A New Formulation for Solids Suitable for a Unified Solution Method for Fluid-Structure Interaction Problems

2004 ◽  
Author(s):  
C. G. Giannopapa ◽  
G. Papadakis
Keyword(s):  
Solution Method ◽  
Fluid Structure Interaction ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Stage Of Development ◽  
Cantilevered Beam ◽  
New Formulation ◽  
Development And Validation ◽  
Velocity Pressure ◽  
Single Set

In fluid-structure interaction problems, the fluid and solid components are solved separately and information is exchanged along the interface. This work shows the first stage of development and validation of a novel unified solution method suitable for computing fluid-structure interaction problems. In the new method, a single set of equations is used to describe both fluid and solid, while the interface between them is contained within the solution domain itself. This can be achieved by reformulating the solid equations to solve for the same primitive variables used in fluids i.e. velocity and pressure. The PISO algorithm is used to handle the velocity-pressure coupling. Although this is a standard approach for fluids, validation is needed for solids. Two cases are examined: wave propagation in a one-dimensional rod and oscillation of a 2D cantilevered beam. Appropriate set of boundary conditions is chosen for the free surface. The new formulation for solids is stable and robust, thus it can be used in the next stage in the development of a robust algorithm for coupled fluid-structure interaction problems.

scholarly journals Linear Stability Analysis and Validation of a Unified Solution Method for Fluid-Structure-Interaction on Structural Dynamic Problems

2005 ◽  
Author(s):  
C. G. Giannopapa ◽  
G. Papadakis
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Solution Method ◽  
Fluid Structure Interaction ◽  
Analytic Solutions ◽  
Computational Domain ◽  
Structural Dynamic ◽  
Fluid Structure ◽  
Structure Interaction

In the conventional approach for fluid-structure interaction problems, the fluid and solid components are treated separately and information is exchanged across their interface. According to the conventional terminology, the current numerical methods can be grouped in two major categories: Partitioned methods and monolithic methods. Both methods use two separate sets of equations for fluid and solid. A unified solution method has been presented [1], which is different from these methods. The new method treats both fluid and solid as a single continuum, thus the whole computational domain is treated as one entity discretised on a single grid. Its behavior is described by a single set of equations, which are solved fully implicitly. In this paper, 2 time marching and one spatial discretisation scheme, widely used for fluids’ equations, are applied for the solution of the equations for solids. Using linear stability analysis, the accuracy and dissipation characteristics of the resulting difference equations are examined. The aforementioned schemes are applied to a transient structural problem (beam bending) and the results compare favorably with available analytic solutions and are consistent with the conclusions of the stability analysis. A parametric investigation using different meshes, time steps and beam sizes is also presented. For all cases examined the numerical solution was stable and robust and proved to be suitable for the next stage of application to full fluid-structure interaction problems.

Linear Stability Analysis and Application of a New Solution Method of the Elastodynamic Equations Suitable for a Unified Fluid-Structure-Interaction Approach

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
C. G. Giannopapa ◽  
G. Papadakis
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Solution Method ◽  
Stokes Equations ◽  
Fluid Structure Interaction ◽  
Analytic Solutions ◽  
Computational Domain ◽  
Fluid Structure ◽  
Structure Interaction

In the conventional approach for fluid-structure-interaction problems, the fluid and solid components are treated separately and information is exchanged across their interface. According to the conventional terminology, the current numerical methods can be grouped in two major categories: partitioned methods and monolithic methods. Both methods use separate sets of equations for fluid and solid that have different unknown variables. A unified solution method has been presented in the previous work of Giannopapa and Papadakis (2004, “A New Formulation for Solids Suitable for a Unified Solution Method for Fluid-Structure Interaction Problems,” ASME PVP 2004, San Diego, CA, July, PVP Vol. 491–1, pp. 111–117), which is different from these methods. The new approach treats both fluid and solid as a single continuum; thus, the whole computational domain is treated as one entity discretized on a single grid. Its behavior is described by a single set of equations, which are solved fully implicitly. In this paper, the elastodynamic equations are reformulated so that they contain the same unknowns as the Navier–Stokes equations, namely, velocities and pressure. Two time marching and one spatial discretization scheme, widely used for fluid equations, are applied for the solution of the reformulated equations for solids. Using linear stability analysis, the accuracy and dissipation characteristics of the resulting difference equations are examined. The aforementioned schemes are applied to a transient structural problem (beam bending) and the results compare favorably with available analytic solutions and are consistent with the conclusions of the stability analysis. A parametric investigation using different meshes, time steps, and beam dimensions is also presented. For all cases examined, the numerical solution was stable and robust and therefore is suitable for the next stage of application to full fluid-structure-interaction problems.

Towards a Unified Solution Method for Fluid-Structure Interaction Problems: Progress and Challenges

2006 ◽  
Author(s):  
G. Papadakis ◽  
C. G. Giannopapa
Keyword(s):  
Stress Tensor ◽  
Solution Method ◽  
Constitutive Relations ◽  
Fluid Structure Interaction ◽  
Strain Tensor ◽  
Internal Stresses ◽  
Fluid Structure ◽  
Structure Interaction ◽  
The Difference ◽  
Fundamental Equations

The paper presents the progress in the development of a novel unified method for solving coupled fluid-structure interaction problems as well as the associated major challenges. The new approach is based on the fact that there are four fundamental equations in continuum mechanics: the continuity equation and the three momentum equations that describe Newton’s second law in three directions. These equations are valid for fluids and solids, the difference being in the constitutive relations that provide the internal stresses in the momentum equations: in solids the stress tensor is a function of the strain tensor while in fluids the viscous stress tensor depends on the rate of strain tensor. The equations are written in such a way that both media have the same unknown variables, namely the three velocity components and pressure. The same discretisation technique (finite volume) and solution method (segregated approach) are used irrespective of the medium. Also the same methodology to handle the pressure-velocity coupling is employed. A common set of variables as well as a unified discretisation and solution method leads to a strong coupling between the two media and is very beneficial for the robustness of the algorithm. Significant challenges include the derivation of consistent boundary conditions for the pressure equation in boundaries with prescribed traction as well as the handling of discontinuity of pressure at the fluid-structure interface.

scholarly journals One-Way Fluid Structure Interaction of a Go-Kart Spoiler Using CFD Analysis

Proceedings ◽  
2020 ◽  
Vol 49 (1) ◽  
pp. 51
Author(s):  
Mohammad AL-Rawi ◽  
Abderrahmane Oumssount
Keyword(s):  
Fuel Economy ◽  
Fluid Structure Interaction ◽  
Cfd Analysis ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Recreational Vehicles ◽  
Rear Spoiler ◽  
Applied Forces ◽  
Air Flow Velocity ◽  
Velocity Pressure

The spoiler on a go-kart is required to prevent the vehicle becoming airborne at speeds of 80 km/h or more. An optimal spoiler design balances this safety aspect with speed and fuel economy. This paper reports the results of a project to improve the aerodynamic aspects of a go-kart spoiler design using CFD Analysis. We investigated the design of a rear spoiler with three proposed angles (θ1 = 9.5°, θ2 = 19.5°, θ3 = 29.5°). The drag force produced by each of the three designs is compared. Different computational results are discussed such as the air flow velocity, pressure and the applied forces in terms of CFD analysis using one-way fluid structure interaction (one-way FSI) to determine the spoiler stress, strain and drag coefficient. The findings of this paper have implications for the leisure and tourism industries, and may be applicable to other recreational vehicles’ spoilers.

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