In this blog post, we’ll explore the basic principles and analysis process of computational fluid dynamics (CFD)—which uses computers to calculate and visualize the invisible flow of air and water—as well as its relationship to wind tunnel testing and examples of its application in the automotive and sports industries.
When you see lines representing the airflow around a soccer ball, you might wonder what exactly they’re depicting. This isn’t just a decorative element to make the soccer ball look cool—it’s a visualization of how air moves around a flying soccer ball. Although airflow is difficult to see with the naked eye, it has a significant impact on an object’s motion. The air around a soccer ball does not simply flow along its surface; rather, it separates from the rear, forming complex wake patterns and vortices. These flow patterns affect pressure distribution and aerodynamic drag, thereby altering the soccer ball’s flight characteristics. Changing the smoothness of the ball’s surface or its shape—including irregularities and seams—also alters the surrounding airflow. Therefore, being able to observe and analyze the airflow around an object can be of great help in explaining, predicting, and controlling the object’s motion. In fact, when designing various sports equipment, including soccer balls and golf balls, the surrounding airflow and aerodynamic characteristics are considered key design factors.
A prime example of a method that enables us to calculate and visualize the invisible movement of air or water using computers is Computational Fluid Dynamics (CFD). Fluid mechanics is the field of study that deals with the motion of fluids—such as water and air—that possess the property of flow, as well as the forces acting upon them. The physical states of a fluid, such as velocity, pressure, density, and temperature, can be expressed through equations based on the laws of conservation of mass, momentum, and energy. CFD is a method that discretizes these governing equations into a form that a computer can compute and then numerically finds approximate solutions. Although the original text focused on the Finite Difference Method (FDM), modern CFD utilizes a variety of numerical analysis techniques, including the Finite Volume Method (FVM) and the Finite Element Method (FEM), in addition to the Finite Difference Method. In fact, modern CFD solvers such as NASA’s FUN3D use finite-volume-based discretization methods, and the finite-volume method is also widely used in commercial CFD software. The basic computational principle of CFD can be understood as follows.
First, the fluid domain to be analyzed is divided into numerous small grids or cells. For example, to calculate the airflow around an airplane wing, the calculation domain is defined to include not only the wing itself but also the surrounding airspace, and a grid is generated within that space. The points that make up the grid are called nodes, and depending on the numerical method used, physical quantities are placed at the nodes, the centers of the cells, or the cell faces for calculation. Consider a simple Cartesian grid: based on a point located at the i-th position in the x-direction and the j-th position in the y-direction, neighboring points above, below, to the left, and to the right can be defined. Δx and Δy represent the grid spacing in the x- and y-directions, respectively, while symbols such as uᵢ,ⱼ can denote physical quantities, such as velocity components at a specific location. In actual CFD, various types of grids—such as structured grids, unstructured grids, mixed grids, and overlapping grids—are used to represent the complex geometries of objects, and the grid density is often increased in necessary areas to improve computational accuracy.
Next, the differential equations describing the state of the fluid are transformed into algebraic equations that a computer can solve. In the finite difference method, the differential terms are approximated using difference equations based on the differences between neighboring grid points. To put it simply, using velocity as an example, this is similar to approximating the rate of change using the differences between values obtained at regular intervals, rather than directly handling the continuous changes that occur over extremely short time or distance intervals. In the finite volume method, the computational domain is divided into small control volumes, and conservation laws are applied to each control volume to calculate the transfer of quantities such as mass, momentum, and energy. Regardless of the method used, the “discretization” process—converting the continuous real-world fluid space into finite computational elements that a computer can process—is one of the core steps in CFD.
By applying the resulting equations to the entire computational domain, physical quantities such as velocity, pressure, temperature, and density can be calculated at each location. Rather than simply calculating the value at one point and then sequentially calculating the values at adjacent points, the process is more akin to numerically iterating through a vast number of interdependent algebraic equations to make the solution converge to a stable value. In the past, grids ranging from tens of thousands to several million elements posed a significant computational burden; however, with advances in high-performance computing and parallel computing technologies, it is now possible to perform analyses using much larger grids depending on the scale and purpose of the problem. The latest CFD programs can handle complex 3D geometries as well as turbulence, heat transfer, compressible flow, and multiphase flow; some CFD solvers also utilize modern high-performance computing resources, including GPUs. NASA is also currently expanding GPU support for its CFD solvers and is solving complex fluid problems by combining advancements in CFD with high-performance computing. Without advances in computing, it would have been extremely difficult to perform such extensive numerical calculations within a practical timeframe.
So, how were the interactions between objects and fluids studied before computers became sufficiently advanced? From the past to the present, one of the primary experimental methods used in fluid mechanics to understand these interactions is the use of wind tunnels or water tunnels. In a wind tunnel, an artificial airflow is generated, while in a water tunnel, a water flow is created to measure the flow around an object and the forces acting on it. Using a model of a race car to measure air resistance and aerodynamic characteristics is a classic example of a wind tunnel experiment. Experiments using wind tunnels or water tunnels are crucial for determining the magnitude of forces exerted by a fluid on an object placed within or moving through it, as well as how the surrounding flow changes. Numerous objects that interact with fluids—including cars and airplanes—are subjects of these experiments. Even today, wind tunnel testing is used as a vital means of validating CFD results and verifying actual flow phenomena. NASA also utilizes wind tunnels to validate CFD results and measure flow fields.
However, wind tunnel experiments require facilities of considerable scale and significant costs. While relatively small objects, such as a soccer ball, can be tested using full-scale specimens, testing large objects like cars or aircraft at actual size may require very large wind tunnels and entail enormous operating costs. For this reason, scaled-down models are often used. However, simply reducing the size of a model does not guarantee that the results will be identical to those obtained from the full-scale test. To obtain fluid-dynamically meaningful results, one must consider both the dimensionless parameters governing flow—such as the Reynolds number and Mach number—and the test conditions. Therefore, in actual experiments, test conditions are determined by comprehensively considering the object’s size and velocity, the properties of the fluid, and the purpose of the test.
As CFD has advanced, the design and research processes have also changed significantly. Verifying a wide range of geometries and operating conditions through actual experiments from the outset would require fabricating individual models or test specimens and conducting repeated experiments, which is both time-consuming and costly. CFD allows for the comparison of multiple design options and the analysis of flow characteristics on a computer before actual models are built, making it useful for narrowing down candidate designs. Another advantage is the ability to calculate and visualize the distributions of velocity, pressure, temperature, and other parameters even in areas that are difficult to measure or where it is challenging to install measurement equipment during actual experiments. Consequently, CFD is currently widely used in design and research across various fields, including aerospace, automotive, energy, architecture, electronic device cooling, and marine engineering.
However, it would be inappropriate to view CFD as a complete replacement for wind tunnel tests or real-world testing. To ensure the reliability of CFD results, it is crucial to perform validation—verifying that the numerical analysis process was carried out correctly—and to conduct validation checks to confirm that the simulation adequately reproduces actual physical phenomena. In particular, for phenomena that are difficult to calculate—such as complex turbulence, flow separation, or the interaction between shock waves and boundary layers—the process of comparing experimental results with CFD results remains essential. NASA also emphasizes verification and validation procedures—comparing experimental data with computational results—to ensure the accuracy and reliability of CFD, and it integrates wind tunnel testing and CFD as complementary tools rather than viewing them as competing technologies.
Racing cars are a prime example that illustrates the benefits of CFD. By analyzing the airflow around a racing car using CFD, it is possible to determine where air enters the body, where the flow separates, what kind of wake and vortices form behind the car, and how pressure is distributed across the surface. Using these results, it is also possible to calculate how drag, lift, and downforce are generated. Downforce is an aerodynamic force that presses a car toward the road surface; it can be generated not only by the rear wing but also by various aerodynamic elements such as the front wing, the underbody, and the diffuser. Appropriate downforce helps maximize the grip that tires can achieve on the road surface, which has a particularly significant impact on high-speed cornering performance.
However, simply maximizing downforce is not always beneficial. This is because increasing downforce can simultaneously increase aerodynamic drag. Higher aerodynamic drag can negatively affect the top speed and acceleration performance achievable with the same power output. Therefore, in the aerodynamic design of race cars, it is crucial to strike a balance between securing the necessary downforce and properly managing aerodynamic drag. Using CFD, designers can repeatedly compare changes in pressure distribution, flow separation, wake, drag, and downforce while making incremental adjustments to the body shape. Based on the calculation results, designers modify the shapes of the body and aerodynamic components, then run the revised design through CFD again to verify the changes in performance. If necessary, they validate whether the calculated results are replicated in real-world conditions through wind tunnel testing and actual road tests.
Another field where CFD is actively utilized is sports. By modeling cyclists and their bicycles and running CFD simulations, it is possible to analyze how airflow and pressure distributions change depending on the rider’s posture and the bicycle’s shape. Calculating the flow around the rider and bicycle allows for comparisons of where significant aerodynamic drag occurs and how overall drag changes when the rider’s posture is altered. Particularly in sports like cycling, where speeds are high and air resistance significantly impacts performance, the rider’s posture and the aerodynamic characteristics of the equipment are critical factors.
While wind tunnel tests involving actual people are possible, repeatedly testing every combination of posture and equipment requires considerable time and expense. Furthermore, the information obtainable from such experiments may be limited by the measurement equipment and locations used. CFD allows for the calculation of the flow field around the entire athlete and their equipment and enables the comparison of various conditions, making it a valuable tool for sports aerodynamics research alongside wind tunnel testing. However, since it is difficult to perfectly model human posture, movement, and actual competition environments, it is important to validate CFD results using experimental data and real-world competition data.
The application of CFD is not limited to cycling. In swimming, where drag from water significantly affects performance, CFD can be used to analyze the flow patterns resulting from an athlete’s posture, swimsuit, and movements in the water. In sports involving movement through the air, such as auto racing and cycling, CFD can analyze aerodynamic drag, while in sports involving movement through water, such as swimming, it can analyze hydrodynamic drag and pressure distributions. Thus, in the sports field, CFD is not merely a technology for creating visually appealing flow images but is utilized as an analytical tool to quantitatively understand how athletes and equipment interact with fluids.
Fluid dynamics can seem like a difficult field of study because the movement of fluids—such as air and water—is difficult to observe directly with the naked eye, and flow patterns change complexly depending on various conditions, including an object’s shape, velocity, pressure, viscosity, and temperature. CFD helps us understand these complex phenomena more concretely by calculating these invisible fluid movements and visualizing them in the form of velocity fields, pressure fields, temperature fields, and streamlines. It also plays a crucial role in enhancing the efficiency of design and research processes by allowing various conditions to be tested virtually before actual devices are manufactured or experiments are conducted.
Currently, CFD is used in a wide variety of fields beyond traditional aerodynamics—such as aircraft and automobiles—including space launch vehicles, propulsion systems, thermal-fluid systems, wind around buildings, cooling of electronic devices, energy facilities, ships and offshore structures, and sports science. At the same time, since CFD results can vary depending on the physical models, turbulence models, mesh quality and resolution, boundary conditions, and numerical methods used in the calculations, the results should not be unconditionally accepted as identical to reality. For accurate analysis, it is necessary to check the convergence and mesh dependency of the results and, where possible, verify them by comparing them with experiments or reliable data.
Ultimately, the greatest significance of CFD does not end with making the invisible movement of fluids “visible.” Its true value lies in numerically calculating the invisible flow of air and water, analyzing the results to predict the forces acting on objects and changes in the surrounding environment, and enabling the discovery of better designs. When experiments, theory, and numerical analysis using high-performance computing complement one another, we can gain a more accurate understanding of complex fluid phenomena. CFD is thus a powerful tool used to study and design various objects that interact with fluids, and as computer performance and numerical analysis technologies advance, its scope of application and precision continue to expand.
