A vorticity formulation for computational fluid dynamic and aeroelastic analyses of viscous flows

Morino, L.; Bernardini, Giovanni; Caputi-Gennaro, Giovanni

doi:10.1016/j.jfluidstructs.2009.07.004

Cited by 4 publications

(4 citation statements)

References 24 publications

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“…Specifically, to apply this method, one considers a potential flow and modifies its boundary condition, by replacing the potential-flow boundary condition ∂φ/∂n = χ B (see Eq. 15, where v = ∇φ), with 125where the equivalent source term, χ E , is given by 46 (126) with v α E denoting the contravariant components of v E , where v E is the "irrotational and solenoidal continuation" into the vortical region V ζ of the velocity v (which is irrotational and solenoidal outside the vortical region V ζ ).…”

Section: Relationship With the Lighthill Equivalent Source Methodsmentioning

confidence: 99%

“…A primitive-variable boundary integral formulation unifying aeroacoustics and aerodynamics, and a natural velocity decomposition for vortical fields 46 In Eq. 126, we use a specific set of curvilinear coordinates ξ k (k = 1, 2, 3), with ξ 3 being the coordinate along the normal n, whereas ξ α (α = 1, 2) are curvilinear coordinates over S; in addition, ξ δ 3 denotes the value of ξ 3 just outside the boundary layer, J is the Jacobian of the transformation x = x(ξ k ), whereas a α = ∂x/∂ξ α (α = 1, 2) are the surface base vectors, which are such that dS = ||a 1 × a 2 || dξ 1 dξ 2 .…”

Section: Relationship With the Lighthill Equivalent Source Methodsmentioning

confidence: 99%

“…In order to overcome this drawback, a combination of the two approaches is utilized in Refs. [17], [45] and [46], where the field Jζ is decomposed into symmetric and anti-symmetric fields, with the appropriate coordinate of integration applied to each. This eliminates the discontinuities in the w and v P fields.…”

Section: Expression For Velocitymentioning

confidence: 99%

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A Primitive-Variable Boundary Integral Formulation Unifying Aeroacoustics and Aerodynamics, and a Natural Velocity Decomposition for Vortical Fields

Morino

2011

International Journal of Aeroacoustics

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The paper presents an integrated approach to the study of aeroacoustics and unsteady aerodynamics, which is based upon the use of the boundary integral equation approach. Accordingly, the boundary integral formulation in primitive variables is thoroughly developed, for Euler as well as Navier-Stokes equations. As a result, one obtains explicit time-domain expressions for velocity and pressure in terms of the Cauchy data of the problem (boundary integral), plus the contribution of the nonlinear terms (field integral). It is shown that the representation for the pressure is very closely related to the classical boundary integral formulations in aeroacoustics (such as the Ffowcs Williams and Hawkings equation and the Kirchhoff method). Similarly, the representation for the velocity is closely related to a formulation introduced by the author for unsteady viscous compressible aerodynamics. In the process, however, a new velocity decomposition of the type v = grad ϕ + w is uncovered. The novelty is that the vortical velocity w is not defined in terms of the vorticity ω; on the contrary, w is defined through its own governing equation. Such a decomposition (and the governing equation for w, which does not involve the pressure) arises in a very natural way from the mathematical approach used, and hence is here named the natural velocity decomposition. In addition, two innovative results are obtained. First, for all the cases addressed (incompressible and compressible, inviscid and viscous fields) there exist generalizations of the Bernoulli theorem (formally very similar to the classical Bernoulli theorems, with the potential ϕ of the irrotational portion of the velocity replacing the velocity potential φ). Second, it is shown that the velocity field may be obtained independently of the pressure, which may be evaluated a-posteriori in terms of the potential ϕ (akin to the evaluation of the pressure in a Venturi tube), through the appropriate generalized Bernoulli theorem. The paper is of theoretical nature-no numerical results are included; however, the schemes for computational implementations are presented and the advantages discussed.

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Section: Relationship With the Lighthill Equivalent Source Methodsmentioning

confidence: 99%

Section: Relationship With the Lighthill Equivalent Source Methodsmentioning

confidence: 99%

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A Primitive-Variable Boundary Integral Formulation Unifying Aeroacoustics and Aerodynamics, and a Natural Velocity Decomposition for Vortical Fields

Morino

2011

International Journal of Aeroacoustics

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“…The first term, v P (x, t), is irrotational and is referred to as the irrotational portion of the velocity, whereas the second one, w, is related to the vorticity ζ : [31][32][33][34]. This approach is of interest here because of its close relationship with the present one, where, as we will see, these problems are also avoided.…”

Section: Review Of Pertinent Workmentioning

confidence: 96%

From Aerodynamics towards Aeroacoustics: A Novel Natural Velocity Decomposition for the Navier-Stokes Equations

Morino

Gradassi

2015

International Journal of Aeroacoustics

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A novel formulation for the analysis of viscous incompressible and compressible aerodynamics/aeroacoustics fields is presented. The paper is primarily of a theoretical nature, and presents the transition path from aerodynamics towards aeroacoustics. The basis of the paper is a variant of the so-called natural velocity decomposition, as v = ∇ϕ + w, where w is obtained from its own governing equation and not from the vorticity. With the novel decomposition, the governing equation for w and the generalized Bernoulli theorem for viscous fields assume a very elegant form. Another improvement pertains to the so-called material covariant components of w: for inviscid incompressible flows, they remain constant in time; minor modifications occur when we deal with viscous flows. In addition, interesting simplifications of the formulation are presented for almost-potential flows, namely for flows that are irrotational everywhere except for thin vortex layers, such as boundary layers and wakes. It is shown that, if the thickness is very small, the exact formulation for almost-potential flows is approximately equal to that for quasi-potential flows (zero-thickness wake), as modified by the Lighthill transpiration velocity correction. Simple numerical applications to the flow around a disk and to jet aerodynamics/aeroacoustics (Kelvin-Helmholtz instabilities) are included.

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Aerodynamic Boundary Element Method for Bluff Bodies with Wind Tunnel Data Correlation

Bernardini

Pierfederici

Serafini

et al. 2016

Aerotec. Missili Spaz.

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A vorticity formulation for computational fluid dynamic and aeroelastic analyses of viscous flows

Cited by 4 publications

References 24 publications

A Primitive-Variable Boundary Integral Formulation Unifying Aeroacoustics and Aerodynamics, and a Natural Velocity Decomposition for Vortical Fields

A Primitive-Variable Boundary Integral Formulation Unifying Aeroacoustics and Aerodynamics, and a Natural Velocity Decomposition for Vortical Fields

From Aerodynamics towards Aeroacoustics: A Novel Natural Velocity Decomposition for the Navier-Stokes Equations

Aerodynamic Boundary Element Method for Bluff Bodies with Wind Tunnel Data Correlation

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