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In this video, we'll discuss Aerodynamic Shape Optimization using the adjoint technique.

General optimization problems
Imagine we want to maximize a certain output value Y (like airfoil lif) by changing the input variable X (like the angle of attack). The relationship between both can be expressed through a mathematical function, which we'll call the objective function.

To find the maximum lift value, we can pick a random angle of attack value on the X-axis and then calculate the corresponding lift value on the Y-axis. We can then pick a second point close to it and do the same thing. With these two data points known, we can calculate the local gradient, which indicates the direction in which we need to march to get closer to the maximum.

After enough steps, you will have reached the maximum. The downsides of this technique are that you can miss the peak or get stuck on a local peak, but this is the general procedure used in gradient-based optimization techniques.


Aerodynamic Optimization
In aerodynamic simulations, the airflow around an object is chopped up in small pieces called cells within a mesh. The surface of the object is also chopped up into small pieces called surface cells with nodes on the corners.

To obtain the total drag or lift of the object, we need to integrate the pressure & friction forces on all these local surface cells to get the total value. This indicates that the position of each individual node has an influence on the final drag & lift on the object.

The objective function, therefore, has thousands if not millions of input variables: the X, Y and Z coordinate of each individual node. To obtain the local gradient, you would need to move one node individually and then re-run the entire calculation to calculate the local gradient. With that information, you know whether to push the node inward or outward to increase or decrease the objective function. Once you have obtained all these local gradients, you can put them together into what is called a surface sensitivity map.

As you can imagine, re-running the entire simulation for each node displacement can become very expensive. Luckily, there is something called the adjoint technique.

Adjoint
The adjoint technique allows you to calculate all of these local gradients, or sensitivities, in one single simulation. Here's how this works:

- Normal aerodynamic simulation (primal or forward simulation):
After the computational mesh has been generated, the flow field is typically initialized using a fixed value (zero or something else). Then, the properties defined at the boundary conditions (like an inlet flow velocity for a virtual wind tunnel) propagate through the domain. After enough small time steps, the solution will have converged to a stable flow field.

- Adjoint simulation (dual or backward simulation)
Starting from the aerodynamic simulation data, the adjoint simulation will take small "time" steps. It calculates backward from the objective function to see how each node position affects this objective function. Based on these results, we can then calculate all the local gradients and construct the sensitivity map.

So instead of running a full aerodynamic simulation for each local gradient calculation, which would be prohibitively expensive, we can now calculate all the gradients with just two simulations: the normal (primal) and the adjoint (dual) simulation.

Morphing
The next step is to use the input of the sensitivity map and start implementing it: move the surface inward or outward based on what the map tells you. Once you have morphed the 3D object, you can re-run the aerodynamic simulation to see how much the objective value has changed. You can then also re-run the adjoint simulation to create a new sensitivity map and to the morphing again.

With each cycle, you will get closer to the most optimal shape for your object. You can do this for the entire object or you can define a design space in which the algorithm can operate.

Porsche Taycan
Interestingly enough, the adjoint optimization technique - when asked to increase downforce - starts to create the iconic ducktail spoiler that Porsche has been applying for years.

For more information or to run your own optimization project, just contact AirShaper at info@airshaper.com


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The adjoint code used is part of OpenFOAM v2012 and was developed by the Parallel CFD & Optimization Unit of the National Technical University of Athens (http://velos0.ltt.mech.ntua.gr/research/index.html). Details about the theoretical background of the adjoint method can be found in the publications listed here:
http://velos0.ltt.mech.ntua.gr/research/pubs.html

Aerodynamic Shape Optimization - The Adjoint CFD Method

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How to use coastdown testing for drag measurement

What is coastdown testing?
A coastdown test is one of the most common tests in the automotive industry. It is a way of measuring the mechanical and aerodynamic resistance that acts on a vehicle. 
The vehicle is accelerated to a particular speed and once constant, the clutch is engaged. The vehicle is then allowed to slow or ‘coast’ down in neutral. By recording the distance travelled and the time taken, the aerodynamic drag can be calculated (see also: https://airshaper.com/videos/what-is-aerodynamic-drag/video/DbIIw-WryHY)

How to calculate the drag coefficient
See also: https://airshaper.com/videos/what-is-a-drag-coefficient/video/bEgoZ_dAg7o
For simplicity, let’s assume the vehicle is slowed down by only two forces: 1) mechanical resistance and 2) aerodynamic resistance. Mechanical resistance is primarily due to the rolling resistance of the tyres and therefore remains constant, regardless of the vehicle’s velocity. Whereas aerodynamic resistance changes with the square of speed. In other words, drag force has less of an affect at low speeds, but a large affect at high speeds.

Newtons 2nd law states that the acceleration of an object is directionally proportional to the sum of the forces acting on it. Applying this to our simplified coastdown test, we get an equation which includes a rolling resistance coefficient, Crr and a drag coefficient, Cd.
So how do you calculate the value of two coefficients from a single equation with only one measurement? First, let’s look at two extremes:

1)   No aerodynamic resistance
If the vehicle completed a coastdown test in a vacuum, where there was no air resistance, then only the mechanical resistance would slow it down. Therefore, the car would decelerate at a constant rate, resulting in a linear deceleration curve.

2)   No mechanical resistance
If the vehicle had no rolling resistance and so only the aerodynamic resistance was slowing it down, then the deceleration curve would be non-linear. The car would decelerate faster at high velocity and slower at low velocity.

In reality, the measured curve from your coastdown test would be a combination of both. You can then adjust the coefficients to alter the shape of the curve until the measured curve matches the predicted curve. This process is called least squares regression. Overall, you will end up with a value for aerodynamic drag and a value for mechanical resistance.

As ever in aerodynamics, it is unfortunately not that easy. In reality, the equations mentioned above are much more complex. They need to account for factors such as mechanical resistance in the drivetrain, ambient conditions, wind direction, gravitational force and rotational inertia.

Yet, despite its complexity, coastdown tests are an industry standard for determining the performance of a vehicle. So, if you want to find out the drag coefficient of your car, why not use your cell phone’s GPS and some Excel magic to conduct your own coastdown test?

Drag Measurement  - Coastdown Testing

How to use coastdown testing for drag measurement

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In this third video in our series "How Wind Tunnels Work" we look at wind tunnel measurement techniques - both some of the most widely used as well as some innovative ones.

Forces & moments
One of the most important output parameters of a wind tunnel test are the forces & moments on the object. To obtain these, the object is typically connected to a 3D force balance, which is a device that can measure the forces and moments around three perpendicular axes.

It's important to make sure that the influence of the connection part does not disturb the airflow too much, which is why they're often given an aerodynamic profile.

Surface pressure measurement
To measure the static pressure on the surface, you can use pressure taps. These are small holes drilled perpendicularly to the surface with a tube fitted to each hole in the model. These tubes are then sent to a pressure transducer which is typically located outside the wind tunnel, where the pressures are measured & logged.

If you want to measure the pressure on many locations on the surface of your object, you'll quickly end up with a huge set of cables that needs to be led outside. This is something you need to take into account during the design of your prototype.

Alternatively, you can work with miniaturized pressure transducers that fit within your model and then convert the measurements into digital data which is then sent to the outside world via a single cable to save space.

3D flow measurement
- Smoke: one of the oldest & most common techniques is to release smoke upstream of the object to trace the path of the air. This can lead to very insightful information in terms of where the separation point is located, what the size is of certain vortex structures and so on. But it's quite difficult to determine local flow velocities, so over the years, a number of alternatives have been developed.
- PIV - particle image velocimetry: tracer particles are released upstream of the area of interest. The size, density, ... of these particles are chosen in such a way that they follow the real flow nicely, without dropping to the ground or disturbing the flow pattern. They are then illuminated, typically in a 2D plane, using a laser. Then, they're filmed perpendicularly to that plane by high-speed cameras. By tracking & tracing the position of the individual particles between consecutive shots, one can reconstruct their path and calculate the velocity vector and flow field.
- 3D measurement probes: by measuring the differential pressures at the head of these multi-hole probes, you can obtain the static pressure and total pressure, the angle of attack and the velocity. If you then trace the position of the probe itself in 3D, you can reconstruct a 3D flow field.

How Wind tunnels Work - Measurement techniques, PIV, pressure taps, force balance, pressure probe.

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In this video, we explain the huge variations in size, speed and accuracy of low-speed aerodynamic wind tunnels. This is mainly due to variations in:
- object size
- object velocity
- required accuracy


Object size
When you place an object in the wind tunnel, the air needs to curve around it and fit between the object and the walls of the wind tunnel. This creates 2 problems:
- Blockage ratio: around the object, the cross-section through which the air can flow is reduced. This means the air will locally speed up compared to the reference velocity, which is typically set at the undisturbed beginning of the tunnel using a pitot tube.
To compensate for this, you can calculate the blockage factor. Typically, it's recommended to keep this value below 5-10%.
- Wall effects: a boundary layer of slower moving air is present close to the wall. In reality, this slower moving air is usually not present and can bias the results. Also, the walls can interfere with the flow & pressure patterns around the object if they're too close. In that regard, it can be very interesting to first run a CFD simulation to analyse the flow and see exactly how large this "zone of disturbed air" is to know how far it should form the walls. One example are the vortex structures around wingtips.

In some cases, you'll even see wind tunnels employing an open test section, partially to overcome the challenges of blockage ratio & wall effects.


Object speed
The velocity of the application can vary greatly, with a cyclist going 10 m/s and an airplane 250 m/s. Ideally, you select a wind tunnel with the wind speed that you need. In reality, there will be 2 main constraints:
- Budget: an automotive tunnel can easily cost 5.000€ per hour. Building one also costs over 100 million euros in some cases.
- Availability: tunnels are often overbooked and sometimes they just don't exist in the size/speed combination that you need.

Scaled model testing can help in that case. But keep in mind that you'll need to respect certain similarity numbers - the most important one being the Reynolds number. If you want to keep the Reynolds the number the same when scaling down your model by a factor X (so length_scaled = length_full / X), then you need to scale up the velocity by that same factor X (so velocity_scaled = velocity_full * X). This can make you hit the speed limit or the wind tunnel or even the limit of compressible flow (around Mach 0.3).


Accuracy
The higher the flow quality or the more realistic the setup needs to be, the more tricks you need to pull, like cooling the air, working with a moving ground or even employing gases other than air at different pressures / temperatures.

How Wind tunnels Work – Blockage factor, wall effects, scaled model, similarity number, moving floor

To ensure the accuracy of scale model wind tunnel testing, the models are now highly detailed and consist of moving parts. Modern stings and support designs allow the models to be moved continuously through different attitudes to maximise wind on time.

Scale model wind tunnel testing explained

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In this first video of our series on wind tunnels, we’ll discuss the basic layout.

History
Wind tunnels were invented in the late 19th century and even the Wright Brothers used a simple wind tunnel to study different shapes for their Wright Flyer, the first plane. The principle of a wind tunnel is quite simple: Use a single or multiple fans to force air across an object to study its aerodynamic properties.

Layout
In an open return tunnel, the air is drawn from the environment in which the tunnel is located. This type of wind tunnel is typically cheaper to construct and doesn’t suffer too much from smoke or exhaust gases accumulating inside. It is however quite expensive to operate, as it constantly needs to accelerate “new” air from standstill. It’s also more challenging to achieve a good flow quality as the air needs to curve into the inlet. And the open exit makes it quite noisy as well.

Then there’s the closed return tunnel, in which the exit air is fed back to the inlet. This design is much more energy efficient as the fan only needs to overcome the losses and it’s quieter too and it has the potential for a higher flow quality. Downsides are a higher construction cost and because the air circulates, it can heat up quite a lot and smoke & exhaust gases can accumulate.

Goals
Whichever return type you go for, it’s very important to have good flow characteristics at the test section. Typically, the goal is to have a low turbulence intensity, a uniform flow velocity and a thin boundary layer.

Components
Let’s have a look at how the typical components of a tunnel are set up to achieve this: first, the fan pushes the air forward. Then, in the corners, turning vanes are added to help straighten the flow and reduce pressure losses.

After the last corner, the air hits the settling chamber, where it first passes through a honeycomb structure. This is basically a set of tubes to force the air to move in a parallel way to reduce the swirl. After exiting the honeycomb, the air goes through a number of screens, which are composed of thin wires interwoven to form square or rectangular meshes. These screens impose a static pressure drop which is proportional to the velocity squared, penalizing speeds above average and boosting speeds below average. This helps to reduce variations in longitudinal flow velocity. They also break up large eddeys into smaller ones, which decay faster.


To reduce the pressure drop in the entire circuit and settling chamber, the cross-section is quite large and thus the flow velocity relatively low. To speed up the air and further improve flow uniformity, after the settling chamber the air is then sent through a contraction just before it enters the test section. After the test section, it is slowed down again in the expanding diffuser before it enters the fan again.


So that was it for our first video on how a wind tunnel works. Stay tuned for more as we discuss sizing challenges and measurement techniques!

How Wind tunnels Work – Contraction, Test Section, Diffuser, Fan, Turning Vanes and Settling Chamber

The accuracy and reliability of the wind tunnel test section can be affected by many factors such as blockage and boundary layer control. However, new technologies and approaches help to solve these issues and achieve repeatable testing.

The wind tunnel test section explained

CORRECTION (0:57 to 1:30) for the picture on the right-hand side: 'laminar boundary layer' should be 'turbulent boundary layer'.

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In this video, we look at the aerodynamics of golf ball dimples and how to apply (or not apply) them to your design!

Aerodynamics of a sphere
A golf ball without dimples, a simple sphere, features attached, laminar flow at the front: as the air moves over the surface,  a boundary layer of slower moving air grows thicker as it sticks to this surface. As soon as the flow goes beyond the halfway point and needs to contract, it becomes more & more difficult for the flow to stay attached to the surface and eventually. Separates, resulting in a detached flow. This creates a large wake behind the golf ball, which increases drag and slows it down.

Aerodynamics of a golf ball with dimples
When you apply dimples to the surface, the boundary layer becomes turbulent. It will mix with the surrounding air and retain more kinetic energy. This energy allows the airflow to stay attached further down the back of the golf ball, moving the separation location further downstream to reduce the size of the wake. These dimples may increase the friction drag a little but reduce the pressure drag so much that the golf flies roughly twice as far!

Golf ball dimples on cars, golf ball dimples on planes, ...
So does this mean we should cover every surface on every car or plane with dimples to make it more aerodynamic? No, not quite. It only makes sense to create a turbulent boundary layer just ahead of a separation location. Modern day cars for example, have such a sleek profile that they have attached flow all the way to the back of the car. And even at the back of the car, a turbulent boundary layer would still not be enough to make it follow the negative curvature at the end of the trunk.

Golf ball dimples in sports
Another example is to reduce drag around cylinders. There it does make sense, depending on the Reynolds number, to add roughness or dimples or what so ever, to move the separation location further downstream. But on a golf ball you have dimples everywhere because you don’t know the direction of the golf ball. On a cylinder, if the flow is coming always from the same direction, it makes sense to only add roughness just ahead of the separation location, so not at the rear of the cylinder where the flow is already detached. A practical example of this are the arms of an athlete or cyclist, where the wind always comes from the front or a slight angle of attack, so it makes sense to only add roughness just ahead of the separation location on the arms. This is something you already see on some outfits of the riders.

Golf Ball Dimples Aerodynamics - How do they work and are they relevant for your design?

Golf balls have dimples applied to their surface to manipulate the behaviour of the boundary layer to reduce the wake and overall drag. However, it only makes sense to use dimples just ahead of the separation point.

Why do golf balls have dimples?

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Full Research Paper: https://www.airshaper.com/research
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In this video, we look at how machine learning / deep learning / neural networks can be applied to aerodynamic CFD simulations.

Neural Concept
We interviewed Pierre Baqué, CEO of Neural Concept, a Swiss startup developing & offering Deep Learning software. They have developed algorithms to connect 3D shape morphing, deep learning and aerodynamics.

senseFly
senseFly is a Swiss drone company that wanted to improve the flight time of their fixed-wing drones. senseFly, Neural Concept, EPFL (the technical University of Lausanne - École polytechnique fédérale de Lausanne) and AirShaper teamed up to apply Deep Learning to drone design to improve the aerodynamics, as improvements to the lift/drag ratio directly extend the range / increase flight time.

Deep Learning setup
The Neural Concept software can create & explore new 3D shapes to train its network, but it needs an aerodynamics component to give feedback on the lift/drag performance (and other aerodynamic parameters) of each design. For that, the Neural Concept software connected to the AirShaper cloud via an API interface.

Network Training
The training of the network was done in multiple phases with increasing accuracy. The initial warm-up of the network was done using older, in-house simulations from other projects. In the second phase, medium accuracy AirShaper simulations were applied. And in the final phase, high-accuracy AirShaper simulations were used for final tweaking of the network.

Output
Without any design input, the network came up with special drone shapes that partially matched what engineers had been applying for years in practice (anhedral/dihedral setup, ...). The lift/drag ratio was improved by more than 4%. Because the Reynolds number is quite different compared to large aircraft, so were the suggested design solutions.

AIRBUS
Neural Concept worked on the prediction of shock waves (transonic simulations). These results were presented at NEURIPS.

Future of Deep Learning for Aerodynamics
- Today
For industry specific, repetitive tasks, it pays off to train a network so that new designs can be analysed using the predictive model
- Short term
In the short term, machine learning can be used to make existing CFD codes faster and more accurate
- Long term
It's uncertain if it will ever work, but it might be possible to create generic Neural Networks that cover various industry segments, without needing to train the network.

Machine Learning for Aerodynamics - Deep Learning & Neural Networks applied to CFD simulations

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To understand the advanced aerodynamics behind the T50, let’s travel back into time to some of Gordon Murray’s most famous creations.


Legendary cars by Gordon Murray
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Brabham BT46
Inspired by the ground-effect Lotus Type 78 featuring side skirts and the Chaparral 2J “sucker car”, featuring 2 fans at the rear, Gordon Murray and the team installed a massive fan at the rear of the Brabham Formula One car. Because ‘moveable aerodynamic devices’ were not allowed, its official purpose was actually to improve cooling, which it did. What it unofficially also did, was to draw air from underneath the car. With side skirts around the car closing off the underfloor area from the outside air, the fan was able to maintain a low pressure underneath the car. This led to high amounts of downforce, enabling crazy cornering speeds.

McLaren F1
On sports cars, you’ll often see a diffuser, the upward sloped rear part of the underfloor. It’s there to increase the airspeed underneath the car, which will help to create suction because of the Bernoulli effect. If the upward angle is too aggressive, the air will not be able to follow the curvature and will continue on its own, more horizontal path. This is what we call a “stalled” diffuser. To activate it and make the air follow the curvature, the fans draw air away at the beginning of the diffuser step. This helps to remove the boundary layer and makes the airflow stick to the underfloor surface. It increased downforce by 5% and reduced drag by 2%.

Aerodynamic analysis of the Gordon Murray T50
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Fan
The fan has an 8.5kW electric motor and can spin up to 7.000 rpm. It will eject the air into the wake behind the car, helping to reduce drag by virtually creating a long-tail car. And the 15kg of thrust it produces is around 2.5% of the total drag on the car, so that effect is actually significant as well. Even more so – from what we understand from various interviews, it’s actually more efficient to provide 8.5kW to the fan and not to the drive shafts to increase top speed. Now let’s see how the fan works together with other parts of the car in different aero modes. 

Downforce mode
In down force mode, the fan will source air from the diffuser channels. The car has 2 very pronounced diffuser channels which fit between the engine bay and the rear wheels. They are so high that the exhaust system of the engine was actually moved upward to make room for them! Another consequence is that the suspension arms and even the drive shafts need to cross the diffuser channels to get to the wheels. That’s why the suspension arms have been given an aerodynamic profile, just like in formula One and Indycar, to limit their impact on the airflow.
On the official CFD, or computational fluid dynamics, images we can again see an aggressive step at the beginning of the diffuser, similar to the one we saw on the McLaren F1. Without fan assistance, the air is not able to follow this profile and the diffuser stalls, creating just a mild diffuser effect. But in downforce mode, the fan draws its air from the beginning of the diffuser, at the steep part of the step. This helps to remove the boundary layer and to make the air to stick to the profile. This not only creates downforce at the rear, it also helps to accelerate the air underneath the entire car, creating down force at the center and front of the car as well. That eliminates the need for a big splitter at the nose to correct the aero balance, which is the split between downforce at the front and rear. Also in downforce mode, the aerofoils or flaps at the rear of the car tilt upward. In total, down force mode will generate 50% more overall downforce on the car.

Streamline mode
The rear spoilers drop by 10° to reduce base suction, which is the pressure just behind the car, holding it back. And the fan will now source its air from the top air inlets. This again helps to remove the boundary layer which will help to reduce drag on the parts downstream of these inlets. Together with the virtual long-tail effect, drag is reduced by an impressive 12.5% in streamline mode.

Vmax mode
This is basically the same as streamline mode, but the fan is now powered by the battery instead of the engine, to free up engine power.

Brake mode
The flaps rise even further to their maximum angle of 45°. This mode provides a 100% increase in downforce, which provides more grip for braking. And because the flaps are positioned relatively high on the car, the drag on them creates a backward tilting moment, counteracting the forward tilt caused by the deceleration. This greatly improves the balance of the car under braking. All this reduces the braking distance from 150mph to standstill by 10 meters.

Gordon Murray T50 Aerodynamics - Successor to the McLaren F1 supercar

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In this video we explain how to use Paraview to analyze CFD data:

Installing paraview
Visit https://www.paraview.org/download and select the release & operating system that you need.

Loading data
How to load the mesh & field data in Paraview.

Surface Methods
- Surface pressure map
- Surface friction map
- Surface velocity map
- Surface streamlines using SurfaceLIC

Volume Methods
- 2D slices (sections)
- 2D streamlines
- 3D Isosurfaces

State files
Saving & loading your project setup using paraview state files

Our Latest Videos Gain aerodynamic insight by watching our videos

Aerodynamic Shape Optimization - The Adjoint CFD Method

Drag Measurement - Coastdown Testing

How Wind tunnels Work - Measurement techniques, PIV, pressure taps, force balance, pressure probe.

How Wind tunnels Work – Blockage factor, wall effects, scaled model, similarity number, moving floor

How Wind tunnels Work – Contraction, Test Section, Diffuser, Fan, Turning Vanes and Settling Chamber

Golf Ball Dimples Aerodynamics - How do they work and are they relevant for your design?

Machine Learning for Aerodynamics - Deep Learning & Neural Networks applied to CFD simulations

Gordon Murray T50 Aerodynamics - Successor to the McLaren F1 supercar

CFD Results - How to analyse OpenFOAM data with ParaView - 25-minute Tutorial

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