Flow of Air around an object:
In an ideal situation friction would not exist and the air would flow smoothly around the object. Take Figure 1 [aerospaceweb] for example:
At the front of the ping pong ball where the angle of attack is equal to zero degrees, there is high pressure which shows that it is experiencing a drag force. Also at the rear of the ball where the angle of attack is equal to 180 degrees, shows a high pressure which in fact is equal to the pressure to the front and theoretically this should cancel out drag from both sides. This theory was known as d’Alembert’s Paradox, established by a famous mathematician/physicist called Jean le Rond d’Alembert (1717-1783) [aerospaceweb]. In this ideal situation it indicates that there is no drag which in reality is incorrect. At the time, this confused aero dynamists as it contradicted theory with actual experimental values and as a result d’Alembert’s Paradox was deemed false since he did not take into account the frictional forces. In reality friction causes a phenomenon called flow separation which completely alters how the flow field acts around an object.
In figure 2 [aerospaceweb] the image shows the actual nature of the flow field and therefore, we can see that the flow field is not symmetrical and cannot theoretically cancel out. The objective of this report is to analyze this flow separation and other factors which will contribute to the magnitude of drag by carrying out various experiments.
Experiment 1: Effect of Air Speed on Drag
Experimental Procedure:
We conducted this experiment using a Vertical Nozzle Test machine as shown on fig.1. The Model is suspended as shown, and the force indicated is calibrated so it reads zero when there was no air flow. A jet of air escapes upward towards the model at variable speeds, which are controlled by changing the current on the settling chamber. This in turn pulls the lever down on the force indicator and a result can be noted down in grams. The power input to the jet was then raised constantly ranging from 0 to 16 Amps, the variation of drag was obtained and the results recorded in a data table.
The damper is there in order to cushion the force from the jet of air hitting the model, to reduce vibrations and so being able to get more accurate readings. This is repeated using different currents, and so different velocities. The velocity is calculated using the formula:
Results Table:
Graph:
Discussion:
It is evident from the results that, with increase of speed, there is an increase in drag. When there is no speed (0 m/s) , there is no drag (0 N). At 8.752 m/s, the drag is 0.19N. At 27.402 m/s, the drag is 10.5N. At 36.702 m/s, the drag is 11.5N and at 47.176m/s the drag increased to 14.2N. Hence, a gradual increase in drag was observed.
However, at the range of speed 33.877m/s to 39.241m/s (9.5 Amps to 12.0 Amps) , there was fluctuation in the results. The drag decreased from 11.9N to 10.7 N as the speed increased from 32.358m/s to 33.877m/s, and then increased from 10.7N to 11.0N, 11.5N and 11.9N as the speed increased from 33.877m/s to 35.325m/s, 36.702m/s and to 39.241 m/s respectively. After that, there was steady increase in drag with increase in speed till 47.176m/s at the end of our experiment.
From the graph, we can see, as the speed increases from 0m/s to 32.358m/s the drag increases steadily from 0 to 11.9N. This region is the laminar boundary layer. The gradient is the steepest in this region.
As the speed increases from 32.358m/s to 33.877m/s, the drag randomly decreased from 11.9N to 10.7N and then again randomly increased from 10.7N to 11.0N as the speed increased from 33.877m/s to 35.325m/s. The drag then rose to 11.9 N again as the speed kept increasing to 39.241m/s and so on. The fluctuation in the result can only be explained by the transition layer period.
After 39.241m/s, the drag gradually kept on increasing. However, from the graph, it is noticeable that the gradient is not as steep as that of the laminar boundary layer region. This region must be the turbulent region.
Boundary Layer (For Aircraft):
A very thin layer of air flowing over a surface of an aircraft, mainly the wings or airfoil, is known as boundary layer. It could either be layered or disordered depending on the Reynolds number involved. Laminar boundary layer is layered and turbulent boundary layer is disordered. Another layer forms when the flow is changing from Laminar to Turbulent which is known as the Transition layer. Laminar layer develops at the upstream edge of the solid surface. There are large velocity gradients in this region. In the Turbulent layer, the molecules are in random motion which is accompanied by high energy losses. Beneath the turbulent layer, a sub layer of laminar layer is also formed. ‘In reality, the flow always starts out as laminar. And at some point downstream the laminar boundary layer becomes unstable, and small bursts of turbulent flow begin to grow in the flow.’ (John D Anderson, Jr; Introduction to Flight) The so called burst of turbulent flow and the instability can be detected for sometime, over a certain region and that is the Transition layer. After this, the flow becomes completely turbulent.
Experiment 2: Effect of Surface Roughness on Drag
Experimental Procedure:
To conduct this experiment we used a Horizontal Nozzle Test Machine as show in fig.2. The model is held by a support on a sliding plate. The force reader is calibrated so it’s at zero when there is no air flow. Once the wind tunnel is turned on at a set speed, there will be a force induced on the model, which in turn will move the sliding plate, which will also pull the spring. From here a force meter can be used to show how much drag is induced on the model which is noted. This is done at two different velocities, with four different spheres: two small diameter spheres, one rough and one smooth, and two larger diameter spheres, one rough and one smooth.
Results Table:
Graph:
Based on the results can assume that, for a higher velocity rough ball has lower drag than the smooth ball.
Discussion:
When the smooth ball is subjected to a high speed, the laminar flow tends to leave the surface of the ball earlier creating a larger wake behind the ball. This causes the pressure behind the ball to be significantly lower than the pressure in front of the ball. Because of this the total difference between the pressures increases resulting into increase in total drag.
In other hand, the rough surface of the ball encourages the laminar flow to the turbulence flow very early. Because of that the separation point will be somewhere in the further end of the ball which creates a lower wake behind the ball. In this case the overall pressure becomes very lower compare to the smooth ball. It is generates a lower drag than the smooth ball.
Experiment 3: Effect of Streamlining on Drag
Experimental Procedure:
Apparatus similar to fig.1 was set up, but instead of varying the velocity of the jet of air, we varied the type of model. We used three models, one was streamlines, and two were rods but with different diameters. The force indicator was again calibrated so it read zero when there was no air flow. We then turned on the apparatus so there was a jet of air, and noted the drag. We did this at two different velocities for each model.
Results Table:
Graph:
Discussion:
From the above graph, it can be observed that the wing section has the smallest gradient compared to the other two materials (large and small diameter rod) which means that the wing section has the lowest value of drag compared to the two rod. The drag in this experiment is dependent on the separation point. The relation between drag and separation is that smaller the separation greater the drag and vice versa. When the airflow passes over the three objects used in the experiment, the wing section has the lowest value of separation which results into low value of drag whereas the two rod with larger and smaller diameter has high value of separation which results into high value of drag. Also as large diameter rods tend to generate more drag compared to the streamlined airfoil design, planes have been modified into using the streamlined design rather than those old designs which were invented by the Wright brothers in order to reduce the amount of drag on the plane.
Conclusion
By performing these experiments and looking at the results you can see what factors affect drag. Experiment 1 showed that in general, the higher the velocity of the air flow, the higher the drag. However the rag fluctuates at certain velocities as this is the air flow goes through a transitional layer. Experiment 2 showed that at higher velocities, a model with a rough surface has less drag than a model with a smooth surface of equal size. Furthermore experiment 3 showed that a model which is streamlined has the least drag.
Therefore, from these experiments, the results can be used in order to find the best way to reduce the drag of an aeroplane and how it can be controlled. The results showed that an aeroplane which is streamlined and has a rough surface will greatly reduce drag.
In these experiments, there were many faults which made readings inaccurate and in turn made out results table unreliable. When readings were being taken in each experiment, there were normally fluctuations in the measuring apparatus, which led to inaccurate results. To solve this fault, maybe it would have been appropriate to take the highest and lowest values to which the apparatus showed, and then taking the median.
Also, only measuring one value in the experiments is not very accurate, as errors such as human errors or zero errors cannot be identified. So there should have been more than one set of results measured, possibly three, and then an average can be taken. This makes it much easier to identify any anomalies which may have occurred and also make the results more reliable.
Some of the experiments could have been set up differently, which would have made the results more accurate. For example, in experiment 2 an open wind tunnel was used, which meant the readings for each model’s drag could have been effected by simple things such as breathing, or knocking the sliding plate to which the model was placed on. In a closed wind tunnel, these parameters could either be controlled, or made non-existent, which would lead to much more accurate results.
Furthermore, in experiment 2 and experiment 3, the drag was measured for two different velocities. These velocities were not accurately set on the wind tunnel, so although the two experiments could have had the two velocities at 10m/s or 25m/s, which would mean comparing results for the two different experiments more accurate, they were not set, which could mean the two experiments had 2 different velocities making it harder to compare.
References
[aerospaceweb]:
[NASA]:
