I and welcome to this webinar my name is Erik's Fanny and I'm working for dynamo Nordic today I will show you how splashing and sloshing can be modeled in Alice Tina you see in the smooth particle hydrodynamics method the purpose of this webinar is to demonstrate the capabilities for modeling splashing and sloshing using the smooth particle hydrodynamics module in Alice Tina first I will give you an introduction and motivation followed by the most important aspects of the SPH theory we will look at the most important keywords and how to set up the simulation I will also show a couple of examples and then we will summarize okay so now we go on with the introduction and the theory of SPH and the first question that you might ask yourself is when SPH is useful and typically SPH is a good choice when you have large material distortion or when the material decomposes into many small fragments or droplets or as we are interested in in this webinar when you have fluid problems with moving boundaries and free surfaces and the main characteristics of SPH is that it is particle based and it is typically solved with explicit time integration and as with all numerical methods there are some limitations and issues that you need to be aware of and for SPH local mesh refinement can be problematic and it is also important to be aware of that some types of boundary conditions can be difficult to handle the history of mesh free methods started with some pioneering works in the late 1970s during the 1980s then there has been quite much theoretical developments aiming at improving accuracy and stability of the method and today SPH can be applied to a number of different areas such as forging extrusion and metal cutting impact problems like bird strike and the high velocity impact and also as we are interested in in this webinar we will structure interaction problems and splashing and sloshing the SPH method is a particle based method which means that the continuum is approximated by a set of arbitrarily distributed particles and the material coordinates are independent variables which means that there is no convective term involved in the formulation and this allows large material distortion and also modeling of free surface flows for the particle approximation of a function we write an approximation with a kernel function W as you can see here where H is the smoothing length and we note that if we would set the kernel function W equal to the Dirac Delta then this approximation would be exact but you would learn also theoretically need an infinite amount of particles and the kernel function is typically constructed in such a way that W approaches the Dirac Delta distribution as the smoothing length age goes to zero and very often cubic piecewise functions are used so now we can like a quadrature formula to our particle approximation as you can see here where W J is the weight of particle J and if the kernel function W has compact support we will get a sparse scheme which is of course desirable from a numerical point of view and we also get a similar expression for the gradient of our approximation as you can see here and since this is a particle based method an important aspect is the neighbor search since we need to know the neighbors of each particle in order to compute the contribution and this is done in Alice Tina by a bucket sort similar to the contact search algorithm I will say a little bit more about that when we go through the keywords and when you have these ingredients you can solve for a conservation of mass momentum and energy ok so now we will look at a few key words that are important for SPH simulations and the first two key words that you see here are related to efficiency for MVP then we will look at control s pH section s pH and element s pH where you do your settings for s pH theory and such things then we will look at module and equation of state where you define new or material behavior and I will also say something about contact for s pH particles so the first keyword that we will talk about is control MPP decomposition distributed SPH elements and it ensures that SPH elements are evenly distributed to all processors at the start of the simulation so this it requires no input parameters and I recommend that you always use it in your SPH simulations you can also activate control and PPI oh no Dom which will suppress the output of dump files and full deck restored files the next keyword we will look at is control SPH which contains a couple of important settings for SPH simulations and the first option i would like to mention is NCBS which is the number of time steps between particles working these defaults to one but sometimes it it may be increased to save some computational time if you can increase it or not that will depend on your particular simulation setup another good option is the box ID were particles that leave this box are deactivated in order to save computational time and I recommend that you always specify a box here too in order to deactivate particles that leave your computational domain you may also set I deem which defines the space dimension for SBH particles default is 3d but you may also set to the plane strain or to the axisymmetric problems here form controls the particle approximation theory form equals 15 or 16 is recommended for fluid applications these are both enhanced fluid formulations with the pressure smoothing and form equals 16 gives a formulation will the renormalization which is usually more expensive and more accurate there are several other particle approximation theories available for example form equals zero is default and form equals one is recommended for most solid structural applications Marx V allows particles with the velocity greater than max V to be activated and the contact thickness may be controlled by I thk were ith K equals to 0 implies that the contact thickness is set to zero this is the default you may also set ith k equal to one and then the contact thickness will be computed from the particle volume for the section SP h keyword you can often use the default settings that works in most applications the CS l age option gives a constant for calculation of initial smoothing lengths you typically don't need to change that it's good to be aware of and here you also have the possibility to set each mean and H max which gives scale factors for the minimum and maximum smoothing lengths in the element s pH keyword you miss at the mass were mass greater than 0 gives the mass of the element whereas if you set a negative value then the absolute value will be used as volume of the particle and the density will then be taken from the material called defined in the pit the fluid material properties are specified with mott noodle in combination with a suitable equation of state and in Martin old rule gives the mass density of the fluid PC defines a pressure cutoff which allows a material to numerically cavitate note here that pressure cutoff is negative in tension and mu gives the dynamic viscosity of the material the arid and sierad define a relative volume for erosion in tension and compression respectively the equation of state describes the relation between density and pressure and for splashing and sloshing applications us Murnaghan is often a good choice the u.s. Murnaghan has a pressure density relation given by the equation you can see here and it is specifically designed to model incompressible fluid flow with SPH elements here gamma is often set to 7 and the KC arrow is frequently chosen based on the expected maximum fluid flow velocity V 0 is the initial relative volume which can be left blank and we also note that it is possible to reduce the stiffness of the page particles which will then allow larger time steps at the cost of increased increased compressibility and if you don't want to use us Mulligan than for example us green icing can be an alternative choice for the interaction between SPH particles and the structure you can use contact automatic nodes to surface and here you will set the stage particles as the slaved parts or SSID and the structure will then be the master IDMS ID and as always with the contacts there are plenty of parameters that you can play around with but I will not go into the details of all of them today to generate SPH elements it is possible to use a less pre post and to do that you click on mesh and SPH generation and here you have the possibility to generate SPH parts of different shapes it can be simple shapes like your box or sphere for example it also possible to generate SPH elements within the volume enclosed by a shell volume this is very useful as I will show on the next slide there are some other options as well you can set the density to minus 1 to make its pre post compute the volume of each SPH particle and then you can set the density of your SPH particles on the material cord later you can specify the distance between particles only in each direction and remember to click set parameter them apply the settings here I have used a less pre post to generate SPH particles for a simplified gearbox and you can see the geometry to the left and the generated SPH particles to the right and here I have used the shell volume method in a less pre post and for this to work the surface shell message needs to be watertight but the surface may consist of several different parts as in this example now I will show you some examples and the first example I would like to show you is a wheel rolling through a 10 millimeter thick water layer at 70 km/h and here I used an explicit finite element model for that with rigid rim and rigid ground and for the water I used two point four million as page particles and you can see the splashing of the water in the movie here to show you a bit more realistic splashing example I used the Toyota Auris model from Nitza which is of course explicit finite element model roughly around one and off median elements and I let it run at 56 km/h through 20 millimeter thick water layer and you can see the results here to the right and the pictures at the bottom of the page and typically you could then look at the distribution of water here see how the water impacts different underbody panels you can also extract the water load on on different parts of the car and the simulation time for this example was around 16 hours on 32 cores here I have set up an example of simplified gearbox so we have two years in a box partially filled with oil and here I have modelled the years as rigid and the oil is modeled by 300,000 SPH particles and we apply a prescribed motion of the upper year the upper year then drives the lower year through contact conditions and it it is also possible to model the years as deformable and at the cost of longer simulation time so you have a choice here if you if you want to want them as rigid it works fine you can also do simulations with deformable years and you can see in in the movie you have possibility to study how how the oil is distributed and how it is splashing due to the motion of the gears the last example I would like to show you is a fluid structure interaction case were waterway the impacts are rigid column in a container and the contact forces on the column are compared to experimental data this model was developed by Ellis TC and it is available at Dinah campus calm and as you can see in the figure to the right the force on the column agrees very well between the simulation results and the experimental data in this webinar we have discussed how SPH can be used to model splashing and sloshing and we have seen that SPH can easily be coupled with finite elements models if you would like to learn more than there is and SPH course offered by dynamo in germany which you can have a look at and if you have any questions or comments you are always welcome to contact me at eric spending at dynamo dot SE and by that i would like to thank you for your attention and see you next time goodbye