1. FLOTRAN Characteristics, Capabilities and Analysis Planning Chapter 1

2. Training Manual May 15, 2001 Inventory #001477 1-2 Objectives Describe the phenomena modeled with FLOTRAN elements Discuss the FLOTRAN Element Characteristics Explain CFD terminology Present the governing equations Discuss Solution Algorithm characteristics Outline important user decisions

3. Training Manual May 15, 2001 Inventory #001477 1-3 The FLOTRAN Simulation FLOTRAN simulates fluid flow and heat transfer –The conservation equations (mass and momentum) are solved for a fluid. The result is a flow distribution and pressure field. –An energy equation may also be solved for the fluid domain. For the energy equation, the problem domain may contain both fluid and non-fluid elements –Turbulence, Multiple Species simulations are optional Degrees of Freedom (DOF) –Velocities: VX,VY,VZ –Pressure: PRES –Turbulence (if necessary): ENKE,ENDS –Species Concentrations: SP01…SP06

4. Training Manual May 15, 2001 Inventory #001477 1-4 2D Basic 3D Basic 3D Transition FLOTRAN Element Types and Shapes 2D Type: Fluid141 (triangles and quadrilaterals may be mixed) 3D Type: Fluid142 (hexahedrals, tetrahedrals, pyramids, wedges) Pyramids are the required transition elements between Tet and Hex shapes –Elements are Linear (no mid-side nodes)

5. Training Manual May 15, 2001 Inventory #001477 1-5 Two Dimensional –Cartesian (x-y) or Polar (r-θ) Coordinates –Axisymmetric Coordinates (about x or y axis) Three Dimensional –Cartesian –Cylindrical: VR,V field must be parallel to ANSYS XY plane VX(VR) ; VY(V  ) ;VZ(VZ) r P(r,  ) Origin y x FLOTAN Problem Domains 

6. Training Manual May 15, 2001 Inventory #001477 1-6 Problem Domain - Geometry Equations are formulated in the coordinate system chosen –Required for use of periodic boundaries Stationary or Rotating coordinate systems Structured or Unstructured meshes ALE formulation enables pre-determined change in problem domain. –ALE formulation activates UX,UY,UZ DOF. –Use functions to program both displacements and velocities for boundary movement.

7. Training Manual May 15, 2001 Inventory #001477 1-7 Problem Domain - Coordinate System FLOTRAN Coordinate System Assignment - Command line –2D: et,1,141,,,1 Axisymmetric about Y axis et,1,141,,,2 Axisymmetric about X axis et,1,141,,,3 Polar Coordinates –3D: et,1,142,,,3 : Cylindrical Coordinates GUI Access to the Coordinate System Assignment –Accessed through PREP7 –Element Type > Add/Edit/Delete > Options –FLOTRAN Setup Menu >Flow Environment > Coordinate System

8. Training Manual May 15, 2001 Inventory #001477 1-8 CFD Terminology We provide definitions of the these terms…. – CFD –Turbulent flow –Mach Number – Incompressible fluid – Compressible fluids – Conjugate heat transfer – Distributed resistance – Periodic boundaries – Multiple species transport – Newtonian and non-Newtonian fluids –Free Surface

9. Training Manual May 15, 2001 Inventory #001477 1-9 CFD Terminology Define CFD Computational Fluid Dynamics (CFD) –The science (and art) of obtaining a numerical solution to the set of equations which describe the motion of a fluid. Partial differential equations are discretized, resulting in a series of algebraic equations of the form: –In a completely coupled system, the vector X contains all the DOF –In a segregated Scheme, the variables are solved for sequentially. –In some instances approximate solutions to the matrix systems are suffcient for intermediate steps.

10. Training Manual May 15, 2001 Inventory #001477 1-10 CFD Terminology Define Turbulent Flow According to Webster’s New Collegiate Dictionary, turbulent flow is defined as “a fluid flow in which the velocity (pressure, temperature, species concentration, etc.) at a given point varies erratically in magnitude and direction”. –Turbulence is a flow regime characterized by velocities, pressures, temperatures, and species mass fractions that fluctuate in response to shearing forces. These shear forces can cause an orderly flow to break into eddies with discernible disorder. The flow is in reality constantly changing. In principle, turbulent flow is a transient phenomena. Steady state solutions are obtained through time-averaging.

11. Training Manual May 15, 2001 Inventory #001477 1-11 Turbulence When averaged over time, the velocity fluctuations are zero. Calculating the fluctuations is generally not computationally practical. Turbulence models are designed to determine the effect of the fluctuations on the mean flow.

12. Training Manual May 15, 2001 Inventory #001477 1-12 Turbulence (continued) FLOTRAN’s default treatment is a two-differential equation model, the k-ε model The optional k-ε turbulence model should be activated when the Reynold’s number for the flow indicates the presence of a turbulent regime. The Reynold’s number is a dimensionless parameter which represents the ratio of the inertial to viscous forces. It is defined as: ρ is the density, V is the characteristic velocity, μ is the dynamic viscosity, and D H is a characteristic length or diameter, typically the hydraulic diameter for internal flows.

13. Training Manual May 15, 2001 Inventory #001477 1-13 Turbulence (continued) Reynold’s number ranges for laminar and turbulent flow can be found in fluid dynamics texts, literature, handbooks, etc. Some examples:

14. Training Manual May 15, 2001 Inventory #001477 1-14 CFD Terminology Mach Number Mach number –speed of fluid divided by the speed of sound. In general, Note that supersonic flow is characterized by M>1 while subsonic flow exists when M<1. We estimate the Mach number before analysis to decide whether or not to activate the Solution option for Compressible flow.

15. Training Manual May 15, 2001 Inventory #001477 1-15 CFD Terminology Define Incompressible Fluids In FLOTRAN, the terms “compressible” and “incompressible” denote the algorithm chosen by the user to solve the coupled momentum and pressure equations. –This concerns which terms are considered in the momentum equation. Terms which are zero if the density is perfectly constant are dropped from the equations. This applies to fluids where large pressure changes result in only slight variations in density. –Density variations are primarily a function of temperature gradients rather than pressure gradients. The flow of liquids is generally incompressible, even when natural convection is present.

16. Training Manual May 15, 2001 Inventory #001477 1-16 CFD Terminology Define Compressible Fluids Compressible flow – It refers to (generally high velocity) flow problems where density varies appreciably as a result of pressure and temperature. The static temperature becomes a function of velocity and stagnation temperature. The use of the compressible option should be considered for Mach numbers above 0.3. The compressible option is not appropriate for low mach number flows. Note that for many applications, the incompressible option may be used up to Mach numbers of 0.7.) The equation of state for density must be woven into the pressure equation. The Ideal Gas Law is used:

17. Training Manual May 15, 2001 Inventory #001477 1-17 Compressible Flow Option In a compressible/thermal problem, the total energy equation is solved for total temperature. Static temperature is then determined from: Shock waves (where discontinuous changes in velocity and properties take place) occur frequently in supersonic flows. The solution benefits from mesh refinement in regions near shock waves.

18. Training Manual May 15, 2001 Inventory #001477 1-18 CFD Terminology Define Conjugate Heat Transfer Conjugate heat transfer –the solution of the energy equation in a problem domain with both fluids and solids (i.e., we are solving for the temperature distributions in both fluids and solids simultaneously). These problems are generally considered as “ill-conditioned”, meaning that the solution of the matrix equation derived from the energy (a.k.a. temperature) equation can be difficult….

19. Training Manual May 15, 2001 Inventory #001477 1-19 CFD Terminology Define Distributed Resistances Distributed resistances –Simulation of the hydrodynamic effects of a feature without modeling its detailed geometry. The distributed resistance is the CFD analogy of a beam element. Examples include flow through screens, porous media, or small obstructions. –Values can be obtained from Handbooks or calculated by simulation with FLOTRAN for use in larger simulations. One case with the feature One case without the feature

20. Training Manual May 15, 2001 Inventory #001477 1-20 CFD Terminology Define Periodic Boundaries Periodic Boundaries –two boundaries where the conditions are unknown but identical. All the degrees of freedom are coupled.

21. Training Manual May 15, 2001 Inventory #001477 1-21 CFD Terminology Define Multiple Species Transport Multiple Species Transport –This capability enables the user to track species concentration levels for several fluids as they mix, subject to the limitations that a single momentum equation is solved for the flow field and no chemical reactions are simulated. –Thus, it is not possible to simulate the separation of two fluids that occurs due to density changes.

22. Training Manual May 15, 2001 Inventory #001477 1-22 CFD Terminology Define Newtonian and Non-Newtonian Fluids Newtonian fluids –have a linear relationship between the stress and rate-of-strain. Newtonian fluids have no memory of past configurations or deformations. Non-Newtonian fluids –have a viscosity which may be a function of not only the fluid velocity, but also the velocity gradient. Common Newtonian fluids –include air and water Common non-Newtonian fluids –include blood, polymers and clay slurries

23. Training Manual May 15, 2001 Inventory #001477 1-23 The FLOTRAN Elements (continued) The fluid is single phase but can be a mixture of up to six different fluids or species. You can use Elements 141 & 142 to model heat transfer in solids as well as fluids, but FLOTRAN elements cannot be combined with other ANSYS elements. Conservation laws provide the basis for the formulation: –Conservation of Mass –Conservation of Momentum –Conservation of Energy Transport equation solved for multiple species.

24. Training Manual May 15, 2001 Inventory #001477 1-24 Conservation of Mass The Conservation of Mass equation to a FLOTRAN analysis: The Conservation of Mass equation (or Continuity equation) when combined with the Conservation of Momentum equation leads to an equation for pressure. The above form of the Continuity equation is stated in indicial notation (a repeated index implies a summation of terms). It can be rewritten in 2D, Cartesian coordinates as:

25. Training Manual May 15, 2001 Inventory #001477 1-25 Diffusion terms Advection terms Time-dependent terms Source terms Conservation of Momentum Discuss the application of the Conservation of Momentum equation to a FLOTRAN analysis. FLOTRAN solves the complete Navier-Stokes Equations:

26. Training Manual May 15, 2001 Inventory #001477 1-26 Conservation of Momentum (continued) Additional source terms (ß i ) such as Lorentz forces may exist. The Navier-Stokes equations can be rewritten for 2D, Steady State, Constant properties in Cartesian coordinates as:

27. Training Manual May 15, 2001 Inventory #001477 1-27 Discuss the application of the Conservation of Energy equation to a FLOTRAN analysis. For incompressible flow, the energy equation is simplified into a transport equation: The specific heat may vary. The density for non-fluid regions must be constant. The conductivity for non-fluids may be orthotropic and also vary with temperature. Conservation of Energy

28. Training Manual May 15, 2001 Inventory #001477 1-28 Discuss the application of the Conservation of Energy equation for compressible flow to a FLOTRAN analysis. For compressible flow, the energy equation is solved in terms of total temperature. The viscous work, kinetic energy and viscous dissipation terms can be significant at high velocities. Viscous work termsKinetic energy terms Viscous dissipation Compressible Flow Total Energy Equation

29. Training Manual May 15, 2001 Inventory #001477 1-29 Discuss the application of the transport equation for multiple species to a FLOTRAN analysis. The transport equations are solved for the mass fraction of each specie and based on advection and diffusion processes only. In these equations, Y i is the mass fraction for the ith species and D i is the mass diffusion coefficient for the ith specie in relation to the bulk mixture. Note: To ensure the sum of N specie mass fractions at any location is 1, only N-1 equations are actually solved. Species Transport Equation

30. Training Manual May 15, 2001 Inventory #001477 1-30 FLOTRAN Analysis Capabilities Transient or Steady-state flow –Ramped, Step time dependent boundary conditions Laminar or Turbulent flow –User choice Incompressible or Compressible flow Newtonian or non-Newtonian flow –Power Law, Carreau, Bingham models available –User Programmable models possible Subsonic, Transonic, or Supersonic flow

31. Training Manual May 15, 2001 Inventory #001477 1-31 FLOTRAN Analysis Capabilities (continued) Internal or External flow Forced flow or buoyancy driven flow –Incompressible algorithm with variable density Forced, free or mixed convection heat transfer Conjugate heat transfer Distributed resistance/Fan model Free Surface (2D) with Surface Tension ALE formulation for changing problem domain Interpolation of solution onto revised mesh

32. Training Manual May 15, 2001 Inventory #001477 1-32 FLOTRAN Solution Algorithm Characteristics Sequential solution of the governing equations. Iterative matrix solvers - the symmetric and non-symmetric iterative solvers are separate from those used in the rest of ANSYS. In-memory solution - Memory requirements are minimized by storing only the non-zero matrix terms. Equal Order Method (velocity-pressure) - Equal order interpolation functions simplify boundary condition specification and interpretation of results. Streamline upwind method - the default for treating the non-linear advection terms. Inexpensive, bounded and stable method. (The Streamline Upwind Petrov Galerkin method is a more accurate but slightly less stable alternative.)

33. Training Manual May 15, 2001 Inventory #001477 1-33 FLOTRAN Analysis Decision Making You must make decisions about the expected flow characteristics and subsequently verify these decisions. –Are fluid property variations with temperature important? –Is the flow steady state or transient in nature? –Is the flow laminar or turbulent? –Are “compressible” effects important? –How much of the problem domain should be modeled? –Where should the mesh densities be greatest? Continued advances in CFD will help automate these decisions, but this will not relieve the engineer of the need to understand what phenomena are important.

34. Training Manual May 15, 2001 Inventory #001477 1-34 The Sequence of Events Geometry: –Create within ANSYS (PREP7) or.. –Import from a CAD program (Use Connection Products!) Ensure that the flow domain volume is imported Meshing –Use mapped meshing as much as possible. –Slice volumes as necessary for Mesh sweeping. –ICEM CFD mesh is easily imported into ANSYS. Boundary Conditions –Use solid model boundary conditions if possible FLOTRAN execution –Stability parameters and restarts as necessary Post-Processing

35. Training Manual May 15, 2001 Inventory #001477 1-35 T wall = 20°C V inlet T inlet H = 1 P = 0 Insulated wall, q" = 0 Density =  = 998 kg/m 3 Viscosity =  = 1.0(10 -3 ) kg/m-s Speed of sound = a = 1480 m/s CASE A: V inlet = 0.1 m/s, T inlet = 95°C CASE B: V inlet = 1 m/s, T inlet = 25°C CASES A and B: Consider water flowing through a channel. Exercise Answer the following questions for cases A through D shown below. 1. Is the flow laminar or turbulent? 2. Is the flow compressible or incompressible? 3. Are property variations with temperature important? 4. Where should the mesh be fine?

36. Training Manual May 15, 2001 Inventory #001477 1-36 Answers: V inlet T inlet H = 0.5 m P = 0 T ambient = 20°C Density =  = 1.20 kg/m 3 Viscosity =  = 1.81(10 -5 ) kg/m-s Speed of sound = a = 340 m/s CASE C: V inlet = 50 m/s, T inlet = 20°C CASE D: V inlet = 500 m/s, T inlet = 20°C C L CASES C and D: Consider air flowing through an expanding duct. Exercise (continued)