SpringerLink
Log in

Finite-element thermal analysis of flows on moving domains with application to modeling of a hydraulic arresting gear

  • Published:
Journal of Thermal Analysis and Calorimetry Aims and scope Submit manuscript

Abstract

In this paper, we develop a finite-element framework of simulating the heat transfer of flows on moving domains. A stabilized formulation is utilized to discretize the heat equation posed on an arbitrary Lagrangian–Eulerian frame. The target application is a hydraulic arresting gear, where the relative motion between the rotor and stator is present. In order to perform thermofluid simulations inside such devices, we divide the computational domain into two subdomains: a moving domain containing the rotating parts and a stationary domain containing the rest of the structures. The solutions on the two discontinuous subdomains are communicated through a sliding-interface formulation developed in this paper. We use the numerical framework to study the heat build-up inside a hydraulic arresting gear. The effects of heat sources from fluid viscosity and structural frictions are studied. The simulation results indicate significant heat generations during the operation of arrested landing. Excellent robustness of the developed numerical method is demonstrated, as well as its potential to support real-world engineering applications.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Abbreviations

x :

Physical coordinate

ξ :

Parametric coordinate

t :

Time

u :

Velocity

\( {\hat{\mathbf{u}}} \) :

Velocity of computational domain

ρ :

Density

p :

Pressure of fluid

μ :

Dynamic viscosity of fluid

f :

External body force

T :

Temperature

c :

Specific heat

κ :

Heat conductivity

α :

Thermal diffusivity

S :

Heat source

σ :

Cauchy stress rate

ϵ :

Strain rate

q :

Heat flux

References

  1. Chiu Y-T. Computational fluid dynamics simulations of hydraulic energy absorber. Master’s Thesis, Virginia Tech, 1999.

  2. Caupin F, Herbert E. Cavitation in water: a review. Comptes Rendus Physique. 2006;7(9–10):1000–17.

    CAS  Google Scholar 

  3. **ong Q, Kong S-C. High-resolution particle-scale simulation of biomass pyrolysis. ACS Sustain Chem Eng. 2016;4(10):5456–61.

    CAS  Google Scholar 

  4. Yan J, Yan W, Lin S, Wagner GJ. A fully coupled finite element formulation for liquid-solid-gas thermo-fluid flow with melting and solidification. Comput Methods Appl Mech Eng. 2018;336:444–70.

    Google Scholar 

  5. Zhong H, **ong Q, Zhu Y, Liang S, Zhang J, Niu B, Zhang X. CFD modeling of the effects of particle shrinkage and intra-particle heat conduction on biomass fast pyrolysis. Renew Energy. 2019;141:236–45.

    CAS  Google Scholar 

  6. Izadi A, Siavashi M, **ement jet hydrogen, air and \(\text{ CuH }_{2}\text{ O }\) nanofluid cooling of a hot surface covered by porous media with non-uniform input jet velocity. Int J Hydrog Energy. 2019;44(30):15933–48.

    CAS  Google Scholar 

  7. Xu S, Gao B, Hsu M-C, Ganapathysubramanian B. A residual-based variational multiscale method with weak imposition of boundary conditions for buoyancy-driven flows. Comput Methods Appl Mech Eng. 2019;352:345–68.

    Google Scholar 

  8. Xu F, Wang C, Hong K, Liu Y. Immersogeometric thermal analysis of flows inside buildings with reconfigurable components. J Therm Anal Calorim. 2020. https://doi.org/10.1007/s10973-020-09387-3.

    Article  Google Scholar 

  9. Brooks AN, Hughes TJR. Streamline upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comput Methods Appl Mech Eng. 1982;32:199–259.

    Google Scholar 

  10. Hughes TJR, Tezduyar TE. Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. Comput Methods Appl Mech Eng. 1984;45:217–84.

    Google Scholar 

  11. Oden JT, Babus̆ka I, Baumann CE. A discontinuous \(hp\) finite element method for diffusion problems. J Comput Phys. 1998;146:491–519.

    CAS  Google Scholar 

  12. Baumann CE, Oden JT. A discontinuous \(hp\) finite element method for convection–diffusion problems. Comput Methods Appl Mech Eng. 1999;175:311–41.

    Google Scholar 

  13. Hughes TJR, Liu WK, Zimmermann TK. Lagrangian–Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng. 1981;29:329–49.

    Google Scholar 

  14. Tezduyar T, Aliabadi S, Behr M, Johnson A, Mittal S. Massively parallel finite element computation of 3D flows—mesh update strategies in computation of moving boundaries and interfaces. In: Ecer A, Hauser J, Leca P, Periaux J, editors. Parallel computational fluid dynamics—new trends and advances. Amsterdam: Elsevier; 1995. p. 21–30.

    Google Scholar 

  15. Johnson AA, Tezduyar TE. 3D simulation of fluid-particle interactions with the number of particles reaching 100. Comput Methods Appl Mech Eng. 1997;145:301–21.

    Google Scholar 

  16. Johnson AA, Tezduyar TE. Advanced mesh generation and update methods for 3D flow simulations. Comput Mech. 1999;23:130–43.

    Google Scholar 

  17. Xu F, Moutsanidis G, Kamensky D, Hsu M-C, Murugan M, Ghoshal A, Bazilevs Y. Compressible flows on moving domains: stabilized methods, weakly enforced essential boundary conditions, sliding interfaces, and application to gas-turbine modeling. Comput Fluids. 2017;158:201–20.

    Google Scholar 

  18. Xu F, Morganti S, Zakerzadeh R, Kamensky D, Auricchio F, Reali A, Hughes TJR, Sacks MS, Hsu M-C. A framework for designing patient-specific bioprosthetic heart valves using immersogeometric fluid-structure interaction analysis. Int J Numer Methods Biomed Eng. 2018;34(4):e2938.

    Google Scholar 

  19. Xu F, Bazilevs Y, Hsu M-C. Immersogeometric analysis of compressible flows with application to aerodynamic simulation of rotorcraft. Math Models Methods Appl Sci. 2019;29:905–38.

    Google Scholar 

  20. Bazilevs Y, Hughes TJR. NURBS-based isogeometric analysis for the computation of flows about rotating components. Comput Mech. 2008;43:143–50.

    Google Scholar 

  21. Hsu M-C, Akkerman I, Bazilevs Y. Finite element simulation of wind turbine aerodynamics: validation study using NREL Phase VI experiment. Wind Energy. 2014;17(3):461–81.

    Google Scholar 

  22. Hsu M-C, Bazilevs Y. Fluid-structure interaction modeling of wind turbines: simulating the full machine. Comput Mech. 2012;50:821–33.

    Google Scholar 

  23. Yan J, Augier B, Korobenko A, Czarnowski J, Ketterman G, Bazilevs Y. FSI modeling of a propulsion system based on compliant hydrofoils in a tandem configuration. Comput Fluids. 2016;141:201–11.

    Google Scholar 

  24. Yan J, Korobenko A, Deng X, Bazilevs Y. Computational free-surface fluid-structure interaction with application to floating offshore wind turbines. Comput Fluids. 2016;141:155–74.

    Google Scholar 

  25. Yan J, Deng X, Korobenko A, Bazilevs Y. Free-surface flow modeling and simulation of horizontal-axis tidal-stream turbines. Comput Fluids. 2017;158:157–66.

    Google Scholar 

  26. Yan J, Deng X, Xu F, Xu S, Zhu Q. Numerical simulations of two back-to-back horizontal axis tidal stream turbines in free-surface flows. J Appl Mech. 2020. https://doi.org/10.1115/1.4046317.

    Article  Google Scholar 

  27. Bazilevs Y, Calo VM, Cottrel JA, Hughes TJR, Reali A, Scovazzi G. Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput Methods Appl Mech Eng. 2007;197:173–201.

    Google Scholar 

  28. Yan J, Korobenko A, Tejada-Martínez AE, Golshan R, Bazilevs Y. A new variational multiscale formulation for stratified incompressible turbulent flows. Comput Fluids. 2017;158:150–6.

    CAS  Google Scholar 

  29. Zhu Q, Xu F, Xu S, Hsu M-C, Yan J. An immersogeometric formulation for free-surface flows with application to marine engineering problems. Comput Methods Appl Mech Eng. 2019;361:112748.

    Google Scholar 

  30. Xu S, Liu N, Yan J. Residual-based variational multi-scale modeling for particle-laden gravity currents over flat and triangular wavy terrains. Comput Fluids. 2019;188:114–24.

    Google Scholar 

  31. Xu S, Xu F, Kommajosula A, Hsu M-C, Ganapathysubramanian B. Immersogeometric analysis of moving objects in incompressible flows. Comput Fluids. 2019;189:24–33.

    Google Scholar 

  32. Johnson C. Numerical solution of partial differential equations by the finite element method. Stockholm: Cambridge University Press; 1987.

    Google Scholar 

  33. Brenner SC, Scott LR. The mathematical theory of finite element methods. 2nd ed. Berlin: Springer; 2002.

    Google Scholar 

  34. Almeida RC, Galeão AC. An adaptive Petrov–Galerkin formulation for the compressible Euler and Navier–Stokes equations. Comput Methods Appl Mech Eng. 1996;129(1):157–76.

    Google Scholar 

  35. Arnold DN, Brezzi F, Cockburn B, Marini LD. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J Numer Anal. 2002;39:1749–79.

    Google Scholar 

  36. Takizawa K, Tezduyar TE, Mochizuki H, Hattori H, Mei S, Pan L, Montel K. Space-time VMS method for flow computations with slip interfaces (ST-SI). Math Models Methods Appl Sci. 2015;25:2377–406.

    Google Scholar 

  37. Takizawa K, Tezduyar TE, Kuraishi T, Tabata S, Takagi H. Computational thermo-fluid analysis of a disk brake. Comput Mech. 2016;57:965–77.

    Google Scholar 

  38. Takizawa K, Tezduyar TE, Terahara T, Sasaki T. Heart valve flow computation with the integrated space-time VMS, Slip interface, topology change and isogeometric discretization methods. Comput Fluids. 2017;158:176–88.

    Google Scholar 

  39. Takizawa K, Tezduyar TE, Uchikawa H, Terahara T, Sasaki T, Yoshida A. Mesh refinement influence and cardiac-cycle flow periodicity in aorta flow analysis with isogeometric discretization. Comput Fluids. 2019;179:790–8.

    Google Scholar 

  40. Terahara T, Takizawa K, Tezduyar TE, Tsushima A, Shiozaki K. Ventricle-valve-aorta flow analysis with the space-time isogeometric discretization and topology change. Comput Mech. 2020. https://doi.org/10.1007/s00466-020-01822-4.

    Article  Google Scholar 

  41. Terahara T, Takizawa K, Tezduyar TE, Bazilevs Y, Hsu M-C. Heart valve isogeometric sequentially-coupled FSI analysis with the space-time topology change method. Comput Mech. 2020. https://doi.org/10.1007/s00466-019-01813-0.

    Article  Google Scholar 

  42. Chung J, Hulbert GM. A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-\(\alpha \) method. J Appl Mech. 1993;60:371–5.

    Google Scholar 

  43. Jansen KE, Whiting CH, Hulbert GM. A generalized-\(\alpha \) method for integrating the filtered Navier–Stokes equations with a stabilized finite element method. Comput Methods Appl Mech Eng. 2000;190:305–19.

    Google Scholar 

  44. Saad Y, Schultz M. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput. 1986;7:856–69.

    Google Scholar 

  45. Shakib F, Hughes TJR, Johan Z. A multi-element group preconditioned GMRES algorithm for nonsymmetric systems arising in finite element analysis. Comput Methods Appl Mech Eng. 1989;75:415–56.

    Google Scholar 

  46. Wang C, Wu MCH, Xu F, Hsu M-C, Bazilevs Y. Modeling of a hydraulic arresting gear using fluid–structure interaction and isogeometric analysis. Comput Fluids. 2017;142:3–14.

    Google Scholar 

  47. Wu MCH, Kamensky D, Wang C, Herrema AJ, Xu F, Pigazzini MS, Verma A, Marsden AL, Bazilevs Y, Hsu M-C. Optimizing fluid–structure interaction systems with immersogeometric analysis and surrogate modeling: application to a hydraulic arresting gear. Comput Methods Appl Mech Eng. 2017;316:668–93.

    Google Scholar 

  48. Vladescu S-C, Marx N, Fernández L, Barceló F, Spikes H. Hydrodynamic friction of viscosity-modified oils in a journal bearing machine. Tribol Lett. 2018;66(4):127.

    Google Scholar 

Download references

Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (21406081) and Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (17KJA530001). K. Hong thanks the support from QingLan Project of Jiangsu Province, China. These supports are gratefully acknowledged.

Author information

Authors and Affiliations

  1. National and Local Joint Engineering Research Center for Mineral Salt Deep Utilization, Key Laboratory for Palygorskite Science and Applied Technology of Jiangsu Province, Huaiyin Institute of Technology, Huai’an, 223003, Jiangsu, China

    Kun Hong & Fei Xu

  2. Ansys, Inc., Lebanon, NH, 03784, USA

    Chenglong Wang

  3. Ansys. Inc., Austin, TX, 78746, USA

    Fei Xu

Authors
  1. Kun Hong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chenglong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fei Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fei Xu.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hong, K., Wang, C. & Xu, F. Finite-element thermal analysis of flows on moving domains with application to modeling of a hydraulic arresting gear. J Therm Anal Calorim 144, 963–972 (2021). https://doi.org/10.1007/s10973-020-09583-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10973-020-09583-1

Keywords

Search

Navigation