Aerodynamics of Aircraft, Cars, Ships, Trains and Helicopters

CFD++ applied to Aerodynamics combined with traditional engineering

The aerodynamic analysis is done by solving the air flow around solid bodies. It is a type of study that is widely applied both in the mobility and construction industries, for example: trains, cars, helicopters, aircraft, oil platforms, buildings, bridges, racing cars (MotorSport, StockCar, F1, Nascar, F-Indy ) and about ships.

ATS Solution

With the flow resolution, Navier-Stokes equations and continuity, it is possible to estimate the forces distributed in the model, as well as extract forces concentrated on surfaces or in the complete vehicle such as lift, downforce, drag, lateral forces and moments in the lateral and longitudinal.

motorsports aerodynamics

Compressibility Effects

An important variable for characterizing a flow is the Mach number, which indicates the relationship between the flow velocity and the sound velocity in the fluid under analysis. A Mach number less than 1 means flow with velocity below the speed of sound, while a Mach number greater than 1 means the flow is supersonic.

According to the flow velocity regime, the fluid modeling must be adjusted as a function of the physical phenomena involved.

Therefore, the flow velocity regime is divided into:

● Incompressible subsonic regime (M < 0.3)
● Compressible subsonic regime (0.3 > M > 0.7)
● Transonic regime (0.7 < M < 1.3)
● Sonic regime (M=1)
● Supersonic regime (1.3 < M < 5)
● Hypersonic regime (M > 5).

aircraft aerodynamics

Viscosity Effects

Flow can also be classified with respect to the Reynolds number, which indicates the turbulent condition observed by the fluid. The modeling of turbulence in fluids is a complex subject that is still under development in the literature, so there are several models that seek to equate this phenomenon and the transition between the turbulence stage. A widely accepted value in the literature as a transition point is the Reynolds number equal to 1 million. Reynolds number values below 1 million indicate laminar flow, while values above 1 million indicate turbulent flow. In fact, there is a transition band between laminar and turbulent flow, which is currently the focus of large studies


Computational Fluid Dynamics (CFD)

The most used method for numerical simulation in aerodynamic analysis is the Reynolds Average or RANS (Reynolds Averaged Navier-Stokes, RANS). More and more common is the use of transient Reynols averaging (Unsteady Reynolds Averaged Navier-Stokes, URANS) and large vortex simulation (Large Eddy Simulation, LES). These last two methods are important when transient or vortex effects are decisive for the description of the flow.

Ship aerodynamics helicopter landing

Historically, since the 70s, computational tools have been used to solve the Navier-Stokes equations with more simplified hypotheses such as potential (irrotational, incompressible), full potential (irrotational and compressible) and Euler (rotational, adiabatic and inviscid ). These equations were often solved in a coupled form with a boundary-layer equation solver, which could be integral or differential.

The classic problem of the Reynolds averaging solution is the turbulence closure problem, which is nothing more than the appearance of the Reynolds stresses (six variables) by applying the Reynolds average to the Navier equations. Stokes. More variables than equations occur and the system cannot be solved. To solve this, a turbulence model is implemented to describe the Reynolds stresses. As these turbulence models are not generic enough to cover all types of cases, there is a whole range of models, each suitable for one type of geometry, Mach type, or laminar, turbulent or of transition.

Flow Solution by CFD++

A flow solver like CFD++ brings several advantages for aerodynamic analysis such as accurate and robust interpolation schemes, low numerical dissipation, results validated by the biggest aerospace companies and possibility to obtain more accurate results with thicker meshes. CFD++ has been validated by aeronautical events such as AIAA Drag Prediction Workshop (DPW), AIAA High Lift Prediction Workshop (HLPW), AIAA Ice Prediction Workshop (IPW) and by automotive events such as the Oxford University Automotive CFD Prediction Workshop.

train aerodynamics

Integral Quantities of Aerodynamics

The importance of aerodynamic analysis grows with increasing speed because the aerodynamic coefficients of force and momentum are proportional to the square of the relative wind speed. The coefficients are a signature of the geometry of the body in relation to the wind and change according to the angle between the main axis of the vehicle and the velocity vector, called angle of incidence.

Support Coefficient:

Coeficiente de Sustentação

Drag Coefficient:

Coeficiente de Arrasto

Moment Coefficients:

coeficientes de momento

Experience and quality in our services

ATS has already worked on aerodynamic design and CFD simulation for Akaer, Brazilian Navy (helicopter landing on ships), Vale (cargo trains with or without cover and fuel economy), Vogel and CIMED Stock Car (downforce and drag varying ground and wing distance), Brascopter AlphaOne (moments, drag and lift), Mectron (engine air intakes and wings in turboprop or jet fighters), Desaer (aerodynamic performance of turbo prop aircraft) and ITT (inlet of the Mitsubishi Jet APU).

What's Beyond CFD Simulation?

JSBSim Aerodynamic Performance Simulation

Complementing aerodynamic flow analysis with CFD++, ATS uses DATCOM+ Pro software for aerodynamic analysis and JSBSim flight dynamics software for static and flight control calculations.

For tests in wind tunnels, ATS has experience in tunnels around the world, the most important in Brazil being that of the IAE (Institution of Aeronautics and Space), IPT (Institute of Technological Research) and the University of São Paulo (EESC -USP).

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Segments of activity in which Aerodynamic Analysis is applied

Check out the application segments below!


Check out some of the companies that are part of the history of ATS