Oil Leakage Through a Valve Stem Seal

The simulation of oil leakage through a valve stem seal involves complex fluid-structure interaction between a moving valve stem (rigid body), oil and deformable seal (flexible body). We can  simulate  the problem in a 3D model of a seal and considered a two-way fluid-structure coupling between the seal (structure) and oil (fluid).

 

the physical problem –seal in operation

Governing equations

1) , where M is the mass matrix of the finite element system, u displacement of the nodes. P is non-hydrodynamic force acts on the structure, I is the internal element force. Pf is hydrodynamic force
equals   , where s is vector-area of external face of the element, P is a fluid pressure, calculated from
Navier-Stokes equations. Navier-Stokes equations in integral form applied to calculation grid of fluid flow domain are:

Numerical method – grid structure

Subgrid geometry resolution method.We can use rectangular FINITE-VOLUME grid with LOCAL ADAPTATION. The subgrid resolution is a Boolean operation between a Cartesian volume grid and curvilinear boundary defining the computational domain. The computational domain boundary is represented by a set of planar facets describing the valve stem and the valve seal. The valve seal is described by a volumetric finite element mesh. The valve seal boundary is formed by the outside faces of the finite elementsand provides a direct link between fluid grid and FE mesh .

 

* I found this CFD problem at an ABACUS‘s users conference .

* for discretization scheme , and more details for the solution you can see deformablemesh-appliication-oilleak

* CFD methods provide calculations of the oil metering rate in channel formed by stemand deformed seal. But Finite Element Analysis  or CFD techniques alone are unable to predict the amount of oil flow due to pressure changes between the top and bottom of the seal. Therefore the Fluid Structure Interaction (FSI) techniques is necessary to provide a comprehensive study the oil flow rate in the seal.

 

what is CFD ?

well a friend asked me what exactly is CFD or more formally Computational Fluid Mechanics and how does this field of engineering  contributes in real life .

what is CFD ?

Computational Fluid Dynamics or CFD as it is popularly known, is used to generate flow simulations with the help of computers. CFD involves the solution of the governing laws of fluid dynamics numerically. The complex set of partial differential equations are solved on in geometrical domain divided into small volumes, commonly known as a mesh (or grid).

what is about ?

• CFD allows numerical simulation of fluid flows, results for which are available for study even after the anaylsis is over. This is a big advantage over, say, wind tunnel testing where analysts have a shorter duration to perform flow measurements.
• CFD allows observation of flow properties without disturbing the flow itself, which is not always possible with conventional measuring instruments.
• CFD allows observation of flow properties at locations which may not be accessible to (or harmful for) measuring instruments. For example, inside a combustion chamber, or between turbine blades.
• CFD can be used as a qualitative tool for discarding (or narrowing down the choices between), various designs. Designers and analysts can study prototypes numerically, and then test by experimentation only those which show promise.

CFD uses numerical methods to solve the fundamental nonlinear differential equations that describe fluid flow (the Navier-Stokes and allied equations) for predefined geometries and boundary conditions. The result is a wealth of predictions for flow velocity, temperature, density, and chemical concentrations for any region where flow occurs through virtual modeling techniques.

In the last decades computers improved CFD capabilities giving huge boost to Aeronautics , wind turbines modelling , aircraft design and more .
Remember one key-word above : mesh . The quality of the mesh plays huge role for solving NS-equations .

 

Large-Scale Numerical Simulations and Applications in CFD

 

Adaptive meshes #1

Mesh generation has been an important procedure in computational fluid dynamics (CFD) modeling. A good mesh should be able to :

• capture as many details as possible in the flow
• not overly resolved in the regions with mostly uniform flow.As a result one can achieve optimal accuracy in the solution with minimal computational cost. In order to generate such a mesh, a lot of prior knowledge about the pvv hysics of the modeled problem as well as the assumptions and limitations of the computational scheme is needed. Sometimes the time and cost invested in mesh generation can take up a large percentage of the total modeling effort. Even so, when we encount er complex structural geometries or flows with a wide range of length scales, it is very hard to produce a mesh that is ‘optimal’.vv

For these reasons, adaptive methods in CFD have receivved much attention over the past thirty years due to their flexibility in resolving complex geometries and other problems such as unsteadyvv flow calculations. The goal of these methods is to evenly distribute error over the whole flow domain in order to minimize global inaccuracvy.

The adaptation is usually based on some error indicav tors calculated from solutions given in the past iterations, so that regions with larger errors are refined (and in some cases, those with l ess errors coarsened). So using either h-,p-,hp-refinement we can achieve the optimal grid .For example  for a cylinder , considering the  error , upwind and downwind , we apply there finement at the area which is required , which is  past the cylinder where vortices exist  .

Below appear : on the left the error distribution  and on the right the refined grid after 3 h-refinements (STRUCTURED GRID)

      

this could be applied for  an UNSTRUCTRED GRID like the following ( note that this is not refined, it’s a “coarse grid”)

or apply a refinement at HYBRID grid

                                                              

FoilSim 3

This software is released by NASA and you can observe how an aircraft wing produces lift and drag by changing the values of different factors that produce aerodynamic forces.You can download the  student version here

Automatic triangulation of planar domain # cavendish algorithm

Let’s assume we want to construct a grid over an arbitrary planar domain filling it with triangles .We can use Cavendish’s semi automatic triangulation algorithm  . This algorithm  which will be described generates meshes with triangular elements for the decomposition of a region giving a special advantage to the user to specify the density of the elements , giving that way a mesh , appropriate to the physical and boundary conditions . The algorithm uses a modified algorithm  from the Suhara-Fukuda algorithm and goes like this :

DEFINING THE AREA (interior , boundary nodes and density of elements)

For instance , let’s assume we want to generate a triangular mesh over a circular domain with circle in it ( hole) .We call the domain R. The user is first required to make an arcwise (multiply) .

The domain R with counter-clockwise ordering of boundary nodes

connected polygonal approximation R to the planar structure to be triangulated.The boundary must be composed of a disjoint union of simple, closed, piecewise linear arcs.

In order to provide the facility for triangulations of varying node density, the user is required to cover the region R with a disjoint set of simply connected polygonal zones   , In particular, for each zone user is required to specify (in counter-clockwise order) the x-y co-ordinates which serve to define the boundary
For each zone  there must be an accompanying density factor  > 0.

Zonal decomposition of R

In order to get triangles with very avute angles , we demand all the nodes to lie in the interior area that is defined by the boundary elements .

NODES GENERATING

Starting from node 1 and moving counter clockwise , the algorithm circumscribes the smallest rectangle in the zone Z which belongs .To make things clearer we superimpose a rectangular grid with unit equal to the density .Our purpose is to to randomly generate one interior node in each sub-square of the grid .

Generation of interior node points

Thus applying this to all the other sub-domains Zi we get the interior nodes . As many as five consecutive attempts are made to generate a retainable random point in any one sub-square. If no point is successfully generated after five consecutive attempts, then no node is designated in that sub-square and the next sub-square is considered. This process is repeated until all sub-squares have been tested .The flow chart of the method is the following :

But we are not done . there must be an algorithm that will precises the interconnections of the nodes by checking the neighborhood of each edge such that the choice of the 3rd node , will give as acute interior angels . But this will be discussed latter …

PARALLEL CFD

From the book : PARALLEL CFD (J.H Kwon , A.Ecer , J.Periaux , N.Satofuka ,P.Fox)

Recent years Grid computing continues to challenge the way scientific computing has been done up until a decade ago .Tera-scale computational capacity such as the TERA-GRID  project ,grid  computing environment by US-NSF ,is now available to researchers for challenging problems . TeraGrid integrated high-performance computers, data resources and tools, and experimental facilities. Resources included more than a petaflop of computing capability and more than 30 petabytes of online and archival data storage, with rapid access and retrieval over high-performance networks computer network connections. Researchers can also access more than 100 discipline-specific databases.
Exept for tera-scale or peta-scale scientists need more advanced tools for CFD high performances such as MPICH-G2 , which is the Grid enabled implementation of the message passing Interface (MPI) . The fact that CFD data blocks are highly inteconnected requires efficient distribution of the blocks such that the communication between the Grid sites will be at the minimum (for a job ) .
The inter-connection between the Grid sites is the challenge for the coders , allocating efficiently the blocks anong Grid sites in order to optimise this communication .
In TeraGrid sites resourse scedulers handle internal distributions of parallel tasks or chunks of dispersed sub-tasks across Grid sites ( giving this static distribution of parallel CFD blocks the above optimization) .
The blocks can be grouped together to ensure optimum distribution of the blocks , hence minimum communication between the Grid sites , applying for example METIS graph partioning libraries for the distribution across the clusters .

Block distribution across Grid sites
A parallel CFD job executes on partitioned data blocks called mesh blocks .As the number of the partioned mesh blocks increases , dependencies of one block to other increases (hence the communication overhead) . The purpose is to achieve the balanced communication between Grid sites so that overall time for the job would be the lowest achievable .
There are several paths to distribute blocks across the Grid sites . One of them is with graph-partitioning (using METIS package ) .Metis offers three different options to decide on the weights , lower the weights more efficient the distribution , to be used as criteria to distribute given blocks across partitions of a given graph .
In partioning the graph , Metis offers to use either of the communication volume betwenn pairs of mesh blocks or mesh block size . It is possible to use combination of block-to-block communication and block size as weights of partioning the graph .

For example the following distribution of the blocks is apllied :

MESH blk#1 <———-weight=100——>MESH blk#2

 | GRID site #1 |

————————————————————————

| GRID site #2 |

MESH blk#4 <————-weight=100———->MESH blk#3

Four mesh blocks distributed between two Grid sites based on communication volume with Metis

graph-partitioning .

The problem has 128 and 512 mesh blocks between two Grid sites .Mesh has about 18M tetraedral elements at an airplane surface (512 mesh blocks) .