2,662 research outputs found
Hydrodynamic equations for incompressible inviscid fluid in terms of generalized stream function
Hydrodynamic equations for ideal incompressible fluid are written in terms of
generalized stream function. Two-dimensional version of these equations is
transformed to the form of one dynamic equation for the stream function. This
equation contains arbitrary function which is determined by inflow conditions
given on the boundary. To determine unique solution, velocity and vorticity
(but not only velocity itself) must be given on the boundary. This unexpected
circumstance may be interpreted in the sense that the fluid has more degrees of
freedom, than it was believed. Besides, the vorticity is less observable
quantity as compared with the velocity. It is shown that the Clebsch potentials
are used essentially at the description of vortical flow.Comment: 31 pages, 0 figures, The paper is reduced. Consideration of
nonstationary flow has been remove
Simulations of propelling and energy harvesting articulated bodies via vortex particle-mesh methods
The emergence and understanding of new design paradigms that exploit flow
induced mechanical instabilities for propulsion or energy harvesting demands
robust and accurate flow structure interaction numerical models. In this
context, we develop a novel two dimensional algorithm that combines a Vortex
Particle-Mesh (VPM) method and a Multi-Body System (MBS) solver for the
simulation of passive and actuated structures in fluids. The hydrodynamic
forces and torques are recovered through an innovative approach which crucially
complements and extends the projection and penalization approach of Coquerelle
et al. and Gazzola et al. The resulting method avoids time consuming
computation of the stresses at the wall to recover the force distribution on
the surface of complex deforming shapes. This feature distinguishes the
proposed approach from other VPM formulations. The methodology was verified
against a number of benchmark results ranging from the sedimentation of a 2D
cylinder to a passive three segmented structure in the wake of a cylinder. We
then showcase the capabilities of this method through the study of an energy
harvesting structure where the stocking process is modeled by the use of
damping elements
Hydrodynamic Nambu Brackets derived by Geometric Constraints
A geometric approach to derive the Nambu brackets for ideal two-dimensional
(2D) hydrodynamics is suggested. The derivation is based on two-forms with
vanishing integrals in a periodic domain, and with resulting dynamics
constrained by an orthogonality condition. As a result, 2D hydrodynamics with
vorticity as dynamic variable emerges as a generic model, with conservation
laws which can be interpreted as enstrophy and energy functionals. Generalized
forms like surface quasi-geostrophy and fractional Poisson equations for the
stream-function are also included as results from the derivation. The formalism
is extended to a hydrodynamic system coupled to a second degree of freedom,
with the Rayleigh-B\'{e}nard convection as an example. This system is
reformulated in terms of constitutive conservation laws with two additive
brackets which represent individual processes: a first representing inviscid 2D
hydrodynamics, and a second representing the coupling between hydrodynamics and
thermodynamics. The results can be used for the formulation of conservative
numerical algorithms that can be employed, for example, for the study of fronts
and singularities.Comment: 12 page
A general method to determine the stability of compressible flows
Several problems were studied using two completely different approaches. The initial method was to use the standard linearized perturbation theory by finding the value of the individual small disturbance quantities based on the equations of motion. These were serially eliminated from the equations of motion to derive a single equation that governs the stability of fluid dynamic system. These equations could not be reduced unless the steady state variable depends only on one coordinate. The stability equation based on one dependent variable was found and was examined to determine the stability of a compressible swirling jet. The second method applied a Lagrangian approach to the problem. Since the equations developed were based on different assumptions, the condition of stability was compared only for the Rayleigh problem of a swirling flow, both examples reduce to the Rayleigh criterion. This technique allows including the viscous shear terms which is not possible in the first method. The same problem was then examined to see what effect shear has on stability
Viscous theory of surface noise interaction phenomena
A viscous linear surface noise interaction problem is formulated that includes noise production by an oscillating surface, turbulent or vortical interaction with a surface, and scattering of sound by a surface. The importance of viscosity in establishing uniqueness of solution and partitioning of energy into acoustic and vortical modes is discussed. The results of inviscid two dimensional airfoil theory are used to examine the interactive noise problem in the limit of high reduced frequency and small Helmholtz number. It is shown that in the case of vortex interaction with a surface, the noise produced with the full Kutta condition is 3 dB less than the no Kutta condition result. The results of a study of an airfoil oscillating in a medium at rest are discussed. It is concluded that viscosity can be a controlling factor in analyses and experiments of surface noise interaction phenomena and that the effect of edge bluntness as well as viscosity must be included in the problem formulation to correctly calculate the interactive noise
Aeroacoustic and aerodynamic applications of the theory of nonequilibrium thermodynamics
Recent developments in the field of nonequilibrium thermodynamics associated with viscous flows are examined and related to developments to the understanding of specific phenomena in aerodynamics and aeroacoustics. A key element of the nonequilibrium theory is the principle of minimum entropy production rate for steady dissipative processes near equilibrium, and variational calculus is used to apply this principle to several examples of viscous flow. A review of nonequilibrium thermodynamics and its role in fluid motion are presented. Several formulations are presented of the local entropy production rate and the local energy dissipation rate, two quantities that are of central importance to the theory. These expressions and the principle of minimum entropy production rate for steady viscous flows are used to identify parallel-wall channel flow and irrotational flow as having minimally dissipative velocity distributions. Features of irrotational, steady, viscous flow near an airfoil, such as the effect of trailing-edge radius on circulation, are also found to be compatible with the minimum principle. Finally, the minimum principle is used to interpret the stability of infinitesimal and finite amplitude disturbances in an initially laminar, parallel shear flow, with results that are consistent with experiment and linearized hydrodynamic stability theory. These results suggest that a thermodynamic approach may be useful in unifying the understanding of many diverse phenomena in aerodynamics and aeroacoustics
A 'reciprocal' theorem for the prediction of loads on a body moving in an inhomogeneous flow at arbitrary Reynolds number
Several forms of a theorem providing general expressions for the force and torque
acting on a rigid body of arbitrary shape moving in an inhomogeneous incompressible
flow at arbitrary Reynolds number are derived. Inhomogeneity arises because of
the presence of a wall that partially or entirely bounds the fluid domain and/or a
non-uniform carrying flow. This theorem, which stems directly from Navier–Stokes
equations and parallels the well-known Lorentz reciprocal theorem extensively
employed in low-Reynolds-number hydrodynamics, makes use of auxiliary solenoidal
irrotational velocity fields and extends results previously derived by Quartapelle &
Napolitano (AIAA J., vol. 21, 1983, pp. 911–913) and Howe (Q. J. Mech. Appl.
Maths, vol. 48, 1995, pp. 401–426) in the case of an unbounded flow domain and
a fluid at rest at infinity. As the orientation of the auxiliary velocity may be chosen
arbitrarily, any component of the force and torque can be evaluated, irrespective of
its orientation with respect to the relative velocity between the body and fluid. Three
main forms of the theorem are successively derived. The first of these, given in (2.19),
is suitable for a body moving in a fluid at rest in the presence of a wall. The most
general form (3.6) extends it to the general situation of a body moving in an arbitrary
non-uniform flow. Specific attention is then paid to the case of an underlying timedependent
linear flow. Specialized forms of the theorem are provided in this situation
for simplified body shapes and flow conditions, in (3.14) and (3.15), making explicit
the various couplings between the body’s translation and rotation and the strain rate
and vorticity of the carrying flow. The physical meaning of the various contributions
to the force and torque and the way in which the present predictions reduce to
those provided by available approaches, especially in the inviscid limit, are discussed.
Some applications to high-Reynolds-number bubble dynamics, which provide several
apparently new predictions, are also presented
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