1. 연료레일에서의 맥동저감을 위한 유체-구조 상호작용 해석
연료레일에서의 맥동저감을 위한 유체-구조 상호작용 해석
심 정 연 에이블맥스㈜

2. Contents
연구 배경
이론적 배경
모델 설명
해석 결과 결론

3. 연구 배경
Engine의 효율적 작동을 위해서는 stable fuel rail pressure 유지되어야 하지만 Pressure Pulsation이 발생.
Pressure Pulsation의 주요 원인
- Fuel Injector의 rapid opening/closing (water hammer effect)
Pressure damping device를 사용하여 wave amplitude를 줄일 수 있으나 pressure pulsation이 연료 공급 라인으로 전달 될 수 있음.
“Fuel Rail with Integrated Damping Effect” by Kazuteru Mizuno, et al.
- 연료레일에 Pulsation damper를 장착하지 않고 연료레일 자체의 디자인을
바꾸어 압력 맥동을 줄일 수 있음을 실험을 통해 보임.
- Volume 증가에 따른 맥동 감소 효과는 그리 크지 않으나 Cross sectional shape
의 경우circular, square, rectangular 순으로 맥동 감소효과가 각각 20%까지 증가
- 맥동이 Cabin에서의 소음진동의 원인이 됨.
ADINA-FSI를 활용하여 Cross sectional shape과 Aspect Ratio에 따른 맥동 감소 효과를 Study

4. 이론적 배경 유체 지배방정식 In ALE (Arbitrary Lagrangian-Eulerian) coordinate,
v : velocity vector
w : moving mesh velocity vector
q : temperature
m : effective viscosity
l : second viscosity
Stress tensor
Strain tensor
Specific energy
Slightly compressible flow:
fully compressible flow:
Computational
domain
w(t)
Fixed wall
Eulerian coordinate
Moving wall
Lagrangian coordinate
ALE coordinate

5. at fluid-structure interface
유체 구조 상호 작용
FLUIDS
Structure
Automatic exchange
Between the solvers
Boundary conditions
at fluid-structure interface
Finite Volume
Finite Element
Solving the flow field and extracting the pressure forces upon the structure
Calculating the structure deformation due to external and internal forces

6. Mapping Operators

7. Mechanical Coupling on Interface
Traction Equilibrium
Nodal forces:
 Applied as external forces to the structural model and formulated as natural boundary conditions in the finite element procedure.
: Matrix of the interpolation functions of
the solid elements along the interface

8. Mechanical Coupling on Interface
Displacement Compatibility
Along the entire interface
Tangential velocity >> normal velocity on the interface

9. Solution procedure for coupled system
To achieve the compatibility of the displacement, velocities and accelerations, use one integration scheme for the fully computed system.
For example, using the Euler backward time integration method for velocity and acceleration in both solid and fluid models ensures the compatibility in time integrations
α≥1/2 is required to maintain numerical stability

10. Convergence Criteria
At each time step, the convergence of the equilibrium iterations must be satisfied (in addition to standard fluid and solid convergence checks)
Residuals on the interface S
: Stress residual
: Displacement residual

11. Direct Two-way FSI Coupling
Where k is the equilibrium iteration number
Newton-Raphson method is used to solve the coupled system.
Effective matrix can be expressed as

12. Solution procedure for Direct Two-way FSI Coupling
Apply the ALE procedure to obtain fluid nodal displacements.
Compute temperatures at solid nodes using the mapping operator (TFSI).
Assemble and as usually performed in a structure only problem, but including the fluid pressures in the porous region (PFSI), and using the latest temperature to calculate the material properties (TFSI)
Assemble and as usually performed in a fluid only problem, but using the velocity conditions on the interface. The coupling matrix is also assembled on the interface while the fluid boundary condition is treated.
Assemble and update from the contributions of the fluid stress.
Solve the coupled matrix system using direct or iterative solver.

13. Solution procedure for Iterative Two-way FSI Coupling
Where k is the equilibrium iteration number
Update the fluid mesh.
Assemble and as usually performed in a fluid only problem.
Evaluate the velocity on the FSI boundary.
Solve the fluid equation using a direct or iterative solver.
Calculate the temperature at solid nodes using mapping operator (TFSI).
Calculate the fluid force at solid nodes using.
Assemble and as usually performed in a solid only problem, but adding the fluid force on the interface and the fluid stress in the porous domain. The material properties are calculated using the latest temperature.
Solve the solid equation using a direct or iterative solver.

14. Solution Process

15. 모델 설명 3-D Fuel Rail Model with 4 injectors 압력측정 위치
Inlet Pressure = 350kPa
Injector #1 #2 #3 #4
Injection period: 42.86msec
Injection time length: 5.4msec
Injection period/time length is controlled by time functions.
#1 open #1
#3 open
#4 open
#2 open
K. Mizuno, et al. “Fuel Rail with Integrated Damping Effect”, SAE

16. Fluid & Structure Mesh
Fluid Model – 131,479개의 4-node Tetrahedral elements
Structure Model – 82,063개의 4-node Tetrahedral elements

17. 해석 결과
Pressure band plot

18. 정사각형단면 모델에 대한 해석 결과

19. 직사각형단면 모델 (40x10) 에 대한 해석 결과

20. 단면/가로세로 비에 따른 유체 압력 맥동 비교

21. Conclusions 연료레일의 가로세로비가 큰 경우 유체압력 맥동감소 효과가 최대 62%까지 증가하였음.
연료레일 내의 유체압력 변화에 따라 연료레일이 변형.
유체해석만 이루어진 경우 유체-구조 상호작용 해석을 한 경우에 비해 상대적으로 맥동이 크게 나타남.