Smoothed Particle Hydrodynamics Simulation of Non-isothermal eXtended Pom-Pom Poiseuille Flow

doi:10.19596/j.cnki.1001-246x.8685

Abstract

Abstract:

Smoothed particle hydrodynamics (SPH) simulation of non-isothermal viscoelastic poiseuille flow is carried out, in which the viscoelastic properties of the fluid are modeled and calculated according to the eXtended Pom-Pom (XPP) constitutive model. The SPH discrete format of the temperature equation is derived, and the temperature dependence of viscoelastic properties of fluid is considered based on the principle of time temperature equivalence. The accuracy and effectiveness of the SPH method for simulating non-isothermal XPP poiseuille flow are verified by comparing the SPH results with those obtained by the finite volume method. The numerical convergence of the SPH method is discussed by performing simulations with four different initial particle spacings. The influence of the introduction of the temperature equation on poiseuille flow is studied. The influence of different physical parameters on the flow process is deeply analyzed.

Key words: smoothed particle hydrodynamics, eXtended Pom-Pom model, non-isothermal, poiseuille flow

CLC Number:

O242

Xiaoyang XU, Yuting ZHAO. Smoothed Particle Hydrodynamics Simulation of Non-isothermal eXtended Pom-Pom Poiseuille Flow[J]. Chinese Journal of Computational Physics, 2024, 41(2): 161-171.

Figures/Tables 7

Fig.1 The geometric region of viscoelastic Poiseuille flow

Fig.2 Comparison of SPH solutions with FVM numerical solutions and steady analytical solution

Fig.3 Convergence analysis of SPH solutions and comparison with FVM solution

Fig.4 Comparison between non-isothermal flows and isothermal flow and effect of φ on velocity u at point A with time

Fig.5 Effect of Péclet number on velocity u at point A with time

Fig.6 Temperature distribution with respect to y at seven different times

Fig.7 Effect of different rheological parameters on velocity u at point A with time (a) Re; (b) Wi; (c) β; (d) α; (e) γ; (f) Q

References 22

1	WATERS N D , KING M J . Unsteady flow of an elastico-viscous liquid[J]. Rheologica Acta, 1970, 9 (3): 345- 355. DOI
2	HUANG P Y , FENG J , HU H H , et al. Direct simulation of the motion of solid particles in couette and poiseuille flows of viscoelastic fluids[J]. Journal of Fluid Mechanics, 1997, 343, 73- 94. DOI
3	OLIVEIRA P J , PINHO F T . Analytical solution for fully developed channel and pipe flow of Phan-Thien-Tanner fluids[J]. Journal of Fluid Mechanics, 1999, 387, 271- 280. DOI
4	van OS R G M , PHILLIPS T N . The prediction of complex flows of polymer melts using spectral elements[J]. Journal of Non-Newtonian Fluid Mechanics, 2004, 122 (1-3): 287- 301. DOI
5	BHARATHI M C , KUDENATTI R B . Linear stability of poiseuille flow of viscoelastic fluid in a porous medium[J]. Physics of Fluids, 2022, 34 (11): 114102. DOI
6	GINGOLD R A , MONAGHAN J J . Smoothed particle hydrodynamics: Theory and application to non-spherical stars[J]. Monthly Notices of the Royal Astronomical Society, 1977, 181 (3): 375- 389. DOI
7	LUCY L B . A numerical approach to the testing of the fission hypothesis[J]. The Astronomical Journal, 1977, 82, 1013- 1024. DOI
8	XU X Y , JIANG Y L , YU P . SPH simulations of 3D dam-break flow against various forms of the obstacle: Toward an optimal design[J]. Ocean Engineering, 2021, 229, 108978. DOI
9	PENG Y X , ZHANG A M , MING F R . Numerical simulation of structural damage subjected to the near-field underwater explosion based on SPH and RKPM[J]. Ocean Engineering, 2021, 222, 108576. DOI
10	MENG Z F , ZHANG A M , YAN J L , et al. A hydroelastic fluid-structure interaction solver based on the Riemann-SPH method[J]. Computer Methods in Applied Mechanics and Engineering, 2022, 390, 114522. DOI
11	ZHOU J , XU S L . On SPH method with treatment of gas-liquid interface boundary conditions[J]. Chinese Journal of Computational Physics, 2017, 34 (4): 409- 416.
12	HE F , ZHANG H , HUANG C , et al. A stable SPH model with large CFL numbers for multi-phase flows with large density ratios[J]. Journal of Computational Physics, 2022, 453, 110944. DOI
13	ELLERO M , TANNER R I . SPH simulations of transient viscoelastic flows at low Reynolds number[J]. Journal of Non-Newtonian Fluid Mechanics, 2005, 132 (1-3): 61- 72. DOI
14	杨波, 欧阳洁, 蒋涛, 等. PTT黏弹性流体的光滑粒子动力学方法模拟[J]. 力学学报, 2011, 43 (4): 667- 673.
15	XU X , OUYANG J , LI W , et al. SPH simulations of 2D transient viscoelastic flows using Brownian configuration fields[J]. Journal of Non-Newtonian Fluid Mechanics, 2014, 208-209, 59- 71. DOI
16	VAHABI M , HADAVANDMIRZAEI H , KAMKARI B , et al. Interaction of a pair of in-line bubbles ascending in an Oldroyd-B liquid: A numerical study[J]. European Journal of Mechanics B/Fluids, 2021, 85, 413- 429. DOI
17	MOINFAR Z , VAHABI S , VAHABI M . Numerical simulation of drop deformation under simple shear flow of Giesekus fluids by SPH[J]. International Journal of Numerical Methods for Heat & Fluid Flow, 2023, 33 (1): 263- 281.
18	万启坤, 张月, 郭照立. 两平板间两组分稀薄气体振荡传热数值模拟研究[J/OL]. 计算物理: 1-15[2023-04-23]. http://kns.cnki.net/kcms/detail/11.2011.o4.20230116.1851.001.html.
19	XU X , DENG X L . An improved weakly compressible SPH method for simulating free surface flows of viscous and viscoelastic fluids[J]. Computer Physics Communications, 2016, 201, 43- 62. DOI
20	SHAO S , LO E Y M . Incompressible SPH method for simulating newtonian and non-newtonian flows with a free surface[J]. Advances in Water Resources, 2003, 26 (7): 787- 800. DOI
21	PEI J X , RAHMATJAN I . SPH boundary algorithm based on finite difference method and its application[J]. Chinese Journal of Computational Physics, 40 (3): 343- 352.
22	LYU H G , SUN P N . Further enhancement of the particle shifting technique: Towards better volume conservation and particle distribution in SPH simulations of violent free-surface flows[J]. Applied Mathematical Modelling, 2022, 101, 214- 238. DOI

[1]	Puyang GAO. Non-isothermal Polymer Filling Process via Phase Field Method in Three Dimensions [J]. Chinese Journal of Computational Physics, 2023, 40(6): 689-698.
[2]	ZHU Qiaoli, ZHANG Wenhuan. An iDdQ(q-1) Multiple-relaxation-time Lattice Boltzmann Model with External Force [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 37(5): 551-561.
[3]	JU Long, ZHANG Chunhua, CHEN Songze, GUO Zhaoli. Lattice Boltzmann Study on Displacement Process of Thermal Miscible Fluids in Porous Media [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 36(6): 648-658.
[4]	GONG Xiangfei, YANG Jiming, ZHANG Shudao. A Parallel SPH Method with Background Grid of Adaptive Mesh Refinement [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 33(2): 183-189.
[5]	WANG Zhuang, LI Yuchun, WANG Lishi. SPH Simulations of Parametric Sloshing in Various Shape Aqueducts [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2013, 30(5): 642-648.
[6]	HAN Yawei, QIANG Hongfu. An Improved SPH Method with Physical Viscosity and Application in Dam.break Problem [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 29(5): 693-699.
[7]	ZHENG Xing, MA Qingwei, DUAN Wenyang. K2_SPH Method and Simulation of 2D Breaking Waves [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 29(3): 317-325.
[8]	ZHENG Xing, DUAN Wenyang. K2_.SPH Method and Application for 2D Nonlinear Water Wave Simulation [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2011, 28(5): 659-666.
[9]	QIANG Hongfu, CHEN Fuzhen, GAO Weiran. A modified PUFF equation of state is proposed with considenation of both non-linear volume change and anisotropic strength of material under compression and dilation.Taking 2-D impact of orthotropic material and thermal shock wave under X-ray radiation as examples,a finite element program is developed.The mean stresses obtained by traditional and modified PUFF equation of state are compared.They are obviously different at low compression and tension states.With increase of stress,they tends to be consistent gradually. [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2011, 28(3): 375-384.
[10]	XU Jinzhong, TANG Wenhui. Initial Smoothing Length and Space Between Particles in SPH Method for Numerical Simulation of High-speed Impacts [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 26(4): 548-552.
[11]	YIN Jianwei, MA Zhibo. Reproducing Kernel Particle Method in Smoothed Particle Hydrodynamics [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 26(4): 553-558.
[12]	QIANG Hongfu, GAO Weiran. SPH Method with Fully Variable Smoothing Lengths and Implementation [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2008, 25(5): 569-575.
[13]	DU Rui, SHI Bao-chang. Curved Boundary Treatment in the Lattice Boltzmann Method [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2006, 23(4): 405-411.