Glossary

13.3 Computational fluid dynamics (CFD) basics

5 min read•july 31, 2024

Computational fluid dynamics (CFD) is a powerful tool for solving complex fluid flow problems. It uses numerical methods to analyze and predict fluid behavior, heat transfer, and mass transport in various systems.

CFD simulations involve creating a mesh, applying governing equations, and solving them numerically. This process allows engineers to study intricate flow phenomena, optimize designs, and make informed decisions without costly physical experiments.

Computational Fluid Dynamics Principles

Fundamentals and Applications

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  • Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems involving fluid flows, heat transfer, and mass transfer
  • CFD is based on the fundamental governing equations of fluid dynamics, including the , momentum equation, and energy equation, which are derived from the conservation laws of physics
  • The primary applications of CFD include aerodynamics (aircraft design), hydrodynamics (ship hull optimization), heat exchanger design, combustion modeling, and environmental engineering (pollutant dispersion), among others
  • CFD enables the study of complex fluid flow phenomena, such as turbulence, boundary layer effects, and multiphase flows (gas-liquid, solid-liquid), which are difficult to analyze using experimental or analytical methods

Workflow and Components

  • The basic workflow of a CFD analysis involves pre-processing (geometry and mesh generation), solving (numerical computation), and post-processing (visualization and analysis of results)
  • Pre-processing involves creating a , generating a mesh of control volumes or elements, and specifying boundary conditions and initial conditions
  • The solving stage involves the numerical solution of the governing equations using appropriate numerical methods, such as finite volume, finite difference, or finite element methods
  • Post-processing involves visualizing and analyzing the computed flow fields, such as velocity, pressure, temperature, and species concentrations, using various graphical and quantitative techniques

Governing Equations and Methods in CFD

  • The are a set of partial differential equations that describe the motion of viscous fluid substances, taking into account the conservation of mass, momentum, and energy
  • The continuity equation ensures the conservation of mass, stating that the rate of change of fluid in a control volume is equal to the net rate of mass flow into the control volume: ∂ρ∂t+∇⋅(ρv⃗)=0\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \vec{v}) = 0
  • The momentum equation is derived from Newton's second law and relates the forces acting on a fluid element to its acceleration, considering pressure gradients, viscous stresses, and body forces: ρDv⃗Dt=−∇p+∇⋅τ‾‾+ρg⃗\rho \frac{D \vec{v}}{D t} = -\nabla p + \nabla \cdot \overline{\overline{\tau}} + \rho \vec{g}
  • The energy equation accounts for the conservation of energy, incorporating the effects of heat conduction, convection, and dissipation due to viscous stresses: ρcpDTDt=∇⋅(k∇T)+Φ\rho c_p \frac{D T}{D t} = \nabla \cdot (k \nabla T) + \Phi

Numerical Methods

  • The (FVM) is a common numerical technique used in CFD, which divides the computational domain into a set of control volumes and solves the governing equations by conserving fluxes across the boundaries of these volumes
  • The (FDM) approximates the derivatives in the governing equations using Taylor series expansions and solves the resulting algebraic equations at discrete grid points
  • The (FEM) divides the computational domain into a set of elements, approximates the solution variables using basis functions, and solves the resulting system of equations by minimizing a residual or error function
  • Spectral methods represent the solution variables using a linear combination of basis functions (Fourier series, Chebyshev polynomials) and solve the governing equations in the spectral space, offering high accuracy for smooth solutions but limited applicability to complex geometries

CFD Simulation Setup and Solution

Domain and Mesh Generation

  • Setting up a CFD simulation involves defining the computational domain, generating a suitable mesh, specifying boundary conditions, and selecting appropriate physical models and numerical schemes
  • The computational domain represents the physical space in which the fluid flow, heat transfer, or mass transfer problem is solved, and it is discretized into a mesh of control volumes or elements
  • Mesh generation involves creating a grid of nodes and elements that conforms to the geometry of the computational domain and provides sufficient resolution to capture the relevant flow features and gradients
  • Structured meshes (hexahedral elements) offer higher accuracy and efficiency but are limited to simple geometries, while unstructured meshes (tetrahedral elements) provide more flexibility for complex geometries but may require more computational resources

Boundary Conditions and Physical Models

  • Boundary conditions specify the flow variables (velocity, pressure, temperature) at the boundaries of the computational domain, such as inlets, outlets, walls, and symmetry planes
  • Inlet boundary conditions prescribe the velocity, pressure, or mass flow rate entering the domain, while outlet boundary conditions specify the pressure or outflow conditions leaving the domain
  • Wall boundary conditions impose no-slip (zero velocity) or slip conditions, as well as thermal (temperature, heat flux) or mass transfer (concentration, flux) conditions at solid surfaces
  • Physical models are used to represent the underlying physics of the problem, such as turbulence (RANS, LES, DNS), heat transfer (conduction, convection, radiation), chemical reactions (combustion, multiphase flows), and are selected based on the complexity and accuracy requirements of the simulation

Numerical Schemes and Solvers

  • Numerical schemes, such as upwind, central, or high-resolution schemes, are chosen to discretize the governing equations and ensure numerical stability, accuracy, and convergence
  • Upwind schemes (first-order, second-order) are stable but may introduce numerical diffusion, while central schemes (second-order) are more accurate but may suffer from oscillations or instabilities
  • High-resolution schemes (QUICK, MUSCL) combine the advantages of upwind and central schemes by using flux limiters or slope limiters to preserve monotonicity and reduce numerical diffusion
  • Solvers for the resulting system of algebraic equations can be classified as direct (Gaussian elimination, LU decomposition) or iterative (Gauss-Seidel, Jacobi, Krylov subspace methods), with the choice depending on the problem size, sparsity, and computational resources available

Interpretation and Evaluation of CFD Results

Visualization and Analysis

  • Post-processing of CFD results involves visualizing and analyzing the computed flow fields, such as velocity, pressure, temperature, and species concentrations, using various graphical and quantitative techniques
  • Velocity vector plots, streamlines, and contours can be used to visualize the flow patterns, recirculation zones, and boundary layer effects in the computational domain
  • Pressure and temperature distributions can be analyzed to identify high and low-pressure regions, thermal gradients, and heat transfer characteristics in the flow field
  • Quantitative analysis of CFD results may involve extracting data along lines, planes, or volumes of interest, computing integral quantities (drag, lift, heat flux), and comparing the results with experimental data or analytical solutions

Verification and Validation

  • Critically evaluating CFD results requires an understanding of the assumptions and limitations of the physical models, numerical methods, and boundary conditions used in the simulation
  • Verification is the process of assessing the accuracy of the numerical solution by comparing it with analytical solutions, manufactured solutions, or highly refined simulations
  • Mesh independence studies should be conducted to ensure that the solution is not sensitive to the mesh resolution and that the discretization errors are within acceptable limits
  • Validation of CFD results against experimental data or benchmarks is essential to assess the accuracy and reliability of the simulations and to identify potential sources of error or uncertainty
  • Sensitivity analyses can be performed to investigate the influence of input parameters, such as material properties, boundary conditions, and model constants, on the simulation results and to quantify the associated uncertainties

Key Terms to Review (19)

Aerodynamic analysis: Aerodynamic analysis refers to the study and evaluation of how air interacts with solid objects, especially in terms of force, pressure, and flow behavior. This process helps in understanding and optimizing the performance of vehicles, structures, and various objects by analyzing their shapes and materials to minimize drag and enhance lift. Through computational methods, aerodynamic analysis plays a crucial role in design and engineering by predicting performance in real-world conditions.
Ansys Fluent: Ansys Fluent is a powerful computational fluid dynamics (CFD) software used for simulating fluid flow, heat transfer, and chemical reactions in various engineering applications. It provides advanced numerical methods and models to analyze complex fluid dynamics problems, making it a vital tool for engineers to predict the performance of systems and optimize designs.
Computational domain: The computational domain refers to the specific region of space where computational fluid dynamics (CFD) simulations are performed to analyze fluid flow and heat transfer phenomena. This domain is defined by boundaries that can be physical, such as walls or inlets, or abstract, like the limits of a mathematical model. Understanding the computational domain is crucial for accurately setting up simulations and ensuring that results reflect the real-world scenarios being studied.
Continuity equation: The continuity equation is a fundamental principle in fluid mechanics that expresses the conservation of mass within a control volume. It states that the mass flow rate into a system must equal the mass flow rate out of the system, ensuring that mass is neither created nor destroyed. This principle connects to various processes in fluid dynamics, energy transfer, and mass transport, highlighting its importance across different applications.
Density: Density is a physical property of matter defined as the mass per unit volume of a substance, usually expressed in units like kilograms per cubic meter (kg/m³). It plays a crucial role in various processes, influencing how materials interact with each other and how they behave under different conditions, particularly during fluid flow and heat transfer.
Dirichlet Boundary Condition: A Dirichlet boundary condition specifies the value of a function at a boundary in a differential equation problem, essentially fixing the value at that boundary. This condition is important in modeling systems where temperatures or concentrations are held constant along boundaries, allowing for simplified analysis and solutions in various transport problems.
Finite Difference Method: The finite difference method is a numerical technique used to approximate solutions to differential equations by discretizing the equations into a set of algebraic equations. This method is particularly useful in analyzing transient conduction and heat transfer problems, as it allows for the modeling of temperature changes over time in complex geometries. Additionally, it serves as a foundational tool in computational fluid dynamics and numerical methods for conduction problems, making it essential for solving a variety of engineering challenges.
Finite element method: The finite element method (FEM) is a numerical technique used to find approximate solutions to complex engineering and mathematical problems, particularly those involving partial differential equations. By dividing a large system into smaller, simpler parts called elements, FEM allows for detailed analysis of physical phenomena such as fluid flow and heat conduction, making it a vital tool in computational modeling and simulation.
Finite Volume Method: The finite volume method (FVM) is a numerical technique used to solve partial differential equations, especially those arising in fluid dynamics and heat transfer. It works by dividing the domain into small control volumes and applying conservation principles to each volume, ensuring that fluxes in and out of the volume are accounted for. This approach makes FVM particularly effective for problems involving complex geometries and varying material properties, as well as for capturing conservation laws in participating media.
Grid generation: Grid generation is the process of creating a computational mesh or grid that divides the physical domain into discrete elements, which is essential for numerical simulations in computational fluid dynamics (CFD). This grid helps to solve the governing equations of fluid flow and heat transfer by approximating the physical space with finite volumes, allowing for numerical analysis and modeling of complex fluid behavior. The quality and structure of the grid significantly impact the accuracy and efficiency of the CFD simulations.
Heat Exchangers: Heat exchangers are devices designed to efficiently transfer heat from one fluid to another without mixing them. They play a critical role in many applications, including heating and cooling systems, where managing temperature and energy transfer is essential for optimal performance.
Large eddy simulation (LES): Large eddy simulation (LES) is a mathematical modeling technique used in fluid dynamics to simulate the effects of turbulence by resolving large-scale eddies while modeling the smaller, unresolved scales. This method provides a more accurate representation of turbulent flow compared to traditional approaches, as it captures the significant energy-carrying structures in the flow, allowing for detailed analysis of complex fluid behavior.
Mesh refinement: Mesh refinement is the process of increasing the density of the mesh in computational simulations to improve accuracy and detail in the numerical solutions of fluid dynamics problems. By creating smaller, more numerous elements in regions of interest, mesh refinement helps capture complex flow features, gradients, and boundary layer behaviors that are crucial for accurate predictions in computational fluid dynamics (CFD). This technique ensures that essential physical phenomena are resolved effectively while optimizing computational resources.
Navier-Stokes Equations: The Navier-Stokes equations are a set of nonlinear partial differential equations that describe the motion of fluid substances. They express the conservation of momentum and mass within a fluid and are fundamental in understanding various phenomena such as turbulence, flow patterns, and transport processes.
Neumann Boundary Condition: The Neumann boundary condition specifies the value of a derivative of a function at a boundary, often representing flux or gradient, rather than the value of the function itself. This concept is critical in heat and mass transfer problems, as it allows the modeling of situations where there is no heat or mass accumulation across a boundary, but rather a specified rate of flow or exchange.
OpenFOAM: OpenFOAM is an open-source computational fluid dynamics (CFD) toolbox that provides a wide range of tools for simulating fluid flow, heat transfer, and other related physical phenomena. It allows users to create custom solvers and utilities, making it highly versatile for various applications in engineering and research. With a strong user community and extensive documentation, OpenFOAM has become a popular choice for both academic and industrial CFD projects.
Reynolds-Averaged Navier-Stokes (RANS): The Reynolds-Averaged Navier-Stokes (RANS) equations are a set of equations that describe the flow of incompressible fluids by averaging the effects of turbulence over time. This method allows for the prediction of mean flow characteristics while simplifying the complex interactions present in turbulent flows, making it a fundamental tool in computational fluid dynamics (CFD) for analyzing fluid motion in various applications.
Time-stepping methods: Time-stepping methods are numerical techniques used to solve differential equations by advancing the solution through discrete time intervals. These methods break down complex problems in computational fluid dynamics into manageable steps, allowing for the simulation of fluid behavior over time. The choice of time-stepping method can significantly impact the stability and accuracy of the simulation results.
Viscosity: Viscosity is a measure of a fluid's resistance to flow and deformation, which is influenced by its internal friction. It plays a crucial role in understanding how fluids behave under various conditions, affecting transport properties and flow characteristics in many processes such as heat transfer, mass transfer, and diffusion.
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