8.5 Turbulence modeling in CFD
7 min read•august 20, 2024
Turbulence modeling in CFD tackles the complex, chaotic nature of fluid motion. It's crucial for predicting fluid behavior in engineering applications like and heat transfer. Various approaches, from DNS to RANS, offer different levels of detail and computational cost.
Turbulence models face challenges in balancing accuracy with efficiency. RANS models are widely used but have limitations in complex flows. LES and hybrid methods aim to improve accuracy while managing computational demands. Validation against experiments and DNS is essential for assessing model reliability.
Turbulence in fluid dynamics
- Turbulence is a complex and chaotic state of fluid motion characterized by irregular fluctuations in velocity, pressure, and other flow properties
- Understanding and modeling turbulence is crucial for accurately predicting fluid behavior in various engineering applications (aerodynamics, combustion, and heat transfer)
- Turbulence poses significant challenges in computational fluid dynamics (CFD) due to its multiscale nature and the need for high-resolution simulations
Characteristics of turbulent flows
Randomness and irregularity
Top images from around the web for Randomness and irregularity
WES - Laminar-turbulent transition characteristics of a 3-D wind turbine rotor blade based on ... View original
Is this image relevant?
Computational fluid dynamics modelling in cardiovascular medicine | Heart View original
Is this image relevant?
WES - Laminar-turbulent transition characteristics of a 3-D wind turbine rotor blade based on ... View original
Is this image relevant?
Computational fluid dynamics modelling in cardiovascular medicine | Heart View original
Is this image relevant?
1 of 2
Top images from around the web for Randomness and irregularity
WES - Laminar-turbulent transition characteristics of a 3-D wind turbine rotor blade based on ... View original
Is this image relevant?
Computational fluid dynamics modelling in cardiovascular medicine | Heart View original
Is this image relevant?
WES - Laminar-turbulent transition characteristics of a 3-D wind turbine rotor blade based on ... View original
Is this image relevant?
Computational fluid dynamics modelling in cardiovascular medicine | Heart View original
Is this image relevant?
1 of 2
- Turbulent flows exhibit random and chaotic fluctuations in velocity and pressure fields
- These fluctuations occur over a wide range of length and time scales, making turbulence inherently unpredictable
- The irregular nature of turbulence makes it challenging to describe and model mathematically
Diffusivity and mixing
- Turbulence enhances the mixing and transport of momentum, heat, and mass within the fluid
- The increased diffusivity in turbulent flows leads to rapid mixing and homogenization of fluid properties
- Turbulent mixing plays a crucial role in various applications (combustion, chemical reactions, and heat exchange)
Dissipation and energy cascade
- Turbulence is characterized by an energy cascade, where kinetic energy is transferred from large scales to smaller scales
- At the smallest scales, viscous dissipation converts kinetic energy into heat, ultimately dissipating the turbulent energy
- The of is an important parameter in turbulence modeling
Approaches to turbulence modeling
Direct numerical simulation (DNS)
- DNS involves solving the without any turbulence modeling assumptions
- It resolves all scales of turbulent motion, from the largest eddies down to the Kolmogorov microscales
- DNS requires extremely fine spatial and temporal resolution, making it computationally expensive and limited to low flows
Large eddy simulation (LES)
- LES directly resolves the large-scale turbulent eddies while modeling the effects of smaller scales using subgrid-scale (SGS) models
- It captures the important energy-containing scales of turbulence while reducing computational cost compared to DNS
- LES is suitable for high Reynolds number flows and provides more detailed information than RANS models
Reynolds-averaged Navier-Stokes (RANS)
- RANS models solve the time-averaged Navier-Stokes equations, where the turbulent fluctuations are modeled using turbulence closure models
- RANS models introduce additional transport equations for turbulent quantities (turbulent kinetic energy, dissipation rate)
- These models are computationally efficient and widely used in engineering applications, but they rely on empirical assumptions and have limitations in capturing complex turbulent flows
RANS turbulence models
Spalart-Allmaras model
- The Spalart-Allmaras model is a one-equation turbulence model that solves a transport equation for the turbulent viscosity
- It was developed for aerodynamic flows and has been widely used in the aerospace industry
- The model is known for its robustness and good performance in wall-bounded flows
k-epsilon models
- k-epsilon models are two-equation turbulence models that solve transport equations for the turbulent kinetic energy () and its dissipation rate ()
- The standard is widely used in industrial CFD applications due to its simplicity and reasonable accuracy
- Variants of the k-epsilon model (realizable, RNG) have been developed to improve performance in specific flow scenarios
k-omega models
- k-omega models are two-equation turbulence models that solve transport equations for the turbulent kinetic energy () and the specific dissipation rate ()
- The standard is known for its superior performance in near-wall regions and its ability to handle adverse pressure gradients
- The SST (Shear Stress Transport) k-omega model combines the advantages of k-epsilon and k-omega models, making it suitable for a wide range of flows
Reynolds stress models
- Reynolds stress models (RSM) solve transport equations for the individual components of the Reynolds stress tensor
- RSM models provide a more detailed description of the turbulent stress field compared to eddy-viscosity models
- They can capture anisotropic turbulence and complex flow phenomena, but they are computationally expensive and require careful numerical treatment
LES turbulence models
Smagorinsky model
- The Smagorinsky model is a simple and widely used subgrid-scale (SGS) model for LES
- It models the SGS stresses using an eddy-viscosity approach, where the eddy viscosity is proportional to the local strain rate and a model constant
- The model constant is typically determined empirically and may require tuning for different flow scenarios
Dynamic Smagorinsky model
- The dynamic Smagorinsky model overcomes the limitations of the constant model coefficient by dynamically computing it based on the resolved flow field
- It uses a test filter to determine the model coefficient, adapting it to the local flow conditions
- The dynamic model improves the accuracy and robustness of LES, especially in complex flows with varying turbulence characteristics
Wall-adapting local eddy-viscosity (WALE) model
- The WALE model is an SGS model designed to improve the near-wall behavior of LES
- It accounts for the correct scaling of the eddy viscosity near the wall, avoiding the need for damping functions
- The WALE model is particularly suitable for wall-bounded flows and has been shown to provide accurate results in complex geometries
Hybrid RANS-LES methods
Detached eddy simulation (DES)
- DES is a hybrid approach that combines RANS modeling in attached boundary layers with LES in separated regions
- It uses a RANS model (usually Spalart-Allmaras) near the wall and switches to LES in regions where the turbulent length scale exceeds the local grid spacing
- DES aims to leverage the strengths of both RANS and LES while reducing computational cost compared to full LES
Delayed detached eddy simulation (DDES)
- DDES is an improvement over the original DES formulation to address the issue of grid-induced separation
- It introduces a shielding function that delays the switch from RANS to LES mode, ensuring that the remains in RANS mode
- DDES provides a more robust and grid-independent hybrid RANS-LES approach
Improved delayed detached eddy simulation (IDDES)
- IDDES further enhances the DDES formulation by including wall-modeled LES (WMLES) capabilities
- It allows for a seamless transition between RANS, LES, and WMLES depending on the local flow conditions and grid resolution
- IDDES offers improved accuracy and flexibility in simulating complex turbulent flows with varying levels of wall resolution
Boundary conditions for turbulence
Wall functions
- Wall functions are used to model the near-wall region in RANS and LES simulations
- They provide a simplified representation of the velocity and turbulence profiles in the viscous sublayer and buffer layer
- Wall functions help reduce the computational cost by allowing for coarser grid resolution near the wall
Low-Reynolds number approach
- The low-Reynolds number approach resolves the near-wall region using a fine grid resolution
- It directly solves the turbulence equations down to the wall, capturing the viscous sublayer and buffer layer
- This approach requires a high grid resolution near the wall and is computationally expensive, but it provides accurate results for wall-bounded flows
Turbulence model validation
Comparison with experimental data
- Validation of turbulence models involves comparing simulation results with experimental measurements
- Experimental data from wind tunnel tests, particle image velocimetry (PIV), and laser Doppler anemometry (LDA) are commonly used for validation
- Comparison with experimental data helps assess the accuracy and reliability of turbulence models in predicting real-world flows
Comparison with DNS results
- DNS provides a high-fidelity reference solution for turbulence model validation
- Comparing RANS and LES results with DNS data allows for a detailed assessment of the model's ability to capture turbulent flow features
- DNS data is particularly valuable for validating models in canonical flows (channel flow, isotropic turbulence) where experimental data may be limited
Limitations of turbulence models
Assumptions and simplifications
- Turbulence models rely on various assumptions and simplifications to close the governing equations
- RANS models assume a universal behavior of turbulence and rely on empirical constants that may not be valid for all flow scenarios
- LES models assume that the subgrid-scale turbulence can be adequately represented by simple models, which may not capture all the complex interactions
Accuracy vs computational cost
- There is a trade-off between the accuracy of turbulence models and their computational cost
- DNS provides the most accurate results but is computationally prohibitive for most engineering applications
- RANS models are computationally efficient but may lack accuracy in complex flows with strong unsteadiness, separation, or curvature
- LES offers a balance between accuracy and computational cost but still requires significant computational resources compared to RANS
Key Terms to Review (18)
Aerodynamics: Aerodynamics is the study of the behavior of air as it interacts with solid objects, particularly those that are in motion. This field focuses on understanding the forces and resulting motions caused by air flow, which is essential in designing vehicles, aircraft, and various structures to optimize performance and efficiency.
ANSYS Fluent: ANSYS Fluent is a powerful computational fluid dynamics (CFD) software used to simulate fluid flow, heat transfer, and chemical reactions in various engineering applications. This software offers a wide range of turbulence modeling options, enabling users to analyze complex fluid behavior in diverse scenarios such as aerodynamics, hydrodynamics, and heat exchangers. ANSYS Fluent's versatility and advanced features make it a critical tool for engineers seeking accurate and reliable simulation results in turbulence modeling.
Boundary Layer: A boundary layer is a thin region adjacent to a solid surface where fluid velocity changes from zero (due to the no-slip condition at the surface) to the free stream velocity of the fluid. This concept is essential for understanding the flow characteristics near surfaces and impacts various phenomena such as drag, heat transfer, and turbulence.
Direct numerical simulation (dns): Direct numerical simulation (DNS) is a computational approach used to solve the Navier-Stokes equations directly for fluid flow, capturing all the scales of motion without any turbulence modeling. This method provides highly accurate representations of both laminar and turbulent flows by resolving every detail of the fluid dynamics, allowing for a comprehensive understanding of flow behavior. DNS is crucial for studying complex turbulent flows and aids in validating turbulence models used in other simulations.
Dissipation Rate: Dissipation rate is a measure of the rate at which turbulent kinetic energy is converted into thermal energy due to viscous effects in a fluid. This concept is crucial in turbulence modeling as it helps quantify how energy dissipates in chaotic flow conditions, influencing the accuracy and efficiency of computational fluid dynamics (CFD) simulations. Understanding dissipation rate allows for better predictions of flow behavior, which is essential for designing engineering applications involving turbulence.
Flow Separation: Flow separation occurs when the boundary layer of fluid flowing over a surface detaches from that surface, resulting in a loss of smooth flow and the formation of vortices. This phenomenon is crucial in various applications as it influences drag, lift, and overall fluid behavior around objects. Understanding flow separation helps in predicting performance in diverse fields such as aerodynamics and hydrodynamics.
Hydrodynamics: Hydrodynamics is the study of fluids in motion, focusing on the behavior of liquids and gases and the forces acting upon them. It plays a crucial role in understanding phenomena such as vorticity, circulation, and the fundamental equations that govern fluid behavior, which are essential in both laminar and turbulent flow analysis.
K-epsilon model: The k-epsilon model is a widely used turbulence model in fluid dynamics that helps predict the behavior of turbulent flows by solving two transport equations: one for the turbulent kinetic energy (k) and another for its dissipation rate (epsilon). This model provides a balance between computational efficiency and accuracy, making it suitable for various engineering applications, especially in computational fluid dynamics (CFD). It connects to fundamental concepts in turbulence modeling, which is essential for understanding how fluids behave under turbulent conditions.
K-omega model: The k-omega model is a turbulence modeling approach used in computational fluid dynamics (CFD) that utilizes two transport equations: one for the turbulent kinetic energy (k) and another for the specific dissipation rate (ω). This model is particularly effective for simulating flow in boundary layers and is often used in applications where the effects of viscosity are significant, allowing for accurate predictions of turbulence characteristics in fluid flow scenarios.
Large eddy simulation (LES): Large eddy simulation (LES) is a computational technique used in fluid dynamics to model turbulent flows by resolving the large-scale turbulent structures while modeling the smaller scales. This approach strikes a balance between direct numerical simulation, which resolves all scales, and Reynolds-averaged methods, which apply statistical averaging. LES captures the essential dynamics of turbulence, making it valuable in understanding complex flow behaviors in various applications.
Navier-Stokes equations: The Navier-Stokes equations are a set of nonlinear partial differential equations that describe the motion of fluid substances. These equations are fundamental in fluid dynamics as they account for viscosity, conservation of momentum, and energy, allowing for the analysis of both laminar and turbulent flow behaviors.
OpenFOAM: OpenFOAM is an open-source computational fluid dynamics (CFD) toolbox used for simulating fluid flow, heat transfer, and chemical reactions in complex geometries. It provides a flexible platform for users to develop their own solvers and models, particularly useful in turbulence modeling, enabling the simulation of a wide range of fluid dynamics problems with customizable features.
Reynolds number: Reynolds number is a dimensionless quantity that helps predict flow patterns in different fluid flow situations by comparing inertial forces to viscous forces. It provides insight into whether a flow will be laminar or turbulent and is essential in understanding how fluids behave under varying conditions.
Reynolds-Averaged Navier-Stokes (RANS) Equations: The Reynolds-Averaged Navier-Stokes (RANS) equations are a set of equations used to describe the motion of fluid substances, particularly in turbulent flows, by averaging the effects of turbulence over time. These equations simplify the complex behavior of turbulent flows by separating the mean flow characteristics from the fluctuating components, allowing for more manageable computations in fluid dynamics simulations. RANS is particularly important for understanding turbulent boundary layers and forms the foundation for many turbulence modeling approaches in computational fluid dynamics (CFD).
Strouhal Number: The Strouhal number is a dimensionless quantity used in fluid dynamics to characterize oscillating flow mechanisms. It represents the ratio of inertial forces to elastic forces in a flow field and is particularly useful in analyzing unsteady flows such as vortex shedding behind bluff bodies. This number connects to various phenomena, helping to predict the behavior of fluid flow in diverse applications, including turbulence modeling and the solutions to the Navier-Stokes equations.
Turbulence intensity: Turbulence intensity is a measure of the fluctuating velocity components in a turbulent flow compared to the average flow velocity, often expressed as a percentage. This term highlights the level of turbulence present in a flow and plays a crucial role in understanding the behavior of fluid dynamics, influencing factors like mixing, energy dissipation, and drag forces.
Turbulent kinetic energy: Turbulent kinetic energy is the energy contained in the chaotic fluctuations of velocity in a turbulent flow. It is a crucial measure of the intensity of turbulence and relates to the dissipation of energy in fluid motion, impacting various phenomena such as mixing, drag, and flow stability. Understanding turbulent kinetic energy helps in analyzing and modeling complex fluid behavior, particularly in scenarios involving turbulence modeling, computational fluid dynamics (CFD), and atmospheric boundary layers.
Vortex Shedding: Vortex shedding is a fluid dynamics phenomenon where alternating vortices are formed and released from an object as fluid flows past it, leading to a periodic variation in pressure on the object's surface. This effect is crucial in understanding how objects interact with fluid flow and has significant implications in areas such as flow separation, turbulent boundary layers, turbulence modeling, and environmental turbulence, influencing both design and analysis in engineering applications.