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Generation of Electricity from the Wind Draft of Cars Harish Pudukodu ABSTRACT We developed a theoretical turbine power output model dependent on automobile speed and turbine distance from cars. Analysis of the data from experimental ield tests with rush hour traic, controlled single-car testing, and CFD modeling showed that our turbines generated electricity, but did not support our theoretical model, which assumed laminar low and spherical cars. Our study represents a creative implementation of wind power that may have signiicant economic/environmental implications for the future of renewable energy.
Introduction
method a few assumptions must be made. he assumptions are that the low is irrotational, the low is axisymmetric, the low is laminar, and the object that is causing the low is a sphere moving in the luid ield. According to these assumptions, the formula for velocity potential (as expressed through polar coordinates) is the following:
Motivation In the current era, energy is primarily obtained from coal and oil [1]. Yet, as these sources run thin, the world must look toward more sustainable sources of energy, such as renewable energy. One major form of renewable energy, and the form that is the topic of this research project, is wind energy. Currently, wind energy is not used widely or much [1], but it is a very viable source of energy in the future, especially if it is used in innovative and eicient ways. Wind power has proven to be a growing industry, especially in the past seven years [2].
In this equation, represents velocity potential, U is the velocity of the moving sphere, a is the radius of the sphere, and (r, q) deines a polar coordinate determined by the location being studied. he following diagram depicts the scenario for this model:
he Physics of Wind Turbines Kinetic energy from moving air can be converted to usable electrical energy [3]. he method by which this can happen involves the rotation of blades on a turbine and the use of a generator. he rotation of the blades created by the lift forces of the wind moving causes the spinning of the rotor. he resulting circular motion induces changes in the magnetic lux within the generator, thus generating electrical current. Measurable factors dictate the power of a wind turbine [4], as expressed in the following function [5]:
Equation 1. In the above formula, P denotes power, r represents air density, C is the coeicient of performance (eiciency), A is rotor swept area, and n signiies wind speed. It is important to note that the wind speed component of the power formula is the wind speed that goes through the wind turbine. In the scenario proposed for this research project, that speed is not actually the same as that of the moving vehicle that is causing the blades of the wind turbine to spin. he speed of the wind through the wind turbine caused by a moving object can be calculated using the velocity potential ( ) of the luid ield surrounding the moving object [6]. In order to employ a relatively easy version of this
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Figure 1. he above diagram illustrates that the model suits a scenario in which both the turbine AND the sphere’s center fall on the same plane and the sphere moves at some velocity U. Volume 2 | 2012-2013 | 41
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In order to determine the luid/wind velocity at the given polar coordinate, the gradient of the velocity potential function must be taken. he resulting formula for wind velocity at the given polar coordinate after doing this gradient is:
Equation 2.
ď ś
Procedures To test the hypotheses presented, experimental roadside testing, a controlled single-car experiment, two calibration tests, and CFD tests were conducted. he primary materials required for the three non-CFD experimentation processes were four AL Turbine Complete Wind Turbine Kits (Model Number: A0012), 100-ohm resistors, LabPros/LabQuests, alligator clip wires, and differential voltage probes. he apparatuses were arranged on plywood bases and were staked into the ground. he following is a diagram of a single wind turbine apparatus:
In this equation, v represents the luid velocity vector at the given polar coordinate. his formula can be used to determine the wind velocity at any given coordinate relative to the moving automobile given the accompanying assumptions. For a spherical body with radius a moving to the left in a luid ield at a certain speed, U the luid velocity at a point with a coordinate (r, p/2) is the following:
Equation 3. he following is the result when typical values for the scenario being tested are substituted into this equation:
Â
he following is the result when the above value is substituted into Equation 1, in which typical values are also substituted:
he above value of .45W is a theoretically predicted value for an individual turbine’s power output in this research scenario. Combining (Equation 3) and (Equation 1) results in the complete theoretical power model, which is as follows:
Equation 4. Based on our research, it is hypothesized that if a miniature windmill is placed along the side of a road, then it will generate electricity from the wind draft of passing automobiles AND do so in accordance with the theoretical power output model derived above. 42 | 2012-2013 | Volume 2
Figure 2. his diagram demonstrates an individual apparatus from an aerial view. his apparatus allows for real time measurement of voltage data using Logger Pro measuring devices. One calibration test was conducted before and after the process of ield experimentation, to assure consistency among the wind turbine apparatuses. For the initial calibration test, each turbine apparatus was placed at a known distance in front of a box fan at two diferent speeds and voltage data was collected and analyzed to conirm consistency among the turbines. For the inal calibration test, the same procedure was followed except only one speed was used. Both times, the voltage output of all the turbines was found to be within 5-7% of the mean, thus showing that the turbines were well calibrated with respect to each other. For the experimental roadside testing, a location was found at which the average speed of cars was between 40 and 50 miles per hour and there was suicient space to place the turbines at the side of the road. At this location, the three experimental turbine apparatuses (deemed E1, E2, E3) were staked into a grassy path at the side of the road, with E1 closest to the road, the center of E2 thirty centimeters from the center of E1 (in the direction perpendicular to the road), and the center of E3 thirty centimeters from the center of E2. he control wind turbine (deemed C) was
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REsEaRch placed in a location that, in theory, would not be afected by traic wind. he experimental turbines were placed 2.8 meters away from each other in the direction of traic. Each rotor was angled thirty degrees toward the road from the parallel. An anemometer was staked into the ground thirty centimeters in front of E1, at the same elevation and distance from the road as E1. his experimental setup was implemented for an hour, during which voltage data and anemometer data were automatically taken. Traic data, which entailed the recording of traic pulse starting times and each pulse’s accompanying number of cars in the lane closest to the turbines, was also taken by hand/eye. hree such trials were conducted. he following are diagrams depicting the location and a single turbine: Â
model to perform tests on, so this was used to run various computational experiments. he following is an image of this object model:
Figure 5. In this diagram, one can see the image of a car in the luid ield, where the car is oriented in the picture such that its front is facing left.
he above object model involves a stationary car in a luid ield. In order to accurately model the research scenario, the luid was made to move at given speeds toward the car and boundary conditions were not set on either side of the car. his characterization of the research scenario accurately relects the experimental behavior because it merely involves a change of reference frame from the road to the moving car. here were three primary tests that were conducted on the car object model: a roadside wind speed model determination, an optimal velocity disturbance (roadside wind Figures 3 and 4. hese diagrams depict an overhead sche- speed) determination, and a comparison of experimental matic of the testing location and specs on an individual setup to optimized setup. wind turbine, respectively.
Data
he purpose of the controlled single-car testing was to generate a roadside turbine power output model based only on car speed and turbine distance. Five diferent car speeds were chosen for testing. he three experimental turbines were then tested at ive diferent distances for every speed (each speed was tested twice) and voltage data was taken for every run. A control turbine was also placed in an area so as to only be afected by ambient wind. he following table shows the set of distance and speed values that were tested:
Tables 1 and 2. he above tables display the ive distances (from the lane) and the ive speeds (of the car) that were tested in controlled single-car testing. Note that the intervals between test values are constant. Computational Fluid Dynamics software can be used to model real world scenarios involving luid dynamics. his is done by solving the Navier-Stokes equation for 3D object models with speciic parameters. AutoDesk CFD has a preloaded average-size car-in-a-luid-ield object
he irst of the following four graphs represents the power data obtained from each experimental turbine for each trial in the rush-hour roadside tests. he control data was omitted for reasons that will be discussed later in this paper. he second graph displays anemometer data and traic data for all three trials. he third following graph(Graph 3) shows the results of the controlled single-car testing.
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Graph 1. his is a graph that plots power of each experimental wind turbine vs. time. Note that the power spikes for each turbine occur at approximately the same times.
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REsEaRch view of the E1 voltage data from the irst trial as compared to the traic data: (on the following page)
Graph 2. his is a graph that plots wind speed vs. time
AND marks times that traic pulses occurred. Note that wind speed spikes tend to correspond with traic pulses.
Graph 4. he above graph displays a short interval that displays voltage and traic data. It is clear that there is a strong association between traic pulses and voltage spikes his graph also supports the correlation between traic and electricity generation within a range of timing uncertainty. his method was applied across all three trials and the same results were found, thus supporting the initial hypothesis of correlation.
Graph 3. his graph plots the power outputs of all of the turbines used in the controlled single-car testing vs. time. All of the data taken throughout the range of test values are displayed on this single graph.
Characteristic Analysis he characteristic analysis involved the statistical description of characteristic power spikes (CPS). CPS power values were determined by correlating the traic pulse timings to power spikes that were created by traic (same time as the traic pulses) and invoking the mean value theorem to determine average values for power for each CPS. hese power spikes were analyzed to directly study the efects of car-induced wind efects through the wind turbines. his method resulted in sets of data across the wind turbines and trials that represented power output during traic pulses. hese values were plotted in a bar-graph fashion as such:
Data Analysis he presented roadside testing data were analyzed in four diferent ways to get a multidimensional view of the results: correlation analysis, characteristic analysis, power model analysis, and error analysis. Each of these analysis methods will be discussed in detail in this section of the paper. Correlation Analysis he method of deining the correlation between road traic and increased turbine rotation followed from graphical comparisons between the traic pulse data taken during experimentation and the other forms of data (voltage and anemometer). he hand-written traic data was transposed to a graph and overlaid on the voltage and anemometer graphs to compare traic pulse timings to wind speed and voltage spikes, which would indicate a connection between the passing of automobiles and the increased generation of electricity. Graph 2 provides an example of this graphical comparison across all of the trials and it can be seen that the spikes in anemometer data can be directly attributed to traic pulses. he following is a narrowed 44 | 2012-2013 | Volume 2
Graph 5. he above graph displays one of many CPS data graphs. Each bar represents the average power value of its corresponding spike on the equivalent power data graph (Graph 1). All of the impertinent non-traic-pulse power information was removed before the creation of this CPS data graph.
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REsEaRch hese graphs were generated for all experimental wind turbines for all three trials, independently. he statistics operation available in LoggerPro was then used to determine some characteristics of these sets of data. he data displayed in the CPS power graphs were then used to produce frequency distributions. hese distributions were compared to the corresponding Gaussian distributions using the characteristic data. he following is a graph that displays a frequency distribution:
the distance relation of the power model. he data was then plotted in a log-log fashion, with one plot per trial, to easily deduce the power relation between power and distance and the constants associated with the power model. he following is an example of such a log-log plot:
Graph 7. he above plot displays the logarithm of Graph 6. he above graph displays a frequency distribution of one CPS data set. his graph and its associated Gaussian it show that the nature of traic patterns is highly unpredictable. hese analyses were conducted for all experimental data sets. Due to the unpredictable nature of the traic low, power outputs were expected to be highly varying. his theory is supported by the relatively large standard deviation values. Yet, it was found that on average the frequency distributions showed somewhat moderately good its with the Gaussian prediction, thus indicating that traic low was quasi-random. he following table depicts statistical results (that support the above observations) from the characteristic analysis of the data sets in Table 3. Power Model Analysis In order to compare the CPS data across the traic pulses, the E1 CPS power data was normalized to 1 and the other turbines’ data were scaled to follow the scaling of the E1 data. his produced a set of normalized power values that could then be plotted versus distance to analyze
normalized power values vs. the logarithm of distance values. he presence of a power-relation is quite apparent from the results of this plot.
In the above graph, log(N) represents the logarithm of the normalized power values discussed previously and log(r) represents the logarithm of the distance values. Using this plot and its accompanying linear regression, the power vs. distance relationship could be determined along with important constants expressed in the power and roadside wind speed models. hese values were found for all three trials and the averaged power law result is a power relationship of -1.3 +/- .3, with a predicted optimal power-it of –1.5. he predicted optimal power-it in conjunction with the log-log plot y-intercept information was then used to construct the accompanying models. he following are the two proposed optimal models in terms of theorized parameters:
Equation 5.
Equation 6.
Table 3. he above table displays all of important the statistical characteristics of the experimental roadside testing data. It is clear that the highly luctuating nature of traic low contributes to large standard deviation values.
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Street Broad Scientific he roadside wind speed model was used to scale down the anemometer data for E1 to the other two experimental turbines and thus overlay the theoretical power model values over the experimental values. An example of such an overlay over a small interval is the following:
Graph 8. he above overlay displays the raw data in blue and the power-model-predicted data in red. here is a visible time lapse due to timing diferences in anemometer data collection and E2 turbine data collection, but the moderately accurate predictive power of (Equation 5) and (Equation 6) is clearly apparent in the above graph, especially from the 28th minute to the 30th minute (when the time lapse is ignored).
REsEaRch It is apparent that the data taken from the control turbine were omitted from this study. his is because whenever large packets of traic would pass by the testing location, it was possible that the wind pulses could even afect the control. hus, as a result of unforeseen circumstances the control data needed to be omitted from the study. Yet, the correlation analysis still provides suicient evidence to show the inluence of automobiles on the wind turbines. he controlled single-car testing data was analyzed in two separate ways to generate a complete turbine power output model for the single-car scenario. he data were analyzed for a power-distance relation and a power-speed relation, as will be discussed in the following subsections. Controlled Single-Car Testing Analysis: Power-Distance Relation Analysis he way by which power relationships were determined for the controlled single-car testing data was virtually identical to the way by which they were determined in the power model analysis portion of the experimental roadside testing data analysis. he only diference was that each turbine was analyzed separately at a given speed and their results were compared to determine result validity. he following is a sample log-log plot for power-distance relation:
Error Analysis Error analysis entailed two major components, which were voltage uncertainty and power uncertainty. Yet, in order to obtain these uncertainties many other quantities had to be known. he formula for uncertainty in power was determined through the partial derivative method for absolute uncertainties. After utilizing this tool, the uncertainty in power was found to be:
he following is a table depicting pertinent uncertainties:
Graph 9. he above graph plots the logarithm of controlled single-car testing power values vs. three of the test distances. he strong linear relationship between the plotted variables is quite apparent in the above graph. he regression in the above graph had a slope of approximately –3, thus proposing a power-distance power relation of –3. his relationship was conirmed by the data from other speeds and turbines as well. hus, this section of the controlled single-car testing analysis produced the following result:
Table 4. he above table depicts the important uncertainties present in this study. It is clear that the uncertainties are fairly minimal, thus promoting conidence in the raw data values. 46 | 2012-2013 | Volume 2
Equation 7.
REsEaRch Controlled Single-Car Testing Analysis: Power-Speed Relation Analysis he power-speed relation analysis was conducted in the same manner as the power-distance relation analysis, except this time car speed was varied and the distance was held constant. Just as with the power-distance relation analysis, the turbines were analyzed separately at a given distance and then the results were compared. he following is a sample log-log plot for power-speed relation:
Street Broad Scientific ing for this computational experiment was incredibly similar to the controlled single-car testing procedures. An array of probe points was generated in the CFD model across the Z and X dimensions. he irst portion of the testing involved tests based on distance from the car, so at a given speed of 15 meters per second, the simulation was initiated and the steady state speeds at every point were determined. hese values were then averaged across the axis in the direction of the car. he second portion of the testing involved tests based on car speed, so one constant distance of 2.55 meters from the car was chosen and the simulation was run at a variety of speeds. he results for both tests were then plotted as such:
 Graph 10. he above graph plots the logarithm of con-
trolled single-car testing power values vs. three of the test car speeds. he strong linear relationship between the plotted variables is quite apparent in the above graph. he regression in the above graph had a slope of approximately 5, thus proposing a power-speed power relation of 5. his relationship was conirmed by the data from other speeds and turbines as well. hus, this section of the controlled single-car testing analysis produced the following result:
Graph 11. his graph shows a plot of the logarithm of wind speeds vs. the logarithm of the distance from the car. As can be seen, some of the distance values are within the boundary layer of the car (for the speed values increase in this region), but these were omitted for linear analysis.
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Equation 8. he two resulting power relations were combined to synthesize an experimental single-car turbine power output model. he model is as follows:
Equation 9. It can be noted that this model varies drastically from the experimental roadside testing power output model. his discrepancy along with the associated explanations and conjectures will be addressed in the Discussion section. CFD Analyses: Roadside Wind Speed Model Determination he purpose of this portion of the CFD analysis was to determine a model as a function of car speed and distance from the car for the wind speed generated from the roadside wind induced by the moving car. he method of test-
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Graph 12. his graph shows a plot of the logarithm of speed of interest (SOI, which is another term for roadside wind speed) vs. the logarithm of the car speed. As can be seen, the there is a strong positive linear association between the logarithms of the two plotted variables. Volume 2 | 2012-2013 | 47
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he following velocity dissipation model was generated as a result of the linear regressions done on the above scatterplots:
Equation 10. where some constant, car speed, and the distance from the car. he above model is incredibly similar to the roadside wind speed model generated from the experimental roadside testing:
where the real exponents have uncertainties of approximately .1. he intense similarities between the power relations in these two models indicate that wind speed could be approximated by traic low. To check the validity of the roadside wind speed model, the r-relations for the model were tested across a range of Y values, from .5 meter to 3 meters, for a range of X-values and a given Z value of 12 meters. To do this, an array of points on an XY plane were generated and the roadside wind speeds were probed and plotted for each point tested. After doing this, the same procedures for model determination as before were followed for each set of data grouped into the diferent Y-value sectors. For each of these blocked data sets, the r-relations were determined and the values for found to vary around a center (which was approximately 1 for the Z value of 12, which does not relect the results when using a range of Z-values as was done for the true model determination) by plus or minus .1. his shows that there is an inherent uncertainty of plus or minus .1 within the r-relation for the determined roadside wind speed model, which then furthers the argument of similarity between the experimental and CFD models due to intense overlap. CFD Analyses: Optimal Velocity Disturbance Determination he purpose of this portion of the CFD analysis was to determine the points of maximum wind speed, which would then indicate the optimal dimensions for a roadside wind turbine. In order to do this, wind speeds were measured at numerous points in every dimension after the simulation was run and then plotted to determine the maximum location in the X and Y dimensions. his is depicted in graphs 13 and 14. CFD Analyses: Comparison of Experimental Setup to Optimized Setup In the previous analysis, the location of maximum value was found to be (2.1 m, 1.7 m). he purpose of this analysis was to compare the power output of an optimized turbine 48 | 2012-2013 | Volume 2
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Graph 13. his graph shows a plot of the Z-velocity with respect to X-distance from the center of the car. he exact relationship between the two variables is diicult to determine from this plot, but the maximum values are easily identiiable.
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Graph 14. his graph shows a plot of the Z-velocity with respect to Y-distance from the bottom of the car. he relationship here can be seen to be quite smooth and predictable and the maximum values are easily identiiable. with dimensions to encompass this optimal location to the power output associated with the E2 turbine of the experimental roadside testing. he similarities of the velocity dissipation models between the CFD and roadside analyses shows that the CFD could approximate roadside events well, but yet another sub-test was conducted in order to further the legitimacy and validity of the CFD so as to allow a comparison of the experimental setup to the optimized setup. In order to do this, the simulation was run with the exact conditions of the roadside scenario. Table 6 summarizes these conditions.
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Table 5. he above table displays the experimental roadside testing conditions. Certain values out of these parameter speciications are certainly small and non-ideal and thus have room for improvement.
Table 6. he above table displays the optimal turbine/environment conditions. It can be seen here that the largest diferences between these parameter speciications and the experimental ones lie in the area value, the car speed value, and the Y coordinate value. he coordinate and car speed conditions were imposed upon the simulation and then the steady-state values across a range of Z-values determined to approximate the carefect time interval were recorded. hese values were used to calculate power outputs at every point and then were averaged across the speciic Z-axis. he resultant simulated E2 power output value was found to be .044 W. he actual average E2 power output (during traic pulses) was found to be .042 W in the experimental roadside tests. he closeness of these two values furthers the case for using the CFD model as an accurate approximation for roadside conditions. As such, the comparison of experimental to optimized setup could then be done and the results could have signiicant value. Following the simulation of E2 conditions, the CFD power output was known. he only remaining value necessary to conduct a comparison of experimental to optimized setup was the power output of the optimized setup. he process involved in inding this was the exact same as for the simulation of E2 except with the following parameters outlined in Table 6. he imposition of these parameters generated a Z-averaged power output of 122 W. he ratio of this power output (optimized setup) to that of the experimental setup is 2782.
As such, the mere implementation of a new turbine design to achieve the optimal parameters, which are within reasonable bounds, could theoretically increase the power output observed through the experimental roadside tests almost 3000-fold.
Discussion he primary objectives of this research were to determine whether the proposed idea of using miniature wind turbines on the sides of roads would generate electricity from the wind draft of cars and to test the theoretical power output model generated for this scenario. It was hypothesized that the idea would generate electricity and the power output model would it the data, but the data and its following analysis showed results of a diferent nature. he irst prong of the hypothesis was undoubtedly supported by the data as was shown in the correlation analysis. he second prong of the hypothesis was not supported, but elements of the power model associated with it followed through to the inal proposed models. he initial power model was the following:
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Street Broad Scientific here is deinitely a high degree of uncertainty in the distance relation due to the turbulent nature of the scenario and random nature of traic low, but this optimal proposed model its experimental power data very accurately and the power relations are supported by the CFD testing. he primary reason for the invalidity of the theoretical model is probably the inapplicable assumption of laminar low in the theoretical roadside wind speed model. Although eforts were taken to produce as high quality data as was possible, there are certainly areas of potential improvement. he turbine design could have been slightly more aerodynamic, the generators could have been slightly more eicient, the data set timings could have been better synchronized, and the data collection tools could have been more precise. Furthermore, there were certainly sources of error within the process of experimentation such as the natural imprecision of the testing equipment, slight inconsistencies in turbine yaw, and potentially imprecise distance measurements. hese errors, compounded with the unpredictable nature of turbulent wind and traic, are expressed as higher uncertainties and lower conidence levels in the results. he controlled single-car testing analyses produced a power output model that disagreed with both the theoretical model AND the roadside model. he following is the controlled single-car testing power output model:
where k is a constant. his discrepancy between roadside large-scale traic power output and single-car power output led us to the conjecture that there must also be an additional traic parameter involved in a holistic turbine power output model, which may afect the power-distance and power-speed relations. Research into this traic-parameter-based holistic turbine power output model is an intriguing potential topic of future study. Along with research into the potential traic parameter component of a holistic turbine power output model, there are many other possible ofshoot branches from this experiment that could be studied as future work. One such possibility is the study of the roadside “funneling efect”. his efect was observed during experimentation to be the compounding of wind in abnormally high-speed gusts at the side of the road whenever large packets of relatively fast moving automobiles passed. Another possible topic of future interest is Computational Fluid Dynamics modeling of the aerodynamic scenario we studied in this research project. Yet another possibility for future work could involve the studying of turbine design and roadside turbine arrays to potentially achieve the theoretical optimal power values described in the CFD analysis section. All of these potential topics of future study are key components of the remaining steps in furthering this concept of roadside electricity 50 | 2012-2013 | Volume 2
REsEaRch generation to make it economically feasible. At this point in time, based on our research, the idea is certainly not feasible. Yet, without a doubt there is a possibility that improvements could be made that could allow this idea to become the next innovative foray into the ield of renewable energy.
Acknowledgements I would like to thank Dr. Bennett and Mr. Milbourne, my mentors. I would also like to thank the Research in Physics program and the NCSSM Board of Trustees for allowing me to pursue this fantastic opportunity.
References [1] “Primary Energy Sources â Fuels at the Heart of the Matter.” Classroom Energy. N.p., n.d. Web. 08 Feb. 2012. <http://www.classroom-energy.org/energy_09/3.html>. [2] “Wind Energy Companies.” Wind Energy Companies. Web. 09 Feb. 2012. <http://www.greenchipstocks.com/articles/wind-energy-companies/273>. [3] “Wind Energy Basics.” Wind Energy Basics. N.p., n.d. Web. 12 Feb. 2012. <http://windeis.anl.gov/guid/basics/ indes.cfm>. [4] Constantino, D. “Winning with Wind.” Pit & Quarry (2008): 2. Web. 13 Jan. 2012. [5] Kovarik, homas J., Charles Pipher, and John A. Hurst. Wind Energy. Northbrook, IL: Domus, 1979. Print. [6] Batchelor, George K. “6.8.” An Introduction to Fluid Dynamics. Cambridge [u.a.: Cambridge Univ., 2009. Print.