Computational Fluid Dynamics (CFD) stands at the forefront of engineering innovation, offering unparalleled insights into fluid flow behavior through advanced simulations. This comprehensive article delves into the fundamentals of CFD, its historical evolution, governing equations, convergence principles, and the pivotal role of the Finite Volume Method. From aerospace to environmental engineering, CFD’s applications span diverse industries, revolutionizing design and optimization processes.

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## What is Computational Fluid Dynamics?

Computational Fluid Dynamics (CFD) is a field of study that uses computer-based simulations to analyze and predict fluid flow, heat transfer, and related phenomena such as chemical reactions within a system. By employing numerical methods and algorithms, CFD allows for the detailed examination of how fluids behave under various conditions, facilitating the design and optimization of systems across numerous industries, including aerospace, automotive, and chemical engineering.

## Applications of Computational Fluid Dynamics

The technique is highly versatile and applicable to a broad spectrum of both industrial and non-industrial areas. Some examples include:

- Aircraft and vehicle aerodynamics: analyzing lift and drag forces
- Ship hydrodynamics: studying the behavior of ships in water
- Power plant operations: simulating combustion processes in engines and turbines
- Turbomachinery performance: understanding flows within rotating components
- Cooling systems in electrical engineering: managing heat dissipation in equipment, including microcircuits
- Chemical processing: optimizing mixing, separation, and polymer molding
- Building environments: assessing wind loads and HVAC systems
- Marine engineering: evaluating loads on offshore structures
- Environmental analysis: modeling pollutant dispersion and wastewater flow
- Hydrology and oceanography: studying flows in rivers, estuaries, and oceans
- Meteorology: predicting weather patterns
- Biomedical applications: simulating blood flow in arteries and veins

## History of Computational Fluid Dynamics

The journey of Computational Fluid Dynamics (CFD) began much earlier than the whirring of mid-20th century computers. The 18th and 19th centuries saw the formulation of fundamental equations by Bernoulli and Euler, laying the groundwork for CFD. By the 19th century, the arrival of the Navier-Stokes equations provided the core set used in CFD simulations today.

In the mid-20th century early attempts were made to simulate fluid flows using numerical methods, particularly during World War II for military applications like aircraft design and weather forecasting. The 1960s and 1970s saw significant progress with the emergence of digital computers, enabling researchers like John von Neumann and Stanislaw Ulam to develop foundational numerical techniques such as the finite difference method.

During this period, institutions like NASA contributed groundbreaking CFD codes that expanded simulation capabilities. The 1980s and 1990s witnessed rapid growth in CFD, fueled by advancements in computing power and algorithms. Commercial software packages became available, empowering engineers across various industries to address complex fluid dynamics problems.

Today, CFD has evolved into an essential engineering tool, facilitating optimization, performance enhancement, and cost reduction in diverse applications ranging from aerospace and automotive to energy and environmental engineering. Ongoing advancements in high-performance computing and numerical techniques continue to drive innovation, promising further breakthroughs in the field of Computational Fluid Dynamics.

## Governing equations of CFD

Computational Fluid Dynamics relies on a set of fundamental equations derived from well-established physical principles. These equations express the conservation laws of mass, momentum, and energy within a fluid flow.

**Continuity Equation (Conservation of Mass)**: The rate of change of mass within the control volume is dictated by the flow passing through its boundaries.

Where x,y, and z represent dimensions in a Cartesian framework, u, v, and w denote velocities in the x, y, and z directions, respectively. t stands for time, and ρ represents density.

**Navier-Stokes Equations (Conservation of Momentum)**: These equations describe the conservation of momentum for fluid flow, encompassing the effects of inertia, pressure, viscous stresses, and external forces on fluid motion. In fluid mechanics, the Navier-Stokes equations govern momentum conservation, typically expressed in a three-dimensional framework for Cartesian coordinates.

*x*, *y* and *z* represent dimensions in a Cartesian framework, *u*, *v*, and *w* denote velocities in the *x*, *y* and *z* directions, respectively. t stands for time, *ρ* represents density, *τ* is viscous stress and *g* is body force such as Gravity force.

It should be noted that depending on the requirements of the problem, such as whether the fluid is compressible or not, or whether it is Newtonian or non-Newtonian, the terms of the equations may vary. We have provided their most general form.

**Energy Equation (Conservation of Energy)**: This equation relates the changes in a fluid’s internal energy to heat transfer, work done by the fluid’s stresses, and any heat sources within the flow.

Where V is the vector of velocity and u is internal energy. There are various forms of the energy equation. Depending on the need, different terms can be added to or subtracted from this equation.

## Convergence in Computational Fluid Dynamics

Convergence in Computational Fluid Dynamics refers to the process of ensuring that the numerical solution of fluid flow equations approaches the true physical solution as computational parameters like mesh resolution and time step size are refined. This is essential for obtaining accurate and reliable simulation results. Achieving convergence involves reducing residuals, ensuring grid independence, and stabilizing iterative methods. Techniques such as mesh refinement, under-relaxation, multigrid methods, preconditioning, and residual monitoring are commonly used to aid in convergence. Additionally, proper implementation of boundary conditions, a good initial guess, and validation against experimental data are crucial for enhancing the robustness and accuracy of CFD simulations.

## How does Computational Fluid Dynamics Work?

After defining the problem, including the boundary conditions, domain, and required equations (such as the Navier-Stokes equations), a discretization method is used to convert the continuous equations into a solvable numerical form. Common discretization methods include the Finite Element Method (FEM), Finite Volume Method (FVM), and Finite Difference Method (FDM). The solution domain is then meshed, dividing it into small, discrete cells or elements. The numerical solver iteratively computes the flow variables within these cells until the solution converges. Finally, in the post-processing stage, the required results, such as velocity fields, pressure distributions, and other flow characteristics, are extracted and analyzed.

## Computational Fluid Dynamics example

The lid-driven cavity flow is a classic benchmark problem in CFD used to study the behavior of fluid flow within a square or rectangular cavity. Engineers and researchers typically test their CFD models in this problem to assess the accuracy of their simulations. In other words, this example serves as a fundamental test case for CFD algorithms and is utilized to validate numerical methods and codes.

In simulating lid-driven cavity flow using Computational Fluid Dynamics, a rectangular cavity is defined with stationary walls on three sides and a lid moving at a constant velocity on the top. The governing equations, typically the Navier-Stokes equations for incompressible flow, are discretized using numerical methods like Finite Volume Method (FVM) or Finite Difference Method (FDM). The cavity is meshed, with a finer grid near the walls to capture boundary layer effects accurately. The simulation computes the velocity and pressure fields within the cavity iteratively until a steady-state or time-dependent solution is reached. Post-processing involves analyzing the flow patterns, shear stresses, and other relevant parameters to understand the behavior of fluid flow within the cavity.

Meshed domain and boundary conditions of lid-driven cavity

## Why is the favorite discretization method in CFD simulation the Finite Volume Method?

The Finite Volume Method (FVM) stands out as a preferred choice in CFD simulations owing to its inherent conservation properties, flexibility with irregular grids, and alignment with physical laws governing fluid flow. Through the discretization of governing equations across control volumes, FVM guarantees the preservation of mass, momentum, and energy, rendering it highly applicable across diverse flow scenarios. Its stability, convergence characteristics, and compatibility with turbulence models further contribute to its popularity, enabling accurate predictions of complex fluid behaviors. This method’s widespread acceptance is further accentuated by its proven efficacy in tackling real-world engineering complexities, underlining its indispensability in the realm of fluid mechanics research and industrial applications.

Streamlines illustrating the circular pattern created by the axial-flow swirl generator, demonstrating the mechanism that induces a swirling motion in the water and oil mixture, thereby generating centrifugal force. Figure from ANSYS Fluent simulation, from “Two-phase In-line Separator using axial-flow Swirling Generator CFD Simulation”

## ANSYS FLUENT Capabilities in Computational Fluid Dynamics

ANSYS Fluent is designed for CFD problems based on FVM. Within the ANSYS software suite, all aspects of CFD problem solving, including geometry definition, meshing, problem solving, and post-processing, are executed effectively. ANSYS Fluent possesses the capability to simulate highly intricate cases in CFD, encompassing combustion, multiphase flows, turbulent flows, and more. Moreover, the software can simultaneously simulate the mentioned cases, demonstrating its versatility and robustness in handling complex fluid dynamics scenarios.

At CFDLAND, we have completed numerous projects using ANSYS Fluent, all of which can be viewed in our CFDshop. Additionally, you can submit your CFD projects through the Order Project section. Trust our team of CFD experts to handle even the most complex simulations with proficiency and precision.

Turbulent kinetic energy contour based on ANSYS Fluent simulations from “5-blade Vertical Axis Wind Turbine CFD Simulation”

## Conclusion

In an era defined by digital innovation, Computational Fluid Dynamics emerges as a transformative force in engineering. From its historical roots to contemporary applications, CFD’s evolution reflects a relentless pursuit of accuracy and efficiency. With ANSYS Fluent leading the charge, engineers navigate fluid dynamics complexities with confidence, driving advancements across industries. As CFD continues to push boundaries, its impact on design, optimization, and performance enhancement remains unmatched, shaping a future where fluid dynamics mastery fuels limitless innovation and progress.