Combined heat and mass transfer by hydromagnetic natural convection over a cone embedded in a non-Darcian porous medium with heat generation/absorption effects

 The problem of combined heat and mass transfer by natural convection over a permeable cone embedded in a uniform porous medium in the presence of an external magnetic field and internal heat generation or absorption effects is formulated. The cone surface is maintained at either constant temperature and constant concentration or uniform heat and mass fluxes. In addition, the cone surface is assumed permeable in order to allow for possible fluid wall suction or blowing. The resulting governing equations are non-dimensionalized and transformed into a non-similar form and then solved numerically by an implicit, iterative, finite-difference method. Comparisons with previously published work are performed and excellent agreement between the results is obtained. A parametric study of the physical parameters is conducted and a representative set of numerical results for the temperature and concentration profiles as well as the local Nusselt number and the Sherwood number is illustrated graphically to show special trends of the solutions. Received on 5 June 2000 / Published online: 29 November 2001     

Stability of spatial motion of a body with flow separation and rotation about the symmetry axis

A model describing the spatial motion (without separation and with nonsymmetric separation of the flow in the medium) of a body rotating about its symmetry axis in a resisting medium is constructed. Several criteria for stability of the body rectilinear motion are obtained in the case of frozen axial velocity. The influence of retardation on the stability of rectilinear motion of a cone is considered.     

Free convection flow over a truncated cone embedded in a porous medium saturated with pure or saline water at low temperatures

Steady free convection boundary layer about a truncated cone embedded in a porous medium saturated with pure or saline water at low temperatures has been studied in this paper. The governing coupled partial differential equations are solved numerically using a very efficient finite-difference method. Several new parameters arise and the results are given for some specific values of these parameters. The obtained results for a Boussinesq fluid are compared with known results from the open literature and it is shown that the agreement between these results is very good.     

Radiation effects on mixed convection about a cone embedded in a porous medium filled with a nanofluid

The problem of steady, laminar, mixed convection boundary-layer flow over a vertical cone embedded in a porous medium saturated with a nanofluid is studied, in the presence of thermal radiation. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis with Rosseland diffusion approximation. The cone surface is maintained at a constant temperature and a constant nanoparticle volume fraction. The resulting governing equations are non-dimensionalized and transformed into a non-similar form and then solved by Keller box method. A comparison is made with the available results in the literature, and our results are in very good agreement with the known results. A parametric study of the physical parameters is made and a representative set of numerical results for the local Nusselt and Sherwood numbers are presented graphically. Also, the salient features of the results are analyzed and discussed.     

Finite-difference solution of unsteady natural convection flow past a nonisothermal vertical cone under the influence of a magnetic field and thermal radiation

An analysis is performed to study the heat transfer characteristics of natural convection over a vertical cone under the combined effects of a magnetic field and thermal radiation. The cone surface is subjected to a variable surface temperature. The fluid considered is a gray absorbing/emitting, but non-scattering medium. The boundary layer equations governing the flow are reduced to non-dimensional equations using non-dimensional quantities valid in the free-convection regime. The resulting non-dimensional governing equations are solved by an implicit finite-difference method of the Crank-Nicolson type, which is rapidly convergent and unconditionally stable. Numerical results are obtained for velocity, temperature, local and average skin friction, and local and average Nusselt numbers for various values of parameters occurring in the problem and are presented in the graphical form. Excellent agreement of the results obtained with available data is demonstrated.     

Radiation effect on free convection of a non-Newtonian fluid over a vertical cone embedded in a porous medium with heat generation

The effects of thermal radiation on free convection in a non-Newtonian fluid over a vertical cone embedded in a porous medium in the presence of heat generation are studied. By using similarity transformations, the governing equations describing the problem are transformed to a system of nonlinear ordinary differential equations, which are solved numerically. The results are presented in the graphical form. The effects of various physical parameters and of the local Nusselt number on the velocity and the temperature profiles are discussed.     

Hydrodynamics of gas-solid fluidization of a homogeneous ternary mixture in a conical bed： Prediction of bed expansion and bed fluctuation ratios

Hydrodynamic characteristics of fluidization in a conical or tapered bed differ from those in a columnar bed because the superficial velocity in the bed varies in the axial direction. Fixed and fluidized regions could coexist and sharp variations in pressure drop could occur, thereby giving rise to a noticeable pressure drop-flow rate hysteresis loop under incipient fluidization conditions. To explore these unique properties, several experiments were carried out using homogeneous, well-mixed, ternary mixtures with three dif- ferent particle sizes at varying composition in gas-solid conical fluidized beds with varying cone angles. The hydrodynamic characteristics determined include the minimum fluidization velocity, bed fluctuation, and bed expansion ratios. The dependence of these quantities on average particle diameter, mass fraction of the fines in the mixture, initial static bed height, and cone angle is discussed. Based on dimensional analysis and factorial design, correlations are developed using the system parameters, i.e. geometry of the bed （cone angle）, particle diameter, initial static bed height, density of the solid, and superficial velocity of the fluidizing medium. Experimental values of minimum fluidization velocity, bed fluctuation, and bed expansion ratios were found to agree well with the developed correlations.     

Direct Numerical Simulation of Hypersonic Boundary-Layer Flow on a Flared Cone

The forced transition of the boundary layer on an axisymmetric flared cone in Mach 6 flow is simulated by the method of spatial direct numerical simulation (DNS). The full effects of the flared afterbody are incorporated into the governing equations and boundary conditions; these effects include nonzero streamwise surface curvature, adverse streamwise pressure gradient, and decreasing boundary-layer edge Mach number. Transition is precipitated by periodic forcing at the computational inflow boundary with perturbations derived from parabolized stability equation (PSE) methodology and based, in part, on frequency spectra available from physical experiments. Significant qualitative differences are shown to exist between the present results and those obtained previously for a cone without afterbody flare. In both cases, the primary instability is of second-mode type; however, frequencies are much higher for the flared cone because of the decrease in boundary-layer thickness in the flared region. Moreover, Goertler modes, which are linearly stable for the straight cone, are unstable in regions of concave body flare. Reynolds stresses, which peak near the critical layer for the straight cone, exhibit peaks close to the wall for the flared cone. The cumulative effect appears to be that transition onset is shifted upstream for the flared cone. However, the length of the transition zone may possibly be greater because of the seemingly more gradual nature of the transition process on the flared cone. Received 20 March 1997 and accepted 21 May 1997     

On the Stress State of a Truncated Conic Shell of Medium Thickness with Square Holes

The stress concentration at the periphery of rectilinear holes in truncated cone shells of medium thickness under axial compression has been measured by the photoelastic method. Maximum stress diagrams for various arrangements of holes are presented and compared in some cases with theoretical data     

Technology showcase electronic penetrometer for field tests

The design and construction of a cone penetrometer for field use is described. The penetrometer is mounted on a frame to which two wheels are fitted for towing the device from one test site to the next. An electric motor drives the penetrometer during the test and simultaneous readings are performed of both cone depth and penetration resistance. The device weighs 70 kg and the maximum force on the cone typically exceeds 1.2 kN. The acquired data are transferred to a microcomputer and after each penetration the result is presented to the operator in graphic form. The microcomputer is equipped with a fairly large RAM memory which serves as storage medium for data during measuring work. Afterwards, data are easily moved to a mainframe computer for analysis.     

Structures and stabilization of low calorific value gas turbulent partially premixed flames in a conical burner

Experiments are carried out on partially premixed turbulent flames stabilized in a conical burner. The investigated gaseous fuels are methane, methane diluted with nitrogen, and mixtures of CH₄, CO, CO₂, H₂ and N₂, simulating typical products from gasification of biomass, and co-firing of gasification gas with methane. The fuel and air are partially premixed in concentric tubes. Flame stabilization behavior is investigated and significantly different stabilization characteristics are observed in flames with and without the cone. Planar laser induced fluorescence (LIF) imaging of a fuel-tracer species, acetone, and OH radicals is carried out to characterize the flame structures. Large eddy simulations of the conical flames are carried out to gain further understanding of the flame/flow interaction in the cone. The data show that the flames with the cone are more stable than those without the cone. Without the cone (i.e. jet burner) the critical jet velocities for blowoff and liftoff of biomass derived gases are higher than that for methane/nitrogen mixture with the same heating values, indicating the enhanced flame stabilization by hydrogen in the mixture. With the cone the stability of flames is not sensitive to the compositions of the fuels, owing to the different flame stabilization mechanism in the conical flames than that in the jet flames. From the PLIF images it is shown that in the conical burner, the flame is stabilized by the cone at nearly the same position for different fuels. From large eddy simulations, the flames are shown to be controlled by the recirculation flows inside cone, which depends on the cone angle, but less sensitive to the fuel compositions and flow speed. The flames tend to be hold in the recirculation zones even at very high flow speed. Flame blowoff occurs when significant local extinction in the main body of the flame appears at high turbulence intensities.     

平头弹丸正撞下钢筋混凝土靶板厚度方向的开裂

主要针对钢筋混凝土靶板在受到平头弹丸撞击下发生的厚度方向开裂的问题进行研究,并提出了一个弹丸低速撞击有限厚度板的二阶段模型。模型中第一阶段为侵彻阶段,弹丸受到混凝土介质的侵彻阻力由静阻力和速度效应引起的动阻力组成;模型中第二阶段为开裂阶段,钢筋混凝土靶板发生动态剪切破坏的最大承载力可以通过静态剪切破坏最大承载力乘以一个动态增强因子得到。该模型可以用来预测钢筋混凝土靶板发生厚度方向开裂破坏的临界能量。模型预测与实验结果吻合较好。     

Characteristics of laminar-turbulent boundary layer transition on a cone

The effect of the unit Reynolds number and the Mach number on the transition on a slender circular cone is experimentally investigated. The perturbation spectra in the boundary layer on the cone are measured. It is shown that the location of the transition is determined by the perturbation level at the frequencies causing transition.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 23–27, November–December, 1985.     

Acoustic scattering of a plane wave by a circular penetrable cone

The paper is devoted to the diffraction of a plane wave by an acoustically transparent semi-infinite cone. The problem of diffraction is reduced to a singular integral equation in the framework of the incomplete separation of variables. The Fredholm property and regularization of the integral equation are discussed. Some important integral representations of the wave field are considered. The detailed study of the far-field asymptotics is given. Expressions for the diffraction coefficient of the spherical wave scattered from the vertex of the cone are considered. The reflected from the conical surface waves and those transmitted across the surface are also discussed.     

Diffraction of a spherical acoustic wave on a cone

An exact analytic solution of the problem of diffraction of a plane acoustic wave on a cone of arbitrary aperture angle was obtained and studied in [1]. For the case of spherical wave diffraction on a cone a formula is known [2] which relates the solutions of the spherical and plane wave diffraction problems. This study will employ the results of [1, 2] to derive and investigate an exact analytical solution of the problem of diffraction of a spherical acoustic wave on a cone of arbitrary aperture angle. Results of numerical calculations will be presented and compared with analogous results for a plane wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 200–204, March–April, 1976.The author is indebted to S. V. Kochura for her valuable advice.     

Development of two-dimensional perturbations on the surface of a tangential discontinuity

A study is made of the asymptotic behavior at long times of initially localized small two-dimensional perturbations of the interface of two fluids in the presence of a tangential discontinuity of the velocity; surface tension is taken into account. The development of one-dimensional perturbations was considered earlier in [1]. The asymptotic behavior of the perturbed region is found, i.e., in the xyt space there is found a cone with apex at the origin such that perturbations tend to infinity with increasing t along rays within the cone, while perturbations tend to zero along the remaining rays. Conditions are found under which the instability of the tangential discontinuity is not absolute, i.e., when these conditions are satisfied, flows with tangential discontinuity of the velocity can take place. These conditions, like the shape of the cone, do not depend on the magnitude of the surface tension.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 12–16, May–June, 1979.     

Numerical and analytical study of transverse supersonic flow over a flat cone

Quasisteady supersonic flow over a flat cone on a plane surface is studied. A formula is derived for the angle through which the flow lines turn at the cone. The results are used to justify the use of two-dimensional simulations of the flow. Peak pressures and total impulses are obtained numerically for various cone angles.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Natural Convection on a Horizontal Cone in a Porous Medium with Non-Uniform Wall Temperature/Concentration or Heat/Mass Flux and Suction/Injection

The steady natural convection flow on a horizontal cone embedded in a saturated porous medium with non-uniform wall temperature/concentration or heat/mass flux and suction/injection has been investigated. Non-similar solutions have been obtained. The nonlinear coupled differential equations under boundary layer approximations governing the flow have been numerically solved. The Nusselt and Sherwood numbers are found to depend on the buoyancy forces, suction/injection rates, variation of wall temperature/concentration or heat/mass flux, Lewis number and the non-Darcy parameter.     

Investigation into the interaction of a shock wave with an acute cone

A numerical investigation has been made into the nonstationary axisymmetric flow which arises from the interaction of a shock wave with a fixed acute cone. A solution has been obtained in self-similar coordinates for regimes in which a shock wave attached to the point of the cone is formed in the gas flow. The region of existence of these regimes has been established and the method of stabilization used to calculate the gas-dynamic functions in the disturbed region. The main attention is devoted to studying the transition from regular reflection to Mach reflection, a study of the features of double Mach reflection, and comparison of the results for the axisynuaetric and two-dimensional cases. The pressure distributions along the surface of the cone are given in a form which makes it possible to obtain dependences valid in a wide range of variation of the intensities of the incident shock wave and for different values of the adiabatlc exponent of the gas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 98–104, May–June, 1980.     

Analysis of a rubber cone tensioned by a concentrated force

Using the constitutive equation of a rubber-like materials given by Gao (1997), this paper investigates the problem of a cone under tension of a concentrated force at its apex. Under consideration is the axial-symmetry case and the large strain is taken into account. The stress strain fields near the apex are obtained by both asymptotic analysis and finite element calculation. The two results are consistent well. When the cone angle is 180°, the solution becomes that of non-linear Boussinesq's problem for tension case.