IE010704A

Chapter 7
Homework Assignment

A take-home problem is discussed here that is addressed not to any reader individually but to the industry comprised of many individuals and as a whole.

Despite all that has been said and done, the weakest link in the renewables is and continues to be the technical one. The heavy, international pontification that goes on decrying the need for action in support of reduced emissions and resource conservation has made a fire drill out of the renewables, in which untrained and idealistic volunteer firemen are all running around trying to find their boots and fire helmets. The Europeans have the benefit of some tradition and experience behind them and have the greatest sense about some of the directions the technology may take and so everyone else takes their cues from them. The United States, meanwhile, is being caught in the grips of an embarrassment some doubt she may ever recover from.

The tradition-bound enterprises of the euro Common Market, though, despite the earlier starts, are actually following only tired nostrums - make them bigger, make more of them - and the U.S. pays obeisance to this as if it were Holy Writ. The point is that no one in this still highly nascent technology really has a feel for what wind energy is all about the same way that some experts in other sectors of the energy field have a feel for, say, deep well energy exploration or offshore drilling.

One of the problems is that aerodynamics itself, by its very nature, is partly "owned" and, in a sense, "overseen" by the public and the public relinquishes old ideas about this field and accepts new ones with extreme reluctance and exaggerated misgivings. Some examples of the folklore that have come to be on this account have been explored in other parts of this material. Geese and Ducks. The Baseball Curved Pitch Effect. Lift and Drag. Vortices. Stall. Wind Shear. Blade Pitch Angles. Velocity Averaging. The Bernoulli Principle. All of these concepts, without exception, are in need of being updated in the minds of the great majority of us as they are applied to the new field of wind-derived energy. Customers are needed, customers who see what the eye can't.

Taking just the last item in the above list, the Bernoulli Principle, and merging this with the discussions that have been provided on airflow deflection, a story unfolds that bears additional study. This is the basis for the above-mentioned homework assignment. First, the picture must be drawn and filled in with all the colors and so some discussion is necessary, as follows, and then the problem will be presented.

Two Choices

Diversity of culture is important. In many places of the world some part of the population holds certain things in a sort of forever limbo of blank unregard. It takes diversity to make up for these somewhat universally-held lapses. For example, the word "sierra" in Spanish means "saw" or "sawtooth" and the word "nevada" means "snow-covered". Few English-speaking U.S. Americans seem to have taken the time to learn these Spanish meanings of these familiar terms, applied to mountain ranges out West that are frequently topped with a coating of white even during summer. As a result we have a celebration of the word "Sierra" as applied to the mountains but which has a faintly nonsensical sound, no reflection on those making use of this term, to those whose mother tongue is that spoken South of the Border, not to mention a temperate, arid state composed mostly of desert landscapes going by the name of "Nevada".

Certain aspects of aerodynamics seem to be skimmed over lightly in approximately the same way. Some time will be taken here in looking at a mystery that is rather deep and has a great deal of significance in extracting energy from air in motion. For when a fluid encounters an obstacle in its path it has the choice of either accelerating to squeeze past it or, if room is available, allowing itself to be deflected by it. The degree to which the fluid does one or the other or both is not an insignificant question.

Looking a bit closer at the previous coverage of the lift principle as applied to aircraft wings, an additional fact may be pointed out. As the wing presents a small angle of attack to the airflow and causes a small amount of deflection to it, something else can be noted as well. A twisting force is evident from the theoretical analysis and no doubt is found in practice. The wing is subjected to a torque oriented in such a way as to cause an increase in the wing's angle of attack, that is, tending to nose the aircraft up. This comes about from the forward acceleration of the flow being added to the deflection acceleration and resulting in pressure changes being applied to the wing that cause these forces.

But let's take a more detailed look at each of these two cases of airflow past an airfoil surface. We know that what actually happens is not entirely one or the other but a combination of the two. The problem can then be stated in terms of finding to what degree each is present. We start first by looking at each case individually.

The first case is where all acceleration of the flow is aligned with its motion and no net deflection occurs. This case can be called the "Bernoulli" case since it resembles most the case of the Bernoulli effect in pipe flow. The diagram below applies:

As can be seen, some curvature in the flow paths occur due to pressure effects, but the flowlines continue on uninterrupted in a straight line after their encounter with the airfoil. The flow above it first speeds up and then slows down and the flow beneath it first slows down and then speeds up during their passages by the object. No lifting force is present but the aforementioned twist torque acts on the airfoil tending to increase its angle of attack. This is a viable flow regime. All physical laws are observed and something like this can be reproduced in wind tunnels where deflection is constrained by the walls of the tunnel.

The other case is where all acceleration of the flow is at right angles to its motion, the case of pure deflection. No acceleration occurs in the direction of motion. This case can be called the "Deflection" case. The diagram below applies:

As can be seen here, the flow velocity is essentially unaffected as it bends around the solid object to continue on in a new direction. In this case, a significant amount of lift is present acting on the airfoil and no twist torque occurs. This, again, is a viable flow regime and can best be observed in cases where the flow field is infinitely wide such that no restrictions are made on the amount of deflection that can be introduced, something approximated by, for example, the entire atmosphere.

We know that, in all practical situations, neither of these two cases are present to the exclusion of the other but some combination occurs. It comes down to a question of how much the acceleration is divided up between in-line acceleration (the "Bernoulli" case) and transverse acceleration (the "Deflection" case). At this point in the sophistication of our treatment of the subject we do not have enough tools to answer this very interesting question.

Large Deflectors

As an example of a practical case in which airflow deflection may be useful and made available, consider this. Where wind flows are predominantly from one direction, some savings may be obtainable by providing a large deflector out ahead of and in place of every second or third wind generator facing the wind. These tall aerodynamically designed objects have the function of dividing and concentrating the wind and directing it to the wind generators on either side. Such deflectors would be presumably cheaper to build than the wind generators themselves and would allow the remaining wind generators to operate with greater efficiency, sufficient to make up for the missing units.

Another case involves providing a collection of 20' - 30' long deflectors oriented either vertically or horizontally alongside highways and roads to reduce the wind speeds where high winds are sometimes present such as in traversing mountain passes or on high bridges. Gusty winds are recognized as a dangerous condition for high profile vehicles such as campers or large, lightly loaded trucks. To provide something of this type would be of value to the highway departments and, again, efficiency counts. Deflectors such as those envisioned here may be only long and slender constructions whose duty is to divert large volumes of air with but little to show for it.

A Close Look At The Bernoulli Effect

A few words may be said here about one of the two above cases, the little-understood "Bernoulli" case. Daniel Bernoulli provided the world with his famous equation based on a derivation from conservation of energy and it continues to puzzle and intrigue everyone with its magic. Perhaps because of this, the principle has received some degree of exaggeration and overuse. While scientists and the nontechnical alike recite by rote the equation, few seem willing or able to describe in nontechnical language what happens to provide the paradox everyone sees in the effect, i.e. the apparent anomaly of why a flow restriction such as in a pipe results in a lower pressure on the pipe walls rather than what everyone expects to occur, a higher pressure.

If the reader has patiently followed the train of thought presented in previous chapters the explanation can be easily enough laid out as follows.

The important characteristic of the flow to be taken note of is the mass of the flowing fluid, even if the fluid has a density as light as that of air. When the fluid flowing in a pipe or duct "sees" a reduction of the flow area ahead such as a narrowing of the walls the fluid "bunches up" and sort-of (we said we were going to use nontechnical language and we meant it) "clogs" the pipe as its walls narrow, allowing the pressure downstream to fall in order to provide the pressure difference necessary to propel each slice of its mass through this restriction with a higher velocity. It's a dynamic thing, understandable only in terms of the fact that the fluid is in motion and requires pressure differences in order to change its momentum one way or the other. It should be noted, also, that when flow velocities exceed those of the speed of sound in the fluid, the flow can no longer "see" ahead the flow restriction coming and the bunching and acceleration occurs near the walls of the pipe before it can occur in the center of the flow, where the velocity may actually be reduced, with the result that the Bernoulli equation can no longer be applied uniformly to the entire cross-section. This case is mentioned and covered in more theoretical texts.

Heavy Aircraft

Few others seem to have taken the time and trouble to draw out at length the story of how fluid flows behave the way they do. In the case of aircraft and flight in general, we see now that 440 ton passenger jets flying across the sky deflect air downwards behind their wings and this air continues in motion gradually diffusing as it does so until it reaches the ground as a slight puff of vertical wind that impacts the earth and spreads out sideways in a lazy motion at some distance behind the craft flying ahead and high above. In this way the plane is actually supported by good old terra firma with the air acting as an intermediary to transfer its weight to the ground by its being set in motion as a large amount of mass. It's an attractive idea despite the demystification of the concept of lift it represents in the public's mind. See the below pictorial representation.

Hills, Mountains, and Ridges

The windflow over linear obstacles in its path continues to be treated with great reliance on empirical measurement. Wind generators are often placed on ridge tops to take advantage of the Bernoulli Effect but it also is true that ridges can be too high as well, making this an ineffectual approach. Sometimes the wind is thought of as gaining momentum by sliding downhill after reaching the crest. It's all very confusing and an area ripe for better theoretical investigation.

A rough idea of what seems to occur is that the wind velocity "toggles" over these long upward folds in the otherwise flat surface of the earth, that is, deflects over them with no acceleration at slow wind velocities and, then, accelerates across them with high velocity when its velocity reaches a certain point. This alters the velocity distribution to something other than the usually-assumed Rayleigh distribution and may have implications for wind generator design for machines so emplaced.

As for air's sliding downhill, it may be true that air temperatures can have some impact on wind velocities especially in the cases where colder, dense air near the ground naturally sinks on the downhill side of a ridge. But lest anyone be tempted to draw any universal conclusions, it should be said that atmospheric air generally has a neutral bouyancy, of course, and if the air is of uniform temperature, no such effect is seen as likely.

The Homework Assignment Described

As is now familiar from the above discussion, two possible flow regimes arise when the flow encounters an airfoil pitched to a direction other than that of the flow, that were referred to as the "Bernoulli" (in-line acceleration) and the "deflection" (transverse acceleration). These accelerations are, naturally enough, at right angles (normal) to each other. It seems in most cases that flows observe neither one exclusively but some degree of each is present.

The question, then, and the homework assignment, for the industry as well as the writer of this material himself, that is the subject of this chapter is the following:

          What is the angle of the resulting actual acceleration that is the combination
          of these two accelerations that are normal to each other for any given case
          and how can this angle be determined theoretically?