SHAPE OPTIMIZATION OF SUBMERSIBLE PUMP IMPELLER DESIGN

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1 International Journal of Mechanical Engineering and Technology (IJMET) Volume 8, Issue 11, November 2017, pp , Article ID: IJMET_08_11_024 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed SHAPE OPTIMIZATION OF SUBMERSIBLE PUMP IMPELLER DESIGN Joe Ajay A Scholar, Department of Mechanical Engineering, Karunya University, Coimbatore, India S. Elizabeth Amudhini Stephen Associate Professor of Mathematics, Karunya University, Coimbatore, India ABSTRACT Submersible pumps are universally used in recent days. These pumps which are immersed in the working fluid, work on Forced vortex principle. Impeller shape optimization for a specific purpose has its effect on the H-Q curve of the pump, as stated by 2 nd law of thermodynamics. Hence this research work was focused on the improvement of duty head of the pump without changing the outlet & inlet diameter of the impeller. This optimization was done by means of minimising the head losses that occur in the impeller. Optimization was carried out using optimization algorithms like GA,SA,PS etc and the optimized values are used for design of new impeller. The optimized result was tested using CFD with common turbulence models. The resulting design was casted and experimentation was carried out. Key words: Design optimization, Shape optimization, Turbo machinery, Centrifugal pump Cite this Article: Joe Ajay A, S. Elizabeth Amudhini Stephen, Shape Optimization of Submersible Pump Impeller Design, International Journal of Mechanical Engineering and Technology 8(11), 2017, pp INTRODUCTION Three important characteristics of a pump are Pressure, friction and flow. In any pump system, there are always losses which are added to the overall performance of the system [2]. The losses that contribute to the overall performance of the pump are: Electrical, Hydraulic and Mechanical losses. Design optimization has become part and parcel of design process. Such design optimization can be carried out by minimizing the losses. In the present work head losses are minimized to get maximum head. New optimization techniques that take much less time for computation such as Genetic Algorithm, Particle swarm optimization etc., are used for design optimization [4]. The head of the pump with losses was formulated and found to be nonlinear hence these algorithms were used and evaluated in terms of time and accuracy. The result from the algorithms was studied with CFD and a comparative editor@iaeme.com

2 Shape Optimization of Submersible Pump Impeller Design experimental study of the pump was done to evaluate the existing and optimized designs. Theoretical model to predict the centrifugal pump performance when its impeller is equipped with splitters[2]. This paper compares the differences of the pump with splitter blades with the conventional pump. Hydraulic loss was evaluated to theoretically evaluate the performance of centrifugal pumps and compare with the experimental results given in [8] has found the losses associated with the performance of the pump and formulated in terms of expressions, [12] has used, artificial bee colony algorithm for optimization and shown an improvement of 3.59% in efficiency, [3] has increased the head of the pump by 6% by varying the outlet angle, [10] has used design of experiments method and optimized the head of the pump using CFD analysis. 2. METHODOLOGY The research work carried out is postulated in steps as shown in fig-1. A pump of 5HP rating was taken for study and its duty head was experimentally found to be 25m. The head formulation along with head losses were carried out at first. CFD study with 3 different turbulence models of the existing design was done next. The expression involving the head was taken to be the objective function and optimization techniques were used for optimization. The final part involves the CFD analysis of the optimized design of the impeller and experimentation for the same as in fig -1. Figure 1 Procedure 3. RESEARCH METHODOLOGY 3.1. Head Formulation From Euler's equation for turbo machinery the head of the centrifugal pump without whirl is given as [6]: H th = (1) The losses that contribute to the head of the pump are: Circulation head Loss: As described in [2], is caused by increase in relative velocity at inlet and decrease in relative velocity at the outlet of the impeller, H c = ( ) (2) editor@iaeme.com

3 Joe Ajay.A, S. Elizabeth Amudhini Stephen Inlet incidence loss: has been calculated as described in [2] H i = ( ) (3) Impeller friction loss: A s described in [8] due to surface of the impeller and vanes the there would be emery dissipation and this would be given as H f = ( )( ) (4) Where The hydraulic radius H r = ( ) ( ) Hence the net total head with losses will be:the following with respect to equations 1 to 4 H net = H th H c H i H f (5) 3.2. Experimentation In order to evaluate the performance of the pump, experimentation was carried out. The pump was immersed fully in the tank. 415V is set at the Digital Power panel (as it was industry standard voltage for testing the pump) and the pump was started. The discharge valve is completely closed at first and the discharge head is noted using the pressure gauge, this condition is called shut off condition. The discharge valve is gradually opened until its completely open and the corresponding discharge is noted using the flow meter. This type of experimentation was called as performance experimentation, the duty point was found to be m 3 /s and head of 25m. The experimental layout is as of fig-2. Figure 2 Experimental layout 3.3. CFD Analysis The simulation of the experiment for the duty point was carried out, As stated in [11] three predominant turbulence models were used to simulate the flow the result were checked with the mathematical model prepared in section 3.1. The existing impeller dimension that contribute to the head were measured: editor@iaeme.com

4 Inlet diameter(d 1 ) : 76mm Outlet diameter(d 2 ) :160.4mm Inlet blade angle(β 1 ) : 30 0 Outlet blade angle (β 2): 30 0 Shape Optimization of Submersible Pump Impeller Design Inlet impeller width (b 1 ): 18mm Outlet impeller width(b 2 ) : 10.2mm No. of vanes(z) : 6 Rotational velocity of 2810rpm with boundary conditions of the duty point was specified in the pre processing stage. The three turbulence models taken as per [11] are: K-ε K- ε EARMS Shear stress Transport model (SST) 4. OPTIMIZATION METHODS For the proposed problem, design optimization would be to performed to improve the duty point head (25m). As described in Section 3.1, since the expression for head involves nonlinear terms it would be of choice to use non-traditional optimization techniques. According to the work done in [4], it was identified to use 3 popular solvers namely: Genetic algorithm (GA) Particle swarm optimization (PSO) Pattern search (PS) 4.1. Genetic Algorithm Genetic Algorithm (GA) is a search algorithm based on the conjecture of natural selection and genetics. The algorithm is a multi-path that searches many peaks in parallel, and hence reducing the possibility of local minimum trapping. GA works with a coding of parameters instead of the parameters themselves. The coding of parameter will help the genetic operator to evolve the current state into the next state with minimum computations. GA evaluates the fitness of each string to guide its search instead of the optimization function. There is no requirement for derivatives or other auxiliary knowledge. GA explores the search space where the probability of finding improved performance is high Particle Swarm Optimization Particle swarm optimization (PSO) is a population-based stochastic approach for solving continuous and discrete optimization problems. In particle swarm optimization, simple software agents, called particles, move in the search space of an optimization problem. The position of a particle represents a candidate solution to the optimization problem at hand. Each particle searches for better positions in the search space by changing its velocity according to rules originally inspired by behavioral models of bird flocking Pattern Search Pattern search [5] finds a local minimum of an objective function by the following method, called polling. In this description, words describing pattern search quantities are in bold. The search starts at an initial point, which is taken as the current point in the first step: editor@iaeme.com

5 Joe Ajay.A, S. Elizabeth Amudhini Stephen 1. Generate a pattern of points, typically plus and minus the coordinate directions, times a mesh size, and center this pattern on the current point. 2. Evaluate the objective function at every point in the pattern. 3. If the minimum objective in the pattern is lower than the value at the current point, then the poll is successful, and the following happens: 3a. the minimum point found becomes the current point. 3b. the mesh size is doubled. 3c. the algorithm proceeds to Step If the poll is not successful, then the following happens: 4a. the mesh size is halved. 4b. if the mesh size is below a threshold, the iterations stop. 4c. Otherwise, the current point is retained, and the algorithm proceeds at Step RESULTS & DISCUSSION 5.1. Existing Design Performance Evaluation As described in section 3.2 experiments was conducted on existing design and the head losses were estimated theoretically, with the dimensions of the impeller measured. Experimental Discharge (m 3 /s) Theoretical Head (m) - 1- Table 1 Theoretical head developed by the impeller Circulation head loss (m) -2- Inlet Incident loss (m) -3- Frictional head loss (m) -4- Net Head (m) = The result of the experimental test is postulated below and it can be noted that the duty point had delivery of m3/s and the duty delivery head of 25m. Table 2 Existing impeller performance test Discharge (m 3 /s) Experimental Head (m) Water Power (W) Experimental Power (W) Efficiency (%) It can be seen that the circulation head contributes to the maximum; this is due to the fact that the speed is taken is constant [10]. Inlet incident loss contributes less, this is because of the fact that, the whirl velocity involved in the loss (1.3), is dependent on the discharge and the same is applicable for the frictional loss (1.4) editor@iaeme.com

6 Shape Optimization of Submersible Pump Impeller Design Performance Chart Dischatge (m3/s) Experimental Head (m) Efficiency Figure 3 Performance Chart of the existing design From the fig-3, it is evident that the pump has an efficiency of 26% at duty point. The best efficiency point (BEP) has the discharge of m3/s and head of 20m, but as the industry sells the pump at m3/s and 25m head, this point was taken as duty point Simulation of Existing Design Studies suggest few of the common turbulence models to be used for CFD analysis of pump [11].. Hence common available turbulence models were chosen and used to simulate the duty point of the existing design of the impeller Table 3 Turbulence model comparison Turbulence model Head (m) K-ε K- ε EARMS SST 38.6 From table-5.3 we find that the K-ε model is much closer to the net theoretical head (38.29m), hence it would be convenient to use the same for simulation purpose of the optimized model. Figure 4 Simulation of existing design From fig-4, it is evident that the head has converged to the value of 38.22m at the outlet Optimization Computation The design optimization described is coded with MATLAB in the described algorithms were used for optimization. Twenty trails were performed as described in [4] and the average for each parameter was taken as the design parameters from the each solver. The net head was evaluated theoretically for each parameter from the solvers editor@iaeme.com

7 b1 (m) b2(m) B1(deg) B2(deg) Z Joe Ajay.A, S. Elizabeth Amudhini Stephen Table 4 GA result table Trial.No b 1 (m) b 2 (m) B 1 (deg) B 2 (deg) Z Trails Figure 5 Performance of Genetic algorithm From the fig-5 we see that there are not much variations in inlet width and outlet angle parameter but No. of vanes, outlet width and inlet angle show considerable variations during trail runs. Table 5 PS result table Trial. No b 1 (m) b 2 (m) B 1 (deg) B 2 (deg) Z editor@iaeme.com

8 b1(m) Z Shape Optimization of Submersible Pump Impeller Design b2(m) B1(deg) B2(deg) Trails Figure 6 Performance of Pattern Search algorithm From Fig 6, it is evident that there has not been any change in the existing design that the Pattern Search solver identifies and there has not been any change in the head of the pump. Table 6 PSO result table Trial. No b 1 (m) b 2 (m) B 1 (deg) B 2 (deg) Z editor@iaeme.com

9 b1(m) B1(deg) B2(deg) Joe Ajay.A, S. Elizabeth Amudhini Stephen Trails Figure 7 Performance of Particle swarm Optimization algorithm From Fig-7, it is identified that there is not been much variations in any of the parameter and the solver solves more evenly than that of GA and PS, The head for these parameters the head of the pump increases significantly. Method Inlet width-b 1 (m) Table 7 Optimized parameters Outlet width-b 2 (m) Inlet angle-β 1 (deg) Outlet angle-β 2 (deg) No.of blades-z Head (m) Existing Design GA PS PSO From table 5.7 it is identified that the maximum head of 29.37m is contributed by PSO. Hence these design parameters are taken for simulation purposes Theoretical characteristics of optimized design: The design changes contributed by PSO were used to calculate the theoretical head developed along with the loss estimation. Table 8 Theoretical head of optimized design Discharge (m 3 /s) Theoretical Head (m) Circulation head (m) Inlet Incident Loss (m) Frictional head (m) Net Head (m) editor@iaeme.com

10 Head (m) Head (m) Head (m) Shape Optimization of Submersible Pump Impeller Design Circulation Head Loss Discharge (m3/s) Existing Circulatoin head (m) Optimized Circulatoin head (m) Figure 8 Circulation head loss comparison From fig-8, indicates that the circulation head for the pump has decreased by 22.17%. The circulation head loss remains constant due to the fact that the speed remains constant [1]. The decrease is due to the increase in the slip developed in the flow at outlet and independent of the discharge. Inlet Incident Loss Discharge (m3/s) Existing Inlet Incident Loss (m) Optimized Inlet Incident Loss (m) Figure 9 Inlet incident loss comparison From the fig-9, indicates a decrease of 32.67% in the inlet incident loss at duty point. This is contributed by the increase in inlet width of the impeller, by the fact that the outlet whirl velocity is dependent on the discharge and so it is observed as in Eq Frictional Head Loss Discharge (m3/s) Existing Frictional head (m) Optimized Frictional head (m) Figure 10 Frictional head loss comparison From the fig-10, it is identified an increase by 1.11% in frictional loss which is contributed by decrement in the outlet angle. This value of increase is not significant for all the discharge editor@iaeme.com

11 Efficiency (%) Joe Ajay.A, S. Elizabeth Amudhini Stephen 5.5. Simulation of the Optimized Design Finally the optimized design was simulated to find its effectiveness compared to the existing design. This design was tested as in the section 5.3; k-epsilon turbulence model was used to simulate the model and it was found that there is 2.36% improvement in the head. Figure 11 Simulated result of optimized impeller This improvement is mainly contributed by increased number of vanes in other words the increased slip of the flow at the impeller outlet, head has increased Experimentation of the Optimized Design After simulation the design was fabricated with grey cast iron and it was tested according to the industry specified voltage of 415V. The Discharge valve was fully closed to measure the shutoff condition and fully opened for 'full open condition'. The discharge was noted by varying the head in terms of 5m, the results are tabulated in table-5.9. Table 9 Optimized impeller performance by experimentation Discharge (m 3 Input Power Water Power /s) Experimental head(m) (W) (W) Efficiency (%) Efficiency Discharge (m3/s) Optimized Efficency (%) Existing Efficiency (%) Figure 12 Efficiency comparison From the Fig-12, it is clear that the efficiency of the pump at duty point has significantly increased by 20.42%. This increase was compensated at the full open condition of the pump editor@iaeme.com

12 Head (m) Shape Optimization of Submersible Pump Impeller Design by decrease of 33.4% according to 2 nd law of thermodynamics, but as the pump is not operated at full open condition, this could be neglected H Vs Q Curve Discharge (L/s) Experimental Head (m) Optimized Head (m) Figure 13 Head Vs discharge curve comparison From Fig-13, it is clear that there has been significant increase in head and at duty point the increase is 12.56%. But this increase is compensated at the full open condition by a discharge of m 3 /s, by 2 nd law of thermodynamics Optimized Performance Discharge (m3/s) Optimized Efficency (%) Optimized Experimental head(m) Figure 14 Performance graph of optimized impeller Fig-14 was constructed according to [1]. It shows optimized head with increased discharge by 12.56%. As the discharge increases the efficiency calculated by Eq-7 remains almost a straight line in the range of 26% to 31%. The head exhibits almost linear characteristics. The work is wrapped up by comparing the improvement in the performance and the changes in the parameters. It could be shown in table-5.10 that the changes in the parameters are within the 10% variation [12]. All the means of evaluating the performance has shown the improvement and is listed in table Table 10 Design parameters of the impeller Parameters Existing dimension Optimized dimension Inlet width (m) Outlet width (m) Inlet angle (deg) Outlet angle (deg) No.of blades editor@iaeme.com

13 Joe Ajay.A, S. Elizabeth Amudhini Stephen Table 11 Optimized Head Method Percentage improvement (%) Theoretical Simulation CONCLUSIONS A commercially available pump with duty point delivery head of 25m and discharge of m 3 /s was desired to improve the delivery head of the pump. In order to optimize the head, the head losses within the impeller were identified and the design parameters of impeller that contribute to these losses were measured and used to calculate the head of the pump. The existing performance of the pump was evaluated by experimentation and the H-Q characteristics were determined. Once the design was optimized, to check the optimization CFD simulation was performed on the existing design for choosing the turbulence model. As suggested by [11] different turbulence models were used to simulated the duty point condition and K-ε model proved close to the net theoretical head, hence it was chosen to evaluate the optimized design. The mathematical model developed for the head (with losses) was used as objective function and design parameters were given variation of 10% from the existing dimensions. Popular algorithms for design optimization as specified in [4] were used, include: Genetic algorithm (GA), Particle swarm optimization (PSO), Pattern search algorithm (PS). The optimization code was made to run for 20 trails as in [4] and the average were taken as the optimized parameters. It was observed that PSO algorithm contributed maximum head by 17.48% improvement. The changes in losses were: Circulation loss decreased by: 22.17%; Inlet incident loss decreased by 32.67% ; Frictional loss increased by 1.11%. The increase in frictional loss is due to the fact that there is decrease in the outlet angle. As a pre-final step in the design process simulation of the duty point was done for the pump with K- ε model and it was found that there was an improvement by 2.36% in the head. The optimized impeller design was then casted and experimentation as described in [1] were conducted and it was found that there was an improvement of 12.56% in delivery head of the pump at duty point and efficiency of the pump at duty point increased by 20.42%. Figure 15 Existing impeller editor@iaeme.com

14 Shape Optimization of Submersible Pump Impeller Design Figure 16 Optimized impeller 7. NOMENCLATURE H th - Theoretical head (m) H c - Circulation head loss (m) H i - Inlet incident loss (m) H f - Frictional head loss (m) H net - Net theoretical head loss (m) Q-Discharge (m 3 /s) b 2 - Width at exit (m) b 1 - Width at entrance (m) β 2 - Blade angle at exit ( 0 ) β 1 - Blade angle at entrance ( 0 ) D 2 - Impeller outer diameter (m) D 1 - Impeller inlet diameter (m) Slip µ= Inlet tangential velocity U 1 = Outlet tangential velocity U 2 = Figure 17 Existing and optimized impeller cut section editor@iaeme.com

15 Joe Ajay.A, S. Elizabeth Amudhini Stephen Inlet whirl velocity C 1 = Outlet whirl velocity C 2 = Inlet whirl velocity at blade exit C u1 = µ* + Outlet whirl velocity at blade exit C u2 = µ* + REFERENCES [1] Austin.J.L, Church.H, "Centrifugal pumps and Blowers," in Centrifugal pumps and Blowers. Alahabad, India: Metropolitan Book Co, Pvt, Ltd, 1973, ch. 10, p [2] Berge Djebedjian, "Theoretical model to predict the performance of centrifugal pump equipped with splitter blades," Mansoura Engineering Journal, pp. M50-M70, [3] Bacharoudis.E.C, Filios.A.E, Mentzos.M.D, Margaris.D.P, "Parametric Study of a Centrifugal Pump Impeller by Varying the Outlet Blade Angle," The Open Mechanical Engineering Journal, pp , [4] Elizabeth Amudhini Stephen.S, Mercy Shanthi.R., Joe Ajay.A, "Optimization of thermal comfort in office buildings using non-traditional optimization techniques," International Journal of Mathematics and Computer Applications Research (IJMCAR), vol. 3, no. 1, pp , Mar [5] Elizabeth Amudhini Stephen.S, Joe Ajay.A, Review of ten non-traditional optimization techniques, International Journal of Mathematics and Computer Applications Research (IJMCAR) ISSN , Volume 5(2013), Issue 1,Page [6] Igor J. Karassik, Joseph P. Messina, Paul Cooper, Charles C. Heald, " Pump handbook," 2nd ed. McGraw-Hill Book Company. [7] Johann friedrich Guilich, Centrifugal pumps. Springer, [8] Khin Cho Thin, Mya Mya Khaing, Khin Maung Aye, "Design and Performance Analysis of Centrifugal Pump," World Academy of Science, Engineering and Technology, pp , [9] Kim.J.H,Oh.K.T, Pyun.K.B, Kim.C.K, Choi.Y.S, Yoon.J.Y, "Design optimization of a centrifugal pump impeller and volute using computational fluid dynamics," in 26th IAHR Symposium on Hydraulic Machinery and Systems, [10] Ling Zhou,Weidong Shi, Suquing Wu, "Performance Optimization in a Centrifugal Pump Impeller by Orthogonal Experiment and Numerical Simulation," Advances in Mechanical Engineering, [11] Liu.H.L,Liu.M.M,Dong.L,Ren.Y,Du.H, "Effects of computational grids and turbulence models on numerical simulation of centrifugal pump with CFD," in, 2012, p. 26 th IAHR Symosium on Hydraulic Machinery and Systems. [12] Shahram Derakhshan,Maryam Pourmahdavi, Ehsan Abdolahnejad, Amin Reihani, Ashkan Ojaghi, "Numerical shape optimization of a centrifugal pump impeller using artificial bee colony algorithm," Computers & Fluids, pp , [13] Suthep Kaewnai,Manuspong Chamaoot, Somchai Wongwises, "Predicting performance of radial flow type impeller of centrifugal pump using CFD," Journal of Mechanical Science and Technology, p. 1620~1627, 2009.(13) [14] Vasilis Grapsas,Fotis stamatelos,john Anagnostopoulos,Dimitris papantonis, "Numerical Study and Optimal Blade Design of a Centrifugal Pump by Evolutionary Algorithms," editor@iaeme.com

16 Shape Optimization of Submersible Pump Impeller Design Knowledge-Based Intelligent Information and Engineering Systems,Springer-Verlag Berlin Heidelberg, p , 2008.(15) [15] ZAYA.J, "Aerodynamic Optimization of Ground Vehicles with the Use of Fluent s Adjoint Solver," 2013.(11) [16] Zhuang.B,Luo.X,Zhang.Y,Wang.X,Xu.H,Nishi.M, "Design optimization for a shaft-less double suction mini turbo pump," in 25th IAHR Symposium on Hydraulic Machinery and Systems, 2010.(12) [17] Shyam Narayan Shukla, Ruchi Khare and Vishnu Prasad, Performance Evaluation of Turbulence Models for Flow Simulation of Double Suction Centrifugal Pump. International Journal of Civil Engineering and Technology, 7(6), 2016, pp [18] A. Joe Ajay and S. Elizabeth Amudhini Stephen. Design and Optimization of Submersible Pump Impeller. International Journal of Mechanical Engineering and Technology, 8(2), 2017, pp [19] S. Sivakumar and K. Siddappa Naidu. Design of Wind Solar and Pumped - Storage Hybrid Power Supply System. International Journal of Electrical Engineering & Technology, 8(4), 2017, pp editor@iaeme.com