International Journal of Advanced Research in Engineering and Technology RESEARCH IN–      INTERNATIONAL JOURNAL OF ADVANC...
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 649...
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 649...
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 649...
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 649...
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 649...
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 649...
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 649...
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 649...
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 649...
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 649...
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Numerical simulation of flow modeling in ducted axial fan using simpson’s 13rd rule

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Numerical simulation of flow modeling in ducted axial fan using simpson’s 13rd rule

  1. 1. International Journal of Advanced Research in Engineering and Technology RESEARCH IN– INTERNATIONAL JOURNAL OF ADVANCED (IJARET), ISSN 09766480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEME ENGINEERING AND TECHNOLOGY (IJARET)ISSN 0976 - 6480 (Print)ISSN 0976 - 6499 (Online) IJARETVolume 3, Issue 1, January- June (2012), pp. 107-117© IAEME: www.iaeme.com/ijaret.html ©IAEMEJournal Impact Factor (2011): 0.7315 (Calculated by GISI)www.jifactor.com NUMERICAL SIMULATION OF FLOW MODELING IN DUCTED AXIAL FAN USING SIMPSON’S 1/3rd RULE Manikandapirapu P.K.1 Srinivasa G.R.2 Sudhakar K.G.3 Madhu D. 4 1 Ph.D Candidate, Mechanical Department, Dayananda Sagar College of Engineering, Bangalore. 2 Professor and Principal Investigator, Dayananda Sagar College of Engineering, Bangalore. 3 Dean (Research and Development), CDGI, Indore, Madhya Pradesh . 4 Professor and Head, Mechanical Department, Government Engg. College, KRPET-571426.ABSTRACT The paper presents to develop the numerical simulation of flow model forthree dimensional flow and one dimensional flow in Ducted Axial Fan by using thenumerical integral procedure of Simpson’s 1/3rd rule. Main objective of this paper is todevelop the numerical flow model and measure the pressure rise for varying thefunctional parameters of inlet velocity, whirl velocity, rotor speed and diameter of bladefrom hub to tip in ducted axial fan by using the code of MATLAB for Simpson’s 1/3rdrule. In this main phase of paper, the analogy of three dimensional flow and onedimensional flow of numerical flow modeling have been investigated to optimize theparameter of pressure rise in ducted axial flow fan by using the integration procedure ofSimpson’s 1/3rd rule. Keywords: Numerical Integration, Simpson’s 1/3rd rule, Pressure rise, Whirl velocity,Pressure Ratio, Flow ratio, Rotor speed, Axial Fan.1.0 INTRODUCTION Mining fans and cooling tower fans normally employ axial blades and or required towork under adverse environmental conditions. They have to operate in a narrow band ofspeed and throttle positions in order to give best performance in terms of pressure rise,high efficiency and also stable condition. Since the range in which the fan has to operateunder stable condition is very narrow, clear knowledge has to be obtained about thewhole range of operating conditions if the fan has to be operated using active adaptive 107
  2. 2. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEMEcontrol devices. The performance of axial fan can be graphically represented as shown infigure 1. Fig: 1 Graphical representation of Axial Fan performance curve2. TEST FACILITY AND INSTRUMENTATION Experimental setup, fabricated to create stall conditions and to introduce unstallconditions in an industrial ducted axial fan is shown in figure 2. ndustrial Fig: 2 Ducted Axial Fan Rig A 2 HP Variable frequency 3 3-phase induction electrical drive is coupled to icalthe electrical motor to derive variable speed ranges. Schematic representation ofducted fan setup is shown in figure 3. 108
  3. 3. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEME Fig: 3 Ducted Axial Fan - Schematic The flow enters the test duct through a bell mouth entry of cubic profile. The bellmouth performs two functions: it provides a smooth undisturbed flow into the duct andalso serves the purpose of metering the flow rate. The bell mouth is made of fiberreinforced polyester with a smooth internal finish. The motor is positioned inside a 381mm diameter x 457 mm length of fan casing. The aspect (L/D) ratio of the casing is 1.2.The hub with blades, set at the required angle is mounted on the extended shaft of theelectric motor. The fan hub is made of two identical halves. The surface of the hub ismade spherical so that the blade root portion with the same contour could be seatedperfectly on this, thus avoiding any gap between these two mating parts. An outlet ductidentical in every way with that at inlet is used at the downstream of the fan. A flowthrottle is placed at the exit, having sufficient movement to present an exit area greaterthan that of the duct.3.0 NUMERICAL ANALYSIS Numerical analysis is the study of algorithms that use numerical approximation forthe problems of mathematical analysis. In Numerical algorithm is a step-by-stepprocedure for calculations. Algorithms are used for calculation, data processing, andreasoning. More precisely, an algorithm is an effective method expressed as a finite list ofwell-defined instructions for calculating a function. Starting from an initial state andinitial input for the instructions describe a computation that, when executed, will proceedthrough a finite number of well-defined successive states, eventually producing outputand terminating at a final ending state. Mathematical analysis, which mathematiciansrefer to simply as analysis, is a branch of pure mathematics that includes the theories ofdifferentiation, integration and measure, limits, infinite series, and analytic functions. 109
  4. 4. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEME3.1 MATLAB MATLAB is a programming environment for algorithm development, dataanalysis, visualization, and numerical computation. MATLAB is a wide range ofapplications, including signal and image processing, communications, control design, testand measurement, financial modeling and analysis, and computational biology.MATLAB contains mathematical, statistical, and engineering functions to support allcommon engineering and science operations. These functions, developed by experts inmathematics, are the foundation of the MATLAB language. The core math functions usethe LAPACK and BLAS linear algebra subroutine libraries and the FFT Discrete FourierTransform library. Because these processor-dependent libraries are optimized to thedifferent platforms that MATLAB supports, they execute faster than the equivalent C orC++ code.4.0 FLOW MODELING The aim of the flow modeling is to measure the pressure rise as a function ofwhirl velocity and rotor speed for different diameter of blade from hub to tip in ductedaxial flow fan. In this flow modeling equation helps to optimize the parameter of pressurerise for different whirl velocity in a ducted axial fan.4.1 Three Dimensional Flow Equation ଵ ஼ഇ మ ሺ‫݌݀ + ݌‬ሻሺ‫ݎ݀ + ݎ‬ሻ݀ߠ − ‫ − ߠ݀ ݎ ݌‬ሺ‫݌݀ + ݌‬ሻ ݀‫= ߠ݀ ݎ‬dm (4.1) ଶ ௥ ଵ ௗ௣೚ ௗ௖ೣ ௖௾ ௗ = ܿ௫ + ( ‫ܿ ݎ‬௾ ) (4.2) ఘ ௗ௥ ௗ௥ ௥ ௗ௥ ଵ ௗ௣ ௗ௩ೌ ௗ௩ೢ Stagnation pressure rise = + ‫ݒ‬௔ + ‫ݒ‬௪ (4.3) ఘ ௗ௥ ௗ௥ ௗ௥ ‫( ݌‬Vw.U).dr – Va . dVa – Vw. dVw = dp (4.4) Stagnation Pressure rise = Total Input Power = 500 Watts as an assumption forthis Analytic and simulation studies of ducted Axial Fan. If integrate that equation4.4, obtain that final form of equation. మ ௩ೌ మ ௩ೌ500 ( ‫ݎ‬ଶ – ‫ݎ‬ଵ ) – ቈቀ ଶ ቁ ௥మ – ቀ ଶ ቁ ௥భ ቉ − ቂ ቀ ೢቁ ௥మ − ቀ ೢቁ ௥భ ቃ = ሾ݀‫݌‬ሿ ௩మ ௩మ ଵ (4.5) ଶ ଶ ఘ 110
  5. 5. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEME4.2 One Dimensional Flow Equation మ ௩ೢ Pressure rise dp = ࣋ ݀‫ݎ‬ ௥ ࣒ ×૜.૚૝ ×ࡺPressure Rise = dp =࣋ ቀ ቁ ଶ × ‫ݎ݀ ݎ ׬‬ (4.6) ૟૙5.0 NUMERICAL MODELING From this flow modeling equation, adopt and continue the procedure ofnumerical integration scheme. In this numerical integration procedure, MATLABcode has computed for developing the pressure rise in ducted axial fan usingSimpson’s 1/3 rule.Simpson’s 1/3 Rule ௕ ௛‫׬‬௔ ‫= ݔ݀ݕ‬ ଷ [y0 + 4(y1 + y3 + y5 + …….. +yn-1) + 2(y2 + y4 + y6 +……. + yn-2) + yn] (5.1)5.1 MATLAB CODE FOR THREE DIMENSIONAL FLOWS USING ૚SIMPSON’S RULE ૜Objective ଵ To compute the pressure rise in three dimensional flow equations by using Simpson’s ଷrule.%Three Dimensional Flow equation using simpson’s 1/3rd rulei=0;for n=0:1:8; i=i+1; r=[0.08255:0.013:0.199]; f=208.62*r; disp(f);endn =input(enter the intervals);h =(0.199-0.08255)/n;Vwdw = [17.2216:2.710:38.9181];s=17.2216;z=38.9181;sum=0;for j=(1:1:n/2); x=(0.08255-h)+(2*h*j); sum=sum+(4*Vwdw(j)); if j~=n/2 sum=sum+(2*Vwdw(j)); end end 111
  6. 6. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEME sum=(sum+s+z); ans =(sum*h)/3; disp (ans); r2=input(enter the final radius);r1=input( enter the initial radius);res= 500*(r2-r1);disp(res);answer=res-ans;disp (answer);PR= 1.048*(answer);fprintf(,Pressure Rise in N/m2=%g,PR)MATLAB OUTPUT FOR SIMPSONS 1/3RD RULE17.2216 19.9336 22.6457 25.3578 28.0698 30.7819 33.4939 36.2060 38.9181 17.2216 19.9336 22.6457 25.3578 28.0698 30.7819 33.4939 36.2060 38.9181 17.2216 19.9336 22.6457 25.3578 28.0698 30.7819 33.4939 36.2060 38.9181 17.2216 19.9336 22.6457 25.3578 28.0698 30.7819 33.4939 36.2060 38.9181 17.2216 19.9336 22.6457 25.3578 28.0698 30.7819 33.4939 36.2060 38.9181 17.2216 19.9336 22.6457 25.3578 28.0698 30.7819 33.4939 36.2060 38.9181 17.2216 19.9336 22.6457 25.3578 28.0698 30.7819 33.4939 36.2060 38.9181 17.2216 19.9336 22.6457 25.3578 28.0698 30.7819 33.4939 36.2060 38.9181 17.2216 19.9336 22.6457 25.3578 28.0698 30.7819 33.4939 36.2060 38.9181Enter the intervals 9 2.4455Enter the final radius 0.186Enter the initial radius 0.08255 51.7250 49.2795Pressure Rise in N/m2 = 51.6449 112
  7. 7. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEME5.2 MATLAB CODE FOR ONE DIMENSIONAL FLOW EQUATION ૚USING SIMPSON’S RULE ૜Objective ଵTo compute the pressure rise in one dimensional flow equation by using Simpson’s ଷrule.%(Simpson 1/3rd rule for one dimensional flow equation );i=0;for n=0:1:8; i=i+1; r=[0.08255:0.013:0.199]; f=325.89*r; disp(f);endn =input(enter the intervals);h =(0.199-0.08255)/n;Vwdw = [26.9022:4.2366:60.7948];s=26.9022;z=60.7948;sum=0;for j=(1:1:n/2); x=(0.08255-h)+(2*h*j); sum=sum+(4*Vwdw(j)); if j~=n/2 sum=sum+(2*Vwdw(j)); end end sum=(sum+s+z); ans =(sum*h)/3; disp (ans);PR= 1.048*(ans);fprintf(,Pressure Rise in N/m2=%g,PR)MATLAB RESULTS FOR SIMPSONS 1/3RD RULE26.9022 31.1388 35.3754 39.6119 43.8485 48.0851 52.3216 56.5582 60.7948 26.9022 31.1388 35.3754 39.6119 43.8485 48.0851 52.3216 56.5582 60.7948 26.9022 31.1388 35.3754 39.6119 43.8485 48.0851 52.3216 56.5582 60.7948 26.9022 31.1388 35.3754 39.6119 43.8485 48.0851 52.3216 56.5582 60.7948 26.9022 31.1388 35.3754 39.6119 43.8485 48.0851 52.3216 56.5582 60.7948 113
  8. 8. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEME 26.9022 31.1388 35.3754 39.6119 43.8485 48.0851 52.3216 56.5582 60.7948 26.9022 31.1388 35.3754 39.6119 43.8485 48.0851 52.3216 56.5582 60.7948 26.9022 31.1388 35.3754 39.6119 43.8485 48.0851 52.3216 56.5582 60.7948 26.9022 31.1388 35.3754 39.6119 43.8485 48.0851 52.3216 56.5582 60.7948Enter the intervals 9 3.8207Pressure Rise in N/m2=4.004115.3 CALCULATION OF ERROR PERCENTAGECase 1: Three Dimensional Flows Theoretical value of pressure rise for three dimensional flow of ducted Axial fan = 51.5308 N/m2 Numerical Modeling of pressure rise for three dimensional flow of ducted axial fan using Simpson’s 1/3rd Rule = 51.198 N/m2 ்௛௘௢௥௜௧௜௖௔௟ ௏௔௟௨௘ –ே௨௠௘௥௜௖௔௟ ௠௢ௗ௘௟௜௡௚ ௏௔௟௨௘ Error Percentage = (5.2) ்௛௘௢௥௜௧௜௖௔௟ ௏௔௟௨௘ ହଵ.ହଷ଴଼ –ହଵ.ଵଽ଼ Error Percentage = ∗ 100 ହଵ.ହଷ଴଼ Error Percentage (%) = 0.646Case 2: One Dimensional Flow Theoretical value of pressure rise for one dimensional flow of ducted Axial fan = 5.034 N/m2 Numerical Modeling of pressure rise for one dimensional flow of ducted axial fan using Simpson’s 1/3rd Rule = 4.00411 N/m2 ்௛௘௢௥௜௧௜௖௔௟ ௏௔௟௨௘ –ே௨௠௘௥௜௖௔௟ ௠௢ௗ௘௟௜௡௚ ௏௔௟௨௘ Error Percentage = (5.3) ்௛௘௢௥௜௧௜௖௔௟ ௏௔௟௨௘ ହ.଴ଷସ – ସ.଴଴ସଵଵ Error Percentage = ∗ 100 ହ.଴ଷସ Error Percentage (%) = 20.45 114
  9. 9. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEME6.0 CONCLUSION In this paper, an attempt has been made to develop the numericalsimulation of three dimensional flows and one dimensional flow code usingMATLAB in Simpson’s 1/3rd rule for ducted axial fan . It is useful to design theoperating condition of axial fan to measure the parameters of pressure rise as afunction of pressure ratio, rotor speed, and diameter of blade from hub to tip inducted axial fan. Further, this work can be extended by working on the flowsimulation characteristic study in control system algorithm. The results so fardiscussed, indicate that numerical simulation of flow modeling using Simpson’s1/3rd rule for ducted axial fan is very promising.ACKNOWLEDGEMENT The authors gratefully thank AICTE (rps) Grant. for the financial support ofpresent work.NOMENCLATURE cx = Axial velocity in m/s ܿఏ = Whirl velocity in m/s r2 = Radius of blade tip in m r1 = Radius of blade hub in m N = Tip speed of the blades in rpm va = Axial velocity in m/s dp= P2 - P1 = Pressure rise in N/m2 d = Diameter of the blade in m ρair = Density of air in kg/m3 vw = Whirl velocity in m/s η = Efficiency of fanREFERENCES[1] Day I J,”Active Suppression of Rotating Stall and Surge in AxialCompressors”, ASME Journal of Turbo machinery, vol 115, P 40-47, 1993[2] Patrick B Lawlees,”Active Control of Rotating Stall in a Low SpeedCentrifugal Compressors”, Journal of Propulsion and Power, vol 15, No 1, P 38-44, 1999 115
  10. 10. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEME[3]C A Poensgen ,”Rotating Stall in a Single-Stage Axial Compressor”, Journal ofTurbo machinery, vol.118, P 189-196, 1996[4] J D Paduano,” Modeling for Control of Rotating stall in High Speed MultistageAxial Compressor” ASME Journal of Turbo machinery, vol 118, P 1-10, 1996[5] Chang Sik Kang,”Unsteady Pressure Measurements around Rotor of an AxialFlow Fan Under Stable and Unstable Operating Conditions”, JSME InternationalJournal, Series B, vol 48, No 1, P 56-64, 2005.[6] A H Epstein,”Active Suppression of Aerodynamic instabilities in turbomachines”, Journal of Propulsion, vol 5, No 2, P 204-211, 1989[7] Bram de Jager,”Rotating stall and surge control: A survey”, IEEE Proceedingsof 34th Conference on Decision and control, 1993[8] S Ramamurthy,”Design, Testing and Analysis of Axial Flow Fan,” M EThesis, Mechanical Engineering Dept, Indian Institute of Science, 1975[9] S L Dixon, Fluid Mechanics and Thermodynamics of Turbo machinery, 5thed., Pergamon, Oxford, 1998[10] William W Peng, Fundamentals of Turbo machinery, John Wiley & sons.Inc,2008[11] Curtis F Gerald, Applied Numerical Analysis, 5th Edition, Addison-Wesley Publishing Company. Inc.1998[12] Rao V Dukkipati, MATLAB for Mechanical Engineers, First Edition, NewAge International Publishers, 2008 116
  11. 11. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEMEAUTHORSManikandapirapu P.K. received his B.E degree from Mepco SchlenkEngineering college, M.Tech from P.S.G College of Technology,AnnaUniversity,and now is pursuing Ph.D degree in Dayananda Sagar Collegeof Engineering, Bangalore under VTU University. His Research interestinclude: Turbomachinery, fluid mechanics, Heat transfer and CFD.Srinivasa G.R. received his Ph.D degree from Indian Institute of Science,Bangalore. He is currently working as a professor in mechanicalengineering department, Dayananda Sagar College of Engineering,Bangalore. His Research interest include: Turbomachinery,Aerodynamics, Fluid Mechanics, Gas turbines and Heat transfer.Sudhakar K.G received his Ph.D degree from Indian Institute of Science,Bangalore. He is currently working as a Dean (Research andDevelopment) in CDGI, Indore, Madhyapradesh. His Research interestinclude: Surface Engineering, Metallurgy, Composite Materials, MEMSand Foundry Technology.Madhu D received his Ph.D degree from Indian Institute of Technology(New Delhi). He is currently working as a Professor and Head inGovernment Engineering college, KRPET-571426, Karnataka. HisResearch interest include: Refrigeration and Air Conditioning, AdvancedHeat Transfer Studies, Multi phase flow and IC Engines. 117

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