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Verification of parabolized stability equations for its application to compressible boundary layers 被引量:4
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作者 张永明 周恒 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第8期987-998,共12页
Parabolized stability equations (PSE) were used to study the evolution of disturbances in compressible boundary layers. The results were compared with those obtained by direct numerical simulations (DNS), to check... Parabolized stability equations (PSE) were used to study the evolution of disturbances in compressible boundary layers. The results were compared with those obtained by direct numerical simulations (DNS), to check if the results from PSE method were reliable or not. The results of comparison showed that no matter for subsonic or supersonic boundary layers, results from both the PSE and DNS method agreed with each other reasonably well, and the agreement between temperatures was better than those between velocities. In addition, linear PSE was used to calculate the neutral curve for small amplitude disturbances in a supersonic boundary layer. Compared with those obtained by linear stability theory (LST), the situation was similar to those for incom- pressible boundary layer. 展开更多
关键词 direct numerical simulations linear stability theory parabolized stability equations
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An implicit upwind parabolized Navier-Stokes code for chemically nonequilibrium flows 被引量:3
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作者 Bing Chen Li Wang Xu Xu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2013年第1期36-47,共12页
The previously developed single-sweep parabolized Navier-Stokes (SSPNS) space marching code for ideal gas flows has been extended to compute chemically nonequilibrium flows. In the code, the strongly coupled set of ... The previously developed single-sweep parabolized Navier-Stokes (SSPNS) space marching code for ideal gas flows has been extended to compute chemically nonequilibrium flows. In the code, the strongly coupled set of gas dynamics, species conservation, and turbulence equations is integrated with the implicit lower-upper symmetric GaussSeidel (LU-SGS) method in the streamwise direction in a space marching manner. The AUSMPW+ scheme is used to calculate the inviscid fluxes in the crossflow direction, while the conventional central scheme for the viscous fluxes. The k-g two-equation turbulence model is used. The revised SSPNS code is validated by computing the Burrows-Kurkov non-premixed H2/air supersonic combustion flows, premixed H2/air hypersonic combustion flows in a three-dimensional duct with a 15° compression ramp, as well as the hypersonic laminar chemically nonequilibrium air flows around two 10° half-angle cones. The results of these calculations are in good agreement with those of experiments, NASA UPS or Prabhu's PNS codes. It can be concluded that the SSPNS code is highly efficient for steady supersonic/ hypersonic chemically reaction flows when there is no large streamwise separation. 展开更多
关键词 parabolized Navier-Stokes (PNS) equations Chemical nonequilibrium Space marching algorithm Lower-upper symmetric Gauss-Seidel (LU-SGS) method AUSMPW+ scheme
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Improvement for expansion of parabolized stability equation method in boundary layer stability analysis 被引量:1
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作者 Yufeng HAN Jianxin LIU Jisheng LUO 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2018年第12期1737-1754,共18页
An improved expansion of the parabolized stability equation(iEPSE) method is proposed for the accurate linear instability prediction in boundary layers. It is a local eigenvalue problem, and the streamwise wavenumber ... An improved expansion of the parabolized stability equation(iEPSE) method is proposed for the accurate linear instability prediction in boundary layers. It is a local eigenvalue problem, and the streamwise wavenumber α and its streamwise gradient dα/dx are unknown variables. This eigenvalue problem is solved for the eigenvalue dα/dx with an initial α, and the correction of α is performed with the conservation relation used in the PSE. The i EPSE is validated in several compressible and incompressible boundary layers. The computational results show that the prediction accuracy of the i EPSE is significantly higher than that of the ESPE, and it is in excellent agreement with the PSE which is regarded as the baseline for comparison. In addition, the unphysical multiple eigenmode problem in the EPSE is solved by using the i EPSE. As a local non-parallel stability analysis tool, the i EPSE has great potential application in the eNtransition prediction in general three-dimensional boundary layers. 展开更多
关键词 parabolized stability equation(PSE) INSTABILITY non-parallelism boundary layer
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Self-consistent parabolized stability equation(PSE) method for compressible boundary layer 被引量:1
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作者 Yongming ZHANG Caihong SU 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2015年第7期835-846,共12页
The parabolized stability equation (PSE) method has been proven to be a useful and convenient tool for the investigation of the stability and transition problems of boundary layers. However, in its original formulat... The parabolized stability equation (PSE) method has been proven to be a useful and convenient tool for the investigation of the stability and transition problems of boundary layers. However, in its original formulation, for nonlinear problems, the complex wave number of each Fourier mode is determined by the so-called phase-locked rule, which results in non-self-consistency in the wave numbers. In this paper, a modification is proposed to make it self-consistent. The main idea is that, instead of allowing wave numbers to be complex, all wave numbers are kept real, and the growth or decay of each mode is simply manifested in the growth or decay of the modulus of its shape function. The validity of the new formulation is illustrated by comparing the results with those from the corresponding direct numerical simulation (DNS) as applied to a problem of compressible boundary layer with Mach number 6. 展开更多
关键词 parabolized stability equation (PSE) boundary layer direct numericalsimulation (DNS) SELF-CONSISTENT
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Applications of parabolized stability equation for predicting transition position in boundary layers 被引量:1
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作者 李佳 罗纪生 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2012年第6期679-686,共8页
The phenomenon of laminar-turbulent transition exists universally in nature and various engineering practice. The prediction of transition position is one of crucial theories and practical problems in fluid mechanics ... The phenomenon of laminar-turbulent transition exists universally in nature and various engineering practice. The prediction of transition position is one of crucial theories and practical problems in fluid mechanics due to the different characteristics of laminar flow and turbulent flow. Two types of disturbances are imposed at the entrance, i.e., identical amplitude and wavepacket disturbances, along the spanwise direction in the incompressible boundary layers. The disturbances of identical amplitude are consisted of one two-dimensional (2D) wave and two three-dimensional (3D) waves. The parabolized stability equation (PSE) is used to research the evolution of disturbances and to predict the transition position. The results are compared with those obtained by the numerical simulation. The results show that the PSE method can investigate the evolution of disturbances and predict the transition position. At the same time, the calculation speed is much faster than that of the numerical simulation. 展开更多
关键词 transition position incompressible boundary layer parabolized stabilityequation (PSE) numerical simulation
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Improved nonlinear parabolized stability equations approach for hypersonic boundary layers 被引量:1
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作者 Shaoxian Ma Yi Duan +1 位作者 Zhangfeng Huang Shiyong Yao 《Chinese Physics B》 SCIE EI CAS CSCD 2021年第5期424-436,共13页
The nonlinear parabolized stability equations(NPSEs)approach is widely used to study the evolution of disturbances in hypersonic boundary layers owing to its high computational efficiency.However,divergence of the NPS... The nonlinear parabolized stability equations(NPSEs)approach is widely used to study the evolution of disturbances in hypersonic boundary layers owing to its high computational efficiency.However,divergence of the NPSEs will occur when disturbances imposed at the inlet no longer play a leading role or when the nonlinear effect becomes very strong.Two major improvements are proposed here to deal with the divergence of the NPSEs.First,all disturbances are divided into two types:dominant waves and non-dominant waves.Disturbances imposed at the inlet or playing a leading role are defined as dominant waves,with all others being defined as non-dominant waves.Second,the streamwise wavenumbers of the non-dominant waves are obtained using the phase-locked method,while those of the dominant waves are obtained using an iterative method.Two reference wavenumbers are introduced in the phase-locked method,and methods for calculating them for different numbers of dominant waves are discussed.Direct numerical simulation(DNS)is performed to verify and validate the predictions of the improved NPSEs in a hypersonic boundary layer on an isothermal swept blunt plate.The results from the improved NPSEs approach are in good agreement with those of DNS,whereas the traditional NPSEs approach is subject to divergence,indicating that the improved NPSEs approach exhibits greater robustness. 展开更多
关键词 nonlinear parabolized stability equations(NPSEs) hypersonic boundary layers streamwise wavenumber
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AN IMPLICIT-EXPLICIT UPWIND ALGORITHM FOR THE PARABOLIZED NAVIER-STOKES EQUATIONS
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作者 刘铁刚 王汝权 宋松和 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 1994年第2期129-135,共7页
In this paper, a second-order implicit-explicit upwind algorithm has been developed for three-dimensional Parabolized Navier-Stokes(PNS) equations. The agreement between the results of the new upwind algorithm and tho... In this paper, a second-order implicit-explicit upwind algorithm has been developed for three-dimensional Parabolized Navier-Stokes(PNS) equations. The agreement between the results of the new upwind algorithm and those of the im- plicit upwind algorithm and its ability in marching a long distance along the stream- wise direction have been shown for the supersonic viscous flow past a sphere-cone body. The CPU time is greatly reduced. 展开更多
关键词 parabolized Navier-Stokes (PNS) equations supersonic viscous flow upwind(TVD) algoritm space marching
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A STABILIZED CRANK-NICOLSON MIXED FINITE VOLUME ELEMENT FORMULATION FOR THE NON-STATIONARY PARABOLIZED NAVIER-STOKES EQUATIONS
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作者 罗振东 《Acta Mathematica Scientia》 SCIE CSCD 2015年第5期1055-1066,共12页
A time semi-discrete Crank-Nicolson (CN) formulation with second-order time accuracy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed ... A time semi-discrete Crank-Nicolson (CN) formulation with second-order time accuracy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed finite volume element (SCNMFVE) formu- lation based on two local Gaussian integrals and parameter-free with the second-order time accuracy is established directly from the time semi-discrete CN formulation so that it could avoid the discussion for semi-discrete SCNMFVE formulation with respect to spatial wriables and its theoretical analysis becomes very simple. Finally, the error estimates of SCNMFVE solutions are provided. 展开更多
关键词 non-stationary parabolized Navier-Stokes equations stabilized Crank-Nicolson mixed finite volume element formulation error estimate
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Heat Transfer Enhancement of the Absorber Tube in a Parabolic Trough Solar Collector through the Insertion of Novel Cylindrical Turbulators
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作者 Yasser Jebbar Fadhil Fluiful Wisam Khudhayer 《Fluid Dynamics & Materials Processing》 EI 2024年第6期1279-1297,共19页
This study includes an experimental and numerical analysis of the performances of a parabolic trough collector(PTC)with and without cylindrical turbulators.The PTC is designed with dimensions of 2.00 m in length and 1... This study includes an experimental and numerical analysis of the performances of a parabolic trough collector(PTC)with and without cylindrical turbulators.The PTC is designed with dimensions of 2.00 m in length and 1.00 m in width.The related reflector is made of lined sheets of aluminum,and the tubes are made of stainless steel used for the absorption of heat.They have an outer diameter of 0.051 m and a wall thickness of 0.002 m.Water,used as a heat transfer fluid(HTF),flows through the absorber tube at a mass flow rate of 0.7 kg/s.The dimensions of cylindrical turbulators are 0.04 m in length and 0.047 m in diameter.Simulations are performed using the ANSYS Fluent 2020 R2 software.The PTC performance is evaluated by comparing the experimental and numerical outcomes,namely,the outlet temperature,useful heat,and thermal efficiency for a modified tube(MT)(tube with novel cylindrical turbulators)and a plain tube(PT)(tube without novel cylindrical turbulators).According to the results,the experimental outlet temperatures recorded 63.2°C and 50.5°C for the MT and PT,respectively.The heat gain reaches 1137.5 Win the MT and 685.8 Win the PT.Compared to the PT collector,the PTC exhibited a(1.64 times)higher efficiency. 展开更多
关键词 Parabolic trough collector turbulators absorber tube ANSYS thermal efficiency
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WEAK-STRONG UNIQUENESS FOR THREE DIMENSIONAL INCOMPRESSIBLE ACTIVE LIQUID CRYSTALS
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作者 Fan YANG Congming LI 《Acta Mathematica Scientia》 SCIE CSCD 2024年第4期1415-1440,共26页
The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models.In this paper,we study the weak-strong uniqueness for the Leray-Hopf type weak so... The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models.In this paper,we study the weak-strong uniqueness for the Leray-Hopf type weak solutions to the incompressible active liquid crystals in R^(3).Our results yield that if there exists a strong solution,then it is unique among the Leray-Hopf type weak solutions associated with the same initial data. 展开更多
关键词 analysis of parabolic and elliptic types weak-strong uniqueness active liquid crystals weak solution energy equality
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BLOW-UP CONDITIONS FOR A SEMILINEAR PARABOLIC SYSTEM ON LOCALLY FINITE GRAPHS
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作者 吴艺婷 《Acta Mathematica Scientia》 SCIE CSCD 2024年第2期609-631,共23页
In this paper, we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs. Under some appropriate assumptions on the curvature condition CDE’(n,0), the polynomial volume growth of ... In this paper, we investigate a blow-up phenomenon for a semilinear parabolic system on locally finite graphs. Under some appropriate assumptions on the curvature condition CDE’(n,0), the polynomial volume growth of degree m, the initial values, and the exponents in absorption terms, we prove that every non-negative solution of the semilinear parabolic system blows up in a finite time. Our current work extends the results achieved by Lin and Wu (Calc Var Partial Differ Equ, 2017, 56: Art 102) and Wu (Rev R Acad Cien Serie A Mat, 2021, 115: Art 133). 展开更多
关键词 semilinear parabolic system on graphs BLOW-UP heat kernel estimate on graphs
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A Stable FE-FD Method for Anisotropic Parabolic PDEs with Moving Interfaces
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作者 Baiying Dong Zhilin Li Juan Ruiz-Alvarez 《Communications on Applied Mathematics and Computation》 EI 2024年第2期992-1012,共21页
In this paper,a new finite element and finite difference(FE-FD)method has been developed for anisotropic parabolic interface problems with a known moving interface using Cartesian meshes.In the spatial discretization,... In this paper,a new finite element and finite difference(FE-FD)method has been developed for anisotropic parabolic interface problems with a known moving interface using Cartesian meshes.In the spatial discretization,the standard P,FE discretization is applied so that the part of the coefficient matrix is symmetric positive definite,while near the interface,the maximum principle preserving immersed interface discretization is applied.In the time discretization,a modified Crank-Nicolson discretization is employed so that the hybrid FE-FD is stable and second order accurate.Correction terms are needed when the interface crosses grid lines.The moving interface is represented by the zero level set of a Lipschitz continuous function.Numerical experiments presented in this paper confirm second orderconvergence. 展开更多
关键词 Anisotropic parabolic interface problem Hybrid finite element and finite difference(FE-FD)discretization Modified Crank Nicolson scheme
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一类退化抛物方程高初始能量下解的有限时刻爆破及整体存在性
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作者 刘功伟 杨坤 《Chinese Quarterly Journal of Mathematics》 2024年第1期97-110,共14页
We consider the initial-boundary value problem for finitely degenerate parabolic equation. We first give sufficient conditions for the blow-up and global existence of the parabolic equation at high initial energy leve... We consider the initial-boundary value problem for finitely degenerate parabolic equation. We first give sufficient conditions for the blow-up and global existence of the parabolic equation at high initial energy level. Then, we establish the existence of solutions blowing up in finite time with initial data at arbitrary energy level. Finally, we estimate the upper bound of the blow-up time under certain conditions. 展开更多
关键词 High energy Degenerate parabolic equations Blow up Global existence
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Improving Heat Transfer in Parabolic Trough Solar Collectors by Magnetic Nanofluids
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作者 Ritesh Singh Abhishek Gupta +2 位作者 Akshoy Ranjan Paul Bireswar Paul Suvash C.Saha 《Energy Engineering》 EI 2024年第4期835-848,共14页
A parabolic trough solar collector(PTSC)converts solar radiation into thermal energy.However,low thermal efficiency of PTSC poses a hindrance to the deployment of solar thermal power plants.Thermal performance of PTSC... A parabolic trough solar collector(PTSC)converts solar radiation into thermal energy.However,low thermal efficiency of PTSC poses a hindrance to the deployment of solar thermal power plants.Thermal performance of PTSC is enhanced in this study by incorporating magnetic nanoparticles into the working fluid.The circular receiver pipe,with dimensions of 66 mm diameter,2 mm thickness,and 24 m length,is exposed to uniform temperature and velocity conditions.The working fluid,Therminol-66,is supplemented with Fe3O4 magnetic nanoparticles at concentrations ranging from 1%to 4%.The findings demonstrate that the inclusion of nanoparticles increases the convective heat transfer coefficient(HTC)of the PTSC,with higher nanoparticle volume fractions leading to greater heat transfer but increased pressure drop.The thermal enhancement factor(TEF)of the PTSC is positively affected by the volume fraction of nanoparticles,both with and without a magnetic field.Notably,the scenario with a 4%nanoparticle volume fraction and a magnetic field strength of 250 G exhibits the highest TEF,indicating superior thermal performance.These findings offer potential avenues for improving the efficiency of PTSCs in solar thermal plants by introducing magnetic nanoparticles into the working fluid. 展开更多
关键词 Parabolic trough solar collector(PTSC) magnetic nanofluid(MNF) heat transfer convective heat transfer coefficient(HTC) thermal enhancement factor(TEF)
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A Stabilized Crank-Nicolson Mixed Finite Element Method for Non-stationary Parabolized Navier-Stokes Equations
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作者 Yan-jie ZHOU Fei TENG Zhen-dong LUO 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2017年第2期409-416,共8页
In this study, a time semi-discrete Crank-Nicolson (CN) formulation with second-order time accu- racy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete sta... In this study, a time semi-discrete Crank-Nicolson (CN) formulation with second-order time accu- racy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed finite element (SCNMFE) formulation based on two local Gauss integrals and parameter- free with the second-order time accuracy is established directly from the time semi-discrete CN formulation. Thus, it could avoid the discussion for semi-discrete SCNMFE formulation with respect to spatial variables and its theoretical analysis becomes very simple. Finaly, the error estimates of SCNMFE solutions are provided. 展开更多
关键词 parabolized Navier-Stokes equations stabilized Crank-Nicolson mixed finite element formulation error estimate
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Optimization of the Physical Aperture of the Parabolic Reflector Antenna
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作者 Nkordeh Nsikan Akindele Ayoola +2 位作者 Ololade Oladoyin Amadi Eberi Ibinabo Bobmanuel 《Open Journal of Applied Sciences》 2024年第1期182-192,共11页
In fields like astronomy and radar technology, high-gain antennas are required for long-distance communication. Due to its relatively large gain, the use of parabolic antennas has become very popular over time, becaus... In fields like astronomy and radar technology, high-gain antennas are required for long-distance communication. Due to its relatively large gain, the use of parabolic antennas has become very popular over time, because they can easily achieve gains of above 30 dB at microwave and higher frequencies. Today, most systems’ success depends on how well the antennas perform. These antennas are available in different types and sizes. Each antenna’s effective area usually has less than the actual physical area of the antenna surface. This means that the unused area of the antenna is massive, and a waste. The aim of the research is to show that the actual physical aperture of a parabolic antenna can be reduced as much as possible to equal the effective area, as given by the antenna formula, thereby saving manufacturing costs, improve the aesthetics. In other words, the focus of this work is to experimentally show that reflector antenna can be made of smaller sizes but better performance. Measurements were taken from different positions from a parabolic antenna, the signal level measured and compared with signal levels for optimal performance. 展开更多
关键词 PARABOLIC ANTENNA RECEPTION MANUFACTURING COST
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Global Existence and Decay of Solutions for a Class of a Pseudo-Parabolic Equation with Singular Potential and Logarithmic Nonlocal Source
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作者 Xiaoxin Yang 《Journal of Applied Mathematics and Physics》 2024年第1期181-193,共13页
This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utiliz... This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay. 展开更多
关键词 Nonlocal Parabolic Equation Singular Potential Logarithmic Nonlocal Source Global Existence DECAY
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Design and Development of a Parabolic Trough Solar Air Heater for a Greenhouse Dryer
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作者 Eric King’ori Isaac N. Simate 《Journal of Power and Energy Engineering》 2024年第9期1-18,共18页
Design and Development of a Parabolic Trough Solar Air Heater (PTSAH) for a Greenhouse Dryer (GD) was done to improve the dryer’s performance. The materials used for the fabrication of the PTSAH included galvanized s... Design and Development of a Parabolic Trough Solar Air Heater (PTSAH) for a Greenhouse Dryer (GD) was done to improve the dryer’s performance. The materials used for the fabrication of the PTSAH included galvanized sheets covered with aluminium foil, an absorber tube made of GI pipe painted matt black to increase heat absorbance at the focal line, mild steel square tubes, shutter plywood, and an axial fan to push air through the absorber tube. Key geometrical parameters used for the design of the PTSAH were a rim angle of 98 degrees, focal length of 0.2608 m, height of 0.3451 m, length of 2 m, and an aperture width of 1.2 m. The PTSAH’s total aperture surface area was 2.4 m2, while its absorber tube surface area was 0.1587 m2. The PTSAH was experimentally tested to establish its thermal performance. It was found that the ambient air recorded an average value of 31.1˚C and that the air heater could increase the air temperature by 45.6˚C above ambient with a thermal efficiency of 5.3%. It can, therefore, be concluded that the PTSAH can significantly improve the performance of a GD by supplying the GD with air at a higher temperature than ambient. 展开更多
关键词 Solar Air Heater Greenhouse Dryer Parabolic Trough Thermal Performance
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Nonautonomous Breather and Rogue Wave in Spinor Bose–Einstein Condensates with Space-Time Modulated Potentials 被引量:2
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作者 丁崔崔 周勤 +3 位作者 徐四六 Houria Triki Mohammad Mirzazadeh 刘文军 《Chinese Physics Letters》 SCIE EI CAS CSCD 2023年第4期6-10,共5页
To study controlled evolution of nonautonomous matter-wave breathers and rogue waves in spinor Bose–Einstein condensates with spatiotemporal modulation,we focus on a system of three coupled Gross–Pitaevskii equation... To study controlled evolution of nonautonomous matter-wave breathers and rogue waves in spinor Bose–Einstein condensates with spatiotemporal modulation,we focus on a system of three coupled Gross–Pitaevskii equations with spacetime-dependent external potentials and temporally modulated gain-loss distributions.With different external potentials and gain-loss distributions,various solutions for controlled nonautonomous matterwave breathers and rogue waves are derived by the Darboux transformation method,such as breathers and rogue waves on arched and constant backgrounds which have the periodic and parabolic trajectories.Effects of the gain-loss distribution and linear potential on the breathers and rogue waves are studied.Nonautonomous two-breathers on the arched and constant backgrounds are also derived. 展开更多
关键词 EINSTEIN NONAUTONOMOUS PARABOLIC
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Dynamically Characterizing the Structures of Dirac Points via Wave Packets
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作者 梁丹丹 沈鑫 李志 《Chinese Physics Letters》 SCIE EI CAS CSCD 2023年第11期9-13,共5页
Topological non-trivial band structures are the core problem in the field of topological materials.We investigate the topological band structure in a system with controllable Dirac points from the perspective of wave ... Topological non-trivial band structures are the core problem in the field of topological materials.We investigate the topological band structure in a system with controllable Dirac points from the perspective of wave packet dynamics.By adding a third-nearest-neighboring coupling to the graphene model,additional pairs of Dirac points emerge.The emergence and annihilation of Dirac points result in hybrid and parabolic points,and we show that these band structures can be revealed by the dynamical behaviors of wave packets.In particular,for the gapped hybrid point,the motion of the wave packet shows a one-dimensional Zitterbewegung motion.Furthermore,we also show that the winding number associated with the Dirac point and parabolic point can be determined via the center of mass and spin texture of wave packets,respectively.The results of this work could motivate new experimental methods to characterize a system’s topological signatures through wave packet dynamics,which may also find applications in systems of other exotic topological materials. 展开更多
关键词 DIRAC TOPOLOGICAL PARABOLIC
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