CFD: Understanding Fluid Flow Through Computational Analysis

Introduction to Computational Fluid Dynamics (CFD)

Definition of CFD: CFD is the process of mathematically predicting physical fluid flow by solving the governing equations using computational power. Every CFD analysis uses a mathematical model and numerical method based on the Navier-Stokes (N-S) equations. Physical properties are calculated based on defined operating conditions.

Main objectives:

• Minimize the cost of the system
• Understanding and comprehension of the problem
• Improve behavior
• Reduce the time and cost of the design stage

3 Fundamental Principles:

1. Mass is conserved
2. F=m*a (Newton's 2nd Law)
3. Energy is conserved

Mass Conservation Principle: The rate of increase of mass in a fluid element equals the net rate of flow of mass into the fluid element. This can be represented as: ∂ρ/∂t + ∇(ρu) = 0, which simplifies to ∇(u) = 0 for incompressible fluids. In the Lagrangian approach, each property of a fluid particle is a function of its position.

Newton's 2nd Law: The rate of increase of the momentum of a fluid particle (ρ*Du/Dt for the x-axis) equals the sum of the fluid forces acting on the fluid particle.

Energy Equation: Based on the first law of thermodynamics, the rate of increase of energy in a fluid particle equals the net rate of heat added to the fluid particle plus the net rate of work done on the fluid particle.

The governing equations for an unsteady 3D compressible viscous flow are:

1. Continuity equation
2. Momentum equations
3. Energy equation

Navier-Stokes (N-S) Equations

All theoretical fluid dynamics models are based on the N-S equations, which describe the motion of viscous domains. The main structure of a thermo-fluids problem is governed by equations based on the conservation laws:

1. Conservation of mass: Continuity equation
2. Conservation of momentum: Newton's 2nd Law
3. Conservation of energy: 1st law of thermodynamics or energy equation

These principles state that mass, momentum, and energy are stable constants within a closed system.

The movement of fluid can be investigated with:

Lagrangian Method: This method follows a fluid particle that is large enough to detect properties. Coordinates of particles are tracked through the time domain. It is useful when individual particles or fluid elements play a significant role.

Eulerian Method: The velocity field is examined as a function of space and time. A control volume is evaluated, and particle flow within this volume is solved. This is useful when we want the overall behavior of the fluid.

Compressible and incompressible fluids:

Compressible Fluids: The equation of state provides the linkage between the energy equation and mass conservation and momentum equations.

Incompressible Fluids: These include liquids and gases flowing at low speed. Without density variations, there is no linkage between the energy equation and the mass conservation and momentum equations.

Meshing Techniques in CFD

Model generation:

1. Solid modeling: The user describes the boundaries of the model (recommended for 3D and complex geometries).
2. Direct generation method: The user determines the location of every node and the shape and connectivity of every single element.

Size controls in Ansys: Point control or edge, face, or body sizing.

Sweep meshing in Ansys: Results in prism/hex elements instead of tetrahedra, which reduces the amount of elements, thus reducing computational cost.

Inflation layer: Required to accurately capture the boundary layer region for any wall-bounded turbulent flows.

Turbulence Modeling in CFD

Turbulence is a dissipative phenomenon where kinetic energy is converted into heat due to viscous shear stress.

Laminar flow: Solved with the conservation equations.

Turbulent flow: Additional turbulence equations are required to approximate the turbulence.

Different alternatives for turbulent modeling:

1. Linear methods for non-viscous flux.
2. Nonlinear methods for non-viscous flux.
3. RANS methods (Reynolds Averaged Navier-Stokes).
4. DNS methods (Direct Numerical Simulation).

Model Resolution in CFD

Pressure-based technology: Solves the pressure equation to conserve mass and can be used in any flow simulation except in non-reflecting boundary conditions and wet steam multiphase models. There are segregated solvers (equations solved sequentially) and coupled solvers (equations solved at once, higher convergence speed but higher memory required).

Density-based algorithm: Solves the continuity equation along with momentum, energy, and species transport as a coupled set of equations. Additional equations are solved sequentially.