Two phase flow arising in hydraulics

Ivan Straškraba

Applications of Mathematics (2015)

  • Volume: 60, Issue: 1, page 21-33
  • ISSN: 0862-7940

Abstract

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The aim of this paper is to proceed in the study of the system which will be specified below. The system concerns fluid flow in a simple hydraulic system consisting of a pipe with generator on one side and a valve or some more complicated hydraulic elements on the other end of the pipe. The purpose of the research is a rigorous mathematical analysis of the corresponding linearized system. Here, we analyze the linearized problem near the fixed steady state which already have been explicitly described. The theory of mixed linear partial differential systems and other tools are applied to derive as explicit form of the solution as possible.

How to cite

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Straškraba, Ivan. "Two phase flow arising in hydraulics." Applications of Mathematics 60.1 (2015): 21-33. <http://eudml.org/doc/262169>.

@article{Straškraba2015,
abstract = {The aim of this paper is to proceed in the study of the system which will be specified below. The system concerns fluid flow in a simple hydraulic system consisting of a pipe with generator on one side and a valve or some more complicated hydraulic elements on the other end of the pipe. The purpose of the research is a rigorous mathematical analysis of the corresponding linearized system. Here, we analyze the linearized problem near the fixed steady state which already have been explicitly described. The theory of mixed linear partial differential systems and other tools are applied to derive as explicit form of the solution as possible.},
author = {Straškraba, Ivan},
journal = {Applications of Mathematics},
keywords = {compressible fluid; Navier-Stokes equations; hydraulic systems; compressible fluid; Navier-Stokes equations; hydraulic systems},
language = {eng},
number = {1},
pages = {21-33},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Two phase flow arising in hydraulics},
url = {http://eudml.org/doc/262169},
volume = {60},
year = {2015},
}

TY - JOUR
AU - Straškraba, Ivan
TI - Two phase flow arising in hydraulics
JO - Applications of Mathematics
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 1
SP - 21
EP - 33
AB - The aim of this paper is to proceed in the study of the system which will be specified below. The system concerns fluid flow in a simple hydraulic system consisting of a pipe with generator on one side and a valve or some more complicated hydraulic elements on the other end of the pipe. The purpose of the research is a rigorous mathematical analysis of the corresponding linearized system. Here, we analyze the linearized problem near the fixed steady state which already have been explicitly described. The theory of mixed linear partial differential systems and other tools are applied to derive as explicit form of the solution as possible.
LA - eng
KW - compressible fluid; Navier-Stokes equations; hydraulic systems; compressible fluid; Navier-Stokes equations; hydraulic systems
UR - http://eudml.org/doc/262169
ER -

References

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  1. Čarnyj, I. A., Unsteady Motion of Real Fluid in Pipes, Nedra, Moscow (1975). (1975) 
  2. Evans, L. C., Entropy and Partial Differential Equations, Department of Mathematics, UC Berkeley (2008). (2008) MR2597943
  3. Glikson, A., Some case of non-uniform and non-steady state of gas-mixture, Rend. Mat., VI. Ser. 3 451-479 (1970). (1970) 
  4. Landau, L. D., Akhiezer, A. I., Lifshitz, E. M., General Physics Mechanics and Molecular Physics, Nauka, Moscow (1969). (1969) 
  5. Rajagopal, K. R., Tao, L., Mechanics of Mixtures, Series on Advances in Mathematics for Applied Sciences 35 World Scientific, Singapore (1995). (1995) Zbl0941.74500MR1370661
  6. Ruzicka, M. C., 10.1016/S0301-9322(99)00078-6, Int. J. Multiphase Flow 26 (2000), 1141-1181. (2000) Zbl1137.76730DOI10.1016/S0301-9322(99)00078-6
  7. Šklíba, J., Straškraba, I., Štengl, M., Extended mathematical model of safety hydraulic circuit, Report SVÚSS Běchovice, Czech Republic registered as: SVÚSS 88-03022, December 1988. 
  8. Soo, S. L., Fluid Dynamics of Multiphase Systems, Blaisdell Publishing Company. A Division of Ginn and Company Waltham, Ma.-Toronto-London (1967). (1967) Zbl0173.52901
  9. Straškraba, I., Fully nonlinear two-phase flow, Acta Technica 3 (2014), 215-220. (2014) MR3243606
  10. Straškraba, I., Vitásek, E., The flow of a liquid with cavitation, J. Concr. Appl. Math. 8 (2010), 668-681. (2010) MR2641512
  11. Wallis, G. B., One-Dimensional Two Phase Flows, McGraw-Hill, New York (1969). (1969) 

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