Flow Characteristics and Stress Analysis of a Parallel Gate Valve

processes

Article Flow Characteristics and Stress Analysis of a Parallel Gate Valve

Hui Wu 1, Jun-ye Li 1,* and Zhi-xin Gao 1,2

1 SUFA Technology Industry Co., Ltd, CNNC, Suzhou 215129, China; [email protected] (H.W.); [email protected] (Z.-x.G.) 2 Institute of Process Equipment, College of Energy Engineering, Zhejiang University, Hangzhou 310027, China; [email protected] * Correspondence: [email protected]; Tel.: +86-0512-6662-1921

Received: 29 September 2019; Accepted: 24 October 2019; Published: 3 November 2019

Abstract: Gate valves have been widely used in the piping system and have attracted a lot of attention from researchers. In this paper, a wedge-type double disk parallel gate valve is chosen to be analyzed. The Reynolds number varying from 200 to 500,000, and the valve opening degree varying from 20% to 100%, and the groove depth varying from 2.3 mm to 9 mm are chosen to investigate their effects on the flow and loss coefficients of the gate valve. The results show that the loss coefficient decreases and the flow coefficient increases with the increase of the Reynolds number and the valve opening degree, while with the increase of the groove depth, the loss coefficient barely changes, but the flow coefficient increases if the Reynolds number is larger than 10,000. In addition, the effects of the gaps between the disk and the limit stop on the stress distribution of the bolt are also investigated, and the results show that if the gaps are negative, high stress will act on the bolt at the contact position between the bolt and the limit stop.

Keywords: gate valve; stress analysis; Computational Fluid Dynamics (CFD); flow coefficient; loss coefficient

1. Introduction As a kind of on–off valve, gate valves are widely used in various process industries. When compared with other valves, it needs smaller torque during the open and close processes of the valve, and it also results in smaller flow resistance. However, due to the complexity of the sealing device, more components in gate valves are needed, which might lead to high proneness of gate valve failure [1–3]. Researches about various valves have been focused in the past years. For instance, Qian et al. [4,5] applied Tesla valves in the hydrogen decompression process and investigated the pressure drop and Mach number in multi-stage Tesla valves. Yuan et al. [6] and Jin et al. [7] conducted numerical simulations to study the cavitation inside the poppet valve and the globe valve, and the cavitation characteristics and the structural parameters that affected the cavitation were found. Dasgupta et al. [8] and Zhang et al. [9] and Qian et al. [10] focused on the dynamic valve open and close processes of a proportional valve, a pressure relief valve, and a pilot-control globe valve respectively. Furthermore, Jin et al. [11] and Qian et al. [12,13] investigated the structural parameters of a pilot-control angle valve and a micro Tesla valve, Xu et al. [14] focused on the pulsatile flow of a mechanical heart valve, Chen et al. [15] investigated the thermal stress of a pressure-reducing valve, and Qian et al. [16] analyzed the possibility of the noise distribution in perforated plates connecting pressure-relief valve. Specific to the gate valves, lots of works have also been done focusing on different issues. There are works regarding the flow resistance and the temperature distributions. Solek and Mika [17] investigated the relationship between the loss coefficient and the Reynolds number for gate valves with ice slurry

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flow, and their experiments showed that the loss coefficient remained constant in the turbulent regime, but decreased with the increase of the Reynolds number in the laminar regime. Alimonti [18] and Lin et al. [19] studied the flow characteristics and resistance characteristics of a gate valve with different openings and different inlet velocities, and it was found that the flow resistance could be gradually stabilized when the opening was larger than 2/8 [19]. Long and Shurong [20] numerically investigated the flow and temperature distributions in the stem gate valve while using axisymmetric models, and Hu et al. [21] performed experiments and numerical simulations to study the temperature and the convection heat transfer coefficient distributions in a gate valve. In the meantime, there are also works regarding structure optimization [22,23], the corrosion erosion distributions [24–26], and the stress analysis [27–29]. Kolesnikov and Tikhonov [22] focused on the conicity of the output channel of the wedge gate valve and Xu et al. [23] focused on the seal and piston of a subsea gate valve. Babaev and Kerimov [24] found that there was fretting corrosion for a parallel slide gate valve. Lin et al. [25,26] found that the erosion rate in a gate valve was related to the pipe diameter, the cavity width, and the inlet velocity [25], while the open degree had little effects but a large Stokes number could increase the difference of erosion distributions for different valve placements [26]. As for the stress analysis, Liao et al. [27] found that the fatigue of the inlet valve sleeve resulting from collision stress was the main reason for the valve failure. Zakirnichnaya and Kulsharipov [28] analyzed the stress-strain of the wedge gate valves while using fluid-structure interaction technology and they found that the safe operation resources value of the wedge is lower than the valve body. Punitharani et al. [29] applied the finite element analysis (FEA) method to evaluate the residual stresses in a gate valve, and they found that there were large tensile and compressive residual stresses on the circular bead of the gate valve. Gate valves can be classified into the wedge gate valve, the parallel gate valve, the double disk parallel gate valve, and the double disk wedge gate valve, etc. according to the form of the sealing device. As described above, works regarding parallel gate valves [18,19] and wedge gate valves [22] have been done by researchers. In this paper, a wedge-type double disk parallel gate valve is chosen to be analyzed. The computational fluid dynamics method is used to investigate the flow and loss characteristics under different Reynolds number and different groove depth. Moreover, the structural stress analysis where the valve failure might occur is also done while using a numerical method that is proven by the previous studies [27–31]. This work is helpful for the understanding of the flow characteristics of the gate valve and the judgment of the reason for valve failure in the future.

2. Model Description

2.1. Physic Model Figure1 shows the structure of the investigated gate valve and the nominal diameter is 100 mm. Figure2 shows the detailed illustration of the disk component, which mainly consists of the disk, the disc frame, the nut, the limit stop, and the bolt. Processes 2019, 7, x FOR PEER REVIEW 3 of 13 ProcessesProcesses 20192019,, 77,, 803x FOR PEER REVIEW 3 of 13 Processes 2019, 7, x FOR PEER REVIEW 3 of 13

Figure 1. The structure of the wedge--typetype doubledouble diskdisk parallelparallel gategate valve.valve. FigureFigure 1. 1. ThThee structure structure of of the the wedge wedge-type-type double double disk disk parallel parallel gate gate valve. valve.

Figure 2. The structure of the disk component. Figure 2. The structure of the disk component. FigureFigure3 3 shows shows the the gaps gaps between between the the disk disk and and the the limit limit stop. stop.. During DuringDuring the thethe mechanical mechanicalmechanical machining machiningmachining Figure 3 shows the gaps between the disk and the limit stop. During the mechanical machining process,process, therethere mightmight bebe anan asymmetryasymmetry degreedegree ofof thethe openingopening sizesize ofof thethe machine.machine.. If thethe asymmetryasymmetry process, there might be an asymmetry degree of the opening size of the machine. If the asymmetry degree is too too large, large, gaps gaps C2 C2 and and C3 C3 can can become become negative, negative, which which will will lead lead to extra to extra force force acting acting on the on degree is too large, gaps C2 and C3 can become negative, which will lead to extra force acting on the thebolt. bolt. bolt.

Figure 3. The illustration of the gaps between the disk and the limit stop. Figure 3. The illustration of the gaps between the disk and the limitlimit stopstop.. Figure 3. The illustration of the gaps between the disk and the limit stop.

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FigureFigure4 4 shows shows the the simpliﬁed simplified model model of of the the bolt bolt and and the the limit limit stop; stop; here, here, the the nominal nominal diameter diameter ofof thethe threadthread isis 66 mm,mm, thethe diameterdiameter ofof thethe boltbolt isis chosenchosen asas 77 mm,mm, andand thethe minimumminimum diameterdiameter ofof thethe threadthread isis chosenchosen asas 4.9174.917 mm.mm.

FigureFigure 4.4. The simplifiedsimplified modelmodel ofof thethe boltbolt andand thethe limitlimit stop.stop. 2.2. Numerical Model 2.2. Numerical Model The commercial software package ANSYS is used in this paper. The software Fluent that is based The commercial software package ANSYS is used in this paper. The software Fluent that is based on the finite volume method is used to analyze the flow and resistance characteristics, and the software on the finite volume method is used to analyze the flow and resistance characteristics, and the Mechanical based on the finite element method is used to predict the stress of the bolt. To solve the software Mechanical based on the finite element method is used to predict the stress of the bolt. To fluid field, the continuity and the momentum equations are used and are shown in the following. solve the fluid field, the continuity and the momentum equations are used and are shown in the following. ∂ =  uj 0 (1) ∂xj  uj  0 (1) xj ∂ + =  ρuiuj pδij τij 0 (2) ∂xj  −     ui u j p ij ij  0 x (2) here ρ stands for the density of the fluid, uj stands for the velocity of the fluid, p stands for the pressure ofhere the ρfluid, stands and forτ theij stands density for of the the viscous fluid, u stress.stands Thefor the Realizable velocity k-ofε theturbulence fluid, p stands model for [32 the] is pressure used to solveof the the fluid, turbulent and τij flowstands inside for the the viscous investigated stress. wedge-type The Realizable double k-ε turbulence disk parallel model gate valve,[32] is andused the to transportsolve the equationsturbulent flow for turbulence inside the kineticinvestigated and turbulence wedge-type dissipation double disk are shown,parallel asgate follows valve, and the transport equations for turbulence kinetic" and !turbulence# dissipation are shown, as follows ∂ ∂ µt ∂k ( ) = +  + + + ρku µ t k Gk Gb ρε YM SK (3) ∂xj ku∂xj  σ k ∂xj  Gk  G b −  − Y M  S K (3) xj  x j k  x j " # 2 ∂ ∂ µt ∂ε ε ε  2 ( ) = + t +    + + ρεu uµ   ρ C 1 CS Sε   ρ CC2  C C GC1 ε S C3εGb Sε (4) x x x 1 2 1 3 b k  (4) ∂ j ∂xjj  xσ jε∂ j  x j − kvk + √vε k here the model constants appear in above equations are σk = 1.0, σε = 1.2, C1ε = 1.44, and C2 = 1.9. here the model constants appear in above equations are σk = 1.0, σε = 1.2, C1ε = 1.44, and C2 = 1.9. The hybrid grid is adopted during the computational fluid dynamics simulations and it is shown The hybrid grid is adopted during the computational fluid dynamics simulations and it is shown in Figure5. A grid independence check is done for the wedge-type double disk parallel gate valve in Figure 5. A grid independence check is done for the wedge-type double disk parallel gate valve with a different total number of cells, N, and the pressure drop, ∆p, between the upstream and the with a different total number of cells, N, and the pressure drop, ∆p, between the upstream and the downstream of the gate valve is shown in Table1. From Table1, it can be found that, when the cell downstream of the gate valve is shown in Table 1. From Table 1, it can be found that, when the cell numbers increase from 13.3 105 to 25.3 105, the variation of the pressure drop is within 0.9%, so the numbers increase from 13.3× × 105 to 25.3× × 105, the variation of the pressure drop is within 0.9%, so method that is used to generate the grid 2 is adopted in this study. the method that is used to generate the grid 2 is adopted in this study.

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Figure 5. TheThe hybrid grid used in this study. Table 1. Pressure drop under a diﬀerent number of cells. Table 1. Pressure drop under a different number of cells. Grid 1 Grid 2 Grid 3 Grid 1 Grid 2 Grid 3 N 105 6.7 13.3 25.3 N × 105 × 6.7 13.3 25.3 ∆p (pa) 104.54 102.95 102.08 ∆p (pa) 104.54 102.95 102.08

Water under room temperature is chosen as the working fluid fluid inside inside the the investigated investigated gate gate valve. valve. During the fluid fluid flowing flowing process, the temperaturetemperature of water in the upstream of the gate valve and the ambient temperaturetemperature areare the the same, same, which which makes makes a smalla small variation variation of waterof water temperature. temperature. Therefore, Therefore, the theEnergy Energy equation equation is not is not solved. solved. Symmetrical Symmetrical models models are are used used to to save save simulation simulation time. time. TheThe velocity inleinlett and the pressure outlet boundary conditions are applied, and the outlet pressure is set as the atmosphere inin order order to to investigate investigate the the flow flow and and loss coelossffi coefficientcients of thes of wedge-type the wedge double-type doubledisk parallel disk parallelgate valve. gate In valv addition,e. In addition, the no-slip the wall no is-slip adopted wall for is adopted the wall boundary.for the wall For boundary. the stress analysisFor the stress of the analysisbolt, the of symmetry the bolt, planethe symmetry is set as frictionlessplane is set support, as frictionless and the support, face of and the boltthe face is set of as the fixed bolt support. is set as fixed support. 2.3. Model Validation 2.3. Model Validation The numerical results are compared with the experimental results of Lin et al. [19] in order to validateThe thenumerical used methods results in are this compared study. Here, with the the mentioned experimental numerical results methods of Lin et are al. used [19] toin solveorder the to validateturbulent the incompressible used methods gas in flowthis study in a parallel. Here, gatethe mentioned valve. Table numerical2 shows themethods comparison are used of theto solve loss thecoe ffiturbulentcients, and incompressibleξE represents gas the flow experimental in a parallel results gate and valve.ξN represents Table 2 shows the numerical the comparison results. of From the Tableloss coefficients2, it can be, foundand ξE the represents relative errorsthe experimental between the results experimental and ξN resultsrepresents and the the numerical numerical results. results Frareom within Table 3%, 2, it thus can thebe found applied the methods relative errors in this between study are the appropriate experimental and results they can and provide the numerical results withresults su arefficiently within precise. 3%, thus the applied methods in this study are appropriate and they can provide results with sufficiently precise. Table 2. The comparison between the numerical results and the experimental results. Table 2. The comparison between the numerical results and the experimental results. Valve Opening Degree 3/8 5/8 1 Valve Opening Degree 3/8 5/8 1 ξE [17] 10.82 3.69 2.03 ξE [17] ξN 10.82 11.03 3.743.69 1.98 2.03 ξN Error (%)11.03 1.93 1.3.74 2.5 1.98 − Error (%) 1.9 1.3 −2.5 3. Results and Discussion 3. Results and Discussion The flow and loss characteristics of the wedge-type double disk parallel gate valve are numerically investigated,The flow and and the loss effects characteristics of the valve opening of the degree wedge and-type the double groove diskdepth parallel are studied. gate In valve addition, are numericallythe stress analysis investigated, is done to and uncover the effects the possible of the reasonvalve opening for the gate degree valve and failure. the groove depth are studied. In addition, the stress analysis is done to uncover the possible reason for the gate valve failure.

3.1. Flow and Loss Characteristics

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3.1. Flow and Loss Characteristics ProcessesWhen 2019, water7, x FOR flows PEER REVIEW through the wedge-type double disk parallel gate valve, there is a pressure6 of 13 drop. The loss coefficient is often used as an indicator of the valve flow capacity, and the greater When water flows through the wedge-type double disk parallel gate valve, there is a pressure the loss coefficient, the smaller the valve flow capacity, but the greater the pressure drop. The loss drop. The loss coefficient is often used as an indicator of the valve flow capacity, and the greater the coefficient of a valve can be calculated from the below equation. loss coefficient, the smaller the valve flow capacity, but the greater the pressure drop. The loss coefficient of a valve can be calculated from the below∆p equation. ξ = (5) 1/2pρv2 = (5) 1/ 2v2 Figure6 shows the pressure drop ∆p and the loss coefficient ξ of the investigated gate valve with the ReynoldsFigure 6 shows number the varying pressure from drop 200 ∆p and to 500,000. the loss Itcoefficient can be found ξ of the that investigated the pressure gate drop valve almost with theexponentially Reynolds number increases varying with the from increase 200 to of 500,000 the Reynolds. It can be number. found that For thethe losspressure coeffi dropcient, almost as the exponentiallyincrease of the increases Reynolds with number, the itincrease decreases of rapidlythe Reynolds first and number. then has For very the small loss variation, coefficient, and as there the increaseis the largest of the variation Reynolds of thenumber, loss coe it ffidecreasescient when rapidly the flow first is and laminar. then has very small variation, and there is the largest variation of the loss coefficient when the flow is laminar.

FigureFigure 6 6.. TheThe pressure pressure drop drop and and the the loss loss coefficient coeﬃcient with with different diﬀerent Reynolds number.

TheThe capacity capacity of of water water flows flows through through the the investigated investigated gate gate valve valve can can be be represented represented by by the the flow flow coefficient,coefficient, which can be expressed in the following s1000 1000ρ KQv 10 (6) Kv = 10Q p (6) ∆pρ00 here Q is the volume flux (m3/h), ρ0 is the density of water at 15 °C, Kv is the flow coefficient and it 3 representshere Q is the the volume flux when flux (m the/ h),pressureρ0 is the drop density of the of water gate atvalve 15 ◦ C, is K 100v is kPa the. flowFigure coe ffi7 cientshows and the it relationshiprepresents the between flux when the the flow pressure coefficient drop and of the the gate Reynolds valve is 100number kPa.. FigureIt can 7be shows found the that relationship the flow coefficientbetween the increases flow coe withfficient the increase and the Reynoldsof Reynolds number. number, It and can the be foundsmaller that the theReynolds flow coe number,fficient theincreases larger withthe variation the increase of the of flow Reynolds coefficient. number, and the smaller the Reynolds number, the larger the variation of the flow coefficient.

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When water flows through the wedge-type double disk parallel gate valve, there is a pressure drop. The loss coefficient is often used as an indicator of the valve flow capacity, and the greater the loss coefficient, the smaller the valve flow capacity, but the greater the pressure drop. The loss coefficient of a valve can be calculated from the below equation. p = (5) 1/ 2v2 Figure 6 shows the pressure drop ∆p and the loss coefficient ξ of the investigated gate valve with the Reynolds number varying from 200 to 500,000. It can be found that the pressure drop almost exponentially increases with the increase of the Reynolds number. For the loss coefficient, as the increase of the Reynolds number, it decreases rapidly first and then has very small variation, and there is the largest variation of the loss coefficient when the flow is laminar.

Figure 6. The pressure drop and the loss coefficient with different Reynolds number.

The capacity of water flows through the investigated gate valve can be represented by the flow coefficient, which can be expressed in the following 1000 KQv 10 (6) p0 here Q is the volume flux (m3/h), ρ0 is the density of water at 15 °C, Kv is the flow coefficient and it represents the flux when the pressure drop of the gate valve is 100 kPa. Figure 7 shows the relationship between the flow coefficient and the Reynolds number. It can be found that the flow Processes 2019, 7, 803 7 of 13 coefficient increases with the increase of Reynolds number, and the smaller the Reynolds number, the larger the variation of the flow coefficient.

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FigureFigure 7. 7. TheThe flow flow coefficient coefficient with with different different Reynolds number.

To investigateinvestigate thethe internalinternal flow flow and and pressure pressure fields, fields, the the pressure pressure and and velocity velocity distributions distributions on theon thesymmetry symmetry plane plane when when the Reynoldsthe Reynolds number number is about is about 100,000 100,000 are shown are shown in Figure in Fig8. Iture can 8. beIt can found be foundthat, when that, thewhen investigated the investigated gate valve gate valve is in the is in fully the openfully open position, position, the whole the whole main main pipe pipe in the in gate the gatevalve valve is full is of full water of water with highwith speed,high speed, and the and main the resistancemain resistance of the gateof the valve gate isvalve the channelis the ch forannel the formovement the movement of the disk. of the Thus, disk. the Thus pressure, the pressure drop is relatively drop is relative small ifly the small gate if valve the gate is in valve the fully is in open the fullyposition open and position the loss and coe thefficient loss iscoefficient close to zero.is close to zero.

(a) (b)

Figure 8 8.. Pressure and velocity distributions on the symmetry plane: ( (aa)) Pressure Pressure distribution distribution;; and, and, (b) Velocity distribution.distribution.

3.2. Effects Effects of Valve Opening Degree Figure 99 showsshows thethe internalinternal flowflow fieldsfields andand pressurepressure distributionsdistributions underunder twotwo didifferentfferent valve opening degrees. degrees. Pressure Pressure drop drop mainly mainly appears appears at the at thedownstream downstream of the of gate the gatevalve valve that results that results from thefrom throttling the throttling effect e ff ofect two of two disks. disks. With With the the decrease decrease of of the the valve valve open openinging degree, degree, the the flow flow area decreases and the throttling effect effect increases, so the upstream pressure increases as the downstream pressure remains constant. Together Together with with Figure Figure 88,, itit cancan bebe foundfound that,that, whenwhen thethe gategate valvevalve isis inin aa 100100%% opening degree, the wate waterr flows flows directly to the downstream pipe, and there is no swirl in the main pipe of the valve. As As the the valve valve opening opening degree degree decreases, decreases, the maximum velocity increases and it appears appears under under the the valve valve disks. disks. When When compar comparinging the the gate gate valve valve with with a 60 a% 60% opening opening degre degreee and andthe gatethe gate valve valve with with a 20% a 20%opening opening degree, degree, the maximum the maximum velocity velocity increases increases from 2.2 from m/s 2.2 to m9.3/s m/s. to 9.3 From m/s. theFrom water the water streamline streamline under under different different valve valve opening opening degree, degree, it can it can be be found found that that there there is is a a local recirculation region region with with low low velocity velocity behind behind the the valve valve disk, disk, and the and smaller the smaller the valve the opening valve opening degree, degree,the greater the thegreater local the recirculation local recirculation region. region.

(a)

(b)

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Figure 7. The flow coefficient with different Reynolds number.

To investigate the internal flow and pressure fields, the pressure and velocity distributions on the symmetry plane when the Reynolds number is about 100,000 are shown in Figure 8. It can be found that, when the investigated gate valve is in the fully open position, the whole main pipe in the gate valve is full of water with high speed, and the main resistance of the gate valve is the channel for the movement of the disk. Thus, the pressure drop is relatively small if the gate valve is in the fully open position and the loss coefficient is close to zero.

(a) (b)

Figure 8. Pressure and velocity distributions on the symmetry plane: (a) Pressure distribution; and, (b) Velocity distribution.

3.2. Effects of Valve Opening Degree Figure 9 shows the internal flow fields and pressure distributions under two different valve opening degrees. Pressure drop mainly appears at the downstream of the gate valve that results from the throttling effect of two disks. With the decrease of the valve opening degree, the flow area decreases and the throttling effect increases, so the upstream pressure increases as the downstream pressure remains constant. Together with Figure 8, it can be found that, when the gate valve is in a 100% opening degree, the water flows directly to the downstream pipe, and there is no swirl in the main pipe of the valve. As the valve opening degree decreases, the maximum velocity increases and it appears under the valve disks. When comparing the gate valve with a 60% opening degree and the gate valve with a 20% opening degree, the maximum velocity increases from 2.2 m/s to 9.3 m/s. From the water streamline under different valve opening degree, it can be found that there is a local Processesrecirculation2019, 7, 803 region with low velocity behind the valve disk, and the smaller the valve opening8 of 13 degree, the greater the local recirculation region.

(a)

Processes 2019, 7, x FOR PEER REVIEW 8 of 13 (b)

FigureFigure 9 9.. PressurePressure and and flow flow fields fields under under different different valve valve opening opening degrees degrees:: (a) (20a)% 20% opening opening;; and, and, (b) 60(b%) 60% opening opening..

TheThe loss loss coefficient coefficient and and flow flow coefficient coefficient under under different different valve opening degree degree are are shown in FigureFiguress 10 and 11.. It It can can be be found found that that the the valve valve opening opening degree degree does does not not affect affect the relationship betweenbetween the the loss loss coefficient, coefficient, the flow flow coefficient, coefficient, and the Reynol Reynoldsds number number.. If the Re Reynoldsynolds number isis smaller smaller than than 5 5000,000, the the loss loss coefficient coefficient decreases decreases with with the the increase increase of of the the Reynolds Reynolds number number rapidly, rapidly, andand the the flow flow coefficient coefficient increases sharply as the increase increase of the the Reynolds Reynolds number. number. While While the the R Reynoldseynolds numbernumber is is larger larger than than 5000, 5000, the the loss loss coe ffi coefficientcient barely barely varies varies with the with increase the increase of the Reynolds of the Reynolds number, number,but the flow but coe theffi cient flow still coefficient increases still with increases a reduced with increment a reduced as the increment increase of as the the Reynolds increase number. of the Reynolds number.

FigureFigure 10 10.. LossLoss coefficients coeﬃcients under under different diﬀerent valve valve opening opening degree degree and and Reynolds number.

Figure 11. Flow coefficients under different valve opening degree and Reynolds number.

3.3. Effects of the Groove Depth When the wedge-type double disk parallel gate valve is fully closed, the contact area between the gate valve disks and the valve seat is an annulus, and the size of the annulus can be judged by the groove depth. Three different groove depths are chosen, namely groove depth 1 (2.3 mm), groove depth 2 (4.5 mm), and groove depth 3 (9 mm) to investigate the effects of the groove depth on the flow and loss characteristics of the investigated gate valve.

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Figure 9. Pressure and flow fields under different valve opening degrees: (a) 20% opening; and, (b) 60% opening.

The loss coefficient and flow coefficient under different valve opening degree are shown in Figures 10 and 11. It can be found that the valve opening degree does not affect the relationship between the loss coefficient, the flow coefficient, and the Reynolds number. If the Reynolds number is smaller than 5000, the loss coefficient decreases with the increase of the Reynolds number rapidly, and the flow coefficient increases sharply as the increase of the Reynolds number. While the Reynolds number is larger than 5000, the loss coefficient barely varies with the increase of the Reynolds number, but the flow coefficient still increases with a reduced increment as the increase of the Reynolds number.

Processes 2019, 7, 803 9 of 13 Figure 10. Loss coefficients under different valve opening degree and Reynolds number.

FigureFigure 11 11.. FlowFlow coefficients coeﬃcients under under different diﬀerent valve valve opening opening degree degree and and Reynolds Reynolds number. number.

3.3.3.3. Effects Effects of of the the Groove Groove Depth Depth WhenWhen the the wedge wedge-type-type double double disk disk parallel parallel gate gate valve valve is is fully fully closed, closed, the the contact contact area area between between thethe gate gate valve valve disks disks and and the the valve valve seat seat is is an an annulus, annulus, and and the the size size of of the the annulus annulus can can be be judged judged by by thethe groove groove depth. depth. T Threehree different different groove groove depth depthss are are chosen, chosen, namely namely groove groove depth depth 1 1 (2.3 (2.3 mm), mm), groove groove depthdepth 2 2 (4.5 (4.5 mm), andand groovegroove depthdepth 33 (9 (9 mm) mm) to to investigate investigate the the eff effectsects of theof the groove groove depth depth on theon flowthe and loss characteristics of the investigated gate valve. flowProcesses and 2019loss, 7characteristics, x FOR PEER REVIEW of the investigated gate valve. 9 of 13 The pressure and velocity distributions of the investigated gate valve with groove depth 3 are shownThe in Figurepressure8, and velocity the pressure distributions and velocity of the distributionsinvestigated gate of the valve investigated with groove gate depth valve 3 are with grooveshown depth in Figure 1 and 8, grooveand the depth pressure 2 are and shown velocity in Figure distributions 12. Together of the withinvestigated Figures 8gate and valve 12, it with can be foundgroove that depth the 1 groove and groove depth depth does 2 not are a shownffect the in water Figure streamline, 12. Together which with isFigure becauses 8 and the 12 flow, it can channel be isfound similar that under the groove different depth groove does depth. not affect While the forwater the streamline water pressure, which in is thebecause investigated the flow gatechannel valve, althoughis similar the under pressure different distributions groove depth. arealmost While for the the same, water the pressure value of in water the investigated pressure increases gate valve, as the groovealthough depth the decreases,pressure distributions which results are from almost the the resistance same, the loss value in theof water vicinity pressure of the increases valve seat. as the groove depth decreases, which results from the resistance loss in the vicinity of the valve seat.

(a)

(b)

FigureFigure 12. 12.Pressure Pressure andand flowflow fieldsfields under different different groove groove depth depth:: (a ()a Groove) Groove depth depth 1; 1;and, and, (b) ( bGroove) Groove depthdepth 2. 2.

The loss coefficient and flow coefficient of the investigated gate valve with different groove depth are shown in Table 3 and Figure 13. It can be seen from Table 3 that the groove depth does not affect the loss coefficient. Although pressure drop increases with the decrease of the groove depth, the difference can be neglected in the expression of the loss coefficient. When the Reynolds number is smaller than 10,000, the flow coefficient is not affected by the groove depth, while the Reynolds number is larger than 10,000, the flow coefficient increases with the increase of the groove depth, and the larger the Reynolds number, the larger the difference of the flow coefficient. Therefore, a large groove depth should be designed if possible.

Table 3. Loss coefficients under different groove depth.

Groove Depth Groove Depth 3 Re Groove Depth 2 1 200 3.763 3.763 3.763 800 1.570 1.569 1.570 5000 0.429 0.428 0.425 40,000 0.293 0.293 0.292 100,000 0.254 0.253 0.252 200,000 0.233 0.233 0.232 300,000 0.223 0.223 0.222 400,000 0.217 0.216 0.215 500,000 0.212 0.212 0.211

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The loss coefficient and flow coefficient of the investigated gate valve with different groove depth are shown in Table3 and Figure 13. It can be seen from Table3 that the groove depth does not a ffect the loss coefficient. Although pressure drop increases with the decrease of the groove depth, the difference can be neglected in the expression of the loss coefficient. When the Reynolds number is smaller than 10,000, the flow coefficient is not affected by the groove depth, while the Reynolds number is larger than 10,000, the flow coefficient increases with the increase of the groove depth, and the larger the Reynolds number, the larger the difference of the flow coefficient. Therefore, a large groove depth should be designed if possible.

Table 3. Loss coeﬃcients under diﬀerent groove depth.

Re Groove Depth 1 Groove Depth 2 Groove Depth 3 200 3.763 3.763 3.763 800 1.570 1.569 1.570 5000 0.429 0.428 0.425 40,000 0.293 0.293 0.292 100,000 0.254 0.253 0.252 200,000 0.233 0.233 0.232 300,000 0.223 0.223 0.222 400,000 0.217 0.216 0.215 Processes 2019, 7, x FOR500,000 PEER REVIEW 0.212 0.212 0.211 10 of 13

FigureFigure 13. 13. FlowFlow coefficients coefficients under under different different groove groove depth. depth. 3.4. Stress Analysis of the Bolt 3.4. Stress Analysis of the Bolt The wedge-type double disk parallel gate valve has a complex actuator component, where there is The wedge-type double disk parallel gate valve has a complex actuator component, where there a high possibility of the occurrence of valve failure. The following part focuses on the stress distribution is a high possibility of the occurrence of valve failure. The following part focuses on the stress on the bolt in order to find out one of the reasons for valve failure. distribution on the bolt in order to find out one of the reasons for valve failure. 3.4.1. Effects of the Gap C2 3.4.1. Effects of the Gap C2 If the limit stop shifts to the gate during the mechanical machining process, the gap C2 will becomeIf the negative. limit stop To shifts investigate to the the gate eff ectduring of gap the C2 mechanical on the state machining of the stress process, distribution the gap of C2 the will bolt, becomethe value negative. of gap C2To isinvestigate assumed tothe be effect0.5 of mm. gap C2 on the state of the stress distribution of the bolt, − the valueThe stressof gap linearization C2 is assumed analysis to be − of0.5 the mm. transverse cross-section of the bolt is shown in Figure 14a, andThe the distributionstress linearizat of theion total analysis stress, ofT thes, which transverse equals cross to the-section membrane of the stress bolt is plus shown the bendingin Figure stress, 14a, andis shown the distribution in Figure 14 ofb. the total stress, Ts, which equals to the membrane stress plus the bending stress, is shown in Figure 14b.

(a) (b)

Figure 14. The path of the stress linearization analysis and the stress distribution along the path: (a) The path of the stress linearization analysis; and, (b) The stress distribution along the path.

It can be found in Figure 14 that the maximum of the stress is 152.1 MPa, and the location where there is the maximum stress is 32.5 mm away from the end face of the bolt, where the contact position of the bolt and the limit stop is.

Processes 2019, 7, x FOR PEER REVIEW 10 of 13

Figure 13. Flow coefficients under different groove depth.

3.4. Stress Analysis of the Bolt The wedge-type double disk parallel gate valve has a complex actuator component, where there is a high possibility of the occurrence of valve failure. The following part focuses on the stress distribution on the bolt in order to find out one of the reasons for valve failure.

3.4.1. Effects of the Gap C2 If the limit stop shifts to the gate during the mechanical machining process, the gap C2 will become negative. To investigate the effect of gap C2 on the state of the stress distribution of the bolt, the value of gap C2 is assumed to be −0.5 mm. The stress linearization analysis of the transverse cross-section of the bolt is shown in Figure 14a, Processes 2019, 7, 803 11 of 13 and the distribution of the total stress, Ts, which equals to the membrane stress plus the bending stress, is shown in Figure 14b.

(a) (b)

Figure 14.14. The path ofof thethe stressstresslinearization linearization analysis analysis and and the the stress stress distribution distribution along along the the path: path (a: )(a The) pathThe path of the of stressthe stress linearization linearization analysis; analysis and,; and, (b) The(b) The stress stress distribution distribution along along the the path. path.

It can be found found in in Fig Figureure 1144 that that the the maximum maximum of of the the stress stress is is 152.1 152.1 MPa, MPa, and and the the location location where where therethere is the maximum stress stress is is 32.5 32.5 mm mm away away from from the the end end face face of of the the bolt, bolt, where where the the contact contact position position of the bolt and the limit stop is is.. Processes 2019, 7, x FOR PEER REVIEW 11 of 13 3.4.2. Eﬀects of the Gap C3 3.4.2. Effects of the Gap C3 If the limit stop shifts away from the gate during the mechanical machining process, the gap C3 will becomeIf the limit negative. stop shif Thets valueaway from of gap the C3 gate is assumed during the to bemechanical1 mm to machining investigate process, the eﬀect the of gap gap C3 C3 − onwill the become state of negative. the stress The distribution value of gap of C3 the is bolt. assumed to be −1 mm to investigate the effect of gap C3 on the state of the stress distribution of the bolt. Figure 15a shows the stress linearization analysis of the transverse cross-section of the bolt and Figure 15a shows the stress linearization analysis of the transverse cross-section of the bolt and Figure 15b shows the distribution of the total stress. Figure 15b shows the distribution of the total stress.

(a) (b)

FigureFigure 15.15. TheThe pathpath ofof thethe stress stress linearization linearization analysis analysis and and the the stress stress distribution distribution along along the the path: path (a:) ( Thea) pathThe path of the of stress the stress linearization linearization analysis; analysis; and, and, (b) The(b) The stress stress distribution distribution along along the the path. path.

ItIt can be be seen seen from from Figure Figure 15 15that that the themaximum maximum of the of stress the stress is 303.1 is MPa 303.1 and MPa the and location the locationwhere wherethere is there the maximum is the maximum stress is stress32.5 mm is 32.5away mm from away the end from face the of end theface bolt. of Combin the bolt.ing Figure Combinings 14 Figuresand 15, 14it isand found 15, itthat is foundthe stress that distribution the stress distribution along the axial along direction the axial of direction the bolt is of almost the bolt the is almostsame when the gap C2 or C3 is negative. Hence, the machining accuracy has great influence on the service life of the valve.

4. Conclusions Numerical methods are adopted to investigate the flow and loss characteristics and the stress distribution of the wedge-type double disk parallel gate valve. The effects of the Reynolds number, the valve opening degree, and the groove depth are focused. In the meantime, the effects of the gaps between the disk and the limit stop are also discussed. The results show that the loss coefficient decreases, but the flow coefficient increases with the increase of Reynolds number. When Reynolds number is smaller than 5000, the variation of the flow and loss coefficients is very large. While Reynolds number is larger than 5000, the variation of the flow coefficient decreases and the loss coefficient almost remains the same. The valve opening degree has great influence on the flow and loss characteristics, with the decrease of the valve opening degree, the loss coefficient increases rapidly, and the flow coefficient obviously decreases. As for the groove depth, it has negligible effects on the loss coefficient, but the larger the groove depth, the larger the flow coefficient if the Reynolds number is greater than 10,000. The existence of the gaps between the disk and the limit stop is to eliminate the stress acting on the bolt, if the gaps are negative, high stress will appear at the contact position between the bolt and the limit stop. During the design process, a large groove depth should be chosen to provide a large flow coefficient. While, during the machining process, the machining accuracy should be satisfied to avoid stress concentration of the bolt.

Processes 2019, 7, 803 12 of 13 the same when the gap C2 or C3 is negative. Hence, the machining accuracy has great inﬂuence on the service life of the valve.

4. Conclusions Numerical methods are adopted to investigate the flow and loss characteristics and the stress distribution of the wedge-type double disk parallel gate valve. The effects of the Reynolds number, the valve opening degree, and the groove depth are focused. In the meantime, the effects of the gaps between the disk and the limit stop are also discussed. The results show that the loss coefficient decreases, but the flow coefficient increases with the increase of Reynolds number. When Reynolds number is smaller than 5000, the variation of the flow and loss coefficients is very large. While Reynolds number is larger than 5000, the variation of the flow coefficient decreases and the loss coefficient almost remains the same. The valve opening degree has great influence on the flow and loss characteristics, with the decrease of the valve opening degree, the loss coefficient increases rapidly, and the flow coefficient obviously decreases. As for the groove depth, it has negligible effects on the loss coefficient, but the larger the groove depth, the larger the flow coefficient if the Reynolds number is greater than 10,000. The existence of the gaps between the disk and the limit stop is to eliminate the stress acting on the bolt, if the gaps are negative, high stress will appear at the contact position between the bolt and the limit stop. During the design process, a large groove depth should be chosen to provide a large flow coefficient. While, during the machining process, the machining accuracy should be satisfied to avoid stress concentration of the bolt.

Author Contributions: Conceptualization, H.W. and J.-y.L.; Data curation, J.-y.L. and Z.-x.G.; Formal analysis, H.W. and J.-y.L.; Investigation, J.-y.L.; Methodology, H.W.; Project administration, H.W. and J.-y.L.; Resources, H.W. and J.-y.L.; Software, J.-y.L. and Z.-x.G.; Supervision, H.W.; Validation, J.-y.L.; Writing—review & editing, J.-y.L. Funding: This research received no external funding. Conﬂicts of Interest: The authors declare no conﬂict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

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