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Finite element analysis of fluid flows with moving boundary

  • Thermal Engineering · Fluid Engineering · Energy and Power Engineering
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Abstract

The objective of the present study is to analyze the fluid flow with moving boundary using a finite element method. The algorithm uses a fractional step approach that can be used to solve low-speed flow with large density changes due to intense temperature gradients. The explicit Lax-Wendroff scheme is applied to nonlinear convective terms in the momentum equations to prevent checkerboard pressure oscillations. The ALE (Arbitrary Lagrangian Eulerian) method is adopted for moving grids. The numerical algorithm in the present study is validated for two-dimensional unsteady flow in a driven cavity and a natural convection problem. To extend the present numerical method to engine simulations, a piston-driven intake flow with moving boundary is also simulated. The density, temperature and axial velocity profiles are calculated for the three-dimensional unsteady piston-driven intake flow with density changes due to high inlet fluid temperatures using the present algorithm. The calculated results are in good agreement with other numerical and experimental ones.

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Abbreviations

C p :

Specific heat at constant pressure

f j :

Body force in thex j -direction

n k :

Thek-th component of the unit outward normal to Γ

p :

Pressure

p * :

Pressure correction

:

Relative pressure value

T :

Temperature

t :

Time

Δt :

Time increment

u :

Velocity

\(\tilde u_k \) :

Velocity of the fluid relative to the moving grid (=U k -U kg )

U kg :

Grid velocity

\(\hat u_j \) :

Prescribed velocity component

W p :

Piston velocity

\(\hat W\) :

Velocity of the fluid relative to the moving grid (=W-W g )

W g :

Grid velocity

z p (t):

Current piston position

Γ 1 :

The boundary surface at which prescribed velocity boundary conditions are imposed.

Γ 2 :

The boundary surface at which natural boundary conditions are imposed.

k :

The coefficient of thermal conductivity

λ:

Second viscosity coefficient (=−2/3μ)

μ:

Fluid viscosity

ρ:

Density

ν:

Kinematic viscosity coefficient

N j ,N p ,N T :

Weighting function

o :

Previous time step

n :

Next time step

i :

Dummy variable (i=1, 2, 3)

j :

Direction variable (j=1, 2, 3)

k :

Dummy variable (k=1, 2, 3)

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Authors and Affiliations

  1. Graduate School, Department of Mechanical Engineering, Chonnam National University, 500-757, Kwangju, Korea

    Kyung Se Cha & Chan Guk Park (Professor)

  2. School of Mechanical and Automotive Engineering, Sunchon National University, 540-742, Sunchon, Korea

    Jong Wook Choi

Authors
  1. Kyung Se Cha
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  2. Jong Wook Choi
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  3. Chan Guk Park
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Correspondence to Kyung Se Cha.

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Cha, K.S., Choi, J.W. & Park, C.G. Finite element analysis of fluid flows with moving boundary. KSME International Journal 16, 683–695 (2002). https://doi.org/10.1007/BF03184818

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  • DOI: https://doi.org/10.1007/BF03184818

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