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Failure analysis of cavitation in a hydraulic loader
Engineering Failure Analysis 66 (2016) 312–320
Contents lists available at ScienceDirect
Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Failure analysis of cavitation in a hydraulic loader Li Mo a, Qi Yang a,⁎, Yu Yang b, Zhichun Zeng a a b
School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China School of Petroleum Engineering, Southwest Petroleum University, Chengdu 610500, China
a r t i c l e
i n f o
Article history: Received 26 February 2016 Received in revised form 15 April 2016 Accepted 24 April 2016 Available online 27 April 2016 Keywords: Hydraulic loader Cavitation Vapor/liquid two-phase flow Numerical calculations Structural parameters
a b s t r a c t Cavitation is one of the major failure modes in hydraulic loaders. The failure mechanism is related to damage induced by cavitation at the working surface. Moreover, the vibrations caused by cavitation reduce the efficiency of the unit and lead to irregular output. To further explore the cavitationinduced failure mechanism in hydraulic loaders, a vapor/liquid two-phase flow numerical calculation method was used to obtain the radial distribution of water vapor volume fraction in the internal flow field with different structural parameters of a prototype hydraulic loader. This method was also used to predict the intensity of cavitation under different conditions. It was found that with an increase of the stator and rotor blade angle, blade number and blade thickness, the water vapor volume fraction and intensity of cavitation reduced; however, with an increase of the stator and rotor vortex pit depth, water vapor volume fraction and cavitation intensity increased. Moreover, the clearance of the assembly had little effect on cavitation. The results of the numerical simulation are in good agreement with the experimental observations, which verifies the reliability of the calculation method for cavitation failure analysis of a hydraulic loader and provides a good basis for structure optimization. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction The mechanism of cavitation-induced damage on surfaces is highly complex. Most work in this field has focused on centrifugal pumps and turbines [1–3]. Ji and co-workers [4–7] studied the cavitation evolution around a propeller under unstable conditions by experiment and simulation, and obtained a relationship between the blade installation angle and the intensity of cavitation. They also assessed the pressure fluctuations and vibrations caused by cavitation, and found that when the blade installation angle was 18° and 35°, the pressure fluctuated sharply. Cavitation creates a vortex in the flow field. By increasing the depth of the boundary, the stability of the flow field can be improved. Pouffary [8] adopted a cavitation flow theory to study the effect of cavitation on the pressure distribution of the internal flow field and head of a pump. The experimental results verified the accuracy of the simulation and revealed a trend between the number of cavitation bubbles and the failure of the pump. Liu [9] used two-phase flow cavitation theory to simulate the effect of cavitation on the pump performance and compared experimental and simulated results. Liu demonstrated that the diameter of the bubble affects the volume fraction of the vacuole phase. Coutier-Delgosha [2], Rossetti and co-workers [10–14] investigated cavitation on a curved blade and the effect of flow rate and cavitation coefficient on the pump performance. Chou and co-workers [15–17] reported for wind and hydro-power turbines, that the major failure types of the machinery in contact with the liquid phase were cavitation, corrosion, and fatigue. The hydraulic loader is a key piece of equipment in heat-recovery-type liquid nitrogen pump trucks. It is mostly used to load the engine to provide constant heat to the system. The conventional approach to study hydraulic coupling machinery relies on estimations
⁎ Corresponding author. E-mail address: [email protected] (Q. Yang).
http://dx.doi.org/10.1016/j.engfailanal.2016.04.033 1350-6307/© 2016 Elsevier Ltd. All rights reserved.
L. Mo et al. / Engineering Failure Analysis 66 (2016) 312–320
313
Fig. 1. A 2D diagram of the hydraulic loader used in the simulations. 1. Principal axis; 2. right bearing shell; 3. right stator; 4. rotor; 5. left stator; 6. left bearing shell; 7. inlet; 8. outlet.
based on empirical measurements. This method cannot solve all problems that occur during operation such as the fracture of the stator of rotor blades, or vibration of the unit. Therefore, a new and more effective method is urgently needed to improve the cavitation performance of hydraulic loaders. 2. Numerical model This paper studies on cavitation. The result of cavitation is to produce a lot of bubbles in the liquid. When the local pressure is lower than the water vaporization pressure, bubbles are produced in the water. Within a very short time, air bubbles are formed (which contain water vapor) and subsequently implode rapidly (i.e., transient cavitation). A higher fraction of water vapor indicates a greater number of air bubbles and more severe cavitation. Therefore, the water vapor volume fraction is used to reflect the occurrence of cavitation and cavitation intensity [19]. Cavitation process is unsteady in theory, but the unsteady calculation needs larger memory and takes more time. Steady calculation can also reflect the status of cavitation. So the mixture model for steady vapor/liquid two-phase turbulent flow is used to analyze. The internal flow field in hydraulic loader is three dimensional incompressible. Because the internal structure of hydraulic loader is complex and easy to cause separation, the internal flow is turbulent for processing. This article uses the SST (Shear Stress Transport) turbulence model which is applicable to revolver. The advantage is that taking into account the turbulent shear stress, which will not cause excessive prediction to eddy viscosity. Its transport behavior can be obtained by eddy viscosity equation includes limited number. The turbulent eddy viscosity is defined as follows [20]:
υt ¼ α 1 k= maxðα 1 ω; S F 2 Þ
ð1Þ
Fig. 2. Rotor structure. r, Rotor blade number; s, stator blade number; θ; blade angle; t, blade thickness; d, assembly clearance between rotor and stator; h, vortex pit depth.
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Table 1 Parameters of the hydraulic loader. Rated speed (r/min)
External diameter (mm)
Inner diameter (mm)
s-r
θ
t (mm)
d (mm)
h (mm)
4000
290
85
s12r14
45°
11
3.5
30
Table 2 Model parameters. θ (°)
30; 45; 55; 60; 65; 75; 90
r s t (mm) d (mm) h (mm)
10; 11; 12; 13; 14; 15; 16; 17; 18; 19 9; 12; 15 6; 8; 10; 11; 12; 14; 16 2; 2.5; 3; 3.5; 4; 4.5; 5 25; 30; 33; 35
where S is the invariant measure of the strain rate. F2 is a second blending function that function is the same as the blending function F1. For the free shear flow that contains inappropriate hypothesis, it is used to constrain limited number of wall layers. k is the turbulent kinetic energy and ω is turbulence frequency. The blending function F1 is defined by: 4 F 1 ¼ tanh arg1
ð2Þ
n o hpffiffiffi i 0 2 2 arg1 ¼ min max k= β ωy ; 500υ= y ω ; 4ρk= CDkω σ ω2 y
ð3Þ
h i ‐10 CDkω ¼ max 2ρ∇k∇ω=ðσ ω2 ωÞ; 1:0 10
ð4Þ
where y is the distance to the nearest wall; υ is kinematic viscosity. F2 is defined by: 2 F 2 ¼ tanh arg2
ð5Þ
h pffiffiffi i 0 2 arg2 ¼ max 2 k= β ωy ; 500υ= y ω
ð6Þ
All constant are computed by a blend from the corresponding constants of the k-ε and the k-ω model. The constants for this model are: β′ = 0.09, α1 = 5/9, σω2 = 0.856 [20].
Fig. 3. Computational domain.
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315
Fig. 4. Calculation results with different grid quantity.
The cavitation simulations were conducted by using the CFD code ANSYS-CFX. The cavitation model is as follow: The growth process of bubbles in a liquid can be described by the Rayleigh-Plesset equation [21]. Ignoring the surface tension yields and the second-order terms, this equation can be expressed as follows: dRB =dt ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2jpv ‐pj=3ρl
ð7Þ
where RB is the bubble radius and Pv is the vapor pressure at ambient temperature (here: 3574 Pa). The rate of change of mass of a single bubble is expressed as 2
dmB =dt ¼ 4πRB ρv
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2jpv ‐pj=3ρl :
ð8Þ
If the unit volume contains NB bubbles, the volume rate of bubbles, rg, is expressed as 3
r v ¼ 4πRB NB =3
ð9Þ
The vapor phase is the secondary phase for a small volume ratio. The overall quality conversion between liquid water and steam is defined as follows: •
Slv ¼ 3 Fr v ρv
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2jpv ‐pj=3ρl sgnðpv −pÞ=RB :
There F is an empirical calibration coefficient.
Fig. 5. Grid model of the hydraulic loader. ω, Rotor speed; R, basin model diameter; r, radial position.
ð10Þ
316
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Fig. 6. Failures of different components of a hydraulic loader.
Eq. (4) can be applied to describe condensation. Evaporation is influenced by nucleation. When the water vapor volume fraction increases, the nucleation density decreases. Thus, rnuc (1 − rv) instead of rnuc is used when evaporation takes place. Here, rnuc is the nucleation point volume fraction and RB is the nucleus diameter. The cavitation model can then be revised to •
Slv ¼
(
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 F vap r nuc ð1‐r v Þρv 2ðpv ‐pÞ=3ρl =RB ifp a mplt; pv pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 F cond rv ρv 2ðp‐pv Þ=3ρl =RB ifp a mpgt; pv
ð11Þ
We used the following values in this empirical formula: RB = 10−6 m, rnuc = 5 × 10−4, Fvap = 50 and Fcond = 0.01. These model parameters are appropriate for all types of fluid and equipment [21]. 3. Geometry model and computational domain The structure of the hydraulic loader analyzed is shown in Fig. 1. It comprises a rotor (Fig. 2), right and left stators, a bearing shell, principal axis, and sealing elements. The stator and rotor are oriented in the same direction as the straight blade. The water chamber is formed between two adjacent blades. When the drive shaft rotates, water in the rotor chamber is jilted to the outer edge by centrifugal force and guided into the stator chamber. The stator chamber is fixed but water at the outer edge flows back to the hub forming a small eddy in the water chamber. (Parameters see Tables 1 and 2) For a hydraulic loader prototype, different basin models were set up with different blade angles, blade thicknesses, blade numbers, assembly clearances, and vortex pit depths of the rotor and stator. Because the computational domain is symmetrical, it is only necessary to analyze half the domain (Fig. 3). 4. Meshing and boundary conditions Because the calculations in the basin model, as well the smooth mesh and subsequent flow field calculations are complicated, automatic dividing grid mesh module was adopted. A tetrahedral grid with strong adaptability was used. Due to the assembling clearance between rotor and stator is small, local refinement is necessary. The independence of the numerical results to the grid was demonstrated through calculation with the global element size from 3 mm to 8 mm. Grid quantity and the calculation results are shown in Fig. 4. With the increase of grid quantity, the pressure decreases. When the element size is 4 mm (grid quantity about 660,000), calculation results tend to be stable. With the increase of grid quantity, more computation time and larger computational memory are required. In theory, if the grid is denser, the result will be more precise. But considering the calculation time and the limited computer memory, the global unit size was set to 4 mm with local refinement and five inflation layers were set to mesh in this paper. The computational domain was divided into 154,572 nodes and 666,425 grid units, as shown in Fig. 5.
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The boundary conditions were as follows: Rotating speed: 4000 r/min; Mass flow at inlet: 2.8 kg/s; water vapor volume group was 0; Pressure at outlet: 5 MPa; Symmetry conditions: The entire model is symmetrical and a plane of symmetry was used; Static wall conditions: No slip; with a standard wall function near the wall; Initial conditions: Non-cavitation results were used as the initial conditions for the cavitation simulations. 5. Results and discussion 5.1. Failure analysis and reliability validation The main failure in different parts of a hydraulic loader is shown in Fig. 6. Spherical pits appear in the areas of annular flow in the bearing shell (Fig. 6a). This damage arises because the change of liquid flow affected by the structure and rotation of the hydraulic loader in the channel inlet manifold causes flow disorder in the annular flow channel of the shell to produce a vortex. Cavitation
Fig. 7. Results of the simulation.
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then occurs on the walls of the flow channel wall. In the stator and rotor blades (Fig. 6b and c), the failure modes are peeling. In the upper blade, a grinding crack, deep groove, and scale-hole can be seen. Failure results from the superposition of local shock pressure from collapsing bubbles and the pressure of the water hammer. Therefore, cavitation is a major cause of failure in hydraulic loaders. In the present study, to identify ways to improve the performance, numerical simulations of cavitation in a hydraulic loader were carried out. We simulated the basin model for the hydraulic loader prototype at a rotor speed of 4000 r/min and the results are shown in Fig. 7. We found that cavitation occurs mostly in the areas of input annular flow (Fig. 7a), and around the rotor blades (Fig. 7b) and stator blades (Fig. 7c). These results are consistent with the experimental observations of cavitation failure in these parts. This proves that the numerical simulation method presented in this paper is reliable. 5.2. Numerical simulation of cavitation Numerical calculations of the system in the absence of cavitation were first carried out. The results of these calculations were then used as the initial conditions for subsequent calculations of cavitation. The effects of blade angle, blade number, blade thickness, assembly clearance, and vortex pit depth on cavitation in the hydraulic loader were determined by analyzing the radial distributions of the water vapor volume fraction in the internal flow field. The radial distribution of the water vapor volume fraction in the hydraulic loader is shown in Fig. 8. It can be seen that water vapor is concentrated on the blade wheel and at the suction surface, which reveals that cavitation is more prevalent at these locations. This is attributed to water flow into the hydraulic loader during rotation of the rotor, which produces a large pressure drop at the suction surface and blade wheel. When the pressure is lower than the saturated vapor pressure, bubbles are nucleated and cavitation ensues. The pressure drop at the back-pressure surface is smaller and fewer bubbles are produced at this location. As shown in Fig. 9, the radial distribution of water vapor volume fraction is similar for all blade angles. With an increase of blade angle, the volume fraction decreases. At radial positions between 0.6 and 0.8, the volume fraction is relatively high, indicating that cavitation is more intense at these positions. The volume fraction is the largest for a blade angle of 45° and lowest for angles of 75° and 90°, at which cavitation is least severe. An increase of blade angle reduces the water flow, which reduces the pressure drop caused by the flow and increases the pressure. In such a situation, the difference between the pressure and the evaporation pressure is reduced, which results in fewer bubbles being generated and less cavitation. As shown in Fig. 10, the distributions of the water vapor volume fraction are similar for all blade numbers; that is, the water vapor is mainly concentrated between radial positions of 0.6 to 0.8. The volume fraction decreases with increasing blade number and with increasing difference between blade numbers of the rotor and stator. This is because a larger number of blades results in reduced water flow between blades. This leads to a lower pressure drop and consequently less cavitation. The water vapor volume fraction decreases with increasing blade thickness, as shown in Fig. 11. The vapor fraction was lowest for thicknesses of 14 mm and 16 mm; thus, blades of this thickness would be effective for reducing the extent of cavitation. The larger blade thickness, similar to the case for a higher blade number as discussed above, results in reduced flow between blades, thereby minimizing the extent of cavitation. As shown in Fig. 12, the radial distribution and absolute values of the water vapor volume fraction are independent of assembly clearance. This is because the changes in assembly clearance are relatively small and have little effect on the water flow.
Fig. 8. Radial distributions of water vapor volume fraction on the stator bladeFig. 9. Radial distributions of water vapor volume fraction for different blade with a blade angle of 55°. angles.
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Fig. 10. Radial distributions of water vapor volume fraction for different blade Fig. 11. Radial distributions of water vapor volume fraction for different blade thicknesses. numbers.
From the results (shown in Fig. 13), the water vapor volume fraction increases with vortex pit depth. This is because a deeper vortex pit leads to a greater distribution of flow, resulting in a higher degree of flow loss. The corresponding pressure drop increases, which results in the generation of more air bubbles and more intense cavitation. 6. Conclusions The radial distributions of water vapor volume fraction within a hydraulic loader were obtained by analyzing the gas-liquid two-phase flow and cavitation for different structural parameters. The following conclusions are drawn: (1) With an increase of blade angle, the water vapor volume fraction decreases. At radial positions of 0.6 to 0.8, there is a relatively large amount of water vapor, which favors strong cavitation. (2) A higher blade number produces a smaller water vapor volume fraction. (3) With increasing blade thickness, the water vapor volume fraction decreases; thus, to reduce the extent of cavitation in a hydraulic loader, a thicker blade can be chosen. (4) The assembly clearance between the rotor and stator has little effect on internal cavitation. (5) With an increase of vortex pit depth, the water vapor volume fraction increases. Therefore, the structure of hydraulic loaders can be improved to reduce cavitation failure. Specifically, a structure with a large blade angle, high blade number, thick blade, and shallow vortex pit depth can be chosen to reduce the impact of cavitation. Acknowledgements This paper is supported by Open Fund (OGE201403-26) of Key Laboratory of Oil & Gas Equipment, Ministry of Education (Southwest Petroleum University), which is gratefully acknowledged.
Fig. 12. Radial distributions of water vapor volume fraction for different assemblyFig. 13. Radial distributions of water vapor volume fraction for different vortex clearances. pit depths.
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References [1] O. Coutier-Delgosha, R. Fortes-Patella, J.L. Reboud, et al., Numerical simulation of cavitating flow in 2D and 3D inducer geometries, Int. J. Numer. Methods Fluids 48 (2) (2005) 135–167. [2] O. Coutier-Delgosha, R. Fortes-Patella, J.L. Reboud, et al., Experimental and numerical studies in a centrifugal pump with 2D-curved blades in cavitating conditions, ASME J. Fluids Eng. 125 (6) (2003) 970–978. [3] O. Coutier-Delgosha, P. Morel, R. Fortes-Patella, Numerical simulation of turbo pumps inducer cavitating behavior, Int. J. Rotating 2 (2005) 135–142. [4] B. Ji, X.W. Luo, R.E.A. Arndt, et al., Numerical simulation of three dimensional cavitation shedding dynamics with special emphasis on cavitation-vortex interaction, Ocean Eng. 87 (2014) 64–77. [5] B. Ji, X.W. Luo, X.X. Peng, et al., Numerical analysis of cavitation evolution and excited pressure fluctuation around a propeller in non-uniform wake, Int. J. Multiphase Flow 43 (2012) 13–21. [6] B. Ji, X.X. Luo, Y.L. Wu, et al., Numerical analysis of unsteady cavitating turbulent flow and shedding horse-shoe vortex structure around a twisted hydrofoil, Int. J. Multiphase Flow 51 (2013) 33–43. [7] X.X. Peng, B. Ji, Y.T. Cao, et al., Combined experimental observation and numerical simulation of the cloud cavitation with U-type flow structures on hydrofoils, Int. J. Multiphase Flow 79 (2016) 10–22. [8] B. Pouffary, R.F. Patella, J.L. Reboud, Numerical simulation of 3D cavitating flows: analysis of cavitation head drop in turbo machinery, J. Fluids Eng. 130 (2008) 1–10. [9] S.H. Liu, Y.L. Wu, Y. Xu, et al., Analysis of two-phase cavitating flow with two-fluid model using integrated Boltzmann equations, Adv. Appl. Math. Mech. Vol. 5 (No. 5) (2013) 607–638. [10] A. Rossetti, G. Pavesi, G. Ardizzon, A. Santolin, Numerical analysis of cavitating flow in a pelton turbine, ASCE J. Energy Eng. 136 (2014) 1–10. [11] H. Ding, F.C. Visser, Y. Jiang, M. Furmanczyk, Demonstration and validation of a 3D CFD simulation tool predicting pump performance and cavitation for industrial applications, ASCE J. Energy Eng. 133 (2011) 1–14. [12] R.B. Medvitz, R.F. Kunz, D.A. Boger, et al., Performance analysis of cavitating flow in centrifugal pumps using multiphase CFD, ASCE J. Energy Eng. 124 (2002) 377–383. [13] R. Fortes-Patella, O. Coutier-Delgosha, J. Perrin, J.L. Reboud, Numerical model to predict unsteady cavitating flow behavior in inducer blade cascades, ASCE J. Energy Eng. 129 (2007) 128–135. [14] I. Mejri, F. Bakir, R. Rey, T. Belamri, Comparison of computational results obtained from a homogeneous cavitation model with experimental investigations of three inducers, ASCE J. Energy Eng. 128 (2006) 1308–1323. [15] J.S. Chou, C.K. Chiu, I.K. Huang, et al., Failure analysis of wind turbine blade under critical wind loads, Eng. Fail. Anal. 27 (2013) 99–118. [16] U. Dorji, R. Ghomashchi, Hydro turbine failure mechanisms: an overview, Eng. Fail. Anal. 44 (2014) 136–147. [17] Z. Mazur, R. Garcia-Illescas, J. Aguirre-Romano, N. Perez-Rodriguez, Steam turbine blade failure analysis, Eng. Fail. Anal. 15 (1–2) (2008) 129–141. [19] R.J. Cebeel, F. Kafyeke, et al., Computational fluid dynamics for engineers, Inc (2005) 88–89. [20] F.R. Menter, M. Kuntz, R. Langtry, Ten years of industrial experience with the SST turbulence model, Turbulence, Heat and Mass Transfer 4, Begell House Inc, 2003. [21] P.J. Zwart, A.G. Gerber, T. Belamri, A Two-Phase Flow Model for Predicting Cavitation Dynamics//ICMF 2004 International Conference on Multiphase Flow. Japan, May 30–June 3, 2004 Paper No.152.
Contents lists available at ScienceDirect
Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Failure analysis of cavitation in a hydraulic loader Li Mo a, Qi Yang a,⁎, Yu Yang b, Zhichun Zeng a a b
School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China School of Petroleum Engineering, Southwest Petroleum University, Chengdu 610500, China
a r t i c l e
i n f o
Article history: Received 26 February 2016 Received in revised form 15 April 2016 Accepted 24 April 2016 Available online 27 April 2016 Keywords: Hydraulic loader Cavitation Vapor/liquid two-phase flow Numerical calculations Structural parameters
a b s t r a c t Cavitation is one of the major failure modes in hydraulic loaders. The failure mechanism is related to damage induced by cavitation at the working surface. Moreover, the vibrations caused by cavitation reduce the efficiency of the unit and lead to irregular output. To further explore the cavitationinduced failure mechanism in hydraulic loaders, a vapor/liquid two-phase flow numerical calculation method was used to obtain the radial distribution of water vapor volume fraction in the internal flow field with different structural parameters of a prototype hydraulic loader. This method was also used to predict the intensity of cavitation under different conditions. It was found that with an increase of the stator and rotor blade angle, blade number and blade thickness, the water vapor volume fraction and intensity of cavitation reduced; however, with an increase of the stator and rotor vortex pit depth, water vapor volume fraction and cavitation intensity increased. Moreover, the clearance of the assembly had little effect on cavitation. The results of the numerical simulation are in good agreement with the experimental observations, which verifies the reliability of the calculation method for cavitation failure analysis of a hydraulic loader and provides a good basis for structure optimization. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction The mechanism of cavitation-induced damage on surfaces is highly complex. Most work in this field has focused on centrifugal pumps and turbines [1–3]. Ji and co-workers [4–7] studied the cavitation evolution around a propeller under unstable conditions by experiment and simulation, and obtained a relationship between the blade installation angle and the intensity of cavitation. They also assessed the pressure fluctuations and vibrations caused by cavitation, and found that when the blade installation angle was 18° and 35°, the pressure fluctuated sharply. Cavitation creates a vortex in the flow field. By increasing the depth of the boundary, the stability of the flow field can be improved. Pouffary [8] adopted a cavitation flow theory to study the effect of cavitation on the pressure distribution of the internal flow field and head of a pump. The experimental results verified the accuracy of the simulation and revealed a trend between the number of cavitation bubbles and the failure of the pump. Liu [9] used two-phase flow cavitation theory to simulate the effect of cavitation on the pump performance and compared experimental and simulated results. Liu demonstrated that the diameter of the bubble affects the volume fraction of the vacuole phase. Coutier-Delgosha [2], Rossetti and co-workers [10–14] investigated cavitation on a curved blade and the effect of flow rate and cavitation coefficient on the pump performance. Chou and co-workers [15–17] reported for wind and hydro-power turbines, that the major failure types of the machinery in contact with the liquid phase were cavitation, corrosion, and fatigue. The hydraulic loader is a key piece of equipment in heat-recovery-type liquid nitrogen pump trucks. It is mostly used to load the engine to provide constant heat to the system. The conventional approach to study hydraulic coupling machinery relies on estimations
⁎ Corresponding author. E-mail address: [email protected] (Q. Yang).
http://dx.doi.org/10.1016/j.engfailanal.2016.04.033 1350-6307/© 2016 Elsevier Ltd. All rights reserved.
L. Mo et al. / Engineering Failure Analysis 66 (2016) 312–320
313
Fig. 1. A 2D diagram of the hydraulic loader used in the simulations. 1. Principal axis; 2. right bearing shell; 3. right stator; 4. rotor; 5. left stator; 6. left bearing shell; 7. inlet; 8. outlet.
based on empirical measurements. This method cannot solve all problems that occur during operation such as the fracture of the stator of rotor blades, or vibration of the unit. Therefore, a new and more effective method is urgently needed to improve the cavitation performance of hydraulic loaders. 2. Numerical model This paper studies on cavitation. The result of cavitation is to produce a lot of bubbles in the liquid. When the local pressure is lower than the water vaporization pressure, bubbles are produced in the water. Within a very short time, air bubbles are formed (which contain water vapor) and subsequently implode rapidly (i.e., transient cavitation). A higher fraction of water vapor indicates a greater number of air bubbles and more severe cavitation. Therefore, the water vapor volume fraction is used to reflect the occurrence of cavitation and cavitation intensity [19]. Cavitation process is unsteady in theory, but the unsteady calculation needs larger memory and takes more time. Steady calculation can also reflect the status of cavitation. So the mixture model for steady vapor/liquid two-phase turbulent flow is used to analyze. The internal flow field in hydraulic loader is three dimensional incompressible. Because the internal structure of hydraulic loader is complex and easy to cause separation, the internal flow is turbulent for processing. This article uses the SST (Shear Stress Transport) turbulence model which is applicable to revolver. The advantage is that taking into account the turbulent shear stress, which will not cause excessive prediction to eddy viscosity. Its transport behavior can be obtained by eddy viscosity equation includes limited number. The turbulent eddy viscosity is defined as follows [20]:
υt ¼ α 1 k= maxðα 1 ω; S F 2 Þ
ð1Þ
Fig. 2. Rotor structure. r, Rotor blade number; s, stator blade number; θ; blade angle; t, blade thickness; d, assembly clearance between rotor and stator; h, vortex pit depth.
314
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Table 1 Parameters of the hydraulic loader. Rated speed (r/min)
External diameter (mm)
Inner diameter (mm)
s-r
θ
t (mm)
d (mm)
h (mm)
4000
290
85
s12r14
45°
11
3.5
30
Table 2 Model parameters. θ (°)
30; 45; 55; 60; 65; 75; 90
r s t (mm) d (mm) h (mm)
10; 11; 12; 13; 14; 15; 16; 17; 18; 19 9; 12; 15 6; 8; 10; 11; 12; 14; 16 2; 2.5; 3; 3.5; 4; 4.5; 5 25; 30; 33; 35
where S is the invariant measure of the strain rate. F2 is a second blending function that function is the same as the blending function F1. For the free shear flow that contains inappropriate hypothesis, it is used to constrain limited number of wall layers. k is the turbulent kinetic energy and ω is turbulence frequency. The blending function F1 is defined by: 4 F 1 ¼ tanh arg1
ð2Þ
n o hpffiffiffi i 0 2 2 arg1 ¼ min max k= β ωy ; 500υ= y ω ; 4ρk= CDkω σ ω2 y
ð3Þ
h i ‐10 CDkω ¼ max 2ρ∇k∇ω=ðσ ω2 ωÞ; 1:0 10
ð4Þ
where y is the distance to the nearest wall; υ is kinematic viscosity. F2 is defined by: 2 F 2 ¼ tanh arg2
ð5Þ
h pffiffiffi i 0 2 arg2 ¼ max 2 k= β ωy ; 500υ= y ω
ð6Þ
All constant are computed by a blend from the corresponding constants of the k-ε and the k-ω model. The constants for this model are: β′ = 0.09, α1 = 5/9, σω2 = 0.856 [20].
Fig. 3. Computational domain.
L. Mo et al. / Engineering Failure Analysis 66 (2016) 312–320
315
Fig. 4. Calculation results with different grid quantity.
The cavitation simulations were conducted by using the CFD code ANSYS-CFX. The cavitation model is as follow: The growth process of bubbles in a liquid can be described by the Rayleigh-Plesset equation [21]. Ignoring the surface tension yields and the second-order terms, this equation can be expressed as follows: dRB =dt ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2jpv ‐pj=3ρl
ð7Þ
where RB is the bubble radius and Pv is the vapor pressure at ambient temperature (here: 3574 Pa). The rate of change of mass of a single bubble is expressed as 2
dmB =dt ¼ 4πRB ρv
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2jpv ‐pj=3ρl :
ð8Þ
If the unit volume contains NB bubbles, the volume rate of bubbles, rg, is expressed as 3
r v ¼ 4πRB NB =3
ð9Þ
The vapor phase is the secondary phase for a small volume ratio. The overall quality conversion between liquid water and steam is defined as follows: •
Slv ¼ 3 Fr v ρv
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2jpv ‐pj=3ρl sgnðpv −pÞ=RB :
There F is an empirical calibration coefficient.
Fig. 5. Grid model of the hydraulic loader. ω, Rotor speed; R, basin model diameter; r, radial position.
ð10Þ
316
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Fig. 6. Failures of different components of a hydraulic loader.
Eq. (4) can be applied to describe condensation. Evaporation is influenced by nucleation. When the water vapor volume fraction increases, the nucleation density decreases. Thus, rnuc (1 − rv) instead of rnuc is used when evaporation takes place. Here, rnuc is the nucleation point volume fraction and RB is the nucleus diameter. The cavitation model can then be revised to •
Slv ¼
(
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 F vap r nuc ð1‐r v Þρv 2ðpv ‐pÞ=3ρl =RB ifp a mplt; pv pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 F cond rv ρv 2ðp‐pv Þ=3ρl =RB ifp a mpgt; pv
ð11Þ
We used the following values in this empirical formula: RB = 10−6 m, rnuc = 5 × 10−4, Fvap = 50 and Fcond = 0.01. These model parameters are appropriate for all types of fluid and equipment [21]. 3. Geometry model and computational domain The structure of the hydraulic loader analyzed is shown in Fig. 1. It comprises a rotor (Fig. 2), right and left stators, a bearing shell, principal axis, and sealing elements. The stator and rotor are oriented in the same direction as the straight blade. The water chamber is formed between two adjacent blades. When the drive shaft rotates, water in the rotor chamber is jilted to the outer edge by centrifugal force and guided into the stator chamber. The stator chamber is fixed but water at the outer edge flows back to the hub forming a small eddy in the water chamber. (Parameters see Tables 1 and 2) For a hydraulic loader prototype, different basin models were set up with different blade angles, blade thicknesses, blade numbers, assembly clearances, and vortex pit depths of the rotor and stator. Because the computational domain is symmetrical, it is only necessary to analyze half the domain (Fig. 3). 4. Meshing and boundary conditions Because the calculations in the basin model, as well the smooth mesh and subsequent flow field calculations are complicated, automatic dividing grid mesh module was adopted. A tetrahedral grid with strong adaptability was used. Due to the assembling clearance between rotor and stator is small, local refinement is necessary. The independence of the numerical results to the grid was demonstrated through calculation with the global element size from 3 mm to 8 mm. Grid quantity and the calculation results are shown in Fig. 4. With the increase of grid quantity, the pressure decreases. When the element size is 4 mm (grid quantity about 660,000), calculation results tend to be stable. With the increase of grid quantity, more computation time and larger computational memory are required. In theory, if the grid is denser, the result will be more precise. But considering the calculation time and the limited computer memory, the global unit size was set to 4 mm with local refinement and five inflation layers were set to mesh in this paper. The computational domain was divided into 154,572 nodes and 666,425 grid units, as shown in Fig. 5.
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The boundary conditions were as follows: Rotating speed: 4000 r/min; Mass flow at inlet: 2.8 kg/s; water vapor volume group was 0; Pressure at outlet: 5 MPa; Symmetry conditions: The entire model is symmetrical and a plane of symmetry was used; Static wall conditions: No slip; with a standard wall function near the wall; Initial conditions: Non-cavitation results were used as the initial conditions for the cavitation simulations. 5. Results and discussion 5.1. Failure analysis and reliability validation The main failure in different parts of a hydraulic loader is shown in Fig. 6. Spherical pits appear in the areas of annular flow in the bearing shell (Fig. 6a). This damage arises because the change of liquid flow affected by the structure and rotation of the hydraulic loader in the channel inlet manifold causes flow disorder in the annular flow channel of the shell to produce a vortex. Cavitation
Fig. 7. Results of the simulation.
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then occurs on the walls of the flow channel wall. In the stator and rotor blades (Fig. 6b and c), the failure modes are peeling. In the upper blade, a grinding crack, deep groove, and scale-hole can be seen. Failure results from the superposition of local shock pressure from collapsing bubbles and the pressure of the water hammer. Therefore, cavitation is a major cause of failure in hydraulic loaders. In the present study, to identify ways to improve the performance, numerical simulations of cavitation in a hydraulic loader were carried out. We simulated the basin model for the hydraulic loader prototype at a rotor speed of 4000 r/min and the results are shown in Fig. 7. We found that cavitation occurs mostly in the areas of input annular flow (Fig. 7a), and around the rotor blades (Fig. 7b) and stator blades (Fig. 7c). These results are consistent with the experimental observations of cavitation failure in these parts. This proves that the numerical simulation method presented in this paper is reliable. 5.2. Numerical simulation of cavitation Numerical calculations of the system in the absence of cavitation were first carried out. The results of these calculations were then used as the initial conditions for subsequent calculations of cavitation. The effects of blade angle, blade number, blade thickness, assembly clearance, and vortex pit depth on cavitation in the hydraulic loader were determined by analyzing the radial distributions of the water vapor volume fraction in the internal flow field. The radial distribution of the water vapor volume fraction in the hydraulic loader is shown in Fig. 8. It can be seen that water vapor is concentrated on the blade wheel and at the suction surface, which reveals that cavitation is more prevalent at these locations. This is attributed to water flow into the hydraulic loader during rotation of the rotor, which produces a large pressure drop at the suction surface and blade wheel. When the pressure is lower than the saturated vapor pressure, bubbles are nucleated and cavitation ensues. The pressure drop at the back-pressure surface is smaller and fewer bubbles are produced at this location. As shown in Fig. 9, the radial distribution of water vapor volume fraction is similar for all blade angles. With an increase of blade angle, the volume fraction decreases. At radial positions between 0.6 and 0.8, the volume fraction is relatively high, indicating that cavitation is more intense at these positions. The volume fraction is the largest for a blade angle of 45° and lowest for angles of 75° and 90°, at which cavitation is least severe. An increase of blade angle reduces the water flow, which reduces the pressure drop caused by the flow and increases the pressure. In such a situation, the difference between the pressure and the evaporation pressure is reduced, which results in fewer bubbles being generated and less cavitation. As shown in Fig. 10, the distributions of the water vapor volume fraction are similar for all blade numbers; that is, the water vapor is mainly concentrated between radial positions of 0.6 to 0.8. The volume fraction decreases with increasing blade number and with increasing difference between blade numbers of the rotor and stator. This is because a larger number of blades results in reduced water flow between blades. This leads to a lower pressure drop and consequently less cavitation. The water vapor volume fraction decreases with increasing blade thickness, as shown in Fig. 11. The vapor fraction was lowest for thicknesses of 14 mm and 16 mm; thus, blades of this thickness would be effective for reducing the extent of cavitation. The larger blade thickness, similar to the case for a higher blade number as discussed above, results in reduced flow between blades, thereby minimizing the extent of cavitation. As shown in Fig. 12, the radial distribution and absolute values of the water vapor volume fraction are independent of assembly clearance. This is because the changes in assembly clearance are relatively small and have little effect on the water flow.
Fig. 8. Radial distributions of water vapor volume fraction on the stator bladeFig. 9. Radial distributions of water vapor volume fraction for different blade with a blade angle of 55°. angles.
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Fig. 10. Radial distributions of water vapor volume fraction for different blade Fig. 11. Radial distributions of water vapor volume fraction for different blade thicknesses. numbers.
From the results (shown in Fig. 13), the water vapor volume fraction increases with vortex pit depth. This is because a deeper vortex pit leads to a greater distribution of flow, resulting in a higher degree of flow loss. The corresponding pressure drop increases, which results in the generation of more air bubbles and more intense cavitation. 6. Conclusions The radial distributions of water vapor volume fraction within a hydraulic loader were obtained by analyzing the gas-liquid two-phase flow and cavitation for different structural parameters. The following conclusions are drawn: (1) With an increase of blade angle, the water vapor volume fraction decreases. At radial positions of 0.6 to 0.8, there is a relatively large amount of water vapor, which favors strong cavitation. (2) A higher blade number produces a smaller water vapor volume fraction. (3) With increasing blade thickness, the water vapor volume fraction decreases; thus, to reduce the extent of cavitation in a hydraulic loader, a thicker blade can be chosen. (4) The assembly clearance between the rotor and stator has little effect on internal cavitation. (5) With an increase of vortex pit depth, the water vapor volume fraction increases. Therefore, the structure of hydraulic loaders can be improved to reduce cavitation failure. Specifically, a structure with a large blade angle, high blade number, thick blade, and shallow vortex pit depth can be chosen to reduce the impact of cavitation. Acknowledgements This paper is supported by Open Fund (OGE201403-26) of Key Laboratory of Oil & Gas Equipment, Ministry of Education (Southwest Petroleum University), which is gratefully acknowledged.
Fig. 12. Radial distributions of water vapor volume fraction for different assemblyFig. 13. Radial distributions of water vapor volume fraction for different vortex clearances. pit depths.
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