1,720,965 research outputs found
Perturbation growth in vortices with axial flow
No full textAim of the present paper is to perform a linear temporal stability analysis of the trailing line vortex
model named q-vortex. Both exponential and non-modal instabilities are inquired with a local
approach, for swirl numbers q near the limit of Gaussian jet. In the range of axial and azimuthal
wavenumbers in which both instabilities are present, the competition between the two linear
mechanisms is analyzed, focusing the attention on a particular swirl value of typical aeronautic
interest in order to extract the dominant effects which lead to vortex breakdown at realistic finite
times.
These instabilities are studied numerically using an accurate Chebyshev collocation spectral
method; the computation of the optimal perturbations has been obtained by means of two different
techniques: “matrix exponentiation” and “direct-adjoint simulation”. Maps of the transient growth
peaks up to Re=10^5 for the parameters space here inquired are obtained. Furthermore, the
competition between the weak viscous exponential growths and the non-modal ones is analysed,
over a certain range of Re numbers
Multimodal analysis for the stability of vortices with axial flow
No full textThe problem of transient behavior of perturbations in the linear stability analysis of vortex columns with axial flow is considered. We use the Batchelor vortex as the base flow and the analysis is carried out by focusing on a region of the parameters space in which both weak viscous exponential instabilities and transient growths of perturbations are present. The competition between the two linear effects is analyzed in a certain range of axial and azimuthal wavenumbers. The numerical discretization has been performed by employing an accurate Chebyshev collocation spectral method. The computations of the growth function evolution and of the optimal perturbations have been conducted by implementing two different strategies, the matrix exponentiation and the direct-adjoint techniques, and a comparison in terms of computational cost and accuracy is presented. Furthermore, some aspects of the competition between viscous instabilities and transient effects, in a swirl numbers range in which are both present, are discusse
Dynamics of free-falling liquid sheet
No full textThe dynamics of free-falling liquid sheet flows, driven by surface tension, is reviewed with reference to studies over the last 40 years. Both theoretical and experimental aspects are addressed. Assessed results as well as unsolved issues open to future work are evidenced
Global dynamics of gravitational liquid sheet flows
No full textUnsteady free-interface vertical liquid sheet flows are studied from the global viewpoint, where the dynamics is termed global because it refers to the whole fluid system. The development of a
proper mathematical model is presented initially, which accounts of pressure disturbances produced by the compliant interface in an air enclosure adjacent to the sheet. Our study has been
restricted to the sinuous (unsymmetric) solution of the linearized set of equations. It is found that, in absence of surface tension, the optimal disturbance energy exhibits a transient growth
characterized by high frequency and low frequency time-periodic oscillations; physical considerations are developed in order to estimate the relevant periods. In presence of surface tension,
the low frequency oscillations disappear and the optimal disturbance energy goes quickly to zero, after exhibiting an initial reduced peak. In order to give insight on the physical relevance
of such behaviours, an equation of energy budget is also derived which is used to estimate the contribution of the various physical effects evaluated via direct numerical simulation of the
linearized model
Modeling of the stability of free-falling liquid curtain
No full textThe physical mechanisms leading to the disintegration of a gravitational (non parallel) two-dimensional plane liquid curtain (sheet), occurring at low fluid flow rates, are not yet fully known. The problem is reconsidered here through the development of an unsteady inviscid mathematical model where the dependent variables are expressed by means of polynomial expansions in terms of powers of the local lateral distance from the centerline position. Surface tension effects are included, and the ambient pressure field may be either applied or induced by the compliant free interface. The linearization around the base flow allows the separation of sinuous and varicose responses. The global linear stability of such a model is analyzed by inspecting both modal and non-modal amplifications of disturbances energy. An equation of energy budget is also derived, which is used to estimate the contribution of the various physical effects evaluated via direct numerical simulations of the governing system of equations
Numerical visualization of nappe oscillation
No full textThe unsteady global dynamics of a gravitational liquid sheet interacting with a onesided adjacent air enclosure,
typically referred to as nappe oscillation, is addressed, under the assumptions of potential flow and presence of surface
tension effects. Preliminary physical insights of the sheet centerline sinuous modes show that the nappe dynamics features
the propagation of two wave fronts both directed downstream or one downstream and the other one upstream depending on
whether the flow Weber number is greater or less than unity, respectively; moreover, the overall system behaves as a driven
damped spring-mass oscillator, where the liquid sheet acts as the mass and the air enclosure as the spring. The findings of the
eigenvalues spectral analysis closely agree with direct numerical simulations of the partial differential equation governing
in the space-time domain the global evolution of the disturbances, starting from an initial gaussian-like shape.
Keywords: liquid sheet, surface tension, numerical visualizatio
Global dynamics analysis of nappe oscillation
No full textThe unsteady global dynamics of a gravitational liquid sheet interacting with a onesided
adjacent air enclosure, typically referred to as nappe oscillation, is addressed,
under the assumptions of potential flow and absence of surface tension effects. To the
purpose of shedding physical insights, the investigation examines both the dynamics
and the energy aspects. An interesting re-formulation of the problem consists of
recasting the nappe global behavior as a driven damped spring-mass oscillator, where
the inertial effects are linked to the liquid sheet mass and the spring is represented
by the equivalent stiffness of the air enclosure acting on the average displacement
of the compliant nappe centerline. The investigation is carried out through a modal
(i.e., time asymptotic) and a non-modal (i.e., short-time transient) linear approach,
which are corroborated by direct numerical simulations of the governing equation.
The modal analysis shows that the flow system is characterized by low-frequency
and high-frequency oscillations, the former related to the crossing time of the
perturbations over the whole domain and the latter related to the spring-mass oscillator.
The low-frequency oscillations, observed in real life systems, are produced
by the (linear) combination of multiple modes. The non-normality of the operator
is responsible for short-time energy amplifications even in asymptotically stable
configurations, which are confirmed by numerical simulations and justified by energy
budget considerations. Strong analogies with the edge-tone problem are encountered;
in particular, the integer-plus-one-quarter resonance criterion is uncovered,
where the basic frequency to be multiplied by n + 1/4 is just the one related to the
spacing among the imaginary parts of the eigenvalues
Surface tension effects on the motion of a free-falling liquid sheet
No full textThe stationary motion of a liquid curtain falling under the effects of inertia, gravity and surface tension is analyzed. An original equation governing the streamwise distribution of thickness and velocity is derived by means of a Taylor expansion in the lateral distance from the mean line of the sheet. Approximate solutions are obtained by means of perturbation approaches involving the two parameters governing the problem, namely the slenderness ratio ε and the Weber number We. The numerical procedure employed in order to integrate the non-linear equation is discussed and a parametric study is presented, together with a comparison with the approximate asymptotic solutions valid for small ε and We
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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