Express Introductory Training in ANSYS Fluent Lecture 3 Turbulence Modeling, Heat Transfer & Transient Calculations

Transcription

1 Express Introductory Training in ANSYS Fluent Lecture 3 Turbulence Modeling, Heat Transfer & Transient Calculations Dimitrios Sofialidis Technical Manager, SimTec Ltd. Mechanical Engineer, PhD PRACE Autumn School Industry Oriented HPC Simulations, September 21-27, University of Ljubljana, Faculty of Mechanical Engineering, Ljubljana, Slovenia 2012 ANSYS, Inc. September 19, Release 14.5

2 Lecture 3. Turbulence Modeling, Heat Transfer & Transient Calculations 14.5 Release Introduction to ANSYS Fluent 2012 ANSYS, Inc. September 19, Release 14.5

3 Introduction Part 1. Lecture Theme: The problem definition for all Turbulence CFD simulations Modeling includes boundary conditions, cell zone conditions and material properties. The accuracy of the simulation results depends on defining these properly. Learning Aims: You will learn: How to define material properties. The different boundary condition types in FLUENT and how to use them. How to define cell zone conditions in FLUENT including solid zones and porous media. How to specify well posed boundary conditions. Learning Objectives: You will know how to perform these essential steps in setting up a CFD analysis. Introduction Material Properties Cell Zone Conditions Boundary Conditions Summary 2012 ANSYS, Inc. September 19, Release 14.5

4 Lecture Theme: Introduction The majority of engineering flows are turbulent. Successfully simulating such flows requires understanding a few basic concepts of turbulence theory and modeling. This allows one to make the best choice from the available turbulence models and near wall options for any given problem. Learning Aims: You will learn: Basic turbulent flow and turbulence modeling theory. Turbulence models and near wall options available in Fluent. How to choose an appropriate turbulence model for a given problem. How to specify turbulence boundary conditions at inlets. Learning Objectives: You will understand the challenges inherent in turbulent flow simulation and be able to identify the most suitable model and near wall treatment for a given problem. Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

5 Observation by Osborne Reynolds [1] Flows can be classified as either : Laminar (Low Reynolds Number) Transition (Increasing Reynolds Number) Turbulent (Higher Reynolds Number) Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

6 Observation by Osborne Reynolds [2] The Reynolds number is the criterion used to determine whether the flow is laminar or turbulent. The Reynolds number is based on the length scale of the flow: L x, d, d, etc. hyd Transition to turbulence varies depending on the type of flow: External flow: Re L. UL. Along a surface : Re X > Around on obstacle : Re L > Internal flow: : Re D > 2300 Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

7 Turbulent Flow Structures [1] A turbulent flow contains a wide range of turbulent eddy sizes. Turbulent flow characteristics: Unsteady, three dimensional, irregular, stochastic motion in which transported quantities (mass, momentum, scalar species) fluctuate in time and space. Enhanced mixing of these quantities results from the fluctuations. Unpredictability in detail. Large scale coherent structures are different in each flow, whereas small eddies are more universal. Small structures Large structures Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

8 Turbulent Flow Structures [2] Energy is transferred from larger eddies to smaller eddies. (Kolmogorov Cascade). Large scale contains most of the energy. In the smallest eddies, turbulent energy is converted to internal energy by viscous dissipation. Energy Cascade Richardson (1922), Kolmogorov (1941) Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

9 Backward Facing Step As engineers, in most cases we do not actually need to see an exact snapshot of the velocity at a particular instant. Instead for most problems, knowing the time averaged velocity (and intensity of the turbulent fluctuations) is all we need to know. This gives us a useful way to approach modelling turbulence. Instantaneous velocity contours. Time averaged velocity contours. Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

10 Velocity Mean and Instantaneous Velocities If we recorded the velocity at a particular point in the real (turbulent) fluid flow, the instantaneous velocity (U) would look like this: u Fluctuating velocity. U Time average of velocity. U Instantaneous velocity. At any point in time: Time U U u The time average of the fluctuating velocity u must be zero: u 0 BUT, the RMS of u' is not necessarily zero: u 2 0 Note you will hear reference to the turbulence energy, k. This is the sum of the three normal fluctuating velocity components: k u v w 2 Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

11 Overview of Computational Approaches Different approaches to make turbulence computationally tractable. DNS (Direct Numerical Simulation) LES (Large Eddy Simulation) RANS (Reynolds Averaged Navier Stokes Simulation) Numerically solving the full unsteady Navier Stokes equations. Resolves the whole spectrum of scales. No modeling is required. But the cost is too prohibitive! Not practical for industrial flows! Solves the spatially averaged N S equations. Large eddies are directly resolved, but eddies smaller than the mesh are modeled. Less expensive than DNS, but the amount of computational resources and efforts are still too large for most practical applications. Solve time averaged Navier Stokes equations. All turbulent length scales are modeled in RANS. Various different models are available. This is the most widely used approach for industrial flows. Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

12 RANS Modeling: Averaging Thus, the instantaneous Navier Stokes equations may be rewritten as Reynolds Averaged equations (RANS): u Rij u iu i u i p u R i ij j u k t x k xi x j x (Reynolds stress tensor) j x j The Reynolds stresses are additional unknowns introduced by the averaging procedure, hence they must be modeled (related to the averaged flow quantities) in order to close the system of governing equations. τ xx xy xz u u v u w R yx yy ij uiu j yz u v v v w 2 zx zy zz u ' w' v ' w' w' 2 ' ' ' ' ' 2 ' ' ' ' ' Symmetric tensor 6 unknowns Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

13 RANS Modeling: The Closure Problem The Reynolds Stress tensor Rij u iuj must be solved. The RANS models can be closed in two ways: Reynolds Stress Models (RSM) R ij is directly solved via transport equations (modeling is still required for many terms in the transport equations). t T u iuj uk u iuj Pij Fij Dij ij ij x k RSM is more advantageous in complex 3D turbulent flows with large streamline curvature and swirl, but the model is more complex, computationally intensive, more difficult to converge than eddy viscosity models. Eddy Viscosity Models Boussinesq hypothesis Reynolds stresses are modeled using an eddy (or turbulent) viscosity, μ T. R ij uu i j ui T x j u x The hypothesis is reasonable for simple turbulent shear flows: boundary layers, round jets, mixing layers, channel flows, etc. i j 2 3 T u x k k ij 2 k 3 ij Note: All turbulence models contain empiricism. Equations cannot be derived from fundamental principles. Some calibrating to observed solutions and 'intelligent guessing' is contained in the models. Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

14 Turbulence Models Available in Fluent RANS based models One Equation Model Spalart Allmaras Two Equation Models Standard k ε RNG k ε Realizable k ε* Standard k ω SST k ω* Reynolds Stress Model k kl ω Transition Model SST Transition Model Detached Eddy Simulation Large Eddy Simulation Increase in Computational Cost Per Iteration * Recommended choice for standard cases. Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

15 Two Equation Models Two transport equations are solved, giving two independent scales for calculating t. Virtually all use the transport equation for the turbulent kinetic energy, k. Dk Dt x j t k k x j P ; P S production dissipation Several transport variables have been proposed, based on dimensional arguments, and used for second equation. The eddy viscosity t is then formulated from the two transport variables. Kolmogorov, w: t k / w, l k 1/2 / w, k / w w is specific dissipation rate. Defined in terms of large eddy scales that define supply rate of k. Chou, : t k 2 /, l k 3/2 / Rotta, l: t k 1/2 l, k 3/2 / l t 2 ( ske) S 2S ij S ij Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

16 RANS:EVM: Standard k ε (SKE) Model The Standard k ε model (SKE) is the most widely used engineering turbulence model for industrial applications. Model parameters are calibrated by using data from a number of benchmark experiments such as pipe flow, flat plate, etc. Robust and reasonably accurate for a wide range of applications. Contains submodels for compressibility, buoyancy, combustion, etc. Known limitations of the SKE model: Performs poorly for flows with larger pressure gradient, strong separation, high swirling component and large streamline curvature. Inaccurate prediction of the spreading rate of round jets. Production of k is excessive (unphysical) in regions with large strain rate (for example, near a stagnation point), resulting in very inaccurate model predictions. Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

17 RANS:EVM: Realizable k epsilon Realizable k ε (RKE) model (Shih): Dissipation rate (ε) equation is derived from the mean square vorticity fluctuation, which is fundamentally different from the SKE. Several realizability conditions are enforced for Reynolds stresses. Benefits: Accurately predicts the spreading rate of both planar and round jets. Also likely to provide superior performance for flows involving rotation, boundary layers under strong adverse pressure gradients, separation, and recirculation. OFTEN PREFERRED TO STANDARD k ε Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

18 RANS: EVM: Spalart Allmaras (S A) Model Spalart Allmaras is a low cost RANS model solving a single transport equation for a modified eddy viscosity. Designed specifically for aerospace applications involving wall bounded flows. Has been shown to give good results for boundary layers subjected to adverse pressure gradients. Used mainly for aerospace and turbomachinery applications. Limitations: The model was designed for wall bounded flows and flows with mild separation and recirculation. No claim is made regarding its applicability to all types of complex engineering flows ANSYS, Inc. September 19, Release 14.5

19 k omega Models In k w models, the transport equation for the turbulent dissipation rate,, is replaced with an equation for the specific dissipation rate, w. The turbulent kinetic energy transport equation is still solved. See Appendix for details of w equation. k w models have gained popularity in recent years mainly because: Much better performance than k models for boundary layer flows. For separation, transition, low Re effects, and impingement, k w models are more accurate than k models. Accurate and robust for a wide range of boundary layer flows with pressure gradient. Two variations of the k w model are available in Fluent. Standard k w model (Wilcox, 1998). SST k w model (Menter). Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

20 SST Model Shear Stress Transport (SST) Model. The SST model is an hybrid two equation model that combines the advantages of both k and k w models. k w model performs much better than k models for boundary layer flows. Wilcox original k w model is overly sensitive to the freestream value (BC) of w, while k model is not prone to such problem. k k w Wall The k e and k w models are blended such that the SST model functions like the k ω close to the wall and the k ε model in the freestream. SST is a good compromise between k and k w models Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

21 RANS: Other Models in Fluent RNG k model. Model constants are derived from renormalization group (RNG) theory instead of empiricism. Advantages over the standard k model are very similar to those of the RKE model. Reynolds Stress model (RSM). Instead of using eddy viscosity to close the RANS equations, RSM solves transport equations for the individual Reynolds stresses. 7 additional equations in 3D, compared to 2 additional equations with EVM. More computationally expensive than EVM and generally difficult to converge. As a result, RSM is used primarily in flows where eddy viscosity models are known to fail. These are mainly flows where strong swirl is the predominant flow feature, for instance a cyclone (see Appendix) ANSYS, Inc. September 19, Release 14.5

22 Turbulence Near a Wall [1] The Structure of Near Wall Flows. Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

23 Velocity, U Turbulence Near a Wall [2] Near to a wall, the velocity changes rapidly. Distance from Wall, y If we plot the same graph again, where: Log scale axes are used. The velocity is made dimensionless, from U/U (,, is friction velocity) The wall distance vector is made dimensionless. Then we arrive at the graph on the next page. The shape of this is generally the same for all flows: Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

24 Turbulence Near a Wall [3] By scaling the variables near the wall the velocity profile data takes on a predictable (universal) form (transitioning from linear to logarithmic behavior). Scaling the non dimensional velocity and non dimensional distance from the wall results in a predictable boundary layer profile for a wide range of flows. Linear Logarithmic Since near wall conditions are often predictable, functions can be used to determine the near wall profiles rather than using a fine mesh to actually resolve the profile. These functions are called wall functions. Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

25 Choice of Wall Modeling Strategy. In the near wall region, the solution gradients are very high, but accurate calculations in the near wall region are paramount to the success of the simulation. The choice is between: Resolving the Viscous Sublayer. First grid cell needs to be at about y + = 1. This will add significantly to the mesh count. Use a low Reynolds number turbulence model (like k omega). Generally speaking, if the forces on the wall are key to your simulation (aerodynamic drag, turbomachinery blade performance) this is the approach you will take. Using a Wall Function. First grid cell needs to be 30<y + <300. (Too low, and model is invalid. Too high and the wall is not properly resolved). Use a wall function, and a high Re turbulence model (SKE, RKE, RNG). Generally speaking, this is the approach if you are more interested in the mixing in the middle of the domain, rather than the forces on the wall. Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

26 Limitations of Wall Functions In some situations, such as boundary layer separation, logarithmic based wall functions do not correctly predict the boundary layer profile. Wall functions applicable. Wall functions not applicable. Non Equilibrium Wall Functions have been developed in Fluent to address this situation but they are very empirical. A more rigorous approach is recommended if affordable. In these cases logarithmic based wall functions should not be used. Instead, directly resolving the boundary layer can provide accurate results. Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

27 Choosing a Near Wall Treatment Standard Wall Functions. The Standard Wall Function options is designed for high Re attached flows. The near wall region is not resolved. Near wall mesh is relatively coarse. Non Equilibrium Wall Functions. For better prediction of adverse pressure gradient flows and separation. Near wall mesh is relatively coarse. Enhanced Wall Treatment* Used for low Re flows or flows with complex near wall phenomena. Generally requires a very fine near wall mesh capable of resolving the near wall region. Can also handle coarse near wall mesh. User Defined Wall Functions. Can host user specific solutions. * Recommended choice for standard cases. Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

28 Inlet Boundary Conditions When turbulent flow enters a domain at inlets or outlets (backflow), boundary conditions for k, ε, ω and/or ' ' must be specified, depending on which j turbulence model has been selected. u i u Four methods for directly or indirectly specifying turbulence parameters: 1) Explicitly input k, ε, ω, or Reynolds stress components (this is the only method that allows for profile definition). Note by default, the Fluent GUI enters k=1 [m²/s²] and =1 [m²/s³]. These values MUST be changed, they are unlikely to be correct for your simulation. 2) Turbulence intensity and length scale. Length scale is related to size of large eddies that contain most of energy. For boundary layer flows: l 0.4δ 99. For flows downstream of grid: l opening size. 3) Turbulence intensity and hydraulic diameter (primarily for internal flows). 4) Turbulence intensity and viscosity ratio (primarily for external flows). The default setting is turbulent intensity=5% and turbulent viscosity ratio=10. This should be reasonable for many flows if more precise information not available. Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

29 Inlet Turbulence Conditions If you have absolutely no idea of the turbulence levels in your simulation, you could use following values of turbulence intensities and viscosity ratios: Usual turbulence intensity ranges from 1% to 5%. The default turbulence intensity value of (that is, 3.7%) is sufficient for nominal turbulence through a circular inlet, and is a good estimate in the absence of experimental data. For external flows, turbulent viscosity ratio of 1 10 is typically a good value. For internal flows, turbulent viscosity ratio of it typically a good value. For fully developed pipe flow at Re=50,000, the turbulent viscosity ratio is around 100. Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

30 Model RANS Turbulence Model Usage Behavior and Usage Spalart Allmaras Economical for large meshes. Performs poorly for 3D flows, free shear flows, flows with strong separation. Suitable for mildly complex (quasi 2D) external/internal flows and boundary layer flows under pressure gradient (e.g. airfoils, wings, airplane fuselages, missiles, ship hulls). Standard k ε Realizable k ε* RNG k ε Standard k ω SST k ω* RSM Robust. Widely used despite the known limitations of the model. Performs poorly for complex flows involving severe pressure gradient, separation, strong streamline curvature. Suitable for initial iterations, initial screening of alternative designs, and parametric studies. Suitable for complex shear flows involving rapid strain, moderate swirl, vortices, and locally transitional flows (e.g. boundary layer separation, massive separation, and vortex shedding behind bluff bodies, stall in wide angle diffusers, room ventilation). Offers largely the same benefits and has similar applications as Realizable. Possibly harder to converge than Realizable. Superior performance for wall bounded boundary layer, free shear, and low Reynolds number flows. Suitable for complex boundary layer flows under adverse pressure gradient and separation (external aerodynamics and turbomachinery). Can be used for transitional flows (though tends to predict early transition). Separation is typically predicted to be excessive and early. Offers similar benefits as standard k ω. Dependency on wall distance makes this less suitable for free shear flows. Physically the most sound RANS model. Avoids isotropic eddy viscosity assumption. More CPU time and memory required. Tougher to converge due to close coupling of equations. Suitable for complex 3D flows with strong streamline curvature, strong swirl/rotation (e.g. curved duct, rotating flow passages, swirl combustors with very large inlet swirl, cyclones). * Recommended choice for standard cases 2012 ANSYS, Inc. September 19, Release 14.5

31 RANS Turbulence Model Descriptions Model Spalart Allmaras Standard k ε RNG k ε Realizable k ε Standard k ω SST k ω RSM Description A single transport equation model solving directly for a modified turbulent viscosity. Designed specifically for aerospace applications involving wall bounded flows on a fine near wall mesh. Fluent s implementation allows the use of coarser meshes. Option to include strain rate in k production term improves predictions of vortical flows. The baseline two transport equation model solving for k and ε. This is the default k ε model. Coefficients are empirically derived; valid for fully turbulent flows only. Options to account for viscous heating, buoyancy, and compressibility are shared with other k ε models. A variant of the standard k ε model. Equations and coefficients are analytically derived. Significant changes in the ε equation improves the ability to model highly strained flows. Additional options aid in predicting swirling and low Reynolds number flows. A variant of the standard k ε model. Its "realizability" stems from changes that allow certain mathematical constraints to be obeyed which ultimately improves the performance of this model. A two transport equation model solving for k and ω, the specific dissipation rate (ε / k) based on Wilcox (1998). This is the default k ω model. Demonstrates superior performance for wall bounded and low Reynolds number flows. Shows potential for predicting transition. Options account for transitional, free shear, and compressible flows. A variant of the standard k ω model. Combines the original Wilcox model for use near walls and the standard k ε model away from walls using a blending function. Also limits turbulent viscosity to guarantee that τ T ~ k. The transition and shearing options are borrowed from standard k ω. No option to include compressibility. Reynolds stresses are solved directly using transport equations, avoiding isotropic viscosity assumption of other models. Use for highly swirling flows. Quadratic pressure strain option improves performance for many basic shear flows ANSYS, Inc. September 19, Release 14.5

32 Summary Turbulence Modeling Guidelines Successful turbulence modeling requires engineering judgment of: Flow physics. Computer resources available. Project requirements. Accuracy. Turnaround time. Choice of Near wall treatment. Modeling procedure 1. Calculate characteristic Reynolds number and determine whether flow is turbulent. 2. If the flow is in the transition (from laminar to turbulent) range, consider the use of one of the turbulence transition models (not covered in this training). 3. Estimate wall adjacent cell centroid y + before generating the mesh. 4. Prepare your mesh to use wall functions except for low Re flows and/or flows with complex near wall physics (non equilibrium boundary layers). 5. Begin with RKE (Realizable k ε) and change to S A, RNG, SKW, or SST if needed. Check the tables on previous slides as a guide for your choice. 6. Use RSM for highly swirling, 3 D, rotating flows. 7. Remember that there is no single, superior turbulence model for all flows! Introduction Theory Models Near Wall Treatments Inlet BCs Summary 2012 ANSYS, Inc. September 19, Release 14.5

33 Introduction Part 2. Lecture Theme: The problem definition for all Heat CFD simulations Transfer includes boundary conditions, cell zone conditions and material properties. The accuracy of the simulation results depends on defining these properly. Learning Aims: You will learn: How to define material properties. The different boundary condition types in FLUENT and how to use them. How to define cell zone conditions in FLUENT including solid zones and porous media. How to specify well posed boundary conditions. Learning Objectives: You will know how to perform these essential steps in setting up a CFD analysis. Introduction Material Properties Cell Zone Conditions Boundary Conditions Summary 2012 ANSYS, Inc. September 19, Release 14.5

34 Lecture Theme: Introduction Heat transfer has broad applications across all industries. All modes of heat transfer (conduction, convection forced and natural, radiation, phase change) can be modeled in Fluent and solution data can be used as input for one way thermal FSI simulations. Learning Aims: You will learn: How to treat conduction, convection (forced and natural) and radiation in Fluent. How to set wall thermal boundary conditions. How to export solution data for use in a thermal stress analysis (one way FSI). Learning Objectives: You will be familiar with Fluent s heat transfer modeling capabilities and be able to set up and solve problems involving all modes of heat transfer. Intro. Energy Equation Wall BCs Applications 1 way Thermal FSI Summary 2012 ANSYS, Inc. September 19, Release 14.5

35 Heat Transfer Modeling in Fluent All modes of heat transfer can be taken into account in the CFD simulation: Conduction. Convection (forced and natural). Fluid solid conjugate heat transfer. Radiation. Interphase energy source (phase change). Viscous dissipation. Species diffusion. Intro. Energy Equation Wall BCs Applications 1 way Thermal FSI Summary 2012 ANSYS, Inc. September 19, Release 14.5

36 Enabling Heat Transfer To model heat transfer, the energy equation must be activated. "Define>Models>Energy"=ON. Intro. Energy Equation Wall BCs Applications 1 way Thermal FSI Summary 2012 ANSYS, Inc. September 19, Release 14.5

37 Energy Equation Introduction Energy transport equation: Unsteady Convection Conduction Species Diffusion Viscous Dissipation Enthalpy Source/Sink Energy E per unit mass is defined as: Pressure work and kinetic energy are always accounted for with compressible flows or when using the density based solvers. For the pressure based solver, they are omitted and can be added through a text command: The TUI command define/models/energy? will give more options when enabling the energy equation. Intro. Energy Equation Wall BCs Applications 1 way Thermal FSI Summary 2012 ANSYS, Inc. September 19, Release 14.5

38 Governing Equation : Convection As a fluid moves, it carries heat with it this is called convection. Thus, heat transfer can be tightly coupled to the fluid flow solution. Energy + Fluid flow equations activated means Convection is computed. Additionally: The rate of heat transfer is strongly dependent of fluid velocity. Fluid properties may vary significantly with temperature (e.g., air). At walls, heat transfer coefficient is computed by the turbulent thermal wall functions. T h T body q q h ( Tbody T ) ht average heat transfer coefficient (W/m 2 K) Intro. Energy Equation Wall BCs Applications 1 way Thermal FSI Summary 2012 ANSYS, Inc. September 19, Release 14.5

39 Governing Equation: Conduction Conduction heat transfer is governed by Fourier s Law. Fourier s law states that the heat transfer rate is directly proportional to the gradient of temperature. Mathematically, qconduction k T Thermal conductivity The constant of proportionality is the thermal conductivity (k). k may be a function of temperature, space, etc. for isotropic materials, k is a constant value. for anisotropic materials, k is a matrix. Intro. Energy Equation Wall BCs Applications 1 way Thermal FSI Summary 2012 ANSYS, Inc. September 19, Release 14.5

40 Governing Equation: Viscous Dissipation Energy source due to viscous dissipation: Also called viscous heating. Often negligible, especially in incompressible flow. Important when viscous shear in fluid is large (e.g., lubrication) and/or in high velocity, compressible flows. Important when Brinkman number approaches or exceeds unity: 2 Ue Br kt Intro. Energy Equation Wall BCs Applications 1 way Thermal FSI Summary 2012 ANSYS, Inc. September 19, Release 14.5

41 Thermal Wall Boundary Conditions Six thermal conditions at Walls: Heat Flux. Temperature. Convection simulates an external convection environment which is not modeled (user prescribed heat transfer coefficient). q conv h ext ( T T ) w ext Radiation simulates an external radiation environment which is not modeled (user prescribed external emissivity and radiation temperature). q rad ext ( T 4 T 4 w Mixed Combination of Convection and Radiation boundary conditions. q h ( T T ) ) 4 4 mixed ext ext w ext ( T Tw ) Via System Coupling Can be used when Fluent is coupled with another system in Workbench using System Couplings. Intro. Energy Equation Wall BCs Applications 1 way Thermal FSI Summary 2012 ANSYS, Inc. September 19, Release 14.5

42 Conjugate Heat Transfer (CHT) At Fluid/Solid or Fluid/Fluid interface, a wall/wall_shadow is created automatically by Fluent while reading the mesh file. By default energy is balanced automatically on the two sides of the walls. Possibility to uncouple and to specify different thermal conditions on each side. Grid Velocity Vectors Temperature Contours Coolant Flow Past Heated Rods Intro. Energy Equation Wall BCs Applications 1 way Thermal FSI Summary 2012 ANSYS, Inc. September 19, Release 14.5

43 Convection Convection heat transfer results from fluid motion. Heat transfer rate can be closely coupled to the fluid flow solution. The rate of heat transfer is always strongly dependent on fluid velocity and fluid properties (uncoupled equations can solve energy after flow solution). Fluid properties may vary significantly with temperature (coupled equations). There are three types of convection. Natural convection: fluid moves due to buoyancy effects. Boiling convection: body is hot enough to cause fluid phase change. Forced convection: flow is induced by some external means. Example: When cold air flows past a warm body, it draws away warm air near the body and replaces it with cold air. Flow and heat transfer past a heated block. Intro. Energy Equation Wall BCs Applications 1 way Thermal FSI Summary 2012 ANSYS, Inc. September 19, Release 14.5

44 Heat Transfer Coefficient In general, h is not constant but is usually a function of temperature gradient. There are three types of convection. Natural Convection Fluid moves due to buoyancy effects. 1/ 4 1/3 h T, h T (Laminar) (Turbulent) T hot T cold Typical values of h (W/m 2 K) 4 4,000 Forced Convection Flow is induced by some external means. T cold h f ( T) T hot 10 75,000 Boiling Convection Body is hot enough to cause fluid phase change. h T 2 T cold ,000 T hot 2012 ANSYS, Inc. September 19, Release 14.5

45 Natural Convection: Gravity Reference Density Momentum equation along the direction of gravity (z in this case). W P UW 2 W abs g t z In Fluent, a variable change is done for the pressure field as soon as gravity is enabled. Hydrostatic reference pressure head and operating pressure are removed from pressure field. Momentum equation becomes. W t P P P g z abs operating 0 P z 2 UW W g where P' is the static gauge pressure used by Fluent for boundary conditions and post processing. This pressure transformation avoids round off error and simplifies the setup of pressure boundary conditions. 0 Intro. Energy Equation Wall BCs Applications 1 way Thermal FSI Summary 2012 ANSYS, Inc. September 19, Release 14.5

46 Radiation Radiative heat transfer is a mode of energy transfer where the energy is transported via electromagnetic waves. Thermal radiation covers the portion of the electromagnetic spectrum from 0.1 to 100 m. Visible Ultraviolet Infrared rays X rays Thermal Radiation Microwaves log 10 (Wavelength), m Solar load (HVAC) Headlight Glass furnace For semi transparent bodies (e.g., glass, combustion product gases), radiation is a volumetric phenomenon since emissions can escape from within bodies. For opaque bodies, radiation is essentially a surface phenomena since nearly all internal emissions are absorbed within the body. Intro. Energy Equation Wall BCs Applications 1 way Thermal FSI Summary 2012 ANSYS, Inc. September 19, Release 14.5

47 When to Include Radiation? Radiation effects should be accounted for if: q rad T 4 max T 4 min Stefan Boltzmann constant W/(m 2 K 4 ) is of the same order or magnitude than the convective and conductive heat transfer rates. This is usually true at high temperatures but can also be true at lower temperatures, depending on the application. Estimate the magnitude of conduction or convection heat transfer in the system as: q conv h T wall T bulk Compare q rad with q conv. Intro. Energy Equation Wall BCs Applications 1 way Thermal FSI Summary 2012 ANSYS, Inc. September 19, Release 14.5

48 Optical Thickness and Radiation Modeling The optical thickness should be determined before choosing a radiation model. Optical Thickness (a+ s )L a= absorption coefficient. s =scattering coefficient (often=0). L= mean beam length. a Absorption Coefficient (m 1 ) (Note: Absorptivity of a Surface). L Mean beam length (m) (a typical distance between 2 opposing walls). Optically thin means that the fluid is transparent to the radiation at wavelengths where the heat transfer occurs. The radiation only interacts with the boundaries of the domain. Optically thick/dense means that the fluid absorbs and re emits the radiation. Intro. Energy Equation Wall BCs Applications 1 way Thermal FSI Summary 2012 ANSYS, Inc. September 19, Release 14.5

49 Choosing a Radiation Model The radiation model selected must be appropriate for the optical thickness of the system being simulated. Available Model In terms of accuracy, DO and DTRM are most accurate. S2S is accurate for optical thickness = 0. Optical Thickness Surface to surface model (S2S) 0 Solar load model 0 (except window panes) Rosseland > 5 P 1 > 1 Discrete ordinates model (DO) Discrete Transfer Method (DTRM) All All Intro. Energy Equation Wall BCs Applications 1 way Thermal FSI Summary 2012 ANSYS, Inc. September 19, Release 14.5

50 Additional Factors in Radiation Modeling Additional guidelines for radiation model selection: Scattering. Scattering is accounted for only with P1 and DO. Particulate effects. P1 and DOM account for radiation exchange between gas and particulates. Localized heat sources. S2S is the best. DTRM/DOM with a sufficiently large number of rays/ ordinates is most appropriate for domain with absorbing media. Intro. Energy Equation Wall BCs Applications 1 way Thermal FSI Summary 2012 ANSYS, Inc. September 19, Release 14.5

51 Phase Change Heat released or absorbed when matter changes state. There are many different forms of phase change. Condensation. Evaporation. Boiling. Melting/Solidification. Multiphase models and/or UDFs are needed to properly model these phenomena. Contours of vapor volume fraction for boiling in a nuclear fuel assembly calculated with the Eulerian multiphase model. Tracks from evaporating liquid pentane droplets and temperature contours for pentane combustion with the non premixed combustion model. Intro. Energy Equation Wall BCs Applications 1 way Thermal FSI Summary 2012 ANSYS, Inc. September 19, Release 14.5

52 Summary After activating heat transfer, you must provide: Thermal conditions at walls and flow boundaries. Fluid properties for energy equation. Available heat transfer modeling options include: Species diffusion heat source. Combustion heat source. Conjugate heat transfer. Natural convection. Radiation. Periodic heat transfer. Double precision solver usually needed to balance accurately the heat transfer rate inside the domain. Intro. Energy Equation Wall BCs Applications 1 way Thermal FSI Summary 2012 ANSYS, Inc. September 19, Release 14.5

53 Introduction Part 3. Lecture Theme: The problem definition for all Transient CFD simulations Calculations includes boundary conditions, cell zone conditions and material properties. The accuracy of the simulation results depends on defining these properly. Learning Aims: You will learn: How to define material properties. The different boundary condition types in FLUENT and how to use them. How to define cell zone conditions in FLUENT including solid zones and porous media. How to specify well posed boundary conditions. Learning Objectives: You will know how to perform these essential steps in setting up a CFD analysis. Introduction Material Properties Cell Zone Conditions Boundary Conditions Summary 2012 ANSYS, Inc. September 19, Release 14.5

54 Lecture Theme: Introduction Performing a transient calculation is in some ways similar to performing a steady state calculation, but there are additional considerations. More data is generated and extra inputs are required. This lecture will explain these inputs and describe transient data post processing. Learning Aims: You will learn: How to set up and run transient calculations in Fluent. How to choose the appropriate time step size for your calculation. How to post process transient data and make animations. Learning Objectives: Transient flow calculations are becoming increasingly common due to advances in High Performance Computing (HPC) and reductions in hardware costs. You will understand what transient calculations involve and be able to perform them with confidence. Introduction Unsteady Flow Time Step Setup Post Processing Summary 2012 ANSYS, Inc. September 19, Release 14.5

55 Motivation Nearly all flows in nature are unsteady! Steady state assumption is possible if we: Ignore unsteady fluctuations. Employ ensemble/time averaging to remove unsteadiness. This is what is done in modeling RANS turbulence. In CFD, steady state methods are preferred. Lower computational cost. Easier to post process and analyze. Many applications require resolution of unsteady flow: Aerodynamics (aircraft, land vehicles, etc.) vortex shedding. Rotating Machinery rotor/stator interaction, stall, surge. Multiphase Flows free surfaces, bubble dynamics. Deforming Domains in cylinder combustion, store separation. Unsteady Heat Transfer transient heating and cooling. Many more Introduction Unsteady Flow Time Step Setup Post Processing Summary 2012 ANSYS, Inc. September 19, Release 14.5

56 Origins of Unsteady Flow Natural unsteadiness. Unsteady flow due to growth of instabilities within the fluid or a non equilibrium initial fluid state. Examples: natural convection flows, turbulent eddies of all scales, fluid waves (gravity waves, shock waves). Forced unsteadiness. Time dependent boundary conditions, source terms drive the unsteady flow field. Examples: pulsing flow in a nozzle, rotor stator interaction in a turbine stage. Kelvin Helmholtz Cloud Instability. Rotor Stator Interaction in an Axial Compressor. Introduction Unsteady Flow Time Step Setup Post Processing Summary 2012 ANSYS, Inc. September 19, Release 14.5

57 Unsteady CFD Analysis [1] Simulate a transient flow field over a specified time period. Solution may approach: Steady state solution: Flow variables stop changing with time. Time periodic solution: Flow variables fluctuate with repeating pattern. Your goal may also be simply to analyze the flow over a prescribed time interval. Free surface flows. Moving shock waves. Extract quantities of interest. Natural frequencies (e.g. Strouhal Number). Time averaged and/or RMS values. Time related parameters (e.g. time required to cool a hot solid, residence time of a pollutant). Spectral data Fourier Transform (FT). Introduction Unsteady Flow Time Step Setup Post Processing Summary 2012 ANSYS, Inc. September 19, Release 14.5

58 Residual Unsteady CFD Analysis [2] Transient simulations are solved by computing a solution for many discrete points in time. At each time point we must iterate & converge to the solution. Time step size = 2 [s] Initial Time = 0 [s] Total Time = 20 [s] Number of time steps = Time (seconds) Several iterations per time step. Introduction Unsteady Flow Time Step Setup Post Processing Summary 2012 ANSYS, Inc. September 19, Release 14.5

59 Convergence Behavior Residual plots for transient simulations are not always indicative of a converged solution. You should select the time step size such that the residuals reduce by around three orders of magnitude within one time step. This will ensure accurate resolution of transient behavior. For smaller time steps, residuals may only drop by 1 2 orders of magnitude look for a monotonic decrease throughout the time step. A residual plot for a simple transient calculation is shown here. Introduction Unsteady Flow Time Step Setup Post Processing Summary 2012 ANSYS, Inc. September 19, Release 14.5

60 Selecting the Transient Time Step Size [1] The time step size is an important parameter in transient simulations. t must be small enough to resolve time dependent features Variable of interest. True solution. Time step too large to resolve transient changes. Note the solution points generally will not lie on the true solution because the true behaviour has not been resolved. t Time Variable of interest. A smaller time step can resolve the true solution. At least, t per period. t Time Introduction Unsteady Flow Time Step Setup Post Processing Summary 2012 ANSYS, Inc. September 19, Release 14.5

61 Selecting the Transient Time Step Size [2] and it must be small enough to maintain solver stability. The quantity of interest may be changing very slowly (e.g. temperature in a solid), but you may not be able to use a large time step if other quantities (e.g. velocity) have smaller timescales. The Courant Number is often used to estimate a time step: Characteristic flow velocity t Courant Number Typical Cell Size This gives the number of mesh elements the fluid passes through in one time step. Typical values are 1 10, but in some cases higher values are acceptable. Introduction Unsteady Flow Time Step Setup Post Processing Summary 2012 ANSYS, Inc. September 19, Release 14.5

62 Selecting the Transient Time Step Size [3] Tips & Tricks for the estimation of the time step: Usual Case: Restrictive but safe for convergence with L=cell characteristic size, V=characteristic velocity. Turbomachinery: 1 L t. 3 V 1 t. 10 Number of Blades Rotational Velocity Natural Convection: t L (g.. T.L) 1/2 Conduction in solids: t L 2. Cp L = Characteristic length V = Characteristic velocity A smaller time step will typically improve convergence. Introduction Unsteady Flow Time Step Setup Post Processing Summary 2012 ANSYS, Inc. September 19, Release 14.5

63 Transient Flow Modeling Workflow Similar set up as steady state simulation, then: 1. Enable the unsteady solver. 2. Set up physical models and boundary conditions as usual. Transient boundary conditions are possible you can use either a UDF or profile to accomplish this. 3. Prescribe initial conditions, according to the type of transient flow: Time History : Cannot be any guess; must be what is the situation at time t=0 [s]. Steady State or Cyclic: Best to use a physically realistic initial condition, such as a steady solution. 4. Assign solver settings and configure solution monitors. 5. Configure animations and data output/sampling options. 6. Select time step size and max iterations per time step. 7. Prescribe the number of time steps. 8. Run the calculations (Iterate). Introduction Unsteady Flow Time Step Setup Post Processing Summary 2012 ANSYS, Inc. September 19, Release 14.5

64 Enabling the Transient Solver To enable the unsteady solver, select the Transient button on the General problem setup form. Introduction Unsteady Flow Time Step Setup Post Processing Summary 2012 ANSYS, Inc. September 19, Release 14.5

65 Set Up Time Step Size Set the time step size. This controls the spacing in time between the solution points. Options are: Number of time steps. Maximum number of iterations per time step. Introduction Unsteady Flow Time Step Setup Post Processing Summary 2012 ANSYS, Inc. September 19, Release 14.5

66 Non Iterative Time Advancement Non iterative Time Advancement (NITA) is available for faster computation time (not always guaranteed). NITA runs about 2x to 10x as fast as ITA scheme. Limitations: Available with pressure based solvers only. NITA schemes are not available for multiphase (except VOF), reacting flows, radiation models, porous media, fan models, etc. Consult the Appendix and Fluent Documentation for additional details. Introduction Unsteady Flow Time Step Setup Post Processing Summary 2012 ANSYS, Inc. September 19, Release 14.5

67 Unsteady Flow Modeling Options Adaptive Time Stepping. Automatically adjusts time step size based on local truncation error analysis. Customization possible via UDF. Extrapolate Variables. Speed up the transient solution by reducing required sub iteration. Using Taylor series expansion solution will be extrapolated to the next time level to improve the predicted initial value. Data Sampling for Time Statistics. Particularly useful for LES turbulence calculations. Introduction Unsteady Flow Time Step Setup Post Processing Summary 2012 ANSYS, Inc. September 19, Release 14.5

68 Residuals Initialization Physically realistic initial conditions should be used. A converged steady state solution is often used as the starting point (for cyclic or steady state flows). If a transient simulation is started from an approximate initial guess, the initial transient will not be accurate. The first few time steps may not converge. A smaller time step may be needed initially to maintain solver stability. For cyclic behavior the first few cycles can be ignored until a repeatable pattern is obtained Time (seconds) Introduction Unsteady Flow Time Step Setup Post Processing Summary 2012 ANSYS, Inc. September 19, Release 14.5

69 Tips for Success in Transient Flow Modeling With Pressure based Solvers, use PISO scheme for Pressure Velocity Coupling: this scheme provides faster convergence for unsteady flows than the standard SIMPLE approach. Select the number of iterations per time step to be around 20. It is better (faster) to reduce the time step size than to do too many iterations per time step. Remember that accurate initial conditions are as important as boundary conditions for unsteady problems. Initial condition should always be physically realistic! To iterate without advancing in time, specify zero time steps. This will instruct the solver to converge the current time step only. Introduction Unsteady Flow Time Step Setup Post Processing Summary 2012 ANSYS, Inc. September 19, Release 14.5

70 Unsteady Flow Modeling Animations [1] You must set up any animations BEFORE performing iterations. Animation frames are written/stored on the fly during calculations. Introduction Unsteady Flow Time Step Setup Post Processing Summary 2012 ANSYS, Inc. September 19, Release 14.5

71 CFD Post: Fourier Transform FT can be applied to signals to extract frequency data. Original Signal. FT of Signal Showing Dominant Frequency. Introduction Unsteady Flow Time Step Setup Post Processing Summary 2012 ANSYS, Inc. September 19, Release 14.5

72 Summary No matter what solver is being used. The time step size will be determined by the minimum of: The value at which the solution will converge. The value needed to resolve mean flow physical time scales (e.g. vortex shedding frequency given by Strouhal number) and/or turbulent eddies (Courant number 1). The solution must converge at every time step. Non convergence within the very first steps may be acceptable when there is a non physical initial condition. If the solution is not converging, it is almost always more efficient to reduce the time step size. Solution monitors are an important tool for ensuring the solution is correct. Watch out for physically unrealistic behavior of monitored variables. Second order temporal discretization is almost always preferred. Introduction Unsteady Flow Time Step Setup Post Processing Summary 2012 ANSYS, Inc. September 19, Release 14.5