11-08-2012, 04:45 PM
CFD Basics
[attachment=31192]
Introduction to CFD Basics
This is a quick-and-dirty introduction to the basic concepts underlying CFD. The concepts are illustrated by applying them to simple 1D model problems. We’ll invoke these concepts while performing "case studies" in FLUENT. Happily for us, these model-problem concepts extend to the more general situations in the case studies in most instances. Since we’ll keep returning to these concepts while performing the FLUENT case studies, it’s worth your time to understand and digest these concepts.
We discuss the following topics briefly. These topics are the minimum necessary to
perform and validate the FLUENT calculations to come later.
1. The Need for CFD
2. Applications of CFD
3. The Strategy of CFD
4. Discretization Using the Finite-Difference Method
5. Discretization Using The Finite-Volume Method
6. Assembly of Discrete System and Application of Boundary Conditions
7. Solution of Discrete System
8. Grid Convergence
9. Dealing with Nonlinearity
10. Direct and Iterative Solvers
11. Iterative Convergence
12. Numerical Stability
13. Turbulence modeling
The Need for CFD
Applying the fundamental laws of mechanics to a fluid gives the governing equations for a fluid. The conservation of mass equation is
∂ρ
∂t + ∇ • (ρV ) = 0
and the conservation of momentum equation is
ρ∂V
∂t + ρ(V • ∇)V = −∇p + ρg + ∇ • τij
These equations along with the conservation of energy equation form a set of coupled, nonlinear partial differential equations. It is not possible to solve these equations analytically for most engineering problems.
However, it is possible to obtain approximate computer-based solutions to the governing equations for a variety of engineering problems. This is the subject matter of Computational Fluid Dynamics (CFD).
Applications of CFD
CFD is useful in a wide variety of applications and here we note a few to give you an idea of
its use in industry. The simulations shown below have been performed using the FLUENT
software.
CFD can be used to simulate the flow over a vehicle. For instance, it can be used to study
the interaction of propellers or rotors with the aircraft fuselage The following figure shows
the prediction of the pressure field induced by the interaction of the rotor with a helicopter
fuselage in forward flight. Rotors and propellers can be represented with models of varying
complexity.
The temperature distribution obtained from a CFD analysis of a mixing manifold is shown below. This mixing manifold is part of the passenger cabin ventilation system on the Boeing 767. The CFD analysis showed the effectiveness of a simpler manifold design without the need for field testing.
Bio-medical engineering is a rapidly growing field and uses CFD to study the circulatory and
respiratory systems. The following figure shows pressure contours and a cutaway view that
reveals velocity vectors in a blood pump that assumes the role of heart in open-heart surgery.
CFD is attractive to industry since it is more cost-effective than physical testing. However, one must note that complex flow simulations are challenging and error-prone and it takes a lot of engineering expertise to obtain validated solutions.
The Strategy of CFD
Broadly, the strategy of CFD is to replace the continuous problem domain with a discrete domain using a grid. In the continuous domain, each flow variable is defined at every point in the domain. For instance, the pressure p in the continuous 1D domain shown in the figure below would be given as
[attachment=31192]
Introduction to CFD Basics
This is a quick-and-dirty introduction to the basic concepts underlying CFD. The concepts are illustrated by applying them to simple 1D model problems. We’ll invoke these concepts while performing "case studies" in FLUENT. Happily for us, these model-problem concepts extend to the more general situations in the case studies in most instances. Since we’ll keep returning to these concepts while performing the FLUENT case studies, it’s worth your time to understand and digest these concepts.
We discuss the following topics briefly. These topics are the minimum necessary to
perform and validate the FLUENT calculations to come later.
1. The Need for CFD
2. Applications of CFD
3. The Strategy of CFD
4. Discretization Using the Finite-Difference Method
5. Discretization Using The Finite-Volume Method
6. Assembly of Discrete System and Application of Boundary Conditions
7. Solution of Discrete System
8. Grid Convergence
9. Dealing with Nonlinearity
10. Direct and Iterative Solvers
11. Iterative Convergence
12. Numerical Stability
13. Turbulence modeling
The Need for CFD
Applying the fundamental laws of mechanics to a fluid gives the governing equations for a fluid. The conservation of mass equation is
∂ρ
∂t + ∇ • (ρV ) = 0
and the conservation of momentum equation is
ρ∂V
∂t + ρ(V • ∇)V = −∇p + ρg + ∇ • τij
These equations along with the conservation of energy equation form a set of coupled, nonlinear partial differential equations. It is not possible to solve these equations analytically for most engineering problems.
However, it is possible to obtain approximate computer-based solutions to the governing equations for a variety of engineering problems. This is the subject matter of Computational Fluid Dynamics (CFD).
Applications of CFD
CFD is useful in a wide variety of applications and here we note a few to give you an idea of
its use in industry. The simulations shown below have been performed using the FLUENT
software.
CFD can be used to simulate the flow over a vehicle. For instance, it can be used to study
the interaction of propellers or rotors with the aircraft fuselage The following figure shows
the prediction of the pressure field induced by the interaction of the rotor with a helicopter
fuselage in forward flight. Rotors and propellers can be represented with models of varying
complexity.
The temperature distribution obtained from a CFD analysis of a mixing manifold is shown below. This mixing manifold is part of the passenger cabin ventilation system on the Boeing 767. The CFD analysis showed the effectiveness of a simpler manifold design without the need for field testing.
Bio-medical engineering is a rapidly growing field and uses CFD to study the circulatory and
respiratory systems. The following figure shows pressure contours and a cutaway view that
reveals velocity vectors in a blood pump that assumes the role of heart in open-heart surgery.
CFD is attractive to industry since it is more cost-effective than physical testing. However, one must note that complex flow simulations are challenging and error-prone and it takes a lot of engineering expertise to obtain validated solutions.
The Strategy of CFD
Broadly, the strategy of CFD is to replace the continuous problem domain with a discrete domain using a grid. In the continuous domain, each flow variable is defined at every point in the domain. For instance, the pressure p in the continuous 1D domain shown in the figure below would be given as