* Technical Institute, Corporate Technology Division Kawasaki Heavy Industries, LTD.
1-1 Kawasaki-cho, Akashi City, Hyogo, 673-8666 Japan (E-mail: [email protected])
** Engineering Division, Precision Machinery Company Kawasaki Heavy Industries, LTD.
234 Matsumoto, Hasetani-cho, Nishi-ku, Kobe City, Hyogo, 651-2239 Japan
ABSTRACT
Pure-tone noise is often generated by a hydraulic system with pressure relief valve. The noise is uncomfortable sound with the peak frequency of several kHz and may become incredibly loud in some kind of conditions. It is necessary for hydraulic machinery manufacturers to possess a design technique to prevent such a loud noise. The mechanism of the noise is, however, not understood enough to prevent it completely. Then, a new CFD method is developed to understand the detailed mechanism of the noise in addition to an experimental investigation. The new CFD method is well validated via a comparison with a variety of experimental results. Through this study, it is revealed that the pure-tone noise is the self-excitation phenomenon caused by the interaction between the fluid resonance and the valve vibration.
A : pressure receiving area of plunger [mm2] c : damping coefficient [N/(m/s)] csound : speed of sound of oil [m/s] dpass : distance along upstream passage [mm] f : natural frequency of plunger vibration [Hz] K : bulk modules of oil [GPa] M : mass of plunger[g] p : static pressure [MPa]
T : time of a cycle [sec] V : volume of chamber behind plunger [mm3] x : plunger displacement [mm] xb : balanced position of plunger [mm]
INTRODUCTION An oil-hydraulic system has various types of noise source derived from flow fluctuation and structural vibration. Among other things, the pure-tone noise is often generated by the system with pressure relief valve [1]. This pure-tone noise is uncomfortable sound with the peak frequency of several kHz and may become incredibly loud in some kind of conditions. Hence, it is one of the important problems in designing hydraulic products to prevent the pure-tone noise generation. However, the detailed mechanism of the pure-tone noise has not been understood clearly enough to prevent it completely. When the pure-tone noise is once generated by a prototype of oil-hydraulic machinery, the
Proceedings of the 9th JFPS International Symposiumon Fluid Power, Matsue, 2014
Oct. 28 - 31, 2014
774
3A2-1 Keynote 5
manufacturer spends an inefficient development period on reducing the pure-tone noise. In order to provide more quiet hydraulic products for its customers timely, it is necessary to understand the mechanism of the pure-tone noise generation and to have a design technique to reduce the pure-tone noise. A computational fluid dynamics (CFD) simulation is applied to understand the detailed mechanism of the pure-tone noise generation in addition to an experimental investigation. In this paper, after describing the experimental investigation, we explain about the development of a new CFD method to simulate the pure-tone noise phenomenon. The CFD method is validated via a comparison with the experiment. Through this approach, the principal mechanism of the pure-tone noise generated by the relief valve becomes clear. Then, the design method and the prediction tools to prevent the pure-tone noise have been developed.
EXPERIMENTAL INVESTIGATION Experimental method In order to identify the cause of the pure-tone noise and investigate its characteristics, the experiment was carried out using a test block shown in Fig. 1. A passage in the test block is a same shape as a part of the passage in our prototype which had generated the pure-tone noise. Figure 2 shows the passage in the test block and measurement point. The pressure fluctuations along the upstream passage were measured by pressure transducers (PHL-A-50MP, Kyowa Electronic Instruments). Noise level beside the test block was also measured. Figure 3 shows a schematic diagram of the relief valve which is used in the experiment. When the system pressure exceeds certain set pressure, the poppet valve opens and the oil flows into the pilot passage. The pressure difference between the both ends of the plunger rises with increasing the pilot flow. Then, the plunger opens to reduce the system pressure to the set pressure. In this way, the system pressure is kept at the set pressure. Figure 4 shows the experimental system which the test block is connected in. The flow rate of oil through the test block was adjusted to arbitrary value by the flow rate controller.
Figure 1 Appearance of test block
Figure 2 Passage in test block and measurement points
Figure 3 Schematic diagram of relief valve
Figure 4 Experimental system Experimental conditions Experimental conditions are shown in Table 1. It is well known that fluid resonance, such as acoustic resonance of a tube, is related to pure-tone noise [1-2]. Two test blocks that had different passage length were prepared to compare the influence of the fluid resonance. Furthermore, the flow rate was continuously changed from 10 to 70 L/min to search a condition in which the pure-tone noise is generated. Because it was revealed from our experience that individual differences of the relief valve affected the pure-tone noise generation, the relief valve which had remarkably generated the pure-tone noise was used in the experiment.
Figure 5 Length of straight part of upstream passage Experimental results Figure 6 shows an example of noise spectrum measured in Case A. This spectrum shows that the pure-tone noise with peak frequency of about 5 kHz is generated. This peak frequency almost accords with the frequency measured beside our prototype. Without going into detail in this paper, it was also confirmed that the pure-tone noise was generated in all range of the flow rate in Case A. The peak frequency of the noise was around 5 kHz and didn’t greatly change by the flow rate. From this frequency behavior, the pure-tone noise is likely to be caused by the fluid resonance.
Figure 6 Noise spectrum with the pure-tone noise (Case A, d=107 [mm], Q=10 [L/min])
Figure 7 shows the time history of the pressure fluctuation at each measurement point in Case A. The frequency of the pressure fluctuation at all measurement points accords with the peak frequency of the pure-tone noise. The amplitude of the pressure fluctuation at P1 and P4 are so large to exceed 10 MPa. On the other hand, the amplitude at P2 and P6 are smaller than that at the other measurement points. This characteristic of the pressure fluctuations indicates that the standing wave is
formed in the upstream passage. Figure 8 shows the fluctuation of pressure distribution along the upstream passage. It is obtained by reconstruction of the time histories of pressure fluctuation in Fig. 7 to clarify the existence of standing wave. Further, it is normalized by the maximum amplitude of the pressure fluctuation of all measurement points during the half cycles shown in Fig. 8. This figure shows that a standing wave of 3/4 wavelength exists between the end of the plunger and measurement point of P6. At the upstream end of the section dpass=220 there is a node of the standing wave, and at the downstream end of the section dpass=0 there is an antinode.
Figure 7 Time history of pressure fluctuation at each measurement point
(Case A, d=107[mm], Q=10[L/min])
Figure 8 Fluctuation of pressure distribution along upstream passage during half cycle
On the other hand, it was confirmed that the pure-tone noise was never generated in any range of flow rate in Case B. As shown in Fig.9, the large pressure fluctuation as seen in Case A is not seen in Case B at all. This is probably caused by the difference of natural frequency of the fluid resonance between Case A and Case B. Thus, these experimental results indicate that the fluid resonance of a tube excited in the upstream passage is one of causes of the pure-tone noise.
Figure 9 Time histories of pressure fluctuation at each measurement point
(Case B, d=84 [mm], Q=10 [L/min]) Investigation of excitation source of fluid resonance It is generally known that amplitude of vibration grows up very greatly by an interaction between fluid fluctuation and vibration of valve located at the end of passage [3-4]. Therefore, the plunger vibration was measured by a non-contact displacement sensor (PU-05, Applied Electronics Corporation) to understand the relationship with the fluid resonance. Figure 10 shows the time history of the plunger displacement in Case A normalized by the distance from balanced position to seated position. The plunger vibrates at about 5 kHz same as the peak frequency of the pure-tone noise. The amplitude of the vibration is as large as the distance from the balanced position to the seated position. Judging from this data, the plunger vibration has a relation with the fluid resonance. In order to understand how the plunger vibration relates to the fluid resonance, we estimate the natural frequency of the plunger vibration. The natural frequency based on a stiffness of the coil spring connected with the plunger k
is estimated at 40 Hz using Eq. (1). This frequency is too low to affect the fluid resonance that probably has the natural frequency of about 5 kHz.
M
kf
21
(1)
Then, we should focus on the effect of compressibility of oil. Figure 11 shows a simplification model to estimate the natural frequency of the plunger vibration based on the compressibility of oil. In this assumption, the oil in the chamber behind the plunger behaves as a coil spring. The equivalent stiffness koil is estimated at 1.9×104 N/mm using Eq. (2).
V
KA
dV
dpA
AdV
Adp
dx
dFkoil
22 (2)
As the results, the natural frequency of the plunger vibration based on the compressibility of oil is estimated at 4.5 kHz. This frequency is near to the frequency of about 5 kHz that is probably the natural frequency of the fluid resonance, but is not same.
Figure 10 Time history of normalized plunger displacement (Case A, d=107[mm], Q=10 [L/min])
Figure 11 Simplification to estimate natural frequency of plunger vibration caused by compressibility of oil
Discussions The measured characteristics of the pure-tone noise phenomenon are summarized as follows, 1) The fluid resonance is excited in the upstream
passage when the pure-tone noise is generated. 2) The plunger largely vibrates when the pure-tone
noise is generated 3) The length of upstream passage affects the
generation of the pure-tone noise 4) The generation and the frequency of the pure-tone
noise isn’t dependent on the flow rate so much 5) The natural frequency of the plunger vibration based
on the compressibility of oil is near to the frequency of about 5 kHz that is probably the natural frequency of the fluid resonance, but is not same.
From these summaries, it is confirmed that the pure-tone noise is caused by the excitation of the fluid resonance in the upstream passage. Moreover, the fluid resonance is probably excited by the plunger vibration. The natural frequency difference between the plunger vibration and the fluid resonance probably influences the pure-tone noise generation. The pure-tone noise seems to be generated even though there is a difference of several hundred Hz between these two natural frequencies. From these characteristics we assume that the pure-tone noise is a self-excitation phenomenon caused by an interaction between the plunger vibration and the fluid resonance. Such an interaction can change the each natural frequency to the peak frequency of the pure-tone noise. To verify this assumption, the CFD simulation is applied. Details are described in the next chapter.
DEVELOPMENT OF NEW CFD METHOD Simulation method of fluid-structure interaction The new CFD method has been developed to clarify the relation between the plunger vibration and the fluid resonance. In this method, three-dimensional unsteady CFD solver is coupled with the plunger vibration. We apply a commercial CFD software STAR-CCM+ as a flow solver. The compressibility of oil is considered to simulate the fluid resonance in the upstream passage and the fluid spring behavior of oil as mentioned above. In the flow solver, the effect of compressibility on the flowfield is described using an approximation that speed of sound is constant in any conditions. In this approximation, density of oil changes depending on pressure as the following expression,
pcsound
20
1
(3)
where ρ0 is density of oil at 1 atm and p is static pressure. In this paper, the speed of sound csound is estimated at 1398 m/s by Eq. (4) using K=1.7 [GPa], and ρ0=870 [kg/m3] as properties of the oil.
0K
csound
(4)
Figure13 shows a structural model of the relief valve considered in the CFD method. One-dimension
translational motion of the plunger is considered in this model. The poppet valve is fixed at an arbitrary position, because the influence of the vibration of the poppet valve to the pure tone noise has not been confirmed by the experiment yet. The coil spring is considered to keep the plunger near the balanced position. The displacement of the plunger is calculated by Eq. (5).
CFDb FxxkxcxM
(5)
where FCFD is fluid force calculated by the flow solver. All flow forces, pressure difference between both ends of the plunger, effect of virtual mass, etc. are considered in FCFD. The second term of the left side of Eq. (5) means a resistance of slide friction between the plunger and the sleeve. The damping coefficient c is set as reasonable value because the real value has not been known. The third term means a restitution force caused by the coil spring. The coefficient k is the design value of elasticity of the coil spring. The CFD cells surrounding the plunger were deformed according to the plunger displacement obtained by the integration of Eq. (5) at each time step of the flow solver. We made a java macro program for the integration. The large eddy simulation (LES) model is applied as a turbulence model.
Figure 13 Structural model of the relief valve Calculation model and mesh Figure 14 shows a three-dimensional model of the test block for CFD simulation. A half model is applied to reduce the computer resources and to improve the calculation speed. Polyhedral cells are used, because they can largely reduce the number of cells from the conventional tetrahedral cells without losing the accuracy of calculations [5]. Layer type polyhedral cells are used near walls to resolve the flow boundary layer accurately. Using a partial fine mesh, total number of cells is reduced and the accuracy of simulation is raised. The mesh is automatically generated by STAR-CCM+. The total number of cells is about 8 millions. The mesh morphing technique, shown in Figure 15, is used to consider the influence of the plunger vibration on the flowfield. The CFD cells surrounding the plunger move at each time step according to the displacement calculated by Eq. (5).
An inflow boundary is set on upstream end of the model. A pressure boundary is set on downstream end of the model. Non-slip boundary condition is used on the wall.
Figure14 Calculation model and mesh
Figure15 Mesh morphing technique Calculation procedure The procedure of the CFD method is shown as follows, 1) Steady-state CFD 2) Unsteady CFD with fixed plunger 3) Unsteady CFD with vibrating plunger base on
Eq.(5). Before the unsteady CFD, 1) the steady-state CFD is carried out to get an initial flowfield for unsteady CFD. Reynolds-Averaged Navier-Stokes (RANS) turbulent model is used instead of LES. The plunger is fixed at the balanced position estimated from the design specifications. Then, 2) the unsteady CFD with fixed plunger is carried out to make a time-dependent turbulent flowfiled. The turbulent model is changed to LES from RANS. Next, 3) the unsteady CFD with the vibrating plunger is carried out. At a start of 3), an initial displacement of 5-10 µm from the balanced position is given impulsively to promote the growth of the phenomenon. The calculation time is about 2 or 3 days with 200 CPU-cores. The time step size of 5 to 10 μsec is
used. It is small enough to resolve the high frequency phenomenon of the pure-tone noise and to solve the flowfield stably.
CFD RESULTS AND DISCCUSSIONS Natural frequency of plunger vibration caused by compressibility of oil Before trying to simulate the interaction between the plunger vibration and the fluid resonance for the test block model, we checked whether the developed CFD method can calculate the natural frequency of the plunger vibration caused by the compressibility of oil. Figure 16 shows the calculation model for this purpose. A long straight passage is used so that a vibration waveform of several cycles is acquired before the arrival of a pressure pulse which is generated at the plunger end by the initial impulsive displacement, proceeds along the passage, and reflects at the inflow boundary. Figure 17 shows the time history of the plunger displacement normalized by the distance from the balanced position to the seated position. As an impulse response, the plunger is moved from the balanced position to the closed direction impulsively at time=0. The plunger vibration converges and almost disappears within about 10 cycles. The frequency of the vibration is 4.5 kHz. This calculated frequency is the same as the frequency estimated in the previous chapter. This simulation result indicates that the new CFD method can evaluate the plunger vibration caused by the compressibility of oil accurately.
Figure 16 Calculation model for impulsive response
Figure 17 Time history of normalized plunger displacement obtained by CFD simulation
Comparisons between Experiment and CFD result In order to validate our new CFD method, the CFD calculations were carried out on conditions same as the experiment. The calculation conditions are shown in Table 1. The identical calculation parameters were used in both cases.
Table 1 CFD calculation conditions
Case d*
[mm] Q
[L/min] Experimental results,
pure-tone noise is 1 107 20 generated 2 84 20 not generated
*See Figure 5 Figure 18 shows the time histories of the plunger displacement and of the pressure fluctuation at P1 in Case 1. The plunger displacement is normalized by the distance from the balanced position to the seated position. The plunger vibration divergently grows up with time together with the growth of the pressure fluctuation. The pressure fluctuation seems to grow up to the same amplitude level as the experiment. Furthermore the calculated peak frequency 5.3 kHz agrees well with the frequency of the experiment (around 5 kHz).
Figure 18 Time histories of normalized plunger displacement and pressure fluctuation at the P1 obtained by CFD simulation (Case 1, d=107 [mm], Q=20 [L/min])
Figure 19 shows instantaneous contours of pressure fluctuation in the upstream passage in Case 1. It is confirmed that the standing wave is formed in the upstream passage. These calculation results show that the CFD simulation reproduces the fluid resonance as seen in the experimental results. Figure 20 shows fluctuation of the pressure distribution along the upstream passage during half cycle in Case 1. It is normalized by the same way as Fig. 8. The number of wave in the upstream passage and each position of nodes and antinodes are excellent agreement with the experiment (Fig. 8). Then, the CFD results in Case 2 are shown in Fig. 21. The plunger vibration and the pressure fluctuation don’t grow up with time. Their amplitudes are much smaller than those in Case 1. This CFD results are also good agreement with the experiment. The small pressure fluctuation is, however, seen in the Fig. 21. The frequency of the pressure fluctuation 5.9 kHz is probably the natural frequency of the fluid resonance, because the short length of the upstream passage in Case 2 raises the natural frequency from that of 5.3kHz in Case 1.
Figure 19 Instantaneous contours of pressure fluctuation in the upstream passage obtained by CFD simulation (Case 1, d=107 [mm], Q=20 [L/min])
Figure 20 Fluctuation of pressure distribution along upstream passage during half cycle obtained by CFD simulation (Case 1, d=107 [mm], Q=20 [L/min])
Figure 21 Time histories of normalized plunger displacement and pressure fluctuation at the P1 obtained by CFD simulation (Case 2, d=84 [mm], Q=20 [L/min]) Discussions The plunger vibration and the pressure fluctuations grow up with time divergently in Case 1. Further, the frequency of the plunger vibration shifts from the natural frequency. These CFD results represent the characteristic of a self-excited phenomenon. Because the CFD simulation agrees well with the experiment, it is reasonable to think that the pure-tone noise is also the self-excitation phenomenon. The schematic chart of the mechanism of the pure-tone noise is inferred in Fig. 22. The pure-tone noise is likely to be generated by energy transformation from the flow to the pressure fluctuation through the interaction between the plunger vibration and the fluid resonance. In the CFD simulation, the fluid resonance is generated even though the natural frequency of the plunger vibration 4.5 kHz slightly differs from the natural frequency of the fluid resonance that is probably about 5.3 kHz. This is probably because this interaction changes the natural frequency of the plunger vibration. The natural frequency of the fluid resonance is possibly changed a little by this interaction phenomenon. When the difference of each natural frequency becomes large, this interaction is broken off and the pure-tone noise is not generated as seen in the experiment of Case B and the CFD simulation of Case 2.
Figure 22 Schematic chart of mechanism of
pure-tone noise generation
CONCLUSIONS The computational fluid dynamics (CFD) simulation is applied to understand the detailed mechanism of the pure-tone noise generation in addition to the experimental investigation. It is revealed that the pure-tone noise is the self-excitation phenomenon caused by the interaction between the fluid resonance and the plunger vibration. The natural frequency of the plunger vibration that affects the pure-tone noise depends on the compressibility of oil in the chamber behind the plunger. The natural frequency of the fluid resonance depends on the length of upstream passage. The CFD method has been developed for the prediction tools to prevent the pure-tone noise in designing hydraulic products. The knowledge obtained through this study is useful for hydraulic system and component design.
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