A Heuristic Approach for Design and Calculation of Pressure Distribution over Naca 4 Digit Airfoil

Transcription

1 IOSR Journal of Engineering (IOSRJEN) ISSN (e): , ISSN (p): PP A Heuristi Approah for Design and Calulation of Pressure Distribution over Naa 4 Digit Airfoil G. Madhan Kumar 1, R. Sriramasubramaniamoorthy 2, G. Johnson 3, M. Keerthana 4 1 Assistant Professor, Department of Aeronautial Engineering, Surya Group of Institutions, Villupuram, Tamil Nadu, India. 2 Student, Department of Aeronautial Engineering, Surya Group of Institutions, Villupuram, Tamil Nadu, India. 3 Student, Department of Aeronautial Engineering, Surya Group of Institutions, Villupuram. Tamil Nadu, India. 4 Student, Department of Aeronautial Engineering, Surya Group of Institutions, Villupuram. Tamil Nadu, India. Abstrat: In reent years of tehnologial perspetive, the pressure distribution of airfoil has ome to be a wide extent of studies using experimental, theoretial and omputational ode solving methods. In this hierarhy, it is more predominant to alulate the value of pressure distribution diretly from the airfoil without any mode of additional requirement of experimental or omputational one. In this paper, we present the method of plotting the NACA 4 digit airfoil and pressure distribution around it at zero degree angle of attak. The obtained results are ompared and ontrasted with experimental and omputational alulations. The empirial formula of C p is given and alulated for NACA 4 digit airfoil and MATLAB odes. Keywords: NACA 4 digit, pressure distribution formula, MATLAB odes, et. I. Introdution NACA airfoil profiles are widely used in the airraft industry for produing lift on the wing span. The geometry of airfoil ditates the airfoil performane and determines its relevane for a speifi appliation. The present analysis deals with the analysis of pressure distribution over the airfoil surfaes along with the lift and moment harateristis. They are ommonly expressed in the form of drag polar for the NACA series and represent the aerodynami performane at various flow field onditions. The Reynolds number is often used to haraterize the flow onditions and predit the behavior of airfoils at various operating flow onditions both for the visous and in visid fluids. Typially the results from the experiments serve as the simulation tool in the airraft industry for omparison with atual performane of the wing. Panel methods are modern numerial tehniques whih are quik to exeute and predit results ompared to the traditional experimental methods that are umbersome proedures and time onsuming. Apart from Panel methods, there are MATLAB odes ontains empirial formula for alulating aurate value of pressure distribution along with lift and moment. II. Naa Airfoil Geometry: Abbott and Von Doenhoff were the first derived the NACA four-digit wing setions in It was found that the thikness distribution of effiient wing setions suh as the Gottingen 398 and the Clark Y were nearly the same when the maximum thikness was set equal to the same value. For NACA four-digit series, the first digit represents the maximum amber in hundredths of hord; the seond digit represents position of maximum hamber in tenths of hord and the last two digits represents the maximum thikness in perent of hord. The thikness distribution for the NACA four-digit setions was seleted to orrespond losely to that for these earlier wing setions and is given by the following equations: y t = ±5t ε ε ε ε ε 4 Where, Where, t Maximum thikness expressed as fration of hord. ε = x/. The leading edge radius is given by r t = t 2 Thus the ordinate at any point is diretly proportional to the thikness ratio and the leading edge radius varies as the square of the thikness ratio. The equations used to define the amberline are: y = m P 2 2Pε ε2 ε P International Conferene On Progressive Researh In Applied Sienes, Engineering And Tehnology 11 Page

2 y = m 1 P 2 1 2P + 2Pε ε 2 ε P To determine the lifting harateristis using thin-aerofoil theory the amber-line slope has to be expressed as a Fourier series. Differentiating the above equation with respet to x gives, dx = d y dε 2m y dx = d dε = 2m P 2 P ε ε P = P ε ε P C (1 P) 2 p Changing the variables from ε to θ, where ε = (1 osθ)/2 gives dx = m P 2 2P 1 + osθ θ θ p dx = m (1 P) 2 2P 1 + osθ θ θ p Where, θ P is the value of orresponding to x = p. To find the pressure distribution over airfoil, using thin airfoil theory the formula for oeffiient of pressure is solved as, C p = 2 x dx π dx 1 x x Integrating the above equation into 4 equal segments, by separating the airfoil in amberwise and hordwise gives finite value of C p in leading edge and trailing edge of the airfoil. The above formula results thikness problem and gives only the results of aurate invisous inompressible flow, but in pratie the flow regime is visous inompressible flow, due to visous boundary layer separation ours in the thikened setion of the airfoil. III. Design And Calulation Of C p Using Matlab Code: 3.1. FLOWCHART MATLAB CODE: Fig.3.1Flowhart for design of NACA 4 digit airfoil using MATLAB ode. International Conferene On Progressive Researh In Applied Sienes, Engineering And Tehnology 12 Page

3 Use str2double ommand for all the input numerial in real and imaginary part, the ratio of them is 1:1. The value of ε is taken as 0 to 1 as well as onditions statements like for, if and else if ommand was purposefully enoded in the MATLAB ode. These odes generate a nested loop for amber line thikness and maximum thikness of the amber of the airfoil. The result obtained are x u, y u and x l, y l are in nested olumns. The results are plotted using Plot ommand. The NACA 4 digit airfoil of any type of numerial an easily be plotted using the above MATLAB ode. 3.2 FLOWCHART FOR PRESSURE DISTRIBUTION CALCULATION: Fig.3.2. Flowhart for alulating the pressure distribution around the airfoil using MATLAB ode. This is the empirial formula (using thin airfoil theory), the integral equation of C P was taken here for alulating the pressure distribution for any NACA 4 digit airfoil by knowing its airfoil onfiguration and the value of C P is alulated and plotted. The upper surfae shows negative C p value and the lower surfae shows positive to negative variation of C p value for various x/ distane ratio GEOMETRY OF NACA 4414: Utilizing the above MATLAB ode, generate the airfoil as shown, Fig.3.3. NACA 4414 Geometry. International Conferene On Progressive Researh In Applied Sienes, Engineering And Tehnology 13 Page

4 3.4. C p OF NACA 4414 USING MATLAB CODE: Utilizing the above MATLAB ode, it was easy to generate C p for any NACA airfoil based on thin airfoil theory appliation. We an generate the value of Cp in front upper amber and rear upper amber as well as in front lower amber and rear lower amber using the empirial relation are plotted and shown in the Fig.3.4. The only disadvantage of olden tehnique shows infinite values starting from leading edge to trailing edge of the airfoil and heuristi thikness problem but here in this alulation finite results are obtained with values of Cp minimum extends to infinite slip and value of Cp maximum is always found to be less than or equal to 1. This ode is futuristially developed and it is helpful for pre analysis part in seletion of airfoil in various design onstraint parameters. Fig.3.4. C p value for NACA 4414 airfoil 3.5. COMPARISON OF CALCULATED VALUE OF MATLAB CODE C P WITH EXPERIMENTAL VALUE: S.No. x/ MATLAB EXPERIMENTAL CODE C C P VALUE P VALUE Table 3.1. Experimental Cpvs MCODE Fig.3.5. Comparison of experimental value vs MATLAB ode value of Cp. International Conferene On Progressive Researh In Applied Sienes, Engineering And Tehnology 14 Page

5 IV. CALCULATION OF C L AND C m/4 : Based on the appliation of thin airfoil theory, the alulation of oeffiient of lift and moment oeffiient at the quarter hord for any type of 4 digit airfoil an be easily undergone utilizing the MATLAB ode to find the better result of zero degree angle of attak for seletion of airfoil in design parameters. The Fourier s series oeffiients like A 0, A 1 and A 2 an be easily estimated for NACA 4 digit airfoil using the MATLAB ode and it was very easy to estimate the value of C L and C M/4. C L = π(a 1 2A 0 ) C M /4 = π 4 (A 1 A 2 ) Where, A 0, A 1 and A 2 are Fourier s oeffiients. The values obtained from MATLAB ode are as follows: A 0 = A 1 = A 2 = C L = C M/4 = V. Future Sope Of This Work This work arries out an important feature of estimation of pressure distribution, lift and moment harateristis with theoretial approah helpful for the engineers as well as design analyst to develop the seletion of NACA 4 digit airfoil with high auray. The future work is to determine the variation of C p and C L for various angle of attak studies in the mode of optimization tehnique. There are various optimization tools in MATLAB ode, whereas tools like GA and MOGA are utilized and many where approahing the new type of airfoil design and analysis framework. For the same optimized airfoil using this work, it is easy to analyze with the help of this MATLAB ode. VI. Conlusion The results of NACA 4414 airfoil and its flow alibrations are alulated in both experimental approah as well as MATLAB ode (Theoretial Approah). The results are ompared and now it is easy to find the value of C p distribution diretly from the MATLAB ode for any NACA 4 digit airfoil and it is onluded to have the better results from the experimental one due to boundary separation of visous flow effet. Referenes [1]. H. Abbot, A von Doenhoff., Theory of Wing Setions, Inluding summary of airfoil data, Dover publiations In. New York. [2]. Haughton, Carpenter, Aerodynamis for Engineering students, 6th Edition, Elsevier publiations. [3]. Vasishtabhargava, ChKoteshwara Rao, Y.D. Dwivedi, Pressure Distribution & Aerodynami harateristis of NACA Airfoils usingcomputational Panel Method for 2D Lifting flow, International Journal of Engineering Researh ISSN: (online), (print)Volume No.6, Issue No.1, pp :18-23, Jan [4]. Charles L Ladson, Computer Program to obtain ordinates for NACA airfoils, Langley Researh Center. Hampton, Virginia. [5]. Braslow, A. L. and Knox, E. C. (1958), Simplified method for determination of ritial height distributed roughness partiles for boundary-layer transition at mah numbers from 0 to 5. NACA TN [6]. [7]. International Conferene On Progressive Researh In Applied Sienes, Engineering And Tehnology 15 Page