CFD Analysis and Simulation Techniques

Introduction to CFD

• CFD is a branch of physics studying fluids (liquids, gases, plasmas) and forces acting on them.
• Fluid mechanics is the branch of physics that studies fluids (liquids, gases, plasmas) and the forces acting on them.
• "Fluid" is a substance continuously deforming under shearing stress.
• "Mechanics" deals with both stationary and moving bodies under force influence.

Flow Solution Approaches

• Fluid flow can be studied analytically, experimentally, or numerically.
• Analytical approach uses mathematical equations to model the flow for cases like Couette flow, Hagen-Poiseuille flow, and Convergent-Divergent Nozzle.
• Experimental approach involves studying a prototype in a test facility. Measurement of fluid properties (temperature, pressure) is done using equipment like hot-wire anemometry, pitot tubes, and mass flow meters. Flow visualization techniques like colored oil and particle tracers (smoke, lasers) are also used.
• Numerical approach uses digital computers to model the flow using conservation laws (mass, momentum, energy) and dividing the fluid region into finite regions. CFD (Computational Fluid Dynamics) is a numerical approach.

Analytical Approach

• Analytical solution involves solving governing equations for the physics of the phenomenon under study.
• A general solution for all physical problems is complex.
• The approach is effective for simple flow cases with simplified geometry, dimensionality and compressibility.
• Examples of such flows include Couette flow, Hagen-Poiseuille flow, and Convergent-Divergent Nozzle.

Experimental Approach

• An experimental solution utilizes a prototype device within a test facility.
• Fluid properties (temperature, pressure) are measured using equipment.
• Hot wire anemometry measures rapidly varying velocities at a point. Other equipment includes pitot tubes and mass flow meters.
• Flow visualization techniques are used for understanding fluid behavior in a physical model (colored oil, smoke, laser light).

Numerical Approach

• Numerical solutions use computer simulations to model fluid flow via the conservation laws for mass, momentum and energy of fluid in motion.
• The fluid region of interest is discretized into finite regions.
• Governing equations are discretized into algebraic equations, which are calculated over time and space by computers.
• The result is a comprehensive description of the fluid's movement.

CFD Advantages

• Performance evaluation of systems before installation
• Comprehensive data on a system.
• Variety of post processing options for deeper insights into the system.
• Low cost compared to experimental testing in terms of time and resources. Simulation of dangerous or expensive experiments is also enabled.

CFD Generic Process

• Model Preparation: Convert geometries to watertight volumes suitable for CFD analysis. Select physics models, material properties, forces, heat sources. Assign boundary conditions.
• Mesh Setup and Meshing: Define mesh settings for surface and volume meshing. Run meshing.
• Solver Run, Monitoring and Post-Processing: Run CFD simulation. Monitor while running. Post-process results after the simulation is complete.

Physics - Governing Equations

• Governing equations model incompressible, viscous, heat-conducting fluids. Equations describe transport of mass, momentum, and energy.
• Fluid behavior is described in Eulerian perspective (at a fixed point) or in Lagrangian perspective (with the fluid particle).

Turbulence - Physics of Turbulence

• Turbulence is an essential feature of fluid flows with significant and irregular velocity field variations in time and position.
• Examples of turbulent flows include: rivers, ocean currents, cyclones, bush fires, and flows over bodies (cars, aircraft).
• Characteristics of turbulence: irregularity, non-repetition, three dimensional unsteady eddies, and property of flow, not fluid property.

Turbulence - Reynolds Number

• Reynolds number (Re) represents the ratio of inertial force to viscous force in a fluid flow. Calculated as:
• Re = ρuL/μ ,
• where: ρ is fluid density, u is flow velocity, L is characteristic length, and μ is dynamic viscosity.
• Re provides a method to characterize the flow patterns (laminar or turbulent) and determine dynamic similarity between flow cases.

Turbulence - Critical Reynolds Number

The critical Reynolds number (Recr) signals the transition from laminar to turbulent flow. Values depend on specific flow conditions. Parameters to consider are pipe diameter (for pipe flow), distance from the leading edge (for flow over a flat plate), and obstacle diameter (for an obstacle in cross flow).

Turbulent Flow vs. Laminar Flow

• Laminar flow exhibits a velocity field with layered velocity vectors at low Reynolds numbers. This is characterized by inertial force being smaller than viscous force.
• Turbulent flow has irregular flow patterns and mixing due to chaotic eddies at high Reynolds numbers. The inertial force is greater than the viscous force.

Challenges in Simulating Turbulent Flows

• Three-dimensional time-dependent flow
• Irregular and chaotic nature
• Non-repetitive
• Vast range of length & time scales
• Length scale reduction with increasing Reynolds Number
• Sensitivity to boundary & initial conditions

Modeling of Turbulence - Methods Comparison

• Various models of turbulence exist, including RANS, LES, and DNS, with differing ranges of modeled physics and computational cost. The most computationally expensive models (DNS) capture the smallest scales of turbulence, while the computationally least expensive (RANS) models often employ approximations.

RANS - Reynolds Decomposition

• Instantaneous velocity components can be decomposed into time-averaged component and fluctuating components (u = ū + u').
• The time average of velocity fluctuations is zero (ū = 0). The time average of variance uu' is not zero (u u'≠ 0).
• Reynolds decomposition provides a framework for deriving Reynolds-Averaged Navier-Stokes equation.

RANS - Reynolds-Averaged Navier-Stokes (RANS) Equation

• The Reynolds stresses (Tij) in RANS equations are unknowns, requiring turbulence models.

RANS - General Form of Turbulence Models

• The general form of turbulence models shows how different parts of the equation influence variables in relation to time and space, including convective term, diffusion term, production term, dissipation term, and unsteady term. Turbulent variables are denoted by φ.

RANS - Turbulence Models

• Spalart-Allmaras, k-ε, Realizable k-ε, and k-ω (including SST k-ω) are different turbulence models with varying characteristics and suitability for specific applications.
• Features like near-wall effects (or near wall damping term) are important aspects of some models.

Near-wall Turbulence - Law of the Wall

The law of the wall describes velocity near a wall in turbulent wall-bounded flow. It's a semi-empirical expression relating velocity to the distance from the wall. This behavior is independent of conditions further from the wall.

Near-wall Turbulence - Y+

• Y⁺ is a nondimensionalized distance from the wall, representing the ratio of turbulent and laminar effects within a computational cell.
• It is useful in numerical models for selecting density of mesh near boundaries.

Near-wall Turbulence - Boundary Layer Regions

• Viscous/Laminar sublayer: Turbulent motion stops near the wall due to the no-slip condition. Viscous shear stresses dominate.
• Buffer Layer: A transition zone between laminar and logarithmic sublayers wherein velocity gradients are high but flow is largely turbulent.
• Logarithmic Layer: A region where the velocity profile follows a logarithmic law.

Near-wall Turbulence - Boundary Layer Resolving Approaches

• Models need computational meshes appropriate for near-wall region phenomena resolution.
• Full boundary layer resolution using many cells to capture steep wall gradients.
• Wall functions use empirical non-linear relationships to model regions further from the wall.

Numerical Methods

• FEM (Finite Element Method) and FVM (Finite Volume Method) are different approaches to numerical modeling. FEM excels at near-wall aspects and has rich expression powers across interfaces, unlike the FVM.

Workshop 1: Manifold Flow Simulation

• This workshop explores CFD analysis workflows using SimLab for a manifold pipe model, analogous to an inlet manifold in an engine.
• The model aims for near-equal flow distribution among passages.
• The workflow involves importing CAD, meshing, setting up the solution, and visualization of results.

Workshop 2: Mixing Elbow Steady State CHT

• This workshop demonstrates a typical industrial mixing pipe scenario.
• Hot and cold water mix within the elbow, necessitating a Conjugate Heat Transfer (CHT) steady state simulation. The simulation is set up by importing CAD, creating the fluid domain, meshing, defining the solution, and visualising the results.

Workshop 3: Mixing Elbow Transient CHT

• This transient workshop considers variable inlet water temperatures.
• The solution utilizes initial conditions from the steady state simulation.
• The solver is disabled for flow, focusing only on heat transfer.

Workshop 4: Thermal FSI Mixing Elbow

• This workshop models a one-way coupled simulation of thermal fluid-structure interaction (FSI).
• Pressure and temperature loads from the CFD simulation of Workshop 2 are mapped onto the structural mesh.

More About CFD Volume Meshing

• CFD mesh tools create boundary layers (BL) and tetrahedral elements for the fluid interior. Input includes surface mesh bodies. The type of fluid bodies (e.g. inlets/outlets) affect how boundary layers are generated. Solid bodies might not need boundary layers.
• Various methods for controlling thickness of the first layer are discussed, along with total layer counts (numbers).

More About Residual and Solution Ratios

• Residual ratio represents the local imbalance of a conserved variable (velocity, pressure, etc), reflecting how accurately Navier-Stokes equations are solved.
• Acusolve simulations converge when both residual and solution ratios fall below predefined tolerances (e.g., 1e-3 for pressure, velocity, temperature; and 1e-2 for turbulence variables).