Particle Image Velocimetry - Science method

Dear Ivan Nepomnyashchikh and Charles Fort thank you a lot for your recommendations!

Ivan Nepomnyashchikh yes, I will still have to figure out what is the best position for the cameras and how I can cover the length of the cylinder.

Hello Ali, did you manage to solve the problem?

There are several main factors to consider:

1) Seed particle characteristic response time which is related to Stokes number. This should always be explicitly calculated for any PIV investigation and is one good gauge for how well the resultant cross-correlated particle velocity represents the actual flow velocity

2) Overlap ratio. In regions with sharp gradients you must pay more attention to using the correct/most advantageous overlap ratio between iterations to best capture the gradients

3) The relative magnitude of your velocity fluctuations to your mean flow. Like any measurement instrument, you have a limited bandwidth. If your fluctuations are on the order of 1/100th or above of full scale/mean you should be able to get reliable measurements without resorting to specialized approaches. Fluctuations below that may still be possible with PIV but require more novel approaches.

4) Based on your physical and assumed temporal scales, you will need to be rigorous in your application of optical distortion corrections as they may be on the order of the magnitude of your fluctuations

Charles Fort Thank you! Based on what (little) I know, ultimately, the similarities between the two seem to far outweigh the their field-specific differences. I would personally prefer DIC to be adopted as an umbrella term for any sort of image pair cross-correlation because the math/physics and practical applications are field specific.

I am not familiar with the cameras you are using, but I am assuming they are double-shuttering and slaved to the laser frequency? It is quite common in double-shuttered cameras for one of the two images to be brighter due to the way the exposure times are handled. Most of the time, one of the two exposures (the first) is quite long until the trigger signal is received. That sets into motion the transfer of the contents of the CCD array and the start of the second exposure. This process has typically been accomplished in a couple of different ways, but both ways result in unequal exposures between the first and second images in an image pair on a double-shuttered camera. Less exposure -> fewer photons captured -> less bright images. The newer cameras do a much better job of evening this out, but the bit-depth of the cameras we use still capture a measurable difference.

Our Flow visualization Stack exchange is up and running!

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We need 5 example questions and 5 users within the first 3 days lest to be taken down. Those interested, please, hurry up.

Note, Stack exchange didn't give me specific instructions how to register. Just gave me the link that I have provided above. Go ahead try it, if you experience any issues with it, please post your experience here.

Intresting questions

OpenPIV is an open source Python software (disclaimer - I am one of the developers) and it's pretty easy to extend to get what you're looking for. Indrajit Nandi

see www.openpiv.net or github.com/openpiv/openpiv-python

we use scikit-image for the image processing and it's a very rich set of tools

Hi Dinar,

what is a CIRCULAR pipe? Is it a pipe with circular cross section? If yes, then surely the radius and the lenght scale of energy-containing eddies near boundary matter. I am just thinking exactly about this topic and a nice application would be the Princeton superpipe, http://www.princeton.edu/~gasdyn/Facilities/Facilities.html ,

and/or the COLA pipe,

https://www.b-tu.de/fg-aerodynamik-stroemungslehre/forschung/ausstattung/colapipe .

Note also this theory-oriented paper:

If you see a chance for collaborative work, it could be nice. Only some research coins are needed: not for profit. For the honor only ...

1. make sure that your tube is also submerged into the fluid bath and the bath walls are straight and perpendicular to the imaging axis. calibration won't be able to compensate for the 2.7 mm tube curvature.

2. not sure there is any point to insert a calibration into the 2.7 mm tube - are you going to use laser sheet through the pipe? if you're going to use a light through or volumetric lighting, the rules of game change, see 3D-PTV like calibration targets - with depth.

3. 15 m/s flow speed through a pipe of 2.7 mm is extremely challenging - the particles will pass the field of view within 0.00018 sec, so to use PIV there you need to image 2.7 mm over e.g. 512 pixels with about 6 micron resolution per pixel and a typical 32 pixel window will be just 180 microns and that means the time is very short. The resolution also means that you need very small holes to make a sufficient number of those for the plate.

4. if the light is PIV-like thin laser sheet and you manage to insert the small plate inside (obviously not 2.7 mm as it's your inner diameter, so e.g. 2 mm, with some spacing on each side to manage to insert the plate, you can make 10 x 10 points and it'll be sufficient I think. The whole point is that your calibration plate would have to be parallel and aligned with the laser sheet and then the only correction is due to small mismatches of the index of refraction, curvature, camera angle, etc.

5. yes, glass plate or just laser-cut metal plate would be fine.

Alex

Dear Chingis,

Thank you for your answer to the question I asked two years ago which remains still relatively unclear to me!

The method you described is the visualization technique ( i.e., photographic and image analysis) which is well-known and widely used. In this regard, methods and devices developed in University of Cape Town (UCT), Helsinki University of Technology (HUT) and McGill bubble size analyzers (MBSA) are typically used to measure bubble diameter in both industrial and batch conditions with a reasonable accuracy. However, my question is the limitation(s) inherently engaged with this or other related techniques. For instance, one problem involved in visualization approach is strong mismatching of the refractive indices between bubbles and water and/or the impact of the inherently variant distance between the focus plane and the bubble.

With the kindest regards from Freiberg,

Ahmad Hassanzadeh

Time delay of PIV primarily depends upon the velocity scale of the fluid flow. In PIV, two consecutive images are captured which are then used to map velocity values spatially. Time delay should not be small enough such that the movement of seeding particles is negligible. It should not be high enough such that the movement of seeding particles is untraceable. Try the highest value first, try to correlate the images. If failed reduce the time delay and try again.

Hi Yoseph,

For our sandbox models, we did strain analysis by tracking the regular grid corners in the surface images. Please read our article in which you can find more details:

Good luck

Faramarz

Hello Sajjad,

Have you tried bubbling the fuel gas through titanium tetrachloride, TiCl₄, before it is sent to the nozzle in the Bunsen burner? The presence of water (steam) in the combustion gas should generate titanium dioxide, TiO₂.

Regards,

Tom Cuff

Thank you for your answer Alex. The problem is that the cc map is not at all Gaussian and often has fancy shapes that are not well fitted by a Gaussian. Hence the peak location becomes very ambiguous. I‘ll try to look for an example when I come back from holidays !

I should make a more specific statement on the ambient light that I was thinking of. It comes from any objects in the lab with their surfaces being able to reflect lights. In this case light source is most likely from the light scattering of laser beam or laser light sheet. The energy of such ambient light is undoubtedly much lower than that of light scattering. If there are objects with excellent reflective surface in the lab, chances are that such energy level may still be high enough to illuminate dark or even low-light area in the filed of view and sensed by the camera sensor with extremely high sensitivity. However, this situation is much less likely to happen because it causes safety issues and should always be avoided.

For open source PIV analysis tool, you can consider PIVlab, a MATLAB-based software package. I have been using DaVis for many years, and PIVlab for about a year. For now I don't see PIVlab is any different from DaVis in terms of velocity determination.

Vortex flows are ubiquitous at all scales of matter organization, from quantum systems to large structures of the universe. In the most general mathematical sense, it is useful to look at these structures in a unified way. When trying to organize my ideas in this field, I have encountered a book on the general theory of vortices that I recommend as a valuable source of information placing the subject in a multidisciplinary context; for the synopsis please see:

Regarding the research suggestions, I agree with the previous comments, but I can add some specific answers:

>>Do you think this topic is linked with dynamic systems analysis? if yes: how this analysis should be done?<<

The answer is definitely yes. You can consider the following paper as an illustration of the methods derived from Dynamical Systems Theory.

>>What kind of theoretical analysis (based on differential equations formulation) could be added to my research (especially to the vortex's stability and/or stochastic factors)?<<

The theory of stable and unstable manifolds discussed in the reference above. It is also useful to consult a book by Ottino: The kinematics of mixing: stretching, chaos and transport

>>What's your best suggestion for making sure that the results obtained (from experiments) are dependable? (Validation by CFD?)<<

The best way to obtain reliable results is to set an experiment as carefully as possible. CFD calculations are generally validated by experiment. However, the use of CFD to validate the experimental results is very useful (I always look at numerical simulations as a parallel experiment).

Hi Nirjhar,

the answer above get straight to the point. We used PIV in our flume experiments too to detect deformations in a slope upon failure. Some results are published in our latest paper on Geotechnique:

Best regards,

Dr. Gianvito Scaringi

As the previous responses pointed out correctly, PIV might not be the right way for this case of the CW laser and 1000 Hz recording. You could consider using particle tracking and especially streaks particle tracking velocimetry. For that case I can recommend (disclosure - I'm involved in its development) the open source particle tracking velocimetry project, OpenPTV (www.openptv.net) or an excellent trackpy project.

You probably don't need the silver coating.  I was able to use Potter's Industries glass microspheres in a water/glycerol solution (1.06 g/cc) successfully and they were much cheaper than the coated sphere options from other suppliers.  Below is a spec sheet for 110P8 which is what I used.

The company I used for acquiring microspheres for PIV was http://www.cospheric.com/

You may look there and see if they have what you want or something similar.

For 2D fields there is also the fundamental difference, that during PIV the particles are illuminated by a laser sheet and thus the cross correlation is calculated only from the particles in your plane of interest. Shadowgraphy however (such as Schlieren) is a line-of-sight averaged technique, where all density fluctuations in your flow are projected on an image plane. If you do your cross-correlation on these Shadowgraph images, you will take into account all movements in the other planes of view, which will falsify your results. Taking this difference into account I would definitely go for PIV.

By using a phase-contrast sequence. Just make sure you have the proper velocity encoding for various vessels, otherwise you might have aliasing. Of course you need a special program - usually at a workstation - to evaluate the velocity of the vessel from the phase-contrast data.

There is the article part II in my profile. It may not help to choose seeding particles but it may be useful in your analyses. Good luck.

Thanks a lot Prof. Liberzon for the response.

I agree that that multi-pass cannot improve much the accuracy. It works as it's described by the previous answers only in some "clean" cases. In turbulent flows it can also lead to errors generating artefacts rather than improving resolution 

In order to quantify most turbulent statistics, Buffin-Bélanger and Roy (2005) suggested an optimal record length (minimum sampling effort to achieve low standard errors) ranging between 60 and 90s with ECMs (20Hz) and ADV (25Hz). 

Depending on the statistics you are interested in, you probably need longer series at16 Hz.

Use angular spectrum approach,  it's more convenient 

One possibility is to spike in latex beads or something similar at known concentration into your sample. Size should be similar to your cells. By counting both cells and beads in the same fields you should be able to calculate your cell concentration.

Dear Dr. Hayder I don't have any software , I wanted the type ALT software.

Regards

What kind of scaling do you mean? There is a well applied scaling between capillary pressure and IFT, but do you mean a property that changes the IFT, such as temperature or composition? In that case I would look at the PVT description of E300.

Just mix some particle like hollow glass bead or TiO2 powder with some water. Add the mixture into the flume. Use the PIV image itself to adjust the density. Usually, several grams of powder was enough for a flume.

Hi Ali, please download a Comsol model from the following link.

It corresponds to a rectangular domain with perfect matched layers. There is a monopole source an a receiver point inside of the domain so you can see how to input the information.

In order to put the monopoles you should define their location first. Please create two points (you find it as more primitives in the section of geometry). Define other points to create the circular array of microphones.

In the section of Pressure Acoustics Frequency domain, create two Monopole Point Sources. Select the point that you created before (in the geometry section) for each monopole and define their strength based on  intensity or power. You can modify the phase of the monopoles as well,

Nevertheless, if you need a free field model, it will be more efficient to use matlab as you have green functions for the sound propagation and there is not need to use solvers for the numerical solution of the Helmholtz equation.

Best regards,

Diego

see Fluid Dynamics of Multiphase Systems by S L Soo  Blaisdell Publ. Co. 1967

chapters 7, 8, 9,1 0

The problem with your image is that parts of the ball are in the shadow, too. If you have the chance to install a second light source on the left side for a better illumination the processing based on hue and saturation as shown by Wolfgang Reichl would be quite robust with appropriate threshold parameters.

Hi Ashley, 

you can use calibration beads for a known size and prepare a calibration curve, however, please note that the refractive index of polystyrene beads is different than cells, hence the results of light scattering won't be accurate. You can obtain accurate measurements using the AMNIS ImageStream / FlowSight, an imaging flow cytometer that takes brightfield as well as fluorescent images, combining flow cytometry with microscopy. Then you can get absolute size values.

Good luck,

Ziv

Water/glycerol mixtures work very well, but the viscosity strongly depends on the temperature (Cheng NS: Formula for the Viscosity of a Glycerol-Water Mixture; Ind Eng Chem Res (2008) 47:3285-3288), 

These two publications list a large number of alternative fluids:

Budwig R.: Refractive index matching methods for liquid flow investigations; Experiments in Fluids (1994) 17:350. doi:10.1007/BF01874416

Wiederseiner S, Andreini N, Epely-Chauvin, G. et al.: Refractive-index and density matching in concentrated particle suspensions: a review; Exp Fluids (2011) 50:1183. doi:10.1007/s00348-010-0996-8

Yes, only PIV.

In the Institute of Auotimotive Engineering of Shanghai Jiao Tong University (Minhang Campus), we have both high speed PIV and low speed PIV systems. In addition, we have PDI system, which also can be used to measure the velocity. But you said you want to rent the system, it is really difficult to move these devices. So I suggest you to bring your test targets to our lab, and conduct the test.

Mandy,

In my micro-PIV experiments I use POLIS PIV system with pulsed laser and Zeiss AxioObserver microscope with fluorescent filter and dichroic mirror behind the objective, so working distance of the objective can be quite small (from 2 to 10 mm in my case). To build in laser source using optical fiber is not a problem.

If you are performing an experimental investigation you can check on the average partical velocity, particle size and Reynolds number from the knowledge  of your experimental apparatus. Based on the system (Ethanol) properties and the particle properties (velocity, diameter and viscosity) you can estimate the dissipation rates and turbulent regime. As for the flow field you can use suitable experimental techniques to capture particle flow filed ( using various laser diagnostic techniques or by high speed camera to capture the motion and then image processing)

sorry about that, in water flow, one of apparatuses used to measure flow velocity is (Acoustic Doppler Velocimeter) ADV. to collect data, it is needed either seeding the water with a special material like sand or other moved with velocity same water flow velocity. these material reflect the wave sound from transmitter of ADV and received again by ADV and hence measured the flow velocity. now I use micro-bubbles to reflect the sound from ADV. to create these bubble I need a secondary tool to generate bubble. in my case I use two frames one for anode and second for cathode based on separation of water molecules. I need some one used ADV to let me know what he/she used to reflect the sound.   

Thank you for your suggestion. The code we are using is a .p file in matlab which we cannot view or change. Hence the presence of scatteredInterpolant function is unsure. Kindly suggest any other method to overcome the problem.

I'm doing something similar. The point is to get the particle concentration [number of particles/unit of volume] and the particles velocity (with PIV). These two parameters allow you to estimate the particle rate, a sort of particle flux [number of particle*m-2*s-1]. The problem in the real cases is the non-constant concentration (the particle distribution in the volume is not homogeneous) and, in many applications a non constant velocity distribution. So, if you are not so far from these assumptions, you can retrive a good estimate of the particle flux (accumulation rate=particle flux * cross section). If you have a tomographic PIV setup (3 or 4 cameras), you can measure the particle distribution and  the velocity of every particle (3D-PTV) in the overall volume of interest (if it is not to big). As a result, you get instantaneously  the accumulation rate distribution in space. 

Hi!

Do you already use LabView for your experiment?

If so, then there should be no problem in creating arbitrary flow patterns. 

Please contact me on PM or radziwon@purpravn.com in case you need some further assistance. I am opened for various forms of collaboration.

Please refer to the following paper:

P. Vedula and R. J. Adrian, “Optimal solenoidal interpolation of turbulent vector fields: Application to PTV and super-resolution PIV,” invited paper, Experiments in Fluids (Special issue), 39, pp. 213-221 (2005)

Disclaimer: I'm working on OpenPIV since 1998, together with Prof. Roi Gurka and a large group of great developers. 

In the recent years we move strongly away from Matlab and towards Python with C++ implementations - precisely in order to be open and free. Matlab is not free and cannot be a good open source solution as the infinite software updates will eventually create the impossible situation. We are still maintaining old Matlab versions but since R2014b there is a new graphics engine that we cannot support anymore.

OpenPIV-Python is the way to go. OpenPIV with C++ is the way to get extreme speed. Soon, OpenPIV-Python with Numba, GPU or other developments will give both the speed and the flexibility.

Please join us on the development www.openpiv.net  

With velocity fields not exhibiting a periodic behaviour, I would just reconstruct statistical properties (mean flow, Reynolds stress, ...).

If you do have a periodic behaviour (which it appears to be the case because you mention a phase difference), the usual way is to reconstruct your global field by shifting in time one of them and then use interpolation to get clean, global instantaneous fields. The problem is that aperiodic perturbations (turbulence or chaotic instabilities) will not be the same between your two measurements.

One solution may be to filter your instantaneous fields in order to get rid of the aperiodic perturbations (that cannot be reconstructed anyway), using spectral filtering or POD, and to do a reconstruction with only the periodic part of your fields. By doing that, you can expect to have a clean reconstruction of your the periodic part of your fields, and rely on statistical properties reconstruction (mean flow, Reynolds stress, ...) to have information on the aperiodic part.

Hope this can help,

Best regards.

Dear Nasser,

You can put the laser beneath the flume and make a perspex tower for the light sheet, or put it on the side (if you have a transparent wall) and use a mirror to shift the sheet by 90 degrees.

Regards,

Dubravka Pokrajac

I have seen it used in reactors before but I can't think of an example right now. If you have visual access to the flow chances are you can use PIV.

If you provide more information about the experiment I will be able to give you a better answer.

I did PIV in water sloshing. At the incipit of the motion, the fluid is at rest and particles are quasi-still. The perfect density matching is difficult to be obtained but if your transient motion is strong enough to respect Stokes number for PIV, you can neglect the residual motion of the particles due to buoyancy.

Are you using water as test fluid or something else?

I used fluorescent particles of 45um with a density of 0.995g/cc in water: rest I applied a sinusoidal motion with A=1.2mm and F=2Hz.

I'm sure that those particles are suitable for your experiment if the fluid is water.

You can also use continuous laser and shorten exposure time on your camera. This is a much cheaper solution suitable for a number of tasks.

I think I've been misunderstood, I have a sample that is 20 mm x 10 mm and I want to be able to study six or seven at once. Hence my pixel size will be about 100 micron. Sounds like I need the particles to be about 50 micron at least.

See this article "Making Artificial Snow for Laboratory Use by Richard A. Sommerfeld and Tara L. Freeman" It can be downloaded in the first 2 links below:

Refer

using sigma plot software it is easy to draw the std deviation and mean.

You might want to look at carbon tetrachloride in pyrex.  At room temperature this combination is a close match.

I fine tune the focus by translating the camera on a slide rather than touching the tele-lens, then I lock the slide and the camera on it. If you can afford motorized slides, you can comfortably focus while looking at the images live on your screen.

If you confirmed that other things are fine, I would suspect the Schiempflug condition. Make sure that the calibration plate is focused well. If you are using circular dots on calibration plate, they should appear circular in image too, throughout the FOV. Otherwise, if it appears elliptical, their centers can't be identified properly, which, in turn, would give u some position-dependent error in the pixel/mm ratio and may cause fictitious velocity gradient that you are observing. If you can't obtain circular images of the dots, you should use small dots, because it would brings down the uncertainty in locating their centers, and hence improve the results. Yet another solution may be to use a calibration plate with checkerboard pattern (together with Zhang's method (http://research.microsoft.com/en-us/um/people/zhang/calib/) to obtain intrinsic and extrinsic camera parameters, given that your FOV is not too distorted), where identifying corners is much easier than identifying centers in case of circular dots. On the internet, there is a freely available program for Zhang's method.

Dolan and JEnner produces a nice variety of Fiber optics, you can take a look and also contact them for special fabrications

I think that the article of Melling (and others, e.g. Mei 1992) addressed precisely this point - Stokes number is not sufficient to describe the limitations the particles might experience while "tracking" the turbulent flows. 

Open PIV for DIC is doubt, but Images from PIV software may be used in Matlab image correlation, in order to get the numerical values, generate the M-code (m file).

PIV algorithm are not similar to PTV algorithm.

here you speak about PTV.

My suggestion : ask Alex Liberzon, he is "the specialist of PTV algorithm, with open source code with PTV, using one or several cameras . His reserachgate page:  https://www.researchgate.net/profile/Alex_Liberzon

I am sure he will answer you the correct answer.

best regards

hubert

Not so related to your question, but there are some clues that some particles are coated with surfactants that cause unexpectedly large slip velocity. It becomes important especially for large particles, e.g. see this one:

T. Hadad and R. Gurka. Effects of particle size, concentration and surface coating on turbulent flow properties obtained using PIV/PTV. Exp. Therm. Fluid Sci., 45:203–212, 2013.

I have an open silicon channel and I want to use a polymer film instead of glass to seal it. Still, I want the film to mimic the properties of glass.

There are two possible error sources. The experimental set-up and the PIV-evaluation.

On the set-up: From what I read I guess you measure in water. Is that right? Do you measure in a round pipe with 20mm diameter? Do you have a square water-filled box around it for reduction of refractive index difference effects? How thick is your pipe wall? Is it plastic or glass? How smooth/wavy is the pipe surface?

Do you measure 2D or 3D? Please show a scetch of your optical beam pass.

On the experient: Redo the experiment with perfect allignment to the channel walls. Your data shows severe misallignment.

On the PIV evaluation: Use elongated PIV evaluation windows, e.g. 8x64 instead of 32x32, stretched in the direction of the pipe wall. Use 0% overlap in the direction of the velocity gradient.

You will learn a lot from the thesis of Cas van Doorne:

It will give you a lot of practical hints on your experiment.

I hope that helps,

Ralph

If you are a Matlab user you might want to check out PIVlab or PTVlab, which is available through the Matlab file exchange. In general, PIV is more suitable for high seeding densities, whereas PTV is best for low seeding densities. Another option would be to use OpenPIV, which is freely available.

Full agree with Peter Apps. If you don't have any documentation to FID, following remarks could help:

We have experience with fast FID (FFID) HFR400 from Cambustion performing in open-circuit wind-tunnel that the best range flame temperature for non-problematic concentration measurements as well as for calibration is from 280 up to 350°C. Below the range the improper calibration occurs, above the range the sealing and tubes suffer and need to be changed frequently.

Another important note is that the flame temperature should be maintained at certain level during measurements, hence between the calibration points. This temp. level is dependent on proper set-up of the FID's working gas pressures (hydrogen and air) and vacuum pump. 

predictive model to monitor fliud velocity  from  various daimeter of draing discharging to creek

The physics-based optical flow method is applicable to your problem.  The physics-based optical flow equation should be derived from the relevant fluid transport equation and imaging process by using the projection method. Thus, the physical and mathematical meanings of the optical flow can be clearly defined. For X-ray images that are transmitting images, it has been done (see T. Liu and L. Shen, “Fluid flow and optical flow” Journal of Fluid Mechanics, Vol. 614, No. 11, pp. 253-291, 2008). 

Regarding to the intensity change, it is indeed a problem for both PIV and optical flow method.  If the time interval between two images is sufficiently smaller than the timescale of the intensity change, the intensity change could be small enough for optical flow computation.  In addition, the intensity change could be corrected or compensated by pre-processing before optical flow computation, which is a normal procedure in our studies.   

Could PIV software  caculate the turbulent dissipation directly?

To obtain a real ensemble averaging of turbulence, the sampling frequency must be high enough ( usually ~10kHz for low Re number) to resolve the smallest scale eddy motions and the sampling time must be long enough to capture all the motions including large-scale eddy motions. For low-frequency PIV, you can only capture the large-scale (low-frequency in time) motions if your sampling time is enough long as STUART BENTON said, so you can only get the low-frequency ensemble averaging instead of the real ensemble averaging because you cannot capture the high-frequency (small-scale in time) fluctuations.

You should be able to track velocities provided your time delay (dt) is OK and your images have sufficient contrast. If the optical density is too high, you'll encounter problems. 

You'll probably want to:

In Research Gate you can look into the page of Dramais:

Performance of image-based velocimetry (LSPIV) applied to flash-flood discharge measurements in Mediterranean rivers by

J Le Coz, A Hauet, G Pierrefeu, G Dramais, B Camenen

You can ask him to send you copy! But

If you google "LSPIV" you already find this paper on the first page with a direct free access and a lot of others!

Both :)

Dantec Dynamics typically provides an installation and training session when new systems are delivered. We also offer PIV workshops on occasion, but the best advice I have for you is to contact your local representative to get specific assistance with your system and measurement application as this may be unique. In the UK, contact Graham Hassel at:

Dantec Dynamics Ltd.

Garonor Way

Royal Portbury

Bristol BS20 7XE

United Kingdom

Tel: + 44 1 275 375 333

Fax: + 44 1 275 375 336

E-Mail: uk@dantecdynamics.com