Unsteady Potential Flow Theory Research Articles

The effect of variable rotary motion of a flapping wing rotor on its aerodynamic performance based on an improved unsteady vortex ring method

In the previous aerodynamic analysis using a potential flow-based unsteady aerodynamic model for the flapping wing rotor (FWR), the average rotary velocity and flapping frequency together with the flapping and twist angles are usually taken as the FWR kinematics of motion. In the present study, an unsteady vortex ring method (UVRM) is developed to take the rotary velocity variation of the FWR during the flapping motion into account based on 3D unsteady potential flow theory. The UVRM is validated by comparing with the published results of a flapping wing and an FWR model. An FWR test model and the corresponding experimental platforms including a wing motion tracking system and a force measurement system are built to measure the FWR motion and associated forces. Three FWR test cases of different input voltages and kinematics of flapping motion are considered to measure the aerodynamic forces and compare with the UVRM results. The results show that the differences between the measured and pre-set flapping angles (-50°∼ 20°) for the FWR are negligible for all the cases, but the differences in the variation amplitudes of the measured twist angle and the corresponding pre-set rigid twist angles can be as much as about 15°. Also, the FWR rotary velocity varies dramatically during a flapping cycle. For one of the cases with the -10°∼30° pre-set twist angle and 4 V input voltage, the difference between the maximum and minimum rotary speed is about 1451°/s, which makes a significant effect on the FWR aerodynamic performance. The results also show that the calculated lift forces using the UVRM and the measured real-time rotary speeds during a flapping motion are very close to the experimental results. While the calculated results by taking the FWR's average rotary speeds show apparent differences (up to about 25%) from the measured lift forces in most of the cases. Overall, the UVRM provides an efficient method for the FWR aerodynamic analysis with higher accuracy by taking the effect of variable rotary motion and twist angle of the FWR during a flapping cycle into account.

Scaling the dynamic response and stability of composite hydrodynamic lifting surfaces

Imperfectly scaled models are commonplace in aerodynamics and hydrodynamics because few facilities can meet all the flow and structural scaling requirements. The objectives of this work are to (1) derive and numerically validate scaling relations for the steady-state and dynamic hydroelastic response and stability of hydrodynamic composite lifting surfaces and (2) to investigate the effect of imperfect scaling on the steady-state and dynamic response, as well as hydroelastic stability of said surfaces. We derive proper scaling laws and validate them through numerical simulations using unsteady potential flow and composite beam theory. We investigate the prediction of inception of a new, low-frequency mode that only develops at sufficiently high speeds using scaled models. We demonstrate scaling effects on the modal frequencies, damping coefficients, and hydroelastic instability boundaries by comparing cases with fully enforced scaling laws and cases with relaxed similarities. Using the same material for both the prototype and reduced length-scale models results in imperfect scaling; the steady-state and dynamic hydroelastic responses are not scaled, and smaller length-scale models exhibit delayed hydroelastic instabilities. The conclusion is that using appropriate materials for model scale tests to satisfy Cauchy number similarity is necessary for similar steady-state response, but dynamic similarity additionally requires similar solid-to-fluid added mass ratio. Proper scaling allows one to accurately interpret and assess the performance and stability of full-scale flexible composite lifting surfaces such as foils, propulsors, turbines, fins, rudders, energy saving devices, and energy harvesters.

An integrated measurement approach for the determination of the aerodynamic loads and structural motion for unsteady airfoils

The structural motion and unsteady aerodynamic loads of a pitching airfoil model that features an actuated trailing edge flap are determined experimentally using a single measurement and data processing system. This integrated approach provides an alternative to the coordinated use of multiple measurement systems for simultaneous position and flow field measurements in large-scale fluid–structure interaction experiments. The measurements in this study are performed with a robotic PIV system using Lagrangian particle tracking. Flow field measurements are obtained by seeding the flow with helium-filled soap bubbles, while the structural measurements are performed by tracking fiducial markers on the model surface. The unsteady position and flap deflection of the airfoil model are determined from the marker tracking data by fitting a rigid body model, that accounts for the motion degrees of freedom of the airfoil model, to the measurements. For the determination of the unsteady aerodynamic loads (lift and pitching moment) from the flow field measurements, two different approaches are evaluated, that are both based on unsteady potential flow and thin airfoil theory. These methods facilitate an efficient non-intrusive load determination on unsteady airfoils and produce results that are in good agreement with reference measurements from pressure transducers.

Non-intrusive determination of the unsteady surface pressure and aerodynamic loads on a pitching airfoil

The unsteady surface pressure distribution and aerodynamic loads on a pitching airfoil are determined non-intrusively using PIV measurements. An experimental test case is considered where the flow around the airfoil is mostly attached while the unsteady effects on the aerodynamic loads are significant. The surface pressure is calculated from the flow velocity measurements in the vicinity of the airfoil surface, that are obtained with a robotic PIV system, by using relations from unsteady potential flow and thin airfoil theory. The proposed approach is a robust and computationally efficient approach to obtain non-intrusive measurements of the unsteady surface pressure distribution and the aerodynamic loads, that are in good agreement with reference data from installed pressure transducer sensors.

Study on Mooring Design and Calculation Method of Ocean Farm Based on Time-Domain Potential Flow Theory

In order to calculate the mooring force of a new semi-submerged Ocean Farm quickly and accurately, based on the unsteady time-domain potential flow theory and combined the catenary model, the control equation of mooring cable is established, and the mooring force of the platform under the wave spectrum is calculated. First of all, based on the actual situation of the ocean environment and platform, the mooring design of the platform is carried out, and the failure analysis and sensitivity analysis of the single anchor chain by the time domain coupling method are adopted: including different water depth, cycle, pretension size, anchor chain layout direction and wind speed, etc. The analysis results confirm the reliability of anchoring method. Based on this, the mooring point location of the platform is determined, the force of each anchor chain in the anchoring process is calculated, and the mooring force and the number of mooring cables are obtained for each cable that satisfies the specification, the results of this paper can provide theoretical calculation methods for mooring setting and mooring force calculation of similar offshore platforms.

Flow Interactions Between Low Aspect Ratio Hydrofoils in In-line and Staggered Arrangements.

Many species of fish gather in dense collectives or schools where there are significant flow interactions from their shed wakes. Commonly, these swimmers shed a classic reverse von Kármán wake, however, schooling eels produce a bifurcated wake topology with two vortex rings shed per oscillation cycle. To examine the schooling interactions of a hydrofoil with a bifurcated wake topology, we present tomographic particle image velocimetry (tomo PIV) measurements of the flow interactions and direct force measurements of the performance of two low-aspect-ratio hydrofoils () in an in-line and a staggered arrangement. Surprisingly, when the leader and follower are interacting in either arrangement there are only minor alterations to the flowfields beyond the superposition of the flowfields produced by the isolated leader and follower. Motivated by this finding, Garrick’s linear theory, a linear unsteady hydrofoil theory based on a potential flow assumption, was adapted to predict the lift and thrust performance of the follower. Here, the follower hydrofoil interacting with the leader’s wake is considered as the superposition of an isolated pitching foil with a time-varying cross-stream velocity derived from the wake flow measurements of the isolated leader. Linear theory predictions accurately capture the time-averaged lift force and some of the major peaks in thrust derived from the follower interacting with the leader’s wake in a staggered arrangement. The thrust peaks that are not predicted by linear theory are likely driven by spatial variations in the flowfield acting on the follower or nonlinear flow interactions; neither of which are accounted for in the simple theory. This suggests that unsteady potential flow theory that does account for spatial variations in the flowfield acting on a hydrofoil can provide a relatively simple framework to understand and model the flow interactions that occur in schooling fish. Additionally, schooling eels can derive thrust and efficiency increases of 63-80% in either a in-line or a staggered arrangement where the follower is between two branched momentum jets or with one momentum jet branch directly impinging on it, respectively.

Unsteady Aerodynamic Model Based on the Leading-Edge Stagnation Point

The significance of the leading-edge stagnation point as an unsteady aerodynamic observable is investigated. Using first-order unsteady potential flow theory, a simple model relating the stagnation point to the unsteady lift is derived for an airfoil undergoing arbitrary unsteady maneuvers. In particular, the dynamic circulatory effects are shown to be accounted for by tracking the stagnation point. Linearization permits the superposition of solutions for thickness and camber. The model is validated using numerical simulations, employing both steady and unsteady panel methods. In addition, its validity is investigated experimentally through steady and unsteady wind-tunnel tests of a wing section. The stagnation point is estimated in real time from the convective heat transfer distribution measured using a hot-film sensor array instrumented around the wing’s leading edge. Applications of these findings to flutter suppression and gust-load alleviation are experimentally demonstrated.

Steady and unsteady pressure measurements on a swept-wing aircraft

AbstractSteady and unsteady pressure measurements are conducted for a tailless aircraft model. The main aim with the presented experimental work is to investigate the difficulties and possibilities involved in using an available pressure sensing system for accurate unsteady pressure measurement. The experimental procedure which is utilised for unsteady pressure measurements is described in detail. In particular, the importance of synchronised timing is recognised. For a harmonically varying pressure a small time delay in the measurement chain can result in a significant phase shift. Also, difficulties and uncertainties that are still present are pointed out. The results from these experiments are compared to numerical results based on unsteady potential flow theory. In general, the experimental and computational results show similar trends. Especially good agreement is found for the steady pressure measurements. For the unsteady pressure measurements a possible Reynolds number dependency is found for the considered test conditions.

Experimental study of pitching and plunging airfoils at low Reynolds numbers

Measurements of the unsteady flow structure and force time history of pitching and plunging SD7003 and flat plate airfoils at low Reynolds numbers are presented. The airfoils were pitched and plunged in the effective angle of attack range of 2.4°–13.6° (shallow-stall kinematics) and −6° to 22° (deep-stall kinematics). The shallow-stall kinematics results for the SD7003 airfoil show attached flow and laminar-to-turbulent transition at low effective angle of attack during the down stroke motion, while the flat plate model exhibits leading edge separation. Strong Re-number effects were found for the SD7003 airfoil which produced approximately 25 % increase in the peak lift coefficient at Re = 10,000 compared to higher Re flows. The flat plate airfoil showed reduced Re effects due to leading edge separation at the sharper leading edge, and the measured peak lift coefficient was higher than that predicted by unsteady potential flow theory. The deep-stall kinematics resulted in leading edge separation that led to formation of a large leading edge vortex (LEV) and a small trailing edge vortex (TEV) for both airfoils. The measured peak lift coefficient was significantly higher (~50 %) than that for the shallow-stall kinematics. The effect of airfoil shape on lift force was greater than the Re effect. Turbulence statistics were measured as a function of phase using ensemble averages. The results show anisotropic turbulence for the LEV and isotropic turbulence for the TEV. Comparison of unsteady potential flow theory with the experimental data showed better agreement by using the quasi-steady approximation, or setting C(k) = 1 in Theodorsen theory, for leading edge–separated flows.

Instability of a long ribbon hanging in axial air flow

A ribbon hanging in a vertical air stream experiences sudden vibrations by flutter when the flow velocity reaches a critical value. The experiments conducted here for strips made of different materials show two distinct behaviours depending on the length of the strip. For short strips, the critical flow velocity depends strongly on the length, whereas for longer strips the critical velocity becomes independent of the length. These behaviours are analysed using a model originally derived by Datta, based on a slender-body approximation and unsteady potential flow theory. This yields an equation of motion similar to that pertaining to a hanging pipe-conveying fluid. The corresponding critical velocities are in relatively good agreement with those of the experiments for a set of 12 different ribbons. An asymptotic critical velocity may thus be defined corresponding to the limit of very long ribbons. The model predicts that this velocity only depends on the ratio between the fluid added mass and the ribbon mass. This is compared with experiments using strips of various widths and materials, and relation is made to the case of a hanging fluid-conveying pipe, addressed in a recent paper, and with the case of long towed cylinders.

811 ガイドベーン中の振動遠心羽根車に働く非定常力の解析(関東支部 茨城講演会)

Lateral fluid forces acting on a rotating centrifugal impeller in whirling motion were analyzed by using unsteady potential flow theory. Impellers operating in diffusers with vanes were modeled and the fluid forces were calculated. Results of fluid forces were converted to mass, damping, stiffness matrices by the Fourier Integral and least square method. The results for impellers with guide vanes showed that the time averaged values of fluid forces remained almost unchanged, while there were significant instantaneous fluctuations due to the impeller/guide vane interactions. And it was found that the elements of matrices for impeller with guide vanes were usually greater than those for impeller without guide vanes.

Theoretical Analysis of Fluid Forces on an Open-Type Centrifugal Impeller in Whirling Motion

For turbomachines operating at supercritical shaft speed, it is important to understand the characteristics of unsteady fluid forces on the impeller that occur due to shaft vibration. The present paper treats the forces on an open-type centrifugal impeller in whirling motion using unsteady potential flow theory. The whirling forces obtained agree reasonably with experimental results and show a destabilizing region at small positive whirl. It was found that the destabilizing force is due to the forces on the hub caused by temporal change in the thickness of the flow channel, with minor contribution of tip leakage on the destabilization.

Theoretical Analysis of Fluid Forces on an Open-Type Centrifugal Impeller in Whirling Motion.

For turbomachineries operating at supercritical shaft speed, it is important to understand the characteristics of unsteady fluid forces on the impeller which occur due to shaft vibration. The present paper treats the forces on an open-type centrifugal impeller in whirling motion using unsteady potential flow theory. The whirling forces obtained agree fairly well with experimental results and show a destabilizing region at small positive whirl. It was found that the destabilizing force is due to the forces on the hub caused by the change in flow thickness, with minor effect of tip leakage on the destabilization.

Investigation of rotor tip vortex interactions with a body

Experiments were conducted to examine rotor tip vortex interactions with a body in low-speed forward flight. Unsteady pressure measurements were made at points along the top and around the circumference of the body surface. Flow visualization of the rotor wake was performed using the wide-field shadowgraph method. Considerable insight into the tip vortex interaction processes was obtained by correlating the pressure loads with the vortex trajectories as they approached, distorted, and impinged on the body surface. Unsteady potential flow theory was explored as a means of predicting the unsteady pressure loads on the body surface, using prescribed tip vortex trajectories measured from flow visualization. The results have shown that the process of tip vortex interaction with a body can be divided into three regimes: 1) close tip vortex/body interactions, which is an inviscid flow regime; 2) vortex/surface impingement; and 3) postvortex/surface impingement; the latter involves viscous effects. The results have also shown that the pressures at points on the body exhibited a high sensitivity to tip vortex convection speed and location, which makes the general prediction of such interactional phenomena difficult with existing rotor/airframe interaction models.

The Effect of Steady Aerodynamic Loading on the Flutter Stability of Turbomachinery Blading

An aeroelastic analysis is presented that accounts for the effect of steady aerodynamic loading on the aeroelastic stability of a cascade of compressor blades. The aeroelastic model is a two-degree-of-freedom model having bending and torsional displacements. A linearized unsteady potential flow theory is used to determine the unsteady aerodynamic response coefficients for the aeroelastic analysis. The steady aerodynamic loading was caused by the addition of (1) airfoil thickness and camber and (2) steady flow incidence. The importance of steady loading on the airfoil unsteady pressure distribution is demonstrated. Additionally, the effect of the steady loading on the tuned flutter behavior and flutter boundaries indicates that neglecting either airfoil thickness, camber, or incidence could result in nonconservative estimates of flutter behavior.

Unsteady Aerodynamic Measurements on a Rotating Compressor Blade Row at Low Mach Number

An experiment was conducted on a heavily instrumented isolated model compressor rotor to study the unsteady aerodynamic response of the blade row to a controlled pitching oscillation of all blades in an undistorted flow, and to a circumferential inlet flow distortion with nonoscillating blades. To accomplish this, miniature pressure transducers were embedded in the blades and the unsteady pressure time histories were recorded. Both phases of the experiment were performed over a wide range of flow coefficient, from Cx/Um = 0.6 to 0.95 in 0.05 steps, and data were taken at each condition for sinusoidal disturbances characterized by one, two, and four per revolution waves. Steady-state data were acquired for flow coefficients from 0.55 to 0.99 in 0.05 steps. In this paper the steady and unsteady results of the portion of this experiment dealing with oscillating blades are compared with analytical predictions, and the steady results are compared with experimental data from previous work. Although the model blades were instrumented at five spanwise stations, only the midspan measurements will be presented herein. The measured pressures for nonoscillating blades were in good agreement with the steady potential flow predictions (and with previous steady experimental data) when the measured exit angle was imposed as the downstream boundary condition for the analysis. It was found that a quasi-steady approach yielded marginally acceptable agreement with the experimental results for the lowest frequency tested. For the higher reduced frequencies, the experimental data could not be modeled in this manner. In contrast, a comparison of the measurements with the Verdon–Caspar unsteady potential flow theory produced generally good agreement except near the leading edge at high mean incidence (i.e., at low flow coefficient). At high incidence the blades in this experiment had very high steady pressure gradients near the leading edge and it is suspected that this may be responsible for the lack of agreement. The agreement was somewhat better at the higher frequencies.

Lateral Fluid Forces on Whirling Centrifugal Impeller (1st Report: Theory)

Lateral fluid forces acting on a rotating centrifugal impeller in whirling motion are analyzed using unsteady potential flow theory. Impellers operating in diffusers with and without vanes are modeled and the fluid forces calculated for different whirl speeds and flow rates. The influences of these parameters are clarified by parametric calculations. The results for whirling impellers operating in vaneless diffusers show that the fluid forces exert a damping effect on the rotor whirling motion at all operating conditions. The results for impellers operating in vaned diffusers or guide vanes show that the time averaged values of fluid forces remain almost unchanged, while there are significant instantaneous fluctuations due to the impeller/guide vane interactions.

Experimental and Theoretical Studies of Two-Dimensional Fixed-Type Cavities

Theoretical and experimental studies have been made of the growth and collapse of fixed cavities in a two-dimensional convergent-divergent nozzle. In this particular configuration an important feature was a re-entrant liquid jet which invaded the growing cavity from the downstream end, travelling upstream along the wall and interrupting the cavity when it reached the nozzle throat. A simple two-dimensional unsteady potential flow theory, developed to model the cycle, gave reasonable agreement with cinephotography and predicted the jet behavior. Because vaporization was neglected the theory overestimated the speed of the cycle.

Coupled Blade-Disk-Shroud Flutter Instabilities in Turbojet Engine Rotors

An energy method is used to investigate a flutter instability of turbojet engine rotors which is caused by the interactions between unsteady air loading and the coupled vibration modes of the rotating blade-disk-shroud system. It is shown, analytically, in this parametric study that under certain circumstances the coupling between blade modes permits the transfer of energy from the air to the blade-disk-shroud system, giving rise to a self-excited instability. Both unsteady potential flow theory and empirical data for oscillating airfoils at high incidence are used.