Flow Lift Research Articles

Optimizing turbine meter performance through geometrical parameter analysis: A simulation-based approach using TOPSIS

The number of blades and their angle in a turbine gas meter directly affect its performance and the amount of lift force, pressure drop and flow rate passing through the blades. In this research, the combination of software simulation and optimization method has been used as an effective research tool to investigate the effect of these geometric parameters on the amount of pressure drop, volume flow rate and lift force. First, the flow in a turbine gas meter is simulated using computational fluid dynamics. The set of governing equations including continuity, linear momentum and angular momentum have been solved by Fluent software. To simulate the turbulent flow, the standard k-ε model is used. In the next step, with the help of TOPSIS model, it has been optimized to check the effect of each of the parameters and determine their optimal values. The results of this research showed that by increasing the number of blades and increasing the blade angle, the lift force increases. Among the two parameters, the number of blades and the angle value, changing the number of blades has a significant effect. Reducing the number of blades and decreasing the blade angle can be effective strategies to minimize pressure drop. Also, the effect of changing the number of blades plays an important role in pressure drop. The pressure drop in the number of 20 blades is the highest and this's due to its large number of blades. In this article, 21 cases have been investigated with the help of TOPSIS and it can be seen that the angle of 30 ° with 12 blades is an optimal model. The ratio of lift force to drag force is observed at an angle of 30°, the number of 20 blades is the highest and its dimensionless value is 78.23. For an angle of 37.5°, the ratio of lift force to drag force for 20 blades has the highest value and its dimensionless value is 915.9. Also, for an angle of 45°, the ratio of lift force to drag force and the number of 20 blades has the highest value, and its dimensionless value is 1190.94.

Towards Wall-Resolved Large-Eddy Simulation of the High-Lift Common Research Model

In the present study, we performed a sixth-order wall-resolved large-eddy simulation (WRLES) of the high-lift Common Research Model (CRM-HL) on the Leadership Class Computing Cluster Summit. During the 4th High-Lift Prediction Workshop (HLPW-4), wall-modeled LES (WMLES) and hybrid Reynolds-averaged Navier–Stokes (RANS)/LES approaches showed promise in predicting the maximum lift and large flow separations near stall. In those simulations, however, laminar and transition regions were not resolved since the flow was assumed to be fully turbulent. If one wants to resolve these regions, the only viable approach is WRLES. The main purpose of the present study is to demonstrate the feasibility of WRLES for a complex real-world configuration at the wind tunnel Reynolds number. A high-order unstructured mesh LES solver called hpMusic was employed in the study. The simulation at solution polynomial order P=5 has more than 14 billion degrees of freedom per equation. Computational results are compared to experimental data in the form of surface oil flows and pressure coefficient profiles. We highlight lessons learned from attempting a grand-challenge type large-scale simulation: 1) such a simulation is feasible but very expensive, estimated to be at least three orders more expensive than WMLES, 2) oil flows produced with WRLES agree very well with experimental oil flows in fine detail, not observed in those produced with WMLES, and 3) flow visualization is a severe bottleneck, and parallel postprocessing capability is needed.

Sweeping JET actuator for the control of flow separation on a hump airfoil

Flow control can effectively improve lift and delay flow separation. Sweeping jet (SWJ) actuators have attracted increasing interest for as active flow control actuators. In this paper, the characteristics of the SWJ actuator were studied through large-eddy simulation and experiments. It was discovered that the oscillation frequency of the SWJ actuator is directly proportional to the mass flow rate, and its working principle was determined. Subsequently, SWJ actuators with [Formula: see text], 1.9%, and 6.6% were applied to flow control on the hump airfoil. It was observed that with an increase in momentum coefficient, the SWJ actuator was able to push the shear layer toward the hump airfoil surface, leading to a reduction in the size of the separation vortex. At [Formula: see text], it was achieved that the reattachment point of the separation vortex shifted upstream from [Formula: see text] to [Formula: see text], and the separation vortex size essentially disappeared. During the investigation of the flow control mechanism of the SWJ actuator, it was found that the SWJ actuator periodically generates a separation vortex V1, which has entrainment effects, resulting in the formation of an external jet on the airfoil surface, effectively inhibiting flow separation.

Fingering stabilization and adhesion force in the lifting flow with a fluid annulus.

The lifting Hele-Shaw cell flow commonly involves the stretching of a viscous oil droplet surrounded by air, in the confined space between two parallel plates. As the upper plate is lifted, viscous fingering instabilities emerge at the air-oil interface. Such an interfacial instability phenomenon is widely observed in numerous technological and industrial applications, being quite difficult to control. Motivated by the recent interest in controlling and stabilizing the Saffman-Taylor instability in lifting Hele-Shaw flows, we propose an alternative way to restrain the development of interfacial disturbances in this gap-variable system. Our method modifies the traditional plate-lifting flow arrangement by introducing a finite fluid annulus layer encircling the central oil droplet, and separating it from the air. A second-order, perturbative mode-coupling approach is employed to analyze morphological and stability behaviors in this three-fluid, two-interface, doubly connected system. Our findings indicate that the intermediate fluid ring can significantly stabilize the interface of the central oil droplet. We show that the effectiveness of this stabilization protocol relies on the appropriate choice of the ring's viscosity and thickness. Furthermore, we calculate the adhesion force required to detach the plates, and find that it does not change significantly with the addition of the fluid envelope as long as it is sufficiently thin. Finally, we detect no distinction in the adhesion force computed for stable or unstable annular interfaces, indicating that the presence of fingering at the ring's boundaries has a negligible effect on the adhesion force.

Surge and lifting analysis of internal transmission gas–liquid two-phase flow lifting pipe

The gas–liquid two-phase flow inside large aspect ratio lifting pipes is often characterized by a complex flow pattern, potentially causing coupling vibration of the lifting pipe. And produce a surge effect, aggravating the vibration of the lifting pipe and thus affecting its fatigue life and the lifting performance of the pipe. In this paper, a combination of numerical simulation and experiment is used to investigate the effects of inlet flow rate (Q) and tube diameter (D) on the vibration and lifting performance of the lifting tube. The obtained conclusions are as follows: with an increase in the inlet gas flow rate, the amplitude of the lifting pipe increases, and the lifting flow increases; with an increase in pipe diameter, the amplitude of the lifting pipe decreases and the overall lifting performance increases. According to the numerical simulation and experimental results, when D = 40 mm lifting pipe at the intake flow between Q = 50-60 L/min, the impact of surge effect is the least, and the liquid lifting quality also reaches the best state at this time, The research presented in this paper provides a reference for the selection of parameters for lifting pipes in engineering applications.

Role of interfacial rheology on fingering instabilities in lifting Hele-Shaw flows.

The lifting Hele-Shaw cell setup is a popular modification of the classic, fixed-gap, radial viscous fingering problem. In the lifting cell configuration, the upper cell plate is lifted such that a more viscous inner fluid is invaded by an inward-moving outer fluid. As the fluid-fluid interface contracts, one observes the rising of distinctive patterns in which penetrating fingers having rounded tips compete among themselves, reaching different lengths. Despite the scholarly and practical relevance of this confined lifting flow problem, the impact of interfacial rheology effects on its pattern-forming dynamics has been overlooked. Authors of recent studies on the traditional injection-induced radial Hele-Shaw flow and its centrifugally driven variant have shown that, if the fluid-fluid interface is structured (i.e., laden with surfactants, particles, proteins, or other surface-active entities), surface rheological stresses start to act, influencing the development of the viscous fingering patterns. In this paper, we investigate how interfacial rheology affects the stability as well as the shape of the emerging fingered structures in lifting Hele-Shaw flows, at linear and early nonlinear dynamic stages. We tackle the problem by utilizing the Boussinesq-Scriven model to describe the interface and by employing a perturbative mode-coupling scheme. Our linear stability results show that interfacial rheology effects destabilize the interface. Furthermore, our second-order findings indicate that interfacial rheology significantly alters intrinsically nonlinear morphological features of the shrinking interface, inducing the formation of narrow sharp-tip penetrating fingers and favoring enhanced competition among them.

Correlation analysis of lift fan lip feature geometry and aerodynamic performance

In hover, the lip of a lift fan plays a crucial role, contributing to nearly half of the lift for the VTOL aircraft power plant. Thus, investigating the geometric parameters that influence lip performance is of significant importance. In this study, four types of lift fan lips were designed, tailored to meet specific application requirements. Numerical analysis, validated through experimental data, was employed to examine the flow field and the geometric factors that lead to variations in lip performance. Based on the findings, the relationship between lip geometric parameters and aerodynamic performance was thoroughly investigated and confirmed. The results demonstrate that, at a rotational speed of 10 000 r/min, the non-dimensional lift and non-dimensional mass flow of the lemniscate lip exhibit improvements of 33% and 9.5%, respectively, compared to lips designed based on NACA65. Among the various lip configurations, it is found that the performance parameters of the lip are optimal when the slope of the inner surface equaled twice the slope of the lemniscate. On the other hand, when the slope deviated from this optimal value, whether greater or lesser, a reduction in lip performance was observed. Specifically, at a rotational speed of 10 000 r/min, the lip designed based on a lemniscate slope could increase the total lift of the lift fan by 5.6% when compared to the lemniscate lip.

A field test of medium-depth geothermal heat pump system for heating in severely cold region

Due to the worldwide attention of fossil fuel consumption and environment pollution, geothermal is recognized to be amongst the prospering alternative energy. Previous researches mainly focused on the shallow-depth geothermal heat pump systems (SD-GHPs), while medium-depth geothermal heat pump system (MD-GHPs) lacked of the experimental support especially in severely cold region. A field test of MD-GHPs using deep borehole heat exchanger (DBHE) was conducted and verified in terms of temperature variation, heat exchange and COP. The indoor temperature remained 20 °C around even though the outdoor temperature was as low as −25.10 °C. The water supply and return water temperature on the customer side performed steadfast heating characteristics that the averages were 35.13 °C and 30.97 °C. Moreover, flow rate and borehole depth are the essential influencing factors on DBHE outlet temperatures. This suggests that lifting flow rates is a fantastic option when only considering the enhancement of the thermal extraction. The DBHE average heat exchange per meter is 1000/1200 m for 61.1/84.9 W/m and 2000 m is 152.6 W/m respectively. Besides, the average heat exchange of DBHEs for working days was 485.4 kW while during Chinese New Year Holidays was 388.6 kW. Correspondingly, the average COPs for MD-GHPs ground side were 4.5 and 5.2, respectively. Results show that MD-GHPs can be extended to severely cold regions and obtain superior performance.

Flow structure and aerodynamic forces of finned cylinders during flow-induced acoustic resonance

This experimental study investigated the impact of self-excitation of acoustic resonance on the fluctuating lift force, flow structure, and aeroacoustic energy transfer of spirally finned cylinders with crimps in cross-flow. Three different finned cylinders with varying fin pitch-to-root diameter ratios (p/Dr) were compared with their equivalent diameter (Deq) bare cylinders. The study found that self-excitation of acoustic resonance occurred at a lower reduced flow velocity for the finned cylinders. During acoustic resonance excitation, finned cylinders with lower p/Dr experienced an abrupt increase in the fluctuating lift force coefficient and acoustic pressure. The decomposition of the fluctuating lift force with respect to the acoustic pressure showed that the earlier onset of resonance and the abrupt increase in the lift force and acoustic pressure were due to the increased susceptibility to flow-induced acoustic resonance. Phase-locked particle image velocimetry (PIV) measurements of the vorticity field supported this finding by showing a well-organized vorticity field in the wake of these finned cylinders. However, the fins and crimps had a significant effect on the distribution of the acoustic particle velocity field compared to the bare cylinder. The presence of the fins and crimps caused the acoustic particle velocity magnitude to be concentrated within the fins and rapidly decline away from the cylinder base. As a result, the acoustic power generated was lower in the case of the finned cylinders. This ultimately resulted in a lower peak acoustic pressure and fluctuating lift force being generated in the case of the crimped spirally finned cylinders.

Impact of GPS radio occultation assimilation on the 18–21 July 2021 heavy rainfall event in Henan

The Gridpoint Statistical Interpolation (GSI) assimilation system and Weather Research & Forecasting (WRF) mesoscale regional model were used to investigate the sensitivity of assimilating Global Positioning System radio occultation (GPS-RO) data for a “21·7” heavy rainfall event in Henan Province. The Ensemble Forecast Sensitivity to Observation (EFSO) algorithm was used to assess the influence of the GPS-RO assimilation relative to conventional heavy rainfall observations in Henan. Sensitivity experiments revealed that the 6-h accumulated precipitation simulated by the three experiments surpassed 200 mm, which was similar to the automated station observations, and the rainfall center location and intensity simulated by the assimilated GPS-RO experiment (EXPR2) were also similar to the observations. Following GPS-RO data assimilation, the upper-level west border continental high pressure was improved, which increased the pressure gradient on the east and west sides of the heavy rainfall, resulting in enhanced dynamic lifting and water vapor flow from the lower level to the whole Henan downpour center. The entire convective convergence rising height increased, which had an optimum influence on the dynamic and thermal conditions of heavy rainfall. The EFSO estimates revealed that most observations improved the model predictions, with the conventional surface pressure and U-wind observations making a positive standardized contribution of approximately 0.05 and 0.075, respectively, but T(Temperature) and Q(Specific humidity) making a negative standardized contribution of approximately −0.025. The GNSS GPS-RO greatly improved the prediction results by decreasing the error by 0.125, and the National Satellite Meteorological Center (NSMC) FY-3D contributed the most to the model.

Plasma Gurney Flap Flight Control at Low Angle of Attack

A flight control concept without movable surfaces using electrofluidic actuators is assessed from low-speed scaled two-dimensional (2-D) rectangular wings up to three-dimensional (3-D) full-scale tapered swept wings at realistic aircraft operating conditions. The plasma Gurney flap concept consists of placing spanwise dielectric barrier discharge (DBD) plasma actuators on both sides of a wing or empennage near the trailing edge, and pointing in opposite directions, to change the flow curvature in this region, thus altering lift. Low-speed wind-tunnel tests and corresponding computational fluid dynamics (CFD) simulations are first carried out for this concept on scaled 2-D rectangular wings. Measured lift moment and flow streamlines are used to validate the simulation (CFD) tool. Simulations with this tool are then performed to assess the effect of wing taper and sweep on the effectiveness of the concept at low speed and to evaluate the concept for full-scale 3-D tapered swept-wing geometries for a single-aisle airliner. The results indicate that the plasma Gurney flap has better performance on tapered and swept wings relative to rectangular wings because of the reduction in the velocity component normal to the plasma actuator. Moreover, the presence of shocks at cruise flight conditions improves the effectiveness of the plasma Gurney flap concept.

Review of Past Gas Production Attempts from Subsurface Gas Hydrate Deposits and Necessity of Long-Term Production Testing

This paper summarizes the conditions, applied techniques, results, and lessons of major field gas production attempts from gas hydrates in the past and the necessity of longer term production testing with the scale of years to fulfill the gap between the currently available information and the knowledge required for commercial development. The temporal and spatial scales of field production test projects employing depressurization have expanded since 2002. The results from the projects have proved the applicability of these techniques in both onshore and offshore conditions. However, many technical and reservoir condition-related issues have emerged in gas production, and the gap between current status and industrial requirements is still large. Sand control, artificial lift, and related flow assurance issues are common technical issues that impact onshore and offshore production testing operations. Different reservoir responses were observed well by well, and discrepancy between model predictions and actual field measurements were seen, although reasonable matches were made for short-term behaviors. Those observations suggest that temporal change of the wellbore and near-wellbore conditions and reservoir heterogeneity that cannot be fully modeled have caused complex short-term responses to the depressurization operations. To ensure the long-term operational stability and reliability of the prediction technologies for production behaviors that are essential for commercialization of gas hydrate resources, gas hydrate production testing with comparable duration with commercial operations are necessary. Due to the locality of geological conditions in gas hydrate reservoirs, numerous gas production tests will be required to understand the factors controlling gas production.

ГЕОДИНАМИЧЕСКАЯ СТРУКТУРА ТЕЧЕНИЙ В ВЕРХНЕЙ И НИЖНЕЙ МАНТИИ И ТЕПЛООБМЕН МЕЖДУ НИМИ

The object of the study is a two-layer geodynamic model of the Earth's mantle, including the upper and lower mantle. The subject of the study is the direction of flow at the top and bottom of the lower mantle. It is determined under the known geodynamic structure in the upper mantle, the known direction of the flow at its roof and in the presence of a lifting flow in the mid-ocean ridge area. The aim of the study is to reveal the character of interaction between the upper and lower mantle large-scale free flowing cells. At the upper-lower mantle boundary, two types of interaction of upper- and lower-mantle flows are possible: either unidirectional flows - cocurrent flow, or oppositely directed - counterflow. Horizontal large-scale currents at the 670 km boundary are a consequence of the horizontal temperature gradient under conditions of free convection. Heat transfer from the flow interface occurs under conditions of free convection, and the intensity of heat transfer at this boundary is determined by the vertical temperature gradient. The analysis of heat transfer in upper-mantle and lower-mantle flows at the 670 km boundary with cocurrent flow and counterflow is presented. The decrease in the average flow temperature for the lower mantle thermal boundary layer near the 670 km boundary with a counterflow at this boundary is estimated. The density and temperature differences in the mantle under the continent and the ocean, providing an excess of the surface level of the continent above the level of the ocean floor, equal to 7 km, are presented. Comparison of the estimated characteristic temperature difference with data on heat flows in the mantle under the ocean and the continent leads to the conclusion that there is a cocurrent flow of upper mantle and lower mantle flows at the 670 km boundary. The influence of the cocurrent flow at the 670 km boundary on the structure of large-scale mantle flows is analyzed. For two different situations of interaction of upper mantle flows under the ocean with the mantle under the continent, large-scale flows in the upper and lower mantle are presented

Lift performance enhancement for flapping airfoils by considering surging motion

The flapping motion has a great impact on the aerodynamic performance of flapping wings. In this paper, a surging motion is added to an airfoil performing pitching-plunging combined motion to figure out how it influences the lift performance and flow pattern of flapping airfoils. Firstly, the numerical methods are validated by a NACA0012 airfoil pitching case and a NACA0012 airfoil plunging case. Then, the E377m airfoil which has typical geometric characteristics of the bird-like airfoil is selected as the calculation model to study how phase differences φ1 between surging motion and plunging motion affect the aerodynamic performance of flapping airfoils. The results show that the airfoil with surging motion has comprehensively better lift performance and thrust performance than the airfoil without surging motion when 15°<φ1 < 90°. It is demonstrated that surging motion has a powerful ability to improve the aerodynamic performance of flapping airfoil by adjusting φ1. Finally, to further explore how flapping airfoil improves lift performance by considering surging motion, the flapping motions of E377m airfoil with the highest lift coefficient and lift efficiency are obtained through trajectory optimization. The surging motion is removed in the highest lift case and highest lift efficiency case respectively, and the mechanism that surging motion adjusts the aerodynamic force is analyzed in detail by comparing the vortex structure and kinematic parameters. The results of this paper help reveal the aerodynamic mechanism of bird flight and guide the design of Flapping wing Micro Air Vehicles (FMAV).

Size effects of vane-type rectangular vortex generators installed on high-lift swept-back wing flap on lift force and flow fields

Size effects of vane-type rectangular vortex generators installed on high-lift swept-back wing flap on lift force and flow fields

Vortex chip incorporating an orthogonal turn for size-based isolation of circulating cells

Size-based label-free separation of rare cells such as CTCs is attractive due to its wider applicability, simpler sample preparation, faster turnaround and better efficiency. Amongst such methods, vortex-trapping based techniques offer high throughput but operate at high flow velocities where the resulting hydrodynamic shear stress is likely to damage cells and compromise their viability for subsequent assays. We present here an orthogonal vortex chip which can carry out size-differentiated trapping at significantly lower (38% of previously reported) velocities. Composed of entry-exit channels that couple orthogonally to a trapping chamber, fluid flow in such configuration results in formation of a vortex which selectively traps larger particles above a critical velocity while smaller particles get ejected with the flow. We call this phenomenon the turn-effect. Critical velocities and optimal architectures for trapping of cells and particles of different sizes are characterized. We explain how shear-gradient lift, centrifugal and Dean flow drag forces contribute to the turn-effect by pushing particles into specific vortex orbits in a size- and velocity-dependent fashion. Selective trapping of human breast cancer cells mixed with whole blood at low concentration is demonstrated. The device shows promising results for gentle isolation of rare cells from blood.

Flow separation control using a bio-inspired nose for NACA 4 and 6 series airfoils

PurposeThis paper aims to achieve an optimum flow separation control over the airfoil using a passive flow control method by introducing a bio-inspired nose near the leading edge of the National Advisory Committee for Aeronautics (NACA) 4 and 6 series airfoil. In addition, to find the optimised leading edge nose design for NACA 4 and 6 series airfoils for flow separation control.Design/methodology/approachDifferent bio-inspired noses that are inspired by the cetacean species have been analysed for different NACA 4 and 6 series airfoils. Bio-inspired nose with different nose length, nose depth and nose circle diameter have been analysed on airfoils with different thicknesses, camber and camber locations to understand the aerodynamic flow properties such as vortex formation, flow separation, aerodynamic efficiency and moment.FindingsThe porpoise nose design that has a leading edge with depth = 2.25% of chord, length = 0.75% of chord and nose diameter = 2% of chord, delays the flow separation and improves the aerodynamic efficiency. Average increments of 5.5% to 6° in the lift values and decrements in parasitic drag (without affecting the pitching moment) for all the NACA 4 and 6 series airfoils were observed irrespective of airfoil geometry such as different thicknesses, camber and camber location.Research limitations/implicationsThe two-dimensional computational analysis is done for different NACA 4 and 6 series airfoils at low subsonic speed.Practical implicationsThis design improves aerodynamic performance and increases the structural strength of the aircraft wing compared to other conventional high lift devices and flow control devices. This universal leading edge flow control device can be adapted to aircraft wings incorporated with any NACA 4 and 6 series airfoil.Social implicationsThe results would be of significant interest in the fields of aircraft design and wind turbine design, lowering the cost of energy and air travel for social benefits.Originality/valueDifferent bio-inspired nose designs that are inspired by the cetacean species have been analysed for NACA 4 and 6 series airfoils and universal optimum nose design (porpoise airfoil) is found for NACA 4 and 6 series airfoils.

The study of hydraulic characteristics of pneumatic lifting pump with air startup and shutdown

Pneumatic lifting pump, as one of the ideal new methods for mining and upgrading, has obvious advantages such as simple structure, safety and reliability. The research of it has important scientific value and engineering significance. Based on Fluent simulation software, using Euler model and SST k-ω turbulence model, with the help of UDF self-programming, the influence of variable air volumes-linear opening, linearly closing on the hydraulic characteristics of the air-water lifting pump is discussed. The results are shown as follows. 1) In the slow linear opening mode of the gas flow, the liquid lifting flow increases, the change trend of it is slower than that of fast linear closing mode. 2) In the slow linear closing mode of the gas flow, the liquid lifting flow reduces, the change trend of it is slower than that of fast linear closing mode. These research results will lay the theoretical foundation for the application of pneumatic lifting technology in river dredging, sewage treatment, oil extraction and other fields.

Computational analysis of NACA 0010 at moderate to high Reynolds number using 2D panel method

Wing structures as found in aircrafts and wind turbine blades are developed using airfoils. Computational methods are often used to predict the aerodynamic characteristics of such airfoils, typically the pressure, lift and drag force coefficients. In the present work, surface pressure coefficient distribution of NACA 0010 is evaluated using the 2D panel and Jukouwski methods for incompressible lifting flows for three Reynolds numbers, Re–3 x105, 5 x105, 1 x 106. The analysis was conducted for various AOA (angle of attack), between –20 to 100 for the airfoil with tripped and untripped conditions. The non–dimensional pressure coefficient along chord direction of airfoil is illustrated for upper and lower surfaces between –20 to 100 angle of attack. The coefficient of lift and drag as well as glide ratio are evaluated for all three Reynolds numbers. The present results from the 2D panel method are validated using the results from Hess and Smith, inverse design methods implemented on conformal mapped symmetric Jukouwski airfoil of 10% thickness to chord at 40 angle of attack.

An Isogeometric Boundary Element Method for 3D lifting flows using T-splines

In this paper an Isogeometric Boundary Element Method for three-dimensional lifting flows based on Morino’s (Morino and Kuo, 1974) formulation is presented. Analysis-suitable T-splines are used for the representation of all boundary surfaces and the unknown perturbation potential is approximated by the same T-spline basis used for the geometry. A novel numerical application of the so-called Kutta condition is introduced that utilises the advantages of isogeometric analysis with regard to the smoothness of the trailing edge curve basis functions. The method shows good agreement with existing experimental results and superior behaviour when compared to a low order panel method. The effect of the tip singularity on Kutta condition is also investigated for different levels of refinement and positions of the trailing edge collocation points.