Hai-min WANG （王海民）， Yue ZHAO （趙越）， Jian-xing WANG （汪建興）， Xiang-shuai KONG （孔祥帥），Huan LIU （劉歡）， Ke-liang LI （李科良）， Xi-fang WANG （王喜芳）

1. School of Energy and Power Engineering， University of Shanghai for Science and Technology， Shanghai 200093， China

2. Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering， University of Shanghai for Science and Technology， Shanghai 200093， China， E-mail: hmwang@usst.edu.cn

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Numerical simulation of flow characteristics for a labyrinth passage in a pressure valve*

Hai-min WANG （王海民）1，2， Yue ZHAO （趙越）1， Jian-xing WANG （汪建興）1， Xiang-shuai KONG （孔祥帥）1，Huan LIU （劉歡）1， Ke-liang LI （李科良）1， Xi-fang WANG （王喜芳）1

1. School of Energy and Power Engineering， University of Shanghai for Science and Technology， Shanghai 200093， China

2. Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering， University of Shanghai for Science and Technology， Shanghai 200093， China， E-mail: hmwang@usst.edu.cn

A tortuous labyrinth passage consists of a series of right angle turns in a disk of high pressure control valve. In this paper，numerical simulations are made for the velocity and pressure distributions in this passage. It is shown that the “series passage” can induce a pressure dropping more effectively. The main function of the “series passage” is to induce a pressure dropping while the“parallel passage” is mainly to regulate the flow-rate. As a cross sectional area process， a series of reduction and expansion， the pressure will also see dropping and partial recovery， which is called the multistage pressure drop. By this way， the velocity can be controlled in a reasonable level anywhere in this tortuous labyrinth passage. With the fluid pressure dropping in a downwards serrated way， the pressure is higher than the local saturate vapor pressure， therefore， no cavitation is induced by the phase transition. Key words: tortuous labyrinth passage， right angle turns， multistage pressure drop， pressure recover

Introduction

The high pressure pump recirculation is one of the most difficult issues and severe duty control valve installations are demanded by the power industry. There are two significant features in this respect. First，the flow must be controlled during a very high pressure drop and second， when not in the controlling flow mode， a tight leak proof shut off is required. Failure to achieve either of these functions will quickly result in a plant shutdown or the loss of the valuable energy over an extended period［1］.

The recirculation valve must perform two important functions［2］. Firstly， it must control the fluid during the large pressure letdown while it is open at all plug positions and secondly， it must ensure that there is no leakage when the valve is closed. This paper will focus on the control of the large pressure drop［3］. The kernel throttling component is a stack formed by welding a number of disks together， and each disk consists of a few tortuous paths just as shown in Fig.1［4］.

Fig.1 The disks with 4 tortuous paths on both sides

Figure 1 shows three significant features of the disk channel. （1） Right angle turns. To yield a great pressure drop and to consume the energy of the fluid，a series right angle turns make up the passage. （2）Expanding passage size. The flow area is continuallyincreasing as the fluid pressure decreases. （3） Large number of stages. When the fluid flows through a right angle turn， the pressure will drop at once and then we will see a expanding size， the pressure will recover partly， thus the fluid will experience a number of stages before it flows into the pressure equalizing ring.

As the pressure drop in the passage is mainly caused by the loss of the local resistance. The structure of the passage and the boundary conditions are both the key factors that determine the pressure drop results［5］. Many types of orifices or orifice tubes were used to yield a high pressure drop. For example， as the flow zoning in the different subassemblies of the reactor core is formed by installing permanent pressure dropping devices in the foot of the subassembly， Pandey et al.［6］developed orifices having a honey-comb type geometry to meet the requirements of a fuel zone for the flow zoning. Senocak and shyy［7］studied the pressure loss characteristics of the square-edged orifice and the perforated plates. Wu et al.［8］modeled hydraulic control systems that contain flow modulation valves，and the results are highly influenced by the accuracy of the equation describing the flow through an orifice. Abou El-Azm et al.［9］investigated the pressure drop after such fractal orifices and measured the pressure recovery at different stations downstream the orifice. Jankowski et al.［10］developed a simple model to predict the pressure drop and the discharge coefficient for incompressible flow through orifices with length-todiameter ratio greater than zero （orifice tubes） over wide ranges of Reynolds number.

The tortuous passage is widely used to reduce the fluid pressure through multistage throttling in many engineering applications. In our previous work， different passages were used to produce the multistage pressure drop and they were studied by experimental and CFD approaches［11，12］. Xia et al.［13］proposed a new modified relation for predicting the pressure drop in the helical rectangle channel. Moraczewski and Shapley［14］investigated the pressure drop of concentrated suspensions flowing through an axisymmetric contraction-expansion channel at a low Reynolds number. The passage structure and the boundary conditions are both the key factors that determine the pressure drop results. Adachi and Hasegawa［15］studied the transition of the flow in a symmetric channel with periodically expanded grooves. Zhang et al.［16］performed a multi objective optimization to improve the structure of trapezoidal labyrinth channels. Pfau et al.［17］presented a highly resolved experimental data set taken in an inlet cavity of a rotor tip labyrinth seal. Parvaneh et al.［18］revealed the hydraulic performance of asymmetric labyrinth side weirs located on a straight channel. Crookston and Tullis［19］increased the discharge capacity and the hydraulic efficiency of a labyrinth weir with an Arced cycle configuration. Novak et al.［20］focused on the flow at the side weir in a narrow flume.

In this paper， the tortuous passage investigated is different from previous studies， especially， the geometric configuration and the passage size. The distinctive feature of the passage is the narrow dimension， with the smallest cross section being only 0.0025 m× 0.0040 m. Based on this structure， the CFD approach will be used to analyze the pressure drop and the pressure loss coefficient under different operation conditions.

Fig.2 The geometric configuration of a labyrinth passage （prototype）

1. The geometric features of labyrinth passage

The sketch of a labyrinth passage is shown in Fig.2， where the flow direction and path are shown. The flow enters the tortuous pathway and flows inwardly to the plug. Each flow channel consists of several right angle turns （stages）， which accounts for more than one velocity head of the pressure drop. With the flow area continually increasing， the fluid pressure decreases. Thus the velocity is continuously reduced to a very reasonable level at the expanding passage section. There are no local pressure recovery points for the cavitation to take place in the pathway such as what occurs with a drilled hole type pathway. This is the one of the great advantages of the labyrinth passage as compared to the hole type ones.

There are 24 right angle turns in this labyrinth passage. In order to illustrate the features of right angle turns and expanding passage size， along the flow direction， a series of dimension sizes are defined in Fig.2， such as the inlet S0， the first throttling section L1，D，and the first expanding space in the tangential and normal directionsS1，L1，Rand so on. All these sizes are given in Table 1.

Table 1 The dimension size in Fig.2 （m）

In the dimensions in Table 1， we define S0to L6，Ras the “series passage”， where there is only a single way in and out， while afterL6，R， the flow is divided into two parallel parts， which is defined as the“parallel passage”， and it is shown that the narrowest in the “series passage” is 0.0040 m， while it is only 0.0025 m in the “parallel passage”. So it is very difficult to mount the sensors to test the pressure and the velocity in the passage. Therefore， two alternative solutions might be adopted， one is the model experiment，which will scale and enlarge the prototype passage，and the other way is to use the CFD method for a numerical simulation. In the following sections， the model experiment results will be used to validate the CFD results and provide a series of simulation results to analyze the flow characteristics in the prototype labyrinth passage.

2. Validation of the numerical method

In order to validate the current numerical method，a model experiment is conducted by selecting a part of labyrinth passage just as shown in Fig.3. For the convenience of mounting the pressure sensors， the passage is scaled to 4 times of the prototype， the inlet and the outlet are also shown in Fig.3.

Fig.3 A model passage used in experiment （scaled 4 times for the mounting pressure sensor conveniently）

There are total 7 YOKOGAWA EJA110A（0 kPa-500 kPa） pressure differential transmitters used in the experiment as shown in Fig.4（a）. To avoid the severe vortex area and also to ensure the locations not far away from the pressure wave section， the pressure sampling points are located near the throttling section. The locations of all 7 points are shown in Fig.3 too.

The FLUENT software is used to solve the governing equations for the water phase. As the height of the channel is relatively small （only 0.0040 m in the prototype） as compared with the length of the flow passage， so the 2-D and single-precision solver is chosen. The implicit scheme of the segregated algorithm is adopted. Then the standard k-εturbulence model，the second-order upwind scheme， and the SIMPLE algorithm are used for the solutions. Figure 4（b） shows the pressure contours of the selected model passage.

Fig.4（a） The pressure sampling points in the model passage

Fig.4（b） Pressure contours of model passage

Fig.4（c） The simulation vs. the experiment results at different points

Figure 4（c） depicts the simulation and experiment results for the static pressure at each sampling point，wherep is the pressure of monitoring stations selected as required，pxis the positions of the pressure measuring point in the passage. The CFD simulation boundary conditions foor this case are as follows: the water temperature is 15C， the inlet velocity is 9.5 m/s，the inlet static pressure is 355.6 kPa and the outlet static pressure is 118.1 kPa. The Reynolds number is 1.315×105correspondingly at the inlet section. The results indicate that the difference is very small. For example， the maximum difference is at point 6， which is about 4.5%. Therefore， the 2-D CFD simulation approach is valid to investigate the characteristics of the pressure and the velocity in the labyrinth passage.

3. Numerical results of prototype passage

3.1 The boundary conditions

The geometrical structure of the prototype passage is shown in Fig.2. The boundary conditions for different cases are listed in Table 2.

Table 2 The boundary conditions for 3 cases

Fig.5 Flow characteristics of labyrinth passage for Case 1

3.2 The pressure and the velocity in the passage

Figure 5 shows the pressure contours and the velocity vectors of the prototype channel in the following case: the inlet velocity is 6.33 m/s （Reynolds number Re=1.051× 105） and outlet pressure is 1.6 kPa.

The numerical results of the contours in Fig.5（a）show that the pressure in the “series passage” is dropped from 400 kPa to 165 kPa， the difference is 335 kPa. While the pressure difference in the “parallel passage” is only about 163.4 kPa. That is， the former contributes about 83.8% of the total pressure drop. The pressure loss coefficient ξ=16.72.

The velocity vector depicted in Fig.5（b） indicates six large vortex areas in the passage where the right angle turns are distributed along the flow direction. It is also shown that from the first vortex to the fifth in the “series passage”， the area of the vortex section is increased gradually， but every vortex density eddy still maintains at a reasonable level without dramatic changes. Judged from the density variations of the stream lines， they vary also gently. It denotes that the pressure drops evenly too， thus the energy losses are kept within a certain range through each corner.

Fig.6 Flow characteristics of labyrinth passage for Case 2

When the water flows through the right angleturns， the pressure drops and the turbulent kinetic energy increases. Thus a series of low pressure zones are formed in the corners. The generation of the vortex increases the local energy loss， hence a low pressure zone is produced. The feature of this passage is that the effective controls of the pressure drop and velocity can be made by regulating the sizes of the sections of the channel， the shapes of the turns， and the distance between two turns. As the size and the density of the vortex are controlled effectively， a severe cavitation can be avoided， as occurs frequently in the multi-orifice control valves or some single stage throttling control valves.

Another two cases based on the boundary conditions in Table 2 are also simulated and the results are shown in Fig.6 and Fig.7.

Fig.7 Flow characteristics of labyrinth passage for Case 3

Figure 6 shows the pressure contours and the velocity vectors based on the following boundary conditions: the inlet velocity is 5 m/s （Reynolds number Re=8.304× 104）， and outlet pressure is 102 kPa. Figure 7 shows the pressure contours and the velocity vectors based on the following boundary conditions: the inlet velocity is 3.33m/s （Reynolds numberRe= 5.531×104）， and outlet pressure is 243 kPa. The pressure loss coefficientξis 12.96 and 12.26， respectively.

In Case 2， the pressure drops from 355 kPa to 193 kPa in the “series passage”， which contributes 64.0% of the total pressure drop. While in Case 3， the pressure drops from 355 kPa to 287 kPa in the “series passage”， which accounts for 60.7% of the total pressure drop. These two cases are shown in Fig.6（a） and Fig.7（a）， respectively. It indicates that the “parallel passage” can be used to regulate the flow rate in the passage， and if it is necessary to control the pressure drop， the flow rate in the “parallel passage” will be higher than that in the “series passage”. Thus the“series passage” is mainly used to control the pressure drop. So combining the “series passage” with the “parallel passage” can meet both requirements for the pressure drop and the flow rate in engineering applications.

The numerical results also show that when the inlet fluid velocity increases， the flow resistance will increase correspondingly， thus a higher pressure drop will follow， but its magnitude varies step by step and evenly. Therefore， the severe partial cavitation and erosion can be avoided in the wall of the passage. That is， reducing the inlet flow rate and the maximum flow rate is of benefit to alleviate the cavitation and erosion in the passage.

The pressure drops in the “series passage” in all 3 cases see two features of this labyrinth passage: （1）the most pressure drops happen when the fluid flows through the “series passage”， and the percentage will increase with the increase of the flow rate. The explanation is as follows. （2） One main stream from the inlet is divided into two parts at the section “L6，R” in Fig.2. When they flow through two symmetrical and parallel passages， the velocities are deduced to a lower level，thus the throttling capability is weakened even the narrowest size is 0.0025 m， which is smaller than that one in the “series passage”（0.0040 m， as shown in Table 1）. （3） The pressure drop performance relies heavily on the flow rate. As the labyrinth passage investigated here yields a local pressure loss， only a higher inlet pressure can promote the flow rate.

Judging from the concentration of the stream lines shown in Fig.5（b）， Fig.6（b） and Fig.7（b）， the vortex zone will change also according to the inlet velocity， and if the velocity is higher， the area of the vortex zone will expand and the turbulence becomes more severe.

3.3 The downwards serrated curve for pressure drop in passage

Another feature of the labyrinth passage is the right angle turns and the connected expansion sections which causes the pressure drop in a downwards serrated way. As the pressure drop in Case 1 is the largest among the 3 cases， it is selected to study the relationship between the pressure drop and the geometry con-figuration of the passage. The calculated average pressure is based on a cross section normal to the flow direction and the curve is plotted by connecting the representative value， as shown in Fig.8.

Fig.8 The downwards serrated pressure drop in Case 1

As the expanding section is followed by a right angle turn， so the pressure will be partly recovered after each drop. Each expanding section will generate a recovery and for a total of 9 times during the throttling process. Thus it prevents the continuous and steep pressure drop and keeps the velocity in a reasonable level.

The downwards serrated curve also indicates that the most pressure drop is generated in the “series passage”， and the pressure differences between the peak and the valley are much greater than those in the “parallel passage”.

The pressure drop ?pnis defined as:

The ratio of the pressure recovery αnis defined as in Table 3.

The parametersβandγare introduced to describe the geometric characteristics and are defined as:

Table 3 The geometroc parameters β，γand the calculated?pn，σ，α

Theβandγare the key parameters in the passage design， which determine the recovery amplitude. From the calculated value ofαin Table 3， the pressure recovery ratio is changed from 29% to 51% in the “series passage” section and just 9% to 38% in the “parallel passage” even with the value ofβgreater than the former. The reason might lie in the fact that the flow rate in the “series passage” is divided into two parts after the inlet of the “parallel passage” so the velocity is reduced， as shown in Fig.5（b）， and the velocity of the water do not exceed 10 m/s through the main path. The other reason is that the value ofγin the “parallel passage” are smaller than that in the“series passage”.

4. Discussions

The labyrinth passage studied in this paper has three advantages. Firstly， it is composed of many right angle turns， which can generate a great pressure drop and dissipate the energy of the fluid. And secondly，the pressure drops in a downwards serrated way. Lastly，there are many stages during the pressure dropping，just as shown in Fig.2， where there are 10 stages of the pressure drop with much lower velocities than those where there are only three to four stages.

In this section， we will also focus on the following questions:

（1） Why does the pressure drop in the “series passage” contribute the most amount of the total pressure drop？

In section 3， the numerical results in 3 cases all show that the pressure drop in the “series passage” is much greater than that in the “parallel passage”. The first reason is that the flow rate in the “series passage”is double of that in the “parallel passage”. So the velocity there is much higher than that in the “parallel passage” even the section area of the latter is greater. And the second reason is that there are 6 right angle turns in the “series passage” while only 4 in the “parallel passage”. These turns will dissipate much energy and generate a larger pressure drop.

（2） The main functions of the “series passage” and the “parallel passage” for the pressure dropping.

The numerical results indicate if only use the“series passage” to generate the designed pressure drop，it will need less drop stages and shorter length， while the flow rate might not meet the requirements. On the contrary， if only use the “parallel passage” to generate the designed pressure drop， maybe the flow rate is easily to reach， however， it will need more drop stages，and lead to a greater size. So we may say that the“series passage” is mainly responsible for the pressure dropping while the “parallel passage” is mainly responsible for the flow-rate regulation.

（3） The issues that remain to be solved and the future work for the CFD on the flow in the narrow passage.

In this work， only the single liquid phase is investigated when it flows through the passage， the vapor phase is not considered. As the liquid water simulated here is in the state of a mediun temperature and pressure， it is not easy to have the cavitation caused by the phase transfer， and the results also show that the pressure at any location in the passage is not lower than the saturated vapor pressure （15oC， 1.7 kPa）， so the occurrence of cavitation is avoided.

While in engineering applications， the operation temperature may be higher than 250oC， and the operation pressure may be higher than 17 MPa， so the cavitation can not be avoid. However， even with the multiphase model， as is widely used to simulation the cavitation， many difficulties still exist. As the passage is so narrow that the gradient of the density， the velocity and the pressure will become much greater at the interface of two phases. Much work is being carried out and there will be some promising results in the future work.

5. Conclusions

In this paper， a tortuous labyrinth passage consisting of a series of right angle turns in a disk of high pressure control valve is studied. The numerical method is used to simulate the distribution of the velocity and the pressure drop in the passage. Based on the numerical results， the following conclusions can be drawn.

（1） When the fluid flows around each right angle turn， a separation occurs near the back edge. There are 6 vortexes in the “series passage” and 4 vortexes in the symmetric positions in the “parallel passage”. These 10 vortexes correspond to the 10 stages of the pressure drop.

（2） In the tortuous labyrinth passage， the velocity is continuously reduced to a reasonable level at the passage outlet. As the pressure drop takes place， the velocity is controlled by the designed area. There is no cavitation occurring， as is induced by the phase transition.

（3） Compared with the “parallel passage”， the“series passage” can make the pressure drop more efficiently. The main function of the “series passage”is for the pressure dropping while the “parallel passage” is mainly responsible for the flow-rate regulation.

（4） The tortuous labyrinth passage consists of a series of right angle turns and expanding passages， to form a large number of stages. It makes the pressure of the fluid drop in a downwards serrated way with the pressure higher than the saturate vapor pressure.

Acknowledgement

The authors also wish to express their appreciation to Mr. Li Hai in SEC-KSB Nuclear Pumps and Valves and Mr. Zhou Qing-li in State Nuclear Power Technology Corporation （China）.

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10.1016/S1001-6058（16）60667-4

April 3， 2015， Revised March 3， 2016）

* Project supported by the National Natural Science Foundation of China （Grant Nos. 51176127， 51106099）， the Shanghai Science and Technology Commission （Grant No. 13DZ2260900）.

Biography: Hai-min WANG （1971-）， Male， Ph. D.，

Associtate Professor

2016，28（4）:629-636