scholarly journals Evolutionary understanding of airfoil lift

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Tianshu Liu

AbstractThis review attempts to elucidate the physical origin of aerodynamic lift of an airfoil using simple formulations and notations, particularly focusing on the critical effect of the fluid viscosity. The evolutionary development of the lift problem of a flat-plate airfoil is reviewed as a canonical case from the classical inviscid circulation theory to the viscous-flow model. In particular, the physical aspects of the analytical expressions for the lift coefficient of the plate-plate airfoil are discussed, including Newton’s sine-squared law, Rayleigh’s lift formula, thin-airfoil theory and viscous-flow lift formula. The vortex-force theory is described to provide a solid foundation for consistent treatment of lift, form drag, Kutta condition, and downwash. The formation of the circulation and generation of lift are discussed based on numerical simulations of a viscous starting flow over an airfoil, and the evolution of the flow topology near the trailing edge is well correlated with the realization of the Kutta condition. The presented contents are valuable for the pedagogical purposes in aerodynamics and fluid mechanics.

1976 ◽  
Vol 98 (3) ◽  
pp. 521-530 ◽  
Author(s):  
N. H. Kemp ◽  
H. Ohashi

Incompressible flow through an unstaggered cascade in general, unsteady, in-phase motion is considered. By methods of thin-airfoil theory, using the assumptions of wakes trailing back at the through-flow velocity, and the Kutta condition, exact analytical expressions are derived for loading, lift and moment. As application, harmonic motion is considered for plunging, pitching, and sinusoidal gusts. Numerical values of lift and moment for these three cases are given graphically (tables are available from the authors). The results show strong analogies with isolated unsteady thin-airfoil theory. They should prove useful as simple examples of unsteady effects in cascades, and as check cases for other approximate or purely numerical analyses.


1958 ◽  
Vol 4 (1) ◽  
pp. 81-86 ◽  
Author(s):  
R. B. Payne

A numerical solution has been obtained for the starting flow of a viscous fluid past a circular cylinder at Reynolds numbers 40 and 100. The method used is the step-by-step forward integration in time of Helmholtz's vorticity equation. The advantage of working with the vorticity is that calculations can be confined to the region of non-zero vorticity near the cylinder.The general features of the flow, including the formation of the eddies attached to the rear of the cylinder, have been determined, and the drag has been calculated. At R = 40 the drag on the cylinder decreases with time to a value very near that for the steady flow.


2007 ◽  
Vol 580 ◽  
pp. 359-380 ◽  
Author(s):  
S. M. ROPER ◽  
J. R. LISTER

We study steady vertical propagation of a crack filled with buoyant viscous fluid through an elastic solid with large effective fracture toughness. For a crack fed by a constant flux Q, a non-dimensional fracture toughness K=Kc/(3μQm3/2)1/4 describes the relative magnitudes of resistance to fracture and resistance to viscous flow, where Kc is the dimensional fracture toughness, μ the fluid viscosity and m the elastic modulus. Even in the limit K ≫ 1, the rate of propagation is determined by viscous effects. In this limit the large fracture toughness requires the fluid behind the crack tip to form a large teardrop-shaped head of length O(K2/3) and width O(K4/3), which is fed by a much narrower tail. In the head, buoyancy is balanced by a hydrostatic pressure gradient with the viscous pressure gradient negligible except at the tip; in the tail, buoyancy is balanced by viscosity with elasticity also playing a role in a region within O(K2/3) of the head. A narrow matching region of length O(K−2/5) and width O(K−4/15), termed the neck, connects the head and the tail. Scalings and asymptotic solutions for the three regions are derived and compared with full numerical solutions for K ≤ 3600 by analysing the integro-differential equation that couples lubrication flow in the crack to the elastic pressure gradient. Time-dependent numerical solutions for buoyancy-driven propagation of a constant-volume crack show a quasi-steady head and neck structure with a propagation rate that decreases like t−2/3 due to the dynamics of viscous flow in the draining tail.


2011 ◽  
Vol 172 (1) ◽  
pp. 40-46 ◽  
Author(s):  
M. Youssry ◽  
N. Belmiloud ◽  
B. Caillard ◽  
C. Ayela ◽  
C. Pellet ◽  
...  

Author(s):  
Carlos Luis Moreno ◽  
Alejandro Fuenmayor ◽  
Gilberto Núñez ◽  
Jesús De Andrade ◽  
Ricardo Noguera ◽  
...  

Centrifugal pump performance is affected when pumping viscous liquids, requiring a larger power input than the same pump handling water. In applications of chemical, civil, environmental, and mechanical engineering that involve centrifugal pumps, it is a challenge to accurately estimate and even more of a challenge to improve their performance when handling viscous liquids. When accurate performance data is needed, difficult experiments must be conducted with the operating viscous flow. The extension of the applicability of numerical techniques for solving fluid dynamics (CFD) permits the consideration of these tools as a definite possibility for predicting the performance of centrifugal pumps with viscous flows. The purpose of this study is to perform a 3D-CFD steady-state simulation of three different configurations of centrifugal pumps. The first is an impeller-diffuser pump (ns = 19) taken from an ESP model. The second is a Francis Pump-Turbine (ns = 28). Finally, the third configuration possesses an impeller and volute (ns = 32). The objective is to characterize and evaluate their performances with four different fluids from 1 to 420 cSt. These are: water at 25°C, SAE10 and SAE30 oils, and Fuel Oil Medium (FOM). For water flow conditions, the numerical results were compared with experimental data, and found to be consistent with global performance parameters. With regard to the higher viscosity fluids, the CFD calculation was compared with those obtained through the standard empirical method (ANSI/HI9.6.7). This resulted in good agreement between the performance results. The commercial software ANSYS-CFX was used for the CFD calculations. The resulting pump performance curve (head, hydraulic efficiency and power output) is consistent with that expected by theory. In general, as the viscosity of fluids increases, the hydraulic energy losses increase. Of the three pumps, slip factor for SAE30 oil was larger for all volumetric flows since it features the best guidance of the flow in the impeller blade passage. For the ns32 pump and the pump-turbine ns28, the volute losses rose from water to FOM, just like the impeller hydraulic losses. For these two turbo machines, the impeller losses were larger than volute losses. For the pumps with volute, the effects of fluid viscosity on the radial forces were evaluated. It was found that the radial forces decrease when the viscosity increases. This paper attempts to contribute to a better understanding of fluid dynamics within centrifugal pump impellers handling viscous fluids, and intends to shed more light on the approaches that performance prediction models should follow in the future.


1981 ◽  
Vol 103 (2) ◽  
pp. 299-306
Author(s):  
H. Shoji ◽  
H. Ohashi ◽  
N. H. Kemp

We consider incompressible potential flow through a cascade of staggered thin airfoils in general, unsteady, in-phase motion. With the assumptions of the Kutta condition and linearized wakes, exact analytical expressions are derived for pressure distribution, lift, and moment, using conformal mapping applied to the velocity field. The results are then specialized to harmonic motion, and applied to plunging, pitching, and sinusoidal gusts. All the results are expressed in closed-form as quadratures, and reduce to the well-known relations for thin airfoil theory, as the solidity decreases to zero. They agree with the unstaggered results of Kemp and Ohashi when the stagger angle is zero. Typical numerical results are given in the figures. They should serve as a measure of the accuracy of numerical or approximate solutions, as well as representing in a simple way the effects of stagger and solidity on unsteady cascade aerodynamics.


Author(s):  
Zhiheng Li ◽  
Jiawei Yu ◽  
Dakui Feng ◽  
Kaijun Jiang ◽  
Yujie Zhou

Abstract The virtual propeller model can achieve the rapid numerical prediction of the ship self-propulsion performance through viscous flow, which used the improved body-force method. The two-dimensional lift coefficient CL and the drag coefficient CD are very important parameters in this method, which are generally obtained by the potential flow methods and cannot incorporate viscous effects. This study will perform a fully nonlinear unsteady RANS (Reynolds Average Navier-Stokes) simulation to get the KP505 open-water characteristics and then divide its blade into several parts to get the lift coefficient CL and the drag coefficient CD on each one. Then fitting by multivariate regression method, the relationship between CL, CD and propeller parameters is obtained. The Unsteady Blade Element Theory (UBET) is coupled with RANS in house CFD code HUST-Ship (Hydrodynamic Unsteady Simulation Technology for Ship) to calculate the flow around the propeller. RANS equations are solved by the finite difference method and PISO arithmetic. have been made using structured grid with overset technology. The results show that comparing with the EFD data, the maximum differences of the result of the improved body-force method are 4.32% and 2.7% for the thrust coefficient and the torque coefficient respectively near the propeller operating point.


Author(s):  
Ming-ming Liu

Viscous flow past two circular cylinders in tandem arrangement is numerically investigated at a typical Reynolds number of 200 which is based on the diameter of the downstream cylinder. The non-dimensional diameter of the downstream cylinder D is fixed to be 1.0, while the non-dimensional diameter of the upstream cylinder d varies from 0.1 to 1.0 with an interval of 0.1. Moreover, the minimal non-dimensional distance between the two cylinders changes from 0.1 to 4.0. The numerical results show that continuous variation of the mean drag coefficient, the lift coefficient, and the lift frequency is observed with the increase in the gap ratio for d/ D = 0.1 and 0.2. Discontinuities are found for the mean drag coefficient, the lift coefficient, and the lift frequency of the downstream cylinder with the increase in gap ratio for d/ D = 0.9 and 1.0. Multiple lift oscillating frequencies of the downstream cylinder can be detected for d/ D = 0.3–0.8 at special gap ratios. Special attention is paid on d/ D = 0.4, which is a typical example for d/ D = 0.3–0.8. The predominant lift frequency of the downstream cylinder is observed to change from fL-1 to fL-2 as the increase in the gap ratio for d/ D = 0.4, which have not been previously detected. However, the predominant drag frequency of the downstream cylinder is found always to be fD-3 in present investigation scope. Moreover, a conclusion that fD-3 =  fL-1 +  fL-2 can be obtained.


1977 ◽  
Vol 99 (2) ◽  
pp. 195-203 ◽  
Author(s):  
J. H. Horlock ◽  
E. M. Greitzer ◽  
R. E. Henderson

An analysis is presented of the unsteady lift on a cascade of airfoils moving through a circumferential inlet flow distortion. The flow model is based on blades of finite chord, but small pitch/chord ratio. Two separate methods are used to derive the unsteady lift on the blades, leading to the same analytical expressions in both cases. The analytical solution is compared with earlier investigations of the flow past isolated airfoils (Sears), with numerical results for airfoils in a cascade (Henderson/Daneshyar, Whitehead and Smith) and with actuator disk results. It is shown that the present simple model provides results that are consistent with the numerical calculations for small pitch/chord ratios. In addition, the present method provides a means for resolving a discrepancy between existing theories as to the behavior of the cascade lift coefficient at low reduced frequency.


2003 ◽  
Vol 478 ◽  
pp. 47-70 ◽  
Author(s):  
ANDREW L. HAZEL ◽  
MATTHIAS HEIL

We consider the steady propagation of an air finger into a buckled elastic tube initially filled with viscous fluid. This study is motivated by the physiological problem of pulmonary airway reopening. The system is modelled using geometrically nonlinear Kirchhoff–Love shell theory coupled to the free-surface Stokes equations. The resulting three-dimensional fluid–structure-interaction problem is solved numerically by a fully coupled finite element method.The system is governed by three dimensionless parameters: (i) the capillary number, Ca=μU/σ*, represents the ratio of viscous to surface-tension forces, where μ is the fluid viscosity, U is the finger's propagation speed and σ* is the surface tension at the air–liquid interface; (ii) σ=σ*/(RK) represents the ratio of surface tension to elastic forces, where R is the undeformed radius of the tube and K its bending modulus; and (iii) A∞=A*∞/(4R2), characterizes the initial degree of tube collapse, where A*∞ is the cross-sectional area of the tube far ahead of the bubble.The generic behaviour of the system is found to be very similar to that observed in previous two-dimensional models (Gaver et al. 1996; Heil 2000). In particular, we find a two-branch behaviour in the relationship between dimensionless propagation speed, Ca, and dimensionless bubble pressure, p*b/(σ*/R). At low Ca, a decrease in p*b is required to increase the propagation speed. We present a simple model that explains this behaviour and why it occurs in both two and three dimensions. At high Ca, p*b increases monotonically with propagation speed and p*b/(σ*/R) ∝ Ca for sufficiently large values of σ and Ca. In a frame of reference moving with the finger velocity, an open vortex develops ahead of the bubble tip at low Ca, but as Ca increases, the flow topology changes and the vortex disappears.An increase in dimensional surface tension, σ*, causes an increase in the bubble pressure required to drive the air finger at a given speed; p*b also increases with A*∞ and higher bubble pressures are required to open less strongly buckled tubes. This unexpected finding could have important physiological ramifications. If σ* is sufficiently small, steady airway reopening can occur when the bubble pressure is lower than the external (pleural) pressure, in which case the airway remains buckled (non-axisymmetric) after the passage of the air finger. Furthermore, we find that the maximum wall shear stresses exerted on the airways during reopening may be large enough to damage the lung tissue.


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