where Ni and di are the number concentration and diameter of the particles in bin i, and the sum is over every model size bin and each height level in the model. The solar optical depth, r, is then calculated by integrating the volume extinction in the vertical,
The approximate broadband albedo, A, is then calculated using the formula (see equation 24.38 of Seinfeld & Pandis )
We report the total albedo change in this study that contains contributions from the direct effect and indirect effect. The direct effect is small when compared with the indirect effect in these calculations, and its magnitude will depend on the amount of aerosol and the humidity.
Figure 6. Summary plots for the clean air mass. The number of activated drops without the addition of NaCl were 8.8 and 9.8 cm−3 for w =0.2 and 0.5ms−1, respectively. (a) A contour of the number of activated cloud drops when a distribution of NaCl aerosols of different total number and median mass are added to a rising parcel moving at 0.2ms−1. The masses added are on the x-axis, whereas the corresponding number added is on the y-axis. Plus signs denote the different runs used to calculate the contour plot; (b) same as (a) but for an updraught of 0.5ms−1; (c) the difference in the albedo between the control run and the run with the indicated aerosol added (nadd, madd), in units of per cent, of the clouds resulting from seeding; (d) same as (c) but for 0.5ms−1. Please refer to initial conditions in text for dry diameters corresponding to added dry particle masses.
(b) Results from model runs
Figure 6 shows results in the case where the background ammonium sulphate size distribution is taken from that measured in a ‘clean air mass’ . This case represents the most pristine conditions we might expect to find in the maritime boundary layer. Concentrations in the medium case are slightly higher than found over the southeast Pacific (e.g. during the recent VOCALS experiment). The dirty case is very polluted. For the clean case, it can be seen (figure 6) that adding NaCl particles of dry mass less than approximately 1 × 10−19 kg results in no change to the cloud drop number because these particles have too high curvature and too low solute mass to be active CCN. Adding particles of dry mass greater than approximately 1 × 10−16 kg results in aerosols not activating to form cloud drops (figure 6a,b). However, the added sodium chloride aerosols, while not ‘classically’ activating (to form cloud drops), still take on appreciable liquid water, swelling to sizes approaching approximately 10 mm. The result of this is a thick haze having high extinction of solar radiation and hence a high albedo, as can be seen from figure 6c,d. The pre-existing ammonium sulphate aerosols have their activation
Figure 7. Summary plots of the albedo change for the medium and dirty air-mass cases. For the medium case, the number of activated drops without the addition of NaCl were 142 and 179 cm−3 for w =0.2 and 0.5ms−1, respectively, whereas for the dirty case these were 358 and 639 cm−3 for w =0.2 and 0.5ms−1, respectively. (a) The difference in the albedo between the control and the run with the indicated aerosol (nadd,madd) for the medium case with 0.2ms−1 updraught; (b) the same but for 0.5ms−1; (c, d) the corresponding contours of albedo change for the dirty case.
suppressed. Between 1 × 10−19 and 1 × 10−16 kg dry mass, we are able to alter the modelled cloud drop concentration very effectively by changing the number concentration of added aerosols. Although the addition of NaCl particles of mass greater than 1 × 10−16 kg results in no aerosols being activated as CCN, the swelling of these aerosols still has the desired effect of increasing ‘cloud’ albedo, regardless of whether they are activated. However, adding aerosols of this size or greater (which are effectively giant CCN) may result in undesirable effects such as the more efficient production of rain; an effect that will be investigated in future work). The maximum change in albedo for the clean air mass is around 0.4, rising from an albedo of 20 per cent for the control to 60 per cent for the case in which high concentrations of large NaCl particles have been added.
The pattern of aerosols not strictly being activated but still contributing to albedo difference was observed in both the medium and dirty cases, so the plots of cloud drop number are not shown here.
Figure 7a,b shows the model results for the medium loading ammonium sulphate background air-mass case . Qualitatively, the results are similar to the cleaner air-mass results except for two key differences: (i) the magnitude of albedo difference is about a factor of 3 smaller than in the clean case and (ii) for the lower updraught case (w =0.2ms−1) adding relatively few large NaCl reason for this is that a few large NaCl particles are able to reduce the peak supersaturation in the rising parcel enough to reduce the number of cloud drops in the background spectrum that would otherwise activate to form cloud drops, but not enough to suppress activation entirely. This reduction in turn reduces the extinction of the clouds as there are fewer, larger particles than in the control case. Suppressing activation entirely (i.e. when adding many large NaCl particles) results in many large swollen aerosol particles and hence larger extinction, as can be seen from figure 7a,b. In the absence of seeding, the concentrations of cloud droplets generated in the background in the clean, medium and dirty cases were 8.8, 142, 358 cm−3, respectively, for an updraught of 0.2ms−1, and 9.8, 180 and 639 cm−3, respectively, for an updraught of 0.5ms−1.
Figure 7c,d shows the model results for the case in which there is a high concentration of background ammonium sulphate aerosol present, corresponding to a ‘dirty air mass’. Qualitatively, the results are much the same as for both the clean and the medium air mass cases. One difference is that the albedo of the clouds is now less susceptible to the inclusion of additional sea salt aerosol. There was little increase in cloud droplet number even when adding particles approaching 1 × 10−18 kg in mass, especially for the low-updraught case (not shown here).
In the medium and clean cases, a larger increase in cloud droplet number was found for the addition of NaCl aerosol of this or even smaller mass. The reason for this decreased sensitivity is that, in the dirty case, there are already copious (NH4)2SO4 particles present in the background aerosol to deplete the supersaturation at cloud base such that the NaCl particles of approximately 1 × 10−18 kg cannot be activated. Similarly, the point at which drops cease to be activated has also changed. In the previous cases, drops ceased to activate when NaCl particles of mass approximately 1 × 10−16 kg (or larger) were added. In this case, activation of additional drops ceases at a lower threshold sea salt particle mass (typically 7 × 10−17 kg or less). This is because the higher concentration of background aerosol contributes significantly to the reduction in supersaturation in the rising parcel of air, suppressing further activation. Another notable difference is that the maximum change in albedo that is achieved is considerably less than for the clean case, and slightly less than in the medium case too. More noticeable in this case is a region where a reduction in albedo occurs when adding relatively few large-mass NaCl particles.
The modelling suggests the following:
— The enhancement to the albedo is greatest for clean background conditions. This is consistent with previous work by Bower et al. .
— In the clean conditions, the albedo of the control case cloud was approximately 20 per cent, whereas for the case where many large NaCl particles were added it was approximately 60 per cent. This (factor of 3) difference should be easily observable in a field campaign. In the medium and dirty cases, these increases in albedo were a factor of 1.6 and 1.3, respectively. This corresponds to albedos in the control runs for the medium and dirty cases of 35 per cent and 45 per cent with the maximum absolute increases in albedo of 20 per cent and 12 per cent, respectively. The magnitude of these changes will vary slightly with cloud depth (although the trends will be similar), and this will be investigated in future work.
— The values of the albedo in the control runs are typical of observed stratocumulus clouds and are in the same range as those in the cloud modelling section (figure 5).
— For both the medium and dirty cases, a reduction in cloud albedo was found when adding relatively low concentrations of particles that have NaCl masses of approximately 1 × 10−16 and greater. This underscores the findings by Bower et al.  that, for efficient albedo enhancement, the added particles should have masses higher than almost all natural particles and be added in significantly greater numbers; however, current technology is unable at present to generate such large particles in significant concentrations (see §6). Nevertheless, this study has shown that adding smaller particles of 3 × 10−19 kg (0.033 mm) results in smaller, but still significant, albedo enhancement. Furthermore, adding particles of salt mass less than 1 × 10−19 kg in the clean and medium cases and less than 1 × 10−18 in the dirty case produced little change to the drop number.
— While the most efficient albedo enhancement is achieved by adding large NaCl particles, it should be noted that such large particles may also initiate rain that is detrimental to cloud brightening as it tends to reduce cloud lifetime . This effect needs further investigation both with high-resolution models (see §3) and further parcel modelling.
When performing this study, we chose conditions to be relevant to those that seed aerosols would experience as they rise through a stratocumulus cloud layer in the southeast Pacific Ocean and hence we are limited as to the generality of our conclusions. We expect that, in general, the results would not be too different in all marine stratocumulus clouds. However, it is noted that the scheme will not be as effective in marine stratocumulus clouds that are close to significant sources of anthropogenic aerosol.
5. Engineering steps to implement marine cloud brightening
Previous sections have considered the science of cloud brightening by increasing the CCN of marine stratus clouds (by way of a very fine, evaporating spray of sea water microdroplets) and the foreseen impact on global climate. In this section, attention is turned to what are seen as the two major technological challenges that have a vital bearing on the effectiveness: the time scale for development and the overall costs of the scheme. These are, first, how one might generate the mist of microdroplets of the desired size and spray-rate needed and, second, what strategy should be adopted for delivering the spray; for example, whether from mobile or stationary sources and, if from a mobile source (i.e. a ship), the type of vessel and the optimum means of propulsion.
In fact, both these aspects were considered, if not entirely resolved, by Salter et al.  and this section mainly concentrates on new developments. That paper had already concluded that sea-level dispersal of an evaporating spray had decisive advantages over the more direct approach of cloud seeding from aircraft and that, among the several alternative strategies, dedicated sea-going vessels propelled by Flettner rotors (which facilitated an unmanned operation) were the preferred technical choice as well as being, by a considerable margin, the cheapest and ‘greenest’ route. The performance of Flettner rotors had not, however, been examined for more than 80 years and thus in §5c our first results based on CFD
of the dynamic performance of a single rotor are presented. This is preceded, in §5b, by an even more pressing issue—the approach to be used for producing the salt-water spray.
(b) Electrohydrodynamic spray fabrication
We have explored experimentally a number of ways to produce sea water droplets that would be suitable for use in cloud brightening. The critical requirement is that their salt mass ms be high enough that they can convert into cloud droplets at the supersaturation, S, occurring in marine stratocumulus clouds. S depends on updraught speed, and the properties of the air mass. Cloud modelling (described later) provides values of critical mass for a variety of relevant scenarios. They show that significant droplet formation and associated cloud albedo increase can occur for ms values down to about 5 × 10−20 kg. Hence, the initially sprayed droplets, drying to a quarter of their initial size, should minimally be of the order of 150–200nm diameter. For energy efficiency, it is advantageous to make the droplets close to this lower acceptable limit, for it is the number of suitable nuclei formed, not the amount of water sprayed, that is important. The smaller the size of the droplets capable of inducing activation, the smaller the required amount of spray with its associated energy and evaporative air cooling.
We investigated the performance of standard commercial nozzles that are used in fogging systems, toroidal vortex-based nozzles, colliding water jets, ultra-highpressure nozzles (345MPa) and Rayleigh-mode jet break-up from micromachined and radiation-track apertures. These experiments will be detailed in another publication, but, so far, none has produced encouraging results.
The best results to date were obtained using Taylor cone-jets , drawn from porous tips. Upon application of a voltage to a capillary containing a fluid, the most interesting of the spraying modes is the cone-jet, i.e. a cone terminating in an emerging jet. The 49.3◦ half-angle cone first described by Taylor is well understood, but the jet description is much more complex, particularly for high-conductivity liquids such as sea water. Analysis by De la Mora  and Gañán-Calvo & Montanero  show that a critical radius (ri) exists, defined by the flow and the dielectric relaxation constant of the fluid. A highly charged jet of approximate radius 0.2 ri emerges and breaks up monotonically, similar to that of an uncharged Rayleigh jet. Each drop is often accompanied by a satellite drop having a mass a few per cent of that of the parent drop.
Figure 8 shows scanning electron microscope (SEM) images, at different magnifications, of salt particles produced by a Taylor cone emanating from a porous tip, collected on a silicon wafer at a 5.4 kV potential, a current of 0.2 mA
with a flow of 5.6 nl s−1, using 540 ppm of surfactant. The surfactant lowers the instability threshold below air breakdown, eliminating the corona discharge that destroys the uniformity of the particle distribution. The average size of these crystals is of the order of 75–85 nm, having a mass of approximately 10−18 kg, suitable for the intended purpose. The droplets evaporate before they reach the silicon wafer 2 cm away. This near instantaneous evaporation of the droplets is due to their emergence from the jet with velocities approaching the speed of sound, and the heating that takes place in the cone itself . These crystals readily convert at a supersaturation of 0.5 per cent, achieved by cooling the wafer with a thermoelectric chuck in an enclosed environment.
Although each cone-jet produces a very large number of droplets (of the order of 108–109 s−1), scale-up requires 108 jets to reach roughly 1017 nuclei s−1 per sprayer. Small arrays of porous tips work well, but the overall size would be prohibitive. Various efforts have been made to mass produce cone-jet capillaries and associated extraction plates. Perhaps the most relevant for our purposes is the work of Deng et al. , who described the micromachining of silicon capillaries and extraction plates, alignment methods and the production of arrays with up to 331 nozzles, producing remarkably uniform spray, with only a few per cent of size deviation. The density of the capillaries exceeds 100mm−2, suggesting approximately 1m2 in total for the nozzle array that is technically feasible by tiling.
As a low-cost alternative, we have pursued the use of holes in low-dielectric polymeric materials (PEEK, polyimide, PMP) in place of capillaries. This approach was first outlined by earlier studies [48,49]. This technique lowers power consumption, and the fabrication of holes is significantly easier than that of capillaries. These holes must have a large aspect ratio in order to avoid interaction between adjacent holes. The problem can be overcome by using a dielectric thin film (50–75 mm) attached to a porous block that provides flow impedance, isolation and filtration at the same time. Such arrays may then be made by fast and inexpensive laser drilling systems. To fabricate prototypes we were able to make use of a Samurai UV marking system (courtesy of DPSS Lasers Inc., Santa Clara, CA), capable of drilling 50 000 holes s−1. Hence, the drilling of 100 million holes is a manageable task, requiring a hole every 100 mm over a total area of 1m2. The other requirement  is that the water needs to be confined at the rim of each individual hole, or jets will coalesce. To this end, it has been found that the dielectric material needs to be made superhydrophobic, i.e. the fluid contact angle must be in excess of 150◦ . Polyimide films were made superhydrophobic by plasma etching with oxygen, yielding a rough surface, followed by plasma deposition of a 20nm fluorocarbon film. The combination gives rise to the desired surface properties, with water contact angles approaching 160◦. However, the surfactant needed to obtain reliable cone-jet spraying of sea water lowers the contact angle to values that are unacceptable. Using films made at the Stanford Nanofabrication Facility or supplied by commercial sources (Repellix; Integrated Surface Technologies, Inc., Menlo Park, CA), we were unable to find a combination of surfactant and robust surface preparation that satisfies all the requirements.
The surfactant requirement can be eliminated by a number of methods:
increased ambient pressure or smaller apertures. If the ambient pressure is raised slightly (20%), the air breakdown field increases. With slight over-pressurization, corona discharge disappears and there is no need for surfactants. Raising the pressure causes airflow through the extraction apertures and, while the flow through each hole is small, an array of 100 million holes demands a substantial amount of power. The flow of air is of course beneficial in helping the passage of the droplets through the extractor holes. Likewise, when the capillary holes are made smaller than 10 mm, the air breakdown field (increasing with decreasing jet radius) is at all times higher than the field over the cone itself; so no air breakdown occurs here either.
In summary, the fabrication of large arrays of Taylor cones, either by silicon micromachining or by laser drilling in dielectric sheets, seems quite feasible although no such large arrays have yet been constructed. It is estimated that for an array of 100 million holes, roughly 1m2 in size, the electrical power requirement would be less than 100 kW. If airflow is used, then there would be an additional requirement of 270kW for pneumatic power. Because more than 90 per cent of the electrical power ends up as droplet kinetic energy, it can probably be partially recovered by reverse induction using a Kelvin generator arrangement.
As a simpler alternative, we are exploring the spraying of sea water at or near its critical point. In this regime, water has little or no surface tension and a gas-like viscosity and hence should produce fine dispersions. This has been demonstrated in the pharmaceutical industry with the spraying of supercritical carbon dioxide containing dissolved therapeutic compounds. While the distributions resulting from this technique are bound to be wider than those from cone-jets, the resultant particle distribution can on occasion be quite uniform . Results of this investigation will be reported later.
We used the model described in §4 to examine in more detail the conditions under which the electrohydrodynamic spraying technique could produce albedo change values of significance (i.e. not less than about 0.06, or 6%). We present in table 1 the change in albedo (for each air mass) that could be achieved by adding 1000 cm−3 of NaCl particles of mass within the range currently achievable by this technique (i.e. up to about 10−19 kg). We present only the 1000 cm−3 results because our model results showed that this led to the maximum change in albedo. It can be seen that the technique can result in large albedo change in clean air masses. For the medium-polluted air mass, only particles of salt mass larger than or equal to approximately 3 × 10−19 kg result in an albedo change that may be significant for offsetting warming by carbon dioxide, whereas for the dirty air mass all salt masses result in negligible albedo change.
This highlights that, in very clean clouds, the electrohydrodynamic spray technique is feasible. However, in the medium and in the dirty air masses, in particular, we would probably need to produce larger particles of (around 1 × 10−18 kg), as suggested by figure 6.
(c) Computational fluid dynamics studies for optimizing the Flettner propulsive system
(i) Scene setting
The most direct and probably the most obvious route for supplying the additional CCN would seem to be by directly seeding the microparticles from aircraft flying below the bases of the marine clouds to be brightened. Our earlier work on MCB [4,5] had firmly concluded, however, that sea-level injection of microdroplets of sea water would be as effective while offering major environmental and cost-saving benefits. Among the sea-level options for seeding the marine clouds, fixed spraying locations from anchored platforms would have to be too numerous to provide a reasonable coverage of the most suitable regions and their servicing at sea would be both hazardous and expensive. While the spraying equipment could be installed on regular cargo vessels as they plied the oceans, Salter et al.  concluded that it was better to have a vessel—or, rather, fleet of vessels—dedicated to the task of cloud seeding. Given the unusual role that these craft had to play, however, it was imperative that the ship’s design be open to possibly radical innovations. The most important of these was the proposal that the vessel should be propelled not by conventional diesel engine-powered propellers nor by sails, but by Flettner rotors.
A Flettner rotor (named after its inventor, Anton Flettner) is a vertically mounted cylinder that may be rotated about its axis by an external power supply. When air flows past it, the cylinder rotation creates a force (the Magnus force) at right angles to the air flow that propels the vessel on which the cylinder is
mounted. The rotor thus plays the same role as the sails on a yacht but the thrust levels attainable are far greater than for a sail of the same area; moreover, the control of such vessels is very much simpler (without the complex rigging of a sail and with far superior manoeuvrability). This latter feature makes vessels powered by Flettner rotors ideal for unmanned, radio-controlled operation, a measure that clearly brings enormous savings in costs for it dispenses with the need for a crew and the associated multi-faceted support infrastructure. Moreover, it has been estimated  that the cost of providing the power to spin the rotor is an order of magnitude less than that required for a screw-driven vessel of comparable size sailing at the same speed. The fact that that speed would usually be less than half that of a diesel-powered craft in normal operation is immaterial for the purpose of cloud seeding.
Figure 9. Artist’s impression of a Flettner rotor ship. Reproduced from Gadian et al. . (Onlineversion in colour.)
An artist’s impression of such a vessel is shown in figure 9. While the original Flettner vessel that crossed the Atlantic in 1926 was propelled by two purely cylindrical rotors, in the conceptual design of the cloud-seeding craft shown in the figure, the rotors have a number of discs mounted along their length. In fact, Thom  carried out a number of wind-tunnel experiments that suggested that the inclusion of such discs markedly improved rotor performance at high spin rates. Inevitably, however, the scope of that experimental exploration was limited and was certainly not conceived as contributing to the particular requirements of the cloud-seeding craft. Moreover, nearly 80 years on, as in so many areas, computer simulation (while not replacing the need for experiments) has made it feasible to explore a wide range of flow conditions and rotor geometries relatively rapidly and to provide far greater detail than any experiment. Here, therefore, our first results of applying CFD to the Flettner rotor problem are presented.
(bare) cylinder was undertaken by Mittal & Kumar  (hereafter M&K). While that study was limited to laminar flows at a Reynolds number, U∞D/v (5.1),1 of 200 (i.e. two or three orders of magnitude below those that would be encountered in an actual cloud-seeding vessel), their results revealed a potentially worrying feature with a major bearing on the present research. Over a limited range of rotation rates (relative to the wind speed), the flow around the cylinder experienced large-scale temporal periodicities that produced highly undesirable variations in drag and lateral forces on the cylinder. If these were present under operational conditions in the cloud-seeding vessel they would, inter alia, have a seriously adverse effect on the lifetime of the rotor and its support mechanisms. Thus, in the exploratory studies presented later of turbulent flow past the rotor at Reynolds numbers typical of operating conditions, such flow instabilities have been a major feature to watch out for.
(ii) Numerical and physical model
Computations have been performed using an in-house CFD solver, STREAM , to examine the flow around rotating cylinders with and without Thom discs. For these tests, the discs have been taken as flat annular plates of diameter twice that of the cylinder, axially spaced, one cylinder diameter apart. (This corresponded with the spacing shown in figure 9, although in Thom’s original tests the disc diameter was three times that of the rotor and the axial spacing just half the rotor diameter.) The results presented here have been obtained using a multi-block, non-orthogonal grid (figure 10) of around 0.75M
cells, covering a domain extending far enough from the cylinder for boundary effects to be negligible, and extending vertically from one disc to the next, as shown in figure 10. A uniform ‘wind’ velocity was specified around the inlet part of the outer boundary and zero-gradient conditions on the outlet. Symmetry conditions were applied along the two boundaries normal to the cylinder, and no-slip conditions, via ‘wall functions’, were applied at the disc and cylinder surfaces. For comparison, simulations were also performed for a bare cylinder (i.e. without discs).
For most of the test cases, the effects of turbulence were represented by a conventional k–3 linear eddy viscosity model with standard log-law-based ‘wall functions’ to provide the wall boundary condition. Some runs have, however, been made using more advanced stress-transport turbulence models and wall-function treatments (summarized, for example, in Craft et al. ). Although there are some modest quantitative differences in results between the different modelling approaches, cross checks show very similar trends, and because of the two- or threefold time penalty with the more elaborate model, most results were obtained with the simpler eddy viscosity scheme.
(iii) Initial computational results
To validate the procedure, purely laminar flow around a bare rotor for a Reynolds number of 200 was examined, corresponding to the case studied by M&K. In agreement with their results, the present computations confirmed that the Karman vortex street, present behind non-rotating cylinders, disappeared for dimensionless rotation rates, U≡uD/(2U∞), greater than 2 (where u is the angular velocity of the cylinder). Moreover, for a narrow band of rotation rates around U=4.4, longer period, large-amplitude oscillations developed, although by U=5 these also disappeared, again broadly in agreement with the M&K results. As noted already, a major question in the present context is whether these instabilities also arise in turbulent flow at the much higher Reynolds numbers commonly encountered for a Flettner rotor.
Figure 10. Details of the multi-block, non-orthogonal mesh. (Online version in colour.)
The presently predicted results for turbulent flow at Re =8 × 105 are summarized in figure 11, which shows the dependency of the rotor’s lift coefficient, CL, on the non-dimensional rotation rate. For zero rotation, the bare cylinder results display the expected oscillatory pattern associated with the Karman vortex street. As the rotation is increased, these oscillations disappear, and the magnitude of CL increases steadily. By a rotation rate of U=5, a lift coefficient of around 12 is predicted. Although rather less than half the corresponding value found for laminar flow, this is still sufficiently high to underline the value of the Flettner rotor as a propulsive device. A further point to note from the bare cylinder results is that the large-amplitude oscillations seen in the laminar flow calculations around U=4.4 were not detected in the turbulent case for the rotation rates examined. However, as can be seen from figure 11, at rotation rates above U=3, the solution did not exhibit an entirely steady behaviour, indicating that there are nevertheless unsteady three-dimensional structures present in the flow, although not in an organized, regularly repeating form.
Turning now to the effects of the Thom discs, the time histories of the lift coefficient, also included in figure 11, indicate that the mean values of CL are not very different from those of the bare cylinder. A feature worth noting, however, is that, by including the discs, a much steadier flow field is achieved. For the case of no rotation, the Karman vortex street is suppressed, and a constant value of CL (zero) is thus returned. At rotation rates of U=3 and 5, although there are some small undulations in the CL time history, these are very minor (and fairly periodic) compared with the behaviour of the bare cylinder.
Figure 11. Predicted temporal evolution of experimental lift coefficient for turbulent flow at Re =8 × 105 for a range of rotation. (Online version in colour.)
Figure 12 compares the predicted mean lift coefficient, as a function of rotation rate, with and without discs and the very early (but still among the most comprehensive) measurements of Reid  for a bare cylinder. The experimental data for the bare cylinder show a fairly rapid rise in CL as U is increased from 0 to around 3, followed by a more moderate rate of increase thereafter. The present results broadly reproduce this pattern. The numerical results show values slightly higher than the measurements. As noted earlier, the calculations show only minor differences in average CL values between the cases with and without Thom discs. Finally, the question of whether large-amplitude periodicities may arise cannot
yet be answered definitively. The computations of M&K and our own show that, in the laminar-flow regime, these instabilities appeared only over a very narrow range of spin rates. Preliminary turbulent flow studies have suggested that such oscillations may also occur  again over a narrow range of conditions. Further extensive explorations are required, however, before firm conclusions can be reached.
(iv) Examples of future work
Readers will recognize that the results shown earlier, while containing interesting and encouraging pointers, represent just a start on a range of CFD comparisons that will need to be made. As a first step, the computations need to consider a complete rotor rather than just the section between one disc and the next. This will enable the exploration of end effects and the possible variation with height of the wind velocity to be examined as well as potential interference effects
Fortsetzung: Nächste Seite (3)