# Durability of Centrifugal Pump Impeller Blades Exposed to Corrosive–Erosive Wear

Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)

## Abstract

The researchers have developed a theory of the corrosive–erosive wear applicable to the plates and shells of centrifugal or axial pump impellers; the theory takes into consideration the stress state and the stationary temperature field. Omitting the intermediate calculations, we present a system of differential equations in Marguerre-type partial derivatives on a normal deflection w and a stress function of the eighth order, which describe the stress state of a variable-thickness blade in the context of temperature effects. In this research, the blade thickness change function is set as cubic splines. Analytical solution of the equation system with the boundary conditions is based on using the Dorodnitsyn’s integral ratios method. Pursuant to the method, write the original equation system as a divergent system. Limited to binomial approximation and also choosing power polynomials and their derivatives as weights, apply the integral ratios method to the original system of equations to obtain a system of ordinary differential equations (8n order) with variable coefficients. The boundary value problem is solved by the modified method of successive approximations, developed by Prof. V. A. Pukhliy and published by him in the academic press.

## Keywords

Durability Centrifugal pumps Impeller blades Corrosive–erosive wear

## References

1. 1.
Kornishin MS, Karpunin VG, Kleshchyov SI (1975) Computation of plates and shells in an overall corrosion context. In: Proceedings of the X All-Soviet conference of shell and plate theory, Tbilisi, pp 17–24Google Scholar
2. 2.
Ovchinnikov NG, Sabitov KA (1986) Comparative study into the extrapolatory capacities of some corrosive-wear models, exemplified by computing a cylindrical shell. Univ Bull Constru Archit 1:42–45Google Scholar
3. 3.
Mikhailov IA, Pukhly VA (1981) Method and algorithm to compute the erosive wear of impeller blades in radial dust-air superchargers. In: Abstracts of the VI All-Soviet research and engineering conference on compressor construction, Leningrad, p 1981Google Scholar
4. 4.
Marguerre K (1939) Zur theorie der gekrümmten Platte großer Formänderung. Jahrbuch 1939 der deutschen Luftfahrforschung. Bd I, pp 413–418Google Scholar
5. 5.
Ahlberg J, Nielson E, Walsh J (1972) The theory of splines and their applications. Mir, Moscow, p 318Google Scholar
6. 6.
Dorodnitsyn AA (1960) One method to solve equations of laminar boundary layer. J Appl Math Technol Phys 3:111–118Google Scholar
7. 7.
Courant R, Hilbert D (1953) Methods of mathematical physics, vol I. Gostekhizdat, Moscow
8. 8.
Luke VL (1975) Mathematical functions and their approximations. Academic Press. Inc., New York, p 608Google Scholar
9. 9.
Pukhliy VV (1978) Method for analytical solution of 2D boundary-value problems for elliptic-equation systems. J Comput Math Math Phys 18(5):1275–1282Google Scholar
10. 10.
Pukhliy VA (1979) One approach to solve boundary-value problems of mathematical physics. Differ Eqn 15(11):2039–2043Google Scholar
11. 11.
Pukhliy VA (2015) Solving initial-boundary value problems of mathematical physics by modified method of successive approximations. Rev Appl Industriam Math 22(4):493–495Google Scholar
12. 12.
Pukhliy VA (2016) Accelerating the convergence of solutions when using modified method of successive approximations. Rev Appl Industriam Math 23(4):17–20Google Scholar
13. 13.
Lanczos C (1961) Practical methods of applied analysis. Fizmatgiz, Moscow, p 524Google Scholar
14. 14.
Pukhliy VA (1983) Analytical method to solve boundary-value shell theory problems. In: Proceedings of the XIII All-Sovient conference on plates and shells theory. Part IV. TPU Publishing, Tallinn, p 101–107Google Scholar
15. 15.
Pukhliy VA (1986) Cylindrical three-layer panel oblique-angled in plane: modified method of successive approximations to solve its bending problem. Appl Mech 22(10):62–67Google Scholar