Chapter05

IE010224A

Chapter 5
Home Of The Big Wind

By now it should be clear that this material does not follow the mainstream and so can be considered to be a sort of alternative approach even within the alternatives. Before anything else comes plausibility. Written opinions, after all, are not provided the reading public to make the status quo sound plausible. The status quo is plausible and if it weren't, it wouldn't be the status quo. A glimpse has been provided in earlier chapters of the support profferred the yet-to-be-proven-satisfactory concept of the verticals, including the Darrieus machines. This puts us in the position of favoring verticals ahead of horizontals in this instance. To compound our "questionable judgement", we now propose to support another opposite, this time favoring horizontal axis anemometers that have propellers and turn to face the wind, in place of the little rotating cup devices on their vertical axes. This puts us in the position of favoring horizontals, this time, ahead of verticals. It sounds as if our viewpoint is never anything but countervailing. The field of aerodynamics is not highly discrete and exact, though, as can be inferred from a brief look at the phenomenon of flow separation, something else covered in this chapter.

The White Mountains Of New England

It could be. For example, this. It is held popularly that California on the West Coast has the best spot locations for wind, at least in the summertime, in those mountain passes in the coastal and other ranges there. But, 'taint so. No one is saying much about it and it may be the best kept secret in meteorology other than within the annals of the record books, but the winds at the summit of 6288 feet tall Mt. Washington on the East Coast in upstate New Hampshire are quite fierce as well and blow all year 'round, as reported from a weather station located there. A rough estimate of the winds obtained from occasional visits to the Internet site maintained by this activity (they shun averages, favoring extremes and weather records instead) is that their average strengths may be on the order of about two or three times the averages of the winds in some of the windier states in the Midwest. Getting out our pencils, this calculates easily to find us conceptualizing wind machines of specialized design and the same blade diameters producing the "Lanchester-Betz cubed" values of these numbers or roughly 10 to 25 times the energy each machine. If so, then the land area required by arrays of wind machines for the same energy production as is possible in any one of them is reduced to the inverse of these numbers or 4% to 10%, not much larger, if at all, than the land area of this tidy state itself, begging her citizens' kind forbearance for the unwarranted speculativeness of this line of thinking. It is not intended to draw this out at any length but clearly if New Hampshire, which at this writing has the highest electric energy retail rates of all 50 states in the nation, ever wanted to explore wind energy in a way suitable to her own circumstances, she would have good reason for doing so. States like California create a lot of news but other states, even those that share few of the same interests, have their stories to tell and it isn't hard to find them.

Above data and comments downloaded with grateful acknowledgement from the

Mt. Washington, New Hampshire Observatory Internet web site as examples of

weather condition reporting by the staff of Observers and Volunteers who support this effort.

Blade Swept Areas

There is more. Those in support of the renewable energies seem bent on reinventing electrical energy generation or at least redefining the electrical power quantity named in honor of Scotsman James Watt. Plenty of magic can be found in windpower as it is and it rests mostly in the blades, where the raw force and motion arises, and only secondarily in the wires, which only guide and perhaps condition the juice. If this treatment, rambling on though it be, is to be true to its mission of suggesting different approaches, then let it be said that it makes far more sense to rate wind energy projects not by kilowatts or megawatts but by their total blade swept areas, instead, and go on to use Paul Bunyon-like measuring standards like square kilometers or square miles for this purpose. The truth of the matter then can be more plainly seen. A square mile is not a very large area in geographical terms but it takes umpteen hundreds, bordering on thousands, of wind machines of even the largest capacities currently available to tally up the blade swept areas to this amount and it takes nothing less than the forthright attainment of such structural dimensions to enter the same playing field and produce the same orders of magnitude of energy as have become standard and within easy reach by the others.

Wind "Energy" Averages

One more item. It has been a position taken by us, and what we do, for, it seems, forever that wind resource assessment averages need to be upgraded to be based on cubed values, consistent with their use for energy development purposes, rather than what has always been used, linear ones. This advancement may be beginning to be introduced, if belatedly, through the back door. Errors have become noticeable in the calculation of wind roses, the winds from one direction, usually of lower peak values although more steady, sometimes being of less consequence than those of another despite having the greater linear average. So now these polar co-ordinate graphs are produced with two curves within them, one showing the linear averages and the other the cubed. One of these days such a hard-by progressive attitude may infect the calculation of the ordinary omnidirectional wind resource locational averages as well, to result in who knows what revolutionary conspiracies. It is such an eye-opener that the wind industry has been so timid in some of these regards. The linear averaging technique in use and in common practice has at least the disadvantage to it that it cannot be used to scale the output of any particular machine from one location to another; even making use of the handy graphs provided by the turbine manufacturer is not of reliable use where wind distributions vary.

All of the above items are put into words here to, again, indicate that current dogma in the field is not necessarily to be believed with unshakable conviction, by any stretch of the imagination, and plenty of room exists for treatments given it such as what is before the reader herein. Wind energy may have become highly politicized but, with some experience in looking at what's what, it is easy to peek under the curtains.

Anemometers And Vectors

Let's put some teeth in our analysis of anemometers and make our point about the blades to the readers' satisfaction. It has become about time to get around to looking at the blade vector diagram. It is something that will stand us in good stead later on when we get into the stuff that was the reason to say something about all this to begin with. To prove the above conjectures about anemometers using vectors seems about right at this place in our travels.

Vectors are a way of taking a look at what is going on in a relative sense. It is easy to see how air flows past a stationary obstacle. But how does it look if one took a position of viewing it from the standpoint of the moving blade as though it were fixed in space? A vector diagram assumes, then, that the blade is at rest and the whole planet is moving at the speed once attributed to the blade and, not only that, but going around in a circle as well - and taking the whole universe with it(!). Mathematically and physically, it is a much better way of getting a look at how the blade does its work and when it comes time to return to the earth-based reference system then it can be done with new insights in how the wind transfers energy to the blade - less some of the misconceptions that may have been present earlier. That's the theory, anyway.

We won't even relinquish the concept, so much an unwritten part of current thinking, of the "stylus and the wedge" discussed in an earlier chapter. The wind contacts the blade and sort of slides along it, the forces that result pushing it in the only direction it is free to move. (Later we will see a much better model of what happens but this continues to suffice for the moment.)

A New Way To Add And Subtract

It is plain to see what a vector must mean. Its tail is located at the location under study in the flow field. Its length is proportional to the speed of the flow. Its direction is the direction of the flow. But how does vector addition work? And vector subtraction?

Vector Addition And Vector Subtraction

If a blade is moving through still air then it is equivalent to say that it is the blade that is still and the air is moving past it. But if the air is not still and wind is present then vector addition is required. The flow the blade sees is its own motion through it and also the motion of the air caused by the wind which may be and, in fact normally is, in a different direction. Take a look at the above diagram. It shows two vectors. Vector addition requires that the tail of one be placed at the head of the other and a new vector be drawn from the tail of the first to the head of the second. To many of us who have worked with these concepts before, this is elementary but it is important that those who have little interest or background in these matters get this right, as is really quite easy to do.

Vector subtraction is a little trickier but if one remembers that it is only the opposite of addition it is just as simple. Place both vectors with their tails at the same point. Then draw a vector from the tip of one to the tip of the other and that is vector subtraction. To check, then try adding the new vector together with one of the original vectors in the same way as above to result in the other original vector. These procedures make a lot of sense and are quite powerful tools for understanding the air flow in moving reference systems.

Now we have above a few newer diagrams to scrutinize. In each diagram a slant line is placed to the right and extending from the origin. This is not a vector but, believe it or not, is our humble representation of a cross section of a blade as it appears from an end-on view and it is slant because it has a pitch angle. A better way of saying this is that suppose we took a photo of a blade rotating around its axis in a moment of time and then went to some point along the blade length looking at it, again, from end on toward its hub, then this is a two dimensional picture of what we would see. The blade is moving from right to left but is fixed in place in the reference system of the view and so it appears within it that it is encountering air that is moving from left to right.

But this is only half the story. There is wind. As can be seen a new vector is created by the addition of the blade motion vector, V, and the wind vector, W, which is the resultant vector, A, very important because it is the actual airflow that the blade sees. The vector A impinges on the blade from the front side and the back side and in both diagrams is not at the same angle as the blade pitch. In the diagram on the left the blade pitch is less than the angle of vector A and in the diagram on the right the blade pitch is greater than the angle of vector A. Anyone can see that something must be happening in both cases. Due to this mismatch of the angles, on the left, the blade is being forced to speed up and, on the right, it is being forced to slow down. The "stylus and the wedge" is operating, this time with the stylus acting at an angle not at right angles to the blade's motion as we saw in examples covered before but, due to the "frictionless surfaces", nevertheless a valid representation, or at least not a bad one, of what is going on.

Rotating Cups

Well, let's take a moment now and understand where we are. The rotating cup anemometers have seen quite a lot of history and, with it, a good deal of challenge. Do they work, are they accurate, are they linear? Every wind energy conference has, it seems, at least one paper devoted to these subjects. Something that has withstood such a lengthy trail of analysis from so many quarters in the field can't be all bad. And so it must be agreed here that they do suffice, in general, as accurate instrumentation. What seems to have been missing all along is whether any alternatives exist that are as cheap and readily deployable. The answer is in most cases, no. The high tech styles of wind measurement instrumentation, such as sonic-based devices, are not yet being mass merchandised. However, this overshoots the mark. Just the next step down the path are the horizontal, propeller-driven devices now available from certain vendors. These are simple and have the potential of being quite cheap as well.

Whether the rotating cup anemometers are linear or not, and this question is not completely settled yet, the trouble that dogs them constantly in the view of those in the energy field is their lack of physically precise, direct conversion to windspeed. How fast a rotation results from how fast a motion of the wind? Graphs are available but then what adjustments are needed for things like air density and temperature? Suppose different vendors press out on their plastic molding machines new models of them with slightly different dimensions and contours, to what effect? This is the nub of it. Practitioners in the field have long ago put aside these questions after spending some effort on calibration when starting new programs to assure themselves that the accuracy is within tolerance. Tradition plays a part and is a major factor in the case of, for example, the aforementioned Mt. Washington, New Hampshire summit weather observatory, which strictly uses nothing but rotating cup anemometers and those of its own design and fabrication as well. But wouldn't it be better if these questions didn't have to be asked from the very outset?

At one time, it should be said, blade fabrication may have limited the choices. Metal or wood blades are sometimes expensive to machine to the required dimensions. But the practically universally available capability of plastic molding has put all of these questions to rest for good.

Hypoid Propellers

Going back to the vector diagrams above, it can be seen that in order for the blades to measure the windspeed accurately the pitch angle must be exactly equal to the angle of the resultant airflow, vector A, which is what happens by itself as the blades rotate under the influence of the wind, courtesy of Mother Nature. But go to a different location along the blade length and the angle of vector A is different because the tangential speed of the blade is faster or slower there and again we have a problem, unless the pitch angle of the blade is different in exactly the way necessary to correspond to this new angle of vector A. So the sounds reverberate from the rafters, "Eureka, we have it!". All that needs be done is fabricate blades that have pitch angles that vary from root to tip in exactly this correspondence along their entire lengths. It must needs be a steep angle at the root and a shallower angle out at the blade tips and it turns out to be a value that can be described in mathematical terms as directly proportional to the arc cotangent of the radial distance from the axis of rotation. Simplicity itself.

If the blades are so designed, they must rotate with great precision at one rotational rate and one rotational rate only for any particular windspeed since every point at every radial distance along every blade is mathematically and physically requiring this be so. The mathematics being so rigorous, in fact, it becomes a no-brainer to determine what rotational rate corresponds with what windspeed, even no matter the air density or temperature or minor vendor design differences as well. More in the plus column, the rotational rate of the blades so designed is exactly proportional linearly with windspeed, if any doubt existed in this matter, i.e. equal to the windspeed divided by a constant. The constant is a value characteristic of the blade and is equal to the pitch of each blade as it varies with distance from the blade hub centerline.

The above image provided courtesy of the R.M.Young Company

of Traverse City, Michigan which supplies an extensive line of wind monitoring equipment

including this style of anemometer.

We didn't say this wouldn't look unusual. The blades, so pitched with this what can only be described as a "pitch twist", even have an unusual name. They are called, by at least one vendor who makes them, "hypoid".

Maybe side benefits will result from these discussions that will bring some attention to better ways of doing some of this instrumentation. Meanwhile some thought has now been given to the arcane subject of vectors and this will stand us in good stead in material in later chapters.

Flow Separation And Reynolds Numbers

It's been fun talking about fluid flows in the ivory tower in which we sit, where assumptions can all be under our control and made to our liking. But in the real world complications inevitably arise. Talk to anyone who is familiar with airflow aerodynamics and the words "Reynolds Number" inevitably enter the conversation. It happens every time as sure as one and one are two. Those in the public who allow themselves to be addressed as the "lay community" are especially always put out by this reference. The concept has importance in its relation to what is known as flow separation and the additional piling on of these phenomena makes for a certain amount of discomfort when everything else that goes before has not been fully digested yet.

But no matter. For what does an airfoil do anyways? When a fluid encounters an object that is oriented in such a way as to be pointed in a direction other than the path the fluid is taking, the fluid has a couple of choices in how it is accelerated as was mentioned in the last chapter but if it is especially unruly it has even more options. It can, for example, refuse to recognize the shape of the object at all and, especially if the object has tight corners and sharp edges, leap off in an unknown direction of its choice and in this case what is termed "flow separation" occurs.

Since it is important to know when this will happen a great deal of study has been done on this effect. Certain characteristics of the fluid medium play a part. For example, the density of the fluid will encourage this effect and the viscosity of the fluid will discourage it. Other factors have a mixed effect, including the velocity of the fluid and dimensions of the flow.

The Reynolds Number was invented as a way of collecting all of these factors together into one quantity to provide a measure of the tendency of flow separation to occur. It has other sidelights and purposes as well and, in general, enables different systems of different dimensions and scale factors to be directly compared by removing the extraneous factors that inhibit such comparison. It is dimensionless, like a percent quantity is, and deliberately so for the above reason. That is why it is called a "number". Even the wind velocity can be expressed in terms of Reynolds Numbers instead of usual units of measurement such as miles per hour.

The Formal Definition

The formal definition of the Reynolds Number is the flow velocity times a characteristic length dimension of the configuration times the fluid density all divided by the fluid dynamic viscosity. Before going any further it must be said here that it is imperfect science, that is, it has correlative features about it. The assumptions made include that flow separation occurs as a result of linear variation of these independent quantities and this may not be the case for any of them. The flow velocity is a particular culprit. Sometimes increased flow velocity increases flow separation and sometimes the reverse occurs and sometimes it seems to have little effect. Certainly factors other than these fluid flow properties have an effect such as the profile of the airfoil or the shape of the entrance to the weir or duct or pipe. An aircraft traveling at a slow speed tends to have a nose up configuration and high attack angle of the wing surfaces which cause thereby the well known phenomenon of "stall" simply on this basis alone, the flow velocity otherwise (it is suggested!) not itself being a factor. An additional argument for the insensitivity of flow separation due to flow velocity can be seen in the instance of water flowing rapidly through a narrow pipe in which the flow is not constrained by separation-induced turbulence to any large degree no matter how fast the flow as anyone watering their lawn with a garden hose can attest.

The Reynolds Number In Use

But some interesting facts come out of Reynolds Numbers analyses. The dynamic viscosity of a fluid divided by the density of the fluid has a name of its own and is called the "kinematic" viscosity. It is noteworthy that while the dynamic viscosity of water is about ten times that of air at normal pressures and temperatures (after all, water is a fluid and air is a gas) the reverse occurs when the densities are taken into account, that is, the kinematic viscosity of air is about ten times that of water. This comes as something of a surprise in that few tend to think of air as being viscous. This bears repetition. For its density, air is ten times as viscous as water is. This very definitely helps wind generators in that it allows the blades to be narrower and with higher attack angles and greater contour curvatures without seeing the onset of flow separation.

Earlier on it was mentioned that a characteristic length dimension is also included in the definition of the Reynolds Number. Since the identification of this quantity is whatever the user says it is - just like with any good tool such as a wrench or screwdriver that can be applied to many different bolts and nuts on many different engines - then the choice of which length dimension to use for it may be different for different applications. Sometimes it is the dimension along the length of the flow path starting with the entrance to a pipe, sometimes the diameter of the pipe, sometimes this, sometimes that. In cases of wind generators it is probably permissible to make it the blade width without unfairly discriminating against machines with wide blade widths (and, again, the blade shape and attack angle have an effect entirely unaccounted for within its definition). Just as long as the same length dimension, that is, in this instance the blade width, is used consistently for all cases in which the Reynolds Number parameter is calculated by any one person for any one purpose then everything is fine. As to whether the blade width has an effect on advancing or discouraging flow separation, little can be said in this treatment of the subject.

As in all cases in which technology enters the fuzzy realm of speculation and inexactitude, special care must be taken in making assumptions and defining terms at the outset of any analyses made. The Reynolds Number is relatively meaningless without substantiation through empirical correlation. In other words, no one is going to attempt to provide theoretical justification why flow separation occurs at a certain Reynolds Number without backing it up with actual results from field trials. One can be certain that flow will lift off a surface when the pressure drop induced by the sharp flow curvature reaches that necessary to cause a vacuum at the surface but this seems to not necessarily always be the case. If the fluid viscosity as compared to its density is very small then the fluid has a tendency to reverse direction to fill low pressure areas easily and this means that any lowering of the pressure near the surface at all is fair game for the flow to be undercut by fluid further downstream backing up and causing it to lift off the surface, i.e. separate. Streamlines observed with the aid of smoke introduced upstream in wind tunnels indicate that small vortices always form after the flow moves past any solid object at all (an indication of flow separation), no matter how smooth or straight the object is that is placed in the flow path, as a result of thin boundary layers that form near the object surfaces and this means that flow separation may only be a phenomenon that differs from case to case not in occurrence but only in degree.

Flow Separation in Wind Turbines

Be all this as it may, flow separation is invaluable as a useful mechanism at least a couple of instances during wind turbine operation. It has the well known use of introducing a method for limiting the driving force on the blades when the wind speed is of such a magnitude that the generator rating is reached. This has become known as "stall regulation". (One must be careful though in designing for this effect to be sure that just enough stall is introduced at just the right wind speed to limit overstress on the works without jeopardizing normal power production.)

Another albeit lesser known case in which flow separation is of use is in startup. For blades pitched to small angles of attack and even zero angles such as are useful for high efficiency at rated power the blade pitch angles are of little use in allowing for torque production when the blades are not rotating. This also applies to the verticals, which have had little ability to alter blade pitch angles as they are provided as part of the Darrieus and other configurations. In these cases, the differential separation of the flow around the front vs. the rear of the stopped blades, that is, the fact that the flow separation is less around the nose of the blade as opposed to that around the sharp trailing edge, is the factor that introduces the necessary startup torque to the blade to set it in motion irrespective of the blade pitch angle. (At the risk of saying the obvious, less separation means more deflection of the flow and accordingly more driving force on the blade.) Many seem to hold the opinion that the verticals cannot start up by themselves, for example, but if they are provided with more than two blades (such that the blades cannot all be parked in the neutral wind position at the same time) then startup is not any problem at all.

Some features of flow separation are best left to more experienced treatments on the subject, which tend to be highly specialized only making the voids in between all the larger, begging the pardon of all those whose efforts have gone into producing this material. Other writers and other technically qualified persons may hold entirely different opinions about all of what has been discussed. Would that some sort of end would have been reached here in this effort but unhappily as tends to be true in many areas of technology it no doubt forms only the barest of beginnings.