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Combined effect of Reynolds and Grashof numbers on mixed convection in a lid-driven T-shaped cavity filled with water-Al_2O_3 nanofluid

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Journal of Hydrodynamics 2015年第5期27卷 782-794页

作者： MOJUMDER Satyajit SAHA Sourav SAHA Sumon MAMUN M.A.H. Department of Mechanical Engineering Bangladesh University of Engineering and Technology

Lid-driven mixed convection has been given immense importance due to its wide range of applications. A T-shaped cavity is introduced and pertinent parameters controlling mixed convection phenomenon are analyzed in this paper. Water-Al2O3 nanofluid is considered inside the cavity to augment heat transfer rate. Galerkin weighted residual method of finite element analysis is applied for the numerical simulations. Numerical solution is obtained for different solid volume fractions of nanofluid（？= 0- 0.15）, Grashof numbers（Gr= 0.1 ？5 000） and Reynolds numbers（Re= 0.31 ？1 000） in laminar flow regime. Special attention is given on the analysis of flow at the pure mixed convection regime. It is found that Grashof, Reynolds and richardson numbers along with solid volume fraction of nanofluid have significant effect on heat transfer characteristics inside the cavity. Results are presented using streamline and isotherm contours along with related variation of average Nusselt numbers of the heated wall and average fluid temperature inside the cavity.

关键词： mixed convection nanofluid lid-driven T-shaped richardson number finite element

Inertia gravity wave activity in the troposphere and lower stratosphere observed by Wuhan MST radar

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Science China Earth Sciences 2016年第5期59卷 1066-1073页

作者： QING HaiYin ZHOU Chen ZHAO ZhengYu NI BinBin ZHANG YuanNong Department of Space Physics School of Electronic Information Wuhan University

The troposphere and lower stratosphere(TLS) is a region with active atmospheric fluctuations. The Wuhan Mesosphere-Stratosphere-Troposphere(MST) radar is the first MST radar to have become operational in China's Mainland. It is dedicated to real-time atmospheric observations. In this paper, two case studies about inertia gravity waves(IGWs) derived from three-dimensional wind field data collected with the Wuhan MST radar are presented. The intrinsic frequencies, vertical wavelengths, horizontal wavelengths, vertical wavenumber spectra, and energy density are calculated and analyzed. In this paper, we also report on multiple waves existing in the lower stratosphere observed by the Wuhan MST radar. Lomb-Scargle spectral analysis and the hodograph method were used to derive the vertical wavenumber and propagation direction. Meanwhile, an identical IGW is observed by Wuhan MST radar both in troposphere and lower stratosphere regions. Combining the observations, the source of the latter IGW detected in the TLS would be the jet streams located in the tropopause region, which also produced wind shear above and below the tropopause.

关键词： Wuhan MST radar TLS Inertia gravity waves Brunt-Vaisala frequency richardson number

Nonlinear phase dynamics of ideal kink mode in the presence of shear flow

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Plasma Science and Technology 2021年第4期23卷 9-14页

作者： Yi ZHANG Zhibin GUO State Key Laboratory of Nuclear Physics and Technology Fusion Simulation CenterSchool of PhysicsPeking UniversityBeijing 100871People’s Republic of China

We investigate nonlinear phase dynamics of an ideal kink mode,induced by E×B *** the phase is the cross phase(θ_(c))between perturbed stream function of velocity(f)and magnetic field(y),i.e.θ_(c)=θf−θψ.A dimensionless parameter,analogous to the R_(i)chardson number,R_(i)=16gkink w^(2)E^(2)(γkink:the normalized growth rate of the pure kink mode;wE:normalized E×B shearing rate)is defined to measure the competition between phase pinning by the current density and phase detuning by the flow *** R_(i)>1,θ_(c) is locked to a fixed value,corresponding to the conventional eigenmode *** R_(i).1,θ_(c) enters a phase slipping or oscillating state,corresponding to a nonmodal *** nonlinear phase dynamics method provides a more intuitive explanation of the complex dynamical behavior of the kink mode in the presence of E×B shear flow.

关键词： kink mode E×B flow nonlinear phase dynamics richardson number

Experimental investigation of density current patterns using dynamic fractal analysis

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International Journal of Sediment Research 2021年第2期36卷 165-176页

作者： Mohammad Hosseini Mohammad Hadi Fattahi Saeid Eslamian Department of Civil Engineering Najafabad Branch Islamic Azad University Department of Civil Engineering Marvdasht Branch Islamic Azad University Department of Water Engineering Isfahan University of Technology

Density currents are caused by a difference in density, though low, of an entering fluid with the ambient fluid. This type of current is two-phased and found on riverbeds or in reservoirs behind dams, and is nonlinear in nature, complex, and sensitive to initial conditions. Fractal geometry is used as a powerful tool for studying complex natural phenomena. Using experimental studies and changes in inlet current conditions, the fractal and multi-fractal analyses of the interface between the density current and the ambient fluid were done. In addition, a search was made to find a possible connection between the nonlinear patterns. According to the results, with an increase in the inlet discharge and inlet density of the current the fractal dimension decreased. Further, the smaller the range of the singularity spectrum diagram was, i.e., the more it was less than 0.34, the lower the system’s tendency was to be multi-fractal,and the system sensitive to large local changes. In the interface between the density current and the ambient fluid, using the fractal dimension-based richardson number could improve experimental data by 12.4%. Moreover, with an increase in the richardson number, the Reynolds number of the current decreased. Further, upon considering the fractal dimension, the Reynolds number improved by 23% and a good correlation with a coefficient of determination of 0.76.

关键词： Density current Fractal geometry richardson number Multi-fractal analysis Fluid interface

Symmetric　Stability　of　Rotation　and　Boussinesq　Fluid　in　Bounded　Domain　by　Using　Normal　Mode　Method

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Advances in Atmospheric Sciences 1994年第3期11卷 291-295页

作者：任舒展 LASG Institute of Atmospheric Physics Chinese Academy of Sciences Beijing

The stability properties of the equilibria with constant wind shear (both in vertical and horizontal direction) andthe non-constant static stability in bounded, inviscid and adiabatic atmosphere were investigated by using normalmode method. The results show that the stability property is determined by richardson number R, as well as the absolute vorticity. When the absolute vorticity F is positive, i.e. F > 0, (where F = f+ vx ) the sufficient condition forsymmetric stability is Ri > f/ F and when F < 0, the equilibria are unstable for all possible normal mode disturbances. In addition, the most unstable growth rate was also obtained here.

关键词： Symmetric stability richardson number The most unstable growth rate

Preliminary Research on the Size Distribution of Aerosols in Beijing

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Advances in Atmospheric Sciences 2001年第2期18卷 225-230页

作者：张仁健王明星符建中 State Key Laboratory of Atmospheric Boundary Layer Physics and Atmospheric Chemistry Institute of Atmospheric Physics Chinese Academy of Sciences Beijing

number concentration and size distribution of atmospheric aerosols were measured in Beijing by an optical particle counter. The relationship between aerosol size distribution and relative humidity is discussed. The results show that the size distribution, diurnal variation, daily variation of atmospheric aerosols have a good relation to relative humidity and richardson number. Key words Atmospheric aerosol - number concentration - Size distribution - Relative humidity - richardson number This work is financially supported by NKBRSF Project (G1999043400), Knowledge Creative Project (8-2101 and 82303) founded by TAP, CAS.The authors would like to express their thanks to Prof. Zhang Wen for his work in this observation.

关键词： Atmospheric aerosol number concentration Size distribution Relative humidity richardson number

Characterization of Surface Layer Turbulence across a West African Tropical Climate Belt

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Atmospheric and Climate Sciences 2020年第3期10卷 405-420页

作者： David O. Edokpa Precious N. Ede Department of Geography and Environmental Management Rivers State University Port Harcourt Nigeria

This study surveyed the levels of boundary layer surface turbulence across a West African climate region. Five years (2011-2015) temperature and wind speed data at synoptic hours 0000 Hr, 0600 Hr, 1200 Hr and 1800 Hr within 0.125° grid resolution was sourced from Era-Interim Reanalysis platform at 1000 mbar pressure level. Using the richardson (Ri) number technique, results showed that mechanical turbulence of Ri range 0.04 - 0.57 dominates across the surface layer for study locations of Port Harcourt, Enugu, Jos, Kano and Maiduguri than thermal turbulence. However, the least turbulent area was the coastal zone of surveyed region. Results also indicated that the vertical height (L) at which thermal turbulence replaces mechanical turbulence across study locations ranged from 20 - 250 m with lowest replacement levels (20 - 50 m) occurring mainly in the coastal area of Port Harcourt during periods of dawn. The most turbulent periods in the southern coastal location of study region were during key rainy periods from June-August while that for the rest far northern inland areas occur during the dry season/early rainy periods i.e. November-May. The implication of the lower surface turbulence/replacement level within coastal domains most especially during periods of dawn is that emission releases near surface layer will be dispersed after initial rise due to buoyancy at horizontal levels thereby increasing ground level pollutants concentration across sensitive receptors that are close to emission source. At heights of thermal turbulence replacement, emission releases will be transported vertically and then dispersed further away from emission sources, thus impacting sensitive receptors at farther distances. This is the atmospheric boundary layer dynamics that makes ground level pollution worse in the coastal city of Port Harcourt in recent times during periods of dawn. Efforts must be made by concerned Stakeholders towards ensur

关键词： Turbulence richardson number West Africa Nigeria Coastal Area Air Pollution

On a Non-Definite Sturm-Liouville Problem in the Two-Turning Point Case—Analysis and Numerical Results

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Journal of Applied Mathematics and Physics 2016年第9期4卷 1787-1810页

作者： Mervis Kikonko Department of Engineering Sciences and Mathematics Lule&aring University of Technology Lule&aring Sweden Department of Mathematics and Statistics The University of Zambia Lusaka Zambia

In this paper, we study the non-definite Sturm-Liouville problem comprising of a regular Sturm-Liouville equation and Dirichlet boundary conditions on a closed interval. We consider the case in which the weight function changes sign twice in the given interval of definition. We give detailed numerical results on the spectrum of the problem, from which we verify various results on general non definite Sturm-Liouville problems. We also present some theoretical results which support the numerical results. Some numerical results seem to be in contrast with the results that are so far obtained in the case where the weight function changes sign once. This leads to more open questions for future studies in this particular area.

关键词： Eigenvalue Eigenfunction Non-Definite Turning Point richardson number richardson Index Haupt Index Oscillation number Right-Definite Left-Definite

Numerical Study of Mixed Convection in an Isosceles Trapezoidal Cavity with Several Outlets: Application for Primary Air Draft in ASUTO Charcoal Stove

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Modern Mechanical Engineering 2022年第2期12卷 45-61页

作者： Gagnon Koffi Apedanou Kokou N’wuitcha Yendoubé Lare Kossi Napo Laboratoire sur l’Energie Solaire Chair Unesco Faculté des Sciences Université de Lomé Lomé Togo Laboratoire sur l’Energie Solaire Groupe Phénomènes de Transfert et Energétique (LES-GPTE) Faculté des Sciences Université de Lomé Lomé Togo

Mixed convection of heat and mass transfer in an isosceles trapezoidal cavity has been studied numerically. Constant heat flux is imposed through four outlets and the grid is insulated. The inclined walls are maintained in natural convection while the lower horizontal wall is adiabatic. These conditions reflect the air draft zone of the ASUTO charcoal stove. The governing two-di- mensional flow equations have been solved by using the finite difference method and Thomas’s algorithm. The investigations are conducted for different values of richardson (Ri), Reynolds number (Re) and inclination angles of sidewalls. The results are presented in terms of streamlines, isotherms, moisture contours. It was found that for Reynolds number (Re) equal to 100, the flow pattern is strongly dependent on the inclination angle and richardson number. Thus, for high richardson number (Ri) values (10, 100), the dominance of natural convection over the flow structure decreases with the decreasing of the inclination angle of sidewalls of the cavity. For Ri = 1, an optimum air draft corresponds to an inclination angle in the vicinity of 22° while for Ri = 10 or 100 (in dominance of natural convection), the optimum inclination angle for air draft is in the vicinity of 15°.

关键词： Mixed Convection Heat and Mass Transfer Trapezoidal Cavity ASUTO Charcoal Stove richardson number Several Outlets