of the global instability is identified by considering the structural sensitivity of the unstable mode. This approach is compared with the analysis of the perturbation kinetic energy production, a classic approach in linear stability analysis. Multiple steady-state solutions are found at high rotation rates, explaining the quenching of the second shedding mode. Turning points in phase space are associated with the movement of the flow stagnation point. In addition, a method to examine which structural variation of the base flow has the largest impact on the instability features is proposed. This has relevant implications for the passive control of instabilities. Finally, numerical simulations of the flow are performed to verify that the structural sensitivity analysis is able to provide correct indications on where to position passive control devices, e.g. small obstacles, in order to suppress the shedding modes.

• 138.
Aix Marseille Univ, Cent Marseille, CNRS, IRPHE, F-13384 Marseille, France.;Airbus Helicopters, Aerodynam Dept, F-13725 Marignane, France..
KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. Aix Marseille Univ, Cent Marseille, CNRS, IRPHE, F-13384 Marseille, France.. KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
Local and global pairing instabilities of two interlaced helical vortices2019In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 863, p. 927-955Article in journal (Refereed)

We investigate theoretically and experimentally the stability of two interlaced helical vortices with respect to displacement perturbations having wavelengths that are large compared to the size of the vortex cores. First, existing theoretical results are recalled and applied to the present configuration. Various modes of unstable perturbations, involving different phase relationships between the two vortices, are identified and their growth rates are calculated. They lead to a local pairing of neighbouring helix loops, or to a global pairing with one helix expanding and the other one contracting. A relation is established between this instability and the three-dimensional pairing of arrays of straight parallel vortices, and a striking quantitative agreement concerning the growth rates and frequencies is found. This shows that the local pairing of vortices is the driving mechanism behind the instability of the helix system. Second, an experimental study designed to observe these instabilities in a real flow is presented. Two helical vortices are generated by a two-bladed rotor in a water channel and characterised through dye visualisations and particle image velocimetry measurements. Unstable displacement modes are triggered individually, either by varying the rotation frequency of the rotor, or by imposing a small rotor eccentricity. The observed unstable mode structure, and the corresponding growth rates obtained from advanced processing of visualisation sequences, are in good agreement with theoretical predictions. The nonlinear late stages of the instability are also documented experimentally. Whereas local pairing leads to strong deformations and subsequent breakup of the vortices, global pairing results in a leapfrogging phenomenon, which temporarily restores the initial double-helix geometry, in agreement with recent observations from numerical simulations.

• 139.
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
An explicit algebraic model for the subgrid-scale passive scalar flux2013In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 721, p. 541-577Article in journal (Refereed)

In Marstorp et al. (J. Fluid Mech., vol. 639, 2009, pp. 403-432), an explicit algebraic subgrid stress model (EASSM) for large-eddy simulation (LES) was proposed, which was shown to considerably improve LES predictions of rotating and non-rotating turbulent channel flow. In this paper, we extend that work and present a new explicit algebraic subgrid scalar flux model (EASSFM) for LES, based on the modelled transport equation of the subgrid-scale (SGS) scalar flux. The new model is derived using the same kind of methodology that leads to the explicit algebraic scalar flux model of Wikstrom et al. (Phys. Fluids, vol. 12, 2000, pp. 688-702). The algebraic form is based on a weak equilibrium assumption and leads to a model that depends on the resolved strain-rate and rotation-rate tensors, the resolved scalar-gradient vector and, importantly, the SGS stress tensor. An accurate prediction of the SGS scalar flux is consequently strongly dependent on an accurate description of the SGS stresses. The new EASSFM is therefore primarily used in connection with the EASSM, since this model can accurately predict SGS stresses. The resulting SGS scalar flux is not necessarily aligned with the resolved scalar gradient, and the inherent dependence on the resolved rotation-rate tensor makes the model suitable for LES of rotating flow applications. The new EASSFM (together with the EASSM) is validated for the case of passive scalar transport in a fully developed turbulent channel flow with and without system rotation. LES results with the new model show good agreement with direct numerical simulation data for both cases. The new model predictions are also compared to those of the dynamic eddy diffusivity model (DEDM) and improvements are observed in the prediction of the resolved and SGS scalar quantities. In the non-rotating case, the model performance is studied at all relevant resolutions, showing that its predictions of the Nusselt number are much less dependent on the grid resolution and are more accurate. In channel flow with wall-normal rotation, where all the SGS stresses and fluxes are non-zero, the new model shows significant improvements over the DEDM predictions of the resolved and SGS quantities.

• 140. Rempel, Erico L.
KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
Coherent structures and the saturation of a nonlinear dynamo2013In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 729, p. 309-329Article in journal (Refereed)

Eulerian and Lagrangian tools are used to detect coherent structures in the velocity and magnetic fields of a mean-field dynamo, produced by direct numerical simulations of the three-dimensional compressible magnetohydrodynamic equations with an isotropic helical forcing and moderate Reynolds number. Two distinct stages of the dynamo are studied: the kinematic stage, where a seed magnetic field undergoes exponential growth; and the saturated regime. It is shown that the Lagrangian analysis detects structures with greater detail, in addition to providing information on the chaotic mixing properties of the flow and the magnetic fields. The traditional way of detecting Lagrangian coherent structures using finite-time Lyapunov exponents is compared with a recently developed method called function M. The latter is shown to produce clearer pictures which readily permit the identification of hyperbolic regions in the magnetic field, where chaotic transport/dispersion of magnetic field lines is highly enhanced.

• 141.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
The vanishing of strong turbulent fronts in bent pipes2019In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 866, p. 487-502Article in journal (Refereed)

Isolated patches of turbulence in transitional straight pipes are sustained by a strong instability at their upstream front, where the production of turbulent kinetic energy (TKE) is up to five times higher than in the core. Direct numerical simulations presented in this paper show no evidence of such strong fronts if the pipe is bent. We examine the temporal and spatial evolution of puffs and slugs in a toroidal pipe with pipe-to-torus diameter ratio delta = D/d = 0.01 at several subcritical Reynolds numbers. Results show that the upstream overshoot of TKE production is at most one-and-a-half times the value in the core and that the average cross-flow fluctuations at the front are up to three times lower if compared to a straight pipe, while attaining similar values in the core. Localised turbulence can be sustained at smaller energies through a redistribution of turbulent fluctuations and vortical structures by the in-plane Dean motion of the mean flow. This asymmetry determines a strong localisation of TKE production near the outer bend, where linear and nonlinear mechanisms optimally amplify perturbations. We further observe a substantial reduction of the range of Reynolds numbers for long-lived intermittent turbulence, in agreement with experimental data from the literature. Moreover, no occurrence of nucleation of spots through splitting could be detected in the range of parameters considered. Based on the present results, we argue that this mechanism gradually becomes marginal as the curvature of the pipe increases and the transition scenario approaches a dynamical switch from subcritical to supercritical.

• 142.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
Edge state modulation by mean viscosity gradients2018In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 838, p. 379-403Article in journal (Refereed)

Motivated by the relevance of edge state solutions as mediators of transition, we use direct numerical simulations to study the effect of spatially non-uniform viscosity on their energy and stability in minimal channel flows. What we seek is a theoretical support rooted in a fully nonlinear framework that explains the modified threshold for transition to turbulence in flows with temperature-dependent viscosity. Consistently over a range of subcritical Reynolds numbers, we find that decreasing viscosity away from the walls weakens the streamwise streaks and the vortical structures responsible for their regeneration. The entire self-sustained cycle of the edge state is maintained on a lower kinetic energy level with a smaller driving force, compared to a flow with constant viscosity. Increasing viscosity away from the walls has the opposite effect. In both cases, the effect is proportional to the strength of the viscosity gradient. The results presented highlight a local shift in the state space of the position of the edge state relative to the laminar attractor with the consequent modulation of its basin of attraction in the proximity of the edge state and of the surrounding manifold. The implication is that the threshold for transition is reduced for perturbations evolving in the neighbourhood of the edge state in the case that viscosity decreases away from the walls, and vice versa.

• 143.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
Numerical simulation of turbulent channel flow over a viscous hyper-elastic wall2017In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 830, p. 708-735Article in journal (Refereed)

We perform numerical simulations of a turbulent channel flow over an hyper-elastic wall. In the fluid region the flow is governed by the incompressible Navier-Stokes (NS) equations, while the solid is a neo-Hookean material satisfying the incompressible Mooney-Rivlin law. The multiphase flow is solved with a one-continuum formulation, using a monolithic velocity field for both the fluid and solid phase, which allows the use of a fully Eulerian formulation. The simulations are carried out at Reynolds bulk Re = 2800 and examine the effect of different elasticity and viscosity of the deformable wall. We show that the skin friction increases monotonically with the material elastic modulus. The turbulent flow in the channel is affected by the moving wall even at low values of elasticity since non-zero fluctuations of vertical velocity at the interface influence the flow dynamics. The near-wall streaks and the associated quasi-streamwise vortices are strongly reduced near a highly elastic wall while the flow becomes more correlated in the spanwise direction, similarly to what happens for flows over rough and porous walls. As a consequence, the mean velocity profile in wall units is shifted downwards when shown in logarithmic scale, and the slope of the inertial range increases in comparison to that for the flow over a rigid wall. We propose a correlation between the downward shift of the inertial range, its slope and the wall-normal velocity fluctuations at the wall, extending results for the flow over rough walls. We finally show that the interface deformation is determined by the fluid fluctuations when the viscosity of the elastic layer is low, while when this is high the deformation is limited by the solid properties.

• 144.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
Turbulent channel flow over an anisotropic porous wall - drag increase and reduction2018In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 842, p. 381-394Article in journal (Refereed)

The effect of the variations of the permeability tensor on the close-to-the-wall behaviour of a turbulent channel flow bounded by porous walls is explored using a set of direct numerical simulations. It is found that the total drag can be either reduced or increased by more than 20% by adjusting the permeability directional properties. Drag reduction is achieved for the case of materials with permeability in the vertical direction lower than the one in the wall-parallel planes. This configuration limits the wall-normal velocity at the interface while promoting an increase of the tangential slip velocity leading to an almost 'one-component' turbulence where the low- and high-speed streak coherence is strongly enhanced. On the other hand, strong drag increase is found when high wall-normal and low wall-parallel permeabilities are prescribed. In this condition, the enhancement of the wall-normal fluctuations due to the reduced wall-blocking effect triggers the onset of structures which are strongly correlated in the spanwise direction, a phenomenon observed by other authors in flows over isotropic porous layers or over ribletted walls with large protrusion heights. The use of anisotropic porous walls for drag reduction is particularly attractive since equal gains can be achieved at different Reynolds numbers by rescaling the magnitude of the permeability only.

• 145.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. Stanford Univ, Ctr Turbulence Res, Stanford, CA 94305 USA.. Stanford Univ, Ctr Turbulence Res, Stanford, CA 94305 USA.. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. Norwegian Univ Sci & Technol NTNU, Dept Energy & Proc Engn, NO-7491 Trondheim, Norway..
Droplets in homogeneous shear turbulence2019In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 876, p. 962-984Article in journal (Refereed)

We simulate the flow of two immiscible and incompressible fluids separated by an interface in a homogeneous turbulent shear flow at a shear Reynolds number equal to 15 200. The viscosity and density of the two fluids are equal, and various surface tensions and initial droplet diameters are considered in the present study. We show that the two-phase flow reaches a statistically stationary turbulent state sustained by a non-zero mean turbulent production rate due to the presence of the mean shear. Compared to single-phase flow, we find that the resulting steady-state conditions exhibit reduced Taylor-microscale Reynolds numbers owing to the presence of the dispersed phase, which acts as a sink of turbulent kinetic energy for the carrier fluid. At steady state, the mean power of surface tension is zero and the turbulent production rate is in balance with the turbulent dissipation rate, with their values being larger than in the reference single-phase case. The interface modifies the energy spectrum by introducing energy at small scales, with the difference from the single-phase case reducing as the Weber number increases. This is caused by both the number of droplets in the domain and the total surface area increasing monotonically with the Weber number. This reflects also in the droplet size distribution, which changes with the Weber number, with the peak of the distribution moving to smaller sizes as the Weber number increases. We show that the Hinze estimate for the maximum droplet size, obtained considering break-up in homogeneous isotropic turbulence, provides an excellent estimate notwithstanding the action of significant coalescence and the presence of a mean shear.

• 146.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. Ohio Univ, Dept Mech Engn, Athens, OH 45701 USA.. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
Turbulent channel flow of an elastoviscoplastic fluid2018In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 853, p. 488-514Article in journal (Refereed)

We present numerical simulations of laminar and turbulent channel flow of an elastoviscoplastic fluid. The non-Newtonian flow is simulated by solving the full incompressible Navier-Stokes equations coupled with the evolution equation for the elastoviscoplastic stress tensor. The laminar simulations are carried out for a wide range of Reynolds numbers, Bingham numbers and ratios of the fluid and total viscosity, while the turbulent flow simulations are performed at a fixed bulk Reynolds number equal to 2800 and weak elasticity. We show that in the laminar flow regime the friction factor increases monotonically with the Bingham number (yield stress) and decreases with the viscosity ratio, while in the turbulent regime the friction factor is almost independent of the viscosity ratio and decreases with the Bingham number, until the flow eventually returns to a fully laminar condition for large enough yield stresses. Three main regimes are found in the turbulent case, depending on the Bingham number: for low values, the friction Reynolds number and the turbulent flow statistics only slightly differ from those of a Newtonian fluid; for intermediate values of the Bingham number, the fluctuations increase and the inertial equilibrium range is lost. Finally, for higher values the flow completely laminarizes. These different behaviours are associated with a progressive increases of the volume where the fluid is not yielded, growing from the centreline towards the walls as the Bingham number increases. The unyielded region interacts with the near-wall structures, forming preferentially above the high-speed streaks. In particular, the near-wall streaks and the associated quasi-streamwise vortices are strongly enhanced in an highly elastoviscoplastic fluid and the flow becomes more correlated in the streamwise direction.

• 147.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Chemical Science and Engineering (CHE), Centres, Wallenberg Wood Science Center.
KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Chemical Science and Engineering (CHE), Centres, Wallenberg Wood Science Center.
The dynamical states of a prolate spheroidal particle suspended in shear flow as a consequence of particle and fluid inertia2015In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 771, p. 115-158Article in journal (Refereed)

The rotational motion of a prolate spheroidal particle suspended in shear flow is studied by a lattice Boltzmann method with external boundary forcing (LB-EBF). It has previously been shown that the case of a single neutrally buoyant particle is a surprisingly rich dynamical system that exhibits several bifurcations between rotational states due to inertial effects. It was observed that the rotational states were associated with either fluid inertia effects or particle inertia effects, which are always in competition. The effects of fluid inertia are characterized by the particle Reynolds number Rep=4Ga2/ν, where G is the shear rate, a is the length of the particle major semi-axis and ν is the kinematic viscosity. Particle inertia is associated with the Stokes number St=α· Rep, where alpha is the solid-to-fluid density ratio. Previously, the neutrally buoyant case (St=Rep) was studied extensively. However, little is known about how these results are affected when St≢Rep, and how the aspect ratio rp (major axis/minor axis) influences the competition between fluid and particle inertia in the absence of gravity. This work gives a full description of how prolate spheroidal particles in the range 2≤ rp≤ 6 behave depending on the chosen St and Rep. Furthermore, consequences for the rheology of a dilute suspension containing such particles are discussed. Finally, grid resolution close to the particle is shown to affect the quantitative results considerably. It is suggested that this resolution is a major cause of quantitative discrepancies between different studies. Thus, the results of this work and previous direct numerical simulations of this problem should be regarded as qualitative descriptions of the physics involved, and more refined methods must be used to quantitatively pinpoint the transitions between rotational states.

• 148.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Chemical Science and Engineering (CHE), Centres, Wallenberg Wood Science Center.
Effect of fluid inertia on the dynamics and scaling of neutrally buoyant particles in shear flow2014In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 738, p. 563-590Article in journal (Refereed)

The basic dynamics of a prolate spheroidal particle suspended in shear flow is studied using lattice Boltzmann simulations. The spheroid motion is determined by the particle Reynolds number (Re-p) and Stokes number (St), estimating the effects of fluid and particle inertia, respectively, compared with viscous forces on the particle. The particle Reynolds number is defined by Re-p = 4Ga(2)/nu, where G is the shear rate, a is the length of the spheroid major semi-axis and nu is the kinematic viscosity. The Stokes number is defined as St = alpha . Re-p, where alpha is the solid-to-fluid density ratio. Here, a neutrally buoyant prolate spheroidal particle (St = Re-p) of aspect ratio (major axis/minor axis) r(p) = 4 is considered. The long-term rotational motion for different initial orientations and Re-p is explained by the dominant inertial effect on the particle. The transitions between rotational states are subsequently studied in detail in terms of nonlinear dynamics. Fluid inertia is seen to cause several bifurcations typical for a nonlinear system with odd symmetry around a double zero eigenvalue. Particle inertia gives rise to centrifugal forces which drives the particle to rotate with the symmetry axis in the flow-gradient plane (tumbling). At high Re-p, the motion is constrained to this planar motion regardless of initial orientation. At a certain critical Reynolds number, Re-p = Re-c, a motionless (steady) state is created through an infinite-period saddle-node bifurcation and consequently the tumbling period near the transition is scaled as vertical bar Re-p - Re-c vertical bar(-1/2). Analyses in this paper show that if a transition from tumbling to steady state occurs at Re-p = Re-c, then any parameter beta (e. g. confinement or particle spacing) that influences the value of Re-c, such that Re-p = Re-c as beta = beta(c), will lead to a period that scales as vertical bar beta - beta c vertical bar(-1/2) and is independent of particle shape or any geometric aspect ratio in the flow.

• 149. Rowley, Clarence W.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
Spectral analysis of nonlinear flows2009In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 641, p. 115-127Article in journal (Refereed)

We present a technique for describing the global behaviour of complex nonlinear flows by decomposing the flow into modes determined from spectral analysis of the Koopman operator, an infinite-dimensional linear operator associated with the full nonlinear system. These modes, referred to as Koopman modes, are associated with a particular observable, and may be determined directly from data (either numerical or experimental) using a variant of a standard Arnoldi method. They have an associated temporal frequency and growth rate and may be viewed as a nonlinear generalization of global eigenmodes of a linearized system. They provide an alternative to proper orthogonal decomposition, and in the case of periodic data the Koopman modes reduce to a discrete temporal Fourier transform. The Arnoldi method used for computations is identical to the dynamic mode decomposition recently proposed by Schmid & Sesterhenn (Sixty-First Annual Meeting of the APS Division of Fluid Dynamics, 2008), so dynamic mode decomposition can be thought of as an algorithm for finding Koopman modes. We illustrate the method on an example of a jet in crossflow, and show that the method captures the dominant frequencies and elucidates the associated spatial structures.

• 150.
Indian Institute of Science, India .
Shear-imposed falling film2014In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 753, p. 131-149Article in journal (Refereed)

The study of a film falling down an inclined plane is revisited in the presence of imposed shear stress. Earlier studies regarding this topic (Smith, J. Fluid Mech., vol. 217, 1990, pp. 469-485; Wei, Phys. Fluids, vol. 17, 2005a, 012103), developed on the basis of a low Reynolds number, are extended up to moderate values of the Reynolds number. The mechanism of the primary instability is provided under the framework of a two-wave structure, which is normally a combination of kinematic and dynamic waves. In general, the primary instability appears when the kinematic wave speed exceeds the speed of dynamic waves. An equality criterion between their speeds yields the neutral stability condition. Similarly, it is revealed that the nonlinear travelling wave solutions also depend on the kinematic and dynamic wave speeds, and an equality criterion between the speeds leads to an analytical expression for the speed of a family of travelling waves as a function of the Froude number. This new analytical result is compared with numerical prediction, and an excellent agreement is achieved. Direct numerical simulations of the low-dimensional model have been performed in order to analyse the spatiotemporal behaviour of nonlinear waves by applying a constant shear stress in the upstream and downstream directions. It is noticed that the presence of imposed shear stress in the upstream (downstream) direction makes the evolution of spatially growing waves weaker (stronger).

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