## Aerodynamics and Computational Fluid Dynamics

Aerodynamic studies involve the motion of air and its interaction with solid objects within this flow representation. Aerodynamics and aerodynamic principles are used frequently within computational fluid dynamics. Not only are the primary governing equations of aerodynamics used within CFD, but also in boundary layers for both the mesh generation and solver convergence, as well as turbulence modeling, and compressible flow theory. The future of aerodynamics in CFD contains many facets, but particularly in automotive, subsonic travel, hypersonics, and alternative energy development.

Early aerodynamicists such as Otto Lilienthal and Sir Isaac Newton contributed to efforts of understanding fundamental concepts like drag. Subsequent scientists such as  Bernoulli and Euler contributed recognizable principles for the overall study of flow dynamics, and Navier and Stokes, who developed the partial differential equations responsible for computational fluid dynamics. The earliest renditions of aerodynamic studies and mathematical computations involved wind tunnels, moving further into computational simulations with the development in technological prowess for airflow and airfoil modeling.

## Flow Classifications and Equations

The three primary facets to resolve in aerodynamics are lift, drag, and torque. Each of these have unique properties (lift coefficient, drag coefficient, lift force, and more) affected by the air flow involved. In an aerodynamic flow field, the properties you will most likely be looking at are temperature, pressure, velocity, viscosity, and density.

## Velocity-Based Classification

When examining velocity-based classification for flow, we are looking at speed regimes. The four primary velocity qualifications for flow are in subsonic, transonic, supersonic, and hypersonic flows. The beginning of velocity-dependent classifications is approximately when flow speeds move faster than 30% of the speed of sound, where flow characteristics are marked by compressibility effects.

Subsonic flow is a self-explanatory in that it is intended toward air speed that does not exceed the local speed of sound. This will be in velocity calculations for much consumer and ground travel; however, there are also high-speed transport vehicles (trains) in development. Typically, this is represented through a Mach number less than 1, or the flow velocity registered past a boundary.

Transonic flow is a bit of an oddity in the sonic spectrum, as it includes elements on both the sub- and supersonic flow regimes. Typically, the Mach number associated with transonic flow is between 0.8 and 1.2M. Although supersonic commercial flight is certainly a possibility being worked on   in years to come, most commercial flights will occur within the transonic flow regime.

Probably, the most familiar concepts would be the wonderfully heroic ones of sonic boom and supersonic flow, where velocities in the flow regime are greater than the speed of sound (have a Mach number greater than 1). We model and simulate this through various boundary and curvature phenomenon; however, some examples of supersonic flow consist of jet propulsion and bullets.

We also think in terms of hypersonic flows; however, there is no accurate definition (or at least agreed upon consensus) of the value above a Mach number of 1, where velocity is differentiated between supersonic and hypersonic. Historically, hypersonics have had use and function within missile defense systems, spacecrafts, and rocket-powered planes or jets, but forward-thinking engineers might re-think the potential for hypersonic development.

## Density and Pressure-Based Classifications

The other primary flow classifications at work in aerodynamics are in density and pressure-based classifications. Often, these classifications translate into compressible and incompressible flow definitions. These definitions depend upon how variable the density is during the flow. If the density remains nearly constant, we can assume incompressible flow (for ease of simulation, a pivot number to work from for incompressible flow is under Mach 0.3).

For instance, if the flow density changes along a streamline, or while shifting air regime strata along a climbing flight path, it is instead known as a compressible flow. In comparison, engineers can assume compressible flows are above Mach 0.3, but they can be in subsonic, transonic, supersonic, or hypersonic paradigms.

Shifting aircraft travel speeds and modeling flow behaviors on airfoils require consistently adapting and evolving aerodynamic theories to address these significantly more complex compressible airflow characteristics. Many laws, rules, and equations consist of exceptions within the compressibility-incompressibility dynamic of flow. The Prandtl-Glaubert rule, Mach numbers, and the Navier Stokes equation derivations, all maintain fundamental importance (depending on acoustic or convective pressures). Within the Fidelity CFD Platform environment, the Cadence CFD capabilities maintain and aim to improve both density and pressure-based solvers.

## Law of Aerodynamics

Aerodynamics and aerodynamic principles are built around some fundamental equations. Newton’s laws of motion certainly started the study of aerodynamics; however, in the world of computational fluid dynamics, aerodynamic forces are conventionally modeled through the Navier-Stokes equations. Other methods such as Lattice-Boltzmann and High Order solvers are gaining in popularity and capability.

The role of aerodynamics within this set of partial differential equations is largely to serve as a cornerstone for system design and simulation. Making a highly aerodynamic design is pivotal for the overall efficiency of a system, such as a car or an airplane; yet, CFD has its primary function when these aerodynamic principles reduce into more specific and nuanced elements; for example, heat management, noise and acoustic generation, structural integrity, and other types of physics out there.

The key factor in CFD is not to specialize and resolve one physical phenomenon to the absolute best of your ability, but always to determine the tradeoff between time and cost of optimizing as many of these intertwining physical phenomena as possible for the best overall system performance.

## Aerodynamics Propulsion Systems

When discussing the fundamentals of aerodynamics, many of the reductions of underlying aerodynamic principles are modeled for optimizing propulsion mechanisms. Specifically, for airplane aerodynamics, an aerodynamics engineer would be looking at thrust, weight, angle of attack, and drag.

Below, you can find more detail on the exact use-case of aerodynamics in various highlighted industry solutions, but to get you started on the right track, here are two of the more consistently applied and complicated mechanisms in propulsion: angle of attack simulation and drag.

## Aerodynamics Angle of Attack

Angle of Attack (AOA) affects both lift and drag fundamentally throughout the design of an aircraft. AOA is the angle between a reference or chord line on an aircraft, usually, a wing or the center of the body, and the point at which the wing hits the relative wind. Optimizing AOA for particular flight functions is crucial for the overall efficiency of flightpath and airplane bodies, as AOA has a direct relationship with lift and drag: as AOA increases, so too does lift and drag, until AOA hits its stall point, at which point, depending on wing structure and a slew of factors, one can see either a sharp or tapered decline in lift.

As mentioned above, CFD simulations toward aerodynamics attempt to understand many unique physical phenomenon, positions, and environments at once, for optimal system performance. This is certainly the case with AOA measurements, as optimizing airfoil performance entails the consideration of airflow at as many as necessary unique angles of attack.

AOA modeling and simulation relies heavily on mesh creation and accuracy for optimal boundary layer measurements and models, as well as a solver engine capable of handing the intricate computational uncertainties produced with turbulent flow regimes. Other factors that make AOA simulation particularly noteworthy in CFD environments today include adverse pressure gradient changes, separation of airflows, creation of shock waves, and much more.

## Aerodynamic Drag

Drag is a vital force to contend with in aerodynamics. Often, drag is particularly relevant in structural integrity modeling and heat management models. The resistance created, drag force, acts in opposition to the motion of the solid body at work. The simulation of drag force has many unique iterations, such as representing specific turbulent flow vortices and eddies, creation of lift from drag forces and forming drag with local velocity and pressure changes.

Depending on an automotive or aerospace-based vehicle, resultant drag forces will require drastically different force and counterforce designs. Additionally, designing turbomachinery such as large scale fans for wind energy sources will likely require optimizing drag for noise reduction and force generation to encourage as much efficiency of randomly generated force as possible.

## Aerodynamics Simulations

One of the biggest mistakes in aerodynamics simulations is sacrificing other physical components for the sake of aerodynamic perfection. Unfortunately, we do not possess the technology or time to simulate every single physical phenomenon, scenario, and environment to 100% accuracy within any reasonable product timeline; nonetheless, here we are.

In lieu of total representative simulation perfection, in their aerodynamic simulations, engineers are actually hoping to take as much into account as possible, considering computational capabilities and cost availability.

However, two consistently challenging areas for aerodynamic simulation are representing boundary layers and accurately modeling the unique flow regimes as they draw closer to a solid wall, as well as turbulence and the vast number of computational uncertainties created in vortex and eddy modeling. The quality of mesh you use can vastly improve the results and accuracy of your simulations (and we happen to have one of the best meshing tools available for this purpose). Ultimately, increasing the number of cells in your mesh will dictate the accuracy of your simulations, and concurrently, the time and cost necessary to run a simulation.

## Automotive Aerodynamic Simulations

Solutions for aerodynamic CFD modeling in the automotive space are vast, with a constant push towards greater efficiency. One of the most definitive ways to make a vehicle more power efficient is through aerodynamic optimization. Optimizations can be in the form of weight distribution, shape, and form of the vehicle, to ensure airflow is directed in the right areas, managing vortex and eddy creation to minimize drag, and minimizing lift impact on the vehicle’s performance.

One specific example for an automotive engineer in CFD simulations would be: how thin can the surfaces of a car become?

The physical phenomena and quantities at work to be measured here are certainly in structural integrity—it would be sub-ideal to have the roof of a car fly off on a particularly fast stretch of highway—as well as heat management, both in the form of driver and passenger comfort, and with the greater degrees of electrification in vehicle powertrain environments, ensuring that this powertrain does not overheat, and greatly reduce its voltage and current transmission efficiency.

Virtual wind tunnel simulations of vehicles are gaining in popularity, as physical wind tunnels maintain usage around-the-clock with the ever-pressing need for greater degrees of innovation, as car companies are working to make their more electric vehicles (MEV). These virtual wind tunnels allow expressing and studying some of the aerodynamic effects above, but additionally, enable mapping vortex creation and air pressure drops as a car moves through an airflow regime. Vortex creation can increase pressure drag, and therefore, many cars will have rear spoilers to increase downforce and minimize the risk to car adhesion and handling stability.

## Aerospace Aerodynamic Simulations

Most dynamics of an air-based-travel vehicle can be examined under the guise of aerodynamics. Helicopters, UAVs, drones, jets, and airplanes all have unique properties for propulsion, rotational lift, drag, angle of attack necessities, flight duration, and environmental specifications. The development of new aircraft is ever on-the-rise as new speeds and efficiencies of travel, such as supersonic commercial flights, hypersonic jets, and more electric commercial flights all require more finely-tuned attention toward the physical phenomenon reduced from aerodynamics principles. Solving these Navier-Stokes equations in a CFD simulation element enables the aerospace engineer to work towards solutions for the above difficulties.

A particularly common challenge within the aerospace industry that CFD addresses is optimizing the overall efficiency of fuel for flight over known distances (typically, in commercial travel). Simulating the airflow over an entire cross-country flight, across unique or differing jet streams and air densities, and for an evolving climate, requires constant re-assessment of simulations and models.

Wing dynamics can play a very deterministic role in the efficiency of a flight path. The air flow interactions on wing structures are modeled at any scale from viscous stress development as well as disordered fluctuations and turbulence modeling. It is necessary to trust accurate and fast CFD simulations in aerodynamic parameters for the overall health and integrity of power efficiency across airplanes.

## Turbomachinery Aerodynamic Simulations

Whether it be helicopter propeller aerodynamics, large-scale fans for alternative energy and energy efficiency, or marine propellers, one can model the flow dynamics with CFD. Unlike other aerodynamic simulations, not only are turbomachinery being optimized for the air or fluid flow streams that they’re already a part of, such as wind and unique air densities, but these fans are also responsible for generating concurrent flows with their rotational mechanisms. Traditional aerodynamic forces such as lift and drag meet with turbulent flow and vortices on an immensely diverse spectrum of physical events.

For more historic Cadence customers in the EDA or semiconductor spaces, this might appear in an age-old question of: how much can fan size be reduced?

While simulations can certainly verify that typically, there is an inverse relationship in the smaller size of a fan the better its performance, and the greater acoustics generated from its rotational speeds. This acoustic generation, on large scale structures, results in environmental disturbances; however, in the microscale of commercial technologies or high-performance computing, consumers are also looking for minimal noise disruptions with infallible product design. There are many tradeoffs to consider within the overall ecosystem of turbomachinery aerodynamics.

## Aerodynamics Design for CFD Flow

While CFD is looking at flow regimes across the board, the actual flow for CFD tool implementation rarely changes. To run an iteration on a solver you need to have the mesh for it, and to have the mesh, you need to have the geometry for it. While it would be fantastic to say that we are the best-in-class for every possible solver function and mesh generation, the reality is that there are simply too many physical phenomena and partial differential equations to account for holistically. It is likely that there will always be some tools that are better than others at particular functionalities.

With Cadence Computational Fluid Dynamics, we hope that an aerodynamics engineer can take whatever geometries they’ve created and enjoy a best-in-class mesh generator that can funnel seamlessly into a one-stop solve and post-processing flow. Alternatively, we hope that if you’ve found another tool that can give you the solving iterations necessary for the highest quality product, you can take our best-in-class mesh and utilize the two environments for the utmost accurate and secure solutions.

## Meshing for Aerodynamics

If you ask any aerodynamics engineer working in CFD simulations about their favorite part of CFD, it is very likely that none of them will say meshing. Meshing isn’t exactly what you write to your parents about; yet, the quality of mesh empowers solvers to be more accurate and complete iterations faster than if a mesh is done improperly. The Cadence meshing tools are capable of advanced mesh generation for those difficult and pivotal definitions, such as boundary layers, utilizing Delaunay triangulation and hybrid approaches alongside hexahedron cells to maximize accuracy in representation with mesh cell count size.

Fidelity Pointwise® Meshing is a best-in-class mesh generator for CFD, constantly building out its robust capacity and striving towards the NASA 2030 CFD Vision plan for CFD development. For external aerodynamics meshing, Fidelity Pointwise meshing won’t be beat. Furthermore, Cadence also has highly automated meshing capabilities within the Fidelity platform for when efficiency and product schedules are of top priority. Each mesh-generation option will get your simulations off the ground and into convergence with ease, and largely depend on how much time and need for full control you and your engineers’ desire.

## Aerodynamics Solving and Convergence

CFD solvers are always being fine-tuned to interpret more detailed and accurate meshes, implement equations more robustly, allow for greater computational prowess, and save time and cost. In CFD, an aerodynamics engineer would want to ensure the solver can work dynamically on large-scale iteration runs of various Navier-Stokes equations and reductions to ensure total design security. As mentioned, a purely aerodynamically optimized vehicle is probably failing in very many other regards, be it heat, structure, or some other physical phenomenon.

One phenomenon that CFD solvers are always attempting to refine and perfect is turbulence modeling. Turbulence models have long produced what is known as computational uncertainties, and being able to assess and resolve these uncertainties to the greatest degree of accuracy is vital to understanding, and therefore, ensuring, the greatest design for aerodynamic stability. Whether using Reynolds-Averaged Navier-Stokes (RANS), Large Eddy Simulation (LES), a hybrid approach, or some other novel approach to resolve uncertainties, aerodynamics continues to be a unique and tenuous domain to solve for.

## Post-Processing and Aerodynamics

A vital tool in the CFD engineer’s toolkit is post-processing. Post-processing has many different iterations, which enable the visualization of potential problem spots in any design. A popular post-processing representation for aerodynamics is in streamline techniques. Streamlines for aerodynamics showcases flows against and around surfaces to observe air displacement, pressure changes, or velocity changes as flows encounter structures.

With the optimal use of post-processing tools, an engineer can make their iterations significantly easier and take less time, by discovering potential problem spots or areas requiring more attention early. Then, aerodynamics engineers can take the post-processing results back to the mesh and potentially refine cells around problem areas to ensure accurate representation.

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