Wanan Sheng

A Modified Dynamic Stall Model for Low Mach Numbers

The Leishman–Beddoes dynamic stall model is a popular model that has been widely applied in both helicopter and wind turbine aerodynamics. This model has been specially refined and tuned for helicopter applications, where the Mach number is usually above 0.3. However, experimental results and analyses at the University of Glasgow have suggested that the original Leishman–Beddoes model reconstructs the unsteady airloads at low Mach numbers less well than at higher Mach numbers. This is particularly so for stall onset and the return from the fully stalled state. In this paper, a modified dynamic stall model that adapts the Leishman–Beddoes dynamic stall model for lower Mach numbers is proposed. The main modifications include a new stall-onset indication, a new return modeling from stalled state, a revised chordwise force, and dynamic vortex modeling. The comparisons to the Glasgow University dynamic stall database showed that the modified model is capable of giving improved reconstructions of unsteady aerofoil data in low Mach numbers.

A New Stall-Onset Criterion for Low Speed Dynamic-Stall

The Beddoes/Leishman dynamic-stall model has become one of the most popular for the provision of unsteady aerofoil data embedded in much larger codes. The underlying modeling philosophy was that it should be based on the best understanding, or description, of the associated physical phenomena. Even though the model was guided by the flow physics, it requires significant empirical inputs in the form of measured coefficients and constants. Beddoes provided these for a Mach number range of 0.3–0.8. This paper considers one such input for a Mach number of 0.12, where, from the Glasgow data, it is shown that the current stall-onset criterion, and subsequent adjustments, yield problematic results. A new stall criterion is proposed and developed in the best traditions of the model. It is shown to be very capable of reconstructing the Glasgow’s data for stall onset both the ramp-up and oscillatory tests.

On the Generation of a Helicopter Aerodynamic Database

The GOAHEAD (Generation of an Advanced Helicopter Experimental Aerodynamic Database for CFD code validation) consortium was created in the frame of an EU-project in order to create an experimental database for the validation of 3D-CFD and comprehensive aeromechanics methods for the prediction of unsteady viscous flows. This included the rotor dynamics for complete helicopter configurations, i.e. main rotor - fuselage - tail rotor configurations with emphasis on viscous phenomena like flow separation and transition from laminar to turbulent flow. The wind tunnel experiments have been performed during two weeks in the DNW-LLF on a Mach-scaled model of a modem transport helicopter consisting of the main rotor, the fuselage, control surfaces and the tail rotor. For the sake of controlled boundary conditions for later CFD validation, a closed test section has been used. The measurement comprised global forces of the main rotor and the fuselage, steady and unsteady pressures, transition positions, stream lines, position of flow separation, velocity profiles at the test section inlet, velocity fields in the model wake, vortex trajectories and elastic deformations of the main and tail rotor blades.

On thermodynamics in the primary power conversion of oscillating water column wave energy converters

The paper presents an investigation to the thermodynamics of the air flow in the air chamber for the oscillating water column wave energy converters, in which the oscillating water surface in the water column pressurizes or de-pressurises the air in the chamber. To study the thermodynamics and the compressibility of the air in the chamber, a method is developed in this research: the power take-off is replaced with an accepted semi-empirical relationship between the air flow rate and the oscillating water column chamber pressure, and the thermodynamic process is simplified as an isentropic process. This facilitates the use of a direct expression for the work done on the power take-off by the flowing air and the generation of a single differential equation that defines the thermodynamic process occurring inside the air chamber. Solving the differential equation, the chamber pressure can be obtained if the interior water surface motion is known or the chamber volume (thus the interior water surface motion) i...

Prediction of Dynamic Stall Onset for Oscillatory Low-Speed Airfoils

This research presents some common features of oscillatory airfoils, and the method for indicating dynamic stall onset for the unsteady process. Under deep stall conditions, the stall-onset angle in oscillation is independent of the mean angle of the oscillatory motion, and by combining the reduced frequency and the amplitude of the oscillatory motion, the equivalent reduced pitch rate is an analog of this motion to the constant reduced pitch rate of the ramp-up motion. By correlating with the measured data, and with the ramp-up results, the equivalent reduced pitch rate can be defined as a representation for the oscillatory motion. Accordingly, the triple-parameter problem of an oscillation (mean angle, reduced frequency, and amplitude) degrades into the single-parameter problem (equivalent reduced pitch rate). Based on these foundations, an extension of the stall-onset criterion is then made for oscillatory airfoils: a method of extracting the stall-onset parameters directly from oscillatory test data, and an indication of stall onset for the oscillatory airfoils. The results from the new proposed method have shown the consistency with the data of Glasgow University and the public data.

Assessment of Wave Energy Extraction From Seas: Numerical Validation

In developing a wave energy converter (WEC), assessing and rating the device is a difficult, but important issue. Conventionally, a large scaled device (maybe large enough for accommodating a power takeoff (PTO) system) or prototype device is needed to be tested in wave tanks or in seas in different wave conditions so that a power matrix for the device can be defined using scaling or interpolation/extrapolation methods. Alternatively, a pure numerical simulation in time-domain may be used for assessing the power capture capacities of wave energy devices. For the former, it is convincing, but can be especially difficult in the early stages of development, when small scaled models are normally used; and for the latter, the pure numerical simulation may not be very reliable and convincing, especially when the dynamic problem is very complicated. In this paper, a method for assessing the captured wave power for a device from its power capture response is presented. In the proposed method, a measured or calculated linear power capture response of the device is combined with wave spectrum to compute the average captured power function. Once the average captured power function is obtained, the overall average captured power corresponding to the wave state can be easily calculated. If a linear power capture response is obtained from a model test, the power assessment based on this proposed method can be very convincing and reliable. To illustrate the application of the proposed method, an example of a fully linear dynamic system, including the linear hydrodynamics of the floating structure and a linear power takeoff, is considered. For such a system, the frequency-domain analysis can be employed to obtain the performance of the floating device under waves and the power takeoff system. The hydrodynamic performance of the wave energy converter is then used to define the power capture response and to calculate the average captured power functions in different sea states. Then, the captured power of the device in different sea states, i.e, the power matrix, can be calculated, and accordingly, the device can be assessed and rated. To validate the proposed method, a time-domain analysis is also performed for a cross-check. In the time-domain analysis, the hydrodynamic coefficients and responses are first assessed in frequency-domain, and then transformed into the relevant terms by means of impulse response functions for establishing the time-domain (TD) equation. By comparing the results from frequency-domain and time-domain analyses of irregular waves, it can be concluded that the proposed wave energy capture assessment method can be used in assessing or rating the device.

Improved dynamic-stall-onset criterion at low Mach numbers

cN = normal force coefficient, N=qc cp = pressure coefficient, p=q D = drag f = dimensionless separation point in terms of chord length, x=c L = lift of airfoil section M = Mach number m = pitching moment about the axis of the quarter-chord N = normal force q = dynamic pressure, 0:5 V r = reduced pitch rate, _ c=2V (for oscillatory motion of an airfoil, 0 cos!t) r0 = reduced pitch rate that delimits the dynamic stall and quasi-steady stall (normally, 0:01) s = nondimensional time, 2Vt=c T = time-delay constant for angle of attack t = time V = freestream velocity = angle of attack or incidence 0 = lagged angle of attack cr = critical onset angle (dependent on reduced pitch rate) ds = angle of dynamic-stall onset ds0 = constant critical onset angle ss = static stall angle = a step change in a sampled system 0 = amplitude of airfoil oscillation k = reduced frequency, !c=2V = linear fit coefficient for stall-onset incidences ! = frequency of oscillatory motion of airfoils Introduction

Assessment of primary energy conversions of oscillating water columns. I. Hydrodynamic analysis

This is an investigation on the development of a numerical assessment method for the hydrodynamic performance of an oscillating water column (OWC) wave energy converter. In the research work, a systematic study has been carried out on how the hydrodynamic problem can be solved and represented reliably, focusing on the phenomena of the interactions of the wave-structure and the wave-internal water surface. These phenomena are extensively examined numerically to show how the hydrodynamic parameters can be reliably obtained and used for the OWC performance assessment. In studying the dynamic system, a two-body system is used for the OWC wave energy converter. The first body is the device itself, and the second body is an imaginary “piston,” which replaces part of the water at the internal water surface in the water column. One advantage of the two-body system for an OWC wave energy converter is its physical representations, and therefore, the relevant mathematical expressions and the numerical simulation can be straightforward. That is, the main hydrodynamic parameters can be assessed using the boundary element method of the potential flow in frequency domain, and the relevant parameters are transformed directly from frequency domain to time domain for the two-body system. However, as it is shown in the research, an appropriate representation of the “imaginary” piston is very important, especially when the relevant parameters have to be transformed from frequency-domain to time domain for a further analysis. The examples given in the research have shown that the correct parameters transformed from frequency domain to time domain can be a vital factor for a successful numerical simulation.

Power Takeoff Optimization for Maximizing Energy Conversion of Wave-Activated Bodies

This paper presents a fundamental investigation on optimizing the power takeoff (PTO) for maximizing wave energy conversion of the wave-activated bodies (WABs) wave energy converters. In this research, two relative heave motions are taken for capture power, and a linear PTO is considered in the primary analysis. For such a linear dynamic system, the frequency-domain analysis can be carried out, and an analytical formula can be derived for the optimized frequency-dependent PTO damping coefficient, which can be used to determine an optimized PTO damping for maximizing wave energy conversion in regular waves. However, when an optimized PTO is required for maximizing energy conversion from ocean waves, the PTO damping optimization may be very different and much less certain, because it may be based on one of many characteristic periods of the given sea state and the dependency may change from different sea states. For this reason, the optimized PTO damping coefficient for a given sea state must be studied carefully. Another important aspect of the research is to examine whether an optimized nonlinear PTO can take more energy out from waves than that of an optimized linear PTO. For this purpose, the maximized capture powers by the optimized linear and nonlinear PTOs are compared using the time-domain analysis. It has been shown from the examples that the maximized capture power by a nonlinear PTO system may exceed that by the linear PTO, but only marginally (less than 1%). Hence, it can be generally concluded that the maximized power using a linear PTO system can be a very good indicator for the device in extracting the maximal energy from waves regardless of the linear or nonlinear PTO in actual use. This conclusion may help simplify the analysis of the wave energy converters in terms of the energy production as well as the device optimization for improving energy conversion capacity.

Assessment of primary energy conversions of oscillating water columns. II. Power take-off and validations

This is the second part of the assessment of primary energy conversions of oscillating water columns (OWCs) wave energy converters. In the first part of the research work, the hydrodynamic performance of OWC wave energy converter has been extensively examined, targeting on a reliable numerical assessment method. In this part of the research work, the application of the air turbine power take-off (PTO) to the OWC device leads to a coupled model of the hydrodynamics and thermodynamics of the OWC wave energy converters, in a manner that under the wave excitation, the varying air volume due to the internal water surface motion creates a reciprocating chamber pressure (alternative positive and negative chamber pressure), whilst the chamber pressure, in turn, modifies the motions of the device and the internal water surface. To do this, the thermodynamics of the air chamber is first examined and applied by including the air compressibility in the oscillating water columns for different types of the air turbine ...