Unsteady Lift Coefficients Research Articles

Forced streamwise oscillations of a circular cylinder: Locked-on modes and resulting fluid forces

Abstract A computational study of laminar, incompressible flow past a cylinder oscillating in the streamwise direction is performed using the two-dimensional unsteady Navier–Stokes equations in nonprimitive variables. The method of solution is based on a conjugating Fourier spectral analysis with finite-difference approximations. The numerical simulations are conducted at a fixed Reynolds number, R = 200 , and at displacement amplitude-to-cylinder diameter of A = 0.1 and 0.3 . Results show the existence of symmetric/asymmetric modes of vortex formation in the cylinder wake at different values of unsteady loading on the cylinder, which is characterized by the ratio of oscillation frequency, f, to Karman vortex-shedding frequency, f 0 . For this paper, the frequency ratio is chosen from f / f 0 = 0.5 to 3, where switching from asymmetric to symmetric vortex shedding is observed. The relation between these vortex-shedding modes and fluid forces on the cylinder surface is discussed. An analysis of the locked-on modes via Lissajous patterns of unsteady lift coefficient is also included. Previously computed and observed flow fields as well as fluid forces are compared to current numerical results and agreement is found to be excellent.

Lock-in Phenomenon of Pitching Hydrofoil with Cavitation Breakdown

The violent cavitation breakdown occurs periodically during vortex cavitation shedding when a sheet cavity elongates near the trailing edge of a hydrofoil. This causes unsteady and nonlinear fluid forces to act on the hydrofoil. This nonlinear behavior, when the breakdown frequency locks at the pitching frequency of the cavitating hydrofoil, has not yet been clarified. The unsteady lift coefficient and the flow structure of a pitching NACA hydrofoil under the lock-in phenomenon were clarified by load cell measurement and particle and bubble image processing for PIV. As the main result, in the Subcavitation region, when the elongation of the sheet cavity cannot follow the variation of the pitching angle at a highly reduced frequency, the pitching lift coefficient is offset similar to that of nonpitching oscillation. In the Transition region where cavitation breakdown frequently occurs, the reduced frequency range for the pitching lift coefficient can be characterized roughly into the Unlock-in, Quasi-lock-in and Lock-in ranges according to whether or not the breakdown frequency is synchronized with the pitching frequency.

The Unsteady Pressure Field in a High Specific Speed Centrifugal Pump Impeller—Part I: Influence of the Volute

An experimental investigation is presented regarding the unsteady pressure field within a high specific speed centrifugal pump impeller (ωs = 1.7) which operated in a double spiral volute. For this, twenty-five piezoresistive pressure transducers were mounted within a single blade passage and sampled in the rotating impeller frame with a telemetry system. The influence of varying volume flux on the pressure transducers was evaluated in terms of pressure fluctuation magnitudes and phase differences. The magnitude information reveals that the pressure fluctuations from the impeller-volute interaction grew as the volume flux became further removed from the best efficiency point and as the trailing edge of the impeller blade was approached. These fluctuations reached 35% of the pump head in deep part load. The upstream influence of the volute steady pressure field dominates the unsteady pressure field within the impeller at all off design load points. Acquired signal phase information permits the identification of the pressure field unsteadiness within the impeller passage as fundamentally synchronized simultaneously with the volute tongue passing frequency. Special emphasis was placed on the volume flux regime where the pump and impeller pressure discharge characteristic undergo hysteresis, as impeller inlet and outlet recirculation commence and cease. A synthesis of the rotating transducers was performed to obtain unsteady blade loading parameters. The value of the unsteady lift coefficient varies on the order of 200% for a single blade in part load operation (at 45% bep), an abrupt fluctuation occurring as the fore running blade suction side passes a volute tongue. The unsteady moment coefficient and center of pressure are also shown to vary significantly during the impeller-volute tongue interaction.

High frequency oscillating viscous flow over elliptic cylinder at incidence

The problem of high frequency oscillating viscous flow over an elliptic cylinder at incidence is investigated. The method of matched inner-outer asymptotic expansion to second order is used to solve the governing equations. The steady and the unsteady modes of flow, related to the present work, are identified and separated. Both steady and unsteady drag and lift coefficients are presented and discussed. The effect of different parameters such as the Strouhal number, Reynolds number, focal length and angle of attack are explored.

2-D Flow Analysis on Aerodynamic Characteristics of a Square Cylinder Oscillating in the Across-Wind Direction

This paper deals with the evaluation on aerodynamic characteristics of a square cylinder oscillating in the across-wind direction. Two-dimensional flow calculation was executed by using k-ε with a modified production eddy viscosity model. Calculated results were compared with experimental ones mainly obtained in this study. Firstly two patterns of aerodynamic response with different mass-damping parameters were predicted. Secondly unsteady lift acting on a oscillating cylinder were predicted. Although a slight difference was observed between predicted unsteady lift coefficients and experimental ones, accuracy in predicting aerodynamic response was far better than that of unsteady lift coefficients.

Unsteady aerodynamic loading produced by a sinusoidally oscillating delta wing

The unsteady aerodynamic loading produced by an oscillating delta wing was examined for a range of reduced frequencies and mean angles of attack. A three degree of freedom force balance recorded normal and tangential force data. These data were then reduced to provide unsteady lift and drag force coefficient values. The resultant aerodynamic loads were highly transient in nature and lift enhancement up to twice that of steady-state values was achieved for limiting test cases. The delta wing also experienced lift reduction during portions of the pitching cycle. Reduced dynamic drag was seen for instantaneous wing angles of attack below static stall. Hysteresis loops demonstrated the unsteadiness of the resultant flowfields and were seen for all test cases. Force balance measurements supported hypotheses on both unsteady separation mechanisms and dynamics for a delta wing. Unsteady lift integrations over time highlighted relations between reduced frequency and mean angle of attack for total bounded vorticity throughout the pitching cycle.

Numerical simulation of forced convection heat transfer from a cylinder in crossflow

Forced convection heat transfer from an isolated cylinder in crossflow is investigated for Reynolds numbers up to 200 by direct numerical simulation of the Navier-Stokes and energy equations using the spectral element method. The numerical predictions for the size of the wake, the temporal and spatial structure of the von Karman vortex street, the unsteady lift and drag coefficient, and the unsteady local heat transfer coefficient are all in excellent agreement with available experimental data. Various outflow boundary conditions for the velocity field are employed to account for the unboundedness of the domain, while for the temperature field the conditions of uniform heat flux and constant cylinder temperature are simulated.

Verification of calculation methods for unsteady airloads in the prediction of transonic flutter

Various engineering-type methods to calculate unsteady airloads on wings in transonic flow were applied in flutter calculations for a semispan flutter model of a supercritical wing. Verification was performed on the basis of comparing flutter characteristics, in which special attention was given to the prediction of transonic dips in the flutter boundaries. The methods were able to produce useful results when applied complementarity. ^0.95 Nomenclature b = dimensionless shift of aerodynamic center c =wing section chord, m C/n = sectional mean lift coefficient pressure coefficient at 0.95 chord, 0.7 span, upper side / = frequency, Hz k = reduced frequency related to semichord ka,ma = sectional unsteady lift and moment coefficients (AGARD notation, m related to 0.25 chord); kij.my = sectional unsteady lift and moment influence coefficients (induced by strip j, at strip /) MOO = Mach number P0 —

Wind-Tunnel Study of the Flutter Characteristics of a Supercritical Wing

A wind-tunnel flutter test on a supercritical wing model is described. Objectives of the test were to investigate the transonic dip and to make comparisons with calculated flutter characteristics in which a quasi-threedimensional transonic theory was used. The beginning of a transonic dip was measured and a satisfactory agreement with theory could be found. An additional flutter instability in the bottom of the transonic dip could be correlated with the loss of transition strip effectivity at low Reynolds numbers. Nomenclature a,b = correction factors [Eqs. (2)] c =chord Clo = sectional steady lift coefficient CL - wing lift coefficient / = frequency g = damping coefficient k = reduced frequency (related to semichord) k - sectional unsteady lift coefficient, k2D, k3D m = sectional unsteady moment coefficient (related to quarterchord), m2D, m3D MO, = Mach number P0 = stagnation pressure q = generalized coordinate Rec = Reynolds number related to mean aerodynamic chord xt = position of transition strip a = wing angle of incidence A = (mean) sweep angle

Inviscid Flow through Cascades in Oscillatory and Distorted Flow

The present paper deals with the flow through a staggered cascade of airfoils in which unsteady disturbances from the upstream are swept down with the flow, as in the case of unsteady or distorted inlet flow conditions in an axial flow compressor. In the oscillatory case, unsteady normal velocity fluctuations which are carried down with the steady-state flow, like traveling waves, cause varying angles of attack along the chord lengths of the airfoils. Disturbances due to steady-state circumferential inlet distortion can be decomposed into Fourier components of oscillatory flows with some phage lag between the blades. The problem has been formulated under the assumptions of incompressibl e potential flow. An approximate method of solution has been developed for the integral equations involved and numerical results have been obtained for oscillatory flows. The unsteady lift coefficient of the airfoils has been obtained as a function of the frequency of the oscillations. The amplitude of the fluctuating lift for a cascade decreases from the steady state value with increasing frequency more slowly than it does for a single airfoil. The quantitative behavior of this has been studied for different values of stagger angle and solidity of the cascade. Nomenclature J a = distance between the trailing edges of two adjacent airfoils of a cascade c = semichord length of an airfoil CL = lift coefficient denned in Eq. (28) H = transfer function denned in Eq. (29) i = (-1)1/2 ix = unit vector in x direction iy = unit vector in y direction I = I(x) defined in Eq. (19) 3 = (~D1/2 k = number of cycles of distortion around the circumference in the distorted flow K = K(z) defined in Eq. (A13) L = L(x) defined in Eq. (18) N = number of blades of the rotor Ap* = pressure difference—Eq. (26) RI = inner radius of the compressor Rz = outer radius of the compressor -Ravg = average radius of the compressor t* = time £o* = time for one revolution of the rotor T = cascade spacing parameter—a/c vs* = see Eq. (Al) vp* = see Eq. (A2) vax = axial velocity of flow in the annulus Vrot = rotational velocity of the airfoils vrei = flow velocity relative to the blades vx* = x*component of the velocity field ^j/* = ?/*component of the velocity field F* - F*(2*)—Eq. (9) Vx* = real part of V* Vy* = real part of iV* w = unsteady normal velocity distribution of the flow relative to the blades

Kinematically consistent unsteady aerodynamic coefficients in supersonic flow

AbstractA finite element method to determine unsteady aerodynamic influence coefficients, consistent with the stiffness and inertia properties of a lifting surface in supersonic flow, is described. This is basically a kinematic method, which reduces the dynamical equations of a non‐conservative system to a simple and elegant form. It is illustrated by application to a delta wing using triangular elements to calculate steady and unsteady lift and moment coefficients. Throughout the calculations only a coarse grid system has been employed and the answers have been compared with available results.

Experimental Determination of Steady and Unsteady Loads on a Surface Piercing, Ventilated Hydrofoil

Measured steady and unsteady section lift and moment coefficients at two spanwise locations on a surface-piercing ventilated hydrofoil are presented. The foil, of wedge cross section, was supported vertically, and submerged one chord length from the tip. Excitation in rigid-body rolling and pitching modes to the cantilevered foil produced the unsteady loads. All tests were made at a nominal angle of attack of 12 deg.