Far-Field Induced Drag Prediction Using Vorticity Confinement Technique

Snyder, Troy; Povitsky, Alex

doi:10.2514/1.c032719

Cited by 13 publications

(6 citation statements)

References 19 publications

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“…However, separating out induced drag from profile drag, based on the type of measurements used here may not be feasible for flapping wings. Induced power is for fixed wings normally estimated from the in-plane velocity components in the Trefftz plane [49], but for flapping wings the magnitudes of these velocity components are influenced by the profile drag of the wings. Until a suitable method for separating profile and induced components is developed we can only speculate on how much the complexity of the wake influences the estimation of induced power from wakes in freely flying animals.…”

Section: Powermentioning

confidence: 99%

Mechanical power curve measured in the wake of pied flycatchers indicates modulation of parasite power across flight speeds

Johansson¹,

Maeda²,

Henningsson³

et al. 2018

J. R. Soc. Interface.

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How aerodynamic power required for animal flight varies with flight speed determines optimal speeds during foraging and migratory flight. Despite its relevance, aerodynamic power provides an elusive quantity to measure directly in animal flight. Here, we determine the aerodynamic power from wake velocity fields, measured using tomographical particle image velocimetry, of pied flycatchers flying freely in a wind tunnel. We find a shallow U-shaped power curve, which is flatter than expected by theory. Based on how the birds vary body angle with speed, we speculate that the shallow curve results from increased body drag coefficient and body frontal area at lower flight speeds. Including modulation of body drag in the model results in a more reasonable fit with data than the traditional model. From the wake structure, we also find a single starting vortex generated from the two wings during the downstroke across flight speeds (1–9 m s −1 ). This is accomplished by the arm wings interacting at the beginning of the downstroke, generating a unified starting vortex above the body of the bird. We interpret this as a mechanism resulting in a rather uniform downwash and low induced power, which can help explain the higher aerodynamic performance in birds compared with bats.

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Section: Powermentioning

confidence: 99%

Mechanical power curve measured in the wake of pied flycatchers indicates modulation of parasite power across flight speeds

Johansson¹,

Maeda²,

Henningsson³

et al. 2018

J. R. Soc. Interface.

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“…The result not only confirms that, as a generic rule, the drag components expressed by wake integrals must depend on the choice of wake-plane streamwise location but also enables observing specific dynamic processes of flow structures responsible for the streamwise evolution of these force components. The innovative kinematic formula (18) for the x-derivative of induced drag, dD i /dx, reveals that it is exactly determined by a Wv-integral of the disturbance Lamb vector v × ω, while the kinetic formula (21) for dDi/dx = −dDP/dx reveals that assuming x-independence of Di implies neglecting the dissipation over the wake-plane. In the linear and viscous far wake, Di vanishes and DP becomes the total drag D. The numerical examples indicate that the concept of induced and profile drags as fixed numbers can at most be approximately true for attached flows, and these drags must strongly depend on x for more complex separated flows.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…ex ⋅ (vπ × ωπ)dS, (18) of which the right-hand side can be easily calculated or measured. Its second expression comes from (A7).…”

Section: B Physical Root Of the X -Dependencymentioning

confidence: 99%

“…II D that CD,i and CD,P are essentially constant when x > 10. Equation (18) asserts that this occurs when vπ × ωπ ≈ 0 at far wake. The contours of ρex ⋅ (vπ × ωπ) at different x are shown in Fig.…”

Section: Quasiobjective Vs Nonobjective Induced and Profile Dragsmentioning

confidence: 99%

“…The far-field force theory provides a valuable check point of any viscous theory of drag breakdown. Actually, some researchers have also found that Di gradually diminishes as x increases, [15][16][17][18][19] which, however, was attributed to be probably associated with the interchange of the vorticity to entropy caused by numerical dissipations. Thus, a modification by adding an increased entropy drag into the initial induced drag was proposed to reduce its variation with x. Owing to these controversies and artificial modifications, consequently, some researchers simply use D minus DP to define the induced drag, 20 and some others just care about the total drag D only.…”

Section: Introductionmentioning

confidence: 99%

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On the concept and theory of induced drag for viscous and incompressible steady flow

Zou

Gao

et al. 2019

Physics of Fluids

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For steady flow, one usually decomposes the total drag into different components by wake-plane integrals and seeks their reduction strategies separately. Unlike the body-surface stress integral, the induced drag as well as the profile drag has been found to depend on the streamwise location of the wake plane used for drag estimate. It gradually diminishes as the wake plane moves downstream, which was often attributed to numerical dissipation. In this paper, we present an exact general force-breakdown theory and its numerical demonstrations for viscous incompressible flow over an arbitrary aircraft to address this puzzling issue. Based on the theory, the induced and profile drags do depend inherently on the wake-plane location rather than being merely caused by numerical dissipation. The underlying mechanisms are identified in terms of the components, moments, and physical dissipation of the Lamb-vector field produced by the aircraft motion. This theoretical prediction is fully consistent with the linear far-field force theory that the induced drag finally vanishes and the profile drag increases to the total drag at an infinitely far field for viscous flow. Moreover, as a product of this exact theory, a new compact midwake approximation for the induced drag is proposed for the convenience of routine wake survey in industry. Its prediction is similar to conventional formulas for attached flow but behaves much better for separated flow.

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