Intercomponent Energy Research Articles

Spectra scaling of velocity components and pressure–strain correlations for hypersonic boundary layers at a range of wall-to-recovery temperatures

Flow similarity is one of the most desirable features for turbulence under different conditions. For hypersonic boundary layers, different wall temperatures are known to change the turbulence evolution by influencing the intercomponent energy transfer, while the flow similarity has received less attention. Based on direct numerical simulations, this work investigates the spectral distribution of velocity components and pressure–strain correlations for hypersonic boundary layers at Mach 6 and wall-to-recovery temperature ratios equal to 0.3, 0.5, 0.76, and 1. The wall-normal evolution of turbulent structures is compared by the spectra peak scale λSP, wall-normal location ySP, and the vertical profiles of peak scale λP. For all cases, the peak scale profiles exhibit linear increases with a height of 0.1≤y/δ≤0.25. The linear growth of the turbulence scale in the logarithmic region indicates the existence of self-similar structures, and the agreement of peak scales in the outer scaling suggests the flow similarity under different wall temperatures. Likewise, the streamwise pressure–strain term has the peak scale profile linearly dependent on the height for the same vertical range 0.1≤y/δ≤0.25 with velocity components, while the wall-normal and spanwise terms exhibit both linear and constant vertical dependence depending on the wall temperatures. With the increase in wall temperature, the peak scale exhibits broader constant vertical dependence and narrower linear vertical dependence. The cospectral analysis further confirms that the pressure–strain correlations are maximized at different spanwise-vertical aspect ratios of turbulence structures.

Turbulent boundary layer flow over a three-dimensional sinusoidal surface

The sinusoidal roughness effect is investigated using a direct numerical simulation (DNS) of a spatially developing turbulent boundary layer (TBL) over three-dimensional sinusoidal roughness. The validity of Townsend's outer-layer similarity hypothesis is assessed based on comparisons of mean and second-order flow statistics, with a DNS of smooth-wall TBL data set at a similar Reynolds number. The total, Reynolds and dispersive stress tensors are calculated using the double-averaging procedure. The mean and second-order statistical similarities in the outer layer between rough-wall and smooth-wall TBLs are generally observed. The transport between total, turbulent and dispersive kinetic energy is investigated utilising triple-decomposed kinetic energy transports equations. The transport behaviour of turbulent kinetic energy (TKE) is significantly affected by the local mean shear induced by the surface roughness. However, the TKE transport shows good collapse with the smooth-wall case in the outer region of the flow. On the other hand, the transport of dispersive kinetic energy, including local production, redistribution and dissipation, are confined within the roughness sublayer. The intercomponent transfer between TKE and dispersive kinetic energy is quantified from the triple-decomposed kinetic energy transport equations. The intercomponent energy transfer is associated with the local spatial gradients of the turbulent momentum fluxes generated near the roughness canopy.

Pillar[5]arene-porphyrin conjugates: from molecular flowers to photoactive rotaxanes

Our groups are involved in a research program on the development of molecular and supramolecular systems combining pillar[5]arene building blocks with porphyrins. Functionalization of both rims of the pillar[5]arene scaffold with metalloporphyrins generated giant molecular machines mimicking the blooming of a flower as well as light-harvesting devices. On the other hand, we have also used the host-guest properties of pillar[5]arene derivatives to prepare photoactive mechanically interlocked molecules. In such compounds, complementary subunits are associated into a single molecular ensemble but without being connected through covalent bonds. Inter-component photo-induced energy transfer processes remain however extremely fast in these systems despite the exclusive link through mechanical bonds. All these results are described in the present review.

Energy transfer mechanisms in adverse pressure gradient turbulent boundary layers: production and inter-component redistribution

Production and inter-component redistribution of turbulence in adverse pressure gradient (APG) turbulent boundary layers (TBLs) with small and large velocity defects are investigated, along with the structures playing a role in these energy transfer mechanisms. We examine the wall-normal and spectral distributions of energy, production and pressure-strain in APG TBLs, and compare these distributions with those in canonical flows. It is found that the spectral distributions of production and pressure-strain are not affected profoundly by an increase of the velocity defect, although the energy spectra change drastically in the inner layer of the large-defect APG TBL. In the latter, the signature of the inner-layer streaks is absent from the energy spectra. In the outer layer, energetic, production and pressure-strain structures appear to change from wall-attached to wall-detached structures with increasing velocity defect. Despite this, the two-dimensional spectral distributions have similar shapes and wavelength aspect ratios of the peaks in all these flows. Therefore, the conclusion is that the mechanisms responsible for turbulence production and inter-component energy transfer may remain the same within each layer in all these flows. It is the intensity of these mechanisms within one layer that changes with velocity defect, because of the local mean shear variation.

A Curcumin-BODIPY Dyad and Its Silica Hybrid as NIR Bioimaging Probes.

In this paper we describe the synthesis of a novel bichromophoric system in which an efficient photoinduced intercomponent energy transfer process is active. The dyad consists of one subunit of curcumin and one of BODIPY and is able to emit in the far-red region, offering a large Stokes shift, capable of limiting light scattering processes for applications in microscopy. The system has been encapsulated in MCM-41 nanoparticles with dimensions between 50 and 80 nm. Both the molecular dyad and individual subunits were tested with different cell lines to study their effective applicability in bioimaging. MCM-41 nanoparticles showed no reduction in cell viability, indicating their biocompatibility and bio-inertness and making them capable of delivering organic molecules even in aqueous-based formulations, avoiding the toxicity of organic solvents. Encapsulation in the porous silica structure directed the location of the bichromophoric system within cytoplasm, while the dyad alone stains the nucleus of the hFOB cell line.

Analysis of drag reduction effects in turbulent Taylor–Couette flow controlled via axial oscillation of inner cylinder

Analysis of drag reduction effects due to axial oscillation of an inner cylinder in a turbulent Taylor–Couette (TC) flow is performed in the present study. The frictional Reynolds number on the inner cylinder is 218, and the non-dimensional oscillating period is varied from 8 to 32. By examining turbulence statistics, we uncover different impacts of the long- and short-period oscillations on the circumferential (θ) and radial (r) velocity fluctuations in large (uθl, url) and small (uθs, urs) scales. One of the most surprising findings is that the short-period oscillation increases the large-scale Reynolds shear stress ⟨uθlurl⟩ by the strong intensification of uθl exceeding the suppression of url. To understand the phenomena, the spectra of each term in the transport equations of the Reynolds normal stresses ⟨uθ′uθ′⟩ and ⟨ur′ur′⟩ are analyzed. First, it is shown that the short-period oscillation weakens the productions of uθs, urs, and url while it enhances that of uθl. In contrast, the long-period oscillation reduces the productions of uθl and url while it mainly intensifies that of urs. Second, the investigations of the pressure–strain terms indicate that the short-period oscillation mainly impedes the inter-component energy transfer originating from the small-scale background turbulence. However, the long-period oscillation benefits the small-scale inter-component energy communication while it hinders the large-scale one. In addition, the inverse energy transfer in the turbulent TC flow is confirmed by inspecting the inter-scale energy transfer terms. The hindrance of the inter-scale energy transfer by the inner-cylinder oscillation plays a non-negligible role in the reduction of the wall friction drag.

Direct effects of boundary permeability on turbulent flows: observations from an experimental study using zero-mean-shear turbulence

Abstract

Tuning of photo-redox behaviours and thermodynamic and kinetic aspects of intercomponent energy transfer in trimetallic complexes of Ru(II) and Os(II) by exploiting their second coordination sphere.

This paper deals with a thorough investigation of pH-induced tuning of the ground and excited state photophysical as well as electrochemical behaviours of two series of our recently reported homo- and heterotrimetallic complexes of the type [(bpy)2Ru(d-HIm-t)M(t-HIm-d)Ru(bpy)2]6+ and [(bpy)2Os(d-HIm-t)M(t-HIm-d)Os(bpy)2]6+ (M = RuII and OsII) derived from a heteroditopic bpy-tpy (d-HIm-t) type bridging ligand through the exploitation of their second coordination sphere. A small bathochromic shift of the absorption and emission spectral band along with substantial alteration of emission intensity and lifetime of the triads is noted upon deprotonation of the NH motifs at elevated pH values. The lowering of the half wave potential of a M3+/M2+ couple is also observed upon removal of the NH protons. Both ground and excited state pKa values of the triads are estimated from their absorption/emission versus pH spectral profiles. In addition, the variation of the free energy change (ΔG) and the rate of intercomponent energy transfer (ken) in the triads upon stepwise deprotonation of the NH motifs are also addressed in the present study.

Controlling the Direction of Intercomponent Energy Transfer by Appropriate Placement of Metals in Long-Lived Trinuclear Complexes of Fe(II), Ru(II), and Os(II).

In this work, we report the synthesis, photophysics, and electrochemistry of a new array of trinuclear complexes, [(bpy)2Os(d-HIm-t)M(t-HIm-d)Os(bpy)2]6+ (M = FeII, RuII, and OsII), based on a previously reported bipyridine-terpyridine type bridge (d-HIm-t). Photophysical behavior of in situ generated trinuclear OsZnOs complex {[(bpy)2Os(d-HIm-t)Zn(t-HIm-d)Os(bpy)2]6+} was also investigated to understand the complicated photophysics of trinuclear array. Complexes display very rich redox properties demonstrating multiple metal-based oxidation and ligand-based reduction couples. The triads exhibit strong absorption throughout the entire UV-vis spectral region and also emit in the near-infrared domain (NIR) with a sufficiently long lifetime at ambient temperature. Intercomponent energy transfer, either from the periphery to the center or from the center to the periphery, depending upon the relative position of metals, was convincingly demonstrated through steady-state emission and lifetime measurements of the triads together with respective model complexes. Interestingly, Fe2+ does not worsen the emission behavior of the OsFeOs system to a great extent. Present trinuclear complexes act as a visible light absorbing antenna by funneling the absorbed light to the subunit(s) with the lowest energy excited state.

Structure function tensor equations in inhomogeneous turbulence

Exact budget equations for the second-order structure function tensor ⟨𝛿u$_{i}$𝛿u$_{j}$⟩, where 𝛿u is the difference of the i th fluctuating velocity component between two points, are used to study the two-point statistics of velocity fluctuations in inhomogeneous turbulence. The anisotropic generalised Kolmogorov equations (AGKE) describe the production, transport, redistribution and dissipation of every Reynolds stress component occurring simultaneously among different scales and in space, i.e. along directions of statistical inhomogeneity. The AGKE are effective to study the inter-component and multi-scale processes of turbulence. In contrast to more classic approaches, such as those based on the spectral decomposition of the velocity field, the AGKE provide a natural definition of scales in the inhomogeneous directions, and describe fluxes across such scales too. Compared to the generalised Kolmogorov equation, which is recovered as their half-trace, the AGKE can describe inter-component energy transfers occurring via the pressure–strain term and contain also budget equations for the off-diagonal components of ⟨𝛿u$_{i}$𝛿u$_{j}$⟩. The non-trivial physical interpretation of the AGKE terms is demonstrated with three examples. First, the near-wall cycle of a turbulent channel flow at a friction Reynolds number of Re$_{𝜏}$ = 200 is considered. The off-diagonal component ⟨-𝛿u𝛿υ⟩, which cannot be interpreted in terms of scale energy, is discussed in detail. Wall-normal scales in the outer turbulence cycle are then discussed by applying the AGKE to channel flows at Re$_{𝜏}$ = 500 and 1000. In a third example, the AGKE are computed for a separating and reattaching flow. The process of spanwise-vortex formation in the reverse boundary layer within the separation bubble is discussed for the first time.

Surface wave effects on energy transfer in overlying turbulent flow

Phase-resolved wave simulation and direct numerical simulation of turbulence are performed to investigate the surface wave effects on the energy transfer in overlying turbulent flow. The JONSWAP spectrum is used to initialize a broadband wave field. The nonlinear wave field is simulated using a high-order spectral method, and the resultant wave surface provides the bottom boundary conditions for direct numerical simulation of the overlying turbulent flow. Two wave ages of and 25 are considered, corresponding to slow and fast wave fields, respectively, where denotes the celerity of the peak wave and denotes the friction velocity. The energy transfer of turbulent motions in the presence of surface waves is investigated through the spectral analysis of the two-point correlation transport equation. It is found that the production term has an extra peak at the dominant wavelength scale in the vicinity of the surface, and the energy transported to the surface via viscous and spatial turbulent transport is enhanced in the region of . The presence of surface waves results in an inverse turbulent energy cascade in the near-surface region, where small-scale wave-related motions transfer energy back to the dominant wavelength scale. Pressure-related terms reflecting the spatial and inter-component energy transfer are strongly dependent on the wave age. Furthermore, triadic interaction analysis reveals that the energy influx at the dominant wavelength scale is due to the contribution of the neighbouring streamwise turbulent motions, and those at the harmonic wavelength scales contribute the most.

Displacive phase-field crystal model

A phase-field crystal model that spontaneously undergoes displacive phase transitions is introduced by explicitly studying a two-component two-dimensional square crystal reminiscent of a perovskite. When the intercomponent free energy is a simple polynomial, the crystal undergoes displacive transitions in the $\ensuremath{\langle}10\ensuremath{\rangle}$ and $\ensuremath{\langle}11\ensuremath{\rangle}$ directions. When the interaction is a correlation function, displacements in any direction can occur. This displacive phase-field crystal (DPFC) model maps to Landau-Ginzburg-Devonshire (LGD) theories for ferroelectrics, and the DPFC and LGD models are compared in terms of phase transitions and domain walls. Dynamical simulations of quadrijunctions were also performed and found stable spiraling quadrijunctions and unstable nonspiraling quadrijunctions. Last, domain coarsening across a small-angle grain boundary demonstrates multiple forms of non-mean-curvature-driven growth.

Linear analysis of non-local physics in homogeneous turbulent flows

Characterization of non-local physical mechanisms is one of the important challenges toward deeper understanding of turbulent flows. In this investigation, we study the role of pressure in the evolution of three-dimensional incompressible homogeneous turbulent flows. We find that the evolution of turbulence, the nature of inertial physics, and pressure action are dependent on the mean flow invariants. We identify and explain the intercomponent energy transfer induced by the rapid pressure strain correlation for different regimes of flow. Additionally, the structuring effect of pressure on turbulent fluctuations of different alignments is determined and explicated. We exhibit that in regimes of flow where the action of the pressure strain correlation is significant, there is a switching of the flow evolution between diametric stages of evolution. This phenomenon is explained, and its lack of amenability to single-point turbulence modeling is detailed.

Pressure–Rate-of-Strain, Pressure Diffusion, and Velocity–Pressure-Gradient Tensor Measurements in a Cavity Flow

Pressure-related turbulence statistics in a two-dimensional open cavity shear layer flow was investigated experimentally at a Reynolds number of based on a cavity length of 38.1 mm. Time-resolved particle image velocimetry sampled at 4500 frames per second and field of view was used to simultaneously measure the instantaneous velocity and pressure distributions. Direct estimate results of the pressure–rate-of-strain, pressure diffusion, and velocity–pressure-gradient tensor components based on 140,000 measurement samples were presented after a brief review of the theory about the pressure-related terms in the context of turbulence modeling and a discussion about their role in determining an accurate mean flow. The analysis is also augmented with comparisons with experimental data obtained at a higher Reynolds number of . The pressure and streamwise velocity correlation changes its sign from negative values far upstream in the shear layer to positive ones near the trailing corner due to the strong adverse pressure gradient imposed by the corner. The distribution patterns of the pressure diffusion and the turbulence diffusion are considerably different, indicating that the conventional practice of modeling the transport terms all together as Laplacians of the turbulent kinetic energy is not justifiable, at least for the turbulent shear layer flow past a cavity. In the shear layer, turbulence fluctuation energy is redistributed from streamwise to lateral components. This intercomponent energy transfer is reversed on top of the trailing corner, indicating the complexity of the flow, especially around the corner area.

Analysis of intercomponent energy transfer in the interaction of oscillating-grid turbulence with an impermeable boundary

New experimental results are presented that investigate the nature of the intercomponent energy transfer that occurs in the interaction between oscillating-grid turbulence and a solid impermeable boundary, using instantaneous velocity measurements obtained from two-dimensional particle imaging velocimetry (PIV). Estimates of the pressure-strain correlation term (Πijs) of the transport equation of the Reynolds stress tensor, which represents intercomponent energy transfer, are obtained using the PIV data from a balance of the remaining terms of the transport equation. The influence of Πijs on the flow is examined by computing the energy spectra and conditional turbulent statistics associated with events in which intercomponent energy transfer is thought to be concentrated. Data reported here are in support of viscous and “return-to-isotropy” mechanisms governing the intercomponent energy transfer previously proposed, respectively, by Perot and Moin [J. Fluid Mech. 295, 199–227 (1995)] and Walker et al. [J. Fluid Mech. 320, 19–51 (1996)]. However, the data reported also indicate the presence of a weak net intercomponent energy transfer from the boundary-normal velocity components to the boundary-tangential velocity components over a thin region outside the viscous sublayer which is not captured within existing models of intercomponent energy transfer at the boundary.

1st International Seminar on Non-Ideal Compressible-Fluid Dynamics for Propulsion & Power

1st International Seminar on Non-Ideal Compressible-Fluid Dynamics for Propulsion & Power

Experimental study of oscillating-grid turbulence interacting with a solid boundary

The interaction between oscillating-grid turbulence and a solid, impermeable boundary (positioned below, and aligned parallel to, the grid) is studied experimentally. Instantaneous velocity measurements, obtained using two-dimensional particle imaging velocimetry in the vertical plane through the centre of the (horizontal) grid, are used to study the effect of the boundary on the root-mean-square velocity components, the vertical flux of turbulent kinetic energy (TKE) and the terms in the Reynolds stress transport equation. Identified as a critical aspect of the interaction is the blocking of a vertical flux of TKE across the boundary-affected region. Terms of the Reynolds stress transport equations show that the blocking of this energy flux acts to increase the boundary-tangential turbulent velocity component, relative to the far-field trend, but not the boundary-normal velocity component. The results are compared with previous studies of the interaction between zero-mean-shear turbulence and a solid boundary. In particular, the data reported here are in support of viscous and ‘return-to-isotropy’ mechanisms governing the intercomponent energy transfer previously proposed, respectively, by Perot & Moin (J. Fluid Mech., vol. 295, 1995, pp. 199–227) and Walkeret al.(J. Fluid Mech., vol. 320, 1996, pp. 19–51), although we note that these mechanisms are not independent of the blocking of energy flux and draw parallels to the related model proposed by Magnaudet (J. Fluid Mech., vol. 484, 2003, pp. 167–196).

The influence of near-wall density and viscosity gradients on turbulence in channel flows

The influence of near-wall density and viscosity gradients on near-wall turbulence in a channel is studied by means of direct numerical simulation of the low-Mach-number approximation of the Navier–Stokes equations. Different constitutive relations for density $\unicode[STIX]{x1D70C}$ and viscosity $\unicode[STIX]{x1D707}$ as a function of temperature are used in order to mimic a wide range of fluid behaviours and to develop a generalised framework for studying turbulence modulations in variable-property flows. Instead of scaling the velocity solely based on local density, as done for the van Driest transformation, we derive an extension of the scaling that is based on gradients of the semilocal Reynolds number, defined as $Re_{\unicode[STIX]{x1D70F}}^{\star }\equiv Re_{\unicode[STIX]{x1D70F}}\sqrt{(\overline{\unicode[STIX]{x1D70C}}/\overline{\unicode[STIX]{x1D70C}}_{w})}/(\overline{\unicode[STIX]{x1D707}}/\overline{\unicode[STIX]{x1D707}}_{w})$ (the bar and subscript $w$ denote Reynolds averaging and wall value respectively, while $Re_{\unicode[STIX]{x1D70F}}$ is the friction Reynolds number based on wall values). This extension of the van Driest transformation is able to collapse velocity profiles for flows with near-wall property gradients as a function of the semilocal wall coordinate. However, flow quantities like mixing length, turbulence anisotropy and turbulent vorticity fluctuations do not show a universal scaling very close to the wall. This is attributed to turbulence modulations, which play a crucial role in the evolution of turbulent structures and turbulence energy transfer. We therefore investigate the characteristics of streamwise velocity streaks and quasistreamwise vortices and find that, similarly to turbulence statistics, the turbulent structures are also strongly governed by $Re_{\unicode[STIX]{x1D70F}}^{\star }$ profiles and that their dependence on individual density and viscosity profiles is minor. Flows with near-wall gradients in $Re_{\unicode[STIX]{x1D70F}}^{\star }$ ($\text{d}Re_{\unicode[STIX]{x1D70F}}^{\star }/\text{d}y\neq 0$) show significant changes in inclination and tilting angles of quasistreamwise vortices. These structural changes are responsible for the observed modulation of the Reynolds stress generation mechanism and the inter-component energy transfer in flows with strong near-wall $Re_{\unicode[STIX]{x1D70F}}^{\star }$ gradients.

Light harvesting and directional energy transfer in long-lived homo- and heterotrimetallic complexes of Fe(II), Ru(II), and Os(II).

A new family of trimetallic complexes of the form [(bpy)2 M(phen-Hbzim-tpy)M'(tpy-Hbzim-phen)M(bpy)2](6+) (M=Ru(II), Os; M'=Fe(II), Ru(II), Os; bpy=2,2'-bipyridine) derived from heteroditopic phenanthroline-terpyridine bridge 2-{4-[2,6-di(pyridin-2-yl) pyridine-4-yl]phenyl}-1H-imidazole[4,5-f][1,10]phenanthroline (phen-Hbzim-tpy) were prepared and fully characterized. Zn(2+) was used to prepare mixed-metal trimetallic complexes in situ by coordinating with the free tpy site of the monometallic precursors. The complexes show intense absorptions throughout the UV/Vis region and also exhibit luminescence at room temperature. The redox behavior of the compounds is characterized by several metal-centered reversible oxidation and ligand-centered reduction processes. Steady-state and time-resolved luminescence data show that the potentially luminescent Ru(II)- and Os(II)-based triplet metal-to-ligand charge-transfer ((3)MLCT) excited states in the triads are quantitatively quenched, most likely by intercomponent energy transfer to the lower lying (3)MLCT (for Ru and Os) or triplet metal-centered ((3)MC) excited states of the Fe(II) subunit (nonluminescent). Interestingly, iron did not adversely affect the photophysics of the respective systems. This suggests that the multicomponent molecular-wire-like complexes investigated here can behave as efficient light-harvesting antennas, because all the light absorbed by the various subunits is efficiently channeled to the subunit(s) in which the lowest-energy excited states are located.

On the realizability of pressure–strain closures

AbstractThe realizability condition for statistical models of turbulence is augmented to ensure that not only is the Reynolds stress tensor positive semi-definite, but the process of its evolution is physically attainable as well. The mathematical constraints due to this process realizability requirement on the rapid pressure strain correlation are derived. The resulting constraints reveal important limits on the inter-component energy transfer and the consequent flow stability characteristics, as a function of the mean flow. For planar mean flows, the realizability constraints are most stringent for the case of purely sheared flows rather than elliptic flows. The relationship between the constraints and flow stability is explained. Process realizability leads to closure model guidance not only at the two-component (2C) limit of turbulence (as in the classical realizability approach) but throughout the anisotropy space. Consequently, the domain of validity and applicability of current models can be clearly identified for different mean flows. A simple framework for incorporating these process realizability constraints in model formulation is outlined.