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CFD Modeling and Optimization of Primary sedimentation tankZhang, Aibin January 2017 (has links)
In this project, the flow field characteristics of the simplified 2D rectangular primary sedimentation tank in Syvab wastewater treatment plant were achieved by a transient water-air two phases finite-volume method, applying Volume-Of-Fluid (VOF) model. RNG k-ε turbulence model was also employed to calculate the turbulent kinetic energy and its dissipation rate. The undesired hydraulic phenomenon for solid sedimentation was detected in original tank. To reduce the velocity and turbulence intensity of the influent, two categories of optimization methods were proposed, which are installing the baffle and changing the velocity inlet. The modifying effects of different methods were compared by the velocity profiles and the contours of kinetic energy. It turns out that both ways provide a preferred condition for particle settling. In the end, further research was forecasted and the work direction were given. / I detta projekt uppnåddes 2D modellering av avloppsflödesfältets karaktär hos en förenklade och rektangulär primära sedimenteringsbassäng, Syvab avloppsreningsverk, genom en transient-tvåfas-finita-volymmetoden med vatten och luft, som tillämpades med Volume-Of-Fluid (VOF) modellen. RNG k-ε turbulensmodellen användes även för att beräkna den kinetiska energin av turbulas och dess dissipationshastighet. Detta för att oönskade hydrauliska fenomen har uppmärksammats hos sedimenteringsbassängen hos avloppsreningsverket. För att minska flödeshastigheten och turbulens föreslås två optimeringsmetoder, vilket är att installera skärm och att ändra inloppets hastighet. Eeffekterna av de olika metoderna jämförs med hjälp av hastighets- och kinetisk energiprofiler. Det visar sig att båda metoderna kan ge gynsammare tillstånd för sedimentering av partikelar. Som avslutning ges prognos för den fortsatta forskningen och arbetsriktningen inom ämnet.
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Modelling of sediment transport and bed deformation in rivers.Jing, H., Li, C., Guo, Yakun, Zhang, L., Zhu, L., Li, Y. 05 1900 (has links)
yes / A two dimensional (2D) RNG k-ε sediment model including the effects of secondary currents is developed to simulate sediment transport and bed deformation in rivers with continuous bends. Nonuniform suspended and bedload sediment transports and variation of effective bed material size distribution are included in the model. A semi-coupled scheme for sediment model is proposed, which can be used for simulating both the long- and short-term sediment transport whenever riverbed changes. The model is applied to simulate the flow and sediment transport in the Shapotou reservoir in the upper reach of the Yellow River which is a typical natural river reach with continuous bends. River bed deformations caused by suspended and bedload sediment transport are investigated. Good agreement between the numerically simulated results and the field measurements is obtained, indicating that the model is capable of simulating the sediment transport and predicting the bed deformation of rivers having continuous bends with reasonable accuracy. / the Major Research Plan Project, National Natural Science Foundation of China(Grant No.: 91230111 and 51279071); National Key BasicResearch Development Program of China (973 Program, Grant No.: 2010CB429002);Project of Science and Technology of Colleges in Ningxia, China (Grant No.:NGY2012097)
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Desenvolvimento de esquema upwind para equações de conservação e implementação de modelagens URANS com aplicação em escoamentos incompressíveis / Development of a new upwind scheme for conservationlaws and implementation on URANS modelling with application on incompressible flowsCandezano, Miguel Antonio Caro 10 December 2012 (has links)
Nesta tese é apresentado um esquema novo de alta resolução upwind (denominado TDPUS-C3) para reconstrução de fluxos numéricos para leis de conservação não lineares e problemas relacionados em DFC. O esquema é baseado nos critérios de estabilidade CBC e TVD e desenvolvido utilizando condições de diferenciabilidade \'C POT. 3\'. Além disso, é realiozada a implementação da associação do esquema TDPLUS-C3 com a modelagem de turbulência RNG \'\\kappa - \\epsilon\'. O propósito é obter soluções numéricas de sistemas hiperbólicos de leis de conservação para dinâmica dos gases e equações de Navier-Stokes para escoamento incompreensível de fluidos newtonianos e não newtonianos (viscoelásticos). Fazendo o uso do esquema TDPUS-C3, a precisão global dos métodos numéricos é verificada acessando o erro em problemas teste (benchmark) 1D e 2D. Um estudo comparativo entre os resultados do esquema TDPUS-C3 e os esquemas upwind convencionais para leis de conservação hiperbólicas complexas é também realizado. A Associação das modelagens numéricas (upwinding mais RNG \'\\kappa - \\epsilon\') é , então, examinada na simulação de escoamentos turbulentos de fluidos newtonianos envolvendo superfícies livres móveis, usando a metodologia URANS. No geral, em termos do comportamento global, concordância satisfatória é observada / In this thesis, a new high-resolution upwind scheme (named TDPUS-C3) for reconstruction of numerical fluxes for nonlinear conservation laws and related CFD problems in presented. The scheme is based on CBC and TVD stability criteria and developed by employing differentiability condictions (\'C POT. 3\'). In additon, the implementation of an association of the TDPUS-C3 scheme with the RNG \'\\kappa - \\epsilon\' turbulence modelling is also performed. The purpose is to obtain numerical solutions of systems of hyperbolic conservation laws for gas dynamics and Navier-Stokes equations for incompressible flow of Newtonian and non-Newtonian (viscoelstic) fluids. By using the TDPUS-C3 scheme, the global accuracy of the numerical methods is verified by assessing the error on 1D and 2D benchmark test cases. A comparative study between the TDPUS-C3 scheme and convectional upwind schemes to solve standard and complex hyperbolic conservation laws is also accomplished. The association of the numerical modelling (upwinding plus RNG \'\\kappa - epsilon\') is then examined in the simulation of turbulent Newtonian fluid flows involving moving free surfaces, by using URANS methodology. Overall, satisfactory agreement is found in terms of the overall behaviour
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Desenvolvimento de esquema upwind para equações de conservação e implementação de modelagens URANS com aplicação em escoamentos incompressíveis / Development of a new upwind scheme for conservationlaws and implementation on URANS modelling with application on incompressible flowsMiguel Antonio Caro Candezano 10 December 2012 (has links)
Nesta tese é apresentado um esquema novo de alta resolução upwind (denominado TDPUS-C3) para reconstrução de fluxos numéricos para leis de conservação não lineares e problemas relacionados em DFC. O esquema é baseado nos critérios de estabilidade CBC e TVD e desenvolvido utilizando condições de diferenciabilidade \'C POT. 3\'. Além disso, é realiozada a implementação da associação do esquema TDPLUS-C3 com a modelagem de turbulência RNG \'\\kappa - \\epsilon\'. O propósito é obter soluções numéricas de sistemas hiperbólicos de leis de conservação para dinâmica dos gases e equações de Navier-Stokes para escoamento incompreensível de fluidos newtonianos e não newtonianos (viscoelásticos). Fazendo o uso do esquema TDPUS-C3, a precisão global dos métodos numéricos é verificada acessando o erro em problemas teste (benchmark) 1D e 2D. Um estudo comparativo entre os resultados do esquema TDPUS-C3 e os esquemas upwind convencionais para leis de conservação hiperbólicas complexas é também realizado. A Associação das modelagens numéricas (upwinding mais RNG \'\\kappa - \\epsilon\') é , então, examinada na simulação de escoamentos turbulentos de fluidos newtonianos envolvendo superfícies livres móveis, usando a metodologia URANS. No geral, em termos do comportamento global, concordância satisfatória é observada / In this thesis, a new high-resolution upwind scheme (named TDPUS-C3) for reconstruction of numerical fluxes for nonlinear conservation laws and related CFD problems in presented. The scheme is based on CBC and TVD stability criteria and developed by employing differentiability condictions (\'C POT. 3\'). In additon, the implementation of an association of the TDPUS-C3 scheme with the RNG \'\\kappa - \\epsilon\' turbulence modelling is also performed. The purpose is to obtain numerical solutions of systems of hyperbolic conservation laws for gas dynamics and Navier-Stokes equations for incompressible flow of Newtonian and non-Newtonian (viscoelstic) fluids. By using the TDPUS-C3 scheme, the global accuracy of the numerical methods is verified by assessing the error on 1D and 2D benchmark test cases. A comparative study between the TDPUS-C3 scheme and convectional upwind schemes to solve standard and complex hyperbolic conservation laws is also accomplished. The association of the numerical modelling (upwinding plus RNG \'\\kappa - epsilon\') is then examined in the simulation of turbulent Newtonian fluid flows involving moving free surfaces, by using URANS methodology. Overall, satisfactory agreement is found in terms of the overall behaviour
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Structural intrusion, flow disturbance and spillway capacity : CFD modeling of the Torpshammar damWallin, Adéle January 2018 (has links)
At the Torpshammar dam two rectangular beams are situated upstream of the spillway gates to stabilize the sidewalls holding the embankment of the dam. A computational fluid dynamics (CFD) simulation of the dam with the bottom outlets open was made to investigate how the flow and discharge capacity is affected by the beams. The results can be used to avoid unexpected consequences due to turbulence caused by the beams, make the beams strong enough to hold the pressure from the flow and get an estimation of the discharge capacity with the beams. Turbulence is one of the hardest things to simulate so the results were compared with previous simulation work made without the beams and physical model tests to validate the results. Also, a sensitivity analysis was made to investigate the method used. The beams lowered the velocity (to 17 m/s) and the discharge capacity (to 255 m3/s) compared to the previous work. The force on the beams was directed upward and downstream. The beams increased the turbulence and the vortex shedding frequency was higher for the beam closest to the outlet. The velocity and discharge capacity differed with 6 % compared to model test results. The results can therefore only be used as an estimation, a more detailed computational model and more computational cells are needed to get a better result. The sensitivity analysis showed that the velocity and turbulence depend on the method and further studies need to be made to decide which method gives the closest similarity with reality.
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Numerical modeling of flow in continuous bends from Daliushu to Shapotou in Yellow RiverJing, H., Li, C., Guo, Yakun, Zhu, L., Li, Y. January 2014 (has links)
Yes / The upper reach of the Yellow River from Daliushu to Shapotou consists of five bends and has complex topography. A two-dimensional Re-Normalisation Group (RNG) k-ε model was developed to simulate the flow in the reach. In order to take the circulation currents in the bends into account, the momentum equations were improved by adding an additional source term. Comparison of the numerical simulation with field measurements indicates that the improved two-dimensional depth-averaged RNG k-ε model can improve the accuracy of the numerical simulation. A rapid adaptive algorithm was constructed, which can automatically adjust Manning's roughness coefficient in different parts of the study river reach. As a result, not only can the trial computation time be significantly shortened, but the accuracy of the numerical simulation can also be greatly improved. Comparison of the simulated and measured water surface slopes for four typical cases shows that the longitudinal and transverse slopes of the water surface increase with the average velocity upstream. In addition, comparison was made between the positions of the talweg and the main streamline, which coincide for most of the study river reach. However, deviations between the positions of the talweg and the main streamline were found at the junction of two bends, at the position where the river width suddenly decreases or increases. / National Natural Science Foundation of China (Grants No. 11361002 and 91230111), the Natural Science Foundation of Ningxia, China (Grant No. NZ13086), the Project of Beifang University of Nationalities, China (Grant No. 2012XZK05), the Foreign Expert Project of Beifang University of Nationalities, China, and the Visiting Scholar Foundation of State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, China (Grant No. 2013A011).
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Numerical analysis of air-water flows in hydraulic structures using computational fluid dynamics (CFD)Bayón Barrachina, Arnau 15 September 2018 (has links)
Tesis por compendio / The new legal regulations derived from climate change dictate that hydraulic structures must be designed to handle flood events associated with return periods up to 10,000 years. This obviously involves adapting the existing infrastructure to meet such requirements. In order to avoid risks in the restitution of the flow discharged to rivers, such as bank overflows or streambed erosion and scour processes, hydraulic design must be supported by reliable tools capable of reproducing the behavior of hydraulic structures. In the work presented herein, a fully three-dimensional CFD model to reproduce the behavior of different types of air-water flow in hydraulic structures is presented. The flow is assumed to be turbulent, isotropic and incompressible. Several RANS turbulence models are tested and structured rectangular meshes are employed to discretize the analyzed domain. The presence of two fluids is modeled using different VOF approaches and simulations are run using the PIMPLE algorithm. The model is implemented using the open-source platform OpenFOAM and its performance is compared to the commercial code FLOW-3D. The analysis is conducted separately on two different parts of hydraulic structures, namely: the spillway and the stilling basin. Additionally, a case of practical application, where the model reproduces the flow of a real-life case, is also presented in order to prove the suitability of the model to actual design cases. Mesh independence and model validation using experimental data are checked in the results of all the case studies. The sensitivity of the presented model to certain parameters is extensively discussed using different indicator variables. Among these parameters are turbulence closure, discretization scheme, surface tracking approach, CFD code or boundary conditions. Pros and contras of each of them are addressed. The analyzed turbulence models are the Standard k ¿ ¿, the Realizable k ¿ ¿, the RNG k ¿ ¿, and the SST k ¿ ¿. The discretization schemes under study are: a first-order upwind method, the second-order limited Van Leer method, and a second-order limited central difference method. The VOF approaches analyzed are the Partial VOF, as implemented in OpenFOAM, and the TruVOF, as implemented in FLOW-3D. In most cases, the Standard k ¿ ¿ model provides the most accurate estimations of water free surface profiles, although the rest of variables, with few exceptions, are better predicted by the RNG k ¿ ¿. The latter model generally requires slightly longer computation times. The SST k ¿ ¿ reproduces correctly the phenomena under study, although it generally turned out to be less accurate than its k ¿ ¿ counterparts. As regards the comparison among VOF approaches and codes, it is impossible to determine which one performs best. E.g. OpenFOAM, using the Partial VOF, managed to reproduce the in- ternal hydraulic jump structure and all derived variables better than FLOW-3D, using the TruVOF, although the latter seems to capture better the momentum transfer and so all derived variables. In the case of flow in stepped spillways, OpenFOAM captures better the velocity profiles, although FLOW-3D is more accurate when estimating the water free surface profile. It is worth remark- ing that not even their response to certain model parameters is comparable. E.g. FLOW-3D is significantly less sensitive to mesh refinement than OpenFOAM. Given the result accuracy achieved in all cases, the proposed model is fully applicable to more complex design cases, where stilling basins, stepped spillways and hydraulic structures in general must be investigated. / Las nuevas disposiciones legales derivadas del cambio climático dictaminan que las estructuras hidráulicas sean capaces de funcionar correctamente con eventos de inundación asociados a periodos de retorno de hasta 10,000 años. Esto, obviamente, implica adaptar la infraestructura existente para satisfacer dichos requerimientos. A fin de evitar riesgos en la restitución de los caudales vertidos al río, como desbordamientos o procesos erosivos y de socavación, el diseño hidráulico ha de sustentarse en herramientas fiables capaces de reproducir el comportamiento de las estructuras hidráulicas.
En este trabajo, se presenta un modelo numérico CFD completamente tridimensional para reproducir el comportamiento de diferentes tipos de flujo aire-agua en estructuras hidráulicas. Se asume que el flujo es turbulento, isotrópico e incompresible. Diversos modelos de turbulencia RANS son contrastados y se emplean mallas estructuradas rectanuglares para discretizar el dominio analizado. La presencia de dos fluidos es modelada utilizando diferentes enfoques VOF y las simulaciones son ejecutadas empleando el algoritmo PIMPLE. El modelo es implementado mediante la plataforma de código abierto OpenFOAM y su respuesta es comparada con la del modelo comercial FLOW-3D. El análisis se lleva a cabo sobre dos partes diferentes de una estructura hidráulica, a saber, el aliviadero y el cuenco amortiguador, de forma separada. Además, un caso de aplicación práctica, donde el modelo reproduce el flujo en una estructura real, es presentado también a fin de probar la adecuación del modelo a casos de diseño aplicado.
Se comprueban la independencia de la malla y la validación con datos experimentales de los resultados de todos los casos de estudio. La sensibilidad del modelo presentado a ciertos parámetros es analizada de forma exhaustiva empleando diferentes variables indicadoras. Los pros y contras de cada uno de éstos son planteados. Los modelos de turbulencia analizados son el Standard k-epsilon, el Realizable k-epsilon, el RNG k-epsilon y el SST k-omega. Los esquemas de discretización estudiados son: un método de primer orden upwind, uno de Van Leer de segundo orden y un esquema de segundo orden limitado de diferencias centradas. Los enfoques VOF analizados son el Partial VOF, implementado en OpenFOAM, y el TruVOF, implementado en FLOW-3D.
En la mayoría de casos, el modelo k-epsilon aporta las estimaciones más precisas de perfiles de lámina libre de agua, pese a que el resto de variables, con alguna excepción, son mejor predichas por el RNG k-epsilon. Este modelo generalmente requiere mayores tiempos de cálculo. El k-omega reproduce correctamente los fenómenos bajo estudio, pese a que su precisión es generalmente más baja que la de los modelos k-epsilon.
En lo que respecta a la comparación entre enfoques VOF y códigos, es imposible determinar cuál es el mejor. Por ejemplo, OpenFOAM, empleando el Partial VOF, logra reproducir la estructura interna del resalto hidráulico y todas las variables derivadas mejor que FLOW-3D, empleando el TruVOF, a pesar de que este último parece capturar mejor la transferencia de cantidad de movimiento y, por tanto, todas las variables derivadas. En el caso del flujo en aliviaderos escalonados, OpenFOAM captura mejor los perfiles de velocidad, pese a que FLOW-3D es más preciso en la estimación de los perfiles de lámina libre de agua. Conviene recalcar que ni tan sólo su respuesta a ciertos parámetros del modelo es comparable. Por ejemplo, FLOW-3D es significativamente menos sensible al refinado de malla que OpenFOAM.
A la luz de la precisión de los resultados obtenidos en todos los casos, el modelo propuesto es completamente aplicable a casos de diseño más complejos, donde cuencos amortiguadores, aliviaderos escalonados y estructuras hidráulicas en general han de ser investigadas. / Les noves disposicions legals derivades del canvi climàtic dictaminen que cal que les estructures hidràuliques siguen capaces de funcionar correctament amb esdeveniments d'inundació associats a períodes de retorn de fins a 10,000 anys. Això, òbviament, implica adaptar la infraestrctura existent per satisfer aquests requeriments. A fi d'evitar riscs en la restitució dels cabals vessats al riu, com desbordaments o processos erosius i de socavació, el disseny hidràulic ha de recolzar-se en ferramentes fiables capaces de reproduir el comportament de les estructures hidràuliques.
En aquest treball, es prsenta un model numèric CFD completament tridimensional per a reproduir el comportament de diferents tipus de flux aire-aigua en estructures hidràuliques. S'assumeix que el flux és turbulent, isotròpic i incompressible. Diferents models de turbulència RANS són contrastats i s'empren malles estructurades rectangulars per discretitzar el domini analitzat. La presència de dos fluids és modelada utilitzant diferents enfocaments VOF i les simulacions són executades emprant l'algorisme PIMPLE. El model és implementat mitjançant la plataforma de codi obert OpenFOAM i la seua resposta és comparada amb la del codi comercial FLOW-3D. L'anàlisi es du a terme sobre les diferents parts d'una estructura hidràulica, a saber, sobreeixidors esgraonats i vas esmorteïdor, de forma separada. A més, un cas d'aplicació pràctica, on el model reprodueix el flux a una estructura real, és presentat també a fi de provar l'adequació del model a casos de disseny aplicat.
Es comproven la independència de la malla i la validació amb dades experimentals dels resultats de tots els casos d'estudi. La sensibilitat del model presentat a certs paràmetres és analitzada de forma exhaustiva emprant diferents variables indicadores. Els pros i contres de cadascun d'aquests són plantejats. Els models de turbulència analitzats són l'Standard k-epsilon, el Realizable k-epsilon, el RNG k-epsilon i l'SST k-omega. Els esquemes de discretització estudiats són: un mètode de primer ordre upwind, un de Van Leer de segon ordre i un esquema de segon ordre limitat de diferències centrades. Els enfocaments VOF analitzats són el Partial VOF, implementat en OpenFOAM, i el TruVOF, implementat en FLOW-3D.
En la majoria de casos, el model Standard k-epsilon aporta les estimacions més precises de perfils de làmina lliure d'aigua, tot i que la resta de variables, amb alguna excepció, són millor predites pel RNG k-epsilon. Aquest model generalment requereix majors temps de càlcul. El k-omega reprodueix correctament els fenòmens sota estudi, tot i que la seua precisió és generalment més baixa que la dels models k-epsilon.
Pel que fa la comparació entre enfocaments VOF i codis, és impossible determinar quin és el millor. Per exemple, OpenFOAM, emprant el Partial VOF, aconsegueix reproduir l'estructura interna del ressalt hidràulic i totes les variables derivades millor que FLOW-3D, emprant el TruVOF, tot i que aquest últim pareix capturar millor la transferència de quantitat de moviment i, per tant, totes les variables derivades. En el cas del flux en sobreeixidors esgraonats, OpenFOAM captura millor els perfils de velocitat, tot i que FLOW-3D és més precís en estimar els perfils de làmina lliure d'aigua. Cal deixar palès que ni tan sols la seua resposta a certs paràmetres del model és comparable. Per exemple, FLOW-3D és significativament menys sensible al refinament de malla que OpenFOAM.
En base a la precisió dels resultats obtinguts en tots els casos, el model proposat és completament aplicable a casos de disseny més complexos, on vassos esmorteïdors, sobreeixidors esgraonats i estructures hidràuliques en general han de ser investigades. / Bayón Barrachina, A. (2017). Numerical analysis of air-water flows in hydraulic structures using computational fluid dynamics (CFD) [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/90440 / Compendio
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A Ventilation Strategy Based on Confluent Jets : An Experimental and Numerical StudyJanbakhsh, Setareh January 2015 (has links)
This study presents air distribution systems that are based on confluent jets; this system can be of interest for the establishment of indoor environments, to fulfill the goals of indoor climate and energy-efficient usage. The main objective of this study is to provide deeper understanding of the flow field development of a supply device that is designed based on wall confluent jets and to investigate the ventilation performance by experimental and numerical methods. In this study, the supply device can be described as an array of round jets on a flat surface attached to a side wall. Multiple round jets that issue from supply device apertures are combined at a certain distance downstream from the device and behave as a united jet or so-called confluent jets. Multiple round jets that are generated from the supply device move downward and are attached to the wall at the primary region, due to the Coanda effect, and then they become wall confluent jets until the floor wall is reached. A wall jet in a secondary region is formed along the floor after the stagnation region. The characteristics of the flow field and the ventilation performance of conventional wall confluent jets and modified wall confluent jets supply devices are investigated experimentally in an office test room. The study of the modified wall confluent jets is intended to improve the efficiency of the conventional one while maintaining acceptable thermal comfort in an office environment. The results show that the modified wall confluent jets supply device can provide acceptable thermal comfort for the occupant with lower airflow rate compared to the conventional wall confluent jets supply device. Numerical predictions using three turbulence models (renormalization group (RNG k– ε), realizable (Re k– ε), and shear stress transport (SST k– ω) are evaluated by measurement results. The computational box and nozzle plate models are used to model the inlet boundary conditions of the nozzle device. In the isothermal study, the wall confluent jets in the primary region and the wall jet in the secondary region, when predicted by the three turbulence models, are in good agreement with the measurements. The non-isothermal validation studies show that the SST k– ω model is slightly better at predicting the wall confluent jets than the other two models. The SST k– ω model is used to investigate the effects of the nozzle diameter, number of nozzles, nozzle array configuration, and inlet discharge height on the ventilation performance of the proposed wall confluent jets supply device. The nozzle diameter and number of nozzles play important roles in determining the airflow pattern, temperature field, and draught distribution. Increased temperature stratification and less draught distribution are achieved by increasing the nozzle diameter and number of nozzles. The supply device with smaller nozzle diameters and fewer nozzles yields rather uniform temperature distribution due to the dominant effect of mixing. The flow behavior is nearly independent of the inlet discharge height for the studied range. The proposed wall confluent jets supply device is compared with a mixing supply device, impinging supply device and displacement supply device. The results show that the proposed wall confluent jets supply device has the combined behavior of both mixing and stratification principles. The proposed wall confluent jets supply device provides better overall ventilation performance than the mixing and displacement supply devices used in this study. This study covers also another application of confluent jets that is based on impinging technology. The supply device under consideration has an array of round jets on a curve. Multiple jets issue from the supply device aperture, in which the supply device is positioned vertically and the jets are directed against a target wall. The flow behavior and ventilation performance of the impinging confluent jets supply device is studied experimentally in an industrial premise. The results show that the impinging confluent jets supply device maintains acceptable thermal comfort in the occupied zone by creating well-distributed airflow during cold and hot seasons.
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