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Compendium of Results

The slides below summarise a few findings of potentially more general interest that we have extracted from our work on various projects* for various clients - we hope you find them interesting!


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Verification of the VTM's unsteady aerodynamic model.

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Capturing the unsteady aerodynamic behaviour of a helicopter rotor is a extremely complex process, requiring the dynamics of the circulation on the rotor blades, the dynamics of the vorticity in the rotor wake and its interaction with the individual blades of the rotor as well as the structural dynamics of the rotor blades in response to the changing aerodynamic loads to be captured correctly.

Carpenter and Fridovich, in a foundational experiment conducted in 1953 (see NACA TN-3044), showed that, following a sudden increase in the collective pitch that is applied to the rotor blades, the inflow through the rotor would take some time to build up as the wake tube established itself below the rotor. As a result, the thrust produced by the rotor would initially overshoot before relaxing back to its steady-state value.

The diagram at left shows how the VTM is able to reproduce this effect very closely in a simulation that matches one of Carpenter and Fridovich's experimental cases. The quality of the comparison is bedeviled however by an inadequate characterisation of the structural properties of the rotor blades that were used in the experiment.

The figures at right show simulation results for the simplified case where the blades are treated as rigid and inflexible, and hence only the aerodynamic characteristics of the system play a part in the rotor's response to a sudden change in the collective pitch of the rotor blades. The predictions of the VTM are shown to match very closely those of a general-purpose high-resolution Reynolds-Averaged Navier-Stokes (RANS) solver for the variation of the rotor thrust with time.

Carpenter and Fridovich's experiment also informed the development of a very simple low-order model for the dynamics of the inflow through the rotor, called, simply, the Dynamic Inflow Model (see the works of Peters et al.). The diagrams at right show how effective this reduced-order model is at capturing the fundamental response of the rotor to changes in its aerodynamic loading.

The step-like features in the variations of thrust and inflow with time in the diagrams at right are the result of interactions between the rotor blades and the starting vortices that are left behind in the flow as the blades begin to produce lift. The dynamics of these vortices are fully represented in the VTM, somewhat less-adequately represented by the RANS code and missing entirely from the Dynamic Inflow Model.

This simulation thus provides an ideal example of the conundrum that often faces the practising engineer regarding which formulation to use to solve a particular problem: the Dynamic Inflow Model is cheap and fast, but represents the physics in an approximate and incomplete way. RANS solvers are readily available, represent the physics reasonably well and are based on a first-principles description of the fluid mechanics, but are expensive to run. The VTM is accurate and reasonably fast to run in this particular instance, but is specialised to solve this particular type of problem and thus requires some expertise to set up.

The best solution to this type of conundrum always depends on the particular characteristics of the problem at hand. Once properly calibrated, the Dynamic Inflow model is ideal for basic flight simulation or design-level studies. At the opposite end of the spectrum, the VTM comes into its own where prior knowledge is lacking and a more fundamental approach to analysing the problem is required.

We have found, at least in the context of aircraft design, that often a very effective approach is to use the VTM first to calibrate a simpler model such as Dynamic Inflow for use in performing the various parametric studies and tradeoffs that are necessary, and then to use the VTM judiciously again at various strategic intervals to perform a series of spot-checks on the validity of the data that is being produced.



* Except where explicit permission has been obtained to release actual data, geometries and test conditions have generally been changed to protect the intellectual property of the sponsors of the original work.

News

Use the tab above to access the latest news from Sophrodyne Aerospace!

Articles

The tab above leads to a page containing various articles on aeronautical topics that we have written over the last years.

These are in addition to Dr Brown's published academic articles, a list of which can be found here.

Useful tools and downloads Coming soon!

For the moment this tab will take you to our "Articles" page.

The tab above leads to a page containing some simple tools and downloads that may be of use to you in performing your own investigations.


Sophrodyne's Fundamental Approach

Our years of experience in combining numerics and theory lies at the core of Sophrodyne's way of working. We understand that an analysis of a problem using a brute force approach (such as is obtained for example with a pre-packaged general-purpose CFD code) is often necessary and useful in order to obtain basic data - for instance for evaluating a parameter or to validate a model - and we have the tools to do that.

We believe though that this approach only becomes cost-effective and valuable once these individual data are abstracted into a sensible mathematical framework which clearly expresses one's current understanding of the problem. Unlike "ideas" or "hunches", an explicit, simple mathematical model is a tangible object with which the human intellect can engage and interact. A good model allows the strength of your understanding of the problem to be exploited directly in being able to predict the properties of the system that are of interest to you. But often even more important is the fact that predictive errors in the same model are very often an indication of a deficiency somewhere in understanding the problem properly. The key advantage thus of the model-building process during the development of a product is that it invariably promotes the sort of interaction with the problem in which these lapses in understanding can be exposed and rectified before they can cause too much harm.

This is where the experienced practitioner will save you time and effort in achieving your goals.

We understand from first principles the methodologies that underpin most current commercial aerodynamic tools, and can advise regarding both their strengths and their weaknesses. In many instances we have our own analogue methodologies that we have written in-house and understand down to the last line of code. We can use these to perform genetically-independent sanity checks on, and independent verifications of, the data coming out of your models, or to perform the relevant analyses on your behalf. Indeed, over the years we have built up a series of models that work from very limited data to give reliable estimates of the most salient performance characteristics of a wide range of flight vehicles - from subsonic drones and helicopters, through mid-sized commuter aircraft, through to supersonic jets and even hypersonic re-entry vehicles!

We can also help you upgrade and develop your internal modelling capabilities, starting from a clean sheet of paper or based on what you already have available. You may be surprised to find out how broadly used our methodologies are within the aerospace community.

Most importantly, and this is where we specialise in bringing value to organisations such as yours, we can help you understand and generalise your proprietary data into models that can be used over and again, not only today but also in your future products, adding to your reserve of intellectual property and know-how as you develop your product line.

Please feel free to contact us to discuss your problems and requirements.

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