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Academic metadata
PhD thesis
Prirodnomatematičke nauke

Univerzitet u Nišu
Mašinski fakultet
Katedra za hidroenergetiku
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DETERMINATION OF AVERAGED AXISYMMETRIC FLOW IN HYDRAULIC TURBOMACHINERY RUNNER
Niš : [J.B. BogdanovićJovanović]
PDF/A (295 listova)
Biografija: list [264]
Umnoženo za odbranu.
Univerzitet u Nišu, Mašinski fakultet, 2014.
Abstract.
Bibliografija: listovi 256263.
Theoretical and Applied fluid mechanics.
Hydraulic turbomachines and low pressure fans.
Milenković, Dragica (mentor)
Babić, Milun, 1950 (član komisije)
Nikodijević, Dragica (član komisije)
The first chapter of the paper is introductory unfolding, where the task of
hydrodynamic calculation is presented, as well as the schema of flow in the flowthrough part
of turbomachine. It also outlines an overview of recent results in this field, limited to the most
significant results, as well as those who have paved the way to some new methods of study
and recalculation of the hydraulic turbomachinery and low pressure fans.
The main task of the turbomachinery hydrodynamic calculation (the design of flow
components that provide the required operated parameters, and at the same time achieving its
maximum energy efficiency), is a very complex task which requires a unified application of
theoretical and experimental research results.
In order to achieve practically applicable methodology for the turbomschinery
calculation, the simplification of the fluid flow and fluid characteristics is performed:
physical flow is simplified as twodimensional, in some cases even onedimensional flow, the
turbomachinery operates in a steady operating regime, when the flow can be considered
invariant with time, and the fluid in hydraulic turbomachinery and low pressure fans can be
regarded as incompressible. The basic assumption is that the flow in turbomachinery runners
and its stationary parts are axisymmetric, although realistically it is not the case. Also, in the
introductory chapter, the basics of determining the shape of the hydraulic turbomachinery
blades are represented. At the end of this chapter, the application, development and
significance of the numerical simulation of fluid flow regarding turbomachinery design and
testing, with emphasis on the most significant achievements in this field and its application to
the turbomachinery performance, is showed.
In the second chapter of the doctoral thesis a brief overview of the methodology of
numerical simulation of flow, turbulence modeling and application a possibility of CFD
(Computational Fluid Dynamics) methods to flow in turbomachinery is given. Especially the
numerical simulation of flow in hydraulic turbomachinery and low pressure fans runners, but
also in the fixed vane and vaneless stationary parts of turbomachinery, is considered. Due to
the simple application, but also the required computing resources for the purpose of
ix numerical flow simulation, the focus was on solving the Reynoldsaveraged equations (i.e.
RANS equations). The basic equations of fluid flow (partial differential equation) are given,
which are, in the process of the temporal and spatial discretization, transformed into a system
of algebraic equations, suitable for numerical implementation. The system of equations is
closed by using any of the existing models of turbulent flow (i.e. turbulence models), what
was also discussed in this chapter. In the last part of this chapter the principles of numerical
solving of fluid flow are given (beginning with discretization, difference schemes, the
generation of the computational grid, and ending with the convergence criterion of the
obtained solution).
Examples of numerical simulations obtained by using commercial software Ansys Flow
Dynamics, which consists of turbomachinery module and validation of numerical models, are
the subjects of the third chapter. The examples of numerical simulations of different
turbomachines are presented, in following order:
I) low pressure reversible axial flow fan with plane runner blades, II) axialflow propeler pump and
III) centrifugal pump.
For all cases, the physical model is first presented, and then a numerical model is
created, while the results of numerical simulations are given as the display of operating
parameters obtained for a defined number of revolutions. The operated parameters of each
presented turbo machine obtained by numerical simulations of the flow in the range of
operating flow rate, compared with the operating characteristics obtained by experimental
tests of appropriate machines under laboratory conditions, therefore performing the validation
of the model. When it comes to turbomachinery, with respect to their practical application, it
can be considered that the model validation is performed if the relative error of operating
parameters in all current regimes does not exceed 5%. The flow parameters in different
discrete points of the turbomachinery runner, i.e. in different crosssections of the runner
(position, pressure, and velocity) of all presented examples, which are used for the purpose of
averaging, were presented in the form of tables given in the Appendix of this dissertation.
The fourth chapter deals with the determination of averaged axisymmetric flow surface
according to the results obtained by numerical simulation of flow in hydraulic turbines and
low pressure fans. The real flow in the profile cascades of hydraulic turbomachinery and fans
is not axially symmetric, and the can be reduced to axisymmetric flow fictively, if the flow
parameters in the blade channels are averaged according to a circular coordinate. Values of
x flow parameters at discrete points of the considered flow field are obtained by numerical
simulations. According to the results of numerical simulations of flow in turbomachinery
runner, it is possible to determine the averaged flow parameters accordint to the circular
coordinate, and then to determinate the averaged axisymmetric flow surfaces. The
methodology of averaging flow parameters according to the circular coordinate and obtained
equations are presented in this chapter.
The results of determining the meridional flow streamlines of the averaged fluid flow
using the integral equations of continuity, for the cases presented in the chapter 3, are
presented in the fifth chapter. Guided by the theory and the equations given in section 4, the
results of determination of averaged streamlines in hydraulic turbomachinery and low
pressure fans runner, respectively averaged axisymmetric flow surface. In addition, the
specific works of elementary stages on averaged axisymmetric flow surfaces in the
turbomachinery runner are determined, as well as torque and power of the runner. Finally, the
calculation of flow rates of the averaged mechanical flow energy through axisymmetric flow
control surfaces, at the entrance and exit of the work area of the runner, is performed, leading
to the significant information on the fluid energy losses in the turbomachinery runner.
At the end of the dissertation the Conclusion is presented, and in the Appendix tables
the averaged values of flow parameters in the corresponding sections of the turbomachinery
runners are presented. The results of averaging according to the circular coordinate, as
defined in section 4, are presented, and these results are used in section 5.
The first chapter of the paper is introductory unfolding, where the task of
hydrodynamic calculation is presented, as well as the schema of flow in the flowthrough part
of turbomachine. It also outlines an overview of recent results in this field, limited to the most
significant results, as well as those who have paved the way to some new methods of study
and recalculation of the hydraulic turbomachinery and low pressure fans.
The main task of the turbomachinery hydrodynamic calculation (the design of flow
components that provide the required operated parameters, and at the same time achieving its
maximum energy efficiency), is a very complex task which requires a unified application of
theoretical and experimental research results.
In order to achieve practically applicable methodology for the turbomschinery
calculation, the simplification of the fluid flow and fluid characteristics is performed:
physical flow is simplified as twodimensional, in some cases even onedimensional flow, the
turbomachinery operates in a steady operating regime, when the flow can be considered
invariant with time, and the fluid in hydraulic turbomachinery and low pressure fans can be
regarded as incompressible. The basic assumption is that the flow in turbomachinery runners
and its stationary parts are axisymmetric, although realistically it is not the case. Also, in the
introductory chapter, the basics of determining the shape of the hydraulic turbomachinery
blades are represented. At the end of this chapter, the application, development and
significance of the numerical simulation of fluid flow regarding turbomachinery design and
testing, with emphasis on the most significant achievements in this field and its application to
the turbomachinery performance, is showed.
In the second chapter of the doctoral thesis a brief overview of the methodology of
numerical simulation of flow, turbulence modeling and application a possibility of CFD
(Computational Fluid Dynamics) methods to flow in turbomachinery is given. Especially the
numerical simulation of flow in hydraulic turbomachinery and low pressure fans runners, but
also in the fixed vane and vaneless stationary parts of turbomachinery, is considered. Due to
the simple application, but also the required computing resources for the purpose of
ix numerical flow simulation, the focus was on solving the Reynoldsaveraged equations (i.e.
RANS equations). The basic equations of fluid flow (partial differential equation) are given,
which are, in the process of the temporal and spatial discretization, transformed into a system
of algebraic equations, suitable for numerical implementation. The system of equations is
closed by using any of the existing models of turbulent flow (i.e. turbulence models), what
was also discussed in this chapter. In the last part of this chapter the principles of numerical
solving of fluid flow are given (beginning with discretization, difference schemes, the
generation of the computational grid, and ending with the convergence criterion of the
obtained solution).
Examples of numerical simulations obtained by using commercial software Ansys Flow
Dynamics, which consists of turbomachinery module and validation of numerical models, are
the subjects of the third chapter. The examples of numerical simulations of different
turbomachines are presented, in following order:
I) low pressure reversible axial flow fan with plane runner blades, II) axialflow propeler pump and
III) centrifugal pump.
For all cases, the physical model is first presented, and then a numerical model is
created, while the results of numerical simulations are given as the display of operating
parameters obtained for a defined number of revolutions. The operated parameters of each
presented turbo machine obtained by numerical simulations of the flow in the range of
operating flow rate, compared with the operating characteristics obtained by experimental
tests of appropriate machines under laboratory conditions, therefore performing the validation
of the model. When it comes to turbomachinery, with respect to their practical application, it
can be considered that the model validation is performed if the relative error of operating
parameters in all current regimes does not exceed 5%. The flow parameters in different
discrete points of the turbomachinery runner, i.e. in different crosssections of the runner
(position, pressure, and velocity) of all presented examples, which are used for the purpose of
averaging, were presented in the form of tables given in the Appendix of this dissertation.
The fourth chapter deals with the determination of averaged axisymmetric flow surface
according to the results obtained by numerical simulation of flow in hydraulic turbines and
low pressure fans. The real flow in the profile cascades of hydraulic turbomachinery and fans
is not axially symmetric, and the can be reduced to axisymmetric flow fictively, if the flow
parameters in the blade channels are averaged according to a circular coordinate. Values of
x flow parameters at discrete points of the considered flow field are obtained by numerical
simulations. According to the results of numerical simulations of flow in turbomachinery
runner, it is possible to determine the averaged flow parameters accordint to the circular
coordinate, and then to determinate the averaged axisymmetric flow surfaces. The
methodology of averaging flow parameters according to the circular coordinate and obtained
equations are presented in this chapter.
The results of determining the meridional flow streamlines of the averaged fluid flow
using the integral equations of continuity, for the cases presented in the chapter 3, are
presented in the fifth chapter. Guided by the theory and the equations given in section 4, the
results of determination of averaged streamlines in hydraulic turbomachinery and low
pressure fans runner, respectively averaged axisymmetric flow surface. In addition, the
specific works of elementary stages on averaged axisymmetric flow surfaces in the
turbomachinery runner are determined, as well as torque and power of the runner. Finally, the
calculation of flow rates of the averaged mechanical flow energy through axisymmetric flow
control surfaces, at the entrance and exit of the work area of the runner, is performed, leading
to the significant information on the fluid energy losses in the turbomachinery runner.
At the end of the dissertation the Conclusion is presented, and in the Appendix tables
the averaged values of flow parameters in the corresponding sections of the turbomachinery
runners are presented. The results of averaging according to the circular coordinate, as
defined in section 4, are presented, and these results are used in section 5.