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Üst Kapağı Hareketli Z-Şekilli Kavitideki Stokes Akış

Yıl 2021, Cilt: 11 Sayı: 1, 12 - 22, 09.06.2021

Ebutalib Çelik , Murat Luzum , Ali Deliceoğlu

Öz

Durağan, viskoz, Stokes akış için üst kapağı hareketli Z şekilli bir kaviti içindeki akış modelleri ve çatallanmaları araştırılmıştır. Bölge
yükseklikleri ile ilgili iki parametre h_1 ve h_2 olmak üzere Stokes denklemi, öz fonksiyonların sonsuz serisi kullanılarak analitik olarak
çözülmüştür. (h_1, h_2) kontrol uzay diyagramı yeni girdap oluşumunu incelemek için oluşturulmuştur ve daha sonra, çıkıntılı köşenin
Z-şekilli alandaki akış dönüşümü üzerindeki etkisine odaklanılmıştır.

Anahtar Kelimeler

Girdap oluşumu Akış çatallanmaları Tek kapaklı Z-şekilli kaviti

Kaynakça

  • An, B., Bergada, J M., Mellibovsky, F. 2019. The lid-driven right-angled isosceles triangular cavity flow. J. Fluid Mech., 875(9), 476–519. https://doi.org/10.1017/jfm.2019.512
  • Bakker, PG. 1991. Bifurcations in Flow Patterns. In Kluwer. https://doi.org/10.1017/S0022112093211624
  • Botella, O., Peyret, R. 1998. Benchmark Spectral Results on the Lid Driven Cavity Flow. Comput. Fluids, 27(4), 421–433. https://doi.org/10.1016/S0045-7930(98)00002-4
  • Brøns, M., Hartnack, J. N. 1999. Streamline topologies near simple degenerate critical points in two-dimensional flow away from boundaries. Phys. Fluids, 11(2), 314–324. https://doi.org/10.1063/1.869881
  • Bruneau, CH., Saad, M. 2006. The 2D lid-driven cavity problem revisited. Comput. Fluids. https://doi.org/10.1016/j.compfluid.2004.12.004
  • Deliceoĝlu, A., Aydin, SH. 2013. Flow bifurcation and eddy genesis in an L-shaped cavity. Comput. Fluids, 73, 24–46. https://doi.org/10.1016/j.compfluid.2012.12.008
  • Deliceoǧlu, A., Aydin, SH. 2014. Topological flow structures in an L-shaped cavity with horizontal motion of the upper lid. J. Comput. Appl. Math., 259(PART B), 937–943. https://doi.org/10.1016/j.cam.2013.10.007
  • Deliceoğlu, A., Bozkurt, D., Çelik, E. 2019. Flow topology in an L-shaped cavity with lids moving in the same directions. Math. Methods Appl. Sci. https://doi.org/10.1002/mma.5972
  • Deliceoğlu, A., Çelik, E. 2019. A Mechanism of Eddy Generation in A Single Lid-Driven T-Shaped Cavity. Cumhuriyet Science Journal, 40(3), 583–594. https://doi.org/10.17776/csj.569655
  • Driesen, C. H., Kuerten, JGM., Streng, M. 1998. Low-Reynolds-number flow over partially covered cavities. J. Eng. Math., 34(1–2), 3–21. https://doi.org/10.1007/978-94-017-1564-5_1
  • Erturk, E. 2018. Benchmark solutions of driven polar cavity flow at high reynolds numbers. Int. J. Mech. Eng. Technol., 9(8), 776–786.
  • Erturk, E., Corke, TC., Gökçöl, C. 2005. Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers. Int. J. Numer. Methods Fluids, 48(7), 747–774. https://doi.org/10.1002/fld.953
  • Fadle, J. 1940. Die Selbstspannungs-Eigenwertfunktionen der quadratischen Scheibe. Ingenieur-Archiv, 11(2), 125–149. https://doi.org/10.1007/BF02084699
  • Gaskell, PH., Savage, MD., Summers, JL., Thompson, HM. 1995. Modelling and analysis of meniscus roll coating. J. Fluid Mech., 298(11), 113–137. https://doi.org/10.1017/S0022112095003247
  • Gaskell, PH., Savage, MD., Wilson, M. 1997. Stokes flow in a half-filled annulus between rotating coaxial cylinders. J. Fluid Mech., 337(4), 263–282. https://doi.org/10.1017/S0022112097005028
  • Gürcan, F. 2003. Effect of the Reynolds number on streamline bifurcations in a double-lid-driven cavity with free surfaces. Comput. Fluids, 32(9), 1283–1298. https://doi.org/10.1016/S0045-7930(02)00084-1
  • Gürcan, F., Bilgil, H., Şahin, A. 2016. Bifurcations and eddy genesis of Stokes flow within a sectorial cavity PART II: Co-moving lids. Eur. J. Mech. B. Fluids, 56, 200–210. https://doi.org/10.1016/j.euromechflu.2015.02.008
  • Gürcan, F., Gaskell, PH., Savage, MD., Wilson, MCT. 2003. Eddy genesis and transformation of Stokes flow in a double-lid driven cavity. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci., 217(3), 353–363. https://doi.org/10.1243/095440603762870018
  • Gürcan, F., Wilson, MCT., Savage, MD. 2006. Eddy genesis and transformation of Stokes flow in a double-lid-driven cavity. Part 2: Deep cavities. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci., 220(12), 1765–1773. https://doi.org/10.1243/0954406JMES279
  • Gürcan, F. 2005. Streamline topologies near a stationary wall of Stokes flow in a cavity. Appl. Math. Comput., 165(2), 329–345. https://doi.org/10.1016/j.amc.2004.06.017
  • Hartnack, J. N. 1999. Streamline topologies near a fixed wall using normal forms. Acta Mech., 136(1), 55–75. https://doi.org/10.1007/BF01292298
  • Hellebrand, H. 2006. Tape Casting. In Materials Science and Technology. https://doi.org/10.1002/9783527603978.mst0192
  • Hriberšek, M., Škerget, L. 2005. Boundary domain integral method for high Reynolds viscous fluid flows in complex planar geometries. Comput. Methods Appl. Mech. Eng. https://doi.org/10.1016/j.cma.2004.11.002
  • Mahmoodi, M. 2011. Numerical simulation of free convection of a nanofluid in L-shaped cavities. Int. J. Therm. Sci.. https://doi.org/10.1016/j.ijthermalsci.2011.04.009
  • Olsman, WFJ., Colonius, T. 2011. Numerical simulation of flow over an airfoil with a cavity. AIAA Journal, 49(1), 143–149. https://doi.org/10.2514/1.J050542
  • Oztop, HF., Dagtekin, I. 2004. Mixed convection in two-sided lid-driven differentially heated square cavity. Int. J. Heat Mass Transfer. https://doi.org/10.1016/j.ijheatmasstransfer.2003.10.016
  • Papkovich, PF. 1970. Uber eine Form der Lösung des byharmonischen Problems für das Rechteck. Dokl. Acad. Sci. USSR., 27. 334–338.
  • Phillips TN. 1989, Singular Matched Eigenfunction Expansions for Stokes Flow around a Corner, IMA J. Appl. Math., 42(1), 13–26. https://doi.org/10.1093/imamat/42.1.13
  • Robbins, CI., Smith, RCT. (1948). CXIX. A table of roots of sin Z=-Z . The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 39(299), 1004–1005. https://doi.org/10.1080/14786444808521711
  • Shankar, PN. 1993. The eddy structure in stokes flow in a cavity. J. Fluid Mech., 250, 371–383. https://doi.org/10.1017/S0022112093001491
  • Sheu, TWH., Chiang, CY. 2014. Numerical investigation of chemotaxic phenomenon in incompressible viscous fluid flow. Comput. Fluids, 103, 290–306. https://doi.org/10.1016/j.compfluid.2014.07.023
  • Trogdon , SA., Joseph, DD. 1982. Matched eigenfunction expansions for slow flow over a slot, J. Nonnewton Fluid Mech., 10(3–4), 185-213. https://doi.org/10.1016/0377-0257(82)80001-3
  • Yang, G., Sun, J., Liang, Y., Chen, Y. 2014. Effect of Geometry Parameters on Low-speed Cavity Flow by Wind Tunnel Experiment. AASRI Procedia, 9, 44–50. https://doi.org/10.1016/j.aasri.2014.09.009

Stokes Flow in a Z-Shaped Cavity With Moving Upper Lid

Yıl 2021, Cilt: 11 Sayı: 1, 12 - 22, 09.06.2021

Ebutalib Çelik , Murat Luzum , Ali Deliceoğlu

Öz

Flow patterns and their bifurcation for a steady, viscous, Stokes flow inside a Z-shaped cavity with moving upper lid are investigated.
Stokes equation with two parameters h_1 and h_2 which are related to the heights of the field is solved analytically using an infinite series
of eigenfunctions. The (h_1, h_2) control space diagram is constructed to examine the new eddy generation, and attention is then focused
on the effect of the re-entrant corner on the flow transformation in the Z-shaped domain.

Anahtar Kelimeler

Eddy generation Flow bifurcation Single-lid Z-shaped cavity

Kaynakça

  • An, B., Bergada, J M., Mellibovsky, F. 2019. The lid-driven right-angled isosceles triangular cavity flow. J. Fluid Mech., 875(9), 476–519. https://doi.org/10.1017/jfm.2019.512
  • Bakker, PG. 1991. Bifurcations in Flow Patterns. In Kluwer. https://doi.org/10.1017/S0022112093211624
  • Botella, O., Peyret, R. 1998. Benchmark Spectral Results on the Lid Driven Cavity Flow. Comput. Fluids, 27(4), 421–433. https://doi.org/10.1016/S0045-7930(98)00002-4
  • Brøns, M., Hartnack, J. N. 1999. Streamline topologies near simple degenerate critical points in two-dimensional flow away from boundaries. Phys. Fluids, 11(2), 314–324. https://doi.org/10.1063/1.869881
  • Bruneau, CH., Saad, M. 2006. The 2D lid-driven cavity problem revisited. Comput. Fluids. https://doi.org/10.1016/j.compfluid.2004.12.004
  • Deliceoĝlu, A., Aydin, SH. 2013. Flow bifurcation and eddy genesis in an L-shaped cavity. Comput. Fluids, 73, 24–46. https://doi.org/10.1016/j.compfluid.2012.12.008
  • Deliceoǧlu, A., Aydin, SH. 2014. Topological flow structures in an L-shaped cavity with horizontal motion of the upper lid. J. Comput. Appl. Math., 259(PART B), 937–943. https://doi.org/10.1016/j.cam.2013.10.007
  • Deliceoğlu, A., Bozkurt, D., Çelik, E. 2019. Flow topology in an L-shaped cavity with lids moving in the same directions. Math. Methods Appl. Sci. https://doi.org/10.1002/mma.5972
  • Deliceoğlu, A., Çelik, E. 2019. A Mechanism of Eddy Generation in A Single Lid-Driven T-Shaped Cavity. Cumhuriyet Science Journal, 40(3), 583–594. https://doi.org/10.17776/csj.569655
  • Driesen, C. H., Kuerten, JGM., Streng, M. 1998. Low-Reynolds-number flow over partially covered cavities. J. Eng. Math., 34(1–2), 3–21. https://doi.org/10.1007/978-94-017-1564-5_1
  • Erturk, E. 2018. Benchmark solutions of driven polar cavity flow at high reynolds numbers. Int. J. Mech. Eng. Technol., 9(8), 776–786.
  • Erturk, E., Corke, TC., Gökçöl, C. 2005. Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers. Int. J. Numer. Methods Fluids, 48(7), 747–774. https://doi.org/10.1002/fld.953
  • Fadle, J. 1940. Die Selbstspannungs-Eigenwertfunktionen der quadratischen Scheibe. Ingenieur-Archiv, 11(2), 125–149. https://doi.org/10.1007/BF02084699
  • Gaskell, PH., Savage, MD., Summers, JL., Thompson, HM. 1995. Modelling and analysis of meniscus roll coating. J. Fluid Mech., 298(11), 113–137. https://doi.org/10.1017/S0022112095003247
  • Gaskell, PH., Savage, MD., Wilson, M. 1997. Stokes flow in a half-filled annulus between rotating coaxial cylinders. J. Fluid Mech., 337(4), 263–282. https://doi.org/10.1017/S0022112097005028
  • Gürcan, F. 2003. Effect of the Reynolds number on streamline bifurcations in a double-lid-driven cavity with free surfaces. Comput. Fluids, 32(9), 1283–1298. https://doi.org/10.1016/S0045-7930(02)00084-1
  • Gürcan, F., Bilgil, H., Şahin, A. 2016. Bifurcations and eddy genesis of Stokes flow within a sectorial cavity PART II: Co-moving lids. Eur. J. Mech. B. Fluids, 56, 200–210. https://doi.org/10.1016/j.euromechflu.2015.02.008
  • Gürcan, F., Gaskell, PH., Savage, MD., Wilson, MCT. 2003. Eddy genesis and transformation of Stokes flow in a double-lid driven cavity. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci., 217(3), 353–363. https://doi.org/10.1243/095440603762870018
  • Gürcan, F., Wilson, MCT., Savage, MD. 2006. Eddy genesis and transformation of Stokes flow in a double-lid-driven cavity. Part 2: Deep cavities. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci., 220(12), 1765–1773. https://doi.org/10.1243/0954406JMES279
  • Gürcan, F. 2005. Streamline topologies near a stationary wall of Stokes flow in a cavity. Appl. Math. Comput., 165(2), 329–345. https://doi.org/10.1016/j.amc.2004.06.017
  • Hartnack, J. N. 1999. Streamline topologies near a fixed wall using normal forms. Acta Mech., 136(1), 55–75. https://doi.org/10.1007/BF01292298
  • Hellebrand, H. 2006. Tape Casting. In Materials Science and Technology. https://doi.org/10.1002/9783527603978.mst0192
  • Hriberšek, M., Škerget, L. 2005. Boundary domain integral method for high Reynolds viscous fluid flows in complex planar geometries. Comput. Methods Appl. Mech. Eng. https://doi.org/10.1016/j.cma.2004.11.002
  • Mahmoodi, M. 2011. Numerical simulation of free convection of a nanofluid in L-shaped cavities. Int. J. Therm. Sci.. https://doi.org/10.1016/j.ijthermalsci.2011.04.009
  • Olsman, WFJ., Colonius, T. 2011. Numerical simulation of flow over an airfoil with a cavity. AIAA Journal, 49(1), 143–149. https://doi.org/10.2514/1.J050542
  • Oztop, HF., Dagtekin, I. 2004. Mixed convection in two-sided lid-driven differentially heated square cavity. Int. J. Heat Mass Transfer. https://doi.org/10.1016/j.ijheatmasstransfer.2003.10.016
  • Papkovich, PF. 1970. Uber eine Form der Lösung des byharmonischen Problems für das Rechteck. Dokl. Acad. Sci. USSR., 27. 334–338.
  • Phillips TN. 1989, Singular Matched Eigenfunction Expansions for Stokes Flow around a Corner, IMA J. Appl. Math., 42(1), 13–26. https://doi.org/10.1093/imamat/42.1.13
  • Robbins, CI., Smith, RCT. (1948). CXIX. A table of roots of sin Z=-Z . The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 39(299), 1004–1005. https://doi.org/10.1080/14786444808521711
  • Shankar, PN. 1993. The eddy structure in stokes flow in a cavity. J. Fluid Mech., 250, 371–383. https://doi.org/10.1017/S0022112093001491
  • Sheu, TWH., Chiang, CY. 2014. Numerical investigation of chemotaxic phenomenon in incompressible viscous fluid flow. Comput. Fluids, 103, 290–306. https://doi.org/10.1016/j.compfluid.2014.07.023
  • Trogdon , SA., Joseph, DD. 1982. Matched eigenfunction expansions for slow flow over a slot, J. Nonnewton Fluid Mech., 10(3–4), 185-213. https://doi.org/10.1016/0377-0257(82)80001-3
  • Yang, G., Sun, J., Liang, Y., Chen, Y. 2014. Effect of Geometry Parameters on Low-speed Cavity Flow by Wind Tunnel Experiment. AASRI Procedia, 9, 44–50. https://doi.org/10.1016/j.aasri.2014.09.009
Toplam 33 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Araştırma Makaleleri
Yazarlar

Ebutalib Çelik 0000-0002-4500-4465

Murat Luzum 0000-0001-6256-0597

Ali Deliceoğlu 0000-0003-0863-6276

Yayımlanma Tarihi 9 Haziran 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 11 Sayı: 1

Kaynak Göster

APA Çelik, E., Luzum, M., & Deliceoğlu, A. (2021). Stokes Flow in a Z-Shaped Cavity With Moving Upper Lid. Karaelmas Fen Ve Mühendislik Dergisi, 11(1), 12-22.
AMA Çelik E, Luzum M, Deliceoğlu A. Stokes Flow in a Z-Shaped Cavity With Moving Upper Lid. Karaelmas Fen ve Mühendislik Dergisi. Haziran 2021;11(1):12-22.
Chicago Çelik, Ebutalib, Murat Luzum, ve Ali Deliceoğlu. “Stokes Flow in a Z-Shaped Cavity With Moving Upper Lid”. Karaelmas Fen Ve Mühendislik Dergisi 11, sy. 1 (Haziran 2021): 12-22.
EndNote Çelik E, Luzum M, Deliceoğlu A (01 Haziran 2021) Stokes Flow in a Z-Shaped Cavity With Moving Upper Lid. Karaelmas Fen ve Mühendislik Dergisi 11 1 12–22.
IEEE E. Çelik, M. Luzum, ve A. Deliceoğlu, “Stokes Flow in a Z-Shaped Cavity With Moving Upper Lid”, Karaelmas Fen ve Mühendislik Dergisi, c. 11, sy. 1, ss. 12–22, 2021.
ISNAD Çelik, Ebutalib vd. “Stokes Flow in a Z-Shaped Cavity With Moving Upper Lid”. Karaelmas Fen ve Mühendislik Dergisi 11/1 (Haziran 2021), 12-22.
JAMA Çelik E, Luzum M, Deliceoğlu A. Stokes Flow in a Z-Shaped Cavity With Moving Upper Lid. Karaelmas Fen ve Mühendislik Dergisi. 2021;11:12–22.
MLA Çelik, Ebutalib vd. “Stokes Flow in a Z-Shaped Cavity With Moving Upper Lid”. Karaelmas Fen Ve Mühendislik Dergisi, c. 11, sy. 1, 2021, ss. 12-22.
Vancouver Çelik E, Luzum M, Deliceoğlu A. Stokes Flow in a Z-Shaped Cavity With Moving Upper Lid. Karaelmas Fen ve Mühendislik Dergisi. 2021;11(1):12-2.