Wanxu Yang , Ruichuan Li , Jikang Xu , Guangchun Xiao , Wentao Yuan , Yuhang Sun , Qingguang Zhang
{"title":"CFD-based axial steady-state hydrodynamic study and structural optimization of miniature switching valve","authors":"Wanxu Yang , Ruichuan Li , Jikang Xu , Guangchun Xiao , Wentao Yuan , Yuhang Sun , Qingguang Zhang","doi":"10.1016/j.flowmeasinst.2024.102744","DOIUrl":"10.1016/j.flowmeasinst.2024.102744","url":null,"abstract":"<div><div>Miniature switching valve internal flow pattern is relatively complex, in the working process of the hydraulic valve cavity often produces low-pressure areas, and eddy currents, as well as leads to spool deformation and displacement of the hydrodynamic force and other phenomena. This affects the stability of the internal flow field of the hydraulic valve, especially when the hydraulic pressure is too large to block the spool movement, inaccurate action is present, or even spool opening and closing failure is jitter out of control. Other phenomena, this paper designs a new type of spool and body combination of miniature switching hydraulic valves, to reduce its axial hydraulic pressure. Firstly, a three-dimensional model of the hydraulic valve with different seat angles was established; secondly, CFD numerical analysis of the model was carried out using FLUENT, and the axial steady state hydrodynamic force was studied by comparing the simulation results. The results show that by simultaneously modifying the geometry of the spool and the valve body, the axial component of the hydrodynamic force can be significantly reduced, thus significantly changing the magnitude of the axial hydrodynamic force of the switching valve, to satisfy the requirement of reducing the driving force required for the work, and to achieve the reduction of power consumption. Finally through the hydraulic valve comprehensive test bench to verify the accuracy of the miniature switching valve, through the research of this paper, can provide a certain reference for the design and research of the switching valve.</div></div>","PeriodicalId":50440,"journal":{"name":"Flow Measurement and Instrumentation","volume":"100 ","pages":"Article 102744"},"PeriodicalIF":2.3,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Flow measurement in a wind tunnel with blockage screens","authors":"Dishant Sharma, Vishnu Namboodiri V, Rahul Goyal","doi":"10.1016/j.flowmeasinst.2024.102741","DOIUrl":"10.1016/j.flowmeasinst.2024.102741","url":null,"abstract":"<div><div>The small and medium-scale wind turbine development have been improved due to their adaptability in offshore and onshore localities for wind farm applications. Blockage effects caused by numerous impediments restrict the flow-field near the turbine and impact the turbine's performance. The testing and optimization of turbines in such conditions at laboratory-level are challenging due to the unavailability of customized wind tunnel configurations with blockage screens. The present work focuses on the design, development and evaluating aerodynamic performance of wind tunnel with and without blockage screens. A comprehensive design is established by evaluating losses in each section, uncertainties, velocity, forces, and turbulence intensity in the wind tunnel through the experimental analysis. The novel blockage screens are arranged to maintain 5 % and 10 % blockage percentage for wind velocity range of 2–14 m/s. The maximum velocity reduction with 5 % blockage is 41.40 % and this drop reaches to 67.84 % for 10 % blockage. Consequently, available wind power is seen to undergo a maximum reduction of 79.88 % and 96.67 %, respectively.</div></div>","PeriodicalId":50440,"journal":{"name":"Flow Measurement and Instrumentation","volume":"100 ","pages":"Article 102741"},"PeriodicalIF":2.3,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The proposal and calculation method of the annular domain weight function for the electromagnetic flowmeter under annular conductivity distribution","authors":"Yang Yang , Biaohu Yang , Chao Zhang , Bin Yang","doi":"10.1016/j.flowmeasinst.2024.102738","DOIUrl":"10.1016/j.flowmeasinst.2024.102738","url":null,"abstract":"<div><div>Researching on the characteristic of weight function distribution under non-uniform conductivity distribution is of significant importance for expanding the engineering applications of electromagnetic flowmeter. In this paper, the characteristic of weight function distribution is firstly explored for annular conductivity distribution where the center and outer ring are both conductive. The research results indicate an important finding that the average value of the weight function within any small annular domain of the center or outer ring remains constant as the radial position changes. Therefore, the concept of ‘annular domain weight function’ is then innovatively proposed. Furthermore, the relationship is studied between the ratio of the annular domain weight function of the center and outer ring and the annular feature parameters. Ultimately, the correlations are obtained for calculating the annular domain weight functions of the center and outer ring.</div></div>","PeriodicalId":50440,"journal":{"name":"Flow Measurement and Instrumentation","volume":"100 ","pages":"Article 102738"},"PeriodicalIF":2.3,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Research on ultra-clean micro gas flow calibration technology of passive piston type with sealing","authors":"Hongming Yang, Ya Xu, Tong Liu, Tiejun Liu, Zhenwei Huang, Dailiang Xie","doi":"10.1016/j.flowmeasinst.2024.102735","DOIUrl":"10.1016/j.flowmeasinst.2024.102735","url":null,"abstract":"<div><div>Aiming at the portable measurement and calibration needs of ultra-clean micro gas flow meters in the semiconductor industry, this paper designs an ultra-clean micro gas flow standard device based on passive piston type with sealing. The device adopts a horizontal structure, using the O-ring on the piston for radial sealing, unlike the traditional mercury and gap sealing, this design avoids the stringent requirements for piston speed and clearance. To increase automation of the calibration process, an automatic calibration system is built. Mathematical modeling and 6DOF dynamic mesh analysis are used to ensure that the piston operates at a stable stage. Through the uncertainty analysis, the extended uncertainty of the device reaches 0.21 % (<em>k</em> = 2). The uncertainty was verified by normalizing the deviation <em>E</em><sub>n</sub> and the results show that it is feasible to trace the clean gas flow rate with the piston standard device.</div></div>","PeriodicalId":50440,"journal":{"name":"Flow Measurement and Instrumentation","volume":"100 ","pages":"Article 102735"},"PeriodicalIF":2.3,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wei Pu , Leilei Ji , Wei Li , Weidong Shi , Yang Yang , Haoming Li , Xing Zhang
{"title":"Experimental study of solid-liquid two-phase flow field in a centrifugal pump volute under multiple working conditions","authors":"Wei Pu , Leilei Ji , Wei Li , Weidong Shi , Yang Yang , Haoming Li , Xing Zhang","doi":"10.1016/j.flowmeasinst.2024.102739","DOIUrl":"10.1016/j.flowmeasinst.2024.102739","url":null,"abstract":"<div><div>In order to study the variation law of the solid-liquid two-phase flow field in the volute of centrifugal pump and the distribution law of the solid particles in the volute, based on PIV technology, the dynamic and static interference flow field of the volute under different flow conditions (30 m<sup>3</sup>/h, 40 m<sup>3</sup>/h, 50 m<sup>3</sup>/h, 60 m<sup>3</sup>/h, 70 m<sup>3</sup>/h) and different solid phase volume fractions (1 %, 1.5 %, 2 %) is studied. It is found that with the increase of the solid phase volume fraction, the head and efficiency of the centrifugal pump gradually decrease, and the addition of the solid phase has little effect on the pump head when the solid phase volume fraction is small under the condition of the large flow. The high turbulent kinetic energy area in the volute is mainly concentrated near the outer wall of the volute and the area where the tongue is located. Under the same solid phase volume fraction, the turbulent kinetic energy in the volute increases with the increase of the flow rate. The turbulent kinetic energy in the volute decreases with the increase of the solid phase volume fraction. The absolute velocity component of the flow field in the volute is significantly affected by the flow condition.</div></div>","PeriodicalId":50440,"journal":{"name":"Flow Measurement and Instrumentation","volume":"100 ","pages":"Article 102739"},"PeriodicalIF":2.3,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Weiming Tian , Haytham F. Isleem , Abdelrahman Kamal Hamed , Mohamed Kamel Elshaarawy
{"title":"Enhancing discharge prediction over Type-A piano key weirs: An innovative machine learning approach","authors":"Weiming Tian , Haytham F. Isleem , Abdelrahman Kamal Hamed , Mohamed Kamel Elshaarawy","doi":"10.1016/j.flowmeasinst.2024.102732","DOIUrl":"10.1016/j.flowmeasinst.2024.102732","url":null,"abstract":"<div><div>Piano key weirs (PKWs) are an increasingly popular hydraulic structure due to their higher discharge capacity than linear weirs. Accurately predicting the discharge of PKWs is essential for appropriate design and operation. This study utilized eight Machine Learning algorithms, including non-ensemble and ensemble models to predict the discharge of type-A PKWs. Multiple-Linear-Regression (MLR), Support-Vector-Machine (SVM), Gene-Expression-Programming (GEP), and Artificial-Neural-Network (ANN) were adopted as non-ensemble models. While the ensemble models comprised Random-Forest (RF), Adaptive-Boosting (AdaBoost), Extreme-Gradient-Boosting (XGBoost), and Categorical-Boosting (CatBoost). A total of 476 experimental datasets were collected from previous research considering three critical dimensionless input parameters: PKW key widths, PKW height, and total upstream head. The models were trained on 70 % of the dataset and tested on the remaining 30 %. The hyperparameters of the models were optimized using the Bayesian Optimization technique, with 5-fold cross-validation ensuring high performance. Comprehensive analyses, including visual and quantitative methods, were employed to validate model effectiveness. CatBoost model consistently outperformed the other models, achieving the highest Determination-coefficient (R<sup>2</sup> = 0.998) and lowest Root-Mean-Squared-Error (RMSE = 0.002), highlighting its ability to handle complex data patterns and its superior optimization process. XGBoost follows closely behind, showing strong generalization, while ANN and RF perform well, but it's a slight increase in error metrics. The study also incorporated Shapley-Additive-exPlanations (SHAP) and Partial-Dependence-Plot (PDP) analyses, revealing that the total upstream head variable had the most significant impact on the discharge predictions. An interactive Graphical-User-Interface was developed to facilitate practical applications, enabling engineers to predict discharge quickly and economically.</div></div>","PeriodicalId":50440,"journal":{"name":"Flow Measurement and Instrumentation","volume":"100 ","pages":"Article 102732"},"PeriodicalIF":2.3,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abdulilah Mohammad Mayet , Evgeniya Ilyinichna Gorelkina , Muneer Parayangat , John William Grimaldo Guerrero , M. Ramkumar Raja , Mohammed Abdul Muqeet , Salman Arafath Mohammed
{"title":"Enhancing accuracy in X-ray radiation-based multiphase flow meters: Integration of grey wolf optimization and MLP neural networks","authors":"Abdulilah Mohammad Mayet , Evgeniya Ilyinichna Gorelkina , Muneer Parayangat , John William Grimaldo Guerrero , M. Ramkumar Raja , Mohammed Abdul Muqeet , Salman Arafath Mohammed","doi":"10.1016/j.flowmeasinst.2024.102734","DOIUrl":"10.1016/j.flowmeasinst.2024.102734","url":null,"abstract":"<div><div>This research investigates the development of an advanced predictive model aimed at accurately determining the volumetric percentages of water, oil, and gas within oil pipeline systems. Utilizing an innovative approach that incorporates an X-ray source alongside two sodium iodide detectors, the study leverages the Monte Carlo N-Particle (MCNP) simulation code to model the behavior of three-phase fluids under varied conditions. The model meticulously simulates various volumetric configurations of water, oil, and gas, resulting in a comprehensive dataset that provides key spectral information. The initial phase involved the extraction of ten temporal and frequency-related features from each detector, culminating in a pool of twenty features. The analytical process then applied the Grey Wolf Optimization (GWO) algorithm to select the most indicative features for predictive modeling. Out of the initial set, seven features—short-time energy, frequency deviation, relative spectral density, spectral margin, main peak position, spectral coefficient, and frequency intensity—were identified as critical for enhancing model accuracy. These features were subsequently fed into a meticulously structured multilayer perceptron (MLP) neural network. This network, designed with two hidden layers containing 20 and 10 neurons, respectively, demonstrated exceptional capability, achieving a root mean square error (RMSE) of less than 0.06 in the prediction of oil and gas volumetric percentages. The study emphasizes the significant impact of integrating refined feature selection techniques and robust neural network architectures on the precision and reliability of volumetric predictions in multiphase flow systems within oil pipelines. This approach not only enhances predictive accuracy but also contributes to more efficient resource management and operational planning in the oil and gas industry.</div></div>","PeriodicalId":50440,"journal":{"name":"Flow Measurement and Instrumentation","volume":"100 ","pages":"Article 102734"},"PeriodicalIF":2.3,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Three-phase flow measurement by dual-energy gamma ray technique and static-equivalent multi-phase flow simulator","authors":"Mohsen Sharifzadeh, Mojtaba Askari","doi":"10.1016/j.flowmeasinst.2024.102736","DOIUrl":"10.1016/j.flowmeasinst.2024.102736","url":null,"abstract":"<div><div>There is a strong desire to use three-phase flowmeters in upstream operations because of their small size, portability, and cost-effectiveness. Traditional three-phase flowmeterstypically employ two main strategies: fully separating the flow into liquid and gas streams and measuring them using common two- and single-phase meters, or simplifying the direct measurement requirements by homogenization.</div><div>In order to achieve accurate measurements with these meters, it is necessary to first create a suitable simulator for generating various multiphase flow regimes with minimal systematic error. Developing such a simulator on a laboratory scale, rather than using expensive test loops is a crucial and practical option.</div><div>In this research, SEMPF as a Static-Equivalent Multi-Phase Flow with flexibility in creating different multi-phase flow regimes is introduced. In the following, the mechanism of action is validated for both homogenous two- and three-phase mixtures by using dual-energy gamma ray attenuation technique in the Monte Carlo simulator environment. Finally, the three-phase component fraction measurement accuracy by dual-energy gamma meter in three different modes of gasoil-, water-, and air-continuous mixtures were investigated. The experimental results show the maximum accuracy of 2.03 %, 7.23 %, and 5.09 % for gasoil phase measurement in three different conditions that the carrier phase is air, gasoil and water respectively.</div></div>","PeriodicalId":50440,"journal":{"name":"Flow Measurement and Instrumentation","volume":"100 ","pages":"Article 102736"},"PeriodicalIF":2.3,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ehsan Ardekani, Foad Farhani, Mohammad Ali Ardekani
{"title":"Determination of flow angle from measurements of vortex shedding frequency downstream of a triangular bluff model using a single-sensor hot-wire probe","authors":"Ehsan Ardekani, Foad Farhani, Mohammad Ali Ardekani","doi":"10.1016/j.flowmeasinst.2024.102731","DOIUrl":"10.1016/j.flowmeasinst.2024.102731","url":null,"abstract":"<div><div>Experimental aerodynamic studies often require precise measurements of flow angles. However, the conventional multi-hole probe is unsuitable for measuring small flow angles or for use under low-velocity conditions. To overcome these limitations, a new method has been proposed based on measuring the frequency of vortex shedding downstream of a non-polar symmetric body. This technique utilizes a single-sensor hot-wire probe to measure the frequency of the vortex shedding from an equilateral triangular model at different flow angles (<span><math><mrow><mi>α</mi><mo>)</mo></mrow></math></span> by rotating the model using a rotating mechanism. Subsequently, the Strouhal number (St) is determined for each flow angle from the measured vortex shedding frequencies. An empirical correlation is then obtained between the Strouhal number and the flow angle of the form <span><math><mrow><mi>α</mi><mo>=</mo><msup><mi>f</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mrow><mo>(</mo><mrow><mi>S</mi><mi>t</mi></mrow><mo>)</mo></mrow></mrow></math></span>, considering the condition where the Strouhal number is solely a function of the flow angle. The range of flow angles for which the proposed method is applicable, along with acceptable repeatability of the vortex shedding frequency and suitable Strouhal number sensitivity to the variations in the flow angle, was determined. An empirical correlation <span><math><mrow><mi>α</mi><mo>=</mo><mo>−</mo><mn>4153.4</mn><msup><mrow><mi>S</mi><mi>t</mi></mrow><mn>2</mn></msup><mo>−</mo><mn>1819.9</mn><mi>S</mi><mi>t</mi><mo>+</mo><mn>189.51</mn></mrow></math></span> was established, which can be used to determine flow angles in the range of ±10° with an accuracy of 1°. For this purpose, the triangular model is fixed at an angle of 33° to the principal coordinates. The probe is positioned downstream of the model in the defined range: <span><math><mrow><mn>3</mn><mo>≤</mo><mi>x</mi><mo>/</mo><mi>a</mi><mo><</mo><mn>25</mn></mrow></math></span>, <span><math><mrow><mn>4.5</mn><mo>≤</mo><mi>y</mi><mo>/</mo><mi>a</mi><mo>≤</mo><mn>5.1</mn></mrow></math></span>, where <span><math><mrow><mi>a</mi></mrow></math></span> is the side of the equilateral triangular model, and <span><math><mrow><mi>x</mi></mrow></math></span> and <span><math><mrow><mi>y</mi></mrow></math></span> are probe distances in the flow and perpendicular to the flow direction.</div></div>","PeriodicalId":50440,"journal":{"name":"Flow Measurement and Instrumentation","volume":"100 ","pages":"Article 102731"},"PeriodicalIF":2.3,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A binary gas concentration and flow rate measurement system based on scandium-doped aluminum nitride piezoelectric micromachined ultrasonic transducers","authors":"Hanzhe Liu , Yuzhe Lin , Guoqiang Wu , Jifang Tao","doi":"10.1016/j.flowmeasinst.2024.102724","DOIUrl":"10.1016/j.flowmeasinst.2024.102724","url":null,"abstract":"<div><div>This paper presents an ultrasonic binary gas concentration and flow rate measurement system (UBCFS) based on a scandium-doped aluminum nitride (Sc<span><math><mrow><mn>0</mn><mo>.</mo><mn>2</mn></mrow></math></span>Al<span><math><mrow><mn>0</mn><mo>.</mo><mn>8</mn></mrow></math></span>N) piezoelectric micromachined ultrasonic transducer (PMUT) array, enabling the simultaneous measurement of binary gas concentration and flow rate. The ultrasonic propagation time method is employed to determine binary gas concentration and flow rate. To assess the feasibility of the proposed UBCFS, it is integrated into an experimental setup composed of nitrogen (N<sub>2</sub>) and argon (Ar) gas paths. Results indicate that the reported UBCFS measures both gas concentration and flow rate with high accuracy and repeatability. For binary gas flow rate measurements, the mean error and repeatability error are below 0.403% and 0.667%, respectively, across all binary gas concentrations. Within the concentration range of 0% to 100%, the minimum mean error and repeatability error for concentration measurements are 0.03% and 0.04%, respectively, which is almost unaffected by gas flow rate. The performance of the proposed UBCFS based on PMUT arrays surpasses that of most reported or commercialized devices. The compact, cost-effective, and highly reliable UBCFS provides a feasible solution for portable equipment utilized in binary gas detection and control in semiconductor processing.</div></div>","PeriodicalId":50440,"journal":{"name":"Flow Measurement and Instrumentation","volume":"100 ","pages":"Article 102724"},"PeriodicalIF":2.3,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}