Linearized planing-surface theory with surface tension. Part II: Detachment with discontinuous slope

1982 ◽  
Vol 23 (3) ◽  
pp. 259-277 ◽  
Author(s):  
E. O. Tuck
Keyword(s):  
Surface Tension ◽  
Leading Edge ◽  
Correct Choice ◽  
Jump Discontinuity ◽  
Edge Condition ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Surface Theory ◽  
Natural Choice ◽  
Trailing Edges

AbstractIn Part I of this series, surface tension was included in the classical two-dimensional planing-surface problem, and the usual smooth-detachment trailing-edge condition enforced. However, the results exhibited a paradox, in that the classical results were not approached in the limit as the surface tension approached zero. This paradox is resolved here by abandoning the smooth-detachment condition, that is, by allowing a jump discontinuity in slope between the planing surface and the free surface at the trailing edge. A unique solution is obtainable for any input planing surface at fixed wetted length if one allows such jumps at both leading and trailing edges. If, as is the case in practice, the wetted length is allowed to vary, uniqueness may be restored by requiring either, but not both, of these slope discontinuities to vanish. The results of Part I correspond to the seemingly more-natural choice of making the trailing-edge detachment continuous, but it appears that the correct choice is to require the leading-edge attachment to be continuous.

scholarly journals Linearized planing-surface theory with surface tension. Part I: Smooth detachment

1982 ◽  
Vol 23 (3) ◽  
pp. 241-258 ◽  
Author(s):  
E. O. Tuck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Surface Pressure ◽  
Leading Edge ◽  
Surface Slope ◽  
Surface Theory ◽  
Surface Pressure Distribution ◽  
Jump Discontinuities ◽  
Impulsive Pressure

AbstractIn the absence of surface tension, the problem of determining a travelling surface pressure distribution that displaces a portion of the free surface in a prescribed manner has been solved by several authors, and this “planing-surface” problem is reasonably well understood. The effect of inclusion of surface tension is to change, in a dramatic way, the singularity in the integral equation that describes the problem. It is now necessary in general to allow for isolated impulsive pressure, as well as a smooth distribution over the wetted length. Such pressure points generate jump discontinuities in free-surface slope. Numerical results are obtained here for a class of problems in which there is a single impulse located at the leading edge of the planing surface and detachment with continuous slope at the trailing edge. These results do not appear to approach the classical results in the limit as the surface tension approaches zero, a paradox that is resolved in Part II, which follows.

scholarly journals Prediction of noise from serrated trailing edges

2016 ◽  
Vol 793 ◽  
pp. 556-588 ◽  
Author(s):  
B. Lyu ◽  
M. Azarpeyvand ◽  
S. Sinayoko
Keyword(s):  
Noise Reduction ◽  
Analytical Model ◽  
Leading Edge ◽  
Experimental Investigations ◽  
Destructive Interference ◽  
Trailing Edge ◽  
Trailing Edges ◽  
Mach Numbers ◽  
Trailing Edge Serrations ◽  
High Mach

A new analytical model is developed for the prediction of noise from serrated trailing edges. The model generalizes Amiet’s trailing-edge noise theory to sawtooth trailing edges, resulting in a complicated partial differential equation. The equation is then solved by means of a Fourier expansion technique combined with an iterative procedure. The solution is validated through comparison with the finite element method for a variety of serrations at different Mach numbers. The results obtained using the new model predict noise reduction of up to 10 dB at 90$^{\circ }$ above the trailing edge, which is more realistic than predictions based on Howe’s model and also more consistent with experimental observations. A thorough analytical and numerical analysis of the physical mechanism is carried out and suggests that the noise reduction due to serration originates primarily from interference effects near the trailing edge. A closer inspection of the proposed mathematical model has led to the development of two criteria for the effectiveness of the trailing-edge serrations, consistent but more general than those proposed by Howe. While experimental investigations often focus on noise reduction at 90$^{\circ }$ above the trailing edge, the new analytical model shows that the destructive interference scattering effects due to the serrations cause significant noise reduction at large polar angles, near the leading edge. It has also been observed that serrations can significantly change the directivity characteristics of the aerofoil at high frequencies and even lead to noise increase at high Mach numbers.

Interaction and acoustics of separated flows from a D-shaped bluff body

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Guangyuan Huang ◽  
Ka Him Seid ◽  
Zhigang Yang ◽  
Randolph Chi Kin Leung
Keyword(s):  
Vortex Shedding ◽  
Bluff Body ◽  
Leading Edge ◽  
Separated Flows ◽  
Pressure Waves ◽  
Bluff Bodies ◽  
Trailing Edge ◽  
Content Type ◽  
Trailing Edges ◽  
Edge Vortex

Purpose For flow around elongated bluff bodies, flow separations would occur over both leading and trailing edges. Interactions between these two separations can be established through acoustic perturbation. In this paper, the flow and the acoustic fields of a D-shaped bluff body (length-to-height ratio L/H = 3.64) are investigated at height-based Reynolds number Re = 23,000 by experimental and numerical methods. The purpose of this paper is to study the acoustic feedback in the interaction of these two separated flows. Design/methodology/approach The flow field is measured by particle image velocimetry, hotwire velocimetry and surface oil flow visualization. The acoustic field is modeled in two dimensions by direct aeroacoustic simulation, which solves the compressible Navier–Stokes equations. The simulation is validated against the experimental results. Findings Separations occur at both the leading and the trailing edges. The leading-edge separation point and the reattaching flow oscillate in accordance with the trailing-edge vortex shedding. Significant pressure waves are generated at the trailing edge by the vortex shedding rather than the leading-edge vortices. Pressure-based cross-correlation analysis is conducted to clarify the effect of the pressure waves on the leading-edge flow structures. Practical implications The understanding of interactions of separated flows over elongated bluff bodies helps to predict aerodynamic drag, structural vibration and noise in engineering applications, such as the aerodynamics of buildings, bridges and road vehicles. Originality/value This paper clarifies the influence of acoustic perturbations in the interaction of separated flows over a D-shaped bluff body. The contribution of the leading- and the trailing-edge vortex in generating acoustic perturbations is investigated as well.

The Effect of Intake and Exhaust on the Two-Dimensional Airfoil in a Distributed Propulsion System

2016 ◽  
Author(s):  
Yongsheng Wang ◽  
Ming Zhou ◽  
Quanyong Xu
Keyword(s):  
Lift Coefficient ◽  
Leading Edge ◽  
Jet Flow ◽  
Propulsion System ◽  
Two Dimensional ◽  
Original Design ◽  
Trailing Edge ◽  
Distributed Propulsion ◽  
Drag Ratio

A new distributed propulsion system in which micro-engines were embedded into the wings was proposed. To consider the effects of the intake and exhaust of the engines, the system was simplified as a two-dimensional airfoil with a surface ingestion and a trailing edge jet. The influence of the layout was comprehensively studied with CFD. Compared to the original design, the surface ingestion and trailing edge jet can increase the lift coefficient. The lift-drag ratio increases at smaller attack angles (< 3°) and decreases at greater attack angles (> 3°). The lift-drag ratio improvement with surface ingestion at the leading edge is mainly due to the drop in drag, while the increase with ingestion close to the trailing edge is primarily because of the augment of lift. Moreover, increasing the temperature of the jet flow can enlarge the range of the attack angles with a higher lift-drag ratio.

Hydrodynamic Performance of Two-Dimensional Undulating Foils in Triangular Formation

2011 ◽  
Vol 27 (2) ◽  
pp. 177-190 ◽  
Author(s):  
M.-H. Chung
Keyword(s):  
Traveling Wave ◽  
Wave Speed ◽  
Vortex Pair ◽  
Leading Edge ◽  
Viscous Flows ◽  
Chord Length ◽  
Hydrodynamic Performance ◽  
Two Dimensional ◽  
Efficiency Enhancement ◽  
Trailing Edges

ABSTRACTAs inspired by studies of fish schooling in literature, this work investigates hydrodynamic performance of a two-dimensional undulating-foil triad in viscous flows via numerical simulation. The chord of foil oscillates in the form of a streamwise traveling wave. The triad is in triangular formation, i.e., two foils followed by one. A series of triad configuration are computed assuming the same wave speed, amplitude, and frequency of chord traveling wave for each foil. The results show that, to achieve highest thrust efficiency, the two leading foils should separate from each other by 0.4 chord length, perform antiphase undulating motion, and the leading edge of the trailing foil stay 0.2 chord length in front of the trailing edges of the leading foils. An underlining mechanism, vortex pair shedding from the leading foil interacting with boundary-layer vorticity field of the trailing foil, has been identified to explain the efficiency enhancement. This optimal triad configuration is different from that obtained in a previous potential flow analysiss.

Non-Deterministic CFD Simulations on the Effect of Uncertain Tip Clearance on an Axial Rotor Performance

2013 ◽  
Vol 860-863 ◽  
pp. 1499-1505
Author(s):  
Zhi Yi Liu ◽  
Xiao Dong Wang ◽  
Shun Kang
Keyword(s):  
Mass Flow ◽  
Leading Edge ◽  
Tip Clearance ◽  
High Mass ◽  
Separation Flow ◽  
Flow Conditions ◽  
Cfd Simulations ◽  
Trailing Edge ◽  
Trailing Edges ◽  
Main Factor

In the present paper, the non-intrusive Probabilistic Collocation (NIRPC) method is introduced in detail and used to simulate the effects of tip clearance uncertainty on the aerodynamic performance of NASA Rotor 37, which is combined with a commercial CFD software. The tip clearance height is supposed to be a stochastic variable in Beta distribution with four schemes of uncertainty in the random height of the plain tip clearance, the leading edge, the trailing edge and both the leading and trailing edges, respectively. The statistical properties of total performance of the rotor and flow structure within the blade passage in different flow conditions are analyzed. The results show that the Std. of total performances caused by the uncertain plain tip clearance decreases with reducing of the outlet pressure. The maximum of the standard deviation of Mach number appears in the regions where the leakage flow, the shock wave and the separation flow locate, which decreases from the tip to the hub. When the tip clearance is linear distributed, the uncertainty of tip clearance height at the leading edge is the main factor under high mass flow conditions. With the mass flow reaches to choking point, the Std. of total performances caused by the uncertainty of tip clearance height at the trailing edge drops sharply.

scholarly journals Flow Past a Flat Plate With a Vortex/Sink Combination

1996 ◽  
Vol 63 (2) ◽  
pp. 543-550 ◽  
Author(s):  
N. J. Mourtos ◽  
M. Brooks
Keyword(s):  
Flat Plate ◽  
Current Model ◽  
Angle Of Attack ◽  
Separated Flow ◽  
Leading Edge ◽  
Classical Solutions ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Kutta Condition ◽  
Attached Flow

This paper presents a potential flow model for the leading edge vortex over a two-dimensional flat plate at an angle of attack. The paper is an extension of a model by Saffman and Sheffield (1977). A sink has been added in this model in an effort to satisfy the Kutta condition at both the leading edge and the trailing edge of the plate. The introduction of the sink was inspired by the fact that most steady vortices in nature appear in combination with a flow feature which can be interpreted as a sink at their cores when the flow is analyzed in a two-dimensional observation plane. As in the Saffman and Sheffield model, the presence of a vortex results in increased lift; however, in the current model a unique vortex/sink position is found at each angle of attack. A comparison has also been made between the lift and the drag of this model and the corresponding results for two classical solutions of flow over a flat plate: (a) the fully attached flow with the Kutta condition satisfied at the trailing edge only and (b) the Helmholtz solution of fully separated flow.

Contact Problems Involving the Flow Past an Inflated Aerofoil

1982 ◽  
Vol 49 (2) ◽  
pp. 263-265 ◽  
Author(s):  
J.-M. Vanden-Broeck
Keyword(s):  
Potential Flow ◽  
Weber Number ◽  
Angle Of Attack ◽  
Contact Problems ◽  
Critical Value ◽  
Cavitation Number ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Trailing Edges ◽  
Steady Potential

Steady potential flow around a two-dimensional inflated airfoil is considered. The aerofoil consists of a flexible and inextensible membrane which is anchored at both leading and trailing edges. The flow and the aerofoil shape are determined as functions of the angle of attack α, the cavitation number γ, and the Weber number λ. When γ decreases to a critical value γ0 (α, λ), opposite sides of the membrane become tangent to each other at the trailing edge. For γ < γ0 the aerofoil is partially collapsed near the trailing edge. The length of the region of collapse increases as γ decreases and for γ = −∞, the aerofoil is completely collapsed. The shape of the aerofoil and the value of γ0 are determined analytically by a perturbation solution for λ small. Graphs of the results are presented.

scholarly journals Three-dimensional effects in hovering flapping flight

2012 ◽  
Vol 702 ◽  
pp. 102-125 ◽  
Author(s):  
T. Jardin ◽  
A. Farcy ◽  
L. David
Keyword(s):  
Three Dimensional ◽  
Leading Edge ◽  
Flapping Flight ◽  
Length Scale ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Leading Edge Vortex ◽  
Dimensional Flow ◽  
Dimensional Effects ◽  
Edge Vortex

AbstractThis paper aims at understanding the influence of three-dimensional effects in hovering flapping flight. Numerical simulations at a Reynolds number of 1000 are performed to compare two types of flapping kinematics whose plunging phase is characterized by either a rectilinear translation or a revolving motion. In this way, we are able to isolate the three-dimensional effects induced by the free end condition from that induced by the spanwise incident velocity gradient (and the associated implicit Coriolis and centrifugal effects). In the rectilinear translation case, the analysis of the wake and of the aerodynamic loads reveals that the wingspan can be compartmented into three distinct regions whether it is predominantly subjected to an unstable two-dimensional flow, a stable three-dimensional flow or both two-dimensional and three-dimensional effects. It is found that this partitioning exhibits common features for three different aspect ratios of the wing. In conjunction with the previous results of Ringuette, Milano & Gharib (J. Fluid Mech., vol. 581, 2007, pp. 453–468), this suggests that the influence of the tip vortex over the wingspan is driven by a characteristic length scale. In addition, this length scale matches the position of the connecting point between leading and tip vortices observed in the revolving case, providing insight into the connecting process. In both translating and revolving cases, leading edge vortex attachment and strong spanwise velocities are found to be strongly correlated phenomena. Spanwise velocities (that mostly confine at the periphery of the vortices), together with downward velocities, do not only affect the leading edge vortex but also act as an inhibitor for the trailing edge vortex growth. As a consequence, cross-wake interactions between leading and trailing edge vortices are locally limited, hence contributing to flow stabilization.

scholarly journals Experimental Investigation of Rotor-Stator Interaction in a Centrifugal Pump With Several Vaned Diffusers

1989 ◽  
Author(s):  
N. Arndt ◽  
A. J. Acosta ◽  
C. E. Brennen ◽  
T. K. Caughey
Keyword(s):  
Pressure Fluctuations ◽  
Leading Edge ◽  
Maximum Flow ◽  
Suction Side ◽  
Flow Coefficient ◽  
Pressure Measurements ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Impeller Blade ◽  
Rotor Stator Interaction

This paper describes an experimental investigation of rotor–stator interaction in a centrifugal pump with several vaned diffusers. Steady and unsteady diffuser vane pressure measurements were made for a two–dimensional test impeller. Unsteady impeller blade pressure measurements were made for a second two–dimensional impeller with blade number and blade geometry identical to the two–dimensional impeller used for the diffuser vane pressure measurements. The experiments were conducted for different flow coefficients and different radial gaps between the impeller blade trailing edge and the diffuser vane leading edge (5% and 8% of the impeller discharge radius). The largest pressure fluctuations on the diffuser vanes and the impeller blades were found to be of the same order of magnitude as the total pressure rise across the pump. The largest pressure fluctuations on the diffuser vanes were observed to occur on the suction side of the vane near the vane leading edge, whereas on the impeller blades the largest fluctuations were observed to occur at the blade trailing edge. However, the dependence of the fluctuations on the flow coefficient was found to be different for the diffuser vanes and the impeller blades; on the vane suction side, the fluctuations were largest for the maximum flow coefficient and decreased with decreasing flow coefficient, whereas at the blade trailing edge, the fluctuations were smallest for the maximum flow coefficient and increased with decreasing flow coefficient. Increasing the number of the diffuser vanes resulted in a significant decrease of the impeller blade pressure fluctuations. The resulting lift on the diffuser vanes was computed from the vane pressure measurements; the magnitude of the fluctuating lift was found to be larger than the steady lift.

Sign in / Sign up

Export Citation Format

Share Document