8.3 Turbulence modeling in CFD
11 min read•august 20, 2024
Turbulence modeling in CFD is crucial for accurately simulating complex fluid flows. It bridges the gap between simplified models and the chaotic nature of turbulent flows, enabling engineers to predict aerodynamic performance and design more efficient systems.
Various approaches to turbulence modeling exist, from simple to advanced methods like . Each has its strengths and limitations, requiring careful selection based on flow characteristics, computational resources, and desired accuracy.
Fundamentals of turbulence
- Turbulence is a complex fluid flow phenomenon characterized by chaotic changes in pressure and flow velocity
- Understanding the fundamentals of turbulence is crucial for accurately modeling and predicting the behavior of fluids in various aerodynamic applications
- Key concepts in turbulence include characteristics of turbulent flows, , , and the
Characteristics of turbulent flows
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- Turbulent flows exhibit irregular fluctuations and mixing across multiple length and time scales
- These flows are characterized by high levels of , which leads to increased mixing and dissipation of energy
- Turbulent flows are inherently three-dimensional and time-dependent, making them challenging to model and predict accurately
Turbulent vs laminar flow
- Laminar flow is characterized by smooth, parallel layers of fluid with no mixing between the layers
- , on the other hand, is characterized by chaotic and irregular motion of fluid particles, leading to mixing across layers
- The transition from laminar to turbulent flow is governed by the , which represents the ratio of inertial forces to viscous forces
Turbulence intensity
- Turbulence intensity is a measure of the magnitude of turbulent fluctuations relative to the mean flow velocity
- It is defined as the ratio of the root-mean-square of the turbulent velocity fluctuations to the mean flow velocity
- Higher turbulence intensity indicates stronger turbulent fluctuations and increased mixing in the flow
Turbulent kinetic energy
- Turbulent kinetic energy (TKE) is a measure of the kinetic energy associated with turbulent fluctuations in the flow
- TKE is defined as half the sum of the mean squared turbulent velocity fluctuations
- The production, transport, and dissipation of TKE play a crucial role in the dynamics of turbulent flows
Energy cascade in turbulence
- The energy cascade describes the transfer of energy from larger to smaller scales in turbulent flows
- Energy is introduced into the flow at large scales through external forcing or shear, and is then transferred to smaller scales through the breakdown of large eddies into smaller ones
- At the smallest scales (Kolmogorov scales), the energy is dissipated into heat through viscous effects
Turbulence modeling approaches
- Turbulence modeling is essential for simulating and predicting the behavior of turbulent flows in CFD
- Different approaches to turbulence modeling have been developed, each with its own advantages and limitations
- The choice of turbulence modeling approach depends on factors such as the flow characteristics, computational resources, and desired accuracy
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 scales
- DNS requires extremely fine spatial and temporal resolution, making it computationally expensive and limited to low Reynolds number flows
Large eddy simulation (LES)
- LES directly resolves the large-scale turbulent eddies while modeling the effects of smaller scales using a subgrid-scale (SGS) model
- It captures more of the turbulent flow physics compared to RANS models, but at a higher computational cost
- LES is suitable for flows with complex geometries and unsteady phenomena, such as and vortex shedding
Reynolds-averaged Navier-Stokes (RANS)
- RANS models solve the time-averaged Navier-Stokes equations, where the effects of turbulence are modeled using additional transport equations
- The turbulent fluctuations are not resolved directly, but their effects on the mean flow are accounted for through the turbulence model
- RANS models are widely used in industrial CFD applications due to their lower computational cost and robustness
Hybrid RANS-LES methods
- Hybrid methods combine the advantages of RANS and LES by using RANS in near-wall regions and LES in the rest of the domain
- Examples include (DES) and (SAS)
- Hybrid methods aim to provide a balance between computational cost and accuracy for complex turbulent flows
RANS turbulence models
- RANS turbulence models are based on the and the concept of
- They range from simple algebraic models to more advanced models that solve additional transport equations for turbulence quantities
- The choice of RANS model depends on the flow characteristics, computational resources, and required accuracy
Boussinesq approximation
- The Boussinesq approximation relates the Reynolds stresses to the mean velocity gradients through an eddy viscosity
- It assumes that the turbulent stresses are proportional to the mean strain rate, with the proportionality being the eddy viscosity
- The Boussinesq approximation simplifies the modeling of Reynolds stresses, but has limitations in flows with strong anisotropy or non-equilibrium effects
Eddy viscosity concept
- Eddy viscosity represents the effects of turbulent mixing on the mean flow
- It is a scalar quantity that relates the turbulent stresses to the mean strain rate
- The eddy viscosity is modeled using various RANS turbulence models, which differ in their complexity and the number of additional transport equations solved
Algebraic models
- Algebraic models, also known as zero-equation models, express the eddy viscosity as a function of local mean flow variables
- Examples include the Baldwin-Lomax model and the Cebeci-Smith model
- Algebraic models are simple and computationally inexpensive, but have limited accuracy and are not suitable for complex flows
One-equation models
- solve a single transport equation for a turbulence quantity, usually the turbulent kinetic energy
- The eddy viscosity is then derived from the turbulent kinetic energy and a length scale
- Examples include the Spalart-Allmaras model and the Baldwin-Barth model
- One-equation models offer a balance between simplicity and accuracy, but may struggle with flows featuring strong non-equilibrium effects
Two-equation models
- solve two additional transport equations for turbulence quantities, typically the turbulent kinetic energy and a length scale or dissipation rate
- These models provide a more complete description of the turbulence and are widely used in industrial CFD applications
- Examples of two-equation models include the k-epsilon, k-omega, and SST k-omega models
k-epsilon model
- The solves transport equations for the turbulent kinetic energy (k) and the turbulent dissipation rate (epsilon)
- It is a robust and widely-used model, particularly for free-shear flows and wall-bounded flows with small pressure gradients
- The standard k-epsilon model has limitations in flows with strong adverse pressure gradients and separation
k-omega model
- The solves transport equations for the turbulent kinetic energy (k) and the specific dissipation rate (omega)
- It performs well in wall-bounded flows and can handle adverse pressure gradients better than the k-epsilon model
- The standard k-omega model is sensitive to freestream turbulence properties
SST k-omega model
- The Transport (SST) k-omega model combines the advantages of the k-epsilon and k-omega models
- It uses a blending function to switch between the k-omega model near the walls and the k-epsilon model in the freestream
- The is widely used in aerodynamic applications due to its accuracy in predicting flow separation and adverse pressure gradients
Reynolds stress models
- (RSM) solve transport equations for each component of the Reynolds stress tensor
- They provide a more accurate representation of turbulence anisotropy and non-equilibrium effects compared to eddy viscosity models
- RSMs are computationally expensive and may suffer from numerical stiffness and convergence issues
Wall treatment in turbulence modeling
- Proper treatment of the near-wall region is crucial for accurate turbulence modeling, as it significantly influences the overall flow behavior
- Different wall treatment approaches are used depending on the turbulence model and the mesh resolution near the walls
- The choice of wall treatment affects the accuracy and computational cost of the CFD simulation
Wall functions
- are used to bridge the viscous sublayer and the fully turbulent region, avoiding the need to resolve the viscous sublayer with a fine mesh
- They provide a computationally efficient way to model the near-wall flow by using empirical formulas to estimate the velocity and turbulence quantities
- Standard wall functions are based on the log-law and are suitable for flows with mild pressure gradients and attached boundary layers
Low-Reynolds-number models
- Low-Reynolds-number (LRN) models are designed to resolve the viscous sublayer and the buffer layer with a fine mesh near the walls
- They use damping functions to modify the turbulence model equations in the near-wall region
- LRN models provide a more accurate representation of the near-wall flow but require a higher mesh resolution and computational cost
y+ requirements
- The non-dimensional wall distance, y+, is a crucial parameter in determining the appropriate wall treatment and mesh resolution
- For wall functions, the first cell centroid should typically be located within the range of 30 < y+ < 300
- For LRN models, the first cell centroid should be at y+ ≈ 1, with a sufficient number of cells within the viscous sublayer (y+ < 5)
Turbulence model selection
- Selecting the appropriate turbulence model is essential for obtaining accurate and reliable CFD results
- The choice of turbulence model depends on various factors, including the flow characteristics, computational resources, and desired accuracy
- Guidelines and best practices have been established to assist in for different industrial applications
Flow characteristics considerations
- The flow characteristics, such as the Reynolds number, pressure gradients, and flow separation, influence the choice of turbulence model
- For flows with mild pressure gradients and attached boundary layers, simpler models like the k-epsilon or the SST k-omega model may suffice
- For flows with strong adverse pressure gradients, separation, or complex geometries, more advanced models like RSMs or LES may be necessary
Computational cost vs accuracy
- The computational cost and the desired accuracy are important factors in selecting a turbulence model
- Simpler models like RANS are computationally efficient but may sacrifice accuracy in complex flows
- More advanced models like LES or DNS provide higher accuracy but come with a significant increase in computational cost
Industrial applications guidelines
- Guidelines for turbulence model selection have been developed for various industrial applications, such as aerospace, automotive, and wind engineering
- These guidelines take into account the specific flow characteristics, accuracy requirements, and computational constraints of each application
- For example, the SST k-omega model is widely used in aerodynamic applications due to its accuracy in predicting flow separation and adverse pressure gradients
Turbulence model validation
- Validation of turbulence models is essential to ensure their accuracy and reliability in predicting turbulent flows
- Validation involves comparing CFD results obtained using a specific turbulence model with benchmark test cases and experimental data
- Uncertainty quantification techniques are used to assess the sensitivity of the results to model assumptions and numerical errors
Benchmark test cases
- Benchmark test cases are well-established flow problems with known analytical solutions or high-quality experimental data
- Examples include the backward-facing step, the flat plate boundary layer, and the square duct flow
- Turbulence models are validated by comparing their predictions with the benchmark results, assessing their accuracy and limitations
Experimental data comparison
- Validation against experimental data is crucial for assessing the performance of turbulence models in real-world applications
- Experimental data can include velocity profiles, pressure distributions, and turbulence statistics obtained from wind tunnel tests or field measurements
- CFD results are compared with experimental data to evaluate the accuracy and predictive capabilities of the turbulence model
Uncertainty quantification
- Uncertainty quantification (UQ) is the process of assessing the impact of model assumptions, numerical errors, and input uncertainties on the CFD results
- UQ techniques, such as sensitivity analysis and Monte Carlo simulations, help identify the main sources of uncertainty and their propagation through the simulation
- UQ provides a measure of the confidence in the CFD results and helps guide model selection and improvement
Advanced topics in turbulence modeling
- Advanced topics in turbulence modeling address specific challenges and extend the capabilities of standard turbulence models
- These topics include curvature correction, rotation effects, transition modeling, and buoyancy-driven flows
- Incorporating these advanced features can improve the accuracy and applicability of turbulence models in complex flow situations
Curvature correction
- Curvature correction accounts for the effects of streamline curvature on turbulence production and dissipation
- Standard turbulence models often overpredict the turbulence levels in flows with strong curvature, such as in turbomachinery and curved channels
- Curvature correction methods, such as the Spalart-Shur correction, modify the turbulence model equations to improve their accuracy in these flows
Rotation effects
- Rotation effects are important in flows with significant system rotation, such as in turbomachinery and cyclone separators
- Standard turbulence models may not accurately capture the effects of rotation on turbulence production and dissipation
- Rotation-sensitive turbulence models, such as the Spalart-Allmaras model with rotation correction, have been developed to improve the accuracy in rotating flows
Transition modeling
- Transition modeling aims to predict the onset and extent of the transition from laminar to turbulent flow
- Accurate transition modeling is crucial for flows with significant laminar regions, such as in low-Reynolds-number aerodynamics and turbomachinery
- Transition models, such as the γ-Reθ model and the Local Correlation-based Transition Model (LCTM), are used in conjunction with RANS models to predict the transition process
Buoyancy-driven flows
- Buoyancy-driven flows, such as natural convection and stratified flows, are influenced by the interaction between turbulence and density variations
- Standard turbulence models may not accurately capture the effects of buoyancy on turbulence production and dissipation
- Buoyancy-modified turbulence models, such as the Generalized Gradient Diffusion Hypothesis (GGDH) model, are used to improve the accuracy in these flows
Best practices in turbulence modeling
- Best practices in turbulence modeling ensure the reliability and accuracy of CFD simulations
- These practices cover aspects such as mesh resolution requirements, boundary conditions treatment, solver settings, and convergence assessment
- Following these best practices helps to minimize numerical errors and improve the overall quality of the CFD results
Mesh resolution requirements
- Adequate mesh resolution is crucial for capturing the relevant turbulent flow features and ensuring the accuracy of the turbulence model
- The mesh should be fine enough to resolve the boundary layer, with a sufficient number of cells in the wall-normal direction (e.g., )
- Mesh independence studies should be conducted to ensure that the solution is not sensitive to further mesh refinement
Boundary conditions treatment
- Proper treatment of boundary conditions is essential for the accuracy and stability of the CFD simulation
- Inflow boundary conditions should be specified with realistic turbulence quantities, such as turbulence intensity and length scale
- Wall boundary conditions should be consistent with the chosen wall treatment approach (e.g., wall functions or )
Solver settings considerations
- Solver settings, such as the discretization schemes, convergence criteria, and under-relaxation factors, can significantly impact the accuracy and convergence of the CFD simulation
- Second-order or higher-order discretization schemes are recommended for improved accuracy
- Appropriate under-relaxation factors should be used to ensure stability and convergence, especially for complex flows or high-Reynolds-number simulations
Convergence assessment
- Assessing the convergence of the CFD simulation is essential to ensure the reliability of the results
- Convergence should be monitored through residuals, integral quantities (e.g., lift and drag coefficients), and flow field variables
- Residuals should be reduced by several orders of magnitude, and integral quantities should reach a steady state or a statistically steady state (for unsteady simulations)
- Grid convergence studies and time step sensitivity analyses should be conducted to assess the spatial and temporal convergence of the solution
Key Terms to Review (33)
Algebraic Models: Algebraic models are mathematical representations that use algebraic equations to describe complex phenomena, often simplifying the behavior of physical systems for analysis and simulation. In turbulence modeling, these models are used to approximate turbulent flow characteristics and provide solutions that can be integrated into computational fluid dynamics (CFD) simulations.
ANSYS Fluent: ANSYS Fluent is a powerful computational fluid dynamics (CFD) software used to simulate fluid flow, heat transfer, and chemical reactions in complex geometries. It plays a critical role in discretization methods to solve partial differential equations, applies advanced turbulence modeling techniques to accurately predict turbulent flows, and supports unsteady CFD methods for transient analysis. Additionally, ANSYS Fluent is vital for aerodynamic shape optimization, allowing engineers to improve designs for better performance and efficiency.
Boussinesq Approximation: The Boussinesq approximation is an assumption used in fluid dynamics that simplifies the governing equations of flow by considering density variations to be negligible except where they affect buoyancy. This approximation is particularly useful for modeling buoyant flows, such as those found in turbulence modeling, where temperature differences cause density changes that drive fluid motion.
Continuity equation: The continuity equation is a fundamental principle in fluid dynamics that expresses the conservation of mass within a fluid flow. It states that for an incompressible fluid, the mass flow rate must remain constant from one cross-section of a flow to another, linking the velocity and area of flow at different points. This relationship is crucial in understanding how fluids behave in various conditions, from static scenarios to dynamic flow through nozzles and turbulent environments.
Detached Eddy Simulation: Detached Eddy Simulation (DES) is a hybrid turbulence modeling approach that combines the strengths of both Reynolds-Averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES) to simulate turbulent flows, particularly in complex geometries and unsteady conditions. DES works by using RANS in regions with attached flows where turbulence is more isotropic and LES in regions where the flow detaches, allowing for more detailed simulations of unsteady turbulent behaviors without excessive computational costs.
Direct Numerical Simulation: Direct Numerical Simulation (DNS) is a computational fluid dynamics (CFD) method that solves the governing equations of fluid motion without any approximations or turbulence modeling. By resolving all scales of motion, from the largest energy-containing eddies to the smallest dissipative scales, DNS provides highly accurate flow field data. This level of detail allows for a comprehensive understanding of complex fluid behaviors and is essential for analyzing turbulent flows, unsteady boundary layers, and their interactions with surfaces.
Eddy viscosity: Eddy viscosity is a concept used in fluid dynamics to represent the turbulent diffusion of momentum in a fluid flow, essentially quantifying the effects of turbulence on flow characteristics. It serves as a model parameter in turbulence modeling, allowing for a simplification of the complex interactions within turbulent flows by substituting physical viscosity with an effective viscosity that accounts for the chaotic motion of eddies. This helps in predicting flow patterns and behaviors in computational fluid dynamics simulations more accurately.
Eddy viscosity concept: The eddy viscosity concept is a key theoretical framework in turbulence modeling that represents the enhanced mixing of momentum due to the chaotic and swirling motions of fluid particles in a turbulent flow. This concept helps to quantify the effects of turbulence on flow characteristics, allowing for more accurate predictions of velocity profiles and other important parameters in fluid dynamics. By effectively simplifying the complex interactions present in turbulent flows, this approach lays the groundwork for advanced modeling techniques in computational fluid dynamics (CFD).
Energy Cascade: Energy cascade refers to the process in turbulent flows where energy is transferred from larger scales of motion to smaller scales, eventually dissipating as heat. This phenomenon is crucial in understanding how turbulence behaves, illustrating how kinetic energy is progressively transferred through various eddies and vortices, impacting vorticity and circulation, turbulence modeling, and computational fluid dynamics.
Flow Separation: Flow separation occurs when the smooth flow of fluid over a surface breaks away from that surface, typically resulting in a wake region behind the object. This phenomenon is crucial as it affects lift, drag, and overall aerodynamic performance of bodies moving through fluids, influencing many aspects of fluid dynamics including stability and control.
Hybrid RANS-LES methods: Hybrid RANS-LES methods combine Reynolds-Averaged Navier-Stokes (RANS) equations and Large Eddy Simulation (LES) techniques to model turbulent flows. This approach allows for accurate predictions of complex flow behaviors by using RANS in regions where the flow is relatively steady and LES in areas with more turbulent fluctuations, providing a balance between computational efficiency and accuracy.
K-epsilon model: The k-epsilon model is a widely used turbulence model in computational fluid dynamics (CFD) that provides a mathematical framework to simulate the effects of turbulence on fluid flow. This model uses two transport equations, one for the turbulent kinetic energy (k) and another for the rate of dissipation of turbulent kinetic energy (epsilon), allowing for the prediction of turbulence behavior in various flows. It effectively captures the essential features of turbulence, making it a popular choice for modeling complex flow scenarios.
K-omega model: The k-omega model is a turbulence modeling approach used in computational fluid dynamics (CFD) to predict flow behavior in turbulent regimes. It is based on two transport equations: one for the turbulent kinetic energy (k) and the other for the specific dissipation rate (omega), which helps in capturing the effects of turbulence on flow characteristics. This model is especially effective for boundary layer flows and situations with adverse pressure gradients.
Kolmogorov Scale: The Kolmogorov scale is a measure used in turbulence theory that describes the smallest scales of turbulent motion, specifically the size of the smallest eddies in a turbulent flow. It connects to the understanding of how energy is dissipated in turbulent flows, which is crucial for accurate modeling and simulations in computational fluid dynamics.
Laminar flow: Laminar flow is a type of fluid motion where the fluid flows in parallel layers with minimal disruption between them, resulting in smooth and orderly movement. This flow regime is characterized by low velocities and high viscosity, allowing for predictable behavior that can be analyzed using simplified mathematical models.
Large Eddy Simulation: Large Eddy Simulation (LES) is a computational technique used in fluid dynamics to model turbulent flows by resolving the larger scales of turbulence while modeling the smaller scales. This approach provides a more accurate representation of turbulent behavior compared to traditional methods, making it particularly useful for simulating unsteady and complex flow situations where detailed turbulence information is crucial.
Low-Reynolds-Number Models: Low-Reynolds-number models refer to mathematical representations used to simulate fluid flow in scenarios where the Reynolds number is low, typically less than 2000. In these conditions, viscous forces dominate over inertial forces, leading to more stable and predictable flow patterns. These models are crucial in understanding laminar flow characteristics and are often applied in computational fluid dynamics (CFD) to accurately predict the behavior of fluids in micro-scale applications, like in biomedical devices or small-scale aerodynamics.
Navier-Stokes Equations: The Navier-Stokes equations are a set of nonlinear partial differential equations that describe the motion of viscous fluid substances. They form the foundation for fluid dynamics and are crucial for understanding various phenomena, including turbulence and boundary layer behavior, making them essential in aerodynamics and related fields.
One-equation models: One-equation models are simplified turbulence modeling approaches that utilize a single transport equation to estimate turbulent kinetic energy (TKE) or other relevant turbulence properties. These models provide a balance between computational efficiency and accuracy, making them popular in various applications, especially in computational fluid dynamics (CFD) where quick evaluations are essential. By modeling TKE or similar parameters, one-equation models can help predict the behavior of turbulent flows without the complexity of multi-equation models.
OpenFOAM: OpenFOAM is an open-source software framework designed for computational fluid dynamics (CFD) simulations. It enables users to customize and extend their simulations through its modular architecture, making it a popular choice for researchers and engineers working on fluid flow problems, including turbulence modeling, shape optimization, and post-processing of results.
Reynolds Number: Reynolds number is a dimensionless quantity used to predict flow patterns in different fluid flow situations, representing the ratio of inertial forces to viscous forces. It plays a critical role in determining whether a flow is laminar or turbulent, influencing various aerodynamic phenomena such as lift, drag, and boundary layer behavior.
Reynolds Stress Models: Reynolds Stress Models (RSM) are advanced turbulence modeling techniques used to predict the effects of turbulence in fluid flow. They extend beyond simpler models like the k-epsilon and k-omega models by solving additional transport equations for the Reynolds stresses, providing a more accurate representation of turbulent flows. This modeling approach is particularly useful in complex flow scenarios, allowing for better predictions of flow behavior in real-world applications.
Scale-adaptive simulation: Scale-adaptive simulation is a computational fluid dynamics (CFD) technique that dynamically adjusts the level of turbulence modeling based on the flow features present in a simulation. It aims to efficiently capture both large and small-scale turbulent structures, providing a more accurate representation of complex flows while optimizing computational resources. This approach bridges the gap between traditional Reynolds-Averaged Navier-Stokes (RANS) methods and Large Eddy Simulation (LES), allowing for adaptive refinement in regions of interest without excessive computational cost.
Shear stress: Shear stress is the force per unit area that acts parallel to the surface of a material, resulting in deformation. It plays a crucial role in understanding how fluids interact with solid boundaries, affecting force and moment measurements, boundary layer behavior, turbulence modeling, and setting boundary conditions in fluid dynamics.
SST k-omega model: The SST k-omega model is a turbulence modeling approach that combines the strengths of the k-omega model and the k-epsilon model, providing accurate predictions for flows with complex features such as boundary layers and separation. By employing a blending function, it switches between these two models based on the flow conditions, which enhances its performance in predicting turbulent flow behaviors, especially in computational fluid dynamics applications.
Turbulence Intensity: Turbulence intensity is a measure of the magnitude of fluctuations in a turbulent flow relative to the mean flow, typically expressed as a percentage. It plays a crucial role in understanding the behavior of turbulent flows and can affect various phenomena, such as skin friction and heat transfer, the accuracy of turbulence modeling in computational fluid dynamics (CFD), the clarity of post-processing and visualization data, and the response of structures to gusts or rapid changes in flow conditions.
Turbulence model selection: Turbulence model selection refers to the process of choosing an appropriate mathematical model that simulates the effects of turbulence in fluid dynamics simulations. This selection is crucial because different models can produce varying results in Computational Fluid Dynamics (CFD), affecting the accuracy and reliability of predictions in flow behavior, energy dissipation, and mixing processes.
Turbulent flow: Turbulent flow is a type of fluid motion characterized by chaotic and irregular fluctuations in velocity and pressure, resulting from the interactions between layers of fluid. This complex flow pattern leads to mixing and energy dissipation, making it critical for understanding various aerodynamic phenomena such as lift, drag, and heat transfer.
Turbulent kinetic energy: Turbulent kinetic energy (TKE) is the portion of kinetic energy in a fluid flow that is associated with turbulence, which manifests as chaotic and irregular fluctuations in velocity. It plays a critical role in turbulence modeling, influencing the accuracy of simulations and predictions in computational fluid dynamics (CFD), and is essential for understanding the transport of momentum and energy within turbulent flows.
Two-equation models: Two-equation models are mathematical frameworks used in turbulence modeling that rely on two transport equations to predict the behavior of turbulent flows. These models, such as the k-epsilon and k-omega models, help simulate complex fluid dynamics by quantifying key turbulence quantities like kinetic energy and dissipation rate, making them essential for accurate flow predictions in various applications.
Vorticity: Vorticity is a measure of the local spinning motion of a fluid, quantified as the curl of the velocity field. It plays a crucial role in understanding fluid dynamics, as it helps describe how fluid elements rotate and interact. Vorticity connects to circulation, which is the integral of vorticity around a closed path, and is essential in analyzing flow patterns and stability, making it relevant in various areas such as flow visualization, turbulence modeling, and computational fluid dynamics.
Wall functions: Wall functions are mathematical relationships used in computational fluid dynamics (CFD) to simplify the modeling of flow near solid boundaries, specifically to bridge the gap between the wall and the first computational cell in turbulence simulations. They help in predicting the behavior of turbulent flow at the boundary by utilizing empirical data and scaling laws, allowing for efficient computation without resolving the extremely fine details of boundary layers.
Y+ requirements: Y+ requirements refer to the non-dimensional distance from the wall in a turbulent flow simulation, which is crucial for accurately capturing the behavior of the boundary layer in computational fluid dynamics (CFD). These requirements help ensure that the mesh is sufficiently fine near the wall to resolve the turbulence characteristics effectively, impacting the accuracy of turbulence models and overall flow predictions.