Aerospace Science and Technology最新文献

{"title":"Investigating the effects of streamwise riblets on flow separation in low-Reynolds-number compressor cascades using direct numerical simulation","authors":"Qiang Liu ,&nbsp;Xiangwen Chen ,&nbsp;Xinsheng Song","doi":"10.1016/j.ast.2026.111800","DOIUrl":"10.1016/j.ast.2026.111800","url":null,"abstract":"<div><div>The capability of streamwise riblets to reduce skin friction in turbulent boundary layers has been well-documented at high Reynolds numbers. Yet, their fundamental mechanisms in controlling separation bubbles in low-<em>Re</em> compressor cascades are still poorly understood. This study employs direct numerical simulation (DNS) based on the Lattice Boltzmann Method (LBM) to investigate how bio-inspired streamwise riblets alter the dynamics of laminar separation bubbles in a compressor cascade at <em>Re</em> = 0.9 × 10⁵. Rectangular riblets, inspired by shark denticle morphology, are arrayed along the suction surface. Results reveal that riblets induce an earlier onset of separation but significantly shorten the laminar separation bubble by 32 % through promoting earlier shear layer reattachment. A key finding in the baseline smooth case is the identification of a novel mechanism for streamwise vortex formation: secondary vortices generate between shedding roll-ups and develop into streamwise vortices via mutual attraction and wrapping. Riblets alter this process by generating strong counter-rotating streamwise vortex pairs within the riblet valleys, enhancing coherence and delay dissipation of shedding vortices. This stabilization is accompanied by a 53 % reduction in spanwise velocity fluctuations and a redistribution of Reynolds stresses. Consequently, total pressure loss is reduced by 4 %, attributed to modulated vortex dynamics rather than classical shear stress suppression. This work establishes a “dual regulatory mechanism”, wherein riblets simultaneously destabilize the shear layer to promote transition and stabilize vortical structures to prolong their coherence, as a new theoretical framework that extends their role beyond passive drag reduction.</div></div>","PeriodicalId":50955,"journal":{"name":"Aerospace Science and Technology","volume":"173 ","pages":"Article 111800"},"PeriodicalIF":5.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global sensitivity analysis of supersonic laminar wing transition considering multi-source random uncertainties","authors":"Yayun Shi ,&nbsp;Xu Tang ,&nbsp;Pengfei Wu ,&nbsp;Tihao Yang ,&nbsp;Kaixuan Feng ,&nbsp;Bo Wang","doi":"10.1016/j.ast.2026.111765","DOIUrl":"10.1016/j.ast.2026.111765","url":null,"abstract":"<div><div>Laminar flow drag reduction is a key technology for enhancing the overall performance of supersonic civil aircraft. Therefore, it is essential to conduct in-depth research on the transition prediction model for supersonic laminar wings and to evaluate the sensitivity of laminar flow maintenance capability to external disturbances. This paper first establishes a transition prediction method that couples the Reynolds-Averaged Navier-Stokes equations with linear stability theory. Subsequently, the accuracy of this transition prediction method is validated through wind tunnel tests on a standard model, and the transition threshold is calibrated. On this basis, a global sensitivity analysis model for transition prediction is constructed by comprehensively considering multiple sources of uncertainty in geometric parameters and the experimental conditions. Furthermore, an adaptive multiple response Gaussian process method is developed to solve this global sensitivity model. By introducing a learning function oriented toward average error reduction, the computational efficiency of the Kriging method is significantly improved. Ultimately, only 26 calls to the computational fluid dynamics solver are required to complete the solution of the global sensitivity model for supersonic laminar wing transition. The results indicate that the transition location is most significantly influenced by the transition threshold, followed by the angle of attack, while the impact of geometric uncertainty is relatively minor.</div></div>","PeriodicalId":50955,"journal":{"name":"Aerospace Science and Technology","volume":"173 ","pages":"Article 111765"},"PeriodicalIF":5.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146047962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Integrated effectiveness-loss evaluation method for comprehensive performance of turbine film cooling","authors":"Chenfeng Wang ,&nbsp;Guoqing Li ,&nbsp;Jialin Liu ,&nbsp;Ruofan Wang ,&nbsp;Xingen Lu","doi":"10.1016/j.ast.2026.111763","DOIUrl":"10.1016/j.ast.2026.111763","url":null,"abstract":"<div><div>Addressing the escalating cooling demands and energy consumption challenges in modern turbine blade design, an innovative evaluation method integrating cooling effectiveness and aerodynamic loss assessment is developed in this study. These two critical parameters through Generalized Pareto Distribution theory and entropy generation principles are coupled by the proposed methodology, establishing a thermodynamically consistent foundation via rigorous mathematical derivation. Three parts are comprised in the framework: (1) Core modules derived from first principles eliminating empirical parameter dependence; (2) Multi-scale adjustment capability like a micrometer; (3) Dual validation system of sensitivity analysis and experimental-numerical case validation. Strong agreement with established cooling trends is demonstrated through validation using flat plate and cascade experimental data, which makes sure the rationale behind this method. Analysis and results are conducted in numerical simulations: (1) Quantitative trade-off relationships between cooling/loss parameters; (2) Non-adiabatic flow field characteristics through detailed vorticity analysis; (3) Adaptive performance across varying cooling configurations of hole patterns and blowing ratios. Local mechanism details under non-adiabatic condition are reflected by numerical simulations as a local and partial supplement. The comprehensive method combining cooling performance and aerodynamic performance is proved to evaluate film cooling in different film cooling designs and flow conditions.</div></div>","PeriodicalId":50955,"journal":{"name":"Aerospace Science and Technology","volume":"173 ","pages":"Article 111763"},"PeriodicalIF":5.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146048190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Experimental investigation of pulsed fluidic thrust vectoring in a Mach 1.6 axisymmetric jet using transverse air injection for enhanced vectoring efficiency","authors":"Ayushmaan Singh","doi":"10.1016/j.ast.2026.111860","DOIUrl":"10.1016/j.ast.2026.111860","url":null,"abstract":"<div><div>This study experimentally investigates fluidic thrust vectoring (FTV) in a Mach 1.6 axisymmetric jet using pulsed transverse air injection located 3.57 mm upstream of the nozzle exit. The influence of actuation frequency, duty cycle, and momentum ratio on jet deflection and vectoring efficiency is systematically examined, with direct comparison between steady and pulsed injection modes. Experiments were conducted using a precision-machined converging–diverging nozzle, employing wall-pressure measurements, total-pressure rake diagnostics, and Schlieren visualisation. Results show that pulsed injection consistently achieves higher mass-specific vectoring efficiency than steady injection at identical supply pressures, producing comparable jet deflection with reduced secondary mass flow. Maximum efficiency is observed at low duty cycles (20–25%) and forcing frequencies near 200 Hz. Numerical characterisation using a convective timescale and corresponding Strouhal number indicates that this frequency range aligns with dominant supersonic shear-layer instability modes. Analytical scaling relations and symbolic manipulation reveal a nonlinear dependence of vectoring efficiency on duty cycle and frequency, explaining the observed transition between efficient unsteady forcing and quasi-steady behaviour. Schlieren images confirm periodic bow-shock oscillations and transient asymmetry under pulsed actuation, demonstrating the effectiveness of unsteady fluidic control for supersonic jet vectoring.</div></div>","PeriodicalId":50955,"journal":{"name":"Aerospace Science and Technology","volume":"173 ","pages":"Article 111860"},"PeriodicalIF":5.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mechanisms of particle deposition around film cooling holes on nozzle guide vanes in aero-engines","authors":"Xiaohu Chen ,&nbsp;Ziheng Hong ,&nbsp;Mingtao Zang ,&nbsp;Ziyu Jia ,&nbsp;Lianfeng Yang ,&nbsp;Yanhua Wang ,&nbsp;Zhongyi Wang ,&nbsp;Yuzhang Wang","doi":"10.1016/j.ast.2026.111861","DOIUrl":"10.1016/j.ast.2026.111861","url":null,"abstract":"<div><div>To address the challenge of predicting particle deposition characteristics on high-temperature air-cooled turbine in aero-engines, this work develops a high-temperature particle collision and deposition criterion based on the Weber number of molten particles. The effects of film cooling blowing ratio, hole geometry, particle diameter, and thermal barrier coatings (TBCs) on particle deposition behavior near film cooling holes are analyzed. The proposed model accurately predicts particle transport and deposition under large thermal gradients within air-cooled turbine cascade passages across a wide temperature range. Results show that particles are mainly deposited at the exits of the film cooling holes, in the leading-edge stagnation regions, and between the downstream cooling zones, forming pronounced internal blockage, horseshoe-shaped accumulation region, and ridge-like deposition band, respectively. With increasing blowing ratio, both deposition efficiency and deposition rate decrease nonlinearly, and the downstream ridge-like deposition becomes more prominent. When the blowing ratio increases from M = 0.5 to M = 3, particle deposition efficiency decreases by approximately 67 %. Compared with cylindrical holes, fan-shaped holes reduce total particle deposition by 5 %-42 % and suppress the downstream ridge deposition pattern, but increase deposition inside the holes. Applying TBCs increases the overall particle deposition rate by 14 %-27 %, enhances surface deposition, and accentuates the downstream ridge-like deposition structures. The particle diffusion deposition mechanism (<em>St</em> &lt; 0.1), particle diffusion-collision deposition mechanism (0.1 &lt; <em>St</em> &lt; 1), and particle inertial buffering deposition mechanism (<em>St</em> &gt; 1) are the main causes of the aforementioned deposition characteristics. Different blowing ratios, hole geometries, and TBCs all change the spatial scale and intensity of the counter-rotating vortex pairs, which dominate the two basic transport physics of particle ejection and entrainment, thereby determining the particle deposition characteristics. This study provides theoretical insights and quantitative data to support an understanding of particle deposition, film hole blockage, cooling performance degradation, TBCs failure, and blade erosion in turbine environments.</div></div>","PeriodicalId":50955,"journal":{"name":"Aerospace Science and Technology","volume":"173 ","pages":"Article 111861"},"PeriodicalIF":5.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146135559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Inverse analysis of force recovery using soft computing approach for short duration experiments","authors":"Sima Nayak ,&nbsp;Anil Kumar Rout ,&nbsp;Niranjan Sahoo ,&nbsp;Masaharu Komiyama","doi":"10.1016/j.ast.2026.111794","DOIUrl":"10.1016/j.ast.2026.111794","url":null,"abstract":"<div><div>Aerodynamic vehicles experience impulsive forces, which are critical concerns for high-speed atmospheric travel. In high-speed atmospheric flight, vehicles moving at supersonic or hypersonic velocities generate shock waves due to the rapid compression of air in front of them. These shock wave-induced forces can have damaging effects on the vehicle’s surface, making it essential to quantify them for the design and optimization of aerospace structures. Conducting real-time experiments poses significant challenges due to practical limitations; therefore, ground-based testing is performed using aerodynamic models in shock tubes and shock tunnels. A defining characteristic of these facilities is the extremely short duration (milliseconds or less) of test window. Prior to actual experimentation, these models must undergo proper calibration for accurate force prediction. In this study, a hemispherical model equipped with a stress-wave force balance is utilized for calibration. The balance, integrated within the model, includes a piezofilm that records strain signals corresponding to the applied force acting on the model’s nose. Strain signals are captured for different force magnitudes and subsequently used for force training and recovery. In shock tube experiment, the calibrated signals are used for the prediction of unknown forces. Two different flow conditions are examined, determined by the type of diaphragm placed between the driver and driven sections: one using a single Mylar sheet and the other using a double Mylar arrangement. For each condition, three repeated experiments are carried out. It is also observed that the inverse recovery of aerodynamic forces in short-duration experimental environments is inherently nonlinear due to wave dispersion, sensor dynamics, and the absence of equilibrium during impulsive loading. In this work, these nonlinear effects are explicitly addressed through a data-driven soft-computing framework, which enables accurate force prediction without relying on linear system assumptions. By employing an Adaptive Neuro-Fuzzy Inference System (ANFIS), the proposed approach captures the complex and nonlinear relationship between measured strain signals and applied forces under transient shock-tube conditions. The results demonstrate that nonlinear modeling significantly enhances force recovery accuracy as compared to conventional deconvolution methods, particularly in millisecond testing environments.</div></div>","PeriodicalId":50955,"journal":{"name":"Aerospace Science and Technology","volume":"173 ","pages":"Article 111794"},"PeriodicalIF":5.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146071630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Influence of microchannel geometric parameters on the thermal-fluidic performance of a gaseous-cooled scramjet fuel strut","authors":"Tianyun Liu ,&nbsp;Yuan Wang","doi":"10.1016/j.ast.2026.111795","DOIUrl":"10.1016/j.ast.2026.111795","url":null,"abstract":"<div><div>Fuel struts are widely used in scramjet combustors to enhance the fuel-air mixing efficiency and stabilize the combustion process. To address the extreme aerodynamic heating from the mainstream, the present study employed gaseous active cooling based on microchannels to protect the fuel strut. The effects of channel geometric parameters (including leading-edge channel expansion ratios, channel-to-wall angles, and channel widths) on the thermal-fluidic performance were numerically investigated. With a leading-edge channel expansion ratio of 3 and 4, the average cooling effectiveness in the leading-edge region reached a maximum of 11.67 % higher than that without expansion. The variation of the channel-to-wall angle primarily influenced the temperature distribution along the inclined wall. For the strut with a channel-to-wall angle of 45°, the low-temperature zone induced by the expansion fan effectively decreased the wall temperature, while it had the most severe relative pressure loss within channels, reaching a maximum of 0.317 along the inclined wall and 0.297 along the upper wall. Furthermore, while increased channel widths contributed to the temperature reduction of the inclined and upper walls, the accompanying complex wall vortices altered the distribution pattern of total pressure loss within the channels. The present study provides valuable references for the design of the cooling structure for the scramjet fuel strut.</div></div>","PeriodicalId":50955,"journal":{"name":"Aerospace Science and Technology","volume":"173 ","pages":"Article 111795"},"PeriodicalIF":5.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dimensionally-consistent self supervision for spacecraft thermal field prediction with some limited simulation labels","authors":"Qineng Wang,&nbsp;Xinrui Zhou,&nbsp;Yang Gao,&nbsp;Xiaofeng Zhang,&nbsp;Hairun Xie,&nbsp;Yonghe Zhang","doi":"10.1016/j.ast.2026.111757","DOIUrl":"10.1016/j.ast.2026.111757","url":null,"abstract":"<div><div>Accelerating physical simulations via deep learning is a promising yet challenging endeavor, largely due to the prohibitive cost of labeled data generation and the risk of overfitting. This paper presents DSSL, a novel self-supervised learning paradigm that integrates dimensional consistency into the training objective. By subjecting physical state variables to scale transformations derived from governing laws, DSSL compels the network to learn representations that are invariant to scaling. This mechanism effectively shifts the learning focus from statistical memorization to the internalization of physical constraints. In experiments predicting satellite thermal fields, the proposed method demonstrates significant improvements over standard supervised learning, offering a robust solution for high-fidelity physical field reconstruction in low-data regimes.</div></div>","PeriodicalId":50955,"journal":{"name":"Aerospace Science and Technology","volume":"173 ","pages":"Article 111757"},"PeriodicalIF":5.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146048185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An experimental study of ice accretion characteristics on a UAV propeller in forward flight","authors":"Abdallah Samad ,&nbsp;Anvesh Dhulipalla ,&nbsp;Kayde Bowers ,&nbsp;Hui Hu","doi":"10.1016/j.ast.2026.111775","DOIUrl":"10.1016/j.ast.2026.111775","url":null,"abstract":"<div><div>An experimental study was conducted to characterize the dynamic ice accretion process on the rotating propeller blades of a multi-rotor Unmanned-Aerial-Vehicle (UAV) in forward flight and to evaluate the aerodynamic penalties induced by the ice accretion under various icing conditions. The experiments were conducted in an Icing Research Tunnel available at Iowa State University with a UAV propeller model exposed to glaze and rime icing conditions typically encountered by UAVs flying in low-altitude airspace. During the experiments, while a synchronized high-speed imaging approach was employed to acquire “phase-locked” images to reveal the dynamic ice accretion process over rotating propeller blades under different icing conditions, a high-resolution 3D scanning system was utilized to characterize the 3D shapes the ice structures accreted on the blades at the ends of the icing experiments. Simultaneous measurements of generated thrust force and power consumption characteristics of the propeller model were also performed to evaluate the icing-induced performance deteriorations. The acquired ice accretion images were correlated with the quantitative measurements of 3D shapes of the accreted ice structures, time evolution of the generated thrust force and power consumption characteristics of the propeller model to elucidate underlying icing physics. The high-quality, quantitative measurement results can also be used to validate/verify theoretical ice accretion models and numerical simulations for more accurate predictions of UAV inflight icing phenomena.</div></div>","PeriodicalId":50955,"journal":{"name":"Aerospace Science and Technology","volume":"173 ","pages":"Article 111775"},"PeriodicalIF":5.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146048187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Influence of aerodynamic shape on the plasma sheath and terahertz communication of hypersonic vehicles: Laws, mechanisms, and shape schemes","authors":"Rongxin Tang ,&nbsp;Zhuochao Pan ,&nbsp;Kai Yuan ,&nbsp;Ziyang Zhao ,&nbsp;Chengbiao Ding ,&nbsp;Zhengwei Wu ,&nbsp;Wenchong Ouyang","doi":"10.1016/j.ast.2026.111769","DOIUrl":"10.1016/j.ast.2026.111769","url":null,"abstract":"<div><div>A systematic and quantitative investigation of the influence of aerodynamic shape on terahertz communication of hypersonic vehicles is critical for advancing vehicle design and communication systems. However, prior studies have primarily focused on typical vehicle geometries and inter-vehicle type comparisons, with limited systematic analysis of individual shape variables and their coupled effects. Here, a co-simulation model combining non-equilibrium plasma flow and terahertz transmission is developed to systematically explore the effects of nose radius, tail size, fuselage length, and multi-parameter shape variables, and the model is validated through comparisons with shock tube and terahertz ground transmission experiments, and flight data. Results indicate that nose radius exerts the strongest influence compared with tail width and fuselage length. Enlarging the nose radius induces a non-monotonic increase in peak electron density and collision frequency, accompanied by a monotonic growth in sheath thickness, with optimal terahertz communication achieved at a moderate radius with 8 cm. Increasing the tail width enhances electron density and collision frequency but reduces sheath thickness, leading to non-monotonic variations in terahertz attenuation, with narrower tails generally supporting better communication performance. By contrast, fuselage length produces an opposite trend in plasma sheath, yet terahertz attenuation decreases monotonically with increasing length. Finally, a multi-parameter aerodynamic optimization is performed, revealing that a balanced configuration combining a moderate nose radius, narrower tail width, and elongated fuselage achieve the optimal trade-off among plasma sheath properties, minimizes terahertz attenuation, and provides an effective aerodynamic strategy for mitigating blackout problem.</div></div>","PeriodicalId":50955,"journal":{"name":"Aerospace Science and Technology","volume":"173 ","pages":"Article 111769"},"PeriodicalIF":5.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146048189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}