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On the Selection of Optimum Blend of WPO – Combinatorial Mathematics Based Approach
1.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 08 | Aug -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 857 On the Selection of Optimum Blend of WPO – Combinatorial Mathematics Based Approach Geetha.N.K1, Sekar.P2 1Assistant Professor, Department of Mathematics, Sri Krishna College of Engineering and Technology, Coimbatore, India 641008 2Dean, Faculty of Science and Humanities, SRM University, Chennai, India 600089. ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract - This paper presents the methodologyofselection of optimum blend using combinatorial mathematics based approach from blends of waste plastic oil designated as WPO10, WPO20 and WPO30 based on the performance parameters like brake power, specific fuel consumption, mechanical efficiency, brake thermal and indicated thermal efficiency. It is found that WPO20 at 10kg load forms the optimum blend out of all the test fuels. Key Words: Waste plastic oil, Combinatorial mathematics based approach, CMBA, Blend 1. INTRODUCTION With the rapid depletion of fossil fuels at a faster rate, an alternative fuel is needed to fulfill the needs of mankind.Out of the various alternative fuels, Waste Plastic Oil (WPO) is acclaimed to be a suitable alternative fuel as the properties of WPO are very close to diesel [1-3]. Researchers haveputa lot of effort in production and characterization of WPO and its use as fuel on engines in neat and blend form [4-6]. The present study deals with the selectionofoptimumblend of WPO-Diesel. The statistical data for the present study if taken from the experimental results of Ankit et al. [7]. The blends of WPO are designated as WPO10 (10%WPO+ 90%Diesel), WPO20 (20%WPO+80%Diesel) and WPO30 (30%WPO+70%Diesel). The load on the engine is varied as 2kg, 4kg, 6kg, 8kg and 10kg. the results of experimental investigation are shown in Table1. Table - 1: Experimental results Exp No. Blend Load (kg) BP (kW) SFC Kg/kWh) Mech Efficiency (%) BTE (%) ITE (%) 1 WPO 10 2 0.43 0.71 17.21 12 69.72 2 WPO 10 4 0.87 0.43 29.36 20.13 68.55 3 WPO 10 6 1.3 0.34 38.4 24.99 65.08 4 WPO 10 8 1.74 0.27 45.39 32.07 70.66 5 WPO 10 10 2.17 0.24 50.96 35.03 68.75 6 WPO 20 2 0.43 0.71 18.77 12.16 64.78 7 WPO 20 4 0.87 0.41 31.6 20.94 66.25 8 WPO 20 6 1.3 0.33 40.94 26.29 64.23 9 WPO 20 8 1.74 0.27 48.03 31.74 66.08 10 WPO 20 10 2.17 0.24 53.6 36.41 67.93 11 WPO 30 2 0.43 0.71 16.74 12.12 72.42 12 WPO 30 4 0.87 0.42 26.68 20.21 70.46 13 WPO 30 6 1.3 0.32 37.63 27.06 71.93 14 WPO 30 8 1.74 0.27 44.58 31.57 70.83 15 WPO 30 10 2.17 0.24 50.13 36.08 71.98
2.
International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 08 | Aug -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 858 2. COMBINATORIAL MATHEMATICS BASED APPROACH Combinatorial mathematics based approach (CMBA) is an integration of combinatorial mathematics matrix function and analytic hierarchy process and a [8]. The step wise procedure of CMBA is shown below: Step 1: Decision matrix Decision matrix is a collection of data for each experiment and is same as shown in Table1. Step 2: Normalization The size of the matrix is equal to the number of attributes considered. Normalization is to set the attribute data on same scale so that, comparisons can be made easier [9]. Let xij is the normalized value of yij for attribute i, then, )(max ijj ij ij y y x ; if jth attribute is beneficial ij ijj ij y y x )(min ; if, jth attribute is non-beneficial The normalized values of attributes are shown in Table 2. Table – 2: Normalized values of attributes Exp No. Blend Load (kg) BP (kW) SFC Kg/kWh) Mech Efficiency (%) BTE (%) ITE (%) 1 WPO 10 2 0.198 1.000 0.321 0.330 0.963 2 WPO 10 4 0.401 0.606 0.548 0.553 0.947 3 WPO 10 6 0.599 0.479 0.716 0.686 0.899 4 WPO 10 8 0.802 0.380 0.847 0.881 0.976 5 WPO 10 10 1.000 0.338 0.951 0.962 0.949 6 WPO 20 2 0.198 1.000 0.350 0.334 0.895 7 WPO 20 4 0.401 0.577 0.590 0.575 0.915 8 WPO 20 6 0.599 0.465 0.764 0.722 0.887 9 WPO 20 8 0.802 0.380 0.896 0.872 0.912 10 WPO 20 10 1.000 0.338 1.000 1.000 0.938 11 WPO 30 2 0.198 1.000 0.312 0.333 1.000 12 WPO 30 4 0.401 0.592 0.498 0.555 0.973 13 WPO 30 6 0.599 0.451 0.702 0.743 0.993 14 WPO 30 8 0.802 0.380 0.832 0.867 0.978 15 WPO 30 10 1.000 0.338 0.935 0.991 0.994 Step 3: Relative Importance After analyzing the attributes, the relative importance of attributes is assigned. Table 3 shows the scale for pairwise comparison [10]. The geometric mean approach of AHP is used to determine the relative normalized weights of the attributes and the consistency check is carried out. It is required that the consistency ratio value of the relative importance of attributes should be less than 0.10 [11]. The consistency ratio in the present study is found to be 0.068. The consistency evaluation is shown in Table 4. Step 4: Formation of alternate selection attribute matrix The alternative selection matrix is formed by keeping the normalized values for attributes for the alternative as diagonal elements. The matrix is represented by, B. B= (1) Step 5: Permanent function The permanent function used in Combinatorial mathematics characterizes the configuration of a system [12]. The characteristic permanent function for the standardmatrixis shown in Eq. 2.
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International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 08 | Aug -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 859 ................... ].....)(...... .......))()((....... .......))((....... ......))((........[ ]......)(......... ......))((.......[ ].....)(.... .....))((.............[ ....)(........ ....)(............ )( 5 1 1 1 1 1 1 1 1 5 1 1 3 1 2 1 1 2 1 5 1 1 1 1 2 1 1 1 1 1 ln 3 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 3 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 M i M ij M ik M il M im M jn M tM mtojikjlkmlnminnimnlmkljkij M i M ij M ik M il M km M kn M tM mtonmmnlkkljiij M i M ij M jk M l M lm M mn M tM mtomlnmnlmnlmjikjikkijkij M i M ij M ik M jl M m M mn M tM mtonmmnjikjlkillikljkij M i M ij M ik M il M jm M tM mtonjikjlkmlimmilmkljkij M i M ij M jk M l M lm M tM mtonmllmjikjikkijkij M i M ij M ik M jl M tM mtonmjikjlkillikljkij M i M ij M ik M il M tM Mtonmlkkljiij M i M ij M jk M tM Mtonmljikjikkijkij M i M i M ij M tM mtonmlkjiiji DDDdddddddddddd DDDdddddd DDDdddddddddddd DDDdddddddddd DDDDdddddddddd DDDDdddddddd DDDDDdddddddd DDDDDdddd DDDDDDdddddd DDDDDDDddD BPer (2) Table – 3: Scale for pairwise comparison Degree of importance Definition 1 Equal 2 Intermediate between 1 and 3 3 Moderately preferable 4 Intermediate between 3 and 5 5 Strongly preferable 6 Intermediate between 5 and 7 7 Very strongly preferable 8 Intermediate between 7 and 9 9 Extremely strongly preferable ½, 1/3, ¼, 1/5, 1/6, 1/7, 1/8, 1/9 Reciprocals of 2, 3, 4, 5, 6, 7, 8 and 9 Table – 4: Consistency evaluation BP (kW) SFC Kg/kWh) Mech Efficiency (%) BTE (%) ITE (%) Tota l Averag e Consistency Measure BP (kW) 0.353 0.444 0.343 0.235 0.222 1.59 8 0.320 5.259 SFC (Kg/kWh) 0.118 0.222 0.343 0.235 0.222 1.14 0 0.228 5.435 Mech Efficiency (%) 0.176 0.111 0.171 0.353 0.222 1.03 4 0.207 5.360 BTE (%) 0.176 0.111 0.057 0.118 0.222 0.68 5 0.137 5.090 ITE (%) 0.176 0.111 0.086 0.059 0.111 0.54 3 0.109 5.102 CI 0.062 RI 0.91 CR 0.068
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International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 08 | Aug -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 860 Step 6: Rank of alternatives The rank of alternatives is based on the permanent function value of the alternative selection matrix, also called as Index score. The alternative for which the value of Index score is highest is the best choice for the considereddecisionmaking problem. The Index score for all alternatives is sorted and ranked as shown in Table 5. Table – 5: Index score for alternatives Exp No. Blend Load (kg) Index score Rank 10 WPO 20 10 141.4409 1 15 WPO 30 10 141.2131 2 5 WPO 10 10 139.798 3 4 WPO 10 8 132.5319 4 14 WPO 30 8 131.9812 5 9 WPO 20 8 131.8858 6 13 WPO 30 6 123.9184 7 8 WPO 20 6 122.7776 8 3 WPO 10 6 121.7662 9 2 WPO 10 4 115.2242 10 7 WPO 20 4 115.138 11 12 WPO 30 4 114.5299 12 11 WPO 30 2 111.311 13 1 WPO 10 2 110.7055 14 6 WPO 20 2 110.0223 15 3. CONCLUSION The proposed CMBA is adapted to select optimum blend of waste plastic oil. The computation used is comparatively simple compared to other multi attribute decision making methods. The measures of the attributes and their relative importance are used together to rank the alternatives. Hence, it provides a better evaluation. The use of permanent concept characterizes theconsideredapproachasitcontains all possible structural componentsoftheattributesandtheir relative importance hence, no information is lost. This method can deal with problems consideringboth qualitative and quantitative attributes. The uniqueness of CMBA is that it offers a general procedure thatcanbeapplicabletodiverse selection problems that incorporates vagueness and a number of selection attributes. The approach is logical, simple and convenient to implement. NOMENCLATURE BP: Brake power SFC: Specific fuel consumption BTE: Brake thermal efficiency ITE: Indicated thermal efficiency CMBA: Combinatorial mathematics based approach WPO: Waste plastic oil WPO10:10%WPO+90%Diesel WPO20:20%WPO+80%Diesel WPO30:30%WPO+70%Diesel REFERENCES [1] Jindal. S, Nandwana. BP, Rathore. NS, Vashistha. V, Experimental investigations oftheeffectofcompression ratio and injection pressure in a direct injection diesel engine running on jatropha methyl ester, Applied thermal engineering, 2010; 30; 442-448. [2] Paul Daniel M, Vijay Kumar K, Durga Prasad B, Ravi Kumar P, Performance and emission characteristics of diesel engine operated on plastic Pyrolysis oil with exhaust gas recirculation, International journal of ambient energy, 2017; 38(3); 295-299. [3] Damodharan D, Sathiyagnanam AP, Rana D, Rajesh Kumar B, Saravanan S, Extraction and characterization of waste plastic oil with the effect of n-Butanol addition on the performance and emissions of a DI diesel engine
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International Research Journal
of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 08 | Aug -2017 www.irjet.net p-ISSN: 2395-0072 © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 861 fueled with WPO diesel blends, Energy conversion and management, 2017; 131; 117-126. [4] Devraj J, Robinson Y, Ganapathi P, Experimental investigation of performance emission and combustion characteristics of waste plastic Pyrolysis oil blended with di ethyl ether used as fuel for diesel engine,Energy, 2015; 85; 304-309. [5] Rajan kumar, Mishra MK, Singh SK, Arbind Kumar, Experimental evaluation of waste plastic oil and its blend on a single cylinder diesel engine, Journal of mechanical scienceandtechnology,2016;30(10);4781- 4798. [6] Mani M, Nagarajan G, Sampath S, An experimental investigation on a DI diesel engineusing wasteplasticoil with exhaust gas recirculation, Fuel, 2010; 89; 1826- 1832. [7] Ankit Jani, Tushar Patel, Gaurav Rathod, Effect of Varying Load on Performance andEmissionofCIEngine Using WPO Diesel Blend, IOSRJournal ofMechanical and Civil Engineering, 12 (2), PP 37-44, 2015. [8] R. Venkata Rao, Decision making in the manufacturing environment using graph theory and fuzzy multiple attribute decision makingmethods,Volume1,Newyork: Springer, 2007. [9] R.V. Rao, F. Bleicher, D. Singh, V. Kalyankar, “Selecting environmentally conscious manufacturing program using combinatorial mathematics approach,” International conference on engineering project and production management (EPPM 2011), singapore, Sep 20-21, 2011. [10] T.L. Saaty, The analytic hierarchy process, Mc graw hill, 1980. [11] E. Triantaphyllov, S.H. Mann, “An evaluation ofthe eigen value approach for determining the membershipvalues in fuzzy sets,” Fuzztsets and systems, vol. 35, pp. 295- 301, 1990. [12] M. Marcus, Minc, “Permanents,” American mathematics monthly, vol. 72, pp. 571-591, 1965.
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