scholarly journals Vertical Plane Buoyant Jets and Fountains in a Uniform Stagnant Ambient Revisited

Author(s):  
Panagiotis Minos ◽  
Panos N. Papanicolaou

Abstract Planar, vertical buoyant jets are of particular interest, both for research and practical purposes for being related to the disposal of the effluent from wastewater treatment plants or saline, a by-product from desalination plants into a body of stagnant fluid. Analytical, closed form solution is derived for plane buoyant jets based on a buoyant jet width parameter proposed by List and Imberger (1973), and compares to earlier laboratory experiments satisfactorily. The derived entrainment coefficient as a function of the local Richardson number of the flow, takes two asymptotic values for jet-like and plume-like flows, while in fountains it takes values lower than that in jets. Laboratory experiments were performed to measure the penetration height of vertical plane fountains with initial Froude number in the range 20 to 130 using shadowgraph and Planar Laser Induced Fluorescence (PLIF) techniques. Interest was focused on the maximum and terminal, steady-state penetration height before the flow direction reversed. The flow was found to be in a state of unstable equilibrium, as it deviated from the vertical axis, swinging on either side. The equations of motion have been solved numerically using the derived entrainment coefficient function, and the results are congruent to earlier and present experiment for vertical fountains.

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 232
Author(s):  
Panos N. Papanicolaou ◽  
George C. Stamoulis

Turbulent round buoyant jets and fountains issuing vertically into a linearly density-stratified calm ambient have been investigated in a series of laboratory experiments. The terminal (steady-state) height of rise and the mean elevation of subsequent horizontal spreading have been measured in positively buoyant jets (at source level), including pure momentum jets and plumes, as well in momentum-driven negatively buoyant jets (fountains). The results from experiments confirmed the asymptotic analysis that was based on dimensional arguments. The normalized terminal height and spreading elevation with respect to the elevation of injection of momentum-driven (positively) buoyant jets and fountains attained the same asymptotic values. The numerical results from the solution of entrainment equations, using an improved entrainment coefficient function, confirmed the results related to buoyancy dominant flows (plumes), while their predictions in momentum-driven flows were quite low if compared to measurements.


Author(s):  
L. Beji ◽  
M. Pascal ◽  
P. Joli

Abstract In this paper, an architecture of a six degrees of freedom (dof) parallel robot and three limbs is described. The robot is called Space Manipulator (SM). In a first step, the inverse kinematic problem for the robot is solved in closed form solution. Further, we need to inverse only a 3 × 3 passive jacobian matrix to solve the direct kinematic problem. In a second step, the dynamic equations are derived by using the Lagrangian formalism where the coordinates are the passive and active joint coordinates. Based on geometrical properties of the robot, the equations of motion are derived in terms of only 9 coordinates related by 3 kinematic constraints. The computational cost of the obtained dynamic model is reduced by using a minimum set of base inertial parameters.


Author(s):  
Brian J. Olson ◽  
Steve W. Shaw ◽  
Christophe Pierre

This paper investigates the use of order-tuned absorbers to attenuate vibrations of flexible blades in a bladed disk assembly subjected to engine order excitation. The blades are modeled by a cyclic chain of N oscillators, and a single vibration absorber is fitted to each blade. These absorbers exploit the centrifugal field arising from rotation so that they are tuned to a given order of rotation, rather than to a fixed frequency. A standard change of coordinates based on the cyclic symmetry of the system essentially decouples the governing equations of motion, yielding a closed form solution for the steady-state response of the overall system. These results show that optimal reduction of blade vibrations is achieved by tuning the absorbers to the excitation order n, but that the resulting system is highly sensitive to small perturbations. Intentional detuning (meaning that the absorbers are slightly over- or under-tuned relative to n) can be implemented to improve the robustness of the design. It is shown that by slightly undertuning the absorbers there are no system resonances near the excitation order of interest and that the resulting system is robust to mistuning (i.e., small random uncertainties in the system parameters) of the absorbers and/or blades. These results offer a basic understanding of the dynamics of a bladed disk assembly fitted with order-tuned vibration absorbers, and serve as a first step to the investigation of more realistic models, where, for example, imperfections and nonlinear effects are considered, and multi-DOF and general-path absorbers are employed.


1998 ◽  
Vol 120 (2) ◽  
pp. 145-151 ◽  
Author(s):  
J. Wileman ◽  
I. Green

Dynamic stability is investigated for a mechanical seal configuration in which both seal elements are flexibly mounted to independently rotating shafts. The analysis is applicable to systems with both counterrotating and corotating shafts. The fluid film effects are modeled using rotor dynamic coefficients, and the equations of motion are presented including the dynamic properties of the flexible support. A closed-form solution for the stability criteria is presented for the simplifled case in which the support damping is neglected. A method is presented for obtaining the stability threshold of the general case, including support damping. This method allows instant determination of the stability threshold for a fully-defined seal design. A parametric study of an example seal is presented to illustrate the method and to examine the effects of various parameters in the seal design upon the stability threshold. The fluid film properties in the example seal are shown to affect stability much more than the support properties. Rotors having the form of short disks are shown to benefit from gyroscopic effects which give them a larger range of stable operating speeds than long rotors. For seals with one long rotor, counterrotating operation is shown to be superior because the increased fluid stiffness transfers restoring moments from the short rotor to the long.


1993 ◽  
Vol 60 (3) ◽  
pp. 662-668 ◽  
Author(s):  
R. E. Kalaba ◽  
F. E. Udwadia

In this paper we develop an analytical set of equations to describe the motion of discrete dynamical systems subjected to holonomic and/or nonholonomic Pfaffian equality constraints. These equations are obtained by using Gauss’s Principle to recast the problem of the constrained motion of dynamical systems in the form of a quadratic programming problem. The closed-form solution to this programming problem then explicitly yields the equations that describe the time evolution of constrained linear and nonlinear mechanical systems. The direct approach used here does not require the use of any Lagrange multipliers, and the resulting equations are expressed in terms of two different classes of generalized inverses—the first class pertinent to the constraints, the second to the dynamics of the motion. These equations can be numerically solved using any of the standard numerical techniques for solving differential equations. A closed-form analytical expression for the constraint forces required for a given mechanical system to satisfy a specific set of nonholonomic constraints is also provided. An example dealing with the position tracking control of a nonlinear system shows the power of the analytical results and provides new insights into application areas such as robotics, and the control of structural and mechanical systems.


Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 378 ◽  
Author(s):  
Ilyas Khan ◽  
Aisha Alqahtani

This paper introduces a mathematical model of a convection flow of magnetohydrodynamic (MHD) nanofluid in a channel embedded in a porous medium. The flow along the walls, characterized by a non-uniform temperature, is under the effect of the uniform magnetic field acting transversely to the flow direction. The walls of the channel are permeable. The flow is due to convection combined with uniform suction/injection at the boundary. The model is formulated in terms of unsteady, one-dimensional partial differential equations (PDEs) with imposed physical conditions. The cluster effect of nanoparticles is demonstrated in the C 2 H 6 O 2 , and H 2 O base fluids. The perturbation technique is used to obtain a closed-form solution for the velocity and temperature distributions. Based on numerical experiments, it is concluded that both the velocity and temperature profiles are significantly affected by ϕ . Moreover, the magnetic parameter retards the nanofluid motion whereas porosity accelerates it. Each H 2 O -based and C 2 H 6 O 2 -based nanofluid in the suction case have a higher magnitude of velocity as compared to the injections case.


Author(s):  
M.-C. Lin ◽  
S. A. Velinsky ◽  
B. Ravani

Abstract This paper develops theories for evaluating the efficiency of the ball screw mechanism and additionally, for designing this mechanism. Initially, a quasi-static analysis, which is similar to that of the early work in this area, is employed to evaluate efficiency. Dynamic forces, which are neglected by the quasi-static analysis, will have an effect on efficiency. Thus, an exact theory based on the simultaneous solution of both the Newton-Euler equations of motion and the relevant kinematic equations is employed to determine mechanism efficiency, as well as the steady-state motion of all components within the ball screw. However, the development of design methods based on this exact theory is difficult due to the extensive computation necessary and thus, an approximate closed-form representation, that still accounts for the ball screw dynamics, is derived. The validity of this closed-form solution is proven and it is then used in developing an optimum design methodology for the ball screw mechanism based on efficiency. Additionally, the self-braking condition is examined, as are load capacity considerations.


Author(s):  
Valdas Chaika

Abstract Torsional vibration of two flexibly coupled reciprocating machines is investigated. The rotors of the machines are connected by elastic couplings of several types. The system is excited by a harmonic torque. The excitation frequency is proportional to the rotational speed which varies within a wide range. The motion of the system is described by nonlinear ordinary differential equations. These are linearized for the specific case of the rotor assembly design. Applying impedance functions, a closed-form solution of the equations of motion is derived. Three different cases of the system response are analyzed in the frequency domain. The passive vibration control of the rotor assembly using the centrifugal coupling is investigated. An analytical synthesis technique of the coupling parameters is devised.


1992 ◽  
Vol 114 (1) ◽  
pp. 74-79 ◽  
Author(s):  
Wei Yi ◽  
S. Natsiavas

A finite element model is presented for the seismic response of liquid-filled tanks. This type of analysis is complicated for unanchored tanks, because the bases of these tanks separate from their foundations during strong ground motion. This changes the dynamic behavior of these structures considerably and may result in severe loading. The analysis starts by geometrically discretizing the shell structure using cylindrical finite elements. Then, application of Hamilton’s principle in the structural domain yields the equations of motion for the coupled fluid/structure system. The foregoing analytical procedure employs the closed-form solution for the hydrodynamic response problem, resulting in a compact system of equations of motion. Primary attention is paid to the formulation of the nonlinear base uplift problem. Effects due to shell and ground flexibility are also included.


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