Vol. 06, Issue 08,August 2021 IMPACT FACTOR: 7.98 (INTERNATIONAL JOURNAL) 108 NUMERICAL SIMULATION AND OPTIMIZATION FLUID FLOW IN CENTRIFUGAL PUMP
Dheeraj Nigam
Department of Mechanical Engineering, BM College of Technology, RGPV, Bhopal Professor Purushottam Kumar Sahu
Department of Mechanical Engineering, BM College of Technology, RGPV, Bhopal Abstract - In this research finite element simulation and the optimization of the cutting process parameter had done using different cutting tool material. All 31 experiment design and analyzes into the response surface method and all this experiment were project into the simulation environment using Ansys 19.1, a the process parameter outlet pressure, Viscosity, Density and normal Speed are taken into the consideration as a input parameters.
Anova analysis as it is clear that three different method were used in these table one is linear and second one is square and the final one is 2 way interaction, in the linear model one can show the relationship between the output variable with individual input hence in our case the output is Absolute pressure for Blade, Hub and Shroud, so in the linear model the relationship between the Absolute pressure and the outlet pressure or the relation between the Absolute pressure And all the individual component, one in the second method of the square the relation between the Absolute pressure or the effect of the individual multiply by its own and shows the effect on the output or in other word the effect of the outlet pressure* outlet pressure is shown on the response Absolute pressure . Finally in third method of 2 way interaction the effect of the two individual variables simultaneously shown on the response. The value for the R-sq is 90.92% which show that there is strong relationship between the input and the output variables.
Index Terms: Ansys software, Absolute pressure (Blade) and the Absolute pressure (HUB, Ansys Fluid flow (CFX).Taguchi method, response method.
1. INTRODUCTION
The most important as well as integral part in the engineering industries is centrifugal pump. The must thing required for increasing the availability of the pump is its continuous monitoring. The best key elements in gas industry, pulp industry, paper industry, food industry, oil industry, waste water treatment plant etc are the pumps. The critical components of pump that affect its characteristics are bearing and impeller. Therefore, for analysis we have taken the defect with these components. Numbers of serious problems like abnormal noise, high vibration, and leakage are caused by the defect in the cavitation and impeller in a monoblock centrifugal pump.
A decision support tool capable of predicting failure from its symptoms as well as identifying the failure is machine conditioning monitoring system. To find out the different faults in the monoblock centrifugal pump a comparative study is done between Bayes net algorithm and naïve Bayes. From this comparative study conclusion was made that the former i.e.
Bayes net algorithm was the effective one.
This algorithm was then used in our monoblock centrifugal pump and finally we
gained the 100% accuracy from the overall classification. In condition monitoring of rotating machines acoustic emission (AE) signals and vibrations are widely used. By comparing the signals of the machine running in faulty and normal condition, fault detection is possible. Tools used as classification tools and also reported in literature are fuzzy classifier, artificial neural network (ANN) and support vector machine (SVV).
With the help of frequency domain, the most commonly used method in conventional conditional monitoring is Fast Fourier transform. Piezo electric transducer can help measuring the vibrations. In order to understand the severity threshold value is compared with the measured vibration.
To know the pattern of individual frequencies some of the conventional techniques might be used. It is said to be a very complex process. Also expertise and domain experience is demanded for it.
Certain malfunctions are been corresponded by these frequencies.
An analyst can identify the root, type of problem, location and cause as well by understanding these frequencies. However, as an alternate of conventional methods,
Vol. 06, Issue 08,August 2021 IMPACT FACTOR: 7.98 (INTERNATIONAL JOURNAL) 109 influence of the machine learning in fault
diagnosis is more common. This happens mostly due to development in algorithms and increased availability of computational resources. It finds very difficult in computing characteristic fault frequency for complex systems that involve complex systems. The Vibration signals are highly non-stationary in nature even if the characteristics frequencies are available.
Hence we can say that FFT based methods may not be well suited for continues methods instead for such situations machine learning algorithm can be considered as an alternative. To capture the vibration signals, in machine learning algorithm data acquisition system is used.
Relevant features can be classified as well as extracted using a classifier in vibration signals. Therefore, classifiers like support vectors machine, artificial neural network and also vibration signals have been acquired for purpose of classification and experimental setup respectively.
2. METHODOLOGY
2.1 Design of Experiment
Design of experiment is technique developed to understand the behavior of the mechanical system. Data are collecting from the sets of the variable, and it can qualitatively explain the undergoing phenomenon. Hence it is well known that aim of any research is design the experiment with minimum number of the experiment and with this experiment collects maximum information as much as possible. Every experiment focuses on the major number of the factor which can directly affect the results of the experiment.
And such types of factor can be detected by quantities which have major effect on the experiments outcomes. One of the most important concepts for identified such factor is to look after the experiment performed later or by theories.
Table 2.1 Response Surface Regression versus outlet pressure, viscosity,
Density, and normal speed Outlet
pressure Viscocity Densit
y Normal speed
1. 450000 0.03 1300 8.5
2. 450000 0.03 1100 8.5
3. 450000 0.03 1100 8.5
4. 750000 0.03 1100 8.5
5. 600000 0.05 1000 10.0
6. 450000 0.01 1100 8.5
7. 150000 0.03 1100 8.5
8. 450000 0.03 1100 11.5
9. 450000 0.03 1100 8.5
10. 450000 0.03 1100 8.5
11. 300000 0.05 1000 7.0
12. 450000 0.03 1100 8.5
13. 300000 0.05 1200 10.0
14. 300000 0.01 1000 7.0
15. 450000 0.03 1100 8.5
16. 600000 0.05 1200 7.0
17. 600000 0.05 1200 10.0
18. 450000 0.03 900 8.5
19. 450000 0.03 1100 8.5
20. 600000 0.01 1200 10.0
21. 300000 0.05 1000 10.0
22. 450000 0.03 1100 8.5
23. 600000 0.01 1000 10.0
24. 600000 0.01 1200 7.0
25. 300000 0.01 1200 10.0
26. 300000 0.01 1200 7.0
27. 300000 0.05 1200 7.0
28. 450000 0.03 1100 5.5
29. 300000 0.01 1000 10.0
30. 600000 0.01 1000 7.0
31. 600000 0.05 1000 7.0
2.2 Analysis of Variance
Anova analysis is the method in stats use to differentiate between two or more mean, as the name from the definition is different it name should be Analysis of means rather than analysis of the variance, but the analyze variance inference the mean. There are different methods are used of Analysis the means but why Anova analysis is best because of only one reason there are more and more complex types of problem were solved or analysis by the Anova analysis.
Second thing is the Anova analysis the most commonly used method for comparing the mean. And with the help of Anova analysis it is very easy to understand the research.
Anova analysis is also use to make relationship between the response and the predict variable or it is use to investigate the relation between the different independent variable in corresponding to their response. Since in some aspect Anova analysis is different from the regression analysis hence it can predict the qualitative variable (categorical factor), but in moist of the cases of the Minitab Anova analysis is done for both qualitative and quantitative variables.
The table below is the table for Anova analysis as it is clear that three different method were used in these table one is linear and second one is square and the final one is 2 way interaction, in the linear model one can show the relationship between the output variable with individual input hence in our case the output is Absolute pressure for Blade, Hub and
Vol. 06, Issue 08,August 2021 IMPACT FACTOR: 7.98 (INTERNATIONAL JOURNAL) 110 Shroud, so in the linear model the
relationship between the Absolute pressure and the outlet pressure or the relation between the Absolute pressure And all the individual component, one in the second method of the square the relation between the Absolute pressure or the effect of the individual multiply by its own and shows the effect on the output or in other word the effect of the outlet pressure* outlet pressure is shown on the response Absolute pressure. Finally in third method of 2 way interaction the effect of the two individual variables simultaneously shown on the response.
Example if one can know about the process undergoing is affected by the pressure maintain during the experiment, hence by knowing one can identified the minimum and the maximum value of the pressure presented in the experiment, so one can run an experiment by considering that values. In the Design of experiment can be design by the sets of factors and their levels, the value of factor and the level is decided by the operators. So many times with particular factor and the levels same experiment were repeated, these types of repeated experiment were known as replicate experiments.
Table 2.2 Analysis of Variance Table for Absolute pressure having P value and F Value
P Value : P value in the Anova analysis is the most important part and the term, P value shows the effect of the individual variable on the output , As from the American standard of the mechanical engineering P value must be less than 0.05 , if the P value for any factor is less than 0.05 than this the factor which having the more effect on the output , or this is the most responsible factor for producing the output, or the quality of the product or the value of the response is being deflected or
differentiate by changing the value of the individual variable.
Hence for the belter quality of the product or producing the better response the P value must be below 0.05.
F value: F value is the most important term to be considered during the data analysis, of value is taken into the consideration when there are more than one variable have the value of p is less than 0.05, hence the confidence interval of 95%.
Then question is which is the most responsible factor for effecting the response,
Source DF Contribution Seq SS Adj SS
Model 14 90.24 4.529E+11 4.526E+11
Linear 4 82.76 4.151E+11 4.151E+11
Outlet pressure 1 80.61 4.04444E+11 4.04444E+11
Viscosity 1 0.00 6958497 6958497
Density 1 0.06 286246801 286246801
Normal speed 1 2.08 10458166521 10458166521
Square 4 6.69 33554642867 33554642867
Outlet pressure*
Outlet pressure 1 2.38 11927608876 14182159560 Viscosity * Viscosity 1 0.37 1849721339 2524778773 Density*Density 1 0.74 3693656329 2203263808 Normal speed*
Normal speed
1 3.21 16083656329 16083656329 2-Way Interaction 6 0.84 4219142807 4219142807 Outlet
pressure*Viscosity
1 0.00 7760403 7760403
Outlet
pressure*Density
1 0.43 2180539764 2180539764
Outlet
pressure*normal speed
1 0.28 1382965938 1382965938
Viscosity*Density 1 0.01 39209513 39209513 Viscosity* normal
speed 1 0.01 70295873 70295873
Density 8 Normal
speed 1 0.11 537741316 537741316
Error 16 9.71 48739283106 48739283106
Lack-of-Fit 10 3.26 16362593318 16362593318
Pure Error 6 6.45 32376689978 32376689978
Total 30 100 5.1078E+11
Vol. 06, Issue 08,August 2021 IMPACT FACTOR: 7.98 (INTERNATIONAL JOURNAL) 111 or among all the variable having the value
of p is less than 0.05, then there is the relationship between the value of p and the value of f, less or minimum is the value of and correspondence to which higher is the value of F, and the among all the variable, the variable having minimum value of P and the maximum value of F is the factor responsible for the effecting the response.
Table 2.3 Analysis of Variance Table for Absolute pressure having P value and F
Value:
Source DF Contr
ibutio n
F
value P Value
Model 14 90.24 10.62 0.000
Linear 4 82.76 34.07 0.000
Outlet pressure 1 80.61 132.77 0.000
Viscosity 1 0.00 0.00 0.962
Density 1 0.06 0.09 0.763
Normal speed 1 2.08 3.43 0.082
Square 4 6.69 2.75 0.065
Outlet
pressure*Outlet pressure
1 2.38 4.66 0.046
Viscosity*
Viscosity 1 0.37 0.83 0.376
Density*Density 1 0.74 0.72 0.408 Normal speed *
Normal speed 1 3.21 5.28 0.035 2-Way
Interaction 6 0.84 0.23 0.960 Outlet pressure*
Viscosity 1 0.00 0.00 0.960
Outlet pressure*
Density
1 0.43 0.72 0.410 Outlet
pressure*normal speed
1 0.28 0.45 0.510
Viscosity*Densit
y 1 0.01 0.01 0.911
Viscosity*
normal speed 1 0.01 0.02 0.881 Density 8
Normal speed 1 0.11 0.18 0.680
Error 16 9.71
Lack-of-Fit 10 3.26 0.30 0.953 Pure Error 6 6.45
Total 30 100
2.3 Model Summary
Model summary is the final conclusion for the data analysis and for our results as there are three term R –sq, R-sq (Adj) , and the R-sq(pred) gives the final shape to the analysis.
R-sq: According to the research methodology the value for the R-sq is must be above 40% for predicting the good agreement between the input and the output values.
R-sq (Adj): In the corresponding to the value of the r-sq the value of R-sq (adj)
must also be above the 40% for predicting the well relationship between the input and the output variables.
R- sq (prediction): the value for the R-sq prediction is considered for the new set of experiment by using the same output. Or the similar results were used for prediction the new sets of data’s.
Table 2.4 Model summary S R-sq R-sq(adj) R-sq (pred) 55192.4 90.29% 81.78% 72.43%
Analysis of Variance for Absolute pressure (HUB): in the table below shown the Anova analysis is performed for the Absolute pressure (HUB) v/s Outlet pressure, viscosity and the Density. In the very first column the sources are given which include the types of Anova analysis, which are linear square and the 2 way interaction also the variables. In the second column the value for the degree of freedom is shown. at the top sum of the degree of freedom for all of the variable and below the degree of freedom is shown for the individual variable. In the third column the seq. ss are shown and the next to it contribution percentage of the all variable are shown. Then in the next column the value for the adj SS are given which indicate the relationship of the input and the output variable with correspondence to the value of R-sq.
Table 2.5 Regression analysis for the Absolute pressure (HUB)
Source DF Seq SS Adj SS
Model 14 4.54916E
+11
4.54916E +11
Linear 4 4.20014E
+11 4.20014E +11 Outlet pressure 1 4.15499E
+11 4.15499E +11
Viscosity 1 37466 37466
Density 1 48733913 4873391
3 Normal speed 1 80283589
22 8028358
922
Square 4 28428907
42 2842890
742 Outlet pressure*
Outlet pressure 1 13899156
719 1389915 6719 Viscosity*
Viscosity
1 31940978 98
3194097 898 Density*Density 1 19445303
47
1944530 347 Normal speed *
Normal speed 1 93905057
79 9390505
779 2-Way
Interaction 6 24730093
379 2473009 3379
Vol. 06, Issue 08,August 2021 IMPACT FACTOR: 7.98 (INTERNATIONAL JOURNAL) 112 Outlet
pressure*
Viscosity
1 1842806 1842806
Outlet pressure*
Density
1 21274233 76
2127423 376 Outlet
pressure*normal spee
1 58982400 5898240 0 Viscosity*Densit
y
1 1615441 1615441 Viscosity*
normal speed
1 21724921 2172492 1 Density 8
Normal speed
1 26142039 2
2614203 92
Error 16 67309693
572
6730969 3572 Lack-of-Fit 10 14598869
549
1459886 9549 Pure Error 6 52710824
023 5271082
4023
Total 30 5.222225
E+11
Table 2.6 Contribution of F value and P Value of BUB
Source DF Contribu tion in
%
F
value P Value
Model 14 87.11 7.72 0.000
Linear 4 81.19 25.20 0.000 Outlet
pressure
1 79.56 98.77 0.000 Viscosity 1 0.00 0.00 0.998
Density 1 0.09 0.12 0.798
Normal
speed 1 1.54 1.91 0.186
Square 4 5.44 1.69 0.202
Outlet pressure*
Outlet pressure
1 2.66 3.85 0.067
Viscosity*
Viscosity
1 0.61 0.91 0.353 Density*
Density 1 0.37 0.27 0.612
Normal speed * Normal speed
1 1.80 2.23 0.155
2-Way
Interaction 6 0.47 0.10 0.996 Outlet
pressure*
Viscosity
1 0.00 0.00 0.984
Outlet pressure*
Density
1 0.41 0.51 0.487
Outlet pressure*
normal speed
1 0.01 0.01 0.907
Viscosity*
Density 1 0.00 0.00 0.985
Viscosity*
normal speed
1 0.00 0.01 0.944
Density 8 1 0.05 0.06 0.806
Normal speed
Error 16 12.89
Lack-of-Fit 10 2.80 0.17 0.993 Pure Error 6 10.09
Total 30 100
Model Summary: Finally the regression equation is shown give the exact model equation or it will show the relationship between the input and the output variables.
Table 2.7 Model summary for Absolute pressure (HUB)
S R-sq R-sq(adj) R-sq(pred) 64860.3 87.11 % 75.83 % 70.16
3. CONCLUSION
1. From the Graph of Ansys it is clear that the main area of the cavitation exists between the suction side of the blade and Hub in many cases. A secondary area of cavitation is just behind the leading edge of the blade on the pressure side.
2. From analysis it is clear that for occurrence of cavitation, the minimum absolute pressure is equal to Saturation pressure.
3. There were many significant spikes in residual of all 31 experiments in CFX, due to the outlet pressure difference and also by Normal speed and absolute pressure hence all these factor are low enough to induce cavitation.
4. In the first case the or Anova analysis performed for the Absolute pressure (Blade), the value for the linear model is 0.000, which less 0.05 or minimum as compared to both other models, so that linear model play major roles in deflecting Absolute pressure (Blade).
5. In the linear model for the Absolute pressure (Blade), the P value of the Outlet pressure is 0.000, which is less than 0.05 or into the confidence interval, it means the Outlet Pressure in the linear model is the parameter by virtue of which the value of Absolute Pressure (Blade) are getting effected or by changing the value of the Outlet pressure the Absolute pressure (Blade) will get deflected or the quality of the product can be changed by changing the value of outlet pressure in the linear model.
Vol. 06, Issue 08,August 2021 IMPACT FACTOR: 7.98 (INTERNATIONAL JOURNAL) 113 6. In the two way interaction model
Outlet pressure * Density is parameter having the P value 0.410 which nearly to the 0.05, it means in the two way interaction model this is only parameter, by changing the value of which, Absolute Pressure (Blade) were get deflected. Or quality of the product in two way interaction can be change by changing the value of Outlet pressure * Density.
7. The value for the R-sq is 90.92%
which show that there is strong relationship between the input and the output variables.
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