Skip to main content

Advertisement

Springer Nature Link
Log in

Dynamic delayed detached-eddy simulation and acoustic analogy analysis of unsteady flow through a sudden expansion pipe

  • Regular Paper
  • Published:
Journal of Visualization Aims and scope Submit manuscript

Abstract

In the present study, the unsteady flow through a sudden expansion pipe with an expansion ratio of 1:3 is numerically modeled using dynamic delayed detached-eddy simulation (dynamic DDES), and the flow noise mechanism and the downstream noise propagation behaviors are analyzed using Lighthill’s acoustic analogy. The numerical results for turbulent flow with a Reynolds number of 15,000 are validated against planar particle image velocimetry measurements. The acoustic sources are identified as acoustic quadrupoles in the high-shear flow region and acoustic dipoles on the expansion and downstream walls. The volume quadrupole acoustic source, which is particularly energetic in the low frequency region, is found to concentrate in the separating and reattaching area. On the downstream wall, the reattaching flow gives rise to the peak acoustic dipole, which attenuates beyond the station x/d = 10. On the expansion wall, the alternating appearance of a peak sound-pressure level (SPL) pair resembles the pipe circumferential sound mode beyond the cut-off frequency. The SPL distributions on the downstream wall are closely related to the noise propagation behavior. In the low-frequency region, the total noise in the far-downstream pipe section is dominated by acoustic dipoles on the downstream wall and volume acoustic quadrupoles in the high-shear flow region, whereas the major contribution in the high-frequency region is from acoustic dipoles on the expansion and downstream walls.

Graphical abstract

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
$34.99 /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
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Abbreviations

CAA:

Computational aeroacoustics

CFL:

Courant–Friedrichs–Lewy

CMOS:

Complementary metal oxide semiconductor

DES:

Detached-eddy simulation

DDES:

Delayed detached-eddy simulation

DILU:

Diagonal-incomplete lower upper

FIV:

Flow-induced vibration

GAMG:

Geometric–algebraic multi-grid

LCW:

Liquid cooling water

LIC:

Line integral convolution

LES:

Large-eddy simulation

LUST:

Linear-upwind stabilized transport

OpenFOAM:

Open-source field operation and manipulation

PIV:

Particle image velocimetry

POD:

Proper orthogonal decomposition

PBiCG:

Preconditioned bi-conjugate gradient

PIMPLE:

Hybrid of SIMPLE/PISO

PISO:

Pressure-implicit split operator

RANS:

Reynolds-averaged Navier–Stokes

SIMPLE:

Semi-implicit method for pressure-linked equations

SPL:

Sound pressure level

WMLES:

Wall modeled large eddy simulation

d :

Pipe diameter

d h :

Hollow glass spheres diameter

\({\text{Re}}_{{\text{d}}}\) :

Reynolds number

\(St\) :

Strouhal number

\(S_{{{\text{ij}}}}\) :

Surface acoustic contribution

\(T_{{{\text{ij}}}}\) :

Lighthill stress tensor

\(U_{0}\) :

Inflow velocity

\(U_{{\text{m}}}\) :

Mean streamwise velocity

\(V_{{{\text{ij}}}}\) :

Volume acoustic contribution

\(x\) :

Cartesian coordinates in the streamwise direction

\(y\) :

Cartesian coordinates in the wall-normal direction

y + :

Dimensionless wall distance

\(z\) :

Cartesian coordinates in the spanwise direction

\(\hat{\upsilon }\) :

Wall-normal component

\(\Omega\) :

Vorticity

\(\Omega_{{\text{z}}}\) :

Spanwise vorticity

\(\rho_{{\text{h}}}\) :

Hollow glass spheres density

References

  • Aloui F, Souhar M (2000) Experimental study of turbulent asymmetric flow in a flat duct symmetric sudden expansion. J Fluids Eng 122(1):174–177

    Article  Google Scholar 

  • Blevins RD (1977) Flow-induced vibration

    MATH  Google Scholar 

  • Bose ST, Park GI (2018) Wall-modeled large-eddy simulation for complex turbulent flows. Annu Rev Fluid Mech 50:535–561

    Article  MathSciNet  Google Scholar 

  • Cantwell CD, Barkley D, Blackburn HM (2010) Transient growth analysis of flow through a sudden expansion in a circular pipe. Phys Fluids 22(3):034101

    Article  Google Scholar 

  • Casarsa L, Giannattasio P (2008) Three-dimensional features of the turbulent flow through a planar sudden expansion. Phys Fluids 20(1):015103

    Article  Google Scholar 

  • Cimbala, John M (2006) Fluid mechanics: fundamentals and applications. McGraw-Hill Higher Education. ISBN 978-0072472363. OCLC 834846067

  • Cole DR, Glauser MN (1998) Applications of stochastic estimation in the axisymmetric sudden expansion. Phys Fluids 10(11):2941–2949

    Article  Google Scholar 

  • Devenport WJ, Sutton EP (1993) An experimental study of two flows through an axisymmetric sudden expansion. Exp Fluids 14(6):423–432

    Article  Google Scholar 

  • Dhamankar NS, Blaisdell GA, Lyrintzis AS (2018) Overview of turbulent inflow boundary conditions for large-eddy simulations. AIAA J 56(4):1317–1334

    Article  Google Scholar 

  • Ewert R, Schröder W (2003) Acoustic perturbation equations based on flow decomposition via source filtering. J Comput Phys 188(2):365–398

    Article  MathSciNet  Google Scholar 

  • Gritskevich MS, Garbaruk AV, Schütze J (2012) Development of DDES and IDDES formulations for the k–ω shear stress transport model. Flow Turbul Combust 88(3):431–449

    Article  Google Scholar 

  • Guo B, Langrish TA, Fletcher DF (2001) Numerical simulation of unsteady turbulent flow in axisymmetric sudden expansions. J Fluids Eng 123(3):574–587

    Article  Google Scholar 

  • He C, Liu Y (2018) A dynamic detached-eddy simulation model for turbulent heat transfer: impinging jet. Int J Heat Mass Transf 127:326–338

    Article  Google Scholar 

  • He C, Liu Y, Yavuzkurt S (2017) A dynamic delayed detached-eddy simulation model for turbulent flows. Comput Fluids 146:174–189

    Article  MathSciNet  Google Scholar 

  • Jasak H, Jemcov A, Tukovic Z (2007) OpenFOAM: a C++ library for complex physics simulations. In: International workshop on coupled methods in numerical dynamics, IUC Dubrovnik Croatia

  • Javadi A, Nilsson H (2015) LES and DES of strongly swirling turbulent flow through a suddenly expanding circular pipe. Comput Fluids 107:301–313

    Article  Google Scholar 

  • Karantonis K, Kokkinakis IW, Thornber B (2021) Compressibility in suddenly expanded subsonic flows. Phys Fluids 33(10):105106

    Article  Google Scholar 

  • Koronaki ED, Liakos HH, Founti MA, Markatos NC (2001) Numerical study of turbulent diesel flow in a pipe with sudden expansion. Appl Math Model 25(4):319–333

    Article  Google Scholar 

  • Krabben IGW (2020) Determination of the source term disturbing bounded flow performing practical Large Eddy Simulations, University of Twente

  • Lebon B, Nguyen MQ, Peixinho J (2018) A new mechanism for periodic bursting of the recirculation region in the flow through a sudden expansion in a circular pipe. Phys Fluids 30(3):031701

    Article  Google Scholar 

  • Li F, He C, Wang P, Liu Y (2021) Unsteady analysis of turbulent flow and heat transfer behind a wall-proximity square rib using dynamic delayed detached-eddy simulation. Phys Fluids 33(5):055104

    Article  Google Scholar 

  • Lighthill MJ (1952) On sound generated aerodynamically I. General theory. Proc R Soc Lond Ser A Math Phys Sci 211(1107):564–587

    MathSciNet  MATH  Google Scholar 

  • Lighthill MJ (1954) On sound generated aerodynamically II. Turbulence as a source of sound. Proc R Soc Lond Ser A Math Phys Sci 222(1148):1–32

    MathSciNet  MATH  Google Scholar 

  • Lunia K, Majumdera M (2019) Numerical investigation of turbulent flow in a sudden expansion

  • Lyrintzis AS (2003) Surface integral methods in computational aeroacoustics—from the (CFD) near-field to the (Acoustic) far-field. Int J Aeroacoustics 2(2):95–128

    Article  Google Scholar 

  • Meinhart CD, Wereley ST, Santiago JG (2000) A PIV algorithm for estimating time-averaged velocity fields. J Fluids Eng 122(2):285–289

    Article  Google Scholar 

  • Menter FR, Kuntz M, Langtry R (2003) Ten years of industrial experience with the SST turbulence model. Turbul Heat Mass Transf 4(1):625–632

    Google Scholar 

  • Moallemi N, Brinkerhoff JR (2018) Instability and localized turbulence associated with flow through an axisymmetric sudden expansion. Int J Heat Fluid Flow 72:161–173

    Article  Google Scholar 

  • Moussou P (2006) An attempt to scale the vibrations of water pipes. J Press Vessel Technol 128(4):670–676

    Article  Google Scholar 

  • Mullin T, Seddon JRT (2009) Bifurcation phenomena in the flow through a sudden expansion in a circular pipe. Phys Fluids 21(1):014110

    Article  Google Scholar 

  • Nouri-Borujerdi A, Shafiei Ghazani A (2019) Simulation of compressible and incompressible flows through planar and axisymmetric abrupt expansions. J Fluids Eng 10(1115/1):4043497

    Google Scholar 

  • Praveen E (2017) Transition to asymmetric flow in a symmetric sudden expansion: hydrodynamics and MHD cases. Comput Fluids 148:103–120

    Article  MathSciNet  Google Scholar 

  • Qian J, Ma L, Zhan H, Luo Q (2016) The effect of expansion ratio on the critical Reynolds number in single fracture flow with sudden expansion. Hydrol Proces 30(11):1718–1726

    Article  Google Scholar 

  • Roumen L (2021) Pressure fluctuations and acoustic force source term due to water flow through an orifice

  • Roy V, Majumder S, Sanyal D (2010) Analysis of the turbulent fluid flow in an axi-symmetric sudden expansion. Int J Eng Sci Technol 2(6):1569–1574

    Google Scholar 

  • Selvam K, Peixinho J, Willis AP (2016) Flow in a circular expansion pipe flow: effect of a vortex perturbation on localised turbulence. Fluid Dyn Res 48(6):061418

    Article  MathSciNet  Google Scholar 

  • Sreenivasan KR, Strykowski PJ (1983) An instability associated with a sudden expansion in a pipe flow. Phys Fluids 26(10):2766–2768

    Article  Google Scholar 

  • Teyssandiert RG, Wilson MP (1974) An analysis of flow through sudden enlargements in pipes. J Fluid Mech 64(1):85–95

    Article  Google Scholar 

  • Tinney CE, Glauser MN, Eaton EL (2006) Low-dimensional azimuthal characteristics of suddenly expanding axisymmetric flows. J Fluid Mech 567:141–155

    Article  Google Scholar 

  • Yakhot A, Orszag SA (1993) Numerical simulation of turbulent flow in the inlet region of a smooth pipe. J Sci Comput 8(2):111–121

    Article  Google Scholar 

  • Yoder DA, DeBonis JR, Georgiadis NJ (2015) Modeling of turbulent free shear flows. Comput Fluids 117:212–232

    Article  MathSciNet  Google Scholar 

Download references

Funding

The authors gratefully acknowledge financial support provided for this study by the National Natural Science Foundation of China (11725209).

Author information

Authors and Affiliations

  1. Key Lab of Education Ministry for Power Machinery and Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, 200240, China

    Fuqi Li, Peng Wang, Chuangxin He & Yingzheng Liu

  2. Gas Turbine Research Institute, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, 200240, China

    Fuqi Li, Peng Wang, Chuangxin He & Yingzheng Liu

Authors
  1. Fuqi Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chuangxin He
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yingzheng Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yingzheng Liu.

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

Li, F., Wang, P., He, C. et al. Dynamic delayed detached-eddy simulation and acoustic analogy analysis of unsteady flow through a sudden expansion pipe. J Vis 25, 999–1015 (2022). https://doi.org/10.1007/s12650-022-00846-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12650-022-00846-7

Keywords