Planar Laser-induced Fluorescence Research Articles

Mutual effects between a gliding arc discharge and a premixed flame

Mutual effects between a gliding arc (GA) discharge at atmospheric pressure and a premixed CH4/air flame were experimentally investigated. Effects of the flame on the GA were studied using simultaneous measurements of the current, the voltage, and the instantaneous images of the plasma columns. The GA in the flame has a thicker and more diffusive plasma column, and it is more frequently ignited at a smaller breakdown voltage than that in the air. The GA extension velocity and the gliding velocity in the flame are larger than those in the air. The electrode voltage drop of the GA discharge in the flame is about 160 V, whereas that in the air is about 220 V. Compared with the GA in the air, the different features of the GA in the flame can be explained by high-temperature, weakly ionized, and species-abundant environment that are generated by the premixed CH4/air flame. Effects of the gliding arc discharge on the premixed flames were demonstrated using planar laser-induced fluorescence of hydroxyl radicals (OH) and formaldehyde (CH2O). OH and CH2O can be formed in the CH4/air mixture in the presence of the GA due to kinetic effects, and the increase of OH and CH2O shows the great potential of the GA for combustion enhancement.

Thermometry of Spatially Inhomogeneous Methane–Air Flame Using Two-Color Planar Laser-Induced Fluorescence and Coherent Anti-Stokes Raman Scattering Spectroscopy

Thermometry of Spatially Inhomogeneous Methane–Air Flame Using Two-Color Planar Laser-Induced Fluorescence and Coherent Anti-Stokes Raman Scattering Spectroscopy

Analysis of an Accurate Iterative Technique with Attenuation Compensation in Planar Laser Induced Fluorescence

Abstract Iterative techniques in Planar Laser Induced Fluorescence (PLIF) evaluations are theoretically analysed. Correction for laser light attenuation is also incorporated in the analysis. Conditions for the convergence of the results and the scalings for the errors are derived. The results are validated against experiments. It is shown that the optimal strategy for implementation of iterative PLIF evaluation with attenuation correction is on the ensemble mean of the fluorescence field. Compared to the implementation with instantaneous fluorescence images, this approach is not only far more efficient computationally, but also is assured to converge monotonically and extremely rapidly, with minimal errors. This is suggested to be a viable and useful technique for PLIF in general, but especially for cases where a reference cell is unfeasible for explicit attenuation correction.

Experimental and reaction mechanism study on laminar burning velocity and characteristics of OH/NH generation in ammonia co-combustion

Developing fuels without carbon, such as ammonia (NH3), is crucial for achieving carbon reduction. Laminar burning velocity (LBV) is investigated, and distribution characteristics of OH and NH radicals are identified through planar laser-induced fluorescence. Rate of production of main free radicals and sensitivity analysis are also studied. The addition of NH3 to CH4-air mixtures results in a decrease in the LBV, a rise in preheating zone height, a reduction in OH radical fluorescence intensity, and an enhancement in NH radical fluorescence intensity. Simulation reveals that the high NH3 ratio enhance the negative impact of nitrogen-containing elementary reactions on LBV. The addition of NH3 enhances the initial consumption of more OH via reaction R248:NH2+OH=NH+H2O, leading to increased NH production, and indicating a negative effect on LBV. The decrease in OH concentration is the main factor leading to a decrease in LBV. The reactions affecting the OH generation and consumption are R39:H+O2=O+OH and R85:OH+H2=H+H2O, respectively. The addition of NH3 leads to a more significant reduction in R39.

Scalar mixing and entrainment in an axisymmetric jet subjected to external turbulence

The present study aims to understand the process of turbulent entrainment into a jet, as affected by background turbulence, using scalar statistics. Planar laser-induced fluorescence was employed to capture the orthogonal cross sections of the jet at a fixed downstream station with varying background turbulence intensities and length scales. The conditional scalar profiles revealed that the thickness of the scalar turbulent/turbulent interface is greater than that of the traditional turbulent/non-turbulent interface, and the interfacial thickness is an increasing function of the background turbulence intensity. Although nibbling remains the primary entrainment mechanism in the far field, increased occurrence of concentration “holes” within the interfacial layer in the presence of ambient turbulence suggests a more significant role of large-scale engulfment in the turbulent/turbulent entrainment process (although still below 1% of the total mass flux). Enhanced contribution of the area of detached jet patches (i.e., “islands”) to that of the main jet is hypothesized to be evidence of intense detrainment events in the background turbulence. This can potentially contribute to a reduced net entrainment into the jet, which manifests as less negative values of scalar skewness within the jet core.

Immiscible non-Newtonian displacement flows in stationary and axially rotating pipes

We examine immiscible displacement flows in stationary and rotating pipes, at a fixed inclination angle in a density-unstable configuration, using a viscoplastic fluid to displace a less viscous Newtonian fluid. We employ non-intrusive experimental methods, such as camera imaging, planar laser-induced fluorescence (PLIF), and ultrasound Doppler velocimetry (UDV). We analyze the impact of key dimensionless numbers, including the imposed Reynolds numbers (Re, Re*), rotational Reynolds number (Rer), capillary number (Ca), and viscosity ratio (M), on flow patterns, regime classifications, regime transition boundaries, interfacial instabilities, and displacement efficiency. Our experiments demonstrate distinct immiscible displacement flow patterns in stationary and rotating pipes. In stationary pipes, heavier fluids slump underneath lighter ones, resulting in lift-head and wavy interface stratified flows, driven by gravity. Decreasing M slows the interface evolution and reduces its front velocity, while increasing Re* shortens the thin layer of the interface tail. In rotating pipes, the interplay between viscous, rotational, and capillary forces generates swirling slug flows with stable, elongated, and chaotic sub-regimes. Progressively, decreasing M leads to swirling dispersed droplet flow, swirling fragmented flow, and, eventually, swirling bulk flow. The interface dynamics, such as wave formations and velocity profiles, is influenced by rotational forces and inertial effects, with Fourier analysis showing the dependence of the interfacial front velocity's dominant frequency on Re and Rer. Finally, UDV measurements reveal the existence/absence of countercurrent flows in stationary/rotating pipes, while PLIF results provide further insight into droplet formation and concentration field behavior at the pipe center plane.

Fluorescence imaging of plume-surface interaction in large-scale reduced pressure environments

Planar laser-induced fluorescence (PLIF) was applied for the first time in the 20-ft vacuum chamber at the Marshall Space Flight Center to visualize the plume-surface interaction (PSI) of a nitrogen jet seeded with nitric oxide (NO). A Mach 5.3 nozzle was used to simulate the exhaust of a landing spacecraft for two different jet stagnation pressures and one jet stagnation temperature. A flat plate was used to simulate the landing surface, and two different dimensionless altitudes were investigated. The chamber pressure was reduced such that both lunar-relevant environments at 0.01–28 Pa and Martian-relevant environments at ∼600 Pa were investigated. PLIF flow visualization was performed using a pulsed, tunable, ultraviolet laser, which entered the vacuum chamber through a window, and was directed to the test article using remote-controlled mirrors. Fluorescence at ultraviolet wavelengths was imaged using an intensified camera, which was placed inside a pressurized enclosure located inside the vacuum chamber. For the Martian-relevant condition, a Mach disk and stagnation bubble were observed at h/De = 10, whereas a pair of oblique stagnation shocks were observed at h/De = 3. Significantly complex flows, such as different stagnation shock behaviors, were observed for the lunar-relevant conditions based on the h/De and Reynolds number. The results presented here are the first NO-PLIF measurements of the PSI flowfield within rarefied environments. The unique information on jet expansion and plume structure will be useful to aid researchers in validating complex computational simulations and to inform engineering designs of extraterrestrial landing systems.

Wettability-dependent dissolution dynamics of oxygen bubbles on Ti64 substrates

In this study, the dissolution of a single oxygen bubble on a solid surface, here Titanium alloy Ti64, in ultrapure water with different oxygen undersaturation levels is investigated. For that purpose, a combination of shadowgraph technique and planar laser-induced fluorescence is used to measure simultaneously the changes in bubble geometry and in the dissolved oxygen concentration around the bubble. Two different wettabilities of the Ti64 surface are adjusted by using plasma-enhanced chemical vapor deposition. The dissolution process on the solid surface involves two distinct phases, namely bouncing of the oxygen bubble at the Ti64 surface and the subsequent dissolution of the bubble, primarily by diffusion. By investigating the features of oxygen bubbles bouncing, it was found that the boundary layer of dissolved oxygen surrounding the bubble surface is redistributed by the vortices emerging during bouncing. This establishes the initial conditions for the subsequent second dissolution phase of the oxygen bubbles on the Ti64 surfaces. In this phase, the mass transfer of O2 proceeds non-homogeneously across the bubble surface, leading to an oxygen accumulation close to the Ti64 surface. We further show that the main factor influencing the differences in the dynamics of O2 bubble dissolution is the variation in the surface area of the bubbles available for mass transfer, which is determined by the substrate wettability. As a result, dissolution proceeds faster at the hydrophilic Ti64 surface due to the smaller contact angle, which provokes a larger surface area.

High spatiotemporal resolution optical measurements of two-stage ignition and combustion in Engine Combustion Network Spray D flames

This study explores flame structures and combustion dynamics in high-pressure n-dodecane fuel sprays, focusing on the formation and consumption of formaldehyde (CH2O) during autoignition and the development of poly-aromatic hydrocarbons (PAH) as soot precursors. These processes are crucial for optimizing combustion efficiency and reducing emissions. However, traditional approaches, which rely on single-shot measurements or ensemble-averaged visualizations, often overlook critical early-stage processes during low-temperature ignition. To overcome these challenges, we employed an innovative high-speed planar laser-induced fluorescence (PLIF) technique at 50 kHz using a pulse-burst Nd:YAG laser system with an excitation wavelength of 355 nm. This approach, applied for the first time to Engine Combustion Network (ECN) Spray D flames, provides unprecedented insights into the combustion processes at varying ambient temperatures and oxygen concentrations. Additionally, simultaneous high-speed schlieren imaging at 100 kHz was used to visualize spray penetration, first-stage ignition, and thermal expansion zones. Our findings reveal that, similar to Spray A flames, CH2O forms in cold, fuel-rich zones well upstream of the combustion zone. However, in Spray D flames, the schlieren signal softening observed in the jet's head does not lead to complete disappearance, and the CH2O signal is absent from the full head of the spray. During the second-stage ignition, CH2O consumption accelerates due to high-temperature reactions, leading to a significant reduction in its signal. Unlike the mushroom-shaped structure seen in Spray A flames, Spray D flames exhibit a quasi-steady PAH phase structure, with lean peripheral mixtures insufficient for soot precursor formation. Notably, reducing ambient oxygen concentration to 13 % while maintaining or increasing temperature prolongs the presence of CH2O, highlighting its influence on ignition dynamics and oxidation processes in dodecane spray flames. This study provides new insights into the combustion mechanisms of high-pressure sprays and offers valuable data for developing next-generation combustion technologies, including models, aimed at improving efficiency and reducing emissions.

Laser absorption correction for hydroxyl planar laser induced fluorescence measurements in a centrally staged combustor at elevated pressures

Planar laser-induced fluorescence (PLIF) is a crucial spectroscopic technique for measuring minor species [e.g., hydroxyl (OH), methylene (CH), and nitric oxide (NO) radicals] in combustion research, owing to its non-intrusive nature and high sensitivity. However, laser energy attenuation due to absorption poses significant challenges to its application under high-pressure conditions, which may cause asymmetric image intensity distribution along the light propagation direction. An absorption correction method for OH PLIF based on the concept of maximum number density is proposed in the present study. This method offers several key advantages, including simplicity, high accuracy, and versatility, allowing for correcting both time-averaged and instantaneous OH PLIF images. OH PLIF data obtained from a centrally staged combustor at elevated pressures (i.e., 0.3, 0.6, and 1.0 MPa) are utilized to validate the method. Correction for the time-averaged PLIF images achieves a much more symmetric distribution of OH, revealing the overall flame structures that would not have been completely visualized from the original images. The fronts of the pilot and main stage flames have also been recovered from the corrected instantaneous images. This correction algorithm provides an effective way of enhancing data quality for high-cost OH PLIF measurements at pressurized conditions.

Thermal Mixing Analysis in a Ladle Utilizing Physical and Numerical Modeling through Planar Laser-induced Fluorescence (PLIF) Technique

Thermal Mixing Analysis in a Ladle Utilizing Physical and Numerical Modeling through Planar Laser-induced Fluorescence (PLIF) Technique

Soot and Flame Structures in Turbulent Partially Premixed Jet Flames of Pre-Evaporated Diesel Surrogates with Admixture of OMEn

In this study, the soot formation and oxidation processes in different turbulent, pre-evaporated and partially premixed diesel surrogate flames are experimentally investigated. For this purpose, a piloted jet flame surrounded by an air co-flow is used. Starting from a defined diesel surrogate mixture, different fuel blends with increasing blending ratios of poly(oxymethylene) dimethyl ether (OME) are studied. The Reynolds number, equivalence ratio, and vaporization temperature are kept constant to ensure the comparability of the different fuel mixtures. The effects of OME addition on flame structures, soot precursors, and soot are investigated, showing soot reduction when OME is added to the diesel surrogate. Using chemiluminescence images of C2 radicals (line of sight) and subsequent Abel-inversion, flame lengths and global flame structure are analyzed. The flame structure is visualized by means of planar laser-induced fluorescence (PLIF) of hydroxyl radicals (OH). The spatial distribution of soot precursors, such as polycyclic aromatic hydrocarbons (PAHs), is simultaneously measured by PLIF using the same excitation wavelength. In particular, aromatic compounds with several benzene rings (e.g., naphthalene or pyrene), which are known to be actively involved in soot formation and growth, have been visualized. Spatially distributed soot particles are detected by using laser-induced incandescence (LII), which allows us to study the onset of soot clouds and its structures qualitatively. Evident soot formation is observed in the pure diesel surrogate flame, whereas a significant soot reduction with changing PAH and soot structures can be identified with increasing OME addition.

Temperature Field Measurements in Swirl Spray Flames Using Two-Line Planar Laser Induced Fluorescence Thermometry

Abstract This paper investigates the temperature fields in a centrally staged swirl spray combustor using two-line OH planar laser induced fluorescence (PLIF) thermometry at elevated inlet pressures and temperatures up to 0.62 MPa and 650 K. The pilot and main stages of the combustor were supplied with RP-3 kerosene. OH radicals were excited using the Q1(5) and Q1(14) transitions within the A2Σ←X2Π (1,0) band. Two laser excitation systems were operated simultaneously, where the two beams were spatially combined and separated by a small interval in time. The PLIF signals excited at the two wavelengths were captured by two identical sets of imaging system. The calibration coefficient needed for quantitative conversion from fluorescence ratio to temperature was determined based on results from independent coherent anti-Stokes Raman scattering (CARS) measurements. A joint threshold mask was developed to remove the noise and weak signals in the raw PLIF images. The high temperature zones in the temperature field were then obtained, and the pilot and main stage flames were identified. In addition, the radial position of the pilot flame showed marked variations at a nominally fixed condition. By extracting the radial profiles, a consistency between the peaks of PLIF intensity and temperature was found, suggesting that PLIF images could be a qualitative substitute for the high temperature zones in the temperature fields of these swirl spray flames. This study demonstrates the feasibility of temperature field measurements using two-line OH PLIF in aero-engine model combustors.

Fluorescence characteristics of organic tracer molecules for planar laser-induced fluorescence in internal combustion engines, Part B: aromatics

Fluorescence characteristics of organic tracer molecules for planar laser-induced fluorescence in internal combustion engines, Part B: aromatics

Experimental study of rotating direction for dual-axial swirlers on the flow field and combustion characteristics of aero-engine combustor

The flow field structure for aero-engine combustor is one of the most important factors for combustion performance. To investigate how the rotating direction of dual-axial swirlers affects the flow field and combustion characteristics, particle image velocimetry (PIV) experiments were conducted in the primary combustion and intermediate zones. Additionally, planar laser induced fluorescence (PLIF) was used to map the distribution of kerosene and OH in the primary combustion zone. The results show that the swirling jets in co-swirl exhibit greater jet momentum, resulting in a longer primary recirculation zone and a larger deflection angle of the primary jets. This ultimately leads to a higher recirculation rate compared to counter-swirl. The primary jets define the boundary of the flow field structure. The rotating direction primarily affects the flow field structure upstream of the primary jets, exerts a relatively weaker influence on the intermediate zone, which is mainly affected by the deflection direction of the primary jets, and essentially has no impact on the dilution jets. Co-swirl has a relatively stable flow field than counter-swirl, whereas the flow field in counter-swirl is more chaotic, featuring a greater number of vortex cores in the primary recirculation zone. The coupling between the primary and swirling jets affects the mass transfer direction in the intermediate zone, which is reflected in the fact that the mass transfer is from top-left to bottom-right in co-swirl, while it is in the opposite direction in counter-swirl. OH is predominantly found in the swirling shear layers, the primary and secondary combustion zones, whereas kerosene is mainly concentrated in the shear layers of swirling jets. The kerosene distribution in co-swirl shows a larger and more concentrated expansion angle compared to counter-swirl. In contrast, the OH distribution downstream of counter-swirl is broader, with more intense combustion due to enhanced kerosene decomposition and fuel-air mixing. The smaller primary recirculation zone in counter-swirl forces the primary combustion zone to extend downstream, leading to a more intense reaction in the secondary recirculation zone.

An investigation on hydrodynamic behavior of horizontal gas–liquid intermittent flow by S-PLIF and parallel-wire conductance sensors

Horizontal gas–liquid two-phase flows widely exist in a variety of industrial fields such as the environment, chemical industry and energy. Intermittent flow, characterized by the quasi-periodic alternation motion of liquid slugs and large-scale Taylor bubbles, is the most prevalent flow pattern in horizontal gas–liquid two-phase flows. Comprehensive research on the hydrodynamic behavior of gas–liquid intermittent flow is essential for revealing the mass and heat transfer characteristics between phases, thereby establishing physical models of flow parameters. In this study, a structured planar laser-induced fluorescence (S-PLIF) system and paired parallel-wire conductance sensors (PWCSs) are designed to detect the gas–liquid interface structures and the hydrodynamic parameters. The S-PLIF system consists of a laser, a visualization box, a Ronchi ruling-plate and a pair of high-speed cameras. An optical linear prism forms a laser sheet in the transverse direction and the middle of the test section, and the cameras are positioned at 70° and 90° respectively to the plane of the laser sheet, referred to as S-PLIF70 and S-PLIF90. Under the laser excitation, bright and dark stripes generated by the Ronchi ruling-plate are deflected at the gas–liquid interface. The influence of total reflection can be effectively avoided by identifying the deflection position of the stripes, allowing for accurate detection of the gas–liquid interfacial structures. The effects of the interface fluctuations and detached bubbles on the S-PLIF70&90 results are investigated. Fluctuation and evolution characteristics of the gas–liquid interface are analyzed by probability density function (PDF) and power spectral density (PSD). Meanwhile, hydrodynamic parameters, i.e., Taylor bubble nose and tail velocity, Taylor bubble and slug length, and slug frequency, are detected by the PWCSs, and compared with previous correlations. The evolution characteristics of the interfacial structures and hydrodynamic parameters are uncovered as the flow condition changes.

Fluorescence characteristics of organic tracer molecules for planar laser-induced fluorescence studies in internal combustion engines, part A: non-aromatics

Fluorescence characteristics of organic tracer molecules for planar laser-induced fluorescence studies in internal combustion engines, part A: non-aromatics

Optical investigation on lubricant combustion characteristics under the ammonia-methane premixed environment

The combustion process is an indispensable energy conversion step in modern industry and energy production. Especially in high-performance engines and energy conversion systems, understanding and controlling the combustion process is critical to improving efficiency and reducing environmental pollution. As a key component of mechanical systems, the combustion characteristics of lubricants at high temperatures and pressures have a direct impact on system performance and emissions. This study investigated the combustion characteristics of lubricant films in an ammonia-methane premixed environment using Planar Laser-Induced Fluorescence (PLIF) and Planar Laser-Induced Incandescence (PLII). It focused on the effects of varying ammonia concentrations on the emission of soot and polycyclic aromatic hydrocarbons (PAHs) in the constant volume combustion vessel. Experiments varied the ammonia-to-methane molar ratios, initial oil film thickness, and base oil type to study their influence on the lubricant combustion characteristics. Results indicated that ammonia significantly reduced soot formation by altering the dynamics of NH* and OH* and impacting PAH distribution. For the lubricating oil soot formation factors, the increase of the initial mean oil film thickness was more obvious for the promotion of soot formation, the increase of the unsaturated hydrocarbon content in the oil film also promoted the generation of carbon soot to a certain extent, and the initial flame energy ratio had the least influence on the promotion of soot formation. Overall, the study contributed to the understanding of the formation mechanism of soot caused by lubricating oil in zero-carbon and low-carbon blended atmospheres and provided a new insight into the interaction between nitrogen-containing zero-carbon fuels and large-carbon-number hydrocarbons, which is of great significance for controlling soot emissions from engines under zero-carbon fuel blending.

Mixing Of A Starting Turbulent Jet In Homogeneous And Isotropic Turbulence

The mixing of a starting turbulent jet, injected with an injection velocity of U = 18.8 m/s from a tube with a diameter of D = 4mm (Reynolds number Re = 4800, characteristic time scale t* = D/U = 0.21 ms at the nozzle exit), is experimentally investigated in the presence of homogenous and isotropic turbulence (HIT) using Planar Laser-induced Fluorescence (PLIF). The root-mean-square (RMS) velocity of the ambient HIT is 0.38 and 0.63 m/s, corresponding to turbulent Reynolds numbers of Reλ = 190 and 250, respectively. Spatial distributions of mixture fraction and scalar dissipate rate (SDR) were measured within an axial range of y = 0 – 10 D and at different times after the start of injection (ASIs) up to 21.4 t*. Ambient HIT did not alter the location or size of the leading vortex ring in the initial formation stage. However, it was able to enhance the entrainment of ambient fluids in this stage and deform/transport both the leading and the trailing vortex rings at later stages, despite that the ASIs examined were only comparable to its Kolmogorov timescale. Ambient HIT also introduced a significant increase to the fluctuations of the jet penetrations length but only a marginal reduction (less than 10%) to the averaged jet penetration speed. PDFs of the ensemble averaged mixture fraction within the whole jet region showed increased probability of low mixture fraction values – and therefore indicating enhanced entrainment and mixing – in the presence of ambient HIT. Ensemble averaged distributions of the SDR showed no significant alterations by the ambient HIT in the initial formation stage of the leading vortex ring. At later stages, while the high SDRs in the leading vortex ring remained concentrated in a layer along the edge of the vortex ring for Reλ = 0, it became increasingly uniformly distributed with a lower maximum value as the ambient HIT increased. Similar, but less significant, impact of the ambient HIT on the SDR fields was observed in the trailing vortex rings, while no noticeable impact was found in the shear layer close to the nozzle exit.

On The Determination Of Conditional Statistics Along Gradient Trajectories At The Turbulent/Non-Turbulent Interface Of Jet Flows.

Conditional sampling and averaging are valuable techniques for discerning and quantifying notable regions within turbulent flows. These methods have been particularly prevalent in experimental and numerical investigations of turbulent shear flows. Conditional statistics effectively analyze the dynamics and characteristics of turbulent flows, offering insights into transitional behaviors and distinct features within these regimes. This approach is instrumental in studying turbulent shear flows, such as jets or mixing layers, where a well-defined zone separates the turbulent core from the non-turbulent surrounding fluid. This zone, known as the Turbulent/Non-Turbulent Interface (TNTI), plays a crucial role in various phenomenological changes, including the transfer of mass, momentum, and scalar fluxes. While statistics in jet flows are often reported along the radial direction for a given downstream position, this method can obscure the underlying physical processes. Scalar dissipation rate, transport, or turbulent kinetic energy involve velocity or concentration gradients at the flow interface. To date, the impact of sampling direction on conditional statistics within jet flows has not yet been thoroughly discussed. This study focuses on determining gradient trajectories at the interface of turbulent flows. Gradient trajectories have been used to explore structures in turbulent flows, proving effective in analyzing homogeneous shear turbulence. This study introduces a methodology for sampling conditional data by computing gradient trajectories intersecting the TNTI. The primary objective is to verify whether sampling statistics along the gradient of scalar concentration provide a more detailed understanding of the processes occurring near the TNTI. The methodology involves computing a field of gradient trajectories from concentration fields obtained through Planar Laser-Induced Fluorescence (PLIF) in a N2/N2 jet with Re = 2900. Conditional statistics at the TNTI of a jet flow along the gradient trajectory for a given downstream position are calculated and reported. The paper aims to compare conditional statistics along gradient trajectories with those obtained along radial and normal directions at the TNTI. It is expected that gradient trajectory statistics align more closely with normal direction statistics near the interface and diverge as it gets into the jet or coflow fluid.