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**Chapter 9 Advanced Physics**

Introductory FLUENT Training Sharif University of Technology Lecturer: Ehsan Saadati

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**Outline Multiphase Flow Modeling Reacting Flow Modeling**

Discrete phase model Eulerian model Mixture model Volume-of-fluid model Reacting Flow Modeling Eddy dissipation model Non-premixed, premixed and partially premixed combustion models Detailed chemistry models Pollutant formation Surface reactions Moving and Deforming Meshes Single and multiple reference frames Mixing planes Sliding meshes Dynamic meshes Six-degree-of-freedom solver

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**Multiphase Flow Modeling**

Introductory FLUENT Training

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Introduction A phase is a class of matter with a definable boundary and a particular dynamic response to the surrounding flow/potential field. Phases are generally identified by solid, liquid or gas, but can also refer to other forms: Materials with different chemical properties but in the same state or phase (i.e. liquid-liquid) The fluid system is defined by a primary and multiple secondary phases. One of the phases is considered continuous (primary) The others (secondary) are considered to be dispersed within the continuous phase. There may be several secondary phase denoting particles of with different sizes. Primary Phase Secondary phase(s)

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**Multiphase Flow Regimes**

Bubbly flow – Discrete gaseous bubbles in a continuous fluid, e.g. absorbers, evaporators, sparging devices. Droplet flow – Discrete fluid droplets in a continuous gas, e.g. atomizers, combustors Slug flow – Large bubbles in a continuous liquid Stratified / free-surface flow – Immiscible fluids separated by a clearly defined interface, e.g. free-surface flow Particle-laden flow – Discrete solid particles in a continuous fluid, e.g. cyclone separators, air classifiers, dust collectors, dust-laden environmental flows Fluidized beds – Fluidized bed reactors Slurry flow – Particle flow in liquids, solids suspension, sedimentation, and hydro-transport Slug Flow Bubbly, Droplet, or Particle-Laden Flow Gas/Liquid Liquid/Liquid Stratified / Free- Surface Flow Pneumatic Transport, Hydrotransport, or Slurry Flow Gas / Solid Sedimentation Fluidized Bed Liquid / Solid

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**Multiphase Models Available in FLUENT**

FLUENT contains four distinct multiphase modeling approaches: Discrete Phase Model (DPM) Volume of Fluid Model (VOF) Eulerian Model Mixture Model It is important to select the most appropriate solution method when attempting to model a multiphase flow. Depends on whether the flow is stratified or disperse – length scale of the interface between the phases dictates this. Also the Stokes number (the ratio of the particle relaxation time to the characteristic time scale of the flow) should be considered. where and

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**DPM Example – Spray Drier**

Spray drying involves the transformation of a liquid spray into dry powder in a heated chamber. The flow, heat, and mass transfer are simulated using the DPM model in FLUENT. Initial particle Diameter: 2 mm 1.1 mm 0.2 mm Contours of Evaporated Water Stochastic Particle Trajectories for Different Initial Diameters

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**Eulerian Model Example – 3D Bubble Column**

Isosurface of Gas Volume Fraction = 0.175 z = 5 cm z = 10 cm z = 15 cm z = 20 cm Liquid Velocity Vectors

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**The Granular Option in the Eulerian Model**

Granular flows occur when high concentration of solid particles is present. This leads to high frequency of interparticle collisions. Particles are assumed to behave similar to a dense cloud of colliding molecules. Molecular cloud theory is applied to the particle phase. Application of this theory leads to appearance of additional stresses in momentum equations for continuous and particle phases These stresses (granular “viscosity”, “pressure” etc.) are determined by intensity of particle velocity fluctuations Kinetic energy associated with particle velocity fluctuations is represented by a “pseudo-thermal” or granular temperature Inelasticity of the granular phase is taken into account Gravity Gas / Sand Gas Contours of Solids Volume Fraction for High Velocity Gas/Sand Production

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**Mixture Model Example – Gas Sparging**

The sparging of nitrogen gas into a stirred tank is simulated by the mixture multiphase model. The rotating impeller is simulated using the multiple reference frame (MRF) approach. FLUENT simulation provided a good prediction on the gas-holdup of the agitation system. Animation of Gas Volume Fraction Contours Water Velocity Vectors on a Central Plane at t = 15 sec.

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**VOF Example – Automobile Fuel Tank Sloshing**

Sloshing (free surface movement) of liquid in an automotive fuel tank under various accelerating conditions is simulated by the VOF model in FLUENT. Simulation shows the tank with internal baffles (at bottom) will keep the fuel intake orifice fully submerged at all times, while the intake orifice is out of the fuel at certain times for the tank without internal baffles (top). Fuel Tank Without Baffles t = 1.05 sec t = 2.05 sec Fuel Tank With Baffles

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**Reacting Flow Modeling**

Introductory FLUENT Training

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**Applications of Reacting Flow Systems**

FLUENT contains models which are applicable to a wide range of homogeneous and heterogeneous reacting flows Furnaces Boilers Process heaters Gas turbines Rocket engines IC engine CVD, catalytic reactions Predictions of Flow field and mixing characteristics Temperature field Species concentrations Particulates and pollutants Temperature in a Gas Furnace CO2 Mass Fraction Let’s go ahead and get started with an introductory discussion of combustion models and the different kinds of tools that are within Fluent to handle combustion applications. There’s a wide range of problems that can be handled by the Fluent software for homogeneous as well as heterogeneous reacting flows that you might find, for example, in furnaces, boilers, process heaters, gas turbines and rocket engines. So, typically, people who are using our code for these kinds of applications are interested in a number of different results. They’re interested in looking at the flow field and the mixing characteristics for fuel and oxidizer within their application. They’re also interested in the temperature field to answer question like: Is the temperature uniform? Are there hot spots? What’s the maximum temperature within the device? They’re looking at species concentrations, and in particular, oftentimes people are interested in looking at pollutant emission, like NOX, and at particulate dispersion. So there’s a wide range of interests by people that are using our software for combustion modeling and we have a variety of physical models and tools available to handle these problems. Stream Function

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**Background Modeling Chemical Kinetics in Combustion Flow configuration**

Fast Chemistry Global chemical reaction mechanisms (Finite Rate / Eddy Dissipation) Equilibrium/flamelet model (Mixture fraction) Finite rate chemistry Flow configuration Non-premixed reaction systems Can be simplified to a mixing problem Premixed reaction systems Cold reactants propagate into hot products. Partially premixed systems Reacting system with both non-premixed and premixed inlet streams. Fuel Oxidizer Reactor Outlet Fuel + Oxidizer Reactor Outlet So we’re looking for practical approaches to deal with these reaction rates in turbulent flows. So, you can use reduced chemical mechanisms and that’s what is done in the finite rate combustion model. We can also decouple the chemistry from the turbulent flow and mixing problem and we do that with the PDF model and the laminar flamelet model. We can also utilize what’s called a progress variable to perform this decoupling, and that’s what’s the Zimont model is about. We’ll take a look at each of these models in more detail later on. Fuel + Oxidizer Reactor Secondary Fuel or Oxidizer Outlet

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**Overview of Reacting Flow Models in FLUENT**

FLOW CONFIGURATION Premixed Non-Premixed Partially Premixed Fast Chemistry Eddy Dissipation Model (Species Transport) Premixed Combustion Model Non-Premixed Equilibrium Model Partially Premixed Model Reaction Progress Variable* Mixture Fraction Reaction Progress Variable + Finite-Rate Chemistry Laminar Flamelet Model Laminar Finite-Rate Model Eddy-Dissipation Concept (EDC) Model Composition PDF Transport Model CHEMISTRY *Rate classification not truly applicable since species mass fraction is not determined.

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**Pollutant Formation Models**

NOx formation models (predict qualitative trends of NOx formation). FLUENT contains three mechanisms for calculating NOx production. Thermal NOx Prompt NOx Fuel NOx NOx reburning model Selective Non-Catalytic Reduction (SNCR) model Ammonia and urea injection Soot formation models Moos-Brookes model One step and two steps model Soot affects the radiation absorption (Enable the Soot-Radiation option in the Soot panel) SOx formation models Additional equations for SO2, H2S, and, optionally, SO3 are solved. In general, SOx prediction is performed as a post-process.

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**Discrete Phase Model (DPM)**

Description Trajectories of particles/droplets/bubbles are computed in a Lagrangian frame. Particles can exchange heat, mass, and momentum with the continuous gas phase. Each trajectory represents a group of particles, each with the same initial properties. Interaction among individual particles is neglected. Discrete phase volume fraction must be less than 10%. Mass loading is not limited. Numerous submodels are available. Heating/cooling of the discrete phase Vaporization and boiling of liquid droplets Volatile evolution and char combustion for combusting particles Droplet breakup and coalescence using spray models Erosion/Accretion Numerous applications Particle separation and classification, spray drying, aerosol dispersion, bubble sparging of liquids, liquid fuel and coal combustion.

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Surface Reactions Chemical species deposited onto surfaces are treated as distinct from the same chemical species in the gas. Site balance equation is solved for every surface-adsorbed (or “site”) species. Detailed surface reaction mechanisms can be considered (any number of reaction steps and any number of gas-phases or/and site species). Surface chemistry mechanism in Surface CHEMKIN format can be imported into FLUENT. Surface reaction can occur at a wall or in porous media. Different surface reaction mechanisms can be specified on different surfaces. Application examples Catalytic reactions CVD

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**Summary There are four introductory level tutorials on reacting flow.**

Species transport and gas combustion Non-premixed combustion Surface chemistry Evaporating liquid spray A number of intermediate and advanced tutorials are also available. Other learning resources Advanced training course in reacting flow offered by FLUENT User Service Center, All tutorials and lecture notes Web-based training courses

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**Moving / Deforming Mesh**

Introductory FLUENT Training

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Introduction Many flow problems involve domains which contain translating or rotating components. Two types of motion are possible – translational and rotational. There are two basic modeling approaches for moving domains: Moving Reference Frames Frame of reference is attached to the moving domain. Governing equations are modified to account for moving frame. Moving / Deforming Domains Domain position and shape are tracked with respect to a stationary reference frame. Solutions are inherently transient. Computational fluid dynamics (or CFD) has been used to examine problems involving moving domains ever since the advent of computer simulation in the 1960s. The motions can either be: Translational – such as the cyclic oscillation of liquid in a tank or a train moving through a tunnel. Or Rotational – which is perhaps the most common. Examples include flows though turbomachines (pumps, turbines, compressors, and related equipment), electric motors, spinning objects such as car tires, and so forth. There are two basic approaches to modeling flows in moving domains. The first approach involves referring the problem to a moving reference frame. For example, we can define a reference frame which is spinning in concert with a rotating tank. The flow is described with respect to the spinning reference frame. However, the fact that the reference frame itself is moving gives rise to “non-inertial” effects – that is, the equations of motion now have additional acceleration terms added to them to account for the moving frame (more about that later). The benefit of using a moving reference frame is often a problem which is inherently unsteady in the stationary frame becomes steady-state in the moving frame of reference. Moreover, we can couple adjacent zone to the moving zone though grid interfaces to create a simplified model of a complex moving zone system (for example a pump impeller coupled with a scroll casing). The second approach solves the equations using a mesh which is moving with respect to a fixed frame, and we refer all flow variables to the fixed frame. In this case, the solution is inherently unsteady. The main advantage of this approach is that we can allow the mesh (and hence the domain) to deform with time, thus permitting a wide range of problems involving moving and deforming boundaries.

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**CFD Modeling Approaches For Moving Zones**

Sliding Mesh Model (SMM) Single Reference Frame (SRF) Multiple Reference Frames (MRF) Mixing Plane Model (MPM) Moving / Deforming Mesh (MDM) Moving Reference Frames Moving Domain

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**Single Reference Frame (SRF) Modeling**

SRF attaches a reference frame to a single moving domain. All fluid motion is defined with respect to the moving frame. Rotating frames introduce additional accelerations to the equations of fluid mechanics, which are added by Fluent when you activate a moving reference frame. Why use a moving reference frame? Flow field which is transient when viewed in a stationary frame can become steady when viewed in a moving frame. Advantages Steady state solution* Simpler BCs Faster turn-around time Easier to post-process and analyze Centrifugal Compressor (single blade passage) The single reference frame model is the simplest approach for moving zone modeling. In this approach, a single, non-deforming fluid domain is referred to a moving frame of reference. As mentioned previously, the equations of motion are modified to account for the non-inertial motion of the moving frame. In addition, boundary conditions are defined relative to the moving zone. Why use a rotating frame to begin with? The reason is that, for many common classes of moving zone problems, a flowfield which is unsteady when viewed from the stationary frame becomes steady in the moving frame. Steady-state problems are desirable as they are (1) easier and less expensive to solve, (2) possess simpler BCs, and (3) are more straightforward to post-process and analyze. Please note that you may still model natural unsteadiness in the moving frame – for example, vortex shedding from the trailing edge of a rotating fan blade. Now, when you model a rotating zone with the SRF approach, it is important to note that the walls must conform to the following requirements: Walls which move with the reference frame can be any shape (3-D) Walls which are to modeled as stationary (with respect to the fixed frame) must be surfaces of revolution! If your domain does not meet this requirement, you must break your model up into multiple zones and use an approach which supports multiple zones. Finally, it is very common to employ rotationally periodic boundaries in SRF models as it reduces the mesh size from an entire rotating geometry to a single periodic passage. Of course, both your geometry and your flowfield must be rotationally periodic, which can be an issue if, for example, your inflow BC is not periodic. * NOTE: You may still have unsteadiness in the rotating frame due to turbulence, circumferentially non-uniform variations in flow, separation, etc. example: vortex shedding from fan blade trailing edge

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**Multiple Reference Frame (MRF) Modeling**

Many moving zone problems involve stationary components which cannot be described by surfaces of revolution (SRF not valid). Systems like these can be solved by dividing the domain into multiple fluid zones – some zones will be rotating, others stationary. The multiple zones communicate across one or more interfaces. The way in which the interface is treated leads to one of following approaches for multiple zone models: Multiple Reference Frame Model (MRF) Mixing Plane Model (MPM) Sliding mesh model (SMM) interface Multiple Component (blower wheel + casing) There are many moving zone problems which cannot be solved using the SRF approach alone – specifically, applications with stationary components with walls that are not surfaces of revolution. For example, a centrifugal pump impeller typically is situated next to a scroll-shaped casing or volute. Since the casing is not a surface or revolution about the axis of rotation, you cannot include that region in the moving reference frame zone. To address these kinds of problems, you must break up the domain into multiple fluid zones, some which are moving and others which are stationary. The zones communicate across one or more interfaces, thereby permitting a specific degree of interaction between the zones. The way in which the interface is treated leads to one of the following multiple zone approaches: The multiple reference frame model The mixing plane model The sliding mesh model Steady State (Approximate) transient (Best Accuracy)

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**The Mixing Plane Model (MPM)**

The MPM is a technique which permits steady-state solutions for multistage axial and centrifugal turbomachines. Can also be applied to a more general class of problems. Domain is comprised of multiple, single-passage, rotating and stationary fluid zones. Each zone is “self contained” with a inlet, outlet, wall, periodic BCs (i.e. each zone is an SRF model). Steady-state SRF solutions are obtained in each domain, with the domains linked by passing boundary conditions from one zone to another. The BC “links” between the domains are called mixing planes. BCs are passed as circumferentially averaged profiles of flow variables, which are updated at each iteration. Profiles can be radial or axial. As the solution converges, the mixing plane boundary conditions will adjust to the prevailing flow conditions. The mixing plane model is a method which was developed within the turbomachinery community as a way of dealing with multiple blade row compressor and turbine analyses. It has since become more widely applied to pumps, fans, and similar systems. The basic idea is to consider a system of single passage, SRF models which are aligned such that the outlet of an upstream zone feeds the inlet of a downstream zone. We can obtain a steady-state solution to this system in the following manner. First, we establish links between adjacent boundary conditions so that flow data from one domain is passed as a boundary condition to the adjacent zone. We then obtain a provisional solution in each SRF zone in the usual way. At the end of the solution step, we average the flow properties at the interface flow boundaries in the circumferential direction, thereby obtaining a simple radial or axial profile. Profiles are create for each variable required by the adjacent zone’s boundary condition. These profiles are then applied to the adjacent zones (much like one would apply a profile file to a standard Fluent model). By continuously updating the boundary conditions in this fashion, a coupled, steady-state flow solution will be obtained at convergence. Mixing plane (Pressure outlet linked with a mass flow inlet) ADVANTAGE of MPM: Requires only a single blade passage per blade row regardless of the number of blades.

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**The Sliding Mesh Model (SMM)**

The relative motion of stationary and rotating components in a turbo-machine will give rise to transient interactions. These interactions are generally classified as follows: Potential interactions (pressure wave interactions) Wake interactions Shock interactions Both MRF and MPM neglect transient interaction entirely and thus are limited to flows where these effects are weak. If transient interaction can not be neglected, we can employ the Sliding Mesh model (SMM) to account for the relative motion between the stationary and rotating components. wake interaction Shock interaction potential interaction Stator Rotor In the MRF and mixing plane approaches, we assume that interactions between components are weak and therefore could be neglected in the analysis. This, of course, is clearly an approximation. The motion of a moving blade, for instance, past a stationary vane will give rise to unsteady interactions as shown in this slide. These interactions can be classified as follows: First we have potential interactions (or pressure waves). These are a result of hydrodynamic interactions, and are a two-way effect – that is, the waves are felt both upstream and downstream. Next we wake interactions, which are a result of wakes from upstream objects impacting downstream components. Unlike potential interactions, this is a one-way effect. If the flow is compressible and Mach numbers are high enough, we may also have shock wave interactions. Like wake effects, this is a one-way interaction. If the components are sufficiently remove from one another, these interaction effects are small and can often be ignored, thus permitting the use of MRF or mixing plane techniques. However, interaction between closely spaced components is usually very large and cannot be ignored. In addition, there can be complex flows occurring in the vicinity of the interfaces between moving and non-moving zones such that the MRF or mixing plane models will be sensitive to the interface location. When interaction effects cannot be ignored, we can employ the sliding mesh model to simulate the unsteady interaction effects.

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**How the Sliding Mesh Model Works**

Like the MRF model, the domain is divided into moving and stationary zones, separated by non-conformal interfaces. Unlike the MRF model, each moving zone’s mesh will be updated as a function of time, thus making the mathematical problem inherently transient. Another difference with MRF is that the governing equations have a new moving mesh form, and are solved in the stationary reference frame for absolute quantities (see Appendix for more details). Moving reference frame formulation is NOT used here (i.e. no additional accelerations acting as sources terms in the momentum equations). Equations are a special case of the general moving/deforming mesh formulation. Assumes rigid mesh motion and sliding, non-conformal interfaces. cells at time t cells at time t + Δt moving mesh zone The sliding mesh model can be thought of as an extension of the MRF approach, in that we define stationary and moving zones separated by non-conformal interfaces. As the calculation proceeds, the moving zone meshes are updated as a function of time, thereby making the problem inherently unsteady. It should be noted that the meshes are moved in a rigid (non-deforming) manner and communication with adjacent zones will be maintained provided the grid interfaces maintain an overlap with one another (hence the name sliding mesh). Another difference that the sliding mesh model has with MRF is the equations that are used. In the sliding mesh model, a moving mesh formulation is used which refers all flow variables to the stationary or inertial frame, and solves for absolute quantities. More details about this formulation are provided in the Appendix. The primary implication is that, unlike SRF, MRF, and MPM, the momentum equations do not contain Coriolis and centripetal acceleration terms – however, the geometry (mesh) is now a function of time, which wasn’t the case with the Moving Reference Frame approach. It should also be noted that the equations employed for sliding mesh models are a special case of the general moving/deforming mesh formulation which assumes rigid mesh motion and sliding, non-conformal interfaces.

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**Dynamic Mesh (DM) Methods**

Internal node positions are automatically calculated based on user specified boundary/object motion, cell type, and meshing schemes Basic Schemes Spring analogy (smoothing) Local remeshing Layering Other Methods 2.5 D User defined mesh motion In-cylinder motion (RPM, stroke length, crank angle, …) Prescribed motion via profiles or UDF Coupled motion based on hydrodynamic forces from the flow solution, via FLUENT’s six-degree-of-freedom (6DOF) solver. The dynamic mesh model in Fluent is comprised of a “toolbox” of methods for controlling the mesh motion. There are three general-purpose methods for dealing with mesh deformations, and these are: Spring analogy Local Remeshing Layering For specific classes of mesh motion and geometries, there are the several specialized approaches, specifically: The 2.5D method The user-defined mesh motion approach The in-cylinder motion package (design with automotive in-cylinder applications in mind) The 6 degree-of-freedom package It should be noted that these schemes are very flexible, and one can utilize more than one approach in a single model, including the use of stationary and sliding non-conformal interfaces. We will show an example of this ability in a later slide.

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Dynamic Mesh Methods Layering Layers of cells are generated and collapsed as they are overrun by the moving boundary. Layering is appropriate for quad/hex/prism meshes with linear or rotational motion and can tolerate small or large boundary deflections. Local Remeshing In local remeshing, as cells become skewed due to moving boundaries, cells are collapsed and the skewed region is remeshed. Local remeshing is appropriate for tri/tet meshes with large range of boundary motion. Spring Analogy Spring analogy is useful when there are small boundary deformations. The connectivity and cell count is unchanged during motion. Spring analogy is appropriate for tri/tet meshes with small deformations.

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**The Dynamic Mesh (DMM) Model**

A method by which the solver (FLUENT) can be instructed to move boundaries and/or objects, and to adjust the mesh accordingly. Examples: Automotive piston moving inside a cylinder Positive displacement pumps A flap moving on an airplane wing A valve opening and closing An artery expanding and contracting The dynamic mesh model is the name given to a general modeling framework which permits flow solutions in arbitrarily moving and deforming domains. The user defines the boundary motions of the domain, and Fluent will determine the positions of the mesh nodes as a function time. If required the mesh can even be regenerated to accommodate large deformations of the domain. The equations which are solved account for the time varying mesh motions, and are a generalization of the equations used for the sliding mesh model. This powerful technique has been applied to a wide range of problems, including: Automotive piston moving inside a cylinder A flap moving on an airplane wing A valve opening and closing An artery expanding and contracting We will give a brief over overview of the methods and capability of the dynamics mesh approach in this section.

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Summary Five different approaches may be used to model flows over moving parts. Single (Rotating) Reference Frame Model Multiple Reference Frame Model Mixing Plane Model Sliding Mesh Model Dynamic Mesh Model First three methods are primarily steady-state approaches while sliding mesh and dynamic mesh are inherently transient. Enabling these models, involves in part, changing the stationary fluid zones to either Moving Reference Frame or Moving Mesh. Most physical models are compatible with moving reference frames or moving meshes (e.g. multiphase, combustion, heat transfer, etc.) In this presentation, we have covered the five different approaches for modeling moving zones. These are: The single reference frame model The multiple reference frame model The mixing plane model The sliding mesh model The dynamic mesh model Note that the first three approaches are primarily steady-state approaches while the sliding and dynamic mesh approaches are inherently unsteady. Enabling these models primarily involves enabling either Moving Reference Frame or Moving mesh in the BC specification for the Fluid zones. Also note that any model which invokes Moving Mesh must employ the unsteady solver. Most physical models are compatible with moving reference frames or moving meshes. This includes multiphase, combustion, heat transfer and other models. Finally, to obtain robust solutions for most problems, it is suggested that you follow the best practice guidelines outlined in the previous slides.

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**Multiphase Flow Modeling**

Appendix Multiphase Flow Modeling

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**Volume and Particulate Loading**

Volume loading – dilute vs. dense Refers to the volume fraction of secondary phase(s) For dilute loading (less than around 10%), the average inter-particle distance is around twice the particle diameter. Thus, interactions among particles can be neglected. Particulate loading – ratio of dispersed and continuous phase inertia. Light Particulate loading < 10 % 10% < Moderate loading < 50% High particulate loading > 50%

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**Turbulence Modeling in Multiphase Flows**

Turbulence modeling with multiphase flows is challenging. Presently, single-phase turbulence models (such as k–ε or RSM) are used to model turbulence in the primary phase only. Turbulence equations may contain additional terms to account for turbulence modification by secondary phase(s). If phases are separated and the density ratio is of order 1 or if the particle volume fraction is low (< 10%), then a single-phase model can be used to represent the mixture. In other cases, either single phase models are still used or “particle-presence-modified” models are used.

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**Phases as Mixtures of Species**

In all multiphase models within FLUENT, any phase can be composed of either a single material or a mixture of species. Material definition of phase mixtures is the same as in single phase flows. It is possible to model heterogeneous reactions (reactions where the reactants and products belong to different phases). This means that heterogeneous reactions will lead to interfacial mass transfer.

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**Discrete Phase Model (DPM) Overview**

Trajectories of particles, droplets or bubbles are computed in a Lagrangian frame. Particles can exchange heat, mass, and momentum with the continuous gas phase. Each trajectory represents a group of particles, all with the same initial conditions. DPM neglects collisions and other inter-particle interactions. Turbulent dispersion of particles can be modeled using either stochastic tracking (the most common method) or a particle cloud model. Many submodels are available – Heat transfer, vaporization/boiling, combustion, breakup/coalescence, erosion/accretion. Applicability of DPM Flow regime: Bubbly flow, droplet flow, particle-laden flow Volume loading: Must be dilute (volume fraction < 12%) Particulate Loading: Low to moderate Stokes Number: All ranges of Stokes number Application examples Cyclones Spray dryers Particle separation and classification Aerosol dispersion Liquid fuel Coal combustion

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**Discrete Phase Model (DPM) Setup**

Define Models Discrete Phase… Define Injections… Display Particle Tracks…

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**DPM Boundary Conditions**

Escape Trap Reflect Wall-jet

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**The Eulerian Multiphase Model**

The Eulerian multiphase model is a multi-fluid model. This means that all phases are assumed to exist simultaneously. Conservation equations for each phase contain single-phase terms (pressure gradient, thermal conduction etc.) Conservation equations also contain interfacial terms (drag, lift, mass transfer, etc.). Interfacial terms are generally nonlinear and therefore, convergence can sometimes be difficult. Eulerian Model applicability Flow regime Bubbly flow, droplet flow, slurry flow, fluidized bed, particle-laden flow Volume loading Dilute to dense Particulate loading Low to high Stokes number All ranges Application examples High particle loading flows Slurry flows Sedimentation Fluidized beds Risers Packed bed reactors

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**Eulerian Multiphase Model Equations**

Continuity: Momentum for qth phase: The inter-phase exchange forces are expressed as: In general: Energy equation for the qth phase can be similarly formulated. Volume fraction for the qth phase transient convection pressure body shear interphase mass exchange external, lift, and virtual mass forces interphase forces exchange Solids pressure term is included for granular model. Exchange coefficient

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**Eulerian Multiphase Model Equations**

Multiphase species transport for species i belonging to mixture of qth phase Homogeneous and heterogeneous reactions are setup the same as in single phase The same species may belong to different phases without any relation between themselves Mass fraction of species i in qth phase transient convective homogeneous reaction diffusion heterogeneous reaction homogeneous production

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Eulerian Model Setup Define Phases… Define Models Viscous…

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**Mixture Model Overview**

The mixture model is a simplified Eulerian approach, based on the assumption of small Stokes number. Solves the mixture momentum equation (for mass-averaged mixture velocity) Solves a volume fraction transport equation for each secondary phase. Mixture model applicability Flow regime: Bubbly, droplet, and slurry flows Volume loading: Dilute to moderately dense Particulate Loading: Low to moderate Stokes Number: St << 1 Application examples Hydrocyclones Bubble column reactors Solid suspensions Gas sparging

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**Mixture Model Equations**

Solves one equation for continuity of the mixture Solves for the transport of volume fraction of each secondary phase Solves one equation for the momentum of the mixture The mixture properties are defined as: Drift velocity

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Mixture Model Setup Define Models Multiphase… Define Phases…

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**Mixture Model Setup Boundary Conditions**

Volume fraction defined for each secondary phase. To define initial phase location, patch volume fractions after solution initialization.

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Cavitation Submodel The Cavitation model models the formation of bubbles when the local liquid pressure is below the vapor pressure. The effect of non-condensable gases is included. Mass conservation equation for the vapor phase includes vapor generation and condensation terms which depend on the sign of the difference between local pressure and vapor saturation pressure (corrected for on-condensable gas presence). Generally used with the mixture model, incompatible with VOF. Tutorial is available for learning the in-depth setup procedure.

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**Eulerian-Granular Model Setup**

Granular option must be enabled when defining the secondary phases. Granular properties require definition. Phase interaction models appropriate for granular flows must be selected.

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**The Volume of Fluid (VOF) Model Overview**

The VOF model is designed to track the location and motion of a free surface between two or more immiscible fluids. VOF model can account for: Turbulence, energy and species transport Surface tension and wall adhesion effects. Compressibility of phase(s) VOF model applicability: Flow regime Slug flow, stratified/free-surface flow Volume loading Dilute to dense Particulate loading Low to high Turbulence modeling Weak to moderate coupling between phases Stokes number All ranges Application examples Large slug flows Tank filling Offshore separator sloshing Coating

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VOF Model Setup Define Models Multiphase… Define Phases… Define Operating Conditions… Operating Density should be set to that of lightest phase with body forces enabled.

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**UDFs for Multiphase Applications**

When a multiphase model is enabled, storage for properties and variables is set aside for mixture as well as for individual phases. Additional thread and domain data structures required. In general the type of DEFINE macro determines which thread or domain (mixture or phase) gets passed to your UDF. C_R(cell,thread) will return the mixture density if thread is the mixture thread or the phase densities if it is the phase thread. Numerous macros exist for data retrieval. Domain ID = 1 Mixture Domain Phase 2 Domain Mixture Thread Phase 1 Domain Phase 3 Domain 2 3 4 5 Interaction Domain Phase Thread Domain ID

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**Heterogeneous Reaction Setup**

Define Phases…

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**Reacting Flow Modeling**

Appendix Reacting Flow Modeling

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**Eddy Dissipation Model (EDM)**

Applicability Flow Regime: Turbulent flow (high Re) Chemistry: Fast chemistry Configuration: Premixed / Non-Premixed / Partially Premixed Application examples Gas reactions Coal combustion Limitations Unreliable when mixing and kinetic time scales are of similar order of magnitude Does not predict kinetically-controlled intermediate species and dissociation effects. Cannot realistically model phenomena which depend on detailed kinetics such as ignition, extinction. Solves species transport equations. Reaction rate is controlled by turbulent mixing.

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**Non-Premixed Model Applicability Application examples Limitations**

Flow Regime: Turbulent flow (high Re) Chemistry: Equilibrium or moderately non-equilibrium (flamelet) Configuration: Non-Premixed only Application examples Gas reaction (furnaces, burners). This is usually the model of choice if assumptions are valid for gas phase combustion problems. Accurate tracking of intermediate species concentration and dissociation effects without requiring knowledge of detailed reaction rates (equilibrium). Limitations Unreliable when mixing and kinetic time scales are comparable Cannot realistically model phenomena which depend on detailed kinetics (such as ignition, extinction). Solves transport equations for mixture fraction and mixture fraction variance (instead of the individual species equations). Fuel Oxidizer Reactor Outlet

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**Premixed Combustion Model**

Applicability Flow Regime: Turbulent flow (high Re) Chemistry: Fast chemistry Configuration: Premixed only Application examples Premixed reacting flow systems Lean premixed gas turbine combustion chamber Limitations Cannot realistically model phenomena which depend on detailed kinetics (such as ignition, extinction). Uses a reaction progress variable which tracks the position of the flame front (Zimont model). Fuel + Oxidizer Reactor Outlet

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**Partially Premixed Combustion Model**

Applicability Flow Regime: Turbulent flow (high Re) Chemistry: Equilibrium or moderately non-equilibrium (flamelet) Configuration: Partially premixed only Application examples Gas turbine combustor with dilution cooling holes. Systems with both premixed and non-premixed streams Limitations Unreliable when mixing and kinetic time scales are comparable. Cannot realistically model phenomena which depend on detailed kinetics (such as ignition, extinction). In the partially premixed model, reaction progress variable and mixture fraction approach are combined. Transport equations are solved for reaction progress variable, mixture fraction, and mixture fraction variance. Fuel + Oxidizer Reactor Secondary Fuel or Oxidizer Outlet

58
**Detailed Chemistry Models**

The governing equations for detailed chemistry are generally stiff and difficult to solve. Tens of species Hundreds of reactions Large spread in reaction time scales. Detailed kinetics are used to model: Flame ignition and extinction Pollutants (NOx, CO, UHCs) Slow (non-equilibrium) chemistry Liquid/liquid reactions Available Models: Laminar finite rate Eddy Dissipation Concept (EDC) Model PDF transport KINetics model (requires additional license feature) CHEMKIN-format reaction mechanisms and thermal properties can be imported directly. FLUENT uses the In-Situ Adaptive Tabulation (ISAT) algorithm in order to accelerate calculations (applicable to laminar, EDC, PDF transport models).

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**Moving and Deforming Mesh**

Appendix Moving and Deforming Mesh

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**Absolute and Relative Velocities – The Velocity Triangle**

Absolute Velocity – velocity measured w.r.t. the stationary frame Relative Velocity – velocity measured w.r.t. the moving frame. The relationship between the absolute and relative velocities is given by the Velocity Triangle rule: In turbomachinery, this relationship can be illustrated using the laws of vector addition. Blade motion It is important to understand the relationship between the velocity viewed from the stationary and relative frames. This relationship is often called the “velocity triangle,” and can be expressed by the simple vector equation: Here, V is the velocity in the stationary or absolute frame ,W is the velocity viewed from the moving frame, and U is the frame velocity. For a rotating reference frame, U is simply Notice from the picture of the moving turbine blade that a flow approaching the blade in the x direction appears to be moving with a positive angle due to the downward motion of the blade.

61
**Geometry Constraints for SRF**

Single Fluid Domain Walls and flow boundaries Walls and flow boundaries (inlets and outlets) which move with the fluid domain may assume any shape. Walls and flow boundaries which are stationary (with respect to the fixed frame) must be surfaces of revolution about the rotational axis. You can also impose a tangential component of velocity on a wall provided the wall is a surface of revolution. You can employ rotationally-periodic boundaries if geometry and flow permit Advantage - reduced domain size Shroud wall is stationary (surface of revolution) Hub, blade walls rotate with moving frame Axis of rotation

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SRF Set-up: Cell Zones Use fluid BC panel to define rotational axis origin and direction vector for rotating reference frame Direction vectors should be unit vectors but Fluent will normalize them if they aren’t Select Moving Reference Frame as the Motion Type for SRF Enter Moving Frame Velocities Rotational and Translational velocities Rotation direction defined by right-hand rule Negative speed implies rotation in opposite direction Once the solver, physical model, and material selections have been made, you can activate a moving reference frame in the BC panel for the fluid zones. The parameters which must be set as follows: Enter first the rotational axis origin and direction. The origin (x,y,z) corresponds to the origin of the moving frame, while the direction is a unit vector pointing in the direction of the axis. Rotation of the frame is defined using the right-hand-rule. Next, under “Motion Type”, select “Moving Reference Frame”. This indicates to Fluent that the entire cell zone is moving with the translational and rotational speeds you provide. Finally, enter the moving zone velocities – most typically a rotational velocity, though a translational velocity may be employed under special circumstances. Note that the rotational velocity may be positive or negative, a negative speed implying a sense of rotation opposite to the right hand rule.

63
**SRF Set-up: Boundary Conditions**

Inlets: Choice of specification of velocity vector or flow direction in absolute or relative frames. NOTE: Total pressure and temperature definitions depend on velocity formulation! Outlets Static pressure or outflow. Radial equilibrium option. Other Flow BCs Periodics Non-reflecting BCs Target mass flow outlet Walls Specify walls to be… Moving with the domain Stationary NOTE: “Stationary wall” for Wall Motion means stationary w.r.t. the cell zone! Flow boundaries require some special attention for SRF models. First, velocity inlets permit specification of velocity directions or components in either the absolute or relative frames. Use the form which is relevant to the problem at hand. Pressure inlet specifications, however, are closely tied with the velocity formulation. Specifically, if you are using the AVF, the total pressure which is entered into the GUI is the absolute total pressure, which is shown here in the incompressible form. Note that the dynamic term involves the absolute velocity, ½ r V^2. In addition, the direction vector is defined in the absolute frame. In contrast, if you are using the RVF, the total pressure that is entered is assumed to be a relative total pressure, which has a dynamic term that involves the relative velocity, ½ r W^2. The direction vector in this case is defined in the relative frame. These comments also apply to reverse flow specifications at pressure outlets, where the pressure outlet behaves like a pressure inlet. The pressure outlet also has an option for “radial equilibrium”. This option permits a radial variation in pressure due to swirl, as given by the simplified radial equilibrium equation. This condition holds only for cases with axial outflow (flow is parallel to the axis of rotation) – for example, at the outlet of an axial compressor or turbine stage. Other BCs which may be of interest for turbomachinery applications include: Non-reflecting BCs Target mass flow outlet More information about these models can be found in the manual.

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**Periodic repeat interface Non-conformal interface**

Interfaces Fluid zones in multiple zone models communicate across interface boundaries. Conformal interfaces An interior mesh surface separates cells from adjacent fluid zones. Face mesh must be identical on either side of the interface. Non-conformal (NC) interfaces Cells zones are physically disconnected from each other. Interface consists of two overlapping surfaces (type = interface) Fluent NC interface algorithm passes fluxes from on surface to the other in a conservative fashion (i.e. mass, momentum, energy fluxes are conserved). User creates interfaces using DefineGrid Interfaces… Interfaces may be periodic Called periodic repeat interface. Require identical translational or rotational offset. Conformal interface The MRF approach can accommodate two types of interfaces – conformal and non-conformal. Conformal interfaces are simply interior face zones which separate individual fluid zones. By definition, a single face zone divides the cells and the faces and nodes match across the interface. In contrast, non-conformal interfaces consist of cell zones which are physically disconnected from each other. The zones communicate across overlapping interface boundaries. Fluxes are passed conservatively from one side to the other. Clearly, the advantage of this approach is that is permits much more flexibility in the mesh generation with very little penalty in accuracy. In addition, as we will see later, it is easy to change an MRF model with non-conformal interfaces to a sliding mesh model if desired. Thus non-conformal interfaces recommended in general over conformal interfaces. Periodic repeat interface Non-conformal interface

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**Mesh interface between**

The MRF Model The computational domain is divided into stationary and rotating fluid zones. Interfaces separate zones from each other. Interfaces can be Conformal or Non-Conformal. Flow equations are solved in each fluid zone. Flow is assumed to be steady in each zone (clearly an approximation). SRF equations used in rotating zones. At the interfaces between the rotating and stationary zones, appropriate transformations of the velocity vector and velocity gradients are performed to compute fluxes of mass, momentum, energy, and other scalars. MRF ignores the relative motions of the zones with respect to each other. Does not account for fluid dynamic interaction between stationary and rotating components. For this reason MRF is often referred to as the “frozen rotor” approach. Ideally, the flow at the MRF interfaces should be relatively uniform or “mixed out.” Mesh interface between pump rotor and housing Let’s now discuss the MRF approach. This is perhaps the simplest possible way of treating interfaces between moving and stationary zones. To use this approach, you must divide your mesh into separate fluid zones with interfaces between zones. The interfaces may be conformal or non-conformal – we’ll talk about that further in the next slide. We then assume steady-state conditions in each fluid zone and solve the appropriate equations in those zones (either stationary or MRF). At the interfaces, the algorithm simply apply a change of frame for the for velocity vector and related quantities. It should be noted that the fluxes computed in this fashion are local to the interface and ignore the relative motions of the zones with respect to each other. It is as if the rotating zones are “frozen” in place with respect to the stationary zones. Hence, this approach is often referred to as the “frozen rotor approach” Another way of thinking about MRF is as a instantaneous “snapshot” of the flowfield. If the temporal variations at the interface are small – that I, the flow is relatively uniform or mixed out - then this becomes a reasonable approximation.

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**Geometric Constraints for MRF**

Walls and flow boundaries which are contained within the rotating fluid zone interfaces are assumed to be moving with the fluid zones and may assume any shape. Stationary walls and flow boundaries are allowed if they are surfaces of revolution. The interface between two zones must be a surface of revolution with respect to the axis of rotation of the rotating zone. Periodic repeat interfaces are permitted but the periodic angles (or offsets) must be identical for all zones. stationary zone rotating zone It is important to recognize that the interface shape must adhere to a simple rule when used in MRF (or even sliding mesh calculations). Specifically, the interface surface must be a surface of revolution about the axis of rotation. Another way to think of this is that a moving mesh zone must not become disconnected from the adjacent stationary zone at the non-conformal interface boundary. Clearly, a shape such as the oval shown on the right would not be permissible. In addition, if a periodic interface in used, the periodic angles or offsets must be the same for all zones. Interface is not a surface or revolution Correct Wrong!

67
**Equations of Fluid Dynamics for Moving Frames**

Equations of fluid dynamics can be transformed to a moving reference frame with a choice of the velocities which are solved. Relative Velocity Formulation (RVF) Uses the relative velocity and relative total internal energy as the dependent variables. Absolute Velocity Formulation (AVF) Source terms appear in the momentum equations for rotating frames. Refer to Appendix for detailed listing of equations. Relative formulation of x momentum equation: Absolute formulation of x momentum equation: Let us now briefly examine the forms of the Navier-Stokes equations appropriate for moving reference frames. Basically, the transformation from the stationary frame to the moving frame can be done mathematically in two different ways. In the first form, the momentum equations are expressed in terms of the velocity relative to the moving frame. This form is known as the Relative Velocity Formulation. The second form utilizes the velocities referred to the absolute frame of reference in the momentum equations, and is known as the Absolute Velocity Formulation. In both cases, additional acceleration terms result from the transformations. In addition, for compressible flows, the energy variables that are solved for will depend on the forumlation. A complete list of the equations is provided in the Appendix. Momentum source terms

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MRF Set-Up Generate mesh with appropriate stationary and rotating fluid zones Can choose conformal or non-conformal interfaces between cell zones For each rotating fluid zone (Fluid BC), select “Moving Reference Frame” as the Motion Type and enter the rotational axis and moving frame speed. Identical to SRF except for multiple zones Stationary zones remain with “Stationary” option enabled Set up for BCs and solver settings same as SRF. To set up an MRF problem, you will first need to decide what types of interfaces are to be used (that is, conformal or non-conformal). This decision will impact how the mesh is generated in your preprocessor. When the multiple zone mesh is read into Fluent, you will be able to selectively apply the moving reference frame option to the rotating zones. Boundary conditions, physical models, materials, and solver settings will be the same as for SRF problems.

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MPM Set-up Assign motion types and speeds to fluid zones and appropriate BCs for each zone (like SRF). Select upstream and downstream zones which will comprise mixing plane pair. Upstream will always be Pressure Outlet. Downstream can be any inlet BC type. Set the number of Interpolation Points for profile resolution. Should be about the same axial/radial resolution as the mesh. Mixing Plane Geometry determines method of profile averaging. Mixing plane controls Under-relaxation – Profile changes are under-relaxed from one iteration to the next using factor between 0 and 1.

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**SMM Set-up Enable transient solver.**

For moving zones, select Moving Mesh as Motion Type in Fluid BC panel. Define sliding zones as non-conformal interfaces. Enable Periodic Repeat option if sliding/rotating motion is periodic. Other BCs and solver settings are same as the SRF, MRF models. Run calculation until solution becomes time-periodic Setting up a sliding mesh model is relatively straightforward. The geometry, mesh, physical model, materials, and surface boundary condition set up will be identical to an MRF calculation. For a sliding mesh calculation, you will need to turn on the transient solver and define appropriate option depending on the flow solver selected (pressure-based vs density-based). Next, you will select the Moving Mesh option as the Motion Type in the Fluid BC panel for all moving cell zones (stationary zones remain with the Stationary option). You will need to set up all non-conformal interfaces as well (remembering to select Periodic if the interface is adjacent to periodic zones). You will also need to set up your monitors to track the solution as a function of time rather than iteration.

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**Dynamic Mesh Setup Enable transient solver.**

Enable Dynamic Mesh model in DefineDynamic Mesh. Activate desired Mesh Methods and set parameters as appropriate. Define boundary motion in the Dynamic Mesh Zones GUI. UDF may be required. Other models, BCs, and solver settings are same as SMM models. Mesh motion can be previewed using SolveMesh Motion utility. Because of the complexity of the dynamic mesh modeling, setting up a dynamic mesh model in Fluent is more involved than other moving zone models. You will first need to turn on the transient solver and define appropriate options depending on the flow solver selected (pressure-based vs density-based). Next, you will enable the dynamic mesh model in the GUI using DefineDynamic Mesh. You will then define the Mesh methods you wish to apply and set the parameters as appropriate. The boundary motions are defined in a separate GUI. Note that you may need to create a user-defined function to define the mesh motion. Other models, boudary conditions, and solver settings are the same as other moving zone models. It is recommended that prior to running your model, you preview the mesh motion using SolveMesh Motion feature. You can run your mesh through a defined range of physical time, and thereby identifying problems with the mesh motion before you begin the actual CFD calculation.

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Instructor: André Bakker

Instructor: André Bakker

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