Heat Exchanger Pressure Research Articles

Booster heat pump with drop-in zeotropic mixtures applied in ultra-low temperature district heating system

The pursuit of sustainable district heating solutions has driven a growing interest in ultra-low temperature district heating (ULTDH) systems, where booster heat pumps (BHPs) play a pivotal role despite challenges posed by their efficiency limitations under large temperature glide conditions. This paper investigates the potential of drop-in R-1234yf/R-32 zeotropic mixtures in BHPs compared to a baseline R-134a system, within the context of a ULTDH framework. This study focused on the viability of the mixtures of R-1234yf/R-32 with the composition ratio of 80 %/20 % and 90 %/10 %. The investigation reveals disparities in compressor efficiency and heat exchanger pressure drop at the component level. Device-level analysis unveils increased COP for R-1234yf/R-32 mixtures, alongside with maximum second-law efficiencies reaching 0.32. A remarkable enhancement in heating capacity up to 58 % was found. System-level analysis demonstrated exergetic efficiencies and identified preferable district heating temperatures. Exergetic efficiencies of 0.47, 0.55, and 0.59 were achieved for domestic hot water preparation at district heating supply temperatures of 30 °C, 35 °C, and 40 °C, with a subsequent shift in optimal district heating temperatures as central heating station efficiency decreased. Temperature profile analysis underscored challenges stemming from excessive subcooling, highlighting the need for configuration refinements.

Design and Analysis of a Cooling System for the REBCO Coil Based on GM/JT Cycle

High‐field magnets have been used in a wide range of scientific and industrial areas. REBCO (REBa2Cu3Ox, where RE = Rare Earth) coated superconductors (CCs) have been gaining increasing interest due to the potentialities of using them in high‐field magnets. However, the thermal stability of the REBCO CCs coils is limited by longitudinal heat conduction inside the coils and bubbles generated by evaporating helium. So as to enhance the heat transfer in REBCO coil, a cooling system based on GM/JT cycle was designed. In this paper, the design, thermodynamic calculation, and analysis of the cooling system for the REBCO coil are provided systematically. It is found that when the mass flow rate is 0.75 g/s at a pressure of 10 bar, the cooling capacity of the system is up to 10.16 W. Meanwhile, the inlet pressure and counterflow heat exchangers efficiency are key factors for significantly improving the cooling capacity of the system. An open loop experiment also has been carried out and the cooling capacity of 0.79 W at 4.5 K is obtained finally when He mass flow rate is 0.1 g/s. © 2024 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

Accelerated Degradation Test on Electric Scroll Compressor Using Controlled Continuous Liquid Slugging

Refrigerant-based electric scroll compressors are known for their reliability, efficiency, and quiet operation. They are often used in heat pump systems due to their ability to efficiently handle varying levels of load conditions, both for heating and cooling modes of operation. As electric compressors are considered the heart of the heat pump system, being able to determine degradation of compressors prior to failure is of paramount importance for the health of this system. Typical failures for electric scroll compressors range from electrical faults, refrigerant leaks, to mechanical failures and overheating. Specifically, one of the primary failure modes for an electric scroll compressor is mechanical damage due to the high stress effects of refrigerant liquid slugging. These stresses are due to excessively high internal pressures exhibited on the compressor scrolls, which are generated by compressing liquid refrigerant at the suction side of the compressor. This paper provides a new testing methodology that introduces liquid slugging at various degrees of refrigerant quality to degrade a compressor to near the end of useful life. Furthermore, this test aims to determine specific operating conditions and signals that can indicate early compressor degradation. This fault injection configuration consists of a modified heat pump system with the addition of two low pressure heat exchangers added in parallel (with respective electronically controlled expansion valve for each heat exchanger) used to control the refrigerant quality during compressor operations. For a given refrigerant quality, the heat pump system was operated at a fixed compressor performance conditions to sustain liquid slugging for a fixed duration. Afterwards, refrigerant was controlled to be pure vapor at the compressor suction side and the compressor was controlled at several different performance conditions (i.e., fixed compressor suction superheat temperature and compressor pressure ratios, at various compressor speeds), so as to duplicate conditions known to us from the compressor component data sheet for an ideal electric scroll compressor. Through these tests, the results show that the severity of scroll failures depend heavily on the refrigerant quality and the amount of liquid slugging exposure time. Furthermore, symptoms of compressor degradation are detected using the following signals: i) temperature and pressure at the compressor suction side, ii) temperature and pressure at the compressor discharge side, and iii) electric compressor speed and power consumption. To further aid in determining the compressor degradation ground truth, complete compressor teardown was performed to identify sections within the compressor that exhibited significant amounts of wear as compared to a stock compressor.

Effect of climate and component performance on optimized recuperated air Brayton cycles for nuclear microreactor power conversion

Thermodynamic analyses were performed to evaluate recuperated open air Brayton cycles for nuclear microreactors operating with a power output of 3 MWe. Specifically, the efficiencies of the recuperated air Brayton cycles were compared under steady-state operating conditions for different climate conditions, reactor types, turbomachinery efficiencies, and recuperator performance. Recuperator minimum approach temperatures of 5, 10, and 15 °C were evaluated using an effectiveness-number of thermal units approach to encompass the expected range of different heat exchanger designs. Optimal compressor pressure ratio and optimum thermal efficiencies are presented for turbine efficiencies of 80%, 85%, and 90%; compressor efficiencies of 70%, 75%, 80%, and 85%; and turbine inlet temperatures of 500 °C, 650 °C and 850 °C corresponding to different reactor types. Effects of climate on the thermal efficiency of the recuperated air Brayton cycles show the largest effect on the recuperated cycle due to the change in ambient temperature, whereas the humidity of the ambient air has a negligibly small effect. An exergy analysis utilizing a high-performing compressor and turbine and a recuperating heat exchanger with a 10 °C minimum approach temperature showed that the compressor, recuperating heat exchanger, and the ambient heat rejection accounted for nearly 72% of the exergy destruction. The effect of pressure drop through the heat exchangers was quantified in terms of compressor pressure ratio and heat exchanger performance.

The impact of using twisted double tube of innovative turbulator on the efficiency of a flat panel solar collector with geometric optimization

BackgroundFluids as water, ethylene glycol, etc. employed to enhance heat transfer, have a lower thermal conductivity (TC) coefficient compared to metals and even metal oxides. This paper presents computational fluid dynamics (CFD) simulation of the twisted double tube heat exchanger (HE) filled with two-phase MWCNT-TiO2/water hybrid nanofluid (Hnf). MethodsThe FLUENT 16 software is employed for numerical simulations of the HE with novel turbulator. The hybrid nanofluid is simulated using the two-phase mixture model and turbulent flow is modeled utilizing Realizable k-ε turbulence model. The Reynolds number (Re) alters from 7000 to 28000, the volume fraction of nanoparticles (φ) varies from 1.0 to 4.0%, and the pitch ratio of the innovative turbulator is 1.0, 2.0, 3.0, and 4.0. Outcomes proved average Nusselt number (Nuave) and pressure drop are strongly influenced by Re and φ. ResultsThe maximum thermal efficiency and HE pressure drop correspond to φ = 4%, Re = 28000, and a pitch ratio of 4. When φ = 4% and Re = 28000, adding turbulator with a pitch ratio of 4 inside the heat exchanger enhances Nuave by 106.92% in comparison with heat exchanger without turbulators. When φ = 4% and Re = 28000, adding turbulator with a pitch ratio of 4 inside the heat exchanger increases the pressure drop by 296.19% compared to HE without turbulators. Finally, exergy efficiency of HE with a turbulator with a pitch ratio of 4 is improved by 21.83% as Re increases from 7000 to 28000 when φ = 4%.

4E assessment of a hybrid RO/MED-TVC desalination plant powered by CPV/T systems

The growing demand for pure water and the challenges of energy transition encourage the use of renewable energies in desalination. This investigation aims to carry out an energy, exergy, economic and environmental analysis of a hybrid RO/MED-TVC desalination powered by CPV/T systems. The electrical and thermal needs of the hybrid desalination unit are supplied by a concentrated photovoltaic solar field. Computational models are elaborated and validated for the CPV/T, RO and MED-TVC units. Three reverse osmosis desalination configurations with two energy recovery strategies are studied: single stage-RO, double stage-RO and three stage-RO. The results showed that the conversion rate increased from 27 to 48 % and from 37 to 62 % and from 49 to 72 % by increasing the feed pressure from 5000 to 8000 kPa for the reverse osmosis units at one, two and three stages, respectively. The exergy destroyed in the whole system was less for Pelton turbine energy recovery than for a pressure heat exchanger. The number of RO membrane modules was minimum for double RO-stage and maximum for triple RO-stage. The results showed that the MED performance improved by 217 % and the specific thermal consumption was reduced by 68.5 % by increasing the number of effects from 4 to 12. The results highlighted that the production of electricity and thermal energy, electricity injected to the grid and the thermal energy storage are high for Sharm-el-Sheikh and low for Tripoli. The levelized costs of water were 0.424, 0.436, 0.448, 0.457, 0.463, 0.466 and 0.468 US$/m3 for Sharm-el-Sheikh, Nouakchott, Benghazi, Tangier, Doha, El Kuwait and Tripoli, respectively. The values of carbon intensity were also 0.67, 0.68, 0.71, 0.78, 0.84, 0.86 and 0.87 kg CO2/m3 for Sharm-el-Sheikh, Nouakchott, Benghazi, Tangier, Doha, El Kuwait and Tripoli, respectively. The overall results demonstrated that the double-stage-RO with energy recovery from the pressure exchanger combined with the ten-effect MED-TVC was the best solution to achieve efficient desalination using the electricity and heat produced by concentrated photovoltaic thermal systems.

Recent Progress on High Temperature and High Pressure Heat Exchangers for Supercritical CO2 Power Generation and Conversion Systems

Heat exchangers for supercritical CO2 power generation and waste heat to power conversion systems have a significant impact on the overall cycle efficiency and system footprint. Key challenges for supercritical CO2 heat exchangers include ability to withstand high temperature and high pressure (typical temperature range of heat source 350 to 800 °C and typical required operating pressure range 150 to 300 bars), and large pressure differential between fluid streams. Other requirements are low pressure drop, high effectiveness and high reliability under thermal cycling. This paper presents recent developments in supercritical CO2 heat exchangers in terms of material selection, design, manufacture, and operation. Since heat exchangers represent a significant portion of the total system cost, another key challenge is to find a compromise between the heat exchanger type, cost, durability, and performance. This paper explores heat exchanger technologies, manufacturing techniques and materials for high temperature and high pressure heat exchangers for supercritical CO2 applications. It also identifies technology gaps and research needs to accelerate the development of effective designs to facilitate the commercialization of both supercritical CO2 heat exchanger technologies and power cycles.

Process safety consequence modeling using artificial neural networks for approximating heat exchanger overpressure severity

One challenge in accounting for process safety incidents is that accurate modeling is complex, time-intensive, and requires many inputs. Process safety consequence modeling using first principles can be complicated. At the same time, setting up experiments is not always practical. This work proposes an artificial neural network (ANN) framework to predict process safety metrics to prevent overpressure during tube rupture scenarios with reasonable accuracy. Specifically, we apply a feed forward neural network to predict heat exchanger safety rating that is proportional to the heat exchanger pressure normalized with respect to the maximum allowable pressure. By training ANN to a set of tube rupture simulation data, we are able to bypasses the need for solving tedious dynamic and non-smooth system of equations. The ANN-based models yield safety rating predictions that comply with API 521 overpressure standards. We further demonstrate how these predictions can be used to perform real-time monitoring for a network of heat exchangers in a plant setting.

Forecasting the output using ANN models and effect of input factors on machinability of Duplex Steel 2205 in dry-turning operation for high strength and anti-corrosive applications

ABSTRACT The products made of advanced materials are the buzz amid material scientists as they possess enhanced mechanical properties, leading to development of material such as Duplex Steel 2205. The material being hard and having high strength, machinability along with stringent environmental regulations is a challenge keeping in view the wide range of applications that the material caters like pressure vessels, marine equipment and heat exchanger. The current experimental investigation of flank wear and surface roughness was predicted through ANN model and experimentally evaluated under dry-turning conditions using carbide-tipped inserts. Dry turning was performed by selecting the speed levels of 103, 134, and 174 m/min; feed rate (FR) levels of 0.12, 0.15, and 0.18 mm/rev; and depth of cut (DOC) levels of 0.5, 1.0, and 1.5 mm. Experiments were designed using Taguchi-L9 model, optimum cutting speed (134 m/min), feed (0.12 mm/rev), and DOC of (1.0 mm) resulted in least Ra values. The regression model created on the experimental data is in 95% conformance for surface roughness and flank wear. Optimal machining parameters indicate that cutting speed have greatest significance on machining trailed by feed and DOC.

Flow maldistribution and heat transfer characteristics in plate and shell heat exchangers

• The pressure drop, flow maldistribution, and heat transfer rate are measured in a plate and shell heat exchanger. • Friction factor and Nusselt number correlations are provided for water and oil flows. • The plate side showed a better thermal performance than the shell side but a higher friction factor. • Flow maldistribution was more severe on the shell side than on the plate side. • The effectiveness deterioration due to the flow maldistribution was less than 4%. • An analytical comparison indicates that PHEs have a better thermo-hydraulic performance than the PSHE studied. The plate and shell heat exchanger (PSHE) was developed to overcome the traditional gasketed plate heat exchangers (PHE) operation limits. Its constructive characteristics allow higher-pressure and thermal applications, suitable for processes found in power plants and the oil and gas industry. However, studies on the PSHE thermo-hydraulic performance are still scarce. This study presents an experimental and theoretical analysis of the flow and heat transfer characteristics of a PSHE. A test rig operates with water and viscous oil to produce turbulent and laminar flow regimes, typical of the oil and gas industry. The heat transfer rate, pressure drop, and flow distribution are measured. The m 2 -model, developed to predict flow maldistribution on the PHE, is suitable for the plate side of the PSHE. An analytical model is used to correct the effects of maldistribution on the overall heat transfer coefficient and provide Nusselt number correlations. Experiments show that the flow maldistribution increases the heat exchanger pressure drop and deteriorates the heat transfer performance. The maximum and average channel flow rate ratio reaches 2.30 on the shell side and 1.75 on the plate side. Friction factor correlations are created based on the channel pressure drop data. The shell side has an inferior overall performance than the plate side, with a higher maldistribution and a lower Nusselt number. The PSHE effectiveness deterioration due to the maldistribution is 4% in the worst scenario within the experimental range. Results indicate that the PHE thermo-hydraulic performance is superior to the PSHE. Nevertheless, the structural advantages of the PSHE make it appropriate for applications involving high pressures and elevated temperatures.

Vertical ground heat exchanger pressure loss – Experimental comparisons and calculation procedures

Vertical ground heat exchangers (GHEs) used with ground source heat pump systems have been constructed in a variety of configurations including single U-tubes, double U-tubes, quadruple U-tubes, and coaxial-type. Selections of vertical GHE other than single U-tubes are often motivated by a desire to decrease the borehole thermal resistance and therefore reduce the required amount of drilling and/or improve the thermal performance of the system. As with conventional heat exchanger design, the hydraulic performance – i.e. how much pressure loss is incurred – is also very important to the overall system performance. Yet, relatively little attention has been paid to this aspect of the design.In this paper, we present experimental measurements of pressure loss versus flow for four types of vertical GHE in a 200 m deep borehole: a single U-tube, double U-tubes connected in parallel, and in series, a coaxial heat exchanger, and a single U-tube with internal heat transfer enhancing ridges. Procedures for calculating the pressure loss in these configurations are tested. While standard procedures are adequate for the smooth U-tubes, the internally-ridged U-tube required a new correlation. For the coaxial heat exchanger, seemingly minor fittings that intruded into the annulus were shown to be important for calculating the pressure loss. Finally, the effects of using fiber optic cable assemblies inserted into the pipe are investigated and correlations for the excess pressure loss are given.

HARD MACHINING OF P235GH STEEL WITH DIFFERENT PARAMETERS USING GSRS MODELLING

The high-strength and heat-resistant P235GH steel finds wide applications in pressure vessels and heat exchangers. It is a difficult-to-handle material, which reduces the life of the tool during machining, hence spoiling the finish of machined surface. Cutting fluids can improve the life of tools and surface finish. The current investigation observes the effect of machining parameters (revolution and feed rate) and different cutting environments (SAE-40 oil with 5 % boric acid, soybean oil and nanofluid) on the surface finish and flank wear in hard turning of P235GH steel. Machining trials are designed using an L18 orthogonal array with replications. A hybrid approach of grey system based response surface (GSRS) modelling is employed to study the effects of various parameters and their interactions. The chip morphology and flank wear are analysed using scanning electron microscopic images and the predicted optimal machining condition for a better surface finish and reduced tool wear is also validated.

Performance prediction through experiments of recuperator to be installed in turboshaft engine for unmanned aerial vehicle

Abstract It is developing an engine for an unmanned aerial vehicle that performs missions without a person in the turboshaft method. This engine is equipped with a recuperator to drive the engine with higher efficiency, which can extend the distance for performing a given aircraft’s mission. This study evaluates the various performances (heat exchange efficiency and pressure loss) of a recuperator developed for the purpose of installing it on the 100-horsepower engine and conducts the tests in various engine driving environments. These results can more accurately predict the performance of the engine to be developed and can serve as an opportunity to further increase engine efficiency.

Experimental Investigation of TIG Welding Parameters and Weld Joint Strength for Carbon Steel - SA516GR70 Material based on Taguchi Method

This study focuses on experimental study of mechanical characterisation for the carbon steel material SA516GR70, steel alloy welds through tungsten inert gas (TIG) welding process used for the applications of pressure vessel and heat exchanger. Current work describes the preparation of test coupons which is used for sample preparation of tensile, bending and hardness test. Welding process parameters optimization is carried out using Taguchi method for the carbon steel weld material to improve the properties. Using the orthogonal array, experiments are setup and weld joint obtained is used for mechanical testing. Graphs are obtained from the full factorial design using the Mini tab software which is helpful in studying the effects of the parameters on properties. Interpretation of the statistic for various parameters is analysed and the coefficients are determined. Main effects plot, interaction plot and residual plots are plotted which reveal that model fits the data with the average acceptance level of 91.85%.

Experimental Characterization of Additively Manufactured Metallic Heat Exchangers

In this study, three manifold-microchannel heat exchangers were additively manufactured by direct metal laser sintering. The heat exchangers were manufactured from stainless steel (SS17-4) with an overall dimension of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$64.2\times 46.0\times27.1$ </tex-math></inline-formula> mm. The thermal and hydrodynamic performance of the heat exchangers was experimentally evaluated at different air and water flow rates. The microchannel fins had a thickness of 0.48 mm which featured the smallest length scale used in these heat exchangers. While the overall dimensions of the heat exchangers were identical, their interior designs were slightly different. Heat exchanger A was based on the original manifold-microchannel heat exchanger design concept while heat exchangers B and C had pin fins on their air manifolds. Heat exchangers B and C were different in their microchannel orientations as the microchannels in heat exchanger C were along the streamwise direction of the air inlet manifolds. Despite the interior design modifications between the three heat exchangers, results suggested comparable thermal and hydrodynamic performances. For a water inlet temperature of 60 °C, a normalized rate of heat transfer as high as around 4.76 W/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> was achieved for an air-side Reynolds number of around 4000. The air-side convection heat transfer coefficient was obtained as high as around 800 W/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> K. The range of air-side pressure drop was between around 2000 and 4000 Pa, depending on the airflow rate. Heat exchanger A demonstrated the lowest pressure drop and heat exchangers B and C, which incorporated pin fins on their air manifold, caused higher air-side pressure drops.

HEAT EXCHANGER DESIGN OPTIMISATION

In this paper, an optimized model of Shell and Tube Parallel Flow Heat Exchanger of water and oil type is proposed using C++ programming language. Shell and tube heat exchangers are of special importance in boilers, oil coolers, condensers, pre-heaters etc. They are also used in high pressure operations, refrigeration and air conditioning industry and process applications. In this paper, a number of practical cases of shell and tube heat exchangers are taken and the analysis of thermal and constructional design of every case is done. The optimised design is obtained by minimising the pressure drop by maximising the heat exchanger area to reduce pumping and running cost. Also considering that large sizes lead to increased capital cost, heat exchanger area is also optimised to overcome this problem. Effect of design parameters on pressure drop and heat exchanger area is also explained.

A novel wavy chevron design for plate heat exchangers: experimental and numerical analysis

Plate heat exchangers (PHEs) are widely used in multiple industries and applications ranging from refrigeration to paper, oil and gas, chemical and power industries. In the current study, a novel wavy pattern design is introduced for chevron-type PHEs in order to improve the overall performance of the heat exchanger. The new plate design is manufactured and tested within an experimental test rig. A numerical heat transfer model is also developed to analyze variations of the heat exchanger pressure drop and heat transfer coefficient. Hydraulic and thermal performance of the new plate pattern is investigated using the numerical model and experimental test rig. The effects of the proposed plate pattern on the thermal efficiency and pressure drop of the PHE are compared with those of a conventional plate pattern. Experimental and numerical results confirm that the heat transfer rate is virtually constant in the new designed PHE, while the pressure drop decreases remarkably. Consequently, the performance of the developed wavy chevron pattern is increased by about 10–15% in comparison with conventional chevron patterns.

A novel structure of throttle trap valve for self-adjustment of discharge capacity in high pressure heat exchangers

A novel self-adjusting throttle trap valve (TTV) for use in high pressure heat exchangers was developed based on multiphase flow theory. The discharge capacity of liquid water is self-adjusted by the effective flow area occupied by the water vapor. The effect of the pressure difference (△p), gas nozzle outlet diameter (Φ3), gas nozzle inlet diameter (Φ2), and the distance between throttle and gas nozzle (L) on the self-adjusting capacity was investigated by means of CFD simulation and validation experiments. The self-adjusting capacity of the TTV increases with an increase in △p, Φ3, and with a decrease in L, but is relatively unaffected by Φ2. To evaluate the contribution of different structural parameters to the self-adjusting ability, the dimensionless self-adjusting capacity index (SACI) was constructed, based on the relation between the self-adjusting capacity and the gas flow rate. Using the SACI, it was determined that to optimize the self-adjusting capacity, a lower value of Φ3 should be chosen, while the optimal value for L was approximately 6 mm for this simulation model. This research provides new technology for the development and design of a high-efficiency TTV.

Theoretical investigation on the throttle pressure reducing valve through CFD simulation and validating experiments

The throttle pressure reducing valve has potential for the high pressure heat exchanger with the advantage of simple structure, easy operation and maintenance. We investigated the discharge capacity under different pressure difference between inlet and outlet, the area of inlet and throttle though CFD simulation and validating experiments. A theoretical formula of the discharge capacity was developed through the theoretical analysis and simulated results and was well proved by the experiments. The results revealed that the square of discharge capacity is positively proportional to the pressure difference, and the drag coefficient has a linear relationship with the throttle area and the reciprocal of flange area. This research establishes the theoretical basis for the designing and engineering application of throttle pressure reducing valve.

Performance investigation of a novel hybrid system for simultaneous production of cooling, heating, and electricity

A novel hybrid system (a regenerative gas turbine cycle with a heat exchanger integrated with Kalina and ejector refrigeration cycles) is developed for the simultaneous production of cooling, heating, and electricity. The laws of thermodynamics are applied to investigate the system performance from energetic and exergetic standpoints. A parametric study is presented for studying the effects of some key parameters on four criteria of electrical efficiency (ηelec), thermal efficiency (ηth), primary energy ratio (PER), and exergetic efficiency (ηex). The key parameters include compressor pressure ratio, gas turbine inlet temperature, ammonia mass fraction in basic ammonia/water mixture, vapor generator pressure, the pinch-point temperature difference of the heat exchanger (which connects Kalina and ejector sub-cycles), and evaporator temperature. Results of the modeling procedure at the base conditions areηelec = 37.87%, ηth=36.55%, PER=74.42% andηex = 38.85%; also, the produced cooling, heating, and power are 164.7 kW, 836.85 kW, and 1038 kW, respectively. The combustion chamber and evaporator has also the highest and lowest contribution in total exergy destruction (with exergy destruction rates of 939.2 kW and 0.034 kW), respectively. The parametric study shows that compressor pressure ratio and heat exchanger pinch-point temperature difference have the highest and lowest impacts on the performance criteria, respectively.