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Experimental studies of the starting behaviour of small wind turbines have shown that the initial “idling period”, characterised by small rotor acceleration, is usually much longer than the subsequent period of rapid accleration to reach operational rotor speed. Idling obviously reduces the power generation potential of any turbine. The experimental results also imply that most starting torque is generated near the hub, whereas power-producing torque is concentrated near the tip. Therefore this paper considers the computational design of blades for small wind turbines for the dual purposes of (i) efficient power production at rated wind speeds and (ii) rapid starting at smaller wind speeds. Standard blade element theory is used to determine the power coefficient, which is the first objective function to be maximised. A modified blade element method gives the start, whose inverse is the second objective function. During the idling period, the blade angles of attack are relatively large, allowing the lift and drag to be modelled using “generic” flat-plate equations with a small adjustment for the particular aerofoil. No power is extracted from the wind while the blades are accelerated by the aerodynamic torque. Starting is deemed to be complete at a tip speed ratio representing the end of the idling period, which considerably less than the period for power generation.The design is by “differential evolution”. An initial population of blade types is generated randomly and allowed to evolve through random modification and selection of the fittest blades to comprise the next generation. The blade “genes” are the chord and pitch of each blade element; the aerofoil section is the same for all elements and all blades. In multi-objective optimisation, most interest focusses on the members of the population which have at least one objective function greater than every other member, as the final design is usually chosen from these blades. The geometry of the best power extracting blade obtained from the evolutionary optimisation was compared with that arising from standard blade element theory. Good agreement was found for the case of an aerofoil having a pronounced peak in its lift to drag ratio but only a small Reynolds number dependence in the lift coefficient at which the ratio is a maximum. Using an aerofoil with a much flatter lift to drag characteristic, the evolutionary method easily adapted to the significant Reynolds number dependence of the aerofoil characteristics. The effects of blade inertia and the resistive torque of the generator and drive train are also considered. In all cases studied, the best power-producing blade always had relatively poor starting performance, but it was usually possible to choose an alterntive blade with only a small reduction in power output but with a starting time decreased by a factor of around two.

This paper develops a mathematical model for a small wind turbine responding to changes in the wind direction. Here “small” implies that the turbine has a tail fin. Good yaw behaviour, in terms of tracking the changes in wind direction, is necessary to maximize power extraction. However large rates of change of yaw can lead to large stresses in the turbine components. The unsteady tail fin loads are more complex than implied by the “pseudo-static” assumption that the steady-state lift and drag act instantaneously. The aerodynamic model is applied first to data obtained from a 5 kW experimental turbine when it was not extracting power, because this almost removes the effect of the blades from the yaw behaviour. MATLAB's systems identification toolbox was used to optimise the fit of the model parameters to the data. The resulting values of a number of the parameters are shown to be in good agreement with earlier wind tunnel tests of the tail fin design. Some details of the comparisons, mainly in terms of the higher frequency components, suggest the need to characterise similarly the dynamics of wind vanes. When the turbine was extracting power, the flexible blades were deflected backwards by the aerodynamic loads. A blade element analysis suggests that the stabilizing moment due to this “coning” does not alter the form of the yaw response equation. The optimised fit of the model equations gave changes in the parameters broadly in agreement with the blade element analysis, but the quasi-steady analysis did not predict the measured increase in the damping associated with power extraction.

This paper describes a generic free-wake calculation of wind turbine wakes. The expanding, helical, tip vortices are represented by a sequence of straight segments, the blades are modelled as lines of constant bound vorticity, and the hub vortices lie along the axis of rotation. It is shown that this model is consistent with the one-dimensional analysis that leads to the Lanchester-Betz limit, in that the velocity in the far-wake is uniform with radius. Particular attention is paid to turbines operating above the Lanchester-Betz limit. It is shown that the usual relationship between the velocity through the blades and in the far-wake breaks down when there is significant wake expansion, and an empirical modification to that relation is presented. For highly expanding wakes, the dynamics of the turbine depend sensitively on the behaviour of the tip vortices.

The analysis of the self-induced velocity of a single helical vortex (Boersma & Wood 1999) is extended to include equally spaced multiple vortices. This arrangement approximates the tip vortices in the far wake of multi-bladed wind turbines, propellers, or rotors in ascending, descending, or hovering flight. The problem is reduced to finding, from the Biot–Savart law, the additional velocity of a helix due to an identical helix displaced azimuthally. The resulting Biot–Savart integral is further reduced to a Mellin–Barnes integral representation which allows the asymptotic expansions to be determined for small and for large pitch. The Biot–Savart integral is also evaluated numerically for a total of two, three and four vortices over a range of pitch values. The previous finding that the self-induced velocity at small pitch is dominated by a term inversely proportional to the pitch carries over to multiple vortices. It is shown that a far wake dominated by helical tip vortices is consistent with the one-dimensional representation that leads to the Betz limit on the power output of wind turbines. The small-pitch approximation then allows the determination of the blade&s bound vorticity for optimum power extraction. The present analysis is shown to give reasonable estimates for the vortex circulation in experiments using a single hovering rotor and a four-bladed propeller.

Abstract:  Elements of evolutionary computation and molecular biology are combined to design a DNA evolutionary computation. The traditional test problem for evolutionary computation, OneMax problem is addressed. The key feature is the physical separation of DNA strands consistent with OneMax “fitness.”

This paper reviews some recent advances in the technology of small wind turbines, whose upper power limit we take arbitrarily as 50 kW. Small turbines are used mainly for remote power generation either alone or in conjunction with other energy sources and battery storage. They can be divided into three categories: micro, up to 1 kW; mid-range; and mini-turbines, of 20 kW and larger, intended mainly for wind/diesel mini-grids. The paper discusses a number of issues that are category-dependent; for example, low-wind-speed performance is most critical for microturbines. The starting point for the review is the mature level of large wind turbine technology, and it is demonstrated that this maturity has yet to percolate downwards. Nevertheless, there have been a number of very encouraging recent developments. These include improvements to our understanding of the basic aerodynamics and advances in blade manufacturing, the use of micro-processor controls, and the increasing use of design certification and type approval. The developments are highlighted by two case studies of small turbine design in which the authors were involved. We conclude with a brief discussion of current developments in technology, such as fatigue testing of blades and new methods of blade design, which should further increase the level of small turbine technology towards that of large machines.

The velocity field in the immediate vicinity of a curved vortex comprises a circulation around the vortex, a component due to the vortex curvature, and a ‘remainder’ due to the more distant parts of the vortex. The first two components are relatively well understood but the remainder is known only for a few specific vortex geometries, most notably, the vortex ring. In this paper we derive a closed form for the remainder that is valid for all values of the pitch of an infinite helical vortex. The remainder is obtained firstly from Hardin's (1982) solution for the flow induced by a helical line vortex (of zero thickness). We then use Ricca's (1994) implementation of the Moore & Saffman (1972) formulation to obtain the remainder for a helical vortex with a finite circular core over which the circulation is distributed uniformly. It is shown analytically that the two remainders differ by 1/4 for all values of the pitch. This generalizes the results of Kuibin & Okulov (1998) who obtained the remainders and their difference asymptotically for small and large pitch. An asymptotic analysis of the new closed-form remainders using Mellin transforms provides a complete representation by a residue series and reveals a minor correction to the asymptotic expression of Kuibin & Okulov (1998) for the remainder at small pitch.

The influence on several hot wire measurements of the diameter d and overheat ratio a of a wire placed near a conducting wall in a turbulent boundary layer is investigated. These measurements include the mean velocity and second, third and fourth order moments of the longitudinal velocity fluctuation u. A decrease in either d or a reduces the departure of the measured mean velocity from the expected linear sublayer value. The measured influence of d and a precludes the use of a universal correction for the mean velocity. There is no influence of a on the rms, skewness and flatness factors of u. Only a small increase is found in the skewness and flatness factors of u when d is decreased.

This paper presents measurements in the turbulent wake of a circular cylinder rotating with its axis normal to the free-stream velocity; in other words, the axis of rotation was parallel to the streamwise direction. All three mean velocities and six Reynolds stresses were obtained at three positions downstream of the cylinder, with and without rotation of the free-stream. Most emphasis is given to the latter results because of the better flow quality. The ratio of the circumferential velocity of the cylinder to the free-stream velocity — the swirl number — had a maximum value of 0.6. Measurements for two combinations of the free-stream and angular velocities showed the velocity deficit in the wake to be a multi-valued function of the swirl number, implying that the rotation affected the separation of the cylinder's boundary layer in a complex manner. In the turbulent wake, the rotation did not significantly alter the magnitudes of the normal stresses, but caused large changes to the shape of the profiles of the axial and cross-stream normal stresses. Eventually, the primary (cross-stream) shear stress became almost entirely positive, but there was no corresponding change to the (cross-stream) gradient of the streamwise mean velocity. Despite these alterations to the turbulence, the rotationally-activated generation terms in the Reynolds transport equations never dominated the terms that are common to the wakes of rotating and non-rotating cylinders.

This note discusses the interpretation of X-probe measurements obtained in the presence of significant velocities transverse to the plane of the wires. To measure the three mean velocity components, the probe was used in two planes which gave a redundant estimate of the component along the probe axis. A correction of the measured mean velocities for transverse contamination is described and justified. It was found that the corrections reduced the mean component along the probe’s axis by up to 20 percent, while the components orthogonal to that axis were hardly altered.

Mean velocity and turbulence intensity measurements have been made in a fully developed turbulent boundary layer over a d-type surface roughness. This roughness is characterised by regular two-dimensional elements of square cross section placed one element width apart, with the cavity flow between elements being essentially isolated from the outer flow. The measurements show that this boundary layer closely satisfies the requirement of exact self-preservation. Distribution across the layer of Reynolds normal and shear stresses are closely similar to those found over a smooth surface except for the region immediately above the grooves. This similarity extends to distributions of third and fourth-order moments of longitudinal and normal velocity fluctuations and also to the distribution of turbulent energy dissipation. The present results are compared with those obtained for a k-type or sand grained roughness.

The original derivation of the basic theory governing the aerodynamics of both hovercraft and modern floatation ovens, requires the validity of some extremely crude assumptions. However, the basic theory is surprisingly accurate. It is shown that this accuracy occurs because the final expression of the basic theory can be derived by approximating the full Navier-Stokes equations in a manner that clearly shows the limitations of the theory. These limitations are used in discussing the relatively small discrepancies between the theory and experiment, which may not be significant for practical purposes.

A preliminary study to determine the early comparative effects of I131and X-irradiation on the thyroid was performed in young adult sheep. The thyroid region of one group of animals was exposed to X-irradiation, with doses of 750–4500 r given as single or three exposures at weekly intervals. Other animals were given single oral doses of 1.25–5.0 mc I131with estimated average thyroid radiation doses of 24,000–90,000 rad. Only minimal changes in thyroid function were observed, as evaluated by radioiodine uptake and determination of serum protein-bound iodine. Histopathological changes including inflammation, necrosis and fibrosis of the thyroid were observed in the exposed animals and were generally dose dependent. In the X-irradiated animals, tissue damage was observed in the structures contiguous to the thyroid gland.

A single I131contamination event of forage was simulated by administering I131labeled feed to dairy cattle twice daily for 31 days, all feed samples being spiked on day one with 5 µc I131per sample. Peak milk concentration in the dairy cattle occurred on the fourth day with about 0.4 per cent of the first day's dose of 10 µc observed per l. of milk. The peak thyroid concentration in the cattle occurred after 1 week and was about 70 per cent of the first day's dose of I131. In a second study, 5 µc of I131were fed daily to three cows starting before parturition and continuing for a period of 6 months of lactation. Apparent equilibrium of I131in the thyroid was reached after 2 weeks and approached twice the daily feeding level. A suggestion of increased thyroid uptake occurred following parturition. The I131concentration in the colostrum was 2–3 times that in the milk on the seventh day of lactation, after which time a gradual increase was observed. The per cent of the daily dose of I131appearing in the milk varied from 0.4 to 1.0 per cent over a 6-month period. Following an increase in the daily stable iodine content of the cow's diet from 5 mg to 2 g per day, milk concentration of I131decreased 50 per cent and thyroid concentrations decreased more than 90 per cent.

Thyroidal uptake of radioiodine following various routes of administration was studied in young sheep utilizing a double tracer technique and three detection systems. Iodine-125 and I131were given simultaneously by various combinations of intravenous, subcutaneous, oral and topical routes. Thyroid burdens were determined using a whole body monitor with a 9 × 4 in. NaI crystal, a modified Geiger-Mueller tube assembly, a 2 × 2 in. NaI crystal and a 2 × 0.04 in. NaI crystal. Rates and per cent of uptake and effective half life were similar following the oral, intravenous and subcutaneous routes of administration. A lower uptake and a longer effective half life were seen following topical administration. Variations which may be associated with age and season were observed. No correlation could be made between the per cent thyroid uptake and the location or total area of skin involved with topical application. Estimated total radiation dose to the thyroid from oral administration was 6-8 rad/µc, while that from topical administration was 2-3 rad/µc.

Milk from dairy cows fed carrier-free I131was consumed by adult male volunteers either as a single dose or daily doses. During the experiment, the amount of stable iodine in the cows' diet was increased from a recommended level of 5 mg/day to 2 g/day. The resulting I131uptake by the human thyroid was determined by measurements with a 3 x 3 in. NaI thyroid monitor in Hanford's Whole Body Counter Facility. During the low stable iodine phase of the study, results for eight men involved in both single and multiple intakes of I131from the milk indicated an average fractional thyroidal uptake of 0.2, with individual values ranging from 0.1 to 0.3. From the single intake data, the peak thyroid burden occurred at about 24 hr and was eliminated with an effective half-life of about 7 days. The thyroidal uptake of I131for those volunteers consuming milk daily from cows fed 2g/day of stable iodine was reduced by 50–80 per cent.

In a medium characterized by a scalar speed C(x), a shock arrives at the point x, after time T(x), with its magnitude decreased by A(x). Symmetric C, T, and A in two dimensions can be converted to cylindrically symmetric results in three dimensions by applying a dimension-increasing principle: “Let C(x, y), T(x, y), and A(x, y) be even functions of y. They can be extended into three dimensions by using the formulas C(x, y)←C(x, r), T(x, y)←T(x, r), and A(x,y)←A(x,r) [r−1 cosΦ(x, r)]�, where r = (x2+22)� and Φ is an auxiliary function.” When C(x) is a function of a single variable, the auxiliary function Φ is given by cosΦ(x, y) = Ty(x, y). In two dimensions, there is a conformal mapping principle: “Under the conformal mapping x+iy = f(x*+iy*), the functions T(x, y) and A(x, y) go into functions associated with a medium having speed C*,y*) = C(Re[f), Im[f]/f1(x*+iy‡.”There is also an unchanged wavefronts principle: “If g is a smooth function with g(0) = 0 and g'(0)>0 then T*(x) = g(T(x) and A*(x) = A(x)[g'(x)/g'1/2 are associated with a medium having speed C*(x) = C(x)/g'(T(x)).” in two dimensions, alternating the application of the last two principles generates a sequence of media with their associated T(x, y) and A(x, y). Some of these can be extended into three dimensions by applying the first principle.

A COMPOUND near the CeMg9stoichiometric region in the cerium–magnesium system was indexed as cubic from X-ray powder patterns and was claimed to be two phases1. An examination2of structures of this approximate stoichiometry indicated that this would represent a new structure if it existed; consequently a structure determination using single crystal techniques was undertaken. Although a subsequent report3utilizing only powder data indicated a more probable hexagonal cell and isomorphism with the Th2Ni17structure, our preliminary single-crystal data lead to a different result.