OPTIMIZATION OF AXIAL FLOW COMPRESSOR BLADES USING GENETIC ALGORITHM AND COMPUTATIONAL FLUID DYNAMIC

International Journal of Mechanical and Production Engineering Research and Development (IJMPERD) ISSN (P): 2249–6890; ISSN (E): 2249–8001 Vol. 10, Issue 3, Jun 2020, 2063-2072 © TJPR Pvt. Ltd.

OPTIMIZATION OF AXIAL FLOW COMPRESSOR BLADES USING GENETIC ALGORITHM AND COMPUTATIONAL FLUID DYNAMICS Dr. NILESH P SALUNKE1 & Dr. S. A. CHANNIWALA2 1

Principal, Shri Vile Parle Kelavni Mandal's Institute of Technology, Dhule, Maharashtra, India 2

Professor, Mechanical Engineering Department, SVNIT, Surat, India

ABSTRACT Optimization of airfoil blade section using evolutionary algorithm coupled with numerical methods of analysis is becoming a trend nowadays. A new MATLAB code is developed to realize the optimization of high pressure ratio axial flow compressor blades using genetic algorithm coupled with the Computation Fluid Dynamics (CFD) package. Use of Bezier-PARSEC parameterization is made to parameterize the base CDA airfoil. MATLAB code successfully integrates and runs the optimization process and optimum results thus obtained shows a good agreement with experimental results.

KEYWORDS: CFD; MATLAB; Bezier-PARSEC Parameterization & CDA

1. AIRFOIL PARAMETERIZATION Bezier–PARSEC Parameterization [1] This technique was introduced by Derksen and Rogalsky. An airfoil is represented by of some qualitative aerodynamic and mathematical parameters. PARSEC parameters are used to define airfoil coordinates and Bezier curves join those

Original Article

Received: May 29, 2020; Accepted: Jun 19, 2020; Published: Jul 04, 2020; Paper Id.: IJMPERDJUN2020194

coordinates.

Bezier Curves [2] A degree n Bezier curve is defined by n +1 vertex points of a polygon. These vertices are known as control points of the nth order Bezier curve. The general expression for an nth order Bezier curve is as follow.

Where Pi =ith control point The parameter u is dimensionless and ranges between 0 and 1.

The following method is developed to optimize the airfoil making use of parameterization and genetic algorithm coupled with computational fluid dynamics. The method is divided into following steps.

Step 1: The Blade is Split into its Respective Thickness Distribution and Camber Distribution For this, camber and thickness distribution at the same chord wise position of the blade should be available. A polynomial function is fitted for the given camber line and slope at given camber chord locations are calculated.

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The upper coordinate line is also fitted with a polynomial

and the thickness distribution coordinates are calculated by the following relation.

The figure 1 & 2 show a typical compressor blade. The camber is maximum at the 50% of the chord. The thickness distribution is almost a flat surface controlled diffusion airfoil.

Figure 1: Camber Line of Base Airfoil.

Figure 2: Thickness Distribution of Base Airfoil.

Each of two obtained curves is divided into two parts. Each from leading edge to maximum camber/thickness and from max camber/thickness to trailing edge. Curve fitting of these four curves is then separately done and a polynomial equation is obtained for each of them using MATLAB. The leading edge thickness distribution curve showed little deviations near leading edge while other three curves seemed to perfectly superimpose the original ones.

Step 2: Fitting a Bezier curve and Calculation of the Control Points Next step is to determine the control points of Bezier curves that will map with the curve fitted polynomial curves. Genetic Algorithm [3] of MATLAB is used to find the most optimum value for the unknown Bezier curves. The objective function is simply the difference between the actual airfoil shape and the Bezier generated airfoil shape.

MATLAB’s Genetic Algorithm (GA) tool box has been used to minimize the SSE for each Bezier curve. The objective function is to be minimized with two variables viz. b0 and b2. Using the GA tool, the optimized set of control point is calculated. Similarly, other unknown parameters for rest of the three curves were found out.

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Figure 3: Genetic Algorithm Convergence.

The figure 4 shows the comparison between Bezier camber line and actual camber line. Similarly, the figure 5 compares the Bezier thickness line and actual thickness line.

Figure 4: Bezier Curve Fitted Camber Line.

Figure 5: Bezier Curve Fitted Thickness Distribution.

Using the PARSEC parameters, unknown Bezier control points b0, b2, b8, b15 and b17 are found out.

Step 3: Generation of Airfoil from these Parameters

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If the camber and thickness curves are available with the same x coordinates, the airfoil shape can be determined. For the upper surface, the thickness curve is added to the camber curve. For the lower surface, the thickness curve is subtracted from the camber curve.

A MATLAB code generates the airfoil from the above mentioned parameters. A comparison of the original airfoil and the generated airfoil is shown in the following diagram.

Figure 6: Comparison between Original and Parameterized Airfoil.

The generated airfoil strongly agrees with the original profile. The little difference seen between the two airfoils is due to the poor curve fitting of the thickness distribution near the leading edge. The Genetic algorithm is used to fine tune the Bezier curve parameters. The airfoil parameterization is successfully done and we could now finally reperesent the airfoil with the help of a set of Bezier control points instead of an array of airfoil coordinates.

2. BLADE OPTIMIZATION The non-dimensional pressure loss coefficient determines the aerodynamic properties of the blade section. It is defined as

where P’oe is the isentropic total pressure, Poe is mass averaged total pressure at the exit, Poe is the stagnation pressure at the inlet and P1 is the static pressure at the inlet of the cascade. In order to achieve higher pressure ratios across the cascade we need to maximize the conversion of dynamic pressure into static pressure and minimize the losses occurring in the cascade.

3. OBJECTIVE FUNCTION Since loss coefficient is proportional to drag coefficient, the drag coefficient is set as the objective function.

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Figure 7: Flow Chart for Optimization.

This way it completes one operation. The blade parameters are now varied using the Genetic algorithm and a new blade profile is generated and the process is repeated until a converged solution is obtained i.e the objective function (drag) is minimized to a local minimum. The airfoil and its pressure loss coefficient value are saved in the memory of Matlab. The procedure is repeated for every candidate airfoil in each generation.

Figure 8: Working of the Program.

5. CASCADE MODELLING AND MESHING Airfoil is divided into four parts namely upper edge, lower edge, leading edge and trailing edge. In order to capture the flow parameters at leading and trailing edges, which are critical portions, a finer mesh is created near these points. Airfoil is specified as wall type boundary. Left and right edges are specified as inlet and outlet respectively. All other boundaries are specified as periodic ones. [8] The Mesh is shown in figure 9.

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Figure 9: Mesh Around the Airfoil.

RESULTS The optimization of CDA airfoil for pressure ratios 1.2 is carried out using a cyclic process which combines the genetic algorithm, Gambit and FLUENT. The performance of base airfoil i.e. CDA airfoil is compared with the optimized airfoils.

The table 1 below gives a comparison between the CDA and optimized airfoils.

It is observed from table 1 that optimized airfoils for corresponding pressure ratios offer less pressure loss coefficient than that offered by the base airfoil. The pressure distribution and Mach number distribution over optimized airfoil for pressure ratio 1.2 are shown in following figures. From figure 10 a-e. It is observed that the optimized aero foil exhibits good agreement with characteristics of CDA. The optimized airfoil showed close CDA characteristics which confirm its good behavior at higher pressure ratios. The suction peak is low at higher pressure ratios as expected and uniform diffusion is present till trailing edge. The pressure on the lower surface increases uniformly till trailing edge.

Table 1: Pressure Loss Coefficients Comparison CDA Base Airfoil Optimized Airfoils Pressure Ratio Pressure Loss Coefficient Pressure Loss Coefficient 1.2 0.022034 0.021898

(a)

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(b)

(c)

(d)

d Figure 10: Airfoil and its Mach No Distribution & Contours, Static Pressure and its Contours Over Optimized Airfoil for PR 1.1 from (a-e)

6. EXPERIMENTAL VALIDATION www.tjprc.org

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For validation of algorithm a continuous blow down type cascade wind tunnel was designed and fabricated as shown in Plate 1 The various parts are test section, axial flow fan, convergent portion, screens, multilimbed manometer, Prandtl type pitot tube, frequency detector etc. The specification of the wind tunnel and test section is summarizing in table.

Table 2: Specification of Wind Tunnel Sl. No. Parameter Dimension 1 Total length of wind tunnel 3m 2 Type of fan used Axial Fan 3 Maximum height 2m 4 Cross section of test section 50cmx15cm 5 Length of test section 75cm

Figure 10.a: Plate1. Cascade Wind Tunnel Set-up.

7. RESULTS The optimization code needs to be validated but the experimental setup is not providing required Mach number so experiments are conducted for validation with a low pressure ratio airfoil of 1.02 PR for this, an optimized blade section is designed for pressure ratio of 1.02 and is tested for validation in wind tunnel.. Experimental results shows similar trend of CFD results and there by qualitatively validate the present approach of optimization. The Cp distribution results on 1.02 pressure ratio blade profile indicates a qualitative match between analytical results and experimental results which concludes that the optimization has been successful and code is validated. The optimized airfoil showed close CDA characteristics which confirm its good behaviour at higher pressure ratios.

The Figure 11 represents the experimental and CFD results for the static pressure distribution coefficient (Cp) over the optimized 1.02 pressure ratio blade profile for both upper and lower surfaces of the optimized cascade profile.

From the graph obtained it is observe that the experimental results are showing the same trend as the CFD results.

The static pressure distribution obtained by CFD seems to be more uniform compared to experimental results. The upper surface produces suction pressure and lower surface produce positive pressure due to which lift is produced.

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Figure 11: Comparison of Computational and Experimental Cp Distribution on 1.02 Pressure Ratio Blade.

8. CONCLUSIONS A method of airfoil optimization is using parameterization and genetic algorithm coupled with computational fluid dynamics has been shown successfully. MATLAB code is used to implement the Bezier-PARSEC parameterization technique. The parameterized blade shows excellent agreement with the actual blade. This work paves the way for further enhancement i.e. towards the three dimensional parameterization.

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3. Prasanth, V., and S. Anil Lal. "Bezier Parameterization of an airfoil using genetic algorithm." (2010).

4. Ava Shahrokhi, Alireza Jahangirian, “Airfoil shape 5. Pittala, Suresh, and T. Diriba. "Computational Fluid Dynamics Analysis of Impeller Design For A Pump." International Journal of Mechanical Engineering (IJME) 5.4.

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7. GAMBIT User’s Guide Copyright 2007 by The ANSYS, Inc. 8. FLUENT User’s Guide Copyright 2007 by The ANSYS, Inc. 9. Singh, R. Ragoth, and M. Nataraj. "Parametric Study And Optimization Of Centrifugal Pump Impeller By Varying The Design Parameter Using Computational Fluid Dynamics: Part-I." Journal of Mechanical and Production Engineering (JMPE) 2.2

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