Turbulence 9-1 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 Training Manual 9-1 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 Chapter 9 Turbulence Introduction to CFX Turbulence 9-2 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 Training Manual What is Turbulence? Unsteady, irregular (non-periodic) motion in which transported quantities (mass, momentum, scalar species) fluctuate in time and space Identifiable swirling patterns characterize turbulent eddies Enhanced mixing (matter, momentum, energy, etc.) results Fluid properties and velocity exhibit random variations Statistical averaging results in accountable, turbulence related transport mechanisms This characteristic allows for turbulence modeling Contains a wide range of turbulent eddy sizes (scales spectrum) The size/velocity of large eddies is on the order of the mean flow Large eddies derive energy from the mean flow Energy is transferred from larger eddies to smaller eddies In the smallest eddies, turbulent energy is converted to internal energy by viscous dissipation Turbulence 9-3 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 Training Manual Is the Flow Turbulent? External Flows Internal Flows Natural Convection along a surface around an obstacle where where Other factors such as free-stream turbulence, surface conditions, and disturbances may cause transition to turbulence at lower Reynolds numbers is the Rayleigh number is the Prandtl number Flows can be characterized by the Reynolds Number, Re Turbulence 9-4 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 Training Manual Observation by O. Reynolds Laminar (Low Reynolds Number) Transition (Increasing Reynolds Number) Turbulent (Higher Reynolds Number) Turbulence 9-5 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 Training Manual Turbulent Flow Structures Energy Cascade Richardson (1922) Small structures Large structures Turbulence 9-6 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 Training Manual Governing Equations Conservation Equations Continuity Momentum Energy where Note that there is no turbulence equation in the governing Navier-Stokes equations! Turbulence 9-7 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 Training Manual Overview of Computational Approaches Direct Numerical Simulation (DNS) Theoretically, all turbulent (and laminar / transition) flows can be simulated by numerically solving the full Navier-Stokes equations Resolves the whole spectrum of scales. No modeling is required But the cost is too prohibitive! Not practical for industrial flows Large Eddy Simulation (LES) type models 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 Reynolds-Averaged Navier-Stokes (RANS) models 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 calculating industrial flows There is not yet a single, practical turbulence model that can reliably predict all turbulent flows with sufficient accuracy Turbulence 9-8 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 Training Manual RANS Modeling Time Averaging Ensemble (time) averaging may be used to extract the mean flow properties from the instantaneous ones The instantaneous velocity, ui, is split into average and fluctuating components The Reynolds-averaged momentum equations are as follows 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 Fluctuating component Time-average component Example: Fully-Developed Turbulent Pipe Flow Velocity Profile Instantaneous component (Reynolds stress tensor) Turbulence 9-9 ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009 Inventory #002598 Training Manual RANS Modeling The Closure Problem Closure problem: Relate the unknown Reynolds Stresses to the known mean flow variables through new equations The new equations are the turbulence model Equations can be: Algebraic Transport equations 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 Turbulence 9-10 ANSYS