Ma£geschneiderte Werkstoffe gegen Kavitations- Ma£geschneiderte Werkstoffe gegen Kavitations-Erosion

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  • Maßgeschneiderte Werkstoffe gegen Kavitations-

    Erosion

    (Tailored Materials against Cavitation-Erosion)

    Authors: K. Ioakimidis †, M. Mlikota ††

    † Institute of Fluid Mechanics and Hydraulic Machine ry (IHS)

    †† Institute for Materials Testing, Materials Science and Strength of Materials (IMWF)

    University of Stuttgart

    21.01.2014

  • page 2 of 17

    Content

    1 Introduction .......................................................................................................... 3

    2 General Information ............................................................................................. 3 2.1 Cavitation erosion and bubble collapse ......................................................... 6

    2.1.1 The Rayleigh Plesset equation ............................................................... 7 2.1.2 Bubble collapse ....................................................................................... 8

    3 Approach and methodology ................................................................................. 9 3.1 Hydrodynamic point of view ........................................................................... 9

    3.1.1 Grid generation and boundary conditions ............................................. 10 3.1.2 Solving the problem .............................................................................. 11

    3.2 Mechanical point of view ............................................................................. 11 3.2.1 FEM techniques .................................................................................... 11 3.2.2 Material model ...................................................................................... 12 3.2.3 Pressure impingement loading.............................................................. 12

    4 Project results and outlook .................................................................................13 4.1.1 Discussion ............................................................................................ 14 4.1.2 FE erosion model I ................................................................................ 14 4.1.3 FE erosion model II ............................................................................... 15

    5 Conclusions ........................................................................................................16

    6 Future work ........................................................................................................17

    7 References .........................................................................................................17

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    1 Introduction Cavitation is one of the most severe problems in hydraulic machinery. It reduces the range of operation of the turbine and it can even destroy the machine. Therefore it is very important to be able to accurately predict the cavitation behavior and the resulting loading on the material. It is also very important to know the mechanisms of the destruction of the material. This allows in a long term to develop materials which are more resistant to cavitation erosion. This would lead to a severe reduction of the maintenance costs. The primary objective of the project is to provide a preliminary work for the description and prediction of all flow phenomena arising in the two-phase system formed by a collapsing cavitation bubble near a solid boundary as well as material response to it. It is well known that the problem of a bubble collapse near a wall involves complicated unsteady flow phenomena combined with the material subtraction from the solid surface. Obviously, the phenomenon is very complex since it includes both hydrodynamic and material aspects. To improve materials which could resist such an aggressiveness, a collaboration between engineers from the field of fluid mechanics and material mechanics is essential. In the preceding paragraphs we discuss the hydrodynamic mechanisms of bubble collapse (IHS contribution) and the material aspects (IWMF contribution).

    2 General Information Christopher Brennen [1] describes clearly and understandable to everyone the amazing world of bubbles. He gives a brief description of the cavitating phenomena and shows that cavitation is a phenomenon with a wide range of applications. The phenomenon does not occur only in hydraulic machinery, but one can find it in the field of medicine, naval engineering, journal bearing engineering, rocket science, aerospace engineering, etc. There is a wide variety of types of cavitation and the main types occurring as instances in hydraulic machinery are the following:

    � sheet cavitation or attached cavities � traveling bubble cavitation � cavitation clouds � cavitating vortices

    As an example how cavitation looks like in reality see Figure 1.

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    Figure 1: Sheet / Cloud Cavitation created by a NAC A 0012 hydrofoil at an angle of attack (IHS)

    There are also other types of cavitation and it is thinkable, from the combination of the applications variety and the types of cavitation, that there is a big research potential in cavitating phenomena for both fluid mechanics and structural engineers. In the literature cavitation refers as the formation or the development of vapor structures in an originally liquid flow. The phase change takes place at almost constant temperature in the regions where a local drop in pressure occurs and is generated by the flow itself. Practically, constant temperature and pressure drop under the liquid saturation pressure cause cavitation. In contrast, it is known that boiling of a liquid occurs if the liquid is heated at constant pressure. Bubble formation, which is a small pocket of vapor inside a liquid, is common occurrence of both, cavitation and boiling phenomena. Bubbles come in all sizes, shapes and forms and have different dynamical behavior. As an instance, bubbles produced by boiling collapse very slowly and relatively gently, but bubbles produced by cavitation, in most cases collapse violently and are dangerous and noisy. The most important feature arises when a bubble collapses near a wall or essentially on any solid surface, which could be a hydro turbine or a pump or even a teeth or a kidney stone [1]. There is no chance for the solid to survive; an explanation will be given afterwards. In the following we pay attention to the dynamics of a vapor-filled cavitation bubble collapse on a solid metal surface, such those of Kaplan turbine, Francis turbine and we concentrate on hydrodynamic cavitation. The following figures show the damage on various hydraulic machinery components.

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    Figure 2: Cavitation damage of a pump impeller (IHS )

    Figure 3: Close up of the cavitation damage of Figu re 2

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    Figure 4: Cavitation damage of a Kaplan blade (IHS)

    Figure 5: Close up of a Kaplan blade Figure 4

    2.1 Cavitation erosion and bubble collapse It is well known that the violent collapse of such bubbles can severely cause material damage or in other words, is responsible for the material abstraction from a solid

  • page 7 of 17

    surface. Another important issue that may result from that collapse is noise emission. Responsible for that phenomena are high velocities, pressures and temperatures that may result from that collapse [2]. We consider spherical bubbles, since the spherical analysis represents the maximum possible consequences of bubble collapse [2], although collapsing bubbles do not remain spherical. Numerous experimental studies worldwide were done in order to improve understanding of the phenomenon; while in contrast, less computational work is done. However, some recent results show that it is possible to compute a single bubble collapse [4], [5].

    2.1.1 The Rayleigh Plesset equation Under the main consideration of spherical bubbles, Brennen [2] explains the work done by Rayleigh (1917) and Plesset (1949) and he represents the derivation of the Rayleigh-Plesset Equation (RPE), which describes the bubble growth and collapse. Jean-Pierre Franc [2] discusses why the RPE is a useful tool for understanding the mechanism of bubble radius growth and collapse. According to the RPE both Brennen and Franc give an extended discussion of the various aspects of cavitation. Although the RPE is a powerful tool, the derivation has been done under simplifications, thus it cannot describe all the dynamic phenomena occurred by a single bubble collapse. The case of a bubble cloud collapse is more uncomfortable situation, while there is interaction between the bubbles and this factor mitigates the results. The considerations we do to derive the RPE are:

    � spherical bubble radius � the liquid is considered to be incompressible, constant density � the dynamic viscosity of the liquid is assumed to be constant and uniform � the temperature and pressure within the bubble are assumed to be always

    uniform � thermodynamically, considerations of the bubble contents are necessary

    Under these considerations we derive the RPE: ������ − ����� + ��

    ���� − ������ + � � ������ ���� �

    = � ������ + 32 ����� � � + 4� � ���� + 2� �

    (1)

    We count seven terms for this complex nonlinear equation form the left:

    � is the instantaneous