New Developments in Fluid Mechanics and Its Engineering Applications
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Yudong Xie, Yong Wang, Yanjun Liu, Fang Cao, Yongcheng Pan, "Unsteady Analyses of a Control Valve due to FluidStructure Coupling", Mathematical Problems in Engineering, vol. 2013, Article ID 174731, 7 pages, 2013. https://doi.org/10.1155/2013/174731
Unsteady Analyses of a Control Valve due to FluidStructure Coupling
Abstract
Control valves play important roles in the control of the mixedgas pressure in the combined cycle power plants (CCPP). In order to clarify the influence of coupling between the structure and the fluid system at the control valve, the coupling mechanism was presented, and the numerical investigations were carried out. At the same operating condition in which the pressure oscillation amplitude is greater when considering the coupling, the loworder natural frequencies of the plug assembly of the valve decrease obviously when considering the fluidstructure coupling action. The loworder natural frequencies at 25% valve opening, 50% valve opening, and 75% valve opening are reduced by 11.1%, 7.0%, and 3.8%, respectively. The results help understand the processes that occur in the valve flow path leading to the pressure control instability observed in the control valve in the CCPP.
1. Introduction
The steel mills generate vast amounts of blast furnace gas (BFG) and cokeoven gas (COG) in the production. In order to reduce the environmental pollution, some steel mills mix BFG with COG and build combined cycle power plants (CCPP) to make use of the gas [1]. For the normal operation of CCPP, the pressure of mixed gas delivered to the gas turbine should be kept in a steady range.
In CCPP, control valves play important roles in the control of the mixedgas pressure. The signal of mixedgas pressure measured using the pressure meter is compared to the signal of the desired pressure by the controller. The controller output accordingly adjusts the opening/closing actuator of the control valve in order to maintain the actual pressure close to the desired pressure. The opening of the control valve depends on the flow forces and the driving forces of the controlvalve actuator, while the flow forces and the driving forces are affected by the valve opening. Therefore, there is strong coupling interaction between the fluid and the control valve structure.
According to Morita et al. (2007) and Yonezawa et al. (2008), the typical flow pattern around the control valve is transonic [2, 3]. When pressure fluctuations occur, large static and dynamic fluid forces will act on the valves. Consequently, problematic phenomena, such as valve vibrations and loud noises, can occur, with the worst cases resulting in damage of the valve plug and seal [4]. In order to understand the underlying physics of flowinduced vibrations in a steam control valve head, experimental investigations described by Yonezawa et al. (2012) are carried out. Misra et al. (2002) reported that the selfexcited vibration of a piping system occurs due to the coincidence of water hammer, acoustic feedback in the downstream water piping, high acoustic resistance at the control valve, and negative hydraulic stiffness at the control valve [5]. Araki et al. (1981) reported that the steam controlvalve head oscillation mechanism was forced vibration, while selfexcited vibration was not observed [6].
Those studies cited previously are mainly aimed at the modeling of the selfexcited vibration, the analysis of vibration parameters stability, and so on [7–11]. Whereas, the studies on the influence of nonlinear fluidstructure coupling of control valve on the valve control characteristics, such as the pressure regulation feature, are still very limited [12–17]. In the CCPP, the valve control characteristics affected by the fluidstructure coupling are particularly important for the stability of the mixedgas pressure control. It has not been uncommon to see that the instability of the mixedgas pressure causes a severe disturbance or even an emergency shutdown of the whole plant, and the handling of such an emergency often becomes a source of new problems and confusion. In this paper, numerical investigations are carried out to clarify the influence of fluidstructure coupling of control valve on not only the flow field but also the gas pressure regulation and the natural frequency changes of the control valve. This study helps understand the processes that occur in the valve flow path leading to the mixedgas pressure pulsations, which is valuable for the pressure stability control of the mixed gas in the CCPP.
2. FluidStructure Coupling Mechanism of Control Valve
When the mixed gas passes through the control valve, the gas pressure and flow rate change with the valve opening, as shown in Figure 1. and express the inlet pressure and outlet pressure of mixed gas, respectively. and denote the inlet flow rate and outlet flow rate of mixed gas, respectively.
The flow infinitesimal of mixed gas is shown in Figure 2. According to the law of conservation of mass, we can get where , , and represent the direction crosssectional area, direction crosssectional area, and direction crosssectional area of the flow infinitesimal, respectively. expresses the mixedgas density. , , and denote direction velocity component, direction velocity component, and direction velocity component, respectively.
According to the balance equation of dynamic flow, we can obtain
According to the equation of flow continuity, we have
Based on (1)~(3), the flow equation of mixed gas in control valve can be described as where is the bulk modulus of elasticity of the flow.
The discrete pressure distribution of mixedgas flow field, using Galerkin method, can be expressed as follows: where is the shape function matrix and is the pressure vector. can be written as
can be described as Then where is the residual part. The value choice of should make the value of get the minimum. Using Galerkin method, can be calculated as
The discrete flow equation of mixed gas can be described as where is the displacement vector, represents the coordinate transformation matrix, denotes the input exciting vector, expresses the flow domain volume, is the insertion function vector of structure system, is the surface area of the fluidstructure edge, and denotes the surface area of the boundary of flange interface of control valve.
The motion equation of structure domain can be written as where is the mass matrix of structure, denotes the damping matrix, is the structure stiffness matrix, expresses the flownodal force vector of the fluidstructure edge, and is the external exciting vector.
In the fluidstructure edge, the generalized normal force vector of the flow infinitesimal is as follows: where is the shape function vector of the structure infinitesimal, is the surface area of the fluidstructure edge of the infinitesimal, denotes the shape function vector of the flow infinitesimal, and is the pressure vector of the flow infinitesimal.
From (11) and (12), we can get
Based on (10) and (13), the fluidstructure coupling model of control valve can be described as with
3. Influence Analyses of the FluidStructure Coupling
In this section, numerical simulations utilizing ANSYS, CFX, and Workbench were performed. In the analysis, a time step of 0.0005 s was used. A compressible, ideal gas flow was assumed for simulations. Inflow boundary conditions based on an inlet total pressure of 2 MPa and a temperature of 240°C were specified at the inlet plane of the control valve. At the outflow plane of the control valve, a flow rate of 20 kg/s was maintained. The reference pressure of the model environment was normal atmospheric pressure. The initial velocity vector was zero. And the mean residual of the convergence of the solution was less than 0.001.
Figure 3 shows the general structure of the flow field through the control valve, which depicts the streamlines without fluidstructure coupling. For the time period of the simulation, about 32 cycles of data were collected. The progression of the simulation at intervals of is shown in Figure 3. When taking the fluidstructure coupling into account, the general structure of the flow field is shown in Figure 4. As it is seen from Figures 3 and 4, after considering the fluidstructure coupling, some of the secondary flow structures present in the corner regions of the valve housing, and the large recirculation develops in the bottom and upper portion of the valve body as the flow negotiates the transition from the valve assembly to the valve outlet. The flow sharply accelerates around the valve seat region.
(a)
(b)
(c)
(d)
(a)
(b)
(c)
(d)
The unsteady flow, as stated in Figure 4, causes pressure fluctuations with random and impulsive wave forms. The pressure distributions of the flow field through the control valve, considering and not considering the fluidstructure coupling, are shown in Figure 5. The peak pressure presented in Figure 5(a) is 1.9 MPa, while the peak pressure that appeared in Figure 5(b) is 2.3 MPa. Furthermore, the maximum pressure position shown in Figure 5(b) is different from that shown in Figure 5(a). In order to verify the influence of fluidstructure coupling on the gas pressure regulation of the control valve, a sine pressure with an amplitude of 1 MPa and an initial value of 1 MPa was specified at the inlet of the control valve. Figure 6 gives timehistory plots of outlet pressure changes of control valve as compared to the inlet pressure changes without considering fluidstructure coupling. The outlet pressure can follow the inlet pressure signal well, which does not have obvious oscillations. When taking the fluidstructure coupling into account, the timehistory plots of outlet pressure changes of control valve as compared to the inlet pressure changes are shown in Figure 7. The simulation process with fluidstructure coupling has obvious pressure oscillations that are far greater than those obtained from the simulation process without fluidstructure coupling. As a result, the coupled oscillations of the flow in the control valve are maintained at certain operating conditions, and the fluid force acting on the valve plug becomes a random and pulselike wave form, as shown in Figure 8. This fluid force is added to the driving force of the control valve, which brings about the result that the resultant force may be greater or less than the control force used to adjust the valve opening, and consequently, the control precision of the control valve is reduced.
(a) Not considering fluidstructure coupling
(b) Considering fluidstructure coupling
Table 1 shows the natural frequencies obtained by the simulation at different valve opening positions. When taking the fluidstructure coupling into account, the loworder natural frequencies of the plug assembly of the control valve decrease. The firstorder natural frequencies at 25% valve opening, 50% valve opening, and 75% valve opening are reduced by 11.1%, 7.0%, and 3.8%, respectively. As a result, the vibrations become easy to excite due to the pressure fluctuations caused by the fluidstructure coupling. At the same time, the valve plug vibration affects the pressure fluctuation. The pressure fluctuation increases when the valve plug vibration increases, and in some cases with very small valve opening ratios, the valve plug hits the valve seat.

4. Conclusions
Fluidstructure interaction between the structure and the fluid system at the control valve has to be taken into account for the analysis of the control valve characteristics. This is extremely useful in a better understanding of the detailed flow physics that occur in control valves. The general structure of the flow field through the control valve, the valve plug vibration, and the pressure regulation performance are affected by the fluidstructure coupling. The unsteady fluid force due to the coupled oscillations of the flow in the control valve is added to the driving force of the control valve, which brings about the result that the resultant force may be greater or less than the control force used to adjust the valve opening, and consequently, the control precision of the control valve is reduced.
Acknowledgments
This work is supported by the National Natural Science Foundation of China (Grant no. 51305234), Special Funds for Postdoctoral Innovative Projects of Shandong Province (no. 201103033), Independent Innovation Foundation of Shandong University (IIFSDU no. 2011GN045), and Key Laboratory of HighEfficiency and Clean Mechanical Manufacture at Shandong University of Education Ministry.
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Copyright © 2013 Yudong Xie et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.