The XXXth "Caius Iacob" Conference on
Fluid Mechanics and its Technical Applications
25-26 November, 2005
Bucharest, Romania
List of Abstracts
A model for the convective flow in a fluid-saturated porous medium on an impermeable obstacle in a fluid-saturated porous medium is considered where the flow result from the heat released by an exothermic catalytic reaction on the surface converting a reactive component within the convective fluid to an inert product. To particularize, let us assume that Ao B+"heat reaction velocity" =k_0ae-E/RT where: a and T are the reactant concentration and the surface temperature respectively, k0 is a constant coefficient and the E and R constants in the Arrhenius dependence are the activation energy and the gas constant. Semi-similar solutions transform governing partial differential equations in differential systems who are solved by Keller-Box method. Numerical solutions are obtained for a range of parameter values. These show, for large activation energies, that localized rapid change in wall temperature and localized high reaction rates occur near stagnation point.
One presents a part of the theoretical support for an invention patent, based on the method of constant velocity section, concerning the steady and two-dimensional entrance flow of an incompressible and ideal fluid in a channel, because by numerical integration one can not assure the solution stability. One traces the hydrodynamic spectrum of streamline function and velocity distributions in specific areas and sections.
Very few papers deal with the domain decomposition methods for non-linear problems. Most of them regard the variational equations, ie. they come from the minimization of a functional. However, there are many mechanical or engineering problems which are modeled by a non-linear equation which does not come from the minimization of a energy functional. In this paper, we prove the convergence of an iterative method for fixed-point problems, ie. we look for a $u\in V$ satisfying the equation 〈F'(u),v〉= 〈T(u),v〉 for any v∈V. Here, V is a reflexive Banach space, F' is the Gateaux derivative of a convex functional F : V→ R and T : V→ V′ is a contraction operator. As a particular case, if the space V is a Sobolev space, then the proposed method is exactly the additive Schwarz domain decomposition method. Also, in the case of the finite element spaces, our result proves that the multi-level methods (the multigrid method, for instance) can be applied to find the fixed-points of contraction operators.
The paper investigates the stability of a differential constitutive relation with non-monotonic steady flow curve in viscometric creep motion. The proposed constitutive relation,
λ1D1 T /Dt + T = 2 η0λ2 D2 D D/Dt + 2η0 Dis material unstable for a1, a2∈(-1, 1), since admits multiple steady states, at the same values of controlled parameters: (i) values of material constants, λ1, λ2, η0 and (ii) the constant value of applied shear stress. It is proved experimentally that materials which exhibit a yield shear stress behave unstable in viscometric creep motion, at applied stresses in vicinity of the yield value, σ0, and λ2/λ1 < 0.1. The dynamics of the proposed 3-constants differential model (1) is found consistent with experiments performed, with viscoelastic materials as greases or creams, both in cone and plate or double cylinders Couette geometries. In our interpretation, the yield stress is defined by the value of the constant shear stress which corresponds to the coexisting shear rates in the steady flow curve and the plateau region detected in experiments. Therefore, the concept of yield stress is intrinsic related to the dynamics of unstable constitutive relations in viscometric flows.
(where the objective Gordon-Schowalter time derivatives are defined as
Di • /Dt = d • /dt−Ω • + • Ω − ai(D • + • D);
T is the extra-stress, D and Ω are the stretching and the spin tensors and the symbol d • /dt is the material time derivative)
Radiant spherical suspensions have an ε-periodic distribution in a three dimensional incompressible viscous fluid governed by the Stokes-Boussinesq system. We study the border case when the radius of the spheres is of order ε3 and the ratio of the solid/fluid conductivities is of order ε-6. We apply a homogenization procedure by adapting the energy method. The macroscopic behavior is described by a nonlocal law of Brinkman-Boussinesq type and two coupled heat equations, where the radiation and a certain capacity of the vanishing suspensions appear. This result completes those obtained for the thermal flow when the volume of the solid matrix is not vanishing.
A configuration of a hybrid sail system consisting of a solid mast, an impermeable flexible part and a solid leading edge flaps is studied. On this way one obtains a high performance system for ship propulsion. The study includes an analytical, a numerical and an experimental part. For the analytical part the Prandtl's lifting line theory is used, applied to a "wing in mirror". An original method capable to take into account the chord jumps is then used to determine the coefficients of circulation. For the numerical modelling a finite element code is applied. The experiments were carried-out in the "Constanta Naval Academy" wind tunnel.
It is consider a channel which aspirates a viscous fluid from an infinite space. The value of the stream function inside the domain is computed with an algebraic relation deducted from Navier Stokes equations; on the contour it is computed using boundary conditions in the case of small velocities. The computation of stream function in each point of domain is made by a C++ program which after computation saves stream function values and, ulterior, velocity values in .txt files. Besides, the program makes a graphical representation of stream lines spectrum, converting stream lines values into a lines and colours spectrum, and of velocities. From a theoretical point of view the paper proves scientifically the patent named Method and Device for Air Calibration of Gas Flow meters, having a high accuracy.
A vortex model of a round parachute in an incompressible fluid is presented. The canopy surface is replaced by a system of circular vortices located in planes perpendicular to its symmetry axis. The wake is modeled as a vortex sheet that is emanating from the parachute sharp mouth and vent borders subject to the condition that the pressure on these sharp borders remains finite. The wake is allowed to roll up freely. Mathematically the fluid dynamics model leads to a system of four equations of which one is an integral equation that represents the link between the canopy vortex distribution and the normalwash, the second and third give the motion of the free wake, and the fourth one relates the variation of the vorticity on the entire canopy to the vorticity just issued at the sharp edges. A numerical method for solving this system is then given. The wake is replaced by a system of a discrete ring distribution of small, but finite core radii. These radii vary so that the core volumes remain constant. The vortex ring emission problem is solved by in iterative process, so that the flow remains smooth at the canopy edge(s). By this iterative process the vortex position and the time increment are calculated at any time step. The previously emitted vortex rings are convected during the time increment. To prevent the non-realistic vortex scattering, the time increment is divided into a number of sub-steps. Finally, the load distribution over the canopy is calculated at each time step.
Using the method of images we establishe the hypersingular integral equation for the pressure jump across an oscillating airfoil in a tunnel. Employing appropriate quadrature formulas we calculate the jump of the pressure field and then a numerical integration provides the drag coefficient. We notice that for some oscillatory motions the drag is negative i.e. it appears a propulsive force.
A new numerical algorithm for acoustic noise generation is developed. The acoustic approach involves two step comprising an incompressible flow part and an inviscid acoustic part. The acoustic part can be started at any time of the incompressible computation. The formulation can be applied both for isentropic flows and non-isentropic flows. The model is validated for the cases of an isentropic pulsating and oscillating sphere.
Starting from the classical theory and practice of the airfoil, one presents the mathematical relations to obtain the greatest axial propulsion force, for a given mechanical driven power of an aircraft or ship propeller. One put into the evidence the best aerodynamic or hydrodynamic profiles and also its optimum incidence angle for different radii of the propeller blades. In the present one try to apply these results for the propulsion of an small environmental friendly ship, using the solar energy source by means of photo-voltaic panels and which sails in our biosphere reservation Danube Delta.
A study of small perturbations propagation in a simple flow-structure problem shall be made. The flow of a compressible inviscid and isentropic fluid through a nozzle with elastic walls is precised. In presence of a coupling with a structural element bounding the fluid we investigate the influence of Mach number of the unperturbed flow on the speed of propagating waves. Conclusions and final remarks shall be made.
Main topics: hyperbolic systems of conservation laws, gas dynamics.
An analogue of the genuinely nonlinear character of an one-dimensional simple waves solution is identified and essentially used for the construction of some multidimensional extensions (simple waves solutions, regular interactions of simple waves solutions).
A class of exact multidimensional gasdynamic solutions is constructed whose interactive elements are regular. An admissibility criterion is formulated and exemplified for selecting the regular interactive solutions "of a genuinely nonlinear type" where other ("hybrid") solutions are formally possible.
An efficient and accurate calculation method for the prediction of three-dimensional flows with large regions of separation is described. The method is based on a stability/transition interactive boundary layer approach employing an extension to three-dimensional flows of the modified Cebeci-Smith turbulence model. The method is first applied to the calculation of the flowfield about wings at low Reynolds numbers where the transition location is calculated within the three-dimensional separation bubble. The method is then applied to three-dimensional flows at higher Reynolds numbers and the boundary layer parameters are compared with experimental data. Results show good agreement with data and demonstrate the importance of calculating the onset of transition location. The method is also applied to the calculation of wing lift coefficients up to stall. Results demonstrate the ability of the method to predict three-dimensional separated flows reliably, including near stall conditions, showing the potential of the method as a practical and efficient design tool for high lift applications.
Flow field generated by aircraft manoeuvres and departure at high angles of attack are highly complex due to the simultaneous presence and interaction of the three-dimensionality, unsteadiness, separation and reattachment influences. In order to come to grip with the modeling of such a formidable flow regime it is necessary to start with simpler flow regime in which flow separation and reattachment play a fundamental role. Two-dimensional dynamic stall fits the note and so it has been investigated. An axiomatic aerodynamic model has been developed for the general motion of a two dimensional airfoil as it passes in and out of stall, which gives realistic unsteady loads as compared to experimental values.
We study the Stokes system with slip boundary condition in a domain with periodic inclusion of the size of the period. At the limit we obtain a Darcy's law. This model describe the flow of an incompresible viscous fluid through a porous medium under the action of an exterior electric field
The exact solutions corresponding to the primary motion of a second grade fluid caused by the sine and cosine rotational oscillations of a sphere are presented in terms of modified Bessel functions and . The similar solutions within an oscillating sphere are obtained as a limiting case. For all solutions tend to those for a Newtonian fluid.
This paper deals with the study of laminar non-stationary flow of a viscous fluid between non-axial cylinders. We are using the mediation method in Navier-Stokes equation. The problem is reduced to a stationary one for which the conform domain transformation in a circular corona can be applied. For this problem, the solution is determined by using the variables separation method. The flow is accepted for different forms of the pressure gradient : linear, exponential study and stability analysis.
The standard discretization techniques (FDM, FVM, FEM) have limitations in presence of mesh distorsions, free surfaces, deformable boundaries. The remeshing techniques is not a solution because it can be expensive and complicatted for complex geometries. In the last years, a new technique have been developed and used to solve partial differential equations of computational mechanics. This technique know as FREE MESH or MESHLESS method is one in which the nodes-elements conectivity matrix is not necessary in computational process because the computational domain is compose by a set of nodes. The main idea of the method is representation of the field variables (and its derivatives) in the support domain through shape functions. In the present paper, we construct the shape functions using the radial point interpolated method. The strong form of equations is use for all interior nodes and on the Newman boundaries, we use the local Petrov-Galerkin weak form. Numerical examples of a few incompressible flow problems are presented.
The work gives a method for calculating the tractions of the fluid motion, determined by an incoming plan pressure wave, on an artificial hair cell transducer structure. The sensing element of the transducer is a standing high aspect ratio cilium in the shape of a narrow thin curved beam, which can be easily fabricated in micro/nanotechnology. The boundary conditions, stating the cancellation of the velocity components on the solid beam, yield a 2-D system of three integral equations, over the beams's surface, for the traction components.
The paper presents the fundamental solutions of compressibile Stokes equations. These equations are obtained, by liniearisation, from the compressible Navier-Stokes equations for barotropic fluid. They are consisting in continuity equation and balance of the momentum with the pressure and velocity fields as primitive variables. It is supposed that the pressure and velocity fields are harmonic in time with the same angular velocity. By the method of Fourier transform the problem is reduced to finding the fundamental solutions of the Hemholtz equations. The general solutions of the oscillatory compresible Stokes equations yield the solution of oscillatory compressible inviscide fluid flow as particulare case. Using the fundamental solutions the motion induced by an oscillating sphare are presented and a comparision between the solutions obtained for viscousfluid and inviscide fluid is presented.
This work presents a computational study of the steady, axisymmetric, viscous flow around two circular cylinders in tandem. The vorticity - streamfunction formulation of the Navier - Stokes equations are chosen. Numerical solutions have been obtained in bipolar cylindrical coordinates. The finite difference method was used to discretize the model equations. A nested multigrid - defect correction algorithm was employed to solve the discrete equations. Different cylinders spacing and sizes were considered for the upstream cylinder Reynolds number up to 20. Vorticity and pressure distributions on the cylinders surfaces and drag coefficients are presented and compared with those calculated for an isolated cylinder.
Some boundary value problems of Dirichlet, Neumann and mixed type for the Stokes resolvent equations are studied from the point of view of the potential theory. Existence and uniqueness results as well as boundary integral representations of classical solutions are given in the case of certain bounded domains. Examples and applications are included.
This paper deals with the flow of a viscous conducting fluid in a pipe with arbitrary cross-section and arbitrary wall conductivities under the influence of a transverse magnetic field. For the numerical solution a finite element discretization is considered in the domain corresponding to the fluid and inside the walls of the pipe. When the outer medium is considered with an arbitrary conductivity the finite element method is coupled with the boundary element method. The proposed method is illustrated with numerical example. boundary element method
The paper presents mathematical models and methods for the optimization of wind propelled sail airfoils. In order to solve the boundary value problems, direct or inverse methods have been used. Both cases of wind circulation around the sail airfoil and without circulation have been approached. For sail optimization purposes, a slatted sail is considered assimilated to a point vortex.
The aerodynamic shape of a sail, with an optimum curvature, assures a high performance in using the power of the wind. The paper describes the models and the practical methods to increase the wind pressure consumption, as well as to make easier the flowing of the consumed wind pressure. From the oldest times, the man used the wind as a propelling means for crafts. For a long time, they could sail before the wind as the sail propelling plants were primitive and at these times hey didn~Rt know the modern system of building and trimming of sails.In order to use the wind force for propelling a ship or craft, it is necessary a special arrangement that shored allow the spread of a cloth exposed to the wind.
In this paper we set the mathematical model of a saturated-unsaturated water infiltration into a porous medium and we present an existence result for Richards' equation.
We consider an unconfined homogeneous, isotropic aquifer with a steady-state Darcian groundwater flow. The real case of groundwater pumping system in Curtisoara area is considered. The water quality of phreatic aquifer is strongly determined by the riverâ~@~Ys Olt water quality. For this aquifer we propose a numerical method to solve the equation describing the two dimensional dispersion of a pollutant coming from the river Olt toward the aquifer. A numerical solution, obtained with the ADI procedure is used. The influence of the pumping regime on the pollution phenomenon is considered. Our work is based on two models: the first one is a mathematical model describing the water advance in a saturated porous soil using the potential flow theory, and is applied for Curtisoara pumping system and the second model solves the dispersion equations for the groundwater in this area. The results give important information regarding the evolution of groundwater quality.
This paper reports a numerical heat transfer study, which is part of our efforts devoted to defining a cooling concept for a high performance synchronous motor that has a High Temperature Superconductor (HTS) field winding. Whereas the rotor of this machine is the HTS DC field winding, the armature is a high current AC copper "air winding" that is siege of intense power dissipation by Joule and variable magnetic field effects. Consequently, prototyping a low weight/volume motor results in a complex thermal design where an important role is played by the thermal management of the AC winding. Standard lumped thermal circuit models deliver fast, design class results that reveal the heat transfer underlying features. However, there are several difficulties related to this approach consistent with the specific assumptions (e.g., concentrated heat sources, lack of detailed thermal load information, etc.) that may be solved by a more detailed convection and conduction heat transfer model, conveniently solved by numerical analysis, e.g. by FEM technique.
Electroconvection in nematic liquid crystals is a paradigm for pattern formation in anisotropic systems, exhibiting a rich variety of dynamical structures. We present the results of a bifurcation analysis of electroconvection in a planar layer of nematic liquid crystals, based on the recent introduced weak electrolyte model. The linear stability analysis show the existence of steady as well as Hopf bifurcations involving four oblique travelling rolls. Spatiotemporal chaos in the system is also discussed.
Was experimentally determined that, from certain gas flow rates, the bubble column emitted by porous diffusers begins to describe a helical movement is breaking up having the appearance of a fir. The gas flow rates corresponding to this phenomenon are determined.
We consider the saturation model for immiscible flow in porous media. We prove that a particular basic wave solution is stable. In contrast, the planar interface in immiscible Hele-Shaw flow is always unstable. Our stability system contains some terms negelcted by prevoius authors. The result is obtained by direct integration of the stability problem.
The modern injection equipment produce a polution level of the emisions which complies with the Europen Norms, a low fuel consumption level as well as a low level of noise of the Diesel engine. These antagonistic characteristics are achived mainly by optimizing the burning process of the fuel in the burning chanber of the Diesel engine. Obtaining a mixture of optimal aer/fuel ratio depends mainly on a adequate spraying of the fuel such as the drops are as small as possible as well as on the directioning of the pulverised fuel jets by the injector sprayer. For the conventional injection systems, the peak pressure is the the most important measure for the quality of the forming the mixture in the burning chamber. Electro-hydraulic analogy as base of the sonic theory developed by the Romanian scientist George Constantinescu, leads to the possibility of modeling hydraulic systems by electric circuits through sonic resistances, capacities and inductivities. Electro-hydraulic modeling of the high-pressure pipe and injector allows evaluating the adapting condition for optimal adaptation of a chain of sonic qvadripols. By considering the sonic injector circuit at injection phase and writing the transfer functions associated to the sonic qvadripols, we are able to obtain the global transfer function, in its operational form. By solving the circuit we can obtain sonic potential differences and also sonic current in operational form. The are the expressions of pressure and deliveries differences in time range, after solving the Laplace transforms. Experimental results show the highest above the pressure peak at injector level, also it's duration, the amplitude of the second peak and the attenuation in time domain of the pressure signal.
A brief survey of spline approximation techniques for solution of first kind integral equations is provided. In this paper we realize a study on spline-collocation method in combination with different type of regularization algorithms (like multilevel Landweber iteration, and a multilevel Tikhonov scheme with zero'th order and first-order stabilizers). All these methods are applied to several (linear) first kind Fredholm equations. Advantages of developed methods are proved by numerical experiments (coming from some real world problems) when compared to some standard techniques.
This paper deals with the numerical methods that conserve a certain differential form, and their application in the study of the unsteady non-linear heat transfer and fluid flow phenomena. The results of the proposed numerical schemes are compared with the analytic solutions for some particular cases.
The aim of this paper is to introduce the dual primal boundary element tearing and interconnecting (BETI-DP) method with Dirichlet and hypersingular boundary integral operator preconditioners. In previous articles BETI and coupled FETI/BETI methods were introduced. As a natural continuation we present here the BETI-DP method and discuss few general choices of the dual spaces for the three dimensional case. We show that the condition number of the system matrix equiped with the Dirichlet and with the hypersingular boundary integral operator preconditioner behaves in the same manner as the condition number of the system matrix equiped with the Dirichlet preconditioner in the FETI-DP method.
The paper is concerned with the numerical solution of the quasi-variational inequality modelling a contact problem with Coulomb friction. After discretization of the problem by mixed finite elements and with Lagrangian formulation of the problem by choosing appropriate multipliers, the duality approach is improved by splitting the normal and tangential stresses. The novelty of our approach in the present paper consists in the splitting of the normal stress and tangential stress, which leads to a better convergence of the solution, due to a better conditioned stiffness matrix. This better conditioned matrix is based on the fact that these blocks diagonal matrices obtained, contain coefficients of the same size order. For the saddle point formulation of the problem, using static condensation, we obtain a quadratic programming problem.
This paper is one of a set of articles dealing with solutions to PDEs or ODEs using the wavelet - Galerkin method. In order to approximate the solution, a couple of families of coefficients are need; they occur in wavelet series and the are involved in discretizing differential equations that represent mathematical-mechanical models. Following some earlier ideas (see Reference list), we have achieved several algorithms and MATLAB - based programs allowing to obtain high precision results for the necessary functionals. Here it is described the MATLAB evaluation of the integral
A linearized analysis is performed in this paper in order to analyze the onset of the Darcy-Brinkman convection in a fluid-saturated porous layer heated from below, by considering the case when the fluid and solid phases are not in local equilibrium.| The problem is transformed into an eigenvalue equation which is solved in this paper by using an one-term Galerkin approach. Finally, an explicit relationship between| the Darcy-Rayleigh number based on the fluid properties R and the horizontal wave number k is obtained. Minimization of R over k is performed analytically and finally, critical values for R and k are obtained for various values of the three parameters of the problem, namely the Darcy number D, the porosity-scaled conductivity ratio g and the scaled inter-phase heat transfer coefficient H.
The paper deals with the behaviour of the Endless Column, as a linear slender structure, under the gusts supposed to act on its natural site. Slenderness is Column~Rs most intriguing structural parameter although during its long service of almost seventy years any sign of aeroelastic instability never occurred. On the contrary in the most severe climatic conditions ever recorded at Targu-Jiu the Column remained standing motionless. Its elastic response to wind gusts was mathematically developed in the paper by using d~RAlembert principle. The gust action was expressed by its jerk, a mechanical entity firstly used by Jacobi in his doctoral thesis on 13 August 1825. The theoretical response obtained as the horizontal displacement of Column~Rs top was represented graphically as a decreasing function in time. The influence of damping forces was disregarded since the time of gust action was too short to allow them showing any effect.
The work is devoted to several aspects of behavior of 2D micropolar fluid flows. We prove existence of locally in time of solutions.
The authors identify the temperature fluctuations with proper expressions that result from an integro-differential formulation of the energy equation. These expressions are called FLUONS. The dyna-mics of fluons is assumed to be different from the molecular one. The physical-mathematical model includes:It is proposed a probabilization of the fluons ensemble in Markov-type processes. An illustrative numerical example that has the sum expressions for fluons as the starting point is also presented.
- the linearity of the sum expressions, leading to arbitrary (un)grouping of fluons;
- the big but finite number of fluons, that allow the change from determinism to chaos, through fluctuations;
- the application of the energetic minimum and equipartition principles.
A new model of a barotropic inviscid flow is introduced, in order to establish a new (simpler) form of general PDE of the velocity "quasi-potential" for these flows. This model consists mainly in using a new three-orthogonal curvilinear coordinate system (one of them being tied to the local entropy value and another being an intrinsic one). The choice of this new orthogonal curvilinear coordinate system (with two coordinate curves lying on the isentropic surfaces) presents the advantage of enabling the treatment of any 3-D flow (even rotational) as a "quasi-potential" 2-D one, on the respective isentropic rigid surfaces (a particular case of "D. Bernoulli" ones for an isoenergetic flow), introducing a 2-D velocity "quasi-potential", specific to any isentropic surface. On these surfaces the streamlines are orthogonal paths of a family of lines of equal velocity "quasi-potential" (equi"quasi-potential" lines). The method can be generalized for the true "D. Bernoulli" surfaces (the steady flow case). This general method can be extended to some special (but usual) cases in magnetoplasmadynamics (namely neglecting in the expression of the total electric current density the terms given by the densities of the induction and convection electric currents and also, in the general differential equation of motion for the non-isentropic flow of an inviscid electroconducting fluid in an external magnetic field the term due to the electric charges in the considered fluid medium, in the non-relativistic theory). Taking into consideration the flow vorticity effects, there always are some space curves (Selescu) along which the vector equation of motion admits a first integral in the general case. In the particular case of a fluid having an infinite electric conductivity (the highly ionized plasma), these curves also are the isentropic lines of the flow, in both cases enabling the treatment of any 3-D flow as a potential 2-D one
The forces acting on a liquid drop (with radius $a$), immersed in a surrounding immiscible liquid, are investigated theoretically. Under simulated microgravity conditions, when the drop and the bulk surrounding liquid have the same density, the drop is initially at rest and it is called free drop. Then, it is supposed that the initial interfacial tension $\sigma_0$ is lowered to $\sigma_1$ value. Simultaneously, an interfacial tension gradient ($\Pi= \sigma_0 -\sigma_1$) appears, which in our experiments is generated by injecting, on the drop surface, of a chosen quantity of surfactant, much smaller than the volume of the drop. This interfacial tension gradient, firstly, produces a real surface flow (called {\it Marangoni flow}). Further, the drop surface is considered as a two-dimensional liquid interface, with constant surface density and surface viscosities, moving with a distinct front (noted $\theta_f$, in spherical coordinates), which advances continuously. As a consequence of the surface flow, a hydrodynamic pressure will act on the drop and determine various drop movements, especially deformations and oscillations, as well as waves and translational motions. Furthermore, we considered the drop liquid, the bulk surrounding liquid and the surface liquid as Newtonian liquids, which are incompressible and viscous with constant densities and viscosities. From the continuity and Navier-Stokes equations, with appropriate boundary conditions at low Reynolds number, we calculated a general relation of the $F_p$ resultant of the pressure forces, acting on the drop. It is observed that the $F_p$ resultant force depends on the $\theta_f$ angle, namely on the extent to which the drop surface is covered with surfactant. Also, it depends on the interfacial tension gradient, drop volume and surface viscosities, and on the drop radius. A first observation is related to the $F_p$ resultant force, which cancels for $\theta_0\approx 68^{o}$, namely, there is a value of drop surface coverage with surfactant for which $F_p = 0$. The propulsion (lifting) force $F_p >0$, responsible for the upward movement of the drop, and therefore, the translational motion of the drop appears only when the coverage of the drop with surfactant is greater than $\theta_0$. For $0 < \theta_f < 0$, the resultant force is negative ($F_p <0$) and it acts like a "hammer" on the drop. It appears that this force is used for the other type of movements except translations. For small $\Pi$ values of the interfacial tension gradients, the drop behaves like a not deformable drop. For high $\Pi$ values of the interfacial tension gradients, the instabilities of the drop could appear which can be waves on the drop surface, oscillations of the entire drop, rotations and deformations of the drop with possible drop fission at the highest $\Pi$ values.
The aim of this work is to propose a mathematical model for describing the lubrication by the molten powder of the mold-strand gap in the vicinity of the meniscus. The molten powder is considered an incompressible, viscous fluid and the flow is modeled by the Reynolds equation. We study here the simplified case when the surface between the powder and the steel is supposed to be rigid. Some existence and uniqueness results are then established using the variational formulation of the problem. Finally, we analyze the pressure distribution of the molten powder film and we study the effect of the powder viscosity on the powder film pressure.
The paper presents the main issues and preliminary results related to the development of a library of codes for the numerical solution of steady and unsteady Euler and laminar Navier-Sokes equations. The incompressible flows are modeled using Chorin's pseudo-compressibility approach. The numerical solvers proposed herein are based either on a cell-centered second-order finite-volume or on a discontinuous Galerkin spatial discretisation of the governing equations. The convective fluxes are calculated in an upwind manner using an approximate Riemann solver. The time discretisation is fully implicit and second order accurate and is coupled with an explicit dual-time marching scheme in order to avoid the solution of huge nonlinear algebraic systems. The paper presents the algorithms used and provisional numerical results and comparisons for two-dimensional flows are included.
The use of active control to get better characteristics of unsteady internal and external flows is the ultimate goal of the research presented in this paper. Usually, unsteady flows are calculated using Euler and/or Navier-Stokes solvers. Until now, the development of such solvers has reached a considerable level of accuracy and robustness. Further, the efficiency of numerical simulation of an unsteady flow dramatically increases if the unsteady solution is a small perturbation about a steady-state flow, due to disturbances occurring at the boundaries of the flow domain. The main difficulty related to the flow simulation is that any CFD (Computational Fluid Dynamics) technique generates discrete systems with a very large number of states. In order to design an efficient control, the flow solver must be not only accurate and numerically effective, but also it must have a low number of states. The aim of this paper is to analyze and implement methods for model reduction of CFD systems using representative governing equations.
Present-day tendency in maritime transportation domain is represented by designing and building of bigger, faster and more energy-saving ships but at the same time having a required level for stern hull structure noise and vibration more stricter. A ship hull lines design shape, for reaching (obtaining) high hydrodynamic qualities imposes aiming towards following three main objectives: - to minimize forward resistance; - to improve propulsion performance; - to increase the global hydrodynamic stability. A fine wake distribution from an immediately upstream propeller parallel plane disk can leads to: increasing the propulsion efficiency (output), reducing the formation of propeller cavitation (having as an indirect consequence decreasing of noise and vibration level induced in the stern structure). Moreover, the global hull hydrodynamic stability improving by using of a special kind of stern having certain architecture (more appropriate), can not but favourable. Evidently, the dynamics of a cavitating propeller depends on system environment in which it is operating: in this sense the flow field in the case of a propeller mounted behind of a ship hull is very different from that one in an open water test or in a section of a cavitation tunnel. Thus, a propeller that is very efficient in open water can not be suited for a certain kind of stern shape. Due to this reason the wake distribution in the propeller disk plane represents a key factor for designing of a ship hull surface. With a view to fulfilling of the desiderata mentioned above the authors of this project propose a new stern shape concept: with crenellated-corrugated sections (Tanasescu's stern shape). Using the stern shape new concept could imposed lead to improving of water particles axial velocities distribution in propeller disk with a view of a propitious dynamical coupling between propeller upstream flow and propeller through flow. Much more, a stern shape having crenellated-corrugated stern sections can combine the high speed with seakeeping upper characteristics. As supplementary background for justification of our new stern concept having crenellated-corrugated sections we may mention: - stream tube theory (the water particles axial velocities distribution at entrance in the propeller disk can be configured favourably - homogenized - by comprising the radial crenellated-corrugated stern sections in a stream tube that includes also the propeller disk), - Bernoulli effect (increasing of fluid (water) particles flow velocities of fluid (water) particles in the regions within which the fluid pressure is decreased)
This talk deals with the homogenization of some nonlinear problems arising in the modelling of chemical reactive flows through the exterior of a domain containing periodically distributed reactive obstacles (grains). We shall be interested in getting the effective behavior of such reactive flows involving diffusion, different types of adsorption and absorption rates and chemical reactions which take place at the boundary of the obstacles. Also, we shall consider the case in which the fluid is allowed to penetrate the grains and the reactions take place therein. The effective behavior of these reactive flows is described by new boundary-value problems, containing extra zero-order terms capturing the effect of the diffusion, adsorption, absorption and chemical reactions.
This paper deals, in the first part, with the existence of harmonic waves in polynomial third grade fluids. The main results, based on some older remarks of the author, concern the existence / non-existence the propagation of discontinuities, like spherical and cylindrical acceleration waves, all important cases (referring to the signum of the constitutive coefficient α1). It was proved that, like in the case of linear viscous fluids, acceleration waves (spherical and cylindrical) do not propagate for 0<α1. It is proved also that, these discontinuities can propagate if the subclass of third grade fluids with α1< 0 is considered.
The great developing of numerical analysis of the dynamic systems emphasizes the existence of a strong dependence of the initial conditions, described in the phase plane by attractors with a complicated geometrical structure. The complexity of the geometrical structures of such attractors leads to the notion of strange attractor. Strange attractors are defined in many ways but we adopt here the definition of Holmes and Guckenheimer, an attractor is strange if it contains a homoclinical transversal orbit. The Lyapunov exponents are used to determine if there is a real strong dependence on the initial conditions: there is at least a positive exponent if the system has a chaotic evolution and all the Lyapunov exponents are negative if the system has not such an evolution. To draw these conclusions is sufficient to determine the largest Lyapunov exponent, which is easier to calculate. In this paper we shall use the greatest Lyapunov exponent to study two well-known problems who leads to chaotic motions: the problem of the buckled beam and the panel flutter problem. In the problem of the buckled beam we verify the results obtained with the Melnikov theorem with the maximum Lyapunov exponent. The flutter of a buckled plate is also a problem characterized by strong dependence of the initial conditions, existence of attractors with complicated structure existence of periodic unstable motions with very long periods (sometimes infinite periods). Several authors, including Holmes, Holmes and Marsden, Dowell have analyzed this system from different points of view. Using the largest Lyapunov exponent method we obtain the results obtained by Dowell.
The paper studies the planar motion of a plate with holes on a horizontal rigid half-space, with dry friction. The resultant friction force and the pivot friction moment results in closed forms of Legenrde's elliptical integrals for plates with circular boundaries. Numerical application is given for a cicular plate with an excentric hole.
We present new applications of a recent order-monotonicity result on the existence, positivity and uniqueness of solutions for nonlinear evolution equations in abstract Lebesgue spaces.
We consider a non-Fickean diffusion model for binary mixtures. Here, the flux is not governed by Fick's law, it is governed by an evolution equation, derived from the partial balance momenta under hypothesis of ``small'' diffusion velocities. The model is illustrated by two examples. The first example assumes a binary non-reactive mixture with zero average velocity at thermal equilibrium. In this case, Fick's model is recovered as a first order perturbation. The second example adds chemical reactions. There is a significant difference between the shock-wave structure in our model and the classical Zeldovich-Neumann-Doring description.
This work studies the optimum rendezvous in minimum time of two space vehicles on circular and elliptical orbits, the surveyor vehicle being equipped with a low thrust installation, their motion equations being written in the three-dimensional space, in relative motion; the space origin being the target vehicle. The variational problem is of Lagrange type (or Mayer type) and the optimum controls to be determined being the acceleration due to thrust. This controls are impose at constraints. By means of the Legendre-Clebsch condition it is demonstrated that the formulated optimization problem is, indeed, a maximum problem. The optimization of this problem is solved applying the Pontriaghin maximum principle. So, the above defined problem of optimal control is transformed in a well-known into a two point boundary problem. The nonlinear differential equations of the extremals where any kind of approximation was eliminated are precisely integrated by a numerical method, shooting. So, this method becomes applicable for any kind of circular and elliptical orbit of the target. The calculations were performed for circular and elliptical orbits around the Earth.
The paper analyzes two speed regulators for a uniform response in the case of some mechanism with periodic motion. For the first mechanism with one degree of freedom, the conditions for uniform motion are computed in three cases: I. the vibrating mass is a rigid coupling with the elastic force and the damping force, II. the vibrating mass is a rigid coupling with the hardening elastic force and the damping force, III. the vibrating mass is a rigid coupling with the elastic force, the hardening elastic force and the damping force. For the second mechanism with two degree of freedom, the vibrating mass is serially tied with the elastic and damping forces. This analysis leads us to the study of some Duffing's type equations. The obtained equations being nonlinear, we apply the average method and the Van der Pol method. The stability of solutions in the phase's space, the limit cycles for a uniform response of the system and the resonance conditions are studied.
The purpose of this paper is to derive accurate approximation methods to the non-linear quantum Boltzmann equation for a gas of interacting Fermions. Our study refers to a space-homogeneous model where the main mathematical difficulties are introduced by non-linearity in the collision operators and by Pauli's exclusion principle imposed to the one particle distribution function.
It is well known that at high angles of attack, the aerodynamic characteristics of airplanes versus angle of attack behave a hysteresis loop. In this paper a model based on ordinary differential equations for the lift and pitching coefficients is described. It is analyzed the short period case with the aerodynamic coefficients given by equations These equations yield a dynamic model which simulates the hysteresis phenomenon. With the above model, the stability and command characteristics of airplanes are analyzed by comparison with the standard techniques based on delay
This paper focuses upon the elaboration of a method of optimization in problems of pursuit based on the results of the theory of optimal damping. Thus, we determine the function of control which minimizes the functional representing the index of performance, in the given conditions of differential and algebraic restrictions of the variables of state, respectively of command. We analyze the cases which suppose the linearization of the equations of movement and of the index of performance.
The main goal of the paper is to find the solution of the dynamical system that represents the kinematics of steady flight, with respect to the flight path, expressed as continuous closed form functions. Flight kinematics represented as aircraft kinematics relative to Serret-Frenet axes system, followed by the kinematics of this axes system relative to the Earth, provides the kinematics' differential system of the steady flight relative to aircraft trajectory, named "extended steady flight". Stating the starting values for the kinematics variables and common assumptions regarding the differential system, the solution of this system may be found by numerical methods or as an implicit trigonometric equation, sin(x(t))=f(t) . Having in mind the uniqueness of this solution, we have derived a method to construct the analytical closed form of the function with values x(t), comparing the variations properties for the function x(t) relative to those for the function f(t). Finally the numerical values of the function x(t), corresponding to the kinematics variables, and the analytical ones are compared to verify this continuous closed form function. Analytical solution, x(t), requires the zero values for the derivative of f(t) and sign establishment for the derivative of x(t), using a recurrence formula, to derive the values of a specific function named "residual function" in a recurrent manner too.
The classical problem concerning the motion of a material system of particles, in the frame of newtonian mechanics, was considered by many scientists in last two centuries. As regards the problem of relative motion of a material system of particles, S. Koenig established the expressions of linear momentum, angular momentum and kinetic energy, and obtained the corresponding conservation theorems, using a non-inertial moving frame, which has the origin located in the mass center and is translating (so called Koenig frame). Similar results were derived in the case of the motion of a rigid solid (see L. Dragoss, Principles of analytical mechanics, Ed. Tehnica, Bucuresti, 1976). This work describes the relative motion of a continuous material. One obtains the expressions of linear momentum, angular momentum and kinetic energy, as well as the equation of relative motion and the theorem of pseudo-angular momentum. Using the description of relative motion due to V. Arnold, we generalize V. V\^alcovici theorems concerning the relative motion of discrete systems of particles, and we derive equivalent forms of the generalized Koenig theorems obtained by C. Iacob. Finally, we analyze the particular case of a rigid continuum.
A new method for systems stability analysis is presented. This method is called weight functions method and it replaces the problem of Liapunov function finding with a problem of finding a number of functions (weight functions) equal to the number of first order differential equations describing the system. It is known that there are not general methods for finding Liapunov functions. The weight functions method is simpler than the classical method since one function at a time has to found. Particular case of holonomic oscillating systems with dependent variables is analysed and cases in which stability of constrained system can be estimated from stability of free system are evinced.
In this paper, an inverse flight dynamics problem closely related to modern aerial combat characteristics is formulated. Specifically, the problem of how an airplane should be controlled in order to rapidly change its orientation toward a potential target is considered. Such "reorientation" or "pointing" maneuvers are defined, in the present approach, by prescribing the time-variations of the following three state variables: the airplane's azimuth angle, longitudinal attitude angle and sideslip angle. An original solving algorithm for the considered inverse dynamics problem is presented. The control functions corresponding to the desired reorientation maneuver are determined using an iterative procedure consisting, mainly, in (a) solving a second-order nonlinear differential system and (b) solving a linear time-variant algebraic system. Numerical simulation results concerning a coordinated (zero sideslip) reorientation maneuver are included.
| Home |