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**School of Electrical Engineering Systems**

Fractal Applications: From Anaerobic Digestion To Urban Wind Turbulence Thomas Woolmington School of Electrical Engineering Systems Prof. Jonathan Blackledge Date 15/2/2013

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**Anaerobic Digestion Basics**

In its simplest form Anaerobic Digestion is the decomposition of biological matter in an atmosphere that has no oxygen present. This decomposition releases gases. For a good system circa 58% Methane, circa 40% Carbon Dioxide and traces of Carbon Monoxide and Hydrogen Sulphide. These gases are produced as a by-product of bacterial interaction with organic matter. The bacteria thrive in stable PH environments circa and at specific temperature classes for different methanogen families (NÍ Ruanaigh, 2011)

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**Digester Designs of Interest Suspended Solid Up-flow Digester**

Anaerobic Lagoon (Wall et al, 2012) (Hamilton, 2012)

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**Retrofit Current Slatted Units**

Slatted Unit Construction Cross Section of Typical Slatted Unit Finished Installation (Worms, 2001)

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**Project Concept and Justification**

Pros: Bovine agriculture in Ireland requires the use of storage facilities of rumen for a minimum of 16 Weeks (custom built tanks) Anaerobic Digestion has been proven to reduce the carbon equivalent footprint of agriculture. Biogas can be used as a heat source on farms as the vast majority of farms in Ireland have associated domestic dwellings. (If CHP is incorporated electricity can be generated also) Cons: The Anaerobic Digestion process currently only monitors the environmental conditions of a biological “Black Box”. As a result microbiologists manually monitor large AD plants. When CO2 equivalents are applied; agriculture is the largest greenhouse gas producer in Ireland. Lagoon technology does not suit slatted unit tanks (currently used in Irish agriculture) or indeed our Irish climate. The AD process can be simplified (passive) in warmer climates. Lack of awareness of the technology with Irish farmers.

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Fractal Basics Consider a simple trunk - branch - twig structure and add complexity of self symmetry along the structure (Turner et al., 1998)

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Fractal Basics Note that the same shapes are present at different scales and orientation multiple times throughout the image (Kulturservern, 2010)

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Fractal Basics Self symmetry within structures can be quantified by means of fractal analysis (shapes within shapes). When we apply this concept to biological organisms it can in some instances be used as a means to quantify non-Euclidean (linear, area based or volumetric) growth. Consider leaves on a mature tree from season to season.

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Fractal Basics What would happen if the same concept was applied to Methanogen cell structures in active substrate within an anaerobic digester? (Kubota et al., 2008)

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**Year 1 Aims and Methodology**

Main Aims for the previous year! 2 strand approach; Develop a mathematical simulator of fractal structures and determine its mathematical accuracy. Acquire images of organisms that can potentially be used in the mathematical simulator. Ideally the above two streams would merge in order to prove concept Correlation of simulation with image Image Acquisition Mathematical Simulator Direct linking of organism growth rates to simulated model This gives a Quantitative value a reference to the biological growth state within a reactor. This in turn can then be used to provide a closed loop means of monitoring the reactor process

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**Mathematical Modelling**

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**Some Images to date! Image acquisition 400X**

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**Some Images to date! Image acquisition 1000X**

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**BSc Student Dissertation Supervision**

Verification of concept of variable volume digesters Cross between a lagoon and a suspended media up flow digester. Submitted last June (Images courtesy of Mr. A Bogle)

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Experimental Layout Promising and potentially marketable Needs a little mechanical alteration but the results speak for themselves Any input would be greatly appreciated probably mechanical / manufacturing (Image courtesy of Mr. A Bogle)

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**My PhD Problems Encountered**

We have a technology that does not appear to need monitoring! The Inability to obtain suitable images of organisms in situ. We have a maths model but nothing for it to be used on. My PhD

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Thought Process The Fractal model is deigned to look for self similarity within a noisy signal. Theoretically it should be able to quantify how noisy a signal is. Effectively more self similarity means more noise etc.

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Thought Process

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Enter Real world Data A chance discussion took place with Keith Sunderland Access to a large amount of 10Hz urban wind speed data. Add a little bit of tweaking to convert to a wind speed signal Put it into the current simulator and see what happens.

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New Turbulence Metric Effectively the fractal model measures turbulence but it strictly speaking cannot be called fractal as a “fractal” in this instance should be bounded by a limit of Df=2. For comparison the “fractal” model was then compared to the standard turbulence metric (Turbulence intensity (TI)) for comparison. Then with the new metric longitudinal TI (effectively cosine corrected TI per 10 minute mean wind speed)

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**Unfiltered Data Comparison**

Unfiltered results 4502 samples Note! TI>100% giving erratic spikes

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**Filtered Data Comparison TI>100% filtered out**

Filtered results 4327 samples (3.88% of samples filtered out) Note! Trending differences

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**Issues with the TI metric**

An Investigation was made into the origin of the TI longitudinal metric and the principles that it relies on in order to gain an understanding of the non correlation with the “fractal” model. Firstly TI is calculated based on, Secondly it was originally designed as a metric for large rural / offshore turbines where high wind speeds were present in low turbulence environments. It became obvious that the TI metric is unsuitable for use in an urban environment due to low wind speeds and high standard deviation making results appear to be asymptotically high in nature. But consider the following!

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**Investigation into the TI metric**

Df =1 is effectively 0% turbulence However the current TI metric would classify this sample as having 31% turbulence The current TI metric does not allow for trends within the wind speed sample

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**Investigation into the TI metric**

Having said that the TI metric has not been used to its maximum effect in terms of power prediction. Previous studies have shown that for rural and off shore site that the PDF of wind speeds within a 10 minute sample follow a normal Gaussian pattern. Some of the experimental data shows that this is not the case in urban environments logarithmic at low mean wind speeds Rayleigh type for the majority of usable wind speeds In a yet to be published paper co wrote by Keith Sunderland we have proposed that the following chart may be a generic case but as of yet we do not have enough site data to verify if this is true or not.

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**Investigation into the TI metric**

Mean u High Turbulence (urban/suburban) Med Turbulence (Suburban/Rural) Low Turbulence (Rural/Off-shore) Low Exponential PDF Exponential / Rayleigh PDF Rayleigh PDF Medium Rayleigh / Gaussian PDF High Gaussian PDF If this is the case all of the above PDFs can be encompassed by the Weibull distribution. The paper will outline how power can be accurately predicted for any turbine based on just a u mean and TI value for a 10 minute period. Thus dramatically reducing the amount of information that needs to be stored.

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**Some Interesting facts about the Weibull Distribution**

Weibull analysis has long been associated as a means to predict component failure rates in Mechanical and Manufacturing engineering. Up till recently the Weibull distribution model has been accepted to be correct based on numerous sets of empirical data. Weibull distributions have been shown to fit PDFs of numerous wind resource sites It has recently been proved by (Brown and Wohletz, 1995) to always have a Df that lies in the region of (0 ≤ Df ≤ 3). Note! The last point now inherently links the statistical PDF model to fractal and levy index theory

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**If this is the case all of the above PDFs can be encompassed by the Weibull distribution.**

The paper will outline how power can be accurately predicted for any turbine based on just a u mean and TI value for a 10 minute period. Thus dramatically reducing the amount of information that needs to be stored.

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References BROWN, W. & WOHLETZ, K. (1995). Derivation of the Weibull distribution based on physical principles and its connection to the Rossin-Rammler and lognormal distributions. Journal of Applied Physics, 78(4), HAMILTON, D. (2012). Types of Anaerobic Digestion [Online]. Extension.org. Available: [Accessed 1st Febuary 2013]. KUBOTA, K., IMACHI, H., KAWAKAMI, S., NAKAMURA, K., HARADA, H. & OHASHI, A. (2008). Evaluation of enzymatic cell treatments for application of CARD-FISH to methanogens. Journal of Microbiological Methods, 72(1), KULTURSERVERN. (2010). Modulations of Man [Online]. kulturservern. [Accessed 10th February 2013]. NÍ RUANAIGH, A. (2011). Developing Anaerobic Digestion Cooperatives in Ireland. Master of Science Energy Management, Dublin Institute of Technology. TURNER, M. J., BLACKLEDGE, J. M. & ANDREWS, P. R. (1998). Fractal Geometry in Digital Imaging, London, Academic Press. WALL, G., HAMMOND, B., DONLON, P., JOHNSON, N. & SMITH, J. (2000). Commissioning and operation of high rate anaerobic lagoon (HRAL) reactors. 63rd Annual Water Industry Engineers and Operators’ Conference. Warrnambool, Australia: Water Industry Operators of Australia. WORMS, C. (2001). Concrete Slatted Floor Systems [Online]. Worms Lumber and Ready Mix. Available: [Accessed 10th February 2013].

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**Any Questions? References**

BROWN, W. & WOHLETZ, K. (1995). Derivation of the Weibull distribution based on physical principles and its connection to the Rossin-Rammler and lognormal distributions. Journal of Applied Physics, 78(4), HAMILTON, D. (2012). Types of Anaerobic Digestion [Online]. Extension.org. Available: [Accessed 1st Febuary 2013]. KUBOTA, K., IMACHI, H., KAWAKAMI, S., NAKAMURA, K., HARADA, H. & OHASHI, A. (2008). Evaluation of enzymatic cell treatments for application of CARD-FISH to methanogens. Journal of Microbiological Methods, 72(1), KULTURSERVERN. (2010). Modulations of Man [Online]. kulturservern. [Accessed 10th February 2013]. NÍ RUANAIGH, A. (2011). Developing Anaerobic Digestion Cooperatives in Ireland. Master of Science Energy Management, Dublin Institute of Technology. TURNER, M. J., BLACKLEDGE, J. M. & ANDREWS, P. R. (1998). Fractal Geometry in Digital Imaging, London, Academic Press. WALL, G., HAMMOND, B., DONLON, P., JOHNSON, N. & SMITH, J. (2000). Commissioning and operation of high rate anaerobic lagoon (HRAL) reactors. 63rd Annual Water Industry Engineers and Operators’ Conference. Warrnambool, Australia: Water Industry Operators of Australia. WORMS, C. (2001). Concrete Slatted Floor Systems [Online]. Worms Lumber and Ready Mix. Available: [Accessed 10th February 2013]. Any Questions?

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