Sonya Mollinger 5/5/11ES123 Lab 3

In this lab, we examined flow through a turbine and the voltage created. We simulated a typical propeller wing and the resulting flow around it, and did analytical calculations to understand the parameters for our propeller. Finally, we designed a propeller in SolidWorks and tested it for the voltage created by flow.

Experimental

First, we designed a propeller in SolidWorks in order to test it in the laboratory.

Above is a picture of our design. The wings are slightly flexed; the hole in the middle is designed to fit on the mount. The bar at the lower left is 1 inch long, indicating the small size of our propeller.

We designed the propeller this way in order to gain the maximum lift. Therefore, we attempted to flex the wings and give each wing a different angle with respect to the flow. We thought these levels of flex would work to create more lift and more voltage. We used the constraints on the dimensions of the flow tube in order to determine the size of our propeller. Thus, we believed that for our constraints the propeller would work well.

Our experience constructing the propeller was not completely smooth. We were unsure how to create the angle of the wings in SolidWorks, so most of our time was spent attempting to change and move our wings. Eventually, we managed to flex them, but as it turned out they were not flexed very much in the construction. This must be due to our errors in determining the angles that the wings are flexed.

The weight of our propeller was only 1 gram; this would create the difficulties in testing it in the rest of the experiment.

Since the propeller was so light and not flexed, we were unable to test it in the flow tube. Its size at about 1 gram meant that the propeller would simply fly off the motor in the flow and would need to be extracted. This situation was due to our errors in constructing the propeller, as we were unsure how to stay above the mass constraint and still make a small propeller in diameter. Thus, everything did not go smoothly. In effect, the voltage generated was zero, since we were unable to use the propeller. Therefore, we can conclude that a propeller needs to be of significant size compared to the flow, so that it will be able to create a voltage. We also discovered that the flexing of wings needs to be of a very significant degree in Solidworks, in order to create any visible flex when the propeller is printed.

Similar propellers were tested, however, due to their larger size, and these propellers usually attained a peak voltage (anywhere from .002 - .4 V). This seemed to depend largely on the different ways that the propeller obstructed turning easily (various sources of friction). Propellers with less mass to turn usually created more voltage, as long as the wings were of a reasonable size. Furthermore, the peak voltage was usually very different from the average voltage; it was usually reached just after the flow started rushing, and then not again. This must be due to the high speed of the water just as it fully comes out into the tube, and it must then slow down after this point.

Computational

We set up a simulation that would model the flow in two dimensions. This takes a cross-section of the wing and examines how the flow moves across it. A picture of the geometry is below. The geometry roughly corresponds to the dimensions used; the height of the rectangle is 6 cm instead of 5, but is approximately the height of the tube. The wing is close to the size of our wing but is a bit smaller; it is 2 cm long, which is actually less than an inch. The wing is very thin (it is 2.5 mm thick at its thickest), which is similar to our (and many other experiments) thin wings in the actual design.

The inflow velocity is determined by the experimental flow rate, in order to match simulation with experiment as much as possible. The flow rate was 76 liter/min = 76000 cm^3/min. The width of the tube was 25 cm^2, so the inflow velocity was therefore (76000)/25 cm/min = 3040 cm/min = 50 cm/s. This value was used in the simulation.

The angle of the propeller is important to the eventual power created by the turbine, so this parameter was examined extensively during the simulation. We simulated different angles of the wing with respect to the flow: these angles were 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30 degrees. This allowed us to create a moving simulation of the flow as a function of angle. We will examine in detail five angles: 0, 6, 15, 21, and 30. These will give us an idea of how the flow moves at small angles to the flow, and also when the wing is tilted all the way to 30°. This range is the reasonable range that wings might be tilted at in experiments, since the design and construction of an actual wing will also impose constraints (in addition to the desire to attain maximum power).

Blade at 0°:

Above is a picture of the simulation result for flow with the blade at 0°. The fluid velocity is almost entirely uniform around the blade.

The coefficient of lift for 0° can be calculated to be very small, at roughly 0 (it actually comes in at .5*10^-5).

Blade at 6°:

The coefficient of lift for 6° is calculated to be 2.2*10^-5.

Blade at 9°:

The coefficient of lift for 9° is calculated to be 3.15*10^-5.

Blade at 15°:

The coefficient of lift for 15° is calculated to be 2.2*10^-5.

Blade at 21°:

The coefficient of lift for 21° is calculated to be 2.0*10^-5.

Blade at 30°:

The coefficient of lift for 30° is calculated to be 2.3*10^-5.

We can see that the area of fluid with lower velocity increases as the angle goes up. We can also see that the lift coefficient is changing, and not monotonically increasing or decreasing with blade angle.

We can plot the lift forces of all the angles in comsol:

And from this we can see that the lift force peaks at around 9-12 degrees. However, as the force seems to be increasing again after 30 degrees, larger angles might also be better.

We can use this to get an idea of what angle might be ideal to place the blade at, to create the most power. However, the amount of drag created should be taken into account. The drag will increase steadily with angle, so that any increases in lift force after 30 degrees will probably be cancelled by the great increase in drag. Thus, we think that the peak around 9-12 degrees may work.

The lift force also depends on the wing area and length, but these shouldn’t affect the angle of the blade. What might affect it are the relations between the blade angle and other constraints of the propeller – for example, if the area of the blade must be compromised to get a good angle, this would be important in deciding the final design.

Drag Coefficients, from COMSOL:

Next, we can change the shape of the wing slightly in order to try to increase and decrease the lift coefficient. The new geometry is a slightly shorter wing. This has a greatly decreased lift coefficient, at 2.5*10^-5.

On the other hand, making the wing longer gives us a geometry and velocity profile pictured below. This geometry has a larger lift coefficient, at 3.75*10^-5 for 9 degrees.

Analytical

The cross section of the tube was 25 cm^2; the flow rate was 20 gal/min = 76000 cm^3/min. This created an inflow velocity of (76000)/25 cm/min = 3040 cm/min = 50 cm/s = .5 m/s.

The resulting velocity head available for the turbine is ( .5 )2

2∗9.8=1.27∗10−4m=12 .7mm.

The maximum available power is the mass flow through the propeller times the total kinetic energy of the water. Mass flow through the propeller: (76000 cm^3/min)*(density of water) = .076 m^3/min * 1 min/60 sec * 1000 kg/m^3 = 1.267 kg/s. Total kinetic energy of the water per mass: this is the available head * acceleration due to gravity.

v2

2gg=.0127∗9.8=.0012m

2

s2

Power (W = 1 kg*m^2/s^3) = (density of water) (flow rate) (gravity)(head) = (mass flow through propeller)(kinetic energy/ mass) = .15 W.

This is the maximal available power for the propeller.

The maximum efficiency of a turbine happens when v 2v 1

=13 . This gives a maximum power efficiency of 59.3%.

The power is known to be P=.5 ρA v (v12−v22 )=.25 ρA (v1+v2)(v12−v2

2). This gives us the power in terms of the initial flow velocity and the velocity downstream.

The voltage generated by the turbine is proportional to the power it produced. A maximally efficient turbine with radius of propeller at 5 cm creates .2 V. Use a typical weak propeller from the class results (creating around .02 V usually):

v1=.00127ms

Radius was around 2.4 cm (just under half the size of the tube, for the best propeller).

Pmaxeff ∝0.2VPmaxeff ∝r2=25cm2

So we can say that 0.2V∝ (π∗25c m2 ) (Pmaxconst ) . And, Pmaxconst= .225π

=.0025 Vcm2

Now for our turbines, we have V = 0.02 V. We also have an area of 18.08 cm^2, so

Pourconst= .0218.08

=.0011

So, the ratio of the two powers (the efficiency), was therefore around 44% as compared to the maximal efficiency.

The power is ***** how to calculate velocity without power???? Need current.

The Reynolds number of the propeller in this experiment is (density of water)(velocity)(propeller diameter)/(dynamic viscosity of water) = (1000)(.00127)(.05)/.001 = 63.5 To design a turbine that has blades 1 m long, and therefore a diameter of 2 m, the diameter is thus scaling by a factor of 40, so the velocity would need to decrease by 40 and become .0000317 m/s = .00317 cm/s.

Conclusion

Overall, the simulation and analytical work enhanced our understanding of the voltage created by the propeller.

The simulations were very simplified in comparison to the actual experiment done. First of all, the wing cross section did not resemble the one that we created, and was not very similar to many of the wings of other experiments’ propeller. Its ellipse shape was not mimicked in designs, for most designs involved an even width across the wing, simply changing angle and shape; this wing became very thin at the points and thicker at the outside.

In addition, the simulation also left out all the effects of the rest of the propeller, namely the center and other wings. This would greatly affect the flow and direction of the water. The sides of the tube will also add a lot of friction to the flow. The flow is not at a steady velocity, but accelerating and decelerating. The simulation also only examined two-dimensional flow, whereas the wing in reality existed in three dimensions. The simulations could be improved by adding more geometries and more physical effects.

The simulations also will not address a number of important factors that do affect our turbine. For example, the size and weight of our propeller were the main reasons that our design was unsuccessful. Also, the simulations did not correctly resemble the angle of our wings.

Our propeller design had a simple structure and did not add excess mass that would inhibit it turning; this was a good design strategy. However, there were two main things wrong with our propeller. First of all, it was too light and small for the specified design – the large flow rate was too strong for it to hold up. But second of all, our design also did not have enough of an angle for the wings. This would not have created anywhere near enough lift for power to be created.

To modify our propeller, we would first increase the dimensions and the thickness of the blades. We would then attempt to slant the blades at a larger degree. This would involve a big design change, since it is not possible to flex in Solidworks very far; we would probably have to completely change the way we designed the blades and how they attached to the propeller.

One great design that seemed to work was one in which the blades slanted from one circular ring to another circular ring. This was a great way of holding the blades slanted at a significant angle. It was also a good way of making the design more sturdy.