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Parametric analysis on throttling components of multi-stage high pressure reducing valve
Accepted Manuscript Research Paper Parametric analysis on throttling components of high multi-stage pressure reducing valve Cong-wei Hou, Jin-yuan Qian, Fu-qiang Chen, Wei-kang Jiang, Zhi-jiang Jin PII: DOI: Reference:
S1359-4311(17)34066-8 http://dx.doi.org/10.1016/j.applthermaleng.2017.09.081 ATE 11138
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
15 June 2017 12 September 2017 16 September 2017
Please cite this article as: C-w. Hou, J-y. Qian, F-q. Chen, W-k. Jiang, Z-j. Jin, Parametric analysis on throttling components of high multi-stage pressure reducing valve, Applied Thermal Engineering (2017), doi: http:// dx.doi.org/10.1016/j.applthermaleng.2017.09.081
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Title Parametric analysis on throttling components of high multi-stage pressure reducing valve
Authors and Affiliations Cong-wei Hou1, Jin-yuan Qian1, 2, *, Fu-qiang Chen1, Wei-kang Jiang3, Zhi-jiang Jin1,* 1 Institute of Process Equipment, College of Energy Engineering, Zhejiang University, Hangzhou 310027, China 2 Department of Energy Sciences, Lund University, P.O. Box 118, SE-22100 Lund, Sweden 3 State Key Lab of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, PR China
*Corresponding authors. Tel. /fax: +86-571-87951216; E-mail: [email protected] (Jin-yuan Qian); [email protected] (Zhi-jiang Jin)
Abstract High pressure reducing valve (HPRV) is widely used for pressure and temperature control of heated steams in power plant and other related process engineering. The structures of throttling components inside HPRV have important effects on the control performances. In this paper, a parametric study of throttling components in a high multi-stage pressure reducing valve (HMSPRV) is carried out, including the relative angle of inner and outer
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porous shrouded holes, the orifice plate thickness, the number of orifice plates and the diameter of plate holes. A numerical model is established to investigate internal flow and throttling characteristics with RNG k-ε model, and it is validated by the theoretical flux calculation. The results show that, the relative angle is set as 180º can obtain the largest decompression pressure in porous shrouded, while the turbulence degree is the lowest. Setting one orifice plate can decrease the turbulent dissipation rate. The plate thickness has less influence on throttling effects. For ensuring the outlet flux, smaller diameter of plate hole should be chosen with a better flowing property about thermodynamic parameters. The work can be referred by the design work of throttling components in HMSPRV and it can also benefit the further research on similar HPRVs.
Key words High multi-stage pressure reducing valve (HMSPRV), throttling components, structural parameters, flow characteristics, Computational Fluid Dynamics (CFD)
Nomenclature A cross-sectional area of fluid passageway in the valve (m2)
D
diameter of plate hole (mm)
d
diameter of passageway (mm)
e
internal energy of micro-body (J)
f i force of gravity in i direction (m/s2)
2
k
heat transfer coefficient (W/(m2·K))
p hydrostatic pressure of the fluid (MPa)
p pressure difference about before the valve and after the valve (MPa) q
quantity of heat production about unit mass internal heat source (J)
Re Reynolds number V velocity of fluid (m/s)
u
velocity of X direction (m/s)
v
velocity of Y direction (m/s)
w velocity of Z direction (m/s) y+
non-dimensional distance
density of fluid (kg/m3) dynamic viscosity coefficient of fluid (N·s/m2)
thermal conductivity (W/(m·K))
total local resistance factor
1. Introduction With the development of energy conservation and emissions reduction projects, high pressure reducing valves (HPRV) are widely used in many fields like waste heat and pressure utilization stations and nuclear power plants. For instance, HPRV helps to ensure normal operation of steam systems by regulating the steam pressure in the injection process of hydrogen. However, traditional single-stage pressure reducing valves face numerous problems, such as low efficiency and large transmission loss, especially when they are under
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extreme conditions. Therefore, based on a novel HPRV with an orifice plate [1], a high multi-stage pressure reducing valve (HMSPRV) is developed. By adding the inner/outer porous shrouded valve cores and orifice plates as throttling elements, HMSPRVs can meet the requirements of pressure adjustment under high parameters, high flow velocities and large pressure ratio. In our previous work, a novel HMSPRV mathematical model was established [2], and the Mach number on multi-stage orifice plates in HPRV was also investigated [3]. Up to now, there have been lots of literatures describing novel structures about various valves. Alessandro et al. [4] equipped a solenoid injectors with pressure-balanced pilot valve for energy saving and dynamic response. Zhang et al. [5] proposed a self-operated three-way valve used in a hybrid air conditioner, and proved that the valve can realize the switch operation accurately. Sharafian et al. [6] presented a waste heat-driven two-adsorber bed adsorption cooling system with a novel expansion valve and control valves, and the results of the numerical modeling showed the specific cooling power of the system increased up to 6 times. Luo et al. [7] developed a pressure reducing valve with a constant pressure ratio and theoretically analyzed its pressure and leakage characteristics. A fast sampling valve was proposed by Dumitrescu et al. [8] for the purpose to acquire experimental data under conditions representative of combustion strategies. Gou et al. [9] analyzed flow field and cavitation characteristics towards a combined type pressure reducing valves by numerical simulation, and introduced an optimization model for profile line design of throttling cone. He et al. [10] studied the pressure-reducing valve for regulating the bottom pressure of the vanes at the pump suction zone, and found that the triangular-rectangular groove is proved to be more suitable for the valve among all the investigated grooves. A simplified structure for
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the pilot-operated pressure relief valve was proposed by Jang et al. [11], and the effective ranges of its design variables were determined to enable the prediction of the impact of the design variables in the design and production processes. Shahani et al. [12] presented the mathematical modeling of a high pressure regulator with its safety valve, and the performances of regulator and safety valve were investigated. Meanwhile, many other researches focused on the valve flow field analysis. Nay et al. [13] analyzed the flow forces and energy loss characteristics in a flapper-nozzle pilot valve with different null clearances, and showed an increasing energy consumption with the increasing of inlet pressure and null clearance. With a CFD approach, Binod et al. [14] investigated the dynamic modeling of flow process inside a pressure regulating and shut-off valve. Li et al. [15] researched dynamic characteristics of a solenoid valve in exhaust gas turbocharger system, and the mean control pressure values were verified by experimental data. Qiu et al. [16] showed that during the valve opening period cavitation occurs, directly affecting the fuel-offloading process of the high-pressure fuel line and delaying the time for injector needle seating to cut off fuel injection. N. Pourmahmoud et al. [17] studied the effect of inlet gas temperature change on the fluid flow characteristics and energy separation phenomenon within a counter-flow vortex tube. Wang et al. [18] focused on the influence of a circular strainer on unsteady flow behaviors in steam turbine control valves, and numerical results demonstrated that placing the strainer in the main valve resulted in dramatic changes of the flow patterns in the main valve chamber. Leutwyler et al. [19] studied the flow field, resultant force and the aerodynamic torque on a butterfly valve with a symmetric disc. Kourakos et al. [20] studied the valve opening characteristics through the determination of
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flow forces applied on the valve disk. Song et al. [21-22] simulated transient flow of a spring loaded pressure safety valve by using moving mesh, with fluid-structure interaction analysis. From above literatures, it can be found that structure is a key point to determine the performances of valves. However, the literatures about structure optimization and effects of throttling components of HMSPRV are fairly less. In this paper, a numerical model is carried out to obtain the internal fluid fields of superheated steam with different parameters of throttling components, including the relative angle of inner and outer porous shrouded holes, the thickness of the orifice plate, the number of the orifice plates and the diameter of the orifice plate holes. The work can provide a scientific support to improve throttling effects of throttling components and benefit the design work of other similar HPRVs.
2. Numerical Methods 2.1. Mathematical model To analyze the flow inside HMSPRV, the mass conservation equation and momentum conservation equation should be solved firstly. Since the analysis involves in the compressible flow and heat conduction, the energy conservation equation must also be solved. In addition, the equation of flow should be considered to calculate the outlet flux. The equation of flow rate though HPRVs is shown as follows: q
A
2p
(1)
The continuity equation is shown as follows:
u v w 0 t x y z
(2)
Motion equation is used to describe the properties of fluid flow momentum conservation.
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For Newtonian fluid, the Navier-Stokes equation can be obtained by introducing the constitutive equation of the fluid, which is shown as follows: ui ui u j p 2 V t x j xi xi 3 x j
u u j f i i x j xi
(3)
Taking mass and conservation of momentum into account, the energy law is required in numerical model, which is shown as follows: e eu j q t x j x j
T k x j
u p j x j
u j x j
2 u 2 j x j
2
u j uk x k x j
2
(4)
The equation of Reynolds number is shown as follows:
Re
Vd
(5)
2.2. Computational model Fig.1 shows the structure of HMSPRV [23]. Based on the original structure, different parameters of throttling components are designed. In Fig.1, the relative angle of inner and outer porous shrouded holes is 180º, the orifice plate thickness is 30 mm, the number of the orifice plate is 1, and the diameter of orifice plate holes is 10 mm. As for the relative angle, it can make the holes of the outer porous shrouded fixed to be horizontal, while the holes of the inner porous shrouded should be rotated downward to change the relative angle from 180º to 135º by 15º, which is shown in Fig.2. The structure is divided into 7 parts from A1 to A7, including inlet, the control organ, inner and outer porous shrouded, inlet cavity, fluid cavity, orifice plate and outlet. Four different relative angle structures are also shown in Fig.2. The thickness of the orifice plate is 25 mm, 30 mm, 35 mm and 40 mm, respectively. The number of the orifice plates is considered with the one, two
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and three orifice plates. Finally, the diameter of orifice plate hole is set as 7 mm, 8 mm, 9 mm, 10 mm, 11 mm and 12 mm, respectively. It is necessary to choose a suitable turbulence model in numerical simulations. RNG k-ε model is evolved based on the standard k-ε model. The RNG k-ε model is proved to be more accurate to describe the complex flow inside the HPRV [24]. Meanwhile, according to the geometric parameters and physical properties of steam under working status, the Reynolds number is high at turbulent flow state. Thus, the RNG k-ε model is adopted. At the same time, the ideal compressible gas model is also used with the activated energy equation and density-based solver. In terms of discretization of governing equation, finite volume method is used. For the diffusion term, the first order difference is adopted, and the first order upwind is used for the convection, turbulence and turbulence dissipation rate. 2.3 Boundary condition and gird independence check The medium in the valve is compressible superheated steam. Its temperature is 793 K, and its pressure is 10 MPa. For the boundary conditions, pressure inlet and pressure outlet are used. The static pressure is set to 10 MPa and the total temperature is set to 793 K in the inlet. Meanwhile, the static pressure is set to 1 MPa, and the total temperature is set to 793 K in the outlet. Because of the symmetry of structure, half of the actual flow fields are selected to be computed. Symmetry is the symmetry center plane. The rest surfaces, inlet surface and outlet surface are set as smooth and no-slip walls. Mesh generation plays an important role for the accuracy of the numerical model. ANSYS Mesh and ICEM are used for mesh generation. Because the structure is symmetrical, only half of the flow field model is built for the purpose of computation efficiency. Because
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of the complexity of porous shrouded and orifice plates, automatic mesh generation is adopted. An element quality check shows that, with the automatic mesh generation method, the quality of grids is good enough to be computed in the numerical simulation. Before starting the numerical simulation, a gird independence check is necessary. Changing the minimum edge length of cell cube to adjusting the grids number of computing zones, the suitable mesh generation is achieved. The original structure is selected as the model to carry out the independent verification, which is shown in Tab.1. From Tab.1, the model whose grid number is 1,709,708 is selected as the most appropriate meshing way and the minimum edge length of cell cube would be set as 1.4 mm. Here, y is used to describe the wall grid, which has an significant effect on heat-transfer characteristic. The value of y is influenced by parameters of the wall surfaces boundary layer and Reynolds number. As shown in the paper, the Reynolds number of this valve is relatively large, which is more than 10 9. Therefore, y of valve is larger than normal value. Although, y does not have a specific range of value. For y value of the wall grid, it can be seen from Fig.3 that the value of y is located in 100-4000, which is acceptable for engineering application.
3. Results and discussion 3.1 Numerical model verification In order to verify the reliability of the numerical results, a theoretical calculation of the outlet flux under different diameters of orifice plate holes is achieved to prove the accuracy of the numerical simulation. Eq. (1) is used to calculate the outlet flux of HMSPRV. Here, A is passageway cross-sectional area of the valve. The inlet and outlet diameter is 209 mm and 305 mm, respectively, and the average value 257 mm is selected as the passageway
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cross-sectional area diameter. The density ( ) of 10 MPa, 793 K superheated steam is 29.5 kg/m3. The differential pressure ( p ) is 9 MPa. The approximate value ζ is obtained. The different types and values of local resistance factors are listed in the Tab.2. The analysis of the orifice plate hole diameters on the flow field demonstrates that, the diameter of orifice plate hole influences the outlet flux significantly. Tab.3 shows the flow cross-sectional area on the orifice plate changes, changing the diameter of orifice plate hole, correspondingly. The diameter of the orifice plate before the plate is 285 mm, and the area
A1 is 63,794 mm2. The value of area after the plate also equals to A1 . The number of the orifice plate hole is 187, and the area of the flow cross-sectional on the orifice plate is A2 . The value of A2 / A1 is referred to the degree of flow cross-sectional area mutation in the throttling component. When fluid flows into the plate holes, it is the flowing runner sudden contraction model, while when fluid flows out of the holes, it is the flowing runner sudden enlargement model. The local resistance factors of those two models are determined by the degree of flow cross-sectional area mutation. In Tab.3, the theoretical value of outlet flux rises up with the hole enlarging. In fact, ζ does not have huge variation, and the flux does not change a lot. Meanwhile, the simulative tendency of the outlet flux is similar with the theoretical value, with the largest deviation between theoretical value and simulative value 10.26%. Therefore, the simulation results are credible for the following simulations. In addition, a comparison between HMSPRV and other type valves is presented to further improve the reliability. As shown in Tab.4, three different types of valves are used to compare with HMSPRV. Although the four valves are applied to different situations, they have similar working principles, function and research methods. The other three valves are
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also investigated numerically and experimentally. When biofluid flow through the throttle valve, the vortices grow and cause higher pressure drop with valve opening increasing [25]. Experimental flow visualization shows the initial position of cavitation occurred near throttle orifice by using high-speed camera. The experiment on flow resistance coefficient of a DN600 pressure-regulating valve under operation conditions from 0% to 100% openings is used to compare with the computational results [26]. The numerical simulation is employed to predict the cavitation performance of the valve at different inlet flow conditions. It is worth noting that this valve has perforated cylinder structure like HMSPRV. The CFD finite analysis model of internal flow passage of regulating valve is established to calculate the internal field of regulating valve of different opening degree, oil temperature and flow rate [27]. And the deviation of test and simulation is within the permitted error range. 3.2 Relative angle of porous shrouded holes Fig.4 shows the effects of relative angle of porous shrouded holes on pressure profiles in the symmetry plane. When fluid flows through the porous shrouded holes, its flow section shrinks rapidly. At this moment, the fluid experiences adiabatic compression, with temperature rising, velocity increasing and pressure decreasing. Then, the fluid enters into the valve chamber with flow area increasing. The fluid turns into an adiabatic expansion process, and the temperature also declines. With the flow rate decreasing, the pressure increases again. Due to the flow resistance in porous shrouded, based on the energy conservation law, the pressure cannot return to the previous value. Entering into the half bottom of the valve chamber, the bilateral pressure is lower than the middle area. It is a lower pressure area caused by the vortex flow. It is can be seen from Fig.4, the low pressure area becomes smaller
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and smaller with the decreasing of the angle. What is more, because the fluid flows out from the inner porous shrouded holes, the location of the low pressure area moves into the top of the A4 portion. After that, the fluid flows through the orifice plate again, where the orifice plate serves as the second stage throttling component. Finally, the fluid flows through the orifice plate and the pressure decreases to the outlet setting value. As the relative angle changes from 180º to 135º, the flow resistance in porous shrouded makes a difference and the pressure drop also changes. Fig.5 shows the comparison about pressure distribution in Y-axis of 180º, 165º, 150º and 135º. As is shown in Fig.5, the pressure decreased at Y=0.2 m and Y=0 significantly, which are the locations of throttling components. It is also obvious that the pressure reduction in 180º is most successful. Although the pressure of 135º drops to the trough value through the first throttling component, it upturns and tends to be stabilized in a relatively high pressure. Tab.5 shows pressures and pressure ratios after two stage throttling components. It can be found that, the effect of pressure reduction is the best when the angle is 180º. And the first level pressure ratio of 150º is the lowest one among these angles. When the angle is smaller than 150º，the first level pressure ratio increases again. In other words, the throttling effects are mostly influenced by the valve core of the inner and outer porous shrouded in HMSPRV, and if they are arranged horizontally, there can be a better throttling effect. When the relative angle is 180º, the decompression percentage on the porous shrouded is 75.6%, and the decompression percentage on the orifice plate is 24.4%. The velocity profiles and streamlines are shown in Fig.6. The flow velocity is fairly low and the fluid is steady when the fluid flows into inlet. After that, the fluid experiences an
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adiabatic compression when it flows through the valve core of porous shrouded. The pressure reduces while the velocity increases. The drastic change of flow areas forms vortex, which is a high-speed and low-pressure area. Energy consumption and the fluid channel lessen are the negative effects. The vortex area becomes larger and larger with the relative angle decreasing, and the central region of the valve chamber gets closer to the inner porous shrouded holes. The first circulations exist near the valve horizontal internal surface. They flow horizontally due to the block of walls. As a type of vertical circulation, causing by turbulence friction，the secondary circulations extends throughout the full depth of the vortex. Shown in Fig.5, the circulations mostly appear in fluid cavity (A5) and are accompanied with vortexes. Compared with velocity profiles of different angles, the maximum velocity appears after the orifice plate holes, not on the juncture of inner and outer porous shrouded. This is because the degree of mutation at the orifice plate is largest. The value of the maximum velocity is 1275 m/s, while the maximum velocity does not have obvious relation with the relative angle. The Reynolds number of the plane, which is located in the exit of the last orifice plate holes, is calculated. Eq. (5) is used to calculate Reynolds number. The average velocity of superheated steam ( V ) in this location is 350.95 m/s, 343.94 m/s, 357.02 m/s and 357.33 m/s, respectively. The diameter of the plane ( d ) is 285 mm and the density of superheated steam ( )is 29.5 kg/m3. The dynamic viscosity coefficient of steam ( ) depends on its temperature (793 K) and pressure (1 MPa). The value of it is 29.3*10 -6 N·s/m2. Therefore, Reynolds number of four structures is 1.007*108, 0.987*108, 1.024*108 and 1.025*108, respectively. The differences among them are fairly small. The large value of Re reveals the degree of turbulence after orifice plate holes is quite acute.
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As a physical quantity to characterize energy consumption generated by turbulence, the turbulent kinetic energy dissipation rate is influenced by the turbulence intensity. The vortex significantly affects the turbulence intensity. In Fig.7, with the decrease of the relative angle, turbulent dissipation rate increases continuously. Therefore, a larger relative angle means a smaller flow resistance. When the fluid flows through two throttling components in HMSPRV, it is adiabatic isentropic expansion, which can cause the dramatic decline of temperature. However, steam in HMSPRV is always at overheated state, without generating steam condensation condition. In Fig.8, the temperature profiles of inlet and outlet mainly remain unchanged. Likewise, the internal fluid temperature distributions under different relative angles are substantially the same. The lowest temperature appears after the orifice plate holes, similar to the maximum velocity. The lowest temperature is about 450 K similarly. After the lowest temperature area, the temperature swiftly increases again to a higher level, which is just lower than the original value. It can be concluded from Fig.8 that the low temperature becomes larger when the relative angle decreases. That is to say, the fluid temperature under different relative angle is similar with each other. In general, changing the relative angle does not like normal throttling principles. It makes the fluid throttling direction as an object. It can be concluded that 180º would be the ideal relative installation angle between the outer and inner porous shrouded holes. As is mentioned above, 180º has a higher pressure ratio. In addition, 180º causes less vortexes and brings lower turbulent kinetic energy dissipation rate ε. With the decrease of the relative angle, the turbulent kinetic energy dissipation rate increases correspondingly, with more
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abundant vortexes. The maximum velocity is located after the orifice plate holes, about 1,275 m/s, while for temperature, the angle does not have obvious effects on it. 3.3 Number of orifice plates In this part, the number of the orifice plates is discussed. Fig.9 describes the pressure profiles on symmetry plane with 1~3 orifice plates before the first plate. It is obvious that the pressure variation is steady with the increasing of the orifice plates. The low pressure area in the A4 and A5 portions reduces notably by the increasing of orifice plates. Besides, the low pressure area after the last orifice plate holes cuts down accordingly. Taking three orifice plates as an example, the pressure in every part does not change violently, especially between the first and the third orifice plate. Fig.9 compares the pressure variation in the Y direction. It shows obviously that the increase of orifice plates affects pressure decompression effects between the porous shrouded and the last orifice plate. For two or three orifice plates, the pressure decompression between the first and the last orifice plate accounting for the whole decompression is a small part. Moreover, the pressure before the last orifice plate is quite close in all three structures. In other word, the increasing of orifice plates does not have significant effects on pressure decompression. Tab.6 shows the pressure difference after every throttling component. Its corresponding percentages are also shown. The total pressure decompression is 9 MPa. In Tab.6, P1 is the pressure difference value after the porous shroud. It has its largest percentages, which means the porous shrouded occupies a dominant position in total pressure decompression process. However, P1 significantly drops with the increasing of orifice plates, and the throttling
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effects gradually improves. When there are three orifice plates, P1 / P reduces to 54.4%, and the throttling effect gets closer to the porous shrouded. As is can be seen in Fig.10, with the orifice plate increasing, the vortex area decreases before the last orifice plate. It also shows streamlines, which indicates that more vortex area after the last orifice plate with more orifice plates. Reynolds number is 1.007*108, 1.027*108 and 0.995*108, respectively. Fig.11 compares the turbulent dissipation rate in the Y-direction. As shown in Fig.11, the largest value occurs in the last orifice plate and it also shows the turbulent dissipation rate in the place of the last orifice plate rising up with more orifice plates. Although, the largest value among three types structures occurs in the second plate of two orifice plates modeling, approximately 2.2*109 m2/s3. For temperature, it can be concluded that the more orifice plates, the smaller temperature fluctuation. Especially in A4 and A5 portions, the temperature fluctuation area shrinks accordingly. Likewise, the temperature distribution after the last orifice plate is similar in three structures. Meanwhile, the lowest temperature also increases after the orifice plate holes, about 450 K. 3.4 Orifice plate thickness The thickness of orifice plate is the length of fluid flowing through the plate. Here, it is set as 25 mm, 30 mm, 35 mm and 40 mm, respectively, to analyze the relationship between throttling path length and throttling effect. Tab.7 shows the effects of the orifice plate thickness on throttling. It shows that for pressure, velocity and temperature, whatever the thickness becomes longer or shorter, the flow characteristics are similar with each other. It indicates throttling path length not influence factor about the fluid flowing characteristics.
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3.5 Diameter of orifice plate holes The orifice plate hole diameter determines the flow cross-sectional area, which affects throttling seriously. Fig.12 shows that the pressure profiles on symmetry plane with 7~12 mm orifice plate holes respectively. When the diameter is larger than 10mm, the outlet pressure is no longer equal to 1 MPa in Fig.12 (e) and Fig.12 (f). The outlet pressure drops to the negative pressure directly. There are evident stratification phenomena of velocity and temperature after the orifice plate holes, which are shown in Fig.13 (e) and Fig.13 (f). However, it is against the throttling effect. Considering the probable mistakes of boundary conditions or structure settings, the structures in 14 mm and 15 mm is researched to certify the validity of the numerical simulation results. The verification proves the results mentioned above. The critical value of the orifice plate hole diameter is 10 mm. When the diameter is larger than 10 mm, the flow characteristics changes greatly. To avoid it, the diameter is better to set smaller than 10 mm. In Fig.12 (a~d), the plate hole diameter affects the pressure distribution in A3, A4 and A5. Meanwhile, the pressure decreases with the hole shrinking as well. Tab.8 shows that the pressure decompression percentage of the second throttling part rises up with the decreasing of diameter. Besides, when the plate hole diameter is smaller than 8mm, the throttling effect of orifice plate surpasses the porous shrouded. According to Fig.13, the differential pressure between porous shrouded and orifice plate increases significantly by shrinking the orifice plate diameter, which proves the plate diameter has a great influence in pressure distribution. When the diameter is 7 mm, the pressure after porous shrouded is the highest among them. As is mentioned above in Tab.3, the outlet flux decreases with the holes shrinking,
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which leads to the fluid remaining in the valve chamber hampers the generation of the vortex, thus the vortex descends relatively. Then, decreasing of the vortex causes the uniform distribution of pressure in the valve chamber. Fig.14 shows that the vortex region shrinks with the diameter decreasing. The highest velocity has an evident drops as well. The same phenomenon also happens in the region after the orifice plate holes. Reynolds number is 0.903*108, 0.963*108, 0.995*108, 1.007*108, 1.264*108 and 1.293*108, respectively. It is obvious that the rising trend of Reynolds numbers is followed by enlarging orifice plate holes and it shows that the smaller orifice plate holes are beneficial to steady flow. When diameter is larger than 10 mm, Reynolds number rises swiftly from 1.007*10 8 to 1.264*108，which proves the stratification phenomena again. Meanwhile, the temperature distribution is also shown in Fig.14. It can be found that the temperature fluctuation becomes smaller with the holes shrinking. Taking 7 mm as an example, the temperature before the orifice plate holes keeps steady, especially the juncture of the outer and inner porous shrouded. Meanwhile, the low temperature region after the holes also decreases relatively. Therefore, under the premise of ensuring the outlet flux, it is better to decrease diameter of the orifice plate hole to achieve the optimizing flowing condition and less energy consumption. The smaller plate hole diameter shows better flowing condition about thermodynamic parameters including pressure, velocity and temperature.
4 Conclusions In this paper, a parametric study of throttling components of HMSPRV is carried out, including relative angle of inner and outer porous shrouded holes, orifice plate thickness, number of orifice plates and diameter of plate holes. The distribution of pressure, velocity,
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and temperature are analyzed with different structural parameters by numerical methods. The results show that, for porous shrouded, the decompression pressure of the porous shrouded is declined with the angle decreasing, thus the holes of the outer and inner porous shrouded should be arranged horizontally. Generation of the vortex always accompanies with the energy consumption, and smaller angles mean more violent vortex and more energy consumption. Meanwhile, the temperature is not influenced by the relative angle. As for the orifice plate, it is better to set only one plate in the valve in order to decrease the degree of turbulence, and the turbulent kinetic energy dissipation rate. In addition, both orifice plate number and orifice plate thickness are controlling the throttling length, and it does not produce positive effects for throttling. Finally, the orifice plate hole diameter changes the flow cross-sectional area to achieve the pressure regulating. The decreasing of plate hole diameter, pressure distribution tends to uniform distribution and the decompression effect of orifice plate improves obviously. To avoid negative effects, the diameter of plate hole should be set smaller than 10 mm. The work can be referred by the design work of throttling components in HMSPRV and it can also benefit the further research on similar HPRVs.
Acknowledgements This work is supported by the Key Project of Natural Science Foundation of Zhejiang Province, China through Grant No. LZ17E050002, the Key Science-Technology Innovation Team of Zhejiang Province, China through Grant No. 2011R50005, and the Research Project of State Key Laboratory of Mechanical System and Vibration through Grant No. MSV201705.
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[8] Dumitrescu C, Puzinauskas P V, Agrawal A K, et al. A computational study of a fast sampling valve designed to sample soot precursors inside a forming diesel spray plume[J]. Applied Thermal Engineering, 2009, 29(5): 1253-1258. [9] Gou D M, Guo P C, Zheng X B, et al. Numerical simulation analysis and optimum design for combined type pressure reducing valves[J]. Iop Conference Series: Materials Science and Engineering, 2016, 129(1). [10] He X F, Deng B, Huang X, et al. Optimization and Simulation on Pressure-Reducing Valve in Water Hydraulic Vane Pump[J]. Advanced Materials Research, 2014: 569-573. [11] Jang S C, Kang J H. Orifice Design of a Pilot-Operated Pressure Relief Valve[J]. Journal of Pressure Vessel Technology-transactions of The Asme, 2017, 139(3). [12] Shahani A R, Aryaei A, Esmaili H, et al. Mathematical Modeling of a High Pressure Regulator With Safety Valve[C]// ASME 2010, Biennial Conference on Engineering Systems Design and Analysis. 2010:457-463. [13] Aung N Z, Yang Q, Chen M, et al. CFD analysis of flow forces and energy loss characteristics in a flapper–nozzle pilot valve with different null clearances[J]. Energy Conversion and Management, 2014, 83: 284-295. [14] Saha B K, Chattopadhyay H, Mandal P B, et al. Dynamic simulation of a pressure regulating and shut-off valve[J]. Computers & Fluids, 2014, 101: 233-240. [15] Li S, Wu P, Cao L, et al. CFD simulation of dynamic characteristics of a solenoid valve for exhaust gas turbocharger system[J]. Applied Thermal Engineering, 2017, 110: 213-222.
21
[16] Qiu T, Dai H, Lei Y, et al. Dynamic flow behavior during fuel-offloaded process in control valve for unit pump fuel system[J]. Applied Thermal Engineering, 2016, 106: 153-160. [17] Pourmahmoud N, Rahimi M, Rafiee S E, Hassanzadeh A. A numerical simulation of the effect of inlet gas temperature on the energy separation in a vortex tube[J]. Journal of Engineering Science and Technology, 9(1), 81-96,2014. [18] Wang P, Liu Y. Influence of a circular strainer on unsteady flow behavior in steam turbine control valves[J]. Applied Thermal Engineering, 2017, 115: 463-476. [19] Leutwyler Z, Dalton C. A CFD study of the flow field, resultant force, and aerodynamic torque on a symmetric disk butterfly valve in a compressible fluid[J]. Journal of Pressure Vessel Technology, 2008, 130(2): 021302. [20] Kourakos V, Rambaud P, Buchlin J M, et al. Flowforce in a safety relief valve under incompressible, compressible, and two-phase flow conditions [J]. Journal of Pressure Vessel Technology, 2013, 135(1): 011305. [21] Song X G, Wang L, Park Y C. Transient analysis of a spring-loaded pressure safety valve using computational fluid dynamics (CFD)[J]. Journal of pressure vessel technology, 2010, 132(5): 054501. [22] Song X G, Wang L T, Park Y C, et al. A Fluid-structure Interaction Analysis of the Spring-Loaded Pressure Safety Valve during Popping Off[J]. Procedia Engineering, 2015, 130: 87-94.
22
[23] Chen F, Zhang M, Qian J, et al. Thermo-mechanical stress and fatigue damage analysis on multi-stage high pressure reducing valve. Annals of Nuclear Energy, 2017, 110, 753-767. [23] Xu H, Guang Z M, Qi Y Y. Hydrodynamic characterization and optimization of Contra-push check valve by numerical simulation[J]. Annals of Nuclear Energy, 2011, 38(6): 1427-1437. [24] Liu, Xiumei, et al. Biofluid flow through a throttle valve: a computational fluid dynamics study of cavitation[J]. Journal of Mechanics in Medicine & Biology, 2016, 16(03): 1650034. [25] Qu, W. S, et al. Experiment and numerical simulation of cavitation performance on a pressure-regulating valve with different openings[C]. 2015:042035. [26] Gong J, He Z. Flow analysis and experiment of pressure-regulating valve used in wet friction clutch[J]. EMEIT-12, 2012.
23
Tables Tab.1 Grid independent verification
N (104)
91
101
114
129
160
171
186
194
Flux (kg/s) 24.693 24.987 24.941 25.421 25.524 25.913 25.851 25.914
Tab.2 Different types of local resistance factors
location
value
1
inlet
0.04
2
90º standard pipe bend
0.75
3
porous shrouded
1
4
diffusion tube
0.16
5
sudden contraction
0.429~0.468
6
sudden enlargement
0.595~0.793
Tab.3 Flow cross-sectional area of orifice plate, area ratio, and outlet flux under different plate hole diameters
A2/A1
5
6
Theoretical outlet flux(kg/s)
Simulative outlet flux(kg/s)
Deviation (%)
7197
0.11
0.468
0.793
22.61
21.99
-2.7
8
9400
0.15
0.46
0.725
22.89
25.02
9.3
9
11896
0.19
0.452
0.657
23.17
25.50
10.05
10
14687
0.23
0.429
0.595
23.50
25.91
10.26
D (mm)
A2 (mm2)
7
24
Tab.4 Different parameters comparison about four types of valves
Name of valve
Medium
Valve size
Opening
Pressure (MPa)
HMSPRV
compressible superheated steam
209 mm (inlet), 305 mm (outlet)
100%
10 (inlet) ~ 1 (outlet)
Throttle valve
biofluid flow
DN8
PRV
water
DN600
PRV for wet friction clutch
oil
/
2 mm, 1.5 mm, 1.2 mm, 1 mm, 0.8 mm, 0.6 mm, 0.4 mm, 0.2 mm 20%, 40%, 60%, 80%, 100%
0 (outlet)
0.52 (inlet)
0 ~ 12 mm
0.3 (outlet)
Tab.5 Multilevel decompression pressure and pressure ratio under different relative angle
Angle
First level decompression pressure (MPa)
First level pressure ratio
Second level decompression pressure (MPa)
Second level pressure ratio
180º
3.2
3.125
1
3.2
165º
3.3
3.030
1
3.3
150º
3.6
2.778
1
3.6
135º
3.5
2.857
1
3.5
Tab.6 Multilevel decompression pressure difference and percentage under different plate numbers
P1
P1 P
P2
P2 P
P2
P3 P
P2
P4 P
(MPa)
(%)
(MPa)
(%)
(MPa)
(%)
(MPa)
(%)
1
6.8
75.6
2.2
24.4
0
0
0
0
2
5.5
61.1
0.7
7.8
2.8
31.1
0
0
3
4.9
54.4
0.6
6.7
0.9
10.0
2.6
28.9
Number of plate
25
Tab.7 Main parameters values under different thicknesses of the orifice plate
Thickness
25 mm
30 mm
35 mm
40 mm
P1 (MPa)
6.75
6.80
6.78
6.80
P2 (MPa)
2.25
2.20
2.22
2.20
109 (m2/s3)
7.8
0.66
0.59
0.9
Vmax (m/s)
1232.59
1246.72
1246.64
1239.92
Tmin (K)
415.873
409.488
413.78
413.764
Toutlet (K)
790
789
786
786
Tab.8 Multilevel decompression pressure difference and percentage under different plate hole diameters
D (mm)
P1 (MPa)
P1 P (%)
P2 (MPa)
P2 P (%)
7
3.3
36.7
5.7
63.3
8
3.8
42.2
5.2
57.8
9
5.8
64.4
3.2
35.6
10
6.8
75.6
2.2
24.4
26
List of figure captions Fig.1
Structure diagram of HMSPRV
Fig.2
Four different relative angle structures of HMSPRV
Fig.3
non-dimensional distance value (y+) of the wall grid
Fig.4
Pressure profiles on symmetry plane in 180º, 165º, 150º and 135º (MPa)
Fig.5
Comparison about pressure distribution in Y-axis of 180º, 165º, 150º and 135º (MPa)
Fig.6
Velocity profiles and streamlines on symmetry plane of 180º, 165º, 150ºand 135º (m/s)
Fig.7
Turbulent dissipation rate in the Y-direction under different angles
Fig.8
Temperature profiles on symmetry plane in 180º, 165º, 150º and 135º (K)
Fig.9
Pressure profiles on symmetry plane and comparison about pressure distribution in Y-axis of 1~ 3 plates (MPa)
Fig.10 Velocity profiles and streamlines on symmetry plane in 1~3 plates (m/s) Fig.11 Turbulent dissipation rate ε in the Y-direction under different plate number Fig.12 Pressure profiles on symmetry plane with 7~12 mm orifice plate holes (MPa) Fig.13 Comparison about pressure distribution in Y-axis of different plate hole diameters Fig.14 Velocity and temperature profiles on symmetry plane with 7~12 mm orifice plate holes (m/s, K)
27
Fig.1 Structure diagram of HMSPRV
28
Fig.2 Four different relative angle structures of HMSPRV
29
Fig.3
non-dimensional distance value (y+) of the wall grid
30
Fig.4 Pressure profiles on symmetry plane in 180º, 165º, 150º and 135º (MPa)
31
Fig.5 Comparison about pressure distribution in Y-axis of 180º, 165º, 150º and 135º (MPa)
32
Fig.6 Velocity profiles and streamlines on symmetry plane in 180º, 165º, 150º and 135º (m/s)
33
Fig.7 Turbulent dissipation rate in the Y-direction under different angles
34
Fig.8 Temperature profiles on symmetry plane in 180º, 165º, 150º and 135º (K)
35
Fig.9 Pressure profiles on symmetry plane and comparison about pressure distribution in Y-axis of 1~ 3 plates (MPa)
36
Fig.10 Velocity profiles and streamlines on symmetry plane in 1~3 plates (m/s)
37
Fig.11 Turbulent dissipation rate in the Y-direction under different plate number
38
Fig.12 Pressure profiles on symmetry plane with 7~12 mm orifice plate holes (MPa)
39
Fig.13 Comparison about pressure distribution in Y-axis of different plate hole diameters
40
Fig.14 Velocity and temperature profiles on symmetry plane with 7~12 mm orifice plate holes (m/s, K)
41
Highlights: 1. Throttling components have important effects on control performances in HPRV. 2. A parametric study of throttling components on flow characteristics is carried out. 3. Setting one orifice plate can decrease the turbulent dissipation rate. 4. Orifice plate thickness has less influence on throttling effects. 5. Smaller diameter of orifice plate hole shows better throttling effects.
42
S1359-4311(17)34066-8 http://dx.doi.org/10.1016/j.applthermaleng.2017.09.081 ATE 11138
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
15 June 2017 12 September 2017 16 September 2017
Please cite this article as: C-w. Hou, J-y. Qian, F-q. Chen, W-k. Jiang, Z-j. Jin, Parametric analysis on throttling components of high multi-stage pressure reducing valve, Applied Thermal Engineering (2017), doi: http:// dx.doi.org/10.1016/j.applthermaleng.2017.09.081
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Title Parametric analysis on throttling components of high multi-stage pressure reducing valve
Authors and Affiliations Cong-wei Hou1, Jin-yuan Qian1, 2, *, Fu-qiang Chen1, Wei-kang Jiang3, Zhi-jiang Jin1,* 1 Institute of Process Equipment, College of Energy Engineering, Zhejiang University, Hangzhou 310027, China 2 Department of Energy Sciences, Lund University, P.O. Box 118, SE-22100 Lund, Sweden 3 State Key Lab of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, PR China
*Corresponding authors. Tel. /fax: +86-571-87951216; E-mail: [email protected] (Jin-yuan Qian); [email protected] (Zhi-jiang Jin)
Abstract High pressure reducing valve (HPRV) is widely used for pressure and temperature control of heated steams in power plant and other related process engineering. The structures of throttling components inside HPRV have important effects on the control performances. In this paper, a parametric study of throttling components in a high multi-stage pressure reducing valve (HMSPRV) is carried out, including the relative angle of inner and outer
1
porous shrouded holes, the orifice plate thickness, the number of orifice plates and the diameter of plate holes. A numerical model is established to investigate internal flow and throttling characteristics with RNG k-ε model, and it is validated by the theoretical flux calculation. The results show that, the relative angle is set as 180º can obtain the largest decompression pressure in porous shrouded, while the turbulence degree is the lowest. Setting one orifice plate can decrease the turbulent dissipation rate. The plate thickness has less influence on throttling effects. For ensuring the outlet flux, smaller diameter of plate hole should be chosen with a better flowing property about thermodynamic parameters. The work can be referred by the design work of throttling components in HMSPRV and it can also benefit the further research on similar HPRVs.
Key words High multi-stage pressure reducing valve (HMSPRV), throttling components, structural parameters, flow characteristics, Computational Fluid Dynamics (CFD)
Nomenclature A cross-sectional area of fluid passageway in the valve (m2)
D
diameter of plate hole (mm)
d
diameter of passageway (mm)
e
internal energy of micro-body (J)
f i force of gravity in i direction (m/s2)
2
k
heat transfer coefficient (W/(m2·K))
p hydrostatic pressure of the fluid (MPa)
p pressure difference about before the valve and after the valve (MPa) q
quantity of heat production about unit mass internal heat source (J)
Re Reynolds number V velocity of fluid (m/s)
u
velocity of X direction (m/s)
v
velocity of Y direction (m/s)
w velocity of Z direction (m/s) y+
non-dimensional distance
density of fluid (kg/m3) dynamic viscosity coefficient of fluid (N·s/m2)
thermal conductivity (W/(m·K))
total local resistance factor
1. Introduction With the development of energy conservation and emissions reduction projects, high pressure reducing valves (HPRV) are widely used in many fields like waste heat and pressure utilization stations and nuclear power plants. For instance, HPRV helps to ensure normal operation of steam systems by regulating the steam pressure in the injection process of hydrogen. However, traditional single-stage pressure reducing valves face numerous problems, such as low efficiency and large transmission loss, especially when they are under
3
extreme conditions. Therefore, based on a novel HPRV with an orifice plate [1], a high multi-stage pressure reducing valve (HMSPRV) is developed. By adding the inner/outer porous shrouded valve cores and orifice plates as throttling elements, HMSPRVs can meet the requirements of pressure adjustment under high parameters, high flow velocities and large pressure ratio. In our previous work, a novel HMSPRV mathematical model was established [2], and the Mach number on multi-stage orifice plates in HPRV was also investigated [3]. Up to now, there have been lots of literatures describing novel structures about various valves. Alessandro et al. [4] equipped a solenoid injectors with pressure-balanced pilot valve for energy saving and dynamic response. Zhang et al. [5] proposed a self-operated three-way valve used in a hybrid air conditioner, and proved that the valve can realize the switch operation accurately. Sharafian et al. [6] presented a waste heat-driven two-adsorber bed adsorption cooling system with a novel expansion valve and control valves, and the results of the numerical modeling showed the specific cooling power of the system increased up to 6 times. Luo et al. [7] developed a pressure reducing valve with a constant pressure ratio and theoretically analyzed its pressure and leakage characteristics. A fast sampling valve was proposed by Dumitrescu et al. [8] for the purpose to acquire experimental data under conditions representative of combustion strategies. Gou et al. [9] analyzed flow field and cavitation characteristics towards a combined type pressure reducing valves by numerical simulation, and introduced an optimization model for profile line design of throttling cone. He et al. [10] studied the pressure-reducing valve for regulating the bottom pressure of the vanes at the pump suction zone, and found that the triangular-rectangular groove is proved to be more suitable for the valve among all the investigated grooves. A simplified structure for
4
the pilot-operated pressure relief valve was proposed by Jang et al. [11], and the effective ranges of its design variables were determined to enable the prediction of the impact of the design variables in the design and production processes. Shahani et al. [12] presented the mathematical modeling of a high pressure regulator with its safety valve, and the performances of regulator and safety valve were investigated. Meanwhile, many other researches focused on the valve flow field analysis. Nay et al. [13] analyzed the flow forces and energy loss characteristics in a flapper-nozzle pilot valve with different null clearances, and showed an increasing energy consumption with the increasing of inlet pressure and null clearance. With a CFD approach, Binod et al. [14] investigated the dynamic modeling of flow process inside a pressure regulating and shut-off valve. Li et al. [15] researched dynamic characteristics of a solenoid valve in exhaust gas turbocharger system, and the mean control pressure values were verified by experimental data. Qiu et al. [16] showed that during the valve opening period cavitation occurs, directly affecting the fuel-offloading process of the high-pressure fuel line and delaying the time for injector needle seating to cut off fuel injection. N. Pourmahmoud et al. [17] studied the effect of inlet gas temperature change on the fluid flow characteristics and energy separation phenomenon within a counter-flow vortex tube. Wang et al. [18] focused on the influence of a circular strainer on unsteady flow behaviors in steam turbine control valves, and numerical results demonstrated that placing the strainer in the main valve resulted in dramatic changes of the flow patterns in the main valve chamber. Leutwyler et al. [19] studied the flow field, resultant force and the aerodynamic torque on a butterfly valve with a symmetric disc. Kourakos et al. [20] studied the valve opening characteristics through the determination of
5
flow forces applied on the valve disk. Song et al. [21-22] simulated transient flow of a spring loaded pressure safety valve by using moving mesh, with fluid-structure interaction analysis. From above literatures, it can be found that structure is a key point to determine the performances of valves. However, the literatures about structure optimization and effects of throttling components of HMSPRV are fairly less. In this paper, a numerical model is carried out to obtain the internal fluid fields of superheated steam with different parameters of throttling components, including the relative angle of inner and outer porous shrouded holes, the thickness of the orifice plate, the number of the orifice plates and the diameter of the orifice plate holes. The work can provide a scientific support to improve throttling effects of throttling components and benefit the design work of other similar HPRVs.
2. Numerical Methods 2.1. Mathematical model To analyze the flow inside HMSPRV, the mass conservation equation and momentum conservation equation should be solved firstly. Since the analysis involves in the compressible flow and heat conduction, the energy conservation equation must also be solved. In addition, the equation of flow should be considered to calculate the outlet flux. The equation of flow rate though HPRVs is shown as follows: q
A
2p
(1)
The continuity equation is shown as follows:
u v w 0 t x y z
(2)
Motion equation is used to describe the properties of fluid flow momentum conservation.
6
For Newtonian fluid, the Navier-Stokes equation can be obtained by introducing the constitutive equation of the fluid, which is shown as follows: ui ui u j p 2 V t x j xi xi 3 x j
u u j f i i x j xi
(3)
Taking mass and conservation of momentum into account, the energy law is required in numerical model, which is shown as follows: e eu j q t x j x j
T k x j
u p j x j
u j x j
2 u 2 j x j
2
u j uk x k x j
2
(4)
The equation of Reynolds number is shown as follows:
Re
Vd
(5)
2.2. Computational model Fig.1 shows the structure of HMSPRV [23]. Based on the original structure, different parameters of throttling components are designed. In Fig.1, the relative angle of inner and outer porous shrouded holes is 180º, the orifice plate thickness is 30 mm, the number of the orifice plate is 1, and the diameter of orifice plate holes is 10 mm. As for the relative angle, it can make the holes of the outer porous shrouded fixed to be horizontal, while the holes of the inner porous shrouded should be rotated downward to change the relative angle from 180º to 135º by 15º, which is shown in Fig.2. The structure is divided into 7 parts from A1 to A7, including inlet, the control organ, inner and outer porous shrouded, inlet cavity, fluid cavity, orifice plate and outlet. Four different relative angle structures are also shown in Fig.2. The thickness of the orifice plate is 25 mm, 30 mm, 35 mm and 40 mm, respectively. The number of the orifice plates is considered with the one, two
7
and three orifice plates. Finally, the diameter of orifice plate hole is set as 7 mm, 8 mm, 9 mm, 10 mm, 11 mm and 12 mm, respectively. It is necessary to choose a suitable turbulence model in numerical simulations. RNG k-ε model is evolved based on the standard k-ε model. The RNG k-ε model is proved to be more accurate to describe the complex flow inside the HPRV [24]. Meanwhile, according to the geometric parameters and physical properties of steam under working status, the Reynolds number is high at turbulent flow state. Thus, the RNG k-ε model is adopted. At the same time, the ideal compressible gas model is also used with the activated energy equation and density-based solver. In terms of discretization of governing equation, finite volume method is used. For the diffusion term, the first order difference is adopted, and the first order upwind is used for the convection, turbulence and turbulence dissipation rate. 2.3 Boundary condition and gird independence check The medium in the valve is compressible superheated steam. Its temperature is 793 K, and its pressure is 10 MPa. For the boundary conditions, pressure inlet and pressure outlet are used. The static pressure is set to 10 MPa and the total temperature is set to 793 K in the inlet. Meanwhile, the static pressure is set to 1 MPa, and the total temperature is set to 793 K in the outlet. Because of the symmetry of structure, half of the actual flow fields are selected to be computed. Symmetry is the symmetry center plane. The rest surfaces, inlet surface and outlet surface are set as smooth and no-slip walls. Mesh generation plays an important role for the accuracy of the numerical model. ANSYS Mesh and ICEM are used for mesh generation. Because the structure is symmetrical, only half of the flow field model is built for the purpose of computation efficiency. Because
8
of the complexity of porous shrouded and orifice plates, automatic mesh generation is adopted. An element quality check shows that, with the automatic mesh generation method, the quality of grids is good enough to be computed in the numerical simulation. Before starting the numerical simulation, a gird independence check is necessary. Changing the minimum edge length of cell cube to adjusting the grids number of computing zones, the suitable mesh generation is achieved. The original structure is selected as the model to carry out the independent verification, which is shown in Tab.1. From Tab.1, the model whose grid number is 1,709,708 is selected as the most appropriate meshing way and the minimum edge length of cell cube would be set as 1.4 mm. Here, y is used to describe the wall grid, which has an significant effect on heat-transfer characteristic. The value of y is influenced by parameters of the wall surfaces boundary layer and Reynolds number. As shown in the paper, the Reynolds number of this valve is relatively large, which is more than 10 9. Therefore, y of valve is larger than normal value. Although, y does not have a specific range of value. For y value of the wall grid, it can be seen from Fig.3 that the value of y is located in 100-4000, which is acceptable for engineering application.
3. Results and discussion 3.1 Numerical model verification In order to verify the reliability of the numerical results, a theoretical calculation of the outlet flux under different diameters of orifice plate holes is achieved to prove the accuracy of the numerical simulation. Eq. (1) is used to calculate the outlet flux of HMSPRV. Here, A is passageway cross-sectional area of the valve. The inlet and outlet diameter is 209 mm and 305 mm, respectively, and the average value 257 mm is selected as the passageway
9
cross-sectional area diameter. The density ( ) of 10 MPa, 793 K superheated steam is 29.5 kg/m3. The differential pressure ( p ) is 9 MPa. The approximate value ζ is obtained. The different types and values of local resistance factors are listed in the Tab.2. The analysis of the orifice plate hole diameters on the flow field demonstrates that, the diameter of orifice plate hole influences the outlet flux significantly. Tab.3 shows the flow cross-sectional area on the orifice plate changes, changing the diameter of orifice plate hole, correspondingly. The diameter of the orifice plate before the plate is 285 mm, and the area
A1 is 63,794 mm2. The value of area after the plate also equals to A1 . The number of the orifice plate hole is 187, and the area of the flow cross-sectional on the orifice plate is A2 . The value of A2 / A1 is referred to the degree of flow cross-sectional area mutation in the throttling component. When fluid flows into the plate holes, it is the flowing runner sudden contraction model, while when fluid flows out of the holes, it is the flowing runner sudden enlargement model. The local resistance factors of those two models are determined by the degree of flow cross-sectional area mutation. In Tab.3, the theoretical value of outlet flux rises up with the hole enlarging. In fact, ζ does not have huge variation, and the flux does not change a lot. Meanwhile, the simulative tendency of the outlet flux is similar with the theoretical value, with the largest deviation between theoretical value and simulative value 10.26%. Therefore, the simulation results are credible for the following simulations. In addition, a comparison between HMSPRV and other type valves is presented to further improve the reliability. As shown in Tab.4, three different types of valves are used to compare with HMSPRV. Although the four valves are applied to different situations, they have similar working principles, function and research methods. The other three valves are
10
also investigated numerically and experimentally. When biofluid flow through the throttle valve, the vortices grow and cause higher pressure drop with valve opening increasing [25]. Experimental flow visualization shows the initial position of cavitation occurred near throttle orifice by using high-speed camera. The experiment on flow resistance coefficient of a DN600 pressure-regulating valve under operation conditions from 0% to 100% openings is used to compare with the computational results [26]. The numerical simulation is employed to predict the cavitation performance of the valve at different inlet flow conditions. It is worth noting that this valve has perforated cylinder structure like HMSPRV. The CFD finite analysis model of internal flow passage of regulating valve is established to calculate the internal field of regulating valve of different opening degree, oil temperature and flow rate [27]. And the deviation of test and simulation is within the permitted error range. 3.2 Relative angle of porous shrouded holes Fig.4 shows the effects of relative angle of porous shrouded holes on pressure profiles in the symmetry plane. When fluid flows through the porous shrouded holes, its flow section shrinks rapidly. At this moment, the fluid experiences adiabatic compression, with temperature rising, velocity increasing and pressure decreasing. Then, the fluid enters into the valve chamber with flow area increasing. The fluid turns into an adiabatic expansion process, and the temperature also declines. With the flow rate decreasing, the pressure increases again. Due to the flow resistance in porous shrouded, based on the energy conservation law, the pressure cannot return to the previous value. Entering into the half bottom of the valve chamber, the bilateral pressure is lower than the middle area. It is a lower pressure area caused by the vortex flow. It is can be seen from Fig.4, the low pressure area becomes smaller
11
and smaller with the decreasing of the angle. What is more, because the fluid flows out from the inner porous shrouded holes, the location of the low pressure area moves into the top of the A4 portion. After that, the fluid flows through the orifice plate again, where the orifice plate serves as the second stage throttling component. Finally, the fluid flows through the orifice plate and the pressure decreases to the outlet setting value. As the relative angle changes from 180º to 135º, the flow resistance in porous shrouded makes a difference and the pressure drop also changes. Fig.5 shows the comparison about pressure distribution in Y-axis of 180º, 165º, 150º and 135º. As is shown in Fig.5, the pressure decreased at Y=0.2 m and Y=0 significantly, which are the locations of throttling components. It is also obvious that the pressure reduction in 180º is most successful. Although the pressure of 135º drops to the trough value through the first throttling component, it upturns and tends to be stabilized in a relatively high pressure. Tab.5 shows pressures and pressure ratios after two stage throttling components. It can be found that, the effect of pressure reduction is the best when the angle is 180º. And the first level pressure ratio of 150º is the lowest one among these angles. When the angle is smaller than 150º，the first level pressure ratio increases again. In other words, the throttling effects are mostly influenced by the valve core of the inner and outer porous shrouded in HMSPRV, and if they are arranged horizontally, there can be a better throttling effect. When the relative angle is 180º, the decompression percentage on the porous shrouded is 75.6%, and the decompression percentage on the orifice plate is 24.4%. The velocity profiles and streamlines are shown in Fig.6. The flow velocity is fairly low and the fluid is steady when the fluid flows into inlet. After that, the fluid experiences an
12
adiabatic compression when it flows through the valve core of porous shrouded. The pressure reduces while the velocity increases. The drastic change of flow areas forms vortex, which is a high-speed and low-pressure area. Energy consumption and the fluid channel lessen are the negative effects. The vortex area becomes larger and larger with the relative angle decreasing, and the central region of the valve chamber gets closer to the inner porous shrouded holes. The first circulations exist near the valve horizontal internal surface. They flow horizontally due to the block of walls. As a type of vertical circulation, causing by turbulence friction，the secondary circulations extends throughout the full depth of the vortex. Shown in Fig.5, the circulations mostly appear in fluid cavity (A5) and are accompanied with vortexes. Compared with velocity profiles of different angles, the maximum velocity appears after the orifice plate holes, not on the juncture of inner and outer porous shrouded. This is because the degree of mutation at the orifice plate is largest. The value of the maximum velocity is 1275 m/s, while the maximum velocity does not have obvious relation with the relative angle. The Reynolds number of the plane, which is located in the exit of the last orifice plate holes, is calculated. Eq. (5) is used to calculate Reynolds number. The average velocity of superheated steam ( V ) in this location is 350.95 m/s, 343.94 m/s, 357.02 m/s and 357.33 m/s, respectively. The diameter of the plane ( d ) is 285 mm and the density of superheated steam ( )is 29.5 kg/m3. The dynamic viscosity coefficient of steam ( ) depends on its temperature (793 K) and pressure (1 MPa). The value of it is 29.3*10 -6 N·s/m2. Therefore, Reynolds number of four structures is 1.007*108, 0.987*108, 1.024*108 and 1.025*108, respectively. The differences among them are fairly small. The large value of Re reveals the degree of turbulence after orifice plate holes is quite acute.
13
As a physical quantity to characterize energy consumption generated by turbulence, the turbulent kinetic energy dissipation rate is influenced by the turbulence intensity. The vortex significantly affects the turbulence intensity. In Fig.7, with the decrease of the relative angle, turbulent dissipation rate increases continuously. Therefore, a larger relative angle means a smaller flow resistance. When the fluid flows through two throttling components in HMSPRV, it is adiabatic isentropic expansion, which can cause the dramatic decline of temperature. However, steam in HMSPRV is always at overheated state, without generating steam condensation condition. In Fig.8, the temperature profiles of inlet and outlet mainly remain unchanged. Likewise, the internal fluid temperature distributions under different relative angles are substantially the same. The lowest temperature appears after the orifice plate holes, similar to the maximum velocity. The lowest temperature is about 450 K similarly. After the lowest temperature area, the temperature swiftly increases again to a higher level, which is just lower than the original value. It can be concluded from Fig.8 that the low temperature becomes larger when the relative angle decreases. That is to say, the fluid temperature under different relative angle is similar with each other. In general, changing the relative angle does not like normal throttling principles. It makes the fluid throttling direction as an object. It can be concluded that 180º would be the ideal relative installation angle between the outer and inner porous shrouded holes. As is mentioned above, 180º has a higher pressure ratio. In addition, 180º causes less vortexes and brings lower turbulent kinetic energy dissipation rate ε. With the decrease of the relative angle, the turbulent kinetic energy dissipation rate increases correspondingly, with more
14
abundant vortexes. The maximum velocity is located after the orifice plate holes, about 1,275 m/s, while for temperature, the angle does not have obvious effects on it. 3.3 Number of orifice plates In this part, the number of the orifice plates is discussed. Fig.9 describes the pressure profiles on symmetry plane with 1~3 orifice plates before the first plate. It is obvious that the pressure variation is steady with the increasing of the orifice plates. The low pressure area in the A4 and A5 portions reduces notably by the increasing of orifice plates. Besides, the low pressure area after the last orifice plate holes cuts down accordingly. Taking three orifice plates as an example, the pressure in every part does not change violently, especially between the first and the third orifice plate. Fig.9 compares the pressure variation in the Y direction. It shows obviously that the increase of orifice plates affects pressure decompression effects between the porous shrouded and the last orifice plate. For two or three orifice plates, the pressure decompression between the first and the last orifice plate accounting for the whole decompression is a small part. Moreover, the pressure before the last orifice plate is quite close in all three structures. In other word, the increasing of orifice plates does not have significant effects on pressure decompression. Tab.6 shows the pressure difference after every throttling component. Its corresponding percentages are also shown. The total pressure decompression is 9 MPa. In Tab.6, P1 is the pressure difference value after the porous shroud. It has its largest percentages, which means the porous shrouded occupies a dominant position in total pressure decompression process. However, P1 significantly drops with the increasing of orifice plates, and the throttling
15
effects gradually improves. When there are three orifice plates, P1 / P reduces to 54.4%, and the throttling effect gets closer to the porous shrouded. As is can be seen in Fig.10, with the orifice plate increasing, the vortex area decreases before the last orifice plate. It also shows streamlines, which indicates that more vortex area after the last orifice plate with more orifice plates. Reynolds number is 1.007*108, 1.027*108 and 0.995*108, respectively. Fig.11 compares the turbulent dissipation rate in the Y-direction. As shown in Fig.11, the largest value occurs in the last orifice plate and it also shows the turbulent dissipation rate in the place of the last orifice plate rising up with more orifice plates. Although, the largest value among three types structures occurs in the second plate of two orifice plates modeling, approximately 2.2*109 m2/s3. For temperature, it can be concluded that the more orifice plates, the smaller temperature fluctuation. Especially in A4 and A5 portions, the temperature fluctuation area shrinks accordingly. Likewise, the temperature distribution after the last orifice plate is similar in three structures. Meanwhile, the lowest temperature also increases after the orifice plate holes, about 450 K. 3.4 Orifice plate thickness The thickness of orifice plate is the length of fluid flowing through the plate. Here, it is set as 25 mm, 30 mm, 35 mm and 40 mm, respectively, to analyze the relationship between throttling path length and throttling effect. Tab.7 shows the effects of the orifice plate thickness on throttling. It shows that for pressure, velocity and temperature, whatever the thickness becomes longer or shorter, the flow characteristics are similar with each other. It indicates throttling path length not influence factor about the fluid flowing characteristics.
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3.5 Diameter of orifice plate holes The orifice plate hole diameter determines the flow cross-sectional area, which affects throttling seriously. Fig.12 shows that the pressure profiles on symmetry plane with 7~12 mm orifice plate holes respectively. When the diameter is larger than 10mm, the outlet pressure is no longer equal to 1 MPa in Fig.12 (e) and Fig.12 (f). The outlet pressure drops to the negative pressure directly. There are evident stratification phenomena of velocity and temperature after the orifice plate holes, which are shown in Fig.13 (e) and Fig.13 (f). However, it is against the throttling effect. Considering the probable mistakes of boundary conditions or structure settings, the structures in 14 mm and 15 mm is researched to certify the validity of the numerical simulation results. The verification proves the results mentioned above. The critical value of the orifice plate hole diameter is 10 mm. When the diameter is larger than 10 mm, the flow characteristics changes greatly. To avoid it, the diameter is better to set smaller than 10 mm. In Fig.12 (a~d), the plate hole diameter affects the pressure distribution in A3, A4 and A5. Meanwhile, the pressure decreases with the hole shrinking as well. Tab.8 shows that the pressure decompression percentage of the second throttling part rises up with the decreasing of diameter. Besides, when the plate hole diameter is smaller than 8mm, the throttling effect of orifice plate surpasses the porous shrouded. According to Fig.13, the differential pressure between porous shrouded and orifice plate increases significantly by shrinking the orifice plate diameter, which proves the plate diameter has a great influence in pressure distribution. When the diameter is 7 mm, the pressure after porous shrouded is the highest among them. As is mentioned above in Tab.3, the outlet flux decreases with the holes shrinking,
17
which leads to the fluid remaining in the valve chamber hampers the generation of the vortex, thus the vortex descends relatively. Then, decreasing of the vortex causes the uniform distribution of pressure in the valve chamber. Fig.14 shows that the vortex region shrinks with the diameter decreasing. The highest velocity has an evident drops as well. The same phenomenon also happens in the region after the orifice plate holes. Reynolds number is 0.903*108, 0.963*108, 0.995*108, 1.007*108, 1.264*108 and 1.293*108, respectively. It is obvious that the rising trend of Reynolds numbers is followed by enlarging orifice plate holes and it shows that the smaller orifice plate holes are beneficial to steady flow. When diameter is larger than 10 mm, Reynolds number rises swiftly from 1.007*10 8 to 1.264*108，which proves the stratification phenomena again. Meanwhile, the temperature distribution is also shown in Fig.14. It can be found that the temperature fluctuation becomes smaller with the holes shrinking. Taking 7 mm as an example, the temperature before the orifice plate holes keeps steady, especially the juncture of the outer and inner porous shrouded. Meanwhile, the low temperature region after the holes also decreases relatively. Therefore, under the premise of ensuring the outlet flux, it is better to decrease diameter of the orifice plate hole to achieve the optimizing flowing condition and less energy consumption. The smaller plate hole diameter shows better flowing condition about thermodynamic parameters including pressure, velocity and temperature.
4 Conclusions In this paper, a parametric study of throttling components of HMSPRV is carried out, including relative angle of inner and outer porous shrouded holes, orifice plate thickness, number of orifice plates and diameter of plate holes. The distribution of pressure, velocity,
18
and temperature are analyzed with different structural parameters by numerical methods. The results show that, for porous shrouded, the decompression pressure of the porous shrouded is declined with the angle decreasing, thus the holes of the outer and inner porous shrouded should be arranged horizontally. Generation of the vortex always accompanies with the energy consumption, and smaller angles mean more violent vortex and more energy consumption. Meanwhile, the temperature is not influenced by the relative angle. As for the orifice plate, it is better to set only one plate in the valve in order to decrease the degree of turbulence, and the turbulent kinetic energy dissipation rate. In addition, both orifice plate number and orifice plate thickness are controlling the throttling length, and it does not produce positive effects for throttling. Finally, the orifice plate hole diameter changes the flow cross-sectional area to achieve the pressure regulating. The decreasing of plate hole diameter, pressure distribution tends to uniform distribution and the decompression effect of orifice plate improves obviously. To avoid negative effects, the diameter of plate hole should be set smaller than 10 mm. The work can be referred by the design work of throttling components in HMSPRV and it can also benefit the further research on similar HPRVs.
Acknowledgements This work is supported by the Key Project of Natural Science Foundation of Zhejiang Province, China through Grant No. LZ17E050002, the Key Science-Technology Innovation Team of Zhejiang Province, China through Grant No. 2011R50005, and the Research Project of State Key Laboratory of Mechanical System and Vibration through Grant No. MSV201705.
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[8] Dumitrescu C, Puzinauskas P V, Agrawal A K, et al. A computational study of a fast sampling valve designed to sample soot precursors inside a forming diesel spray plume[J]. Applied Thermal Engineering, 2009, 29(5): 1253-1258. [9] Gou D M, Guo P C, Zheng X B, et al. Numerical simulation analysis and optimum design for combined type pressure reducing valves[J]. Iop Conference Series: Materials Science and Engineering, 2016, 129(1). [10] He X F, Deng B, Huang X, et al. Optimization and Simulation on Pressure-Reducing Valve in Water Hydraulic Vane Pump[J]. Advanced Materials Research, 2014: 569-573. [11] Jang S C, Kang J H. Orifice Design of a Pilot-Operated Pressure Relief Valve[J]. Journal of Pressure Vessel Technology-transactions of The Asme, 2017, 139(3). [12] Shahani A R, Aryaei A, Esmaili H, et al. Mathematical Modeling of a High Pressure Regulator With Safety Valve[C]// ASME 2010, Biennial Conference on Engineering Systems Design and Analysis. 2010:457-463. [13] Aung N Z, Yang Q, Chen M, et al. CFD analysis of flow forces and energy loss characteristics in a flapper–nozzle pilot valve with different null clearances[J]. Energy Conversion and Management, 2014, 83: 284-295. [14] Saha B K, Chattopadhyay H, Mandal P B, et al. Dynamic simulation of a pressure regulating and shut-off valve[J]. Computers & Fluids, 2014, 101: 233-240. [15] Li S, Wu P, Cao L, et al. CFD simulation of dynamic characteristics of a solenoid valve for exhaust gas turbocharger system[J]. Applied Thermal Engineering, 2017, 110: 213-222.
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[16] Qiu T, Dai H, Lei Y, et al. Dynamic flow behavior during fuel-offloaded process in control valve for unit pump fuel system[J]. Applied Thermal Engineering, 2016, 106: 153-160. [17] Pourmahmoud N, Rahimi M, Rafiee S E, Hassanzadeh A. A numerical simulation of the effect of inlet gas temperature on the energy separation in a vortex tube[J]. Journal of Engineering Science and Technology, 9(1), 81-96,2014. [18] Wang P, Liu Y. Influence of a circular strainer on unsteady flow behavior in steam turbine control valves[J]. Applied Thermal Engineering, 2017, 115: 463-476. [19] Leutwyler Z, Dalton C. A CFD study of the flow field, resultant force, and aerodynamic torque on a symmetric disk butterfly valve in a compressible fluid[J]. Journal of Pressure Vessel Technology, 2008, 130(2): 021302. [20] Kourakos V, Rambaud P, Buchlin J M, et al. Flowforce in a safety relief valve under incompressible, compressible, and two-phase flow conditions [J]. Journal of Pressure Vessel Technology, 2013, 135(1): 011305. [21] Song X G, Wang L, Park Y C. Transient analysis of a spring-loaded pressure safety valve using computational fluid dynamics (CFD)[J]. Journal of pressure vessel technology, 2010, 132(5): 054501. [22] Song X G, Wang L T, Park Y C, et al. A Fluid-structure Interaction Analysis of the Spring-Loaded Pressure Safety Valve during Popping Off[J]. Procedia Engineering, 2015, 130: 87-94.
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Tables Tab.1 Grid independent verification
N (104)
91
101
114
129
160
171
186
194
Flux (kg/s) 24.693 24.987 24.941 25.421 25.524 25.913 25.851 25.914
Tab.2 Different types of local resistance factors
location
value
1
inlet
0.04
2
90º standard pipe bend
0.75
3
porous shrouded
1
4
diffusion tube
0.16
5
sudden contraction
0.429~0.468
6
sudden enlargement
0.595~0.793
Tab.3 Flow cross-sectional area of orifice plate, area ratio, and outlet flux under different plate hole diameters
A2/A1
5
6
Theoretical outlet flux(kg/s)
Simulative outlet flux(kg/s)
Deviation (%)
7197
0.11
0.468
0.793
22.61
21.99
-2.7
8
9400
0.15
0.46
0.725
22.89
25.02
9.3
9
11896
0.19
0.452
0.657
23.17
25.50
10.05
10
14687
0.23
0.429
0.595
23.50
25.91
10.26
D (mm)
A2 (mm2)
7
24
Tab.4 Different parameters comparison about four types of valves
Name of valve
Medium
Valve size
Opening
Pressure (MPa)
HMSPRV
compressible superheated steam
209 mm (inlet), 305 mm (outlet)
100%
10 (inlet) ~ 1 (outlet)
Throttle valve
biofluid flow
DN8
PRV
water
DN600
PRV for wet friction clutch
oil
/
2 mm, 1.5 mm, 1.2 mm, 1 mm, 0.8 mm, 0.6 mm, 0.4 mm, 0.2 mm 20%, 40%, 60%, 80%, 100%
0 (outlet)
0.52 (inlet)
0 ~ 12 mm
0.3 (outlet)
Tab.5 Multilevel decompression pressure and pressure ratio under different relative angle
Angle
First level decompression pressure (MPa)
First level pressure ratio
Second level decompression pressure (MPa)
Second level pressure ratio
180º
3.2
3.125
1
3.2
165º
3.3
3.030
1
3.3
150º
3.6
2.778
1
3.6
135º
3.5
2.857
1
3.5
Tab.6 Multilevel decompression pressure difference and percentage under different plate numbers
P1
P1 P
P2
P2 P
P2
P3 P
P2
P4 P
(MPa)
(%)
(MPa)
(%)
(MPa)
(%)
(MPa)
(%)
1
6.8
75.6
2.2
24.4
0
0
0
0
2
5.5
61.1
0.7
7.8
2.8
31.1
0
0
3
4.9
54.4
0.6
6.7
0.9
10.0
2.6
28.9
Number of plate
25
Tab.7 Main parameters values under different thicknesses of the orifice plate
Thickness
25 mm
30 mm
35 mm
40 mm
P1 (MPa)
6.75
6.80
6.78
6.80
P2 (MPa)
2.25
2.20
2.22
2.20
109 (m2/s3)
7.8
0.66
0.59
0.9
Vmax (m/s)
1232.59
1246.72
1246.64
1239.92
Tmin (K)
415.873
409.488
413.78
413.764
Toutlet (K)
790
789
786
786
Tab.8 Multilevel decompression pressure difference and percentage under different plate hole diameters
D (mm)
P1 (MPa)
P1 P (%)
P2 (MPa)
P2 P (%)
7
3.3
36.7
5.7
63.3
8
3.8
42.2
5.2
57.8
9
5.8
64.4
3.2
35.6
10
6.8
75.6
2.2
24.4
26
List of figure captions Fig.1
Structure diagram of HMSPRV
Fig.2
Four different relative angle structures of HMSPRV
Fig.3
non-dimensional distance value (y+) of the wall grid
Fig.4
Pressure profiles on symmetry plane in 180º, 165º, 150º and 135º (MPa)
Fig.5
Comparison about pressure distribution in Y-axis of 180º, 165º, 150º and 135º (MPa)
Fig.6
Velocity profiles and streamlines on symmetry plane of 180º, 165º, 150ºand 135º (m/s)
Fig.7
Turbulent dissipation rate in the Y-direction under different angles
Fig.8
Temperature profiles on symmetry plane in 180º, 165º, 150º and 135º (K)
Fig.9
Pressure profiles on symmetry plane and comparison about pressure distribution in Y-axis of 1~ 3 plates (MPa)
Fig.10 Velocity profiles and streamlines on symmetry plane in 1~3 plates (m/s) Fig.11 Turbulent dissipation rate ε in the Y-direction under different plate number Fig.12 Pressure profiles on symmetry plane with 7~12 mm orifice plate holes (MPa) Fig.13 Comparison about pressure distribution in Y-axis of different plate hole diameters Fig.14 Velocity and temperature profiles on symmetry plane with 7~12 mm orifice plate holes (m/s, K)
27
Fig.1 Structure diagram of HMSPRV
28
Fig.2 Four different relative angle structures of HMSPRV
29
Fig.3
non-dimensional distance value (y+) of the wall grid
30
Fig.4 Pressure profiles on symmetry plane in 180º, 165º, 150º and 135º (MPa)
31
Fig.5 Comparison about pressure distribution in Y-axis of 180º, 165º, 150º and 135º (MPa)
32
Fig.6 Velocity profiles and streamlines on symmetry plane in 180º, 165º, 150º and 135º (m/s)
33
Fig.7 Turbulent dissipation rate in the Y-direction under different angles
34
Fig.8 Temperature profiles on symmetry plane in 180º, 165º, 150º and 135º (K)
35
Fig.9 Pressure profiles on symmetry plane and comparison about pressure distribution in Y-axis of 1~ 3 plates (MPa)
36
Fig.10 Velocity profiles and streamlines on symmetry plane in 1~3 plates (m/s)
37
Fig.11 Turbulent dissipation rate in the Y-direction under different plate number
38
Fig.12 Pressure profiles on symmetry plane with 7~12 mm orifice plate holes (MPa)
39
Fig.13 Comparison about pressure distribution in Y-axis of different plate hole diameters
40
Fig.14 Velocity and temperature profiles on symmetry plane with 7~12 mm orifice plate holes (m/s, K)
41
Highlights: 1. Throttling components have important effects on control performances in HPRV. 2. A parametric study of throttling components on flow characteristics is carried out. 3. Setting one orifice plate can decrease the turbulent dissipation rate. 4. Orifice plate thickness has less influence on throttling effects. 5. Smaller diameter of orifice plate hole shows better throttling effects.
42