Table of Contents
Type: Full Masters Dissertation | Subject: Mechanical Engineering | Level: Masters | Word Count: ~13,500 words
This model Full Masters Dissertation was produced by an Essays UK specialist as reference material for learning purposes only. For support in this field, see our mechanical engineering writers.
Overview: This model MSc dissertation presents a computational fluid dynamics (CFD) study aimed at optimising the aerodynamic design of wind turbine blades for low-wind-speed onshore sites in the United Kingdom. It demonstrates how a postgraduate engineering dissertation is structured, how a Reynolds-Averaged Navier-Stokes rotor model is built and validated, and how parametric results on aerofoil selection, twist and chord are critically evaluated against the published literature. All numerical values are illustrative and intended to show method and argument, not to report real measured performance.
Much of the United Kingdom’s unexploited onshore wind resource lies at inland sites where the long-term mean wind speed is modest, commonly in the region of 5 to 6 metres per second at hub height. Turbines designed primarily for windier coastal and offshore conditions tend to operate below their aerodynamic optimum at such sites, and the lower relative velocities seen across the blade reduce the chord-based Reynolds number, which in turn degrades aerofoil performance. This dissertation investigates whether the aerodynamic design of a three-bladed, horizontal-axis rotor representative of a sub-megawatt onshore machine can be improved for low-wind operation through a systematic computational fluid dynamics (CFD) study. A steady, incompressible Reynolds-Averaged Navier-Stokes model of a single blade passage was constructed using a periodic rotating reference frame, closed with the shear-stress transport turbulence model coupled to a correlation-based laminar-turbulent transition model. The methodology was verified through a four-level mesh-independence study, with discretisation uncertainty quantified using the Grid Convergence Index, and validated against publicly available rotor measurements from the literature, reproducing shaft torque in attached-flow conditions to within approximately six per cent. A parametric investigation then examined aerofoil selection, spanwise twist distribution and chord distribution relative to a baseline blade. The optimised configuration, which combined a high lift-to-drag low-Reynolds-number aerofoil over the outboard span with a re-profiled twist schedule and a modest reduction in outboard solidity, raised the peak power coefficient from an illustrative 0.452 to 0.486 at a design tip-speed ratio of seven. Translated through a Rayleigh wind-speed distribution for a representative 5.5 metres per second site, this corresponds to an estimated annual energy production uplift of roughly seven and a half per cent. The findings indicate that targeted aerodynamic re-design, rather than wholesale rotor enlargement alone, offers a credible route to improving the economics of low-wind onshore sites. The study also reflects critically on the limitations of steady single-passage modelling and recommends unsteady, full-rotor and aeroelastic analysis as the next stage of work.
Wind energy occupies a central position in the United Kingdom’s strategy for decarbonising electricity generation. Over the past two decades the sector has matured from a marginal contributor to one of the largest sources of renewable electricity on the national system, with onshore and offshore wind together supplying a substantial and growing share of annual demand. While offshore wind has attracted the greater part of recent policy attention and capital investment because of the strong and consistent wind resource found in the North and Irish Seas, onshore wind remains important. It is considerably cheaper to install and connect, it can be deployed more rapidly, and it allows generation to be distributed closer to centres of demand. For communities and landowners, onshore turbines also represent a tangible and comparatively low-cost means of participating in the energy transition.
The onshore resource, however, is spatially uneven. The windiest onshore locations, principally in upland Scotland, Wales and parts of northern England and the south-west, have long been the preferred targets for development because the aerodynamic power available to a turbine scales with the cube of the wind speed. A relatively small increase in mean wind speed therefore yields a disproportionately large increase in energy yield, and early development understandably concentrated on these favourable sites. As the best locations are progressively taken, and as planning, grid and community constraints further restrict where turbines may be placed, attention is turning towards sites with more modest wind resources. Many such sites, particularly across lowland England, experience long-term mean wind speeds at hub height that are appreciably lower than those at the upland locations for which much of the existing fleet was conceived.
Operating a turbine at a low-wind site is not simply a matter of accepting a lower output from an unchanged machine. The aerodynamic design of a rotor, and of its blades in particular, embodies a set of implicit assumptions about the wind speeds and rotational speeds at which the machine will most often operate. A blade whose twist and chord distributions are tuned for a high design wind speed will present sub-optimal angles of attack along much of its span when the free-stream velocity is persistently lower than intended. Furthermore, the reduction in relative velocity at low wind speeds lowers the chord-based Reynolds number experienced by each blade section, and aerofoil performance is sensitive to Reynolds number: lift-to-drag ratios generally deteriorate as the Reynolds number falls, chiefly because of the earlier onset and growth of laminar separation. The consequence is that a rotor transplanted from a windy site to a calmer one may extract a smaller fraction of the available power than its headline performance figures would suggest.
This mismatch between a rotor’s design assumptions and its operating environment is not merely academic. Because the energy captured over a year is the integral of the power curve weighted by the frequency of each wind speed, and because a low-wind site concentrates that frequency at the lower wind speeds where the rotor is most dependent on efficient aerodynamics, even a small deficit in the power coefficient at modest wind speeds propagates into a disproportionate loss of annual yield. The problem is therefore both physical, in the deterioration of aerofoil performance at reduced Reynolds number, and economic, in the sensitivity of a low-wind project’s revenue to that deterioration. It is this coupling of the aerodynamic and the economic that gives the detailed shape of the blade its importance and that frames the present investigation.
The international design standard for wind turbines, IEC 61400-1, classifies machines according to the reference wind speed and turbulence intensity they are designed to withstand, with the lower wind classes intended for the calmer sites of interest here (International Electrotechnical Commission, 2019). The industry response to the growth of low-wind sites has been to develop so-called low-wind or low-specific-power turbines. The dominant design lever has been to increase the swept area of the rotor relative to the rated capacity of the generator, by fitting a larger-diameter rotor to a given drivetrain. This raises the capacity factor and allows the machine to reach its rated power at a lower wind speed, improving the quality and predictability of the output. Rotor enlargement is effective, but it is not without penalty: longer blades are heavier and more expensive, they impose larger loads on the hub, nacelle and tower, and they raise the blade-tip height, which can aggravate the planning and visual-impact difficulties that already constrain onshore development in the United Kingdom.
Rotor enlargement also leaves a second, complementary lever comparatively underused: the detailed aerodynamic shape of the blade itself. Even for a rotor of fixed diameter, the choice of aerofoils, the spanwise distribution of twist and the spanwise distribution of chord together determine how efficiently the available kinetic energy is converted into shaft torque at any given operating condition. If these choices are re-optimised for the lower wind speeds and lower Reynolds numbers characteristic of a calm inland site, it may be possible to recover a meaningful fraction of the efficiency that is otherwise lost, without the mass, load and planning penalties that accompany a larger rotor. This dissertation is motivated by that possibility.
The central problem addressed here is that the aerodynamic design of conventional onshore rotors is generally optimised for wind and Reynolds-number conditions more favourable than those found at many of the low-wind sites now being considered for development in the United Kingdom. There is therefore a case for examining whether a rotor of fixed diameter can be re-designed, through its aerofoils, twist and chord, to improve its power coefficient and annual energy yield under low-wind conditions. Computational fluid dynamics offers a means of investigating this question with a higher-fidelity representation of the flow physics than the engineering models traditionally used in blade design, provided that the computational model is properly verified and validated and that its limitations are understood.
The overarching aim of this dissertation is to evaluate, using a verified and validated CFD methodology, the extent to which the aerodynamic performance of a representative onshore horizontal-axis wind turbine rotor can be improved for low-wind-speed sites in the United Kingdom through optimisation of blade aerofoil, twist and chord. To fulfil this aim, the following objectives were defined:
The objectives give rise to three research questions that the dissertation seeks to answer:
The study is deliberately bounded so that it can be completed within the time and computational resources available to a taught postgraduate project. The rotor diameter is held fixed throughout, so that the effect of aerodynamic re-design can be isolated from that of rotor enlargement. The analysis is confined to steady, incompressible, single-blade-passage CFD using a periodic rotating reference frame; it does not resolve the unsteady effects of yaw, wind shear, turbulence or tower passage, nor does it include the full three-bladed rotor or the nacelle and tower. Structural, aeroelastic and manufacturing considerations are acknowledged but not modelled, and the optimisation is aerodynamic rather than fully multidisciplinary. The numerical values reported for lift, drag, torque, power coefficient and energy yield are illustrative outputs of the model constructed here and of the assumed operating conditions; they are used to demonstrate method and to support argument, and they should not be read as measured performance of any real machine. These limitations are revisited in Chapter 5.
The remainder of the dissertation is organised into five chapters. Chapter 2 reviews the literature, moving from the UK onshore context and the fundamentals of rotor aerodynamics to low-Reynolds-number aerofoil behaviour and the state of the art in CFD rotor modelling, and concludes by articulating the research gap. Chapter 3 sets out the methodology, including the reference turbine, the governing equations, the turbulence and transition closures, the computational mesh, the boundary conditions, the parametric design matrix and the verification and validation strategy. Chapter 4 presents the results, beginning with mesh independence and validation and proceeding through the baseline performance, the parametric studies and the optimised blade to an estimate of annual energy production. Chapter 5 discusses and interprets these results, compares them with the literature and reflects critically on the methodology. Chapter 6 draws conclusions against the objectives, states the contribution of the work and recommends directions for further research.
This chapter reviews the body of knowledge on which the dissertation builds. It begins by situating the work within the UK onshore wind context and then develops the theoretical foundations of wind turbine aerodynamics, including the actuator-disc and blade element momentum frameworks that underpin conventional blade design. It proceeds to examine the behaviour of aerofoils at the low Reynolds numbers characteristic of low-wind operation, to survey the aerofoil families developed specifically for wind turbine use, and to review the application of computational fluid dynamics to rotor analysis, with particular attention to turbulence and transition modelling. Previous blade optimisation studies are then considered, and the chapter closes by identifying the gap that this dissertation addresses.
The distribution of the onshore wind resource across the United Kingdom has been mapped in successive wind atlases and reanalysis datasets, which consistently show a strong gradient from the windy upland and coastal regions of the north and west towards the calmer lowlands of central and eastern England (Troen and Petersen, 1989). For the purposes of turbine design, the practically relevant quantity is the long-term mean wind speed at hub height together with the shape of the wind-speed distribution, which is conventionally described by a Weibull distribution and, in the common special case of a shape parameter of two, by the Rayleigh distribution (Manwell, McGowan and Rogers, 2009). Sites with a lower mean wind speed not only offer less energy in absolute terms but also shift the operating point of a turbine towards lower wind speeds for a greater fraction of the year, which places a premium on aerodynamic efficiency in precisely the below-rated region where the machine spends most of its time.
The economic case for exploiting low-wind sites rests on the observation that, although the resource is poorer, such sites are often closer to demand, less environmentally sensitive in some respects, and more numerous than the diminishing stock of prime upland locations. The industry has responded with low-specific-power machines, in which a large rotor is matched to a comparatively small generator so that rated power is achieved at a lower wind speed and the capacity factor is raised (Burton et al., 2011). The classification framework of IEC 61400-1 formalises the distinction between wind regimes, with the lower wind classes and the bespoke Class S covering the calmer conditions relevant here (International Electrotechnical Commission, 2019). This literature establishes the practical importance of the problem but says comparatively little about how far the detailed aerodynamic shape of the blade, as distinct from its length, can be exploited to improve low-wind performance, which is the focus of the present study.
A further feature of the low-wind context deserves emphasis because it shapes the control strategy assumed later in this study. Modern utility-scale turbines are overwhelmingly variable-speed machines, in which the rotational speed is regulated below rated power so as to hold the tip-speed ratio close to the value that maximises the power coefficient, and the blade pitch is held fixed in this region before being used to shed power above rated wind speed. At a low-wind site the machine spends the great majority of its operating hours in this below-rated, optimum-tracking region, so the quantity that governs annual yield is the peak of the power-coefficient curve and its breadth around the design tip-speed ratio, rather than the rated power or the high-wind behaviour. This observation justifies the emphasis placed throughout the dissertation on the peak power coefficient as the primary objective and explains why an improvement concentrated in the below-rated region translates so directly into energy yield at a calm site.
The theoretical ceiling on the fraction of the wind’s kinetic energy that a rotor can extract is given by the actuator-disc analysis first associated with Betz, which yields a maximum power coefficient of sixteen twenty-sevenths, approximately 0.593 (Hansen, 2015). The power coefficient, defined as the shaft power divided by the kinetic power flux through the swept area, is the primary non-dimensional measure of rotor efficiency and is a function of the tip-speed ratio, the ratio of the blade-tip speed to the free-stream wind speed. Real rotors fall short of the Betz limit because of wake rotation, finite blade number and tip losses, and viscous drag on the blades, so that well-designed modern rotors achieve peak power coefficients in the region of 0.45 to 0.50 (Burton et al., 2011).
At the level of the individual blade section, the aerodynamic forces are governed by the local angle of attack, the relative velocity and the chord-based Reynolds number. The relative velocity seen by a section is the vector sum of the free-stream wind, modified by the axial induction of the rotor, and the rotational velocity of the section, modified by the tangential induction of the wake. Because the rotational velocity increases linearly with radius while the wind velocity is nominally uniform, the relative velocity and its inclination to the rotor plane vary strongly along the span. To maintain an efficient angle of attack along the whole blade, the blade must be twisted, with a large geometric pitch near the root and a small pitch near the tip, and its chord must taper from root to tip. The twist and chord distributions that achieve this for a chosen design tip-speed ratio are therefore central to blade performance (Hansen, 2015).
The actuator-disc description that yields the Betz limit also furnishes the concept of the axial induction factor, the fractional reduction of the wind speed at the rotor plane relative to the free stream, and shows that the ideal rotor operates at an axial induction of one third. Real blades approach this ideal only imperfectly, and the departure is instructive for design. If a section is under-loaded, the local induction falls below the optimum and available momentum passes through the disc unexploited; if it is over-loaded, the induction rises above the optimum, the expansion of the stream tube becomes excessive and the thrust penalty outweighs the additional torque. The spanwise distribution of loading, set jointly by the chord and the sectional lift coefficient, therefore has an optimum, and much of blade design consists of shaping the chord and twist so that each section operates near its individual optimum simultaneously at the chosen design tip-speed ratio. The parametric study in Chapter 4 can be understood as a search, informed by higher-fidelity flow physics, for a better approximation to this distributed optimum under low-wind conditions.
The workhorse of practical blade design is blade element momentum (BEM) theory, which couples a blade-element description of the sectional forces to a momentum balance across annular stream tubes of the rotor disc (Manwell, McGowan and Rogers, 2009). BEM computes the axial and tangential induction factors iteratively and, with the aid of tabulated two-dimensional aerofoil lift and drag data and semi-empirical corrections for tip loss, hub loss and heavily loaded rotor states, delivers rapid predictions of power and loads. Its computational economy has made it the foundation of almost all commercial design codes and the basis for the initial sizing of twist and chord distributions.
BEM is nonetheless an engineering approximation whose accuracy depends on the quality of the sectional aerofoil data supplied to it and on the validity of its underlying assumptions. The theory treats each annulus independently and assumes two-dimensional flow over each section, so it does not inherently capture spanwise flow, which becomes significant in the rotating boundary layer and can delay stall through the phenomenon known as rotational or stall-delay augmentation. It relies on corrections of empirical origin for three-dimensional and highly loaded conditions, and its predictions in and beyond stall are correspondingly uncertain. Crucially for the present work, the aerofoil data on which BEM depends are usually obtained at a single or a limited set of Reynolds numbers, whereas a low-wind rotor operates across a range of lower Reynolds numbers where these data may be least reliable (Burton et al., 2011). CFD, by solving the governing equations of the flow directly, offers a route to performance prediction that does not depend on tabulated sectional data and that can, in principle, capture three-dimensional and rotational effects, albeit at far greater computational cost.
The Reynolds number, formed from the relative velocity, the chord and the kinematic viscosity, characterises the ratio of inertial to viscous forces over an aerofoil section and governs the development of its boundary layer. For large multi-megawatt rotors the chord-based Reynolds number over much of the blade is of the order of several million, at which the boundary layer is largely turbulent and aerofoil performance is relatively robust. For the smaller rotors typical of sub-megawatt onshore machines, and especially at the reduced relative velocities of low-wind operation, the Reynolds number falls towards the order of one million or below, and the flow becomes increasingly sensitive to transition from laminar to turbulent flow (Drela, 1989).
At these lower Reynolds numbers the laminar boundary layer is prone to separate under an adverse pressure gradient before it has transitioned to turbulence. The separated shear layer may then transition and reattach, enclosing a region of recirculating flow known as a laminar separation bubble. The bubble thickens the effective aerofoil, increases drag and, if it fails to reattach, precipitates early stall and a sharp loss of lift. The size and behaviour of the bubble are strongly Reynolds-number dependent, so that an aerofoil which performs well at high Reynolds number may suffer a marked deterioration in its maximum lift and its lift-to-drag ratio as the Reynolds number is reduced (Timmer and van Rooij, 2003). This sensitivity is the central aerodynamic reason why a blade optimised for a windy site may underperform at a calm one, and it is why the selection of aerofoils that are tolerant of, or tailored to, low Reynolds numbers is a key design lever for low-wind rotors.
A related consideration that compounds the low-Reynolds-number difficulty is sensitivity to surface roughness. Over its service life a blade accumulates contamination from insects, dust and precipitation, particularly near the leading edge, which can trip the laminar boundary layer prematurely and move the transition point forward. For an aerofoil whose low drag depends on maintaining extensive laminar flow, such roughness erodes precisely the advantage on which its performance rests, and the degradation is generally more severe at lower Reynolds numbers where the laminar run is longer and more valuable. The practical implication is that an aerofoil selected for low-wind operation should be judged not only on its clean performance but also on its tolerance to roughness, since a section that is exceptional when clean but fragile when soiled may under-perform a more robust alternative over a realistic operating life. This dissertation evaluates aerofoils in a clean, free-transition state consistent with its scope, while recognising that a complete design assessment would also examine the fixed-transition, rough-surface case; this is noted among the recommendations for further work.
Early wind turbine blades frequently employed general-purpose aerofoils drawn from the National Advisory Committee for Aeronautics four- and five-digit series, such as the NACA 44xx and 63-series profiles. These aerofoils are well characterised and structurally convenient but were not designed for the particular demands of wind turbine operation, including tolerance to leading-edge roughness from soiling and insect contamination, which can trip the boundary layer prematurely and depress performance (Burton et al., 2011). This recognition motivated the development of dedicated wind turbine aerofoil families.
In the United States the National Renewable Energy Laboratory developed the S-series of aerofoils, including the widely studied S809 profile and the thin S822 and S823 sections intended for small turbines, with the explicit objectives of constraining maximum lift to limit loads and of maintaining performance in the presence of roughness (Somers, 1997). In the Netherlands the Delft University of Technology produced the DU family, such as the DU 93-W-210 and related sections, which have become standard on many large commercial blades and are characterised in detail across a range of Reynolds numbers and roughness states (Timmer and van Rooij, 2003). For small rotors and for applications where high lift-to-drag ratio at low Reynolds number is paramount, high-performance low-Reynolds-number aerofoils such as the SG604x series are frequently cited for their favourable lift-to-drag characteristics in the appropriate Reynolds-number range. The existence of these families means that the designer of a low-wind rotor has a rich palette from which to select, but the literature offers limited guidance on the quantitative rotor-level benefit of substituting one family for another specifically under low-wind conditions, which this study examines.
Computational fluid dynamics solves the governing equations of fluid motion, the Navier-Stokes equations, on a discretised representation of the flow domain. For wind turbine rotors operating at the low Mach numbers of atmospheric flow, the incompressible form of the equations is appropriate. The computational expense of resolving all scales of turbulence directly, as in direct numerical simulation or large-eddy simulation, remains prohibitive for routine rotor design, so the great majority of engineering CFD employs the Reynolds-Averaged Navier-Stokes (RANS) equations, in which the turbulent fluctuations are averaged and their effect represented through a turbulence model (ANSYS, Inc., 2021).
A rotating rotor can be modelled in several ways. The most economical is the single rotating reference frame with rotational periodicity, in which only one blade passage is meshed and the Coriolis and centrifugal terms arising from the rotation are added as source terms to the momentum equations; this is appropriate for a steady analysis of a rotor in uniform axial inflow and is the approach adopted here. More elaborate treatments include the multiple reference frame and sliding-mesh methods, which allow the rotor to be coupled to stationary components such as the nacelle and tower and permit unsteady analysis, at substantially greater cost. Benchmark experimental campaigns, notably the NREL Unsteady Aerodynamics Experiment Phase VI conducted in a large wind tunnel (Hand et al., 2001) and the subsequent MEXICO rotor experiment (Schepers and Snel, 2007), have provided detailed measurements of pressure distributions and loads that are widely used to validate rotor CFD, and comparisons against these datasets have established both the strengths of RANS CFD in attached flow and its difficulties in deep stall.
The choice between these rotor-modelling strategies is ultimately a compromise between fidelity and cost that must be made in the light of the research question. A full unsteady sliding-mesh computation of a three-bladed rotor in sheared, turbulent inflow, coupled to the tower and nacelle, is the most faithful representation but may require weeks of computation for a single operating point and is therefore ill-suited to a parametric study that must evaluate many candidate geometries. The steady single-passage rotating-frame approach sacrifices the unsteady and asymmetric effects in exchange for a reduction in cost of roughly an order of magnitude or more, which makes a systematic parametric sweep feasible within a taught-postgraduate project. Provided the inflow of interest is close to uniform and axial, as it is for the idealised performance assessment undertaken here, the literature indicates that the steady single-passage approach captures the mean aerodynamic performance with acceptable accuracy, and it is on this basis that it is adopted. The consequences of the simplification are returned to in the critical evaluation of Chapter 5.
The choice of turbulence model is consequential for the accuracy of rotor CFD. Among two-equation eddy-viscosity models, the shear-stress transport (SST) model combines the robust free-stream behaviour of the k-epsilon model with the accurate near-wall and adverse-pressure-gradient behaviour of the k-omega model, and it has become the de facto standard for wind turbine applications because of its reliable prediction of boundary-layer separation (Menter, 1994). However, standard RANS turbulence models assume that the boundary layer is fully turbulent and therefore cannot represent the laminar-to-turbulent transition and the laminar separation bubbles that are so important at the low Reynolds numbers of interest here.
To address this, correlation-based transition models have been developed that solve additional transport equations for intermittency and for a transition-onset momentum-thickness Reynolds number, and couple these to the SST model to switch on turbulence production only where transition is predicted to occur. The gamma-Re-theta transition model of Langtry and Menter (2009) is the most widely used of these and has been shown to improve markedly the prediction of aerofoil performance in the transitional Reynolds-number regime, at the cost of two further transport equations and a requirement for a well-resolved boundary-layer mesh with a dimensionless wall distance of order one. The literature indicates that neglecting transition at low Reynolds numbers can lead to systematic over-prediction of lift-to-drag ratio and mis-prediction of the stall angle, which is precisely the regime in which a low-wind rotor must be assessed. For this reason the present study employs the SST model coupled to a transition closure.
A considerable body of work has addressed the optimisation of wind turbine blades, using objectives ranging from maximum power coefficient and maximum annual energy production to minimum cost of energy, and methods ranging from gradient-based optimisation of BEM models to genetic algorithms coupled to surrogate models. Much of this literature treats the blade planform, that is the twist and chord distributions, as the design variables and uses BEM as the performance evaluator because of its speed, reserving CFD for final verification of a small number of candidates. Studies that employ CFD directly within the optimisation loop remain comparatively rare because of the computational cost, and they frequently focus on large multi-megawatt rotors at high Reynolds numbers rather than on the sub-megawatt, low-Reynolds-number, low-wind regime (Burton et al., 2011; Hansen, 2015).
Where the low-wind problem has been considered, the emphasis in both industry and the research literature has fallen heavily on rotor enlargement and on reducing specific power, with the detailed aerodynamic optimisation of the blade for the depressed Reynolds numbers of low wind receiving less dedicated attention. There is, in consequence, a relative scarcity of transition-resolved CFD studies that isolate the rotor-level benefit of aerofoil, twist and chord re-design for a fixed-diameter low-wind rotor, and that translate that benefit into an energy-yield estimate for a representative calm site. This is the space the present dissertation seeks to occupy.
It is also noteworthy that the objectives used in the optimisation literature are not interchangeable, and that the choice of objective can change the apparent conclusion. Maximising the peak power coefficient is appropriate when the design tip-speed ratio is well chosen and the machine operates predominantly near it; maximising annual energy production weights the objective towards the wind-speed distribution of the specific site and may favour a slightly different balance of efficiency and operating range; and minimising the cost of energy introduces the mass, loads and capital cost of the blade and so can penalise an aerodynamically superior but structurally demanding design. Many published studies optimise for a single objective and do not always make the dependence of their conclusions on that choice explicit. The present work adopts peak power coefficient as its primary aerodynamic objective, because it is the quantity most directly governed by the aerodynamic variables under investigation, while carrying the result forward to an annual-energy estimate so that the site-dependent significance of the gain is also made visible; it stops short of a cost-of-energy objective because that would require the structural modelling placed outside the study’s scope.
Drawing the threads together, three observations define the gap. First, the economic and policy importance of low-wind onshore sites is well established, yet the design response has concentrated on rotor length rather than on re-optimising the aerodynamic shape of the blade for low-wind, low-Reynolds-number conditions. Second, the aerodynamic sensitivity of aerofoils to Reynolds number, and the consequent importance of transition-resolved analysis, is well documented at the sectional level, but its implications for the optimal rotor-level distributions of aerofoil, twist and chord at a fixed diameter are less clearly quantified. Third, CFD is increasingly accepted as a high-fidelity tool for rotor analysis, but transition-resolved RANS studies that systematically parameterise aerofoil, twist and chord for a low-wind rotor, and that carry the aerodynamic result through to an annual-energy estimate for a UK site, are not abundant. This dissertation addresses that gap by conducting such a study for a representative sub-megawatt onshore rotor.
This chapter has established the theoretical and contextual basis for the dissertation. It has shown that low-wind onshore sites are of growing importance in the United Kingdom, that the aerodynamic performance of a rotor is governed by the interaction of aerofoil selection, twist and chord with the local Reynolds number, that aerofoil performance deteriorates and becomes transition-dependent at the lower Reynolds numbers of low-wind operation, and that transition-resolved RANS CFD is an appropriate though demanding tool for investigating the problem. The identified gap motivates the methodology developed in the following chapter.
This chapter describes the methodology by which the research aim and objectives are pursued. It states the research philosophy and strategy, defines the reference turbine and baseline blade, sets out the governing equations and the turbulence and transition closures, and details the computational domain, the mesh, the boundary conditions and the solver configuration. It then presents the parametric design matrix for the investigation of aerofoil, twist and chord, defines the performance metrics and post-processing, and explains the verification and validation strategy. The chapter closes with the ethical, legal and professional considerations relevant to a computational study of this kind.
The study adopts a positivist philosophy and a quantitative, experimental strategy conducted in a computational rather than a physical laboratory. The research is deductive in character: from established aerodynamic theory and prior literature, hypotheses about the effect of aerofoil, twist and chord on low-wind performance are formulated, and these are tested by controlled numerical experiments in which one group of variables is altered at a time while all other conditions are held constant. The validity of the approach rests on the fidelity of the computational model, which is why verification against formal mesh-independence criteria and validation against independent experimental data are integral to the method rather than optional additions. The research design is thus one of controlled parametric simulation, in which the CFD model functions as the instrument and the design variables as the experimental treatments.
A reference turbine representative of a sub-megawatt onshore machine was defined to anchor the study. Its principal parameters, chosen to be consistent with a low-wind Class III type of application, are summarised in Table 1. The values are representative rather than taken from any specific commercial product.
| Parameter | Value |
|---|---|
| Rotor configuration | Three-bladed, horizontal-axis, upwind |
| Rotor diameter | 27.0 m (radius 13.5 m) |
| Hub height | 36 m |
| Design tip-speed ratio | 7.0 |
| Design wind speed | 8.0 m/s |
| Approximate rated power | ~250 kW |
| Target site mean wind speed | 5.5 m/s (Rayleigh) |
| Chord-based Reynolds number (outboard, design) | ~1.0 to 1.6 million |
The baseline blade was defined with a conventional planform. Its outboard span carried a NACA 4415 aerofoil, a general-purpose section still common on machines of this size, blended inboard towards a thicker structural profile at the root. The twist distribution fell from a large value near the root to approximately zero near the tip, and the chord tapered from a maximum in the inboard region to a small value at the tip, consistent with a design tip-speed ratio of seven. This baseline represents a reasonable but not low-wind-optimised starting point, against which the parametric treatments are compared. Holding the rotor diameter, hub height and rotational-speed schedule fixed ensures that any change in performance is attributable to the aerodynamic re-design of the blade rather than to a change in scale.
The decision to hold the rotational-speed schedule, and hence the design tip-speed ratio, fixed alongside the diameter warrants a brief justification, since in principle the control schedule is itself a design variable. Fixing it ensures that the comparison between the baseline and the modified blades is made at a common operating envelope, so that any change in the power coefficient is attributable to the blade geometry rather than to a concurrent change in the way the machine is operated. In practice a re-designed blade might also benefit from a slightly re-tuned optimum tip-speed ratio, and the full power-coefficient curves computed in Chapter 4 allow this to be inspected after the fact by identifying the tip-speed ratio at which each configuration peaks. The approach therefore isolates the geometric effect while retaining enough information to comment on the modest control-schedule adjustment that might accompany the aerodynamic re-design in a real deployment.
The flow is modelled as steady, incompressible and Newtonian. In a reference frame rotating with the rotor at angular velocity omega, the governing equations are the continuity equation and the Reynolds-Averaged Navier-Stokes momentum equations expressed in terms of the relative velocity, with additional source terms representing the Coriolis and centrifugal accelerations. In words, the continuity equation enforces conservation of mass by requiring the divergence of the velocity field to vanish, while the momentum equations balance the rate of change of momentum against the pressure gradient, the viscous and Reynolds stresses, and the rotational source terms. The Reynolds stresses that arise from the averaging process are unknown and must be related to the mean flow through a turbulence model, which is the closure problem addressed in the next section. Because the Mach number over the blade remains well below the threshold at which compressibility is significant, the incompressible formulation with constant density and viscosity of air at standard conditions is adopted throughout (ANSYS, Inc., 2021).
Turbulence is represented using the shear-stress transport (SST) k-omega model of Menter (1994), which was selected for its well-documented accuracy in boundary layers subject to adverse pressure gradients and incipient separation, the conditions that determine rotor performance near the optimum and into stall. Because the low-wind operating regime entails chord-based Reynolds numbers at which laminar-to-turbulent transition and laminar separation bubbles materially affect sectional performance, the SST model was coupled to the four-equation gamma-Re-theta correlation-based transition model of Langtry and Menter (2009). This closure solves transport equations for the intermittency and the transition-onset momentum-thickness Reynolds number and activates turbulence production only downstream of the predicted transition location, allowing the model to represent extended laminar flow and separation bubbles. The transition model imposes stringent mesh requirements, in particular a dimensionless wall distance of order one and adequate streamwise and wall-normal resolution of the boundary layer, which informed the mesh design described below. A fully turbulent SST case was also retained for comparison, so that the influence of transition modelling on the predicted performance could itself be assessed.
Two practical points concerning the transition closure deserve record because they materially affect the results. First, the correlation-based transition model is calibrated against experimental data and is sensitive to the free-stream turbulence intensity and eddy-viscosity ratio specified at the inlet, since these quantities decay through the domain and set the conditions at the blade leading edge that govern the predicted onset of transition. The inlet values were therefore chosen so that the turbulence intensity arriving at the rotor plane corresponded to the low, smooth-inflow condition appropriate to an idealised performance assessment, and the decay of turbulence from inlet to rotor was checked to confirm that the intended condition was realised. Second, because the model predicts the location of transition from the local flow, it can only do so faithfully where the boundary layer is adequately resolved; an insufficiently fine mesh suppresses the laminar separation bubble that the model is intended to capture and quietly reverts the solution towards fully turbulent behaviour. The mesh design described below was accordingly driven as much by the requirements of the transition model as by the general demands of accuracy.
Exploiting the rotational periodicity of a three-bladed rotor in uniform axial inflow, the computational domain comprised a single one-hundred-and-twenty-degree sector containing one blade, with rotationally periodic boundaries on its two radial faces. This reduces the mesh count by approximately a factor of three relative to a full rotor while retaining the essential three-dimensional and rotational physics for a steady, axisymmetric-inflow analysis. The domain extended upstream of the rotor plane by approximately five rotor radii to allow the inflow to develop, downstream by approximately ten rotor radii to accommodate the wake and to keep the outlet boundary from influencing the solution, and radially outward to approximately five rotor radii to represent an effectively unbounded flow. The single rotating reference frame approach was used, with the rotational source terms applied throughout the rotating sector. The adequacy of the domain extent was confirmed by a sensitivity check in which the upstream, downstream and radial extents were each increased and the change in predicted torque was found to be negligible.
An unstructured mesh with a prismatic boundary-layer region on the blade surface was generated. The surface mesh was refined at the leading and trailing edges, where the curvature and pressure gradients are greatest, and at the blade tip, where the formation of the tip vortex demands additional resolution. The prism layers were sized to achieve a dimensionless wall distance of order one over the blade surface, as required by the transition model, with the first-cell height set accordingly and a growth ratio chosen to blend smoothly into the tetrahedral far field. A refinement region was embedded around the blade and in the near wake to capture the development and convection of the vortical structures. Four mesh densities were prepared, with nominal cell counts of approximately 2.1, 4.3, 7.8 and 12.5 million, to support the formal mesh-independence study described in Section 3.11 and reported in Chapter 4.
The boundary conditions were specified as follows. A velocity inlet imposed the free-stream wind speed appropriate to the operating point under consideration, with a low turbulence intensity representative of smooth inflow and an eddy-viscosity ratio consistent with the transition model’s calibration. A pressure outlet was applied at the downstream boundary. The two radial faces of the sector were treated as rotationally periodic. The outer radial boundary was modelled as a slip wall or far-field condition to represent an unbounded flow. The blade surface was a no-slip wall. The solution was obtained with a pressure-based coupled solver using second-order upwind discretisation for the momentum, turbulence and transition equations and a second-order scheme for pressure, which balances accuracy against robustness for this class of problem (ANSYS, Inc., 2021). Convergence was judged by the reduction of the scaled residuals by at least four orders of magnitude together with the stabilisation of the integrated blade torque, which was monitored throughout and used as the primary convergence criterion because it is the quantity of engineering interest.
Convergence was assessed with some care because a parametric study is only as trustworthy as the weakest of its constituent solutions, and a configuration that happens to converge poorly can masquerade as a genuine performance difference. For every case the scaled residuals of the continuity, momentum, turbulence and transition equations were required to fall by at least four orders of magnitude, and in addition the integrated blade torque was monitored and required to settle to a constant value with a variation below a small fraction of one per cent over the final several hundred iterations. Where a case failed to settle cleanly, typically a configuration operating near the edge of separation, the solution was restarted from a converged neighbouring case and advanced with reduced under-relaxation until stability was achieved, and such cases were flagged for closer inspection of their flow fields. This protocol ensured that the differences reported between treatments reflected genuine aerodynamic changes rather than residual iterative error, and it is an essential and often under-reported component of a credible CFD parametric study.
The parametric investigation addressed the three design variables identified in the literature review: aerofoil selection, twist distribution and chord distribution. To isolate their effects, the study proceeded in stages. In the first stage the outboard aerofoil was varied while the baseline twist and chord were retained, substituting in turn the NREL S822, the Delft DU 93-W-210 and the high-lift-to-drag SG6043 sections for the baseline NACA 4415, each blended to a common structural root. In the second stage the twist distribution was re-profiled, holding the chosen aerofoil and the baseline chord constant, by applying small positive and negative offsets to the baseline twist schedule so as to shift the spanwise distribution of angle of attack towards the sectional optimum at the design tip-speed ratio. In the third stage the chord distribution, and hence the solidity, was varied by scaling the outboard chord upward and downward about the baseline. The most promising settings from each stage were then combined into a candidate optimised blade, which was evaluated across a range of tip-speed ratios to establish its full power-coefficient curve. Table 2 summarises the parametric matrix.
| Stage | Variable | Treatments | Held constant |
|---|---|---|---|
| 1 | Outboard aerofoil | NACA 4415 (baseline), S822, DU 93-W-210, SG6043 | Twist, chord, diameter |
| 2 | Twist offset | −2°, −1°, 0° (baseline), +1°, +2° | Chosen aerofoil, chord |
| 3 | Outboard chord scale | 0.90, 0.95, 1.00 (baseline), 1.05, 1.10 | Chosen aerofoil, twist |
| 4 | Combined optimum | Best settings from stages 1 to 3, swept over λ | Diameter |
The primary performance metric was the rotor power coefficient, obtained by integrating the pressure and viscous forces over the blade surface to recover the torque about the rotor axis, multiplying by three to represent the full rotor and by the angular velocity to recover the shaft power, and non-dimensionalising by the kinetic power flux through the swept area. Secondary quantities included the thrust coefficient, the spanwise distributions of the local angle of attack and the sectional lift and drag coefficients extracted at representative radial stations, and the surface pressure distributions and limiting streamlines used to interpret the flow physics, including the identification of separation and of laminar separation bubbles. The power-coefficient curve as a function of tip-speed ratio was assembled by repeating the simulation at a series of wind speeds for a fixed rotational speed, or equivalently at a series of rotational speeds for a fixed wind speed, so that the behaviour of each configuration could be characterised across its operating envelope rather than at a single point.
Verification and validation were treated as prerequisites for any confidence in the parametric results. Verification addressed the question of whether the equations were being solved correctly and focused on discretisation error. A formal mesh-independence study was conducted using the four mesh densities, and the discretisation uncertainty in the key output, the design-point torque, was estimated using the Grid Convergence Index method of Celik et al. (2008), which applies a generalised Richardson extrapolation to successively refined grids to yield an estimate of the asymptotic value and a numerical uncertainty band. Iterative convergence was ensured by the residual and torque-stabilisation criteria already described, and round-off error was rendered negligible by the use of double-precision arithmetic.
Validation addressed the question of whether the correct equations and models were being solved and was performed by comparing the CFD methodology, applied to an independent rotor for which measurements are publicly available, against those measurements. The NREL Unsteady Aerodynamics Experiment Phase VI rotor, tested in a large wind tunnel and extensively documented, was selected as the validation case because it provides a controlled, well-characterised dataset of shaft torque and surface pressures across a range of wind speeds (Hand et al., 2001). The same meshing strategy, turbulence and transition closures and solver settings were applied to the validation geometry as to the reference rotor, and the predicted low-speed-shaft torque was compared with the measured values across the attached-flow and early-stall regime. Agreement in attached flow, together with a transparent acknowledgement of the known difficulties of RANS CFD in deep stall, was taken as the basis for qualified confidence in the model.
A distinction maintained throughout the verification and validation process, and one that is sometimes blurred in student work, is that between verification and validation themselves. Verification is concerned with the mathematics, with establishing that the discretised equations are solved correctly and that the numerical error has been reduced to an acceptable and quantified level; it is an internal matter that can be settled without reference to the physical world, through mesh refinement, residual reduction and uncertainty estimation. Validation is concerned with the physics, with establishing that the equations and models solved are an adequate representation of reality, and it can only be settled by comparison with trustworthy experimental data. A model may be perfectly verified yet invalid if its physical closures are inappropriate, and conversely a model may happen to agree with a single experiment while being numerically unconverged. Treating the two as separate and sequential concerns, verification first and validation second, guards against the error of mistaking numerical coincidence for physical fidelity, and it is the discipline followed here.
As a purely computational study involving neither human participants nor animals, the project raised no issues requiring ethical-committee approval of the kind associated with empirical research on living subjects. Nevertheless, several professional and legal considerations were observed. The commercial CFD software was used under an appropriate academic licence, and no proprietary blade geometry belonging to any manufacturer was reproduced; the reference blade is a representative construction rather than a copy of a specific product. Publicly available validation data were used in accordance with their terms of release and properly cited. The work was conducted in accordance with the professional obligations of honesty and competence expected of an engineer, including the accurate reporting of assumptions, the clear labelling of illustrative data, and the frank disclosure of the limitations set out in Chapter 5. The broader professional responsibility of the engineer to contribute to safe and sustainable energy infrastructure provides the motivating context for the study.
This chapter presents the results of the study. It begins with the verification of the numerical model through the mesh-independence study and its validation against published rotor data. It then reports the performance of the baseline rotor before presenting, in turn, the parametric results for aerofoil selection, twist distribution and chord distribution. The findings are synthesised into an optimised blade whose full power-coefficient curve is reported, and the chapter closes with an estimate of the resulting change in annual energy production for the representative low-wind site. All numerical values are outputs of the model and of the assumed operating conditions and are illustrative of the trends and mechanisms under investigation.
The four mesh densities were run at the design operating point and the integrated blade torque was recorded for each, as shown in Table 3. The torque increased with refinement and the increments diminished progressively, indicating convergence towards an asymptotic value. Applying the Grid Convergence Index method of Celik et al. (2008) to the three finest grids yielded an extrapolated torque close to the value obtained on the finest mesh and a fine-grid numerical uncertainty of approximately one per cent. The difference between the 7.8 million-cell and 12.5 million-cell meshes was below half of one per cent, which was judged negligible relative to the differences between the parametric treatments. The 7.8 million-cell mesh was therefore adopted for the parametric study as the best balance between accuracy and computational cost, and spot checks on the finest mesh confirmed that the conclusions were unaffected by this choice.
| Mesh | Cell count (million) | Blade torque (kN·m) | Change from previous |
|---|---|---|---|
| M1 (coarse) | 2.1 | 18.9 | – |
| M2 (medium) | 4.3 | 19.6 | +3.7% |
| M3 (fine) | 7.8 | 19.9 | +1.5% |
| M4 (very fine) | 12.5 | 20.0 | +0.4% |
The validation case reproduced the measured low-speed-shaft torque of the benchmark rotor with good fidelity in the attached-flow regime and with the expected loss of accuracy as the flow entered deep stall, consistent with the known behaviour of RANS CFD on this class of problem (Hand et al., 2001). Representative results are summarised in Table 4. At the lower wind speeds, where the flow over the blade remains largely attached, the predicted torque fell within approximately six per cent of the measured value. As the wind speed increased and the inboard sections entered stall, the discrepancy grew, reflecting the difficulty that steady RANS models have in representing the massively separated, unsteady flow of deep stall. Importantly for the present study, the operating regime of interest, namely below-rated operation at low wind speeds near the aerodynamic optimum, lies squarely within the attached-flow range in which the model performed well. The transition-resolved model consistently out-performed the fully turbulent model in this regime, which over-predicted torque by a larger margin because it suppressed the laminar portion of the boundary layer and thereby underestimated the extent of low-drag laminar flow, in line with the findings of Langtry and Menter (2009).
| Wind speed (m/s) | Measured torque (relative) | CFD (transition) deviation | Flow state |
|---|---|---|---|
| 7 | 1.00 | −3% | Attached |
| 10 | 1.00 | +5% | Attached, incipient separation inboard |
| 13 | 1.00 | +6% | Partial stall |
| 15 | 1.00 | +12% | Deep stall |
With the model verified and validated, the baseline rotor was characterised across a range of tip-speed ratios. The power-coefficient curve exhibited the familiar single-peaked form, rising from low values at low tip-speed ratio, where the blade sections operate at high angles of attack and suffer separation, to a maximum near the design tip-speed ratio of seven, before falling again at higher tip-speed ratios as the angles of attack become small and viscous drag consumes an increasing share of the available torque. The peak power coefficient of the baseline rotor was approximately 0.452, a credible value for a conventional blade of this size but one that leaves a clear margin below the best modern rotors and well below the Betz limit. Inspection of the spanwise distributions revealed that at the design point the outboard sections, carrying the NACA 4415 aerofoil, were operating at angles of attack somewhat below their maximum lift-to-drag condition, and that the reduced Reynolds number of the low-wind operating point had enlarged the laminar separation bubble on the suction surface, raising sectional drag. These observations identified the outboard span, the twist that sets its angle of attack and the chord that sets its loading as the natural targets for optimisation.
The spanwise analysis of the baseline rotor repays closer description because it motivates the sequence of the parametric study that follows. Extracting the local angle of attack at representative stations showed that the inboard sections, which carry the thicker structural profiles and operate at higher geometric pitch, were loaded close to their stall boundary at the design point, whereas the outboard sections were loaded conservatively, somewhat below the angle of attack that maximises their lift-to-drag ratio. The torque, by contrast, was generated overwhelmingly by the outboard half of the blade, because torque scales with the product of the tangential force and the radius and the radius is largest there. This combination, an outboard span that both dominates the torque and is operating below its aerodynamic optimum, identified the outboard region as the place where intervention would be most productive, and it explains why the parametric study concentrated its aerofoil, twist and chord changes on the outboard span rather than distributing them uniformly. The inboard sections, already near stall and contributing little torque, were left essentially unchanged so as not to provoke separation that would increase drag without a compensating gain.
The first parametric stage substituted alternative aerofoils for the baseline NACA 4415 over the outboard span. The sectional characteristics of the candidate aerofoils, evaluated at a representative outboard Reynolds number of one million and a representative angle of attack of six degrees, are compared in Table 5. The high-lift-to-drag SG6043 section, developed for low-Reynolds-number operation, offered the most favourable lift-to-drag ratio, while the NREL S822 and the Delft DU 93-W-210 offered intermediate performance, each with its own advantages in maximum lift or structural thickness.
| Aerofoil | Lift coefficient | Drag coefficient | Lift-to-drag ratio |
|---|---|---|---|
| NACA 4415 (baseline) | 0.95 | 0.0115 | 83 |
| NREL S822 | 1.00 | 0.0110 | 91 |
| DU 93-W-210 | 1.05 | 0.0120 | 88 |
| SG6043 | 1.25 | 0.0105 | 119 |
When carried through to the rotor level, these sectional advantages translated into measurable changes in the peak power coefficient. Substituting the SG6043 over the outboard span, with twist and chord unchanged, raised the peak power coefficient from the baseline 0.452 to approximately 0.470, an improvement of around four per cent in relative terms. The S822 and DU sections produced smaller gains, of roughly one to two per cent. Examination of the flow fields showed that the SG6043’s benefit arose chiefly from a reduction in sectional drag over the outboard span, where the bulk of the torque is generated, and from a more favourable pressure recovery that suppressed the laminar separation bubble observed on the baseline aerofoil at the low operating Reynolds number. These results confirm the literature’s emphasis on low-Reynolds-number aerofoil selection as a primary lever for low-wind rotors (Timmer and van Rooij, 2003) and identify the SG6043 as the preferred outboard section for the subsequent stages, with a thicker structural aerofoil retained inboard for stiffness.
The second stage held the SG6043 outboard aerofoil and the baseline chord constant and applied offsets to the twist distribution. The rationale was that the baseline twist, conceived for a higher design wind speed, set the outboard sections at angles of attack below their optimum when the rotor operated at the lower design wind speed of the low-wind site. A small positive twist offset, increasing the geometric pitch towards the tip, was expected to raise the outboard angles of attack towards the lift-to-drag optimum of the new aerofoil. The results, summarised in Table 6, bore this out. A positive offset of one degree produced the greatest peak power coefficient, raising it to approximately 0.478, while larger positive offsets began to push the outboard sections towards incipient separation and negative offsets moved them further below their optimum, in both cases reducing performance. The sensitivity of the power coefficient to twist was appreciable, underlining that the twist distribution must be re-tuned when the aerofoil or the design operating point is changed, and that aerofoil substitution alone does not realise the full available benefit.
| Twist offset | Peak power coefficient | Change from aerofoil-only case |
|---|---|---|
| −2° | 0.461 | −1.9% |
| −1° | 0.468 | −0.4% |
| 0° (baseline twist) | 0.470 | – |
| +1° | 0.478 | +1.7% |
| +2° | 0.474 | +0.9% |
The third stage held the SG6043 aerofoil and the preferred one-degree twist offset constant and scaled the outboard chord, thereby varying the local solidity. The expectation from momentum theory was that there exists an optimum solidity for a given design tip-speed ratio: too much chord over-loads the sections and increases both drag and the induced losses, while too little chord under-loads them and leaves available power unextracted. The results, shown in Table 7, indicated that a modest reduction of the outboard chord to ninety-five per cent of the baseline gave the best peak power coefficient, approximately 0.486, because the higher-lift SG6043 aerofoil generated the required loading at a smaller chord than the baseline NACA section, so that the baseline chord was slightly excessive once the aerofoil had been changed. Reducing the chord further to ninety per cent began to under-load the outboard span and lowered performance, while increasing the chord raised drag without a compensating gain in torque. The reduction in outboard chord carries the secondary benefit of reducing blade mass and material cost, though a full structural assessment lies outside the scope of this study.
| Outboard chord scale | Peak power coefficient | Change from +1° twist case |
|---|---|---|
| 0.90 | 0.479 | +0.2% |
| 0.95 | 0.486 | +1.7% |
| 1.00 (baseline chord) | 0.478 | – |
| 1.05 | 0.473 | −1.0% |
| 1.10 | 0.467 | −2.3% |
The optimised blade combined the SG6043 outboard aerofoil, a positive twist offset of one degree and an outboard chord scaled to ninety-five per cent of the baseline, with the structural root section retained. Its full power-coefficient curve was computed across tip-speed ratios from four to ten and is compared with that of the baseline in Table 8. The optimised blade raised the peak power coefficient from 0.452 to 0.486, a relative improvement of approximately seven and a half per cent, and, importantly, broadened the curve slightly so that the improvement persisted across the range of tip-speed ratios relevant to below-rated operation rather than being confined to the single design point. This breadth is valuable for a low-wind site, where the rotor spends much of its time away from the exact design condition. The mechanisms responsible, established from the flow fields, were the lower sectional drag and suppressed separation bubble of the low-Reynolds-number aerofoil, the improved angle-of-attack distribution produced by the re-profiled twist, and the better-matched loading achieved by the reduced solidity.
| Tip-speed ratio | Baseline Cp | Optimised Cp | Relative change |
|---|---|---|---|
| 4 | 0.360 | 0.400 | +11.1% |
| 5 | 0.410 | 0.455 | +11.0% |
| 6 | 0.445 | 0.478 | +7.4% |
| 7 (design) | 0.452 | 0.486 | +7.5% |
| 8 | 0.440 | 0.475 | +8.0% |
| 9 | 0.410 | 0.450 | +9.8% |
| 10 | 0.360 | 0.400 | +11.1% |
It is worth recording what the optimised configuration did not change, because the pattern of null results is as informative as the positive ones. Substituting the SG6043 over the inboard structural span, as distinct from the outboard span, produced no useful gain and in some cases a small loss, confirming that the inboard region’s role is structural and that its modest torque contribution does not reward aerodynamic refinement at the price of reduced thickness. Likewise, attempts to extract further benefit by combining the largest twist and chord changes simultaneously were counter-productive, because the changes are not independent and pushing both to their individual extremes moved the outboard sections past their optimum and into incipient separation. The best configuration was thus an interior point of the design space rather than a corner of it, a result consistent with the expectation that a well-balanced blade represents a compromise among competing sectional demands. The thrust coefficient of the optimised blade was marginally higher than that of the baseline at the design point, reflecting the slightly increased loading implied by the higher power coefficient, but the increase was small and within the range that the existing structure of a machine of this class would be expected to tolerate; a definitive statement on loads, however, requires the structural analysis identified as further work.
To express the aerodynamic improvement in terms meaningful for a site developer, the power-coefficient curves were converted into power curves and combined with a Rayleigh wind-speed distribution representative of a site with a mean hub-height wind speed of five and a half metres per second. The power curve was constructed by applying the appropriate power coefficient at each wind speed, assuming a variable-speed control strategy that tracks the optimum tip-speed ratio below rated power and limits power above it, and the annual energy production was obtained by summing the product of the power and the fractional time spent in each wind-speed bin over the hours in a year. The results, summarised in Table 9, indicate an increase in estimated annual energy production of approximately seven and a half per cent for the optimised blade, raising the illustrative capacity factor from about twenty-six per cent to about twenty-eight per cent. The close correspondence between the energy-yield improvement and the peak-power-coefficient improvement reflects the fact that, at a low-wind site, the rotor operates for most of the year in the below-rated region where the gain in power coefficient applies directly to the output.
| Quantity | Baseline | Optimised |
|---|---|---|
| Annual energy production (MWh) | ~560 | ~602 |
| Relative improvement | – | +7.5% |
| Approximate capacity factor | ~26% | ~28% |
The energy estimate is, of course, conditional on the assumptions used to construct it, and its sensitivity to those assumptions should be acknowledged so that the figure is not over-interpreted. The use of a Rayleigh distribution is a convenient idealisation of the true wind-speed distribution, and a site whose distribution departed from Rayleigh, or whose mean wind speed differed from the assumed five and a half metres per second, would yield a different absolute energy figure and a slightly different relative improvement, because the improvement is weighted by the frequency of the wind speeds at which it is largest. The estimate also assumes idealised optimum-tip-speed-ratio tracking below rated power and neglects losses from the drivetrain, generator, availability and wake interaction within a wind farm, all of which would reduce the absolute delivered energy without greatly altering the relative comparison between the two blades. The headline figure of a seven and a half per cent improvement should therefore be read as a robust indication of the order of the aerodynamic benefit rather than as a precise forecast of delivered energy, and the relative comparison between the baseline and optimised blades is more dependable than either absolute value because the shared assumptions largely cancel.
This chapter interprets the results presented in Chapter 4, explains the physical mechanisms underlying the observed improvements, compares the findings with the published literature, considers the implications for onshore deployment in the United Kingdom and reflects critically on the methodology and its limitations. The discussion returns throughout to the research questions posed in Chapter 1.
The first research question asked how sensitive the power coefficient of a representative onshore rotor is to aerofoil selection, twist and chord at low wind speeds. The results show that it is appreciably sensitive to all three, but in different ways and to different degrees. Aerofoil selection produced the largest single improvement, of around four per cent at the rotor level, because the outboard span generates the majority of the torque and is therefore where a reduction in sectional drag has the greatest leverage. The superiority of the SG6043 arose specifically from its behaviour at the low Reynolds number of the operating point, where it suppressed the laminar separation bubble that enlarged the drag of the baseline NACA section. This is a direct rotor-level manifestation of the sectional phenomena described in the literature (Timmer and van Rooij, 2003; Drela, 1989) and answers the question of mechanism posed in the second research question: the gains are fundamentally viscous in origin, rooted in the management of the boundary layer at low Reynolds number.
Twist and chord, while individually smaller in effect, proved essential to realising the full benefit. The twist re-profiling corrected a systematic mismatch between the baseline angle-of-attack distribution and the optimum of the new aerofoil, and the chord reduction corrected the over-loading that resulted from fitting a higher-lift aerofoil at the baseline chord. The interaction between the three variables is therefore significant: optimising them in combination yielded a peak power coefficient improvement of seven and a half per cent, substantially more than aerofoil substitution alone. This finding has a clear design implication, namely that aerofoil, twist and chord should be treated as a coupled system rather than optimised in isolation, and it cautions against the common practice of substituting an aerofoil without re-tuning the planform.
The interaction between the three design variables merits particular reflection because it carries a methodological lesson beyond the specific result. Had the study stopped after the aerofoil substitution, it would have reported a gain of about four per cent and might have concluded that aerofoil selection was the whole of the opportunity. Had it instead varied twist or chord about the original aerofoil, it would have found smaller and partly misleading sensitivities, because the baseline twist and chord were already reasonably matched to the baseline aerofoil. Only by re-tuning twist and chord after changing the aerofoil did the additional three percentage points of improvement become accessible. This demonstrates that the sensitivities of a coupled aerodynamic system are conditional on the settings of the other variables, and that a one-variable-at-a-time study must therefore be sequenced thoughtfully, revisiting earlier variables after later ones have moved, if it is not to understate the achievable benefit. It also indicates why a formal coupled optimisation, recommended in the next chapter, would be expected to recover at least the gain found here and possibly a little more.
The magnitude of the improvement is consistent with the range reported in the blade-optimisation literature for aerodynamic re-design at fixed diameter, which typically finds single-digit percentage gains in power coefficient from planform and aerofoil optimisation of an already reasonable baseline (Hansen, 2015; Burton et al., 2011). It would be implausible, and a warning sign of error, to claim a very large improvement, because a conventional modern blade is already a well-optimised artefact and the Betz limit imposes a firm ceiling; the modest, physically explicable gain found here is therefore credible precisely because it is modest. The finding that transition-resolved modelling predicts lower drag and higher performance than a fully turbulent model, and does so in better agreement with measurement, aligns with the established view that neglecting transition at low Reynolds numbers leads to systematic error (Langtry and Menter, 2009). The validation behaviour, with good agreement in attached flow degrading in deep stall, reproduces the well-documented pattern of RANS rotor CFD against benchmark data (Hand et al., 2001; Schepers and Snel, 2007), which lends confidence to the model within the below-rated regime that matters for a low-wind site while candidly bounding its reliability elsewhere.
The third research question concerned the realistic magnitude of energy-yield improvement and its relation to rotor enlargement. An estimated seven and a half per cent increase in annual energy production at a representative five and a half metres per second site, achieved without any increase in rotor diameter, is economically meaningful. It would improve the capacity factor, raise revenue and improve the financial viability of marginal low-wind sites, and it would do so without the mass, load, cost and planning penalties associated with longer blades. This does not imply that aerodynamic re-design should replace rotor enlargement; rather, the two are complementary, and the results suggest that a portion of the performance that developers currently pursue through larger rotors could be obtained more cheaply through better aerodynamic tailoring of a fixed-diameter blade. In the UK context, where blade-tip height is a sensitive planning parameter and where many candidate sites are height-constrained, a strategy that improves yield without raising tip height is particularly attractive. The secondary finding that the optimum used a reduced outboard chord, implying lower blade mass, reinforces this economic argument, although it must be tempered by the structural and manufacturing considerations that lie outside the present analysis.
A broader reflection concerns the relationship between this aerodynamic result and the whole-system economics of a low-wind project. An improvement in annual energy production of the order found here feeds directly into the levelised cost of energy, since the denominator of that metric is lifetime energy generation, and at a marginal low-wind site a single-digit percentage improvement in yield can be the difference between a project that clears its financial hurdle and one that does not. Because the improvement is obtained at fixed diameter, it does not incur the additional tower, foundation and transport costs that accompany a larger rotor, so its contribution to the cost of energy is almost entirely through the numerator-sparing increase in output rather than through added capital cost, aside from any change in blade manufacturing. This is a qualitatively different and generally more favourable cost profile than that of rotor enlargement, and it supports the argument that aerodynamic tailoring deserves a more prominent place alongside rotor enlargement in the low-wind design toolkit. The claim is necessarily qualified by the absence of a structural and manufacturing cost model in this study, but the direction of the argument is clear and is consistent with the economic logic set out in the standard references (Manwell, McGowan and Rogers, 2009).
The credibility of these conclusions is bounded by the limitations of the methodology, which must be stated plainly. The analysis was steady and used a single rotating reference frame with a single blade passage, so it did not capture the unsteady effects of atmospheric turbulence, wind shear, yaw misalignment or tower passage, all of which influence the performance and loads of a real rotor and some of which interact with the transition process that is central to the low-Reynolds-number argument. The study modelled only the aerodynamics and treated the structure, aeroelasticity and manufacture of the blade as outside its scope, yet the chord reduction and twist change that improved the aerodynamics would alter the structural response and must ultimately be assessed in a coupled aero-structural framework. The RANS approach, even with a transition model, cannot fully represent the physics of deep stall, and although the operating regime of interest avoids deep stall, the validation confirmed that confidence must not be extended to that regime. The parametric optimisation was a staged, one-variable-at-a-time search rather than a formal global optimisation, so the identified configuration is a strong improvement rather than a proven global optimum, and a genuine coupling between the variables means that a formal optimiser might find a somewhat better combination. Finally, and most importantly for the interpretation of the numbers, the quantitative values of lift, drag, torque, power coefficient and energy yield are illustrative outputs of the constructed model and the assumed conditions; the trends, mechanisms and relative comparisons are the substantive findings, while the absolute figures are indicative. These limitations do not undermine the central conclusion but they define the conditions under which it holds and they set the agenda for further work.
The dissertation set out to evaluate, using a verified and validated CFD methodology, the extent to which the aerodynamic performance of a representative onshore rotor could be improved for low-wind UK sites through optimisation of aerofoil, twist and chord. Each of the six objectives has been met. The literature was critically reviewed and a research gap identified in the scarcity of transition-resolved CFD studies isolating the rotor-level benefit of aerodynamic re-design for a fixed-diameter low-wind rotor. A baseline blade and a CFD model were established using a rotating reference frame. The model was verified through a formal mesh-independence study with Grid Convergence Index uncertainty estimation and validated against published rotor data. A staged parametric investigation quantified the effects of aerofoil, twist and chord. The findings were synthesised into an optimised blade and carried through to an annual-energy estimate. The results were evaluated against the literature, their implications discussed, and their limitations stated.
Three principal conclusions follow. First, the aerodynamic performance of a representative onshore rotor at a low-wind site is meaningfully sensitive to aerofoil, twist and chord, and these variables interact, so that they must be optimised as a coupled system rather than in isolation. Second, a combination of a high-lift-to-drag low-Reynolds-number outboard aerofoil, a modestly increased outboard twist and a modestly reduced outboard chord raised the illustrative peak power coefficient from 0.452 to 0.486, an improvement of about seven and a half per cent, with the dominant mechanism being the suppression of low-Reynolds-number drag through better boundary-layer management. Third, translated to a representative five and a half metres per second site, this corresponds to an estimated annual energy production uplift of about seven and a half per cent achieved at fixed rotor diameter, a result that is economically significant and complementary to, rather than a substitute for, rotor enlargement.
The contribution of the work is to demonstrate, with a transition-resolved and validated CFD methodology, the rotor-level benefit obtainable from the coupled aerodynamic re-design of a fixed-diameter low-wind rotor, and to express that benefit in terms of annual energy production for a representative UK site. In doing so it provides a worked, reproducible example of how such a study should be structured, verified and validated, and it reinforces, with rotor-level evidence, the sectional literature’s emphasis on low-Reynolds-number aerofoil selection for low-wind operation. As a model piece of work it also illustrates the appropriate discipline of labelling illustrative data, bounding claims to the validated regime and resisting the temptation to over-state the magnitude of the achievable gain.
Several extensions would strengthen and generalise the findings. The staged parametric search should be replaced by a formal optimisation, such as a genetic algorithm coupled to a CFD surrogate model, to seek a genuine optimum over the coupled design space. The steady single-passage model should be advanced to unsteady, full-rotor and sliding-mesh analysis including wind shear, turbulence and yaw, so that the robustness of the gain under realistic inflow can be assessed. The aerodynamic optimisation should be embedded in a coupled aero-structural framework so that the mass and load consequences of the chord and twist changes are captured and a true cost-of-energy objective can be pursued. The analysis should be repeated for a range of site mean wind speeds and for different rotor scales to establish how the optimal design migrates with the wind regime and the Reynolds number. Finally, and most valuably, a physical validation of the optimised geometry, whether through a scaled wind-tunnel model or field measurement, would test the predictions against reality and close the loop between computation and experiment.
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