The 6th Intenational Supecitical CO2 Powe Cycles Symposium Mach 27-29, 2018, Pittsbugh, Pennsylvania Numeical study of supe-citical cabon dioxide flow in steppedstaggeed labyinth seals Yuming Zhu a,b, Yuyan Jiang a, *, Shiqiang Liang a, Yongxian Guo a, Chaohong Guo a, Peng Yue a a Institute of Engineeing Themophysics, Chinese Academy of Sciences b Univesity of Chinese Academy of Sciences ABSTRACT In this pape, a new kind of axial labyinth seals, called stepped-staggeed labyinth seals, has been descibed to educe pocess gas escaping fom the shaft end of SCO2 compesso, and numeical study of supe-citical cabon dioxide flow(sco2) has been applied to evaluate its pefomance compaed to see-though labyinth. The computational fluid dynamic(cfd) calculations wee caied out using the NUMECA commecial code. To minimize the computational cost and keep the desied level of accuacy in the chaacteization, the NIST REFPROP database was used fo the computation of SCO2 in the numeical investigation. It can be obseved that thottling effect exists in both seal cleaance and shoulde cleaance, and stong votex flow occus at staggeed cavity. So, the Stepped-staggeed labyinth seals have bette seal pefomance than see-though labyinth and avoid the assembly poblem of axial intelocking labyinth. Finally, Vaious designs with diffeent stuctue paametes and conditions have been calculated to exploe the pimay design method of stepped-staggeed labyinth seals. Fo the test platfom is unde constuction, expeimental esults of stepped-staggeed labyinth seals ae not available. To pove the potential of the methodology, see-though cases on this numeical model have been opeated and indicate a vey good ageement with the existing see-though labyinth seals expeiment esults. INTRODUCTION Numeous studies have shown that these SCO2 powe cycles have the potential to attain significantly highe cycle efficiency than eithe a conventional steam Rankine cycle o even the ulta-supe-citical (USC) steam Rankine cycle ove a wide tempeatue ange of heat souces with compact components esulting in a smalle system footpint, lowe capital and opeating costs [1,2]. A Typical SCO2 powe cycle is showed as fig.1, which opeates a cycle in supe-citical egion [3]. The citical pessue of CO2 is 7.38MPa and the maximum pessue of cycle may up to 20MPa, so the SCO2 compesso s opeation pessue is much highe than that of taditional ai Fig.1 Typical SCO2 powe cycle (T-S) compesso. Besides, the kinematic viscosity of SCO2 is much smalle than ai, as is shown in table.1, which will lead to a much thinne bounday laye and may incease the leakage of seal. Labyinth seal is a kind of typical mechanical seal, widely used in tubo-machiney. And thee ae many diffeent type of labyinth seal, such as see-though labyinth seal, stepped labyinth seal, staggeed labyinth seal and so on. HaominYuan(2015) studied the see-though labyinth seal used in SCO 2 flow in fig.2 both numeically and expeimentally. In the Sandia National Laboatoy (SNL) SCO 2 Bayton cycle expeiment loop [5] a stepped labyinth seal is adopted fo its compesso as shown in Fig.3. Fo the cases opeating in high pessue condition, see-though o stepped labyinth seal may had to meet the equiement of leakage.
Table 1 The popeties of ai and SCO2 Tempeatue Pessue Density Viscosity Kin. Viscosity (K) (MPa) (kg/m^3) (upa-s) (cm^2/s) Ai 320 10 108.26 21.492 0.0019852 SCO 2 320 10 448.28 32.388 0.00072251 Axial staggeed labyinth is one of the most poweful labyinth seal, which is always used in lage-scale machiney with split cases in fig.4. As the SCO2 tubine machines have the chaacteistics of smalle volume and high unning speed, tubine oto system is sensitive to the case assembly eo. It is difficult to ensue Installation accuacy fo the small-scale split case, so it is in an ugent need fo us to develop new kind of axial labyinth seals to esolve the assembly poblem of axial staggeed labyinth and to meet the acquiement of high pessue seal in high speed shaft end. In this pape, a stepped-staggeed labyinth Fig.2 The see-though labyinth seal in HaominYuan s pape Fig.3 Stepped labyinth seal used in SNL SCO2 Bayton cycle expeiment loop
seal has been developed, as it is shown in fig.5, this new seal uses stepped stuctue to avoid the assembly poblem and fom a staggeed chambe in each step to educe the shaft end leakage, which combines the advantages of stepped and staggeed labyinth seal. Unlike the numeical eseach of taditional ai labyinth seal, the unique fluid behavio of SCO2 nea its citical and pseudo-citical points challenges its numeical modeling [4]. In this pape, an accuate popety database including the popety of supe-citical and two-phase egion has Fig.4 Lage-scale machiney with split cases been developed using NIST REFPROP database. And the computational fluid dynamic(cfd) calculations wee caied out using the NUMECA commecial code to simulate the phase-change pocess which is the key fo the numeical simulation esults. Fo the test platfom is unde constuction, expeimental esults of stepped-staggeed labyinth seals ae not available. In this pape, we use the expeimental esults of SCO2 flow in see-though labyinth seals fom Haomin Yuan s eseach, as is shown in fig.2[4]. The same see-though stuctue cases in fig.8 have been opeated, and the numeical esults have been compaed with the above-mentioned expeimental esults to pove the potential of the methodology. Fig.5 Stepped-staggeed labyinth seal
Numeical methodology and availability This chapte descibes and discusses the numeical pocedue used in this investigation. The fist section intoduces Navie-Stokes equations and solve algoithm. The second pat moves on to descibe in detail about the popety module of SCO2 and phase-change model. Then diffeent tubulence models will be compaed. Afte that the mesh independent poblem will be studied and discussed. And this chapte ends with a compaison between the numeical esults and expeimental esults to pove the availability of the numeical method used in this pape. In this chapte, the inlet condition of see-though stuctue cases used to veify the availability of the numeical model is set as(10mpa,320k). 2.1 Navie-Stokes equations and solve algoithm The fluid is simulated using the Reynolds Aveaged Navie-Stokes (RANS) equations, applied to a otating system. Fo the single otating efeence fame simulation, the govening equations based on elative velocity ae given by: Mass consevation V 0 Consevation of momentum V V ( 2ω V ω ω ) P τ Consevation of enegy 1 1 2 2 2 2 HV V V U V k T ( τ V ) whee V is defined as: V V U U ω 2.2 Model of physical popeties As is epoted in [7,8], they used NIST Refpop to fomulate a CO2 equation into a two-dimensional table fo simulations. The advantage of this method is that the fineness of the table can be contolled by adjusting the numbe of sampling points in the table and the tempeatue and pessue anges coveed by the table. Compaed with the method of diectly invoking the state equation, the method keeps the calculation pecision and save the calculation time-consuming. In this pape, we use a softwae in Table 2 Two physical tables with diffeent esolutions P Range T Range Points MPa K n Table 1 0.005-800 216-2000 101 Table 2 4-20 270-500 101
NUMECA called TabGen to geneate CO2 popety tables. To study the impact of the esolution of CO2 popety tables on the CFD esults accuacy, we make two physical tables with diffeent esolutions, as is shown in table.2, and opeate see-though stuctue cases with the outlet pessue of 7MPa. The numeical esults using popety tables with diffeent esolutions ae showed in table.3. We can find that the diffeence of leakage is negligible and both ae close to the expeimental esult, so the esolution of popety tables may have no effect on calculation pecision, which is diffeent fom the impact on neacitical compesso. To minimize the computational cost and keep the vesatility of popety tables, the popety tables (ange fom 0.0005MPa to 800MPa and fom 216K to 2000K) ae used fo the computation of SCO2 in the numeical investigation Table 3 The numeical esults using popety tables with diffeent esolutions Table 1 Table 2 Expeiment Result Leakage(kg/s) 0.03369 0.033359 0.33 Besides, in NUMECA, the simulation of the physical popeties using condensable fluid model to solve the phase-change condition. This model enables the simulation of complex themodynamic popeties by intepolating vaiables fom specialized tables. Condensable fluid models ae suitable fo single-phase fluids whee the eal gas popeties ae too complex to be modeled as ideal gas models o polynomial fit. This modeling method is moe accuate fo the calculation of the liquid o gaseous zone nea the twophase zone. When the calculated fluid state is in the two-phase egion, the fluid state is consideed as a two-phase mixtue that is unifomly balanced in gas and liquid. When an equilibium mixtue of steam and liquid doplets, such as wet steam, is consideed as a single fluid, its satuated state themodynamic vaiables must be iteatively calculated. 2.3 Tubulence model In NUMECA, the solve is designed fo RANS tubulence model and povides vaious tubulence model to choose fom. To find out the most suitable tubulence model fo the case, we select fou diffeent types of tubulence models: Spalat-Allmaa, SARC, k-epsilon (Extended Wall Function), k- omega (M-SST, Extended Wall Function), and opeate see-though stuctue cases with the outlet pessue of 7MPa. The numeical esults using diffeent tubulence model ae showed in table.4. We can find that the numeical esult with Spalat-Allmaa tubulence model is much close to the expeimental esult. Theefoe, the Spalat-Allmaa tubulence model is used to study the pefomance of stepped-staggeed labyinth seals. Table 4 The numeical esults using diffeent tubulence model Spalat-Allmaa SARC k-epsilon k-omega Expeimental Result Leakage(kg/s) 0.033359 0.03238 0.03239 0.03127 0.033
2.4 Mesh independent To veify the mesh independent and obtain the aveage numbe of computational mesh equied, thee diffeent numbe of gids have been meshed and each gid numbe is Mesh1 =14289, Mesh2 = 25833 and Mesh3 = 63348. In ode to compae with the expeimental data, we opeate see-though stuctue cases with the outlet pessue of 7MPa. The numeical esults using physical tables with diffeent esolutions ae showed in table.5. Fom the table, we can find that it will lead to significant eo when the mesh is too coase, so the mesh with mesh numbe above 30000 is ecommended. Table 4 The numeical esults with diffeent numbe of gids Mesh1 Mesh2 Mesh3 Expeimental Result Leakage(kg/s) 0.03145 0.033359 0.03282 0.033 2.5 Method availability To fully evaluate the availability of the above-stated numeical method, moe outlet pessue condition has been opeated. And the numeical esults opeated by NUMECA has been compaed with the see-though labyinth seal expeimental data and the numeical esults opeated by OpenFOAM epoted in haominyuan[4] shown in fig.6 (in the pictue, the ed point epesent the numeical esults opeated by NUMECA, the black point epesent the numeical esults opeated by NUMECA and the blue point epesent the expeimental data). The esults opeated by numeical method used in this pape shows high degee of coheence with the see-though labyinth seal expeimental data, which poves that this method is feasible and eliable. Fig 6 The expeimental data and the numeical esults opeated by NUMECA and OpenFOAM
RESULTS AND DISCUSSION In this chapte, the eseach stuctues ae descibed, and numeical esults ae pesented and discussed. Fist, the detail stuctue of steppedstaggeed labyinth seal and some stuctue chaacteistic paametes ae intoduced. Then, we compae pefomance between see-though and the new stepped-staggeed labyinth, and ty to explain the diffeence fom details of the flow, including pessue distibution and steam line plot. Afte that, vaious designs with diffeent stuctue paametes and conditions have been calculated to exploe the pimay design method of stepped-staggeed labyinth seals. 3.1 Stuctue of stepped-staggeed labyinth seal Table 5 The 7 stuctue vaiables of stepped-staggeed labyinth seal a/b definition Radial cleaance between shaft and case/ Cavity height units c/b Cavity length/ Cavity height / d/b Tooth width/ Cavity height / e/b Axial cleaance between shaft and case/ Cavity height n Step numbe / Shaft adius m b Cavity height m As is shown in fig.7, a two-step stepped-staggeed labyinth seal is used to investigate the seal pefomance and design method of this new seal, and we chose 3 chaacteistic vaiables and 4 non-dimensional numbes to descibe its detail stuctue (see table 1). Fom fig.10, we can find that the installation diection of case wall and shaft wall is opposite, leaving an installation cleaance e which is one of the main featues of the new seal. In this eseach, we focus on thee non-dimensional numbes (a/b, c/b, d/b) and make a pimay qualitative eseach. And the quantitative analysis of effects of 7 vaiables (including 3 chaacteistic vaiables and 4 non-dimensional numbes) will be studied in ou futue wok. / / seal Fig 7 The stuctue of stepped-staggeed labyinth seal
Leakage(kg/s) 3.2 Compaison of sealing pefomance To compae the sealing pefomance of see-though and the new stepped-staggeed labyinth seal, we opeate a five-tooth see-though labyinth in fig.8 with six seal cavities which is the same as the two-step stepped-staggeed labyinth seal in fig.7. Consideing the seal size used in actual tubine machine, we set Table 6 The value of stepped-staggeed labyinth seal chaacteistic dimensions a/b c/b d/b e/b n b 0.1 1 0.1 1 2 30mm 1mm the shaft adius of all seals to 30mm and the othes dimensions ae shown in table.6. Fig 8 The stuctue of five-tooth see-though labyinth In this study, the inlet opeating condition is fixed at (10 MPa, 320K) and the outlet pessue anges fom 4MPa to 7MPa. The numeical esults ae pesented in fig.9, and it would be easy to conclude that the new stepped-staggeed labyinth seal has bette sealing pefomance than see-though with the same seal cleaance and sealing length. The elative Mach numbe plots obtained by the CFD in fig.10 also pove the validity of this point. Fom fig.10, we can find that the elative Mach numbe distibution of the new labyinth seal is much moe dispesive, which means a much stonge viscous dissipation occuing in seal cavity, so the Mach numbe is smalle and the seal effect is bette. stepped-staggeed labyinth seal see-though labyinth seal Fig 9 The numeical esults of stepped-staggeed and see-though labyinth seal
Leakage(kg/s) Outlet Pessue(MPa) Fig 10 The elative Mach numbe distibution of stepped-staggeed and see-though labyinth seal 3.3 Cleaance atio The data in Fig.11 shows that, the leakage ate inceases with incease in adial cleaance. This is a faily obvious esult as an incease in cleaance aea allows moe fluid to be foced undeneath the tooth. And it should be pointed that it is appoximate to a linea development between leakage and cleaance, when the shaft adius is lage enough. 0.6 0.5257 0.5 0.4 0.3415 0.4049 0.3 0.2 0.1599 0.1 0 0 0.05 0.1 0.15 0.2 0.25 Cleaance atio(a/b) Fig 11 The numeical esults of stepped-staggeed and see-though labyinth seal
3.4 Length/height atio The numeical esults of labyinth with diffeent length/height atio ae compaed in fig.12, and we can find that the seal pefomance is wost when length/height atio is equal to1, which means a squae sealing cavity. Futhemoe, it is emakable that the leakage of the seal (length/height atio=0.5) is vey close to that of the seal (length/height atio=2). And if we show the data in a log coodinate, as is pesented in fig.13, the sealing pefomance exhibits petty good symmety of geometic topology, which is a unique ule and can be a poweful tool to design high-pefomance mechanical seal. Though two seals above with simila geometic topology show the same sealing pefomance, they have the diffeent flow mechanisms as ae shown in fig.14. Fom the steamline pattens, it is obvious that the seal (length/height atio=0.5) has stonge votex effect and even emege additional votex nea the seal cleaance and the seal (length/height atio=2) has a double sealing length to ean a double sealing effect. 0.36 0.34 0.3415 Leakage(kg/s) 0.32 0.3 0.28 0.26 0.24 0.22 0.276 0.2715 0.2 0 0.5 1 1.5 2 2.5 Length/height atio (c/b) Fig 12 The numeical esults of labyinth with diffeent length/height atio Leakage(kg/s) 0.4 0.38 0.36 0.34 0.32 0.3 0.28 0.26 0.24 0.22 0.2 0.276 0.3415 0.2715 0.1 1 10 Length/height atio (c/b) Fig 13 The numeical esults of labyinth with diffeent length/height atio (in a log coodinate)
a) length/height atio=2 b) length/height atio=1 c) length/height atio=0.5 Fig 14 The steamline pattens of cases with diffeent length/height atio
3.5 Tooth width/height atio The numeical esults of labyinth with diffeent tooth width/height atio ae compaed in fig 15, and we can find the ule of seal leakage with change of tooth width/height atio is simila with that of length/height atio, which means that it may exist a best width/height atio which will lead to the least leakage. It is clea that the seal (width/height atio=5) has a double sealing length whee the speed of flow is extemely high, and it will lead to an incease of the fiction loss. When the width/height atio is vey small, the thottling effect must be enhanced, and the sealing pefomance is boosted. 0.4 0.35 0.3415 0.3 0.25 0.2 0.15 0.1 0.05 0.273 0.267 1 0 0.1 0.01 Fig 15 The numeical esults of labyinth with diffeent tooth width/height atio (in a log coodinate) 3.6 Conclusions A. The new stepped-staggeed labyinth seal has bette sealing pefomance than see-though with the same seal cleaance and sealing length. B. The leakage ate inceases with incease in adial cleaance. C. The seal pefomance is wost when length/height atio is equal to 1, and the sealing pefomance shows a good symmety of geometic topology with length/height atio. D. It may exist a best width/height atio which will lead to the least leakage.
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