The effect of bend angle on pressure drop and flow behavior in a corrugated duct

Abstract

In the present study, the effect of bend angle on pressure drop and flow behavior in a small-diameter corrugated duct is numerically investigated and experimentally validated under a fully developed flow condition. The large eddy simulation, together with the proper orthogonal decomposition (POD) method, is employed to study the pressure drop, mean flow pattern, and unsteady flow evolution for a corrugated duct with various bend angles. The results show that the pressure drop exhibits a monotonic increase with increasing bend angle. Specifically, as the bend angle increases from \(0^{\circ }\) to \(90^{\circ }\), the pressure drop of the corrugated duct experiences a striking increase of about 43%. Accordingly, a larger bend angle is found to induce the occurrence of stronger Dean cells or larger swirl intensity downstream the duct bend. Meanwhile, as for larger bend angles, the main turbulent properties of the Dean cells could be, to some extent, governed by the first few POD modes, which appear to be featured with one or a few large-scale vortices. Generally, the larger bend angle causes stronger swirl intensity and wave-like structures, thus rendering severer pressure drop or larger pressure loss coefficient in the corrugated duct.

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Abbreviations

\(a_{j}\left( t \right) \) :

Temporal coefficients

A :

Area

\(C_{D}\) :

Cell-centered values of the coefficient

\(C_{P, \mathrm {sta}}\) :

Nondimensional form of pressure drop

\(C_{P, \mathrm {tot}}\) :

Total pressure loss coefficient

\({\bar{C}}_{P, \mathrm {tot}}\) :

Overall mass averaged total pressure loss coefficient

\(C_\mathrm{{s}}\) :

Smagorinsky constant

D :

Effective diameter of corrugated duct

L :

Length of corrugated duct

\(\dot{m}\) :

Mass flow

N :

POD mode number

P :

Instantaneous pressure

\(P_\mathrm{{sta}}\) :

Static pressure

\(P_\mathrm{{t}}\) :

Local total pressure

\(P_\mathrm{{t{0}}}\) :

Total pressure at the inlet

r :

Variable of integration

R :

Effective radius of corrugated duct

\({{\varvec{R}}}\) :

Covariance matrix

\(R_{\mathrm{c}}\) :

Bend centerline radius

Re:

Reynolds number

\({{\overline{S}}}_{ij}\) :

Rate of strain tensor

Sw:

Swirl number

t :

Time

\(t^{*}\) :

Nondimensional time

u :

x Component of instantaneous velocity

\(u_{i}\) :

i Component of instantaneous velocity

\(u_\mathrm{{in}}\) :

In-plane velocity

\(u_{j}\) :

j Component of instantaneous velocity

\(u_\mathrm{{n}}\) :

Normal velocity

\(u\left( t \right) \) :

Fluctuating velocity component

\({\bar{u}}\left( \xi \right) \) :

Mean velocity field

\(u\left( \xi ,t \right) \) :

Instantaneous velocity field of snapshots

U :

Velocity

\({{\varvec{U}}}\) :

Matrix form of snapshots’ data

\(U_\mathrm{{ax}}\) :

Axial velocity component

\(U_{\theta }\) :

Tangential velocity component

v :

Instantaneous velocity in y direction

V :

Volume of the cell

w :

Instantaneous velocity in z direction

W :

Mean streamwise velocity

\(W_{b}\) :

Inlet velocity

x :

Coordinate axis

\(x_{i}\) :

i Component of coordinate axis

\(x_{j}\) :

j Component of coordinate axis

y :

Coordinate axis

\(y^{+}\) :

Nondimensional distance from the wall

z :

Coordinate axis

\(\beta \) :

Bend angle (\(^{\circ }\))

\(\gamma \) :

Bend curvature ratio

\(\delta _{ij}\) :

Kronecker delta

\({\Delta }\) :

Filter width

\({\Delta }P\) :

Pressure drop

\({\Delta }t\) :

Time step

\(\lambda _{j}\) :

Eigenvalues

\(\Lambda \) :

Matrix form of eigenvalues

\(\mu _{t}\) :

Subgrid-scale eddy viscosity

\(\nu \) :

Kinetic dynamic viscosity

\(\rho \) :

Air density

\(\tau _{kk}\) :

Isotropic part of the subgrid-scale stresses

\(\tau _{ij}\) :

Subgrid-scale stress

\(\phi _{j}\) :

POD modes

\(\varPhi \) :

Matrix form of POD modes

\(\psi _{j}\) :

Eigenvectors

\(\varPsi \) :

Matrix form of eigenvectors

\(\omega _{Z}\) :

Streamwise vorticity

ACCA:

Air Conditioning Contractors of America

ASHRAE:

American Society of Heating, Refrigerating and Air-Conditioning Engineers

CFD:

Computational Fluid Dynamics

CFL:

Courant–Friedrichs–Lewy

ESP:

Electronically scanned pressure

FS:

Full scale

LES:

Large eddy simulation

POD:

Proper orthogonal decomposition

RANS:

Reynolds-averaged Navier–Stokes

SGS:

Subgrid-scale

SIMPLE:

Semi-implicit method for pressure-linked equations

TKE:

Turbulent kinetic energy

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Acknowledgements

This work is supported by Open Fund of Key Laboratory of Icing and Anti/De-icing of Aircraft (Grant No.: AIADL20180102), International Frontier-Interdisciplinary Key Projects of Tongji University (Grant No.: 2019010108), and Fundamental Research Funds for the Central Universities (Grant No.: 22120190286).

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Du, X., Wei, A., Fang, Y. et al. The effect of bend angle on pressure drop and flow behavior in a corrugated duct. Acta Mech (2020). https://doi.org/10.1007/s00707-020-02716-5

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