Cavitation - Science topic

This is an inescapable fundamental review (one of the oldest but most quoted) on drag reduction by bubbles on an external flow; Whether injected or created using cavitating flows, the physical phenomenon is fundamentally the same: a dispersed gas-liquid flow that has often been tackled using two-fluid models.

Ceccio, S.L. (2010). Friction drag reduction of external flows with bubble and gas injection. Annual Review of Fluid Mechanics, 42, 183-203.

Abstract

The lubrication of external liquid flow with a bubbly mixture or gas layer has been the goal of engineers for many years, and this article presents the underlying principles and recent advances of this technology. It reviews the use of partial and super-cavities for drag reduction of axisymmetric moving objects within a liquid. Partial cavity flows can also be used to reduce the friction drag on the nominally two-dimensional portions of a horizontal surface, and the basic flow features of two-dimensional cavities are presented. Injection of gas can lead to the creation of a bubbly mixture near the flow surface that can significantly modify the flow within the turbulent boundary layer, and there have been significant advances in the understanding of the underlying physical process of drag reduction. Moreover, with sufficient gas flux, the bubbles flowing beneath a solid surface can coalesce to form a thin drag-reducing air layer. The current applications of these techniques to underwater vehicles and surface ships are discussed.

Start with higher OD values that you have and then keep reducing the OD values in small steps.... You will notice that images will improve... Stop reducing the OD when you see the image is bright enough, otherwise your CCD sensor will get saturated... If the intensity is high enough the sensor may get damaged as well... Hope this helps....All the best!!

Noted professor Stam Nicolis , I will keep that in mind. Thanks for your time and help!

Sorry for the delay u need more help contact me +256781661909 whatsapp

However, If you look up matching layers in general, you will find that they are quarter wave (in the matching layer material) thick and of impedance (Zh*Zw)^.5, where Zh is the acoustic impedance of the horn material and Zw the acoustic impedance of the water (1.5 MRayls). Ideally, you should also have a matching layer from the transducer into the horn as well, same formula but using the impedances of the ceramic and horn material. The matching layer is designed for one frequency (where the matching layer is a quarter-wave thick) so will not help a lot for high bandwidth (very short) pulses.

Please go through the link and find your required answer.

Ivan Hartman please read through the article attached herewith, i think it will help you to get your answer

Nagalingam,

I was about to offer an idea but just read that you designed this with a restriction to enhance cavitation. Instead of asking us to guess...Please explain the design so we can offer appropriate help.

Hi Federico Verdini,

For the said industrial wastewater, determine or (repeat) the COD by varying dilution factors

(1:10, 1:50, 1:100, 1: 200). After that you may get average range of COD.First confirm intial value of given sample. For more accuracy you can correlate with BOD value.

However you can more details about interference and its limitations in APHA Standard method 5220, SECTION 5-11)

Reg

Prashant. B.B

Great question Andreas Almqvist! One which I've debated a lot!

The complementarity problem is an excellent and effective way of solving the problem of hydrodynamic cavitation. Have you (or someone else) applied this method to highly-loaded contacts (GPa pressures) such a line and point contact geometries out of interest? Great to see answers already from authors adapting the approach for their specific problems here too.

I see the expected pressure magnitude being one of the main drivers behind the choice of model for this phenomena. I have reviewed (a little) the modelling approaches to hydrodynamic cavitation with the late, great Duncan Dowson as part of this publication: . In this article we developed a 'moving mesh' type of approach for modelling the onset of cavitation but did not consider film reformation. This method can be applied to low pressure (MPa) and high pressure (GPa) problems without any difference in the implementation.

For lower pressure environments (MPa) the Elrod-Adams algorithm is still widely used as the baseline method for simulating cavitation including papers published by my group this year: . There are several publications optimising and adapting this method with varying degrees of success in the literature, too many to list here.

More recently this method has been combined with the complementarity condition to formulate the problem as described by Andreas and others. This also links to recent improvements in the solution approach by Woloszynski and the use of the Fischer-Burmeister equation to formulate the complementarity problem (see very recent work by Ron van Ostayen at TU Delft).

The complementarity method is a more stable than Elrod-Adams approach numerically because of the lack of switching functions and more robust mathematical formulation, but this does require a LCP solver which may be prohibitive to some. This is likely why Elrod-Adams remains widely used given it can be used with a standard PDE solver and setup readily with commercial codes, albeit with switching functions included making the problem numerically stiff.

There is also the issue of the change of variable approach from pressure to a derived field used explicitly for the cavitation problem, which then conflates the solution to the lubrication flow in terms of one variable. Therefore several authors use a pressure-only type approach such as that which I explored with Andreas here: . This article uses the Söderfjäll model to create a blending function reducing the density and viscosity of the lubricant rapidly to almost zero in the presence of negative pressure. This simulates the effect of cavitation solely on the lubricant properties and produces the required pressure distribution efficiently with rupture and reformation included. A similar but different approach was used by Gao et al in this paper: . The approach is very useful for where there are many regions of cavitation occurring within the domain.

Note that all the applications discussed so far are conventionally developed for low pressure (MPa) environments, and that in the classic high pressure (GPa) contact problems cavitation is managed with less rigour of the pressure profile shape/value. This is because of the large separation in magnitude between the max pressure and the vapour pressure in such contacts, with the requirement only being to resolve the pressure and pressure gradient to zero at the location of the onset of cavitation (JFO conditions).

For GPa problems the JFO conditions are conventionally achieved either with the use of a free boundary problem (see the classic multilevel solutions of Venner) or with the penalty approach of Wu (see more recent solutions by Habchi). Neither of these approaches fully resolve the problem of cavitation and this has led to several two-phase type models being developed which require very fine grids to resolve the flow. Multi-phase CFD simulations have also been developed recently by Imperial College London to investigate cavitation in much more depth for highly-loaded contacts and resolving all the flow (see Hartinger et al. and Hajishafiee et al.). These two- or multi- phase models also allow variance in the film thickness direction and are therefore not necessarily based on the Reynolds equation, making them more complex descriptions of the flow that are harder to solve numerically.

So the question comes down to whether resolving the full pressure shape/value is of importance to the outcome required, which itself is connected to the magnitude of the expected pressure. There is also the question of what type of solver you have readily available, whether a change of variable doesn't conflate the problem formulation, and if you're interested in very fine detail about the flow features.

Personally I would be in favour of the ALE or complementarity approaches for any problem/geometry but this certainly needs more development, hence my question at the start. I also think a review paper on the topic is well overdue!

Dear Prof.

Looking forward to hear if any special issue under your editorship.

Thanks

Siddhartha

IMHO the type of mesh and the simulated physics are not very closely related to each other.

What matters with no regard to the mesh type, is that you obtain a mesh independent CFD solution in the limit of dx-->0. This applies to all possible mesh types and to all possible CFD physics.

Best regards,

Dr. Th. Frank.

can not plot in Fluent

try in CFD Post

Thanks for your invitation. We can contribute if publication charges are waived.

I think the answer is YES. however, it is very difficult to describe the relationship between ultrasound and chemical reaction with a clear rule or math model.

see

Optimization of solid food waste oil biodiesel by ultrasound-assisted transesterification

https://www.sciencedirect.com/science/article/pii/S001623611931169X

http://journal.ipb.ac.id/index.php/jtep/article/view/7349

Synthesis of Biodiesel Using Microwave Absorption Catalysts

Kinetics for the Synthesis of Biodiesel Based on the Calculation of Hot Spot Temperatures in the Catalyst.

We can get its solution by Homotopy Analysis method(《Beyond Perturbation...》 by Liao Shi Jun).

@ Master Naseem Ahmad ,

Thanks for your kind suggestion.

Many thanks Taimoor

...because this is one of the best validated 2-equation turbulence models with a good balance between accuracy and computational effort. In particular more sensitive to flow separations.

I would like to suggest you some relevant items according to your query : https://www.cfd-online.com/Forums/main/198534-meshing-solver-settings-dealing-high-pressure-gradients.html

Please look at the following below links which may help you in your analysis:

https://www.nrel.gov/docs/fy06osti/38849.pdf

Thanks

Cultured cells are useful for studying the subcellular distribution of proteins, including peripheral membrane proteins. Genetically encoded fluorescently tagged proteins have revolutionized the study of subcellular protein distribution. Nitrogen cavitation is well suited for mammalian and plant cells and fragile bacteria, but is less effective with yeast, fungi, spores, or other cell types with tough cell walls

Hello!

This is because, in the second case, the assembling by threading causes failures in transmission of the oscillation down to the tip. You should adopt other solutions that imply larger surfaces in contact between those two parts: horn and tip.

There's this unfortunate tendency to stick the words ``Casimir effect'' everywhere.

Sonoluminescence is the emission of electromagnetic waves by sound waves-it's a classical effect and doesn't depend on the ability to resolve either the photons or the phonons, whose superpositions the corresponding waves are.

The Casimir effect regards the fluctuations of the intensity of some field about its average value in the vacuum, in the presence of boundaries. This doesn't have anything to do with sonoluminescence beyond pertaining to the shot noise of the photons and/or the phonons involved in sonoluminescence, when these can be resolved, in the presence of boundaries.

If I understand your question you want to have a ultrasonicated volume within a bath. The ultrasound field is not uniform over volume it is designed for utility cleaning. Your use of the bash for cavitation will need to be graded on the results of your beaker position in the bath. A short discussion from Heilsher details this in a more complete fashion. The link is https://www.hielscher.com/probe-type-sonication-vs-ultrasonic-bath-an-efficiency-comparison.htm

Thank you for your contribution, Dr. Rachan Karmakar for your wonderful contribution.

if you will use fluent you can see below link.

@ OPG is used for detecting bone metabolism changes such as myelitis. Bisphosphate efficacy is making bone ageless that inhibits bone metabolism. Therefore, precisely monitoring the level of jaw bone deterioration in cavitations maybe need using other adjunctive methods.

Cavitation is what to do with suction line. A number of parameters include; pipe length, diameter, and roughness, fluid density and viscousity, flow speed and temperature, upstream pressure, elevations.

You may find answer to your question in this article

Hello, what really you want to find out? What solvent you mean?

Acoustic cavitation can be done directly with waste water which normally called hydrodynamic cavitation.

Hi Emanuele Quaranta

If there is a guide blade, maybe their attack angle changed in 3 days and set in steady angle. If this problem cause is electrical, transient time is less than a minute. if it causes is hydrodynamic, transient time is less than a hour. so I think cause of that is mechanical mechanism.

Good Luck

Jochen --

If we assume a constant velocity (resulting in halving the amplitude in going from 20 kHz to 40 kHz), it remains unclear to me if the power intensity then remains constant. Using an electrical analogy, the power developed in a linear resistor is P = I^2 R where I is the current and R is the resistance. If the current I is held constant (analogous to constant mechanical velocity) then the power P remains constant; however, this is only true if R is independent of frequency. (As a further analogy, the hysteresis losses in an electrically-driven magnetostrictive material increase rapidly with frequency. This is why most magnetostrictive transducers are limited to an upper frequency of about 30 kHz.) Thus, this gets to my basic question -- is the acoustic resistance of the cavitating fluid actually independent of frequency since both the bubble size and the bubble density (the cavitation cloud) depend on the frequency? (I'm looking for a reference study with verifiable results.)

Regards.

Hi, there has not been consensus on the cell numbers to load but most authors used 300 like you. I think you are in order but more cell optimal loading test should be done to ascertain the optimal cells to load for the best results.

It would be a highly educational experience if you could try to develop your own solver using MATLAB then write it in a low-level programming environment like Fortran.

But OpenFOAM should be sufficient if you want to get a bit better at programming CFD, and ANSYS/Fluent would be best if you plan on proceeding as a CFD user.

I don't have a solution for your problem, but some of the following comments may help:

1. PDMS is hydrophobic. Bubble problems are much worst when the surface is hydrophobic. Plasma treatment may render the PDMS hydrophilic, but the effect lasts some hours. You need days. There are other treatments, more complicated, to modify the PDMS surface properties. If you are interested look in the literature. Surface modification may also reduce the amount of gases that permeate the PDMS.

2. When you compress the fluid inside the microfluidic device with N2 a large amount of it will dissolve in the liquid. If you immerge your microfluidic device under water during the pressurization, maybe you can protect your liquid inside the device from N2 (it will take time for the N2 to diffuse to your liquid of interest).

3. Even liquid at 1 atm, before your experiment, will have gases dissolved so your vacuum treatment will remove those gases also. So, to minimize bubbles maybe you should try to use liquids that have been under vacuum before the experiment. Since your experiment takes days maybe you should also immerge your device on degassed water to avoid dissolving gases from the atmosphere.

4. You probably need a small amount of dissolved gases to break the cells, so 2 and 3 may not help.

5. Other possible solutions:

a) use traps to confine the cell debris and inject bubble free fluid

b) break the cells with other methods that do not require massive pressurization (e.g. ultrasonics)

Hello Mounir,

Thank you for your feedback. I was actually referring to the particular code base that Mohammed is using in his project. Thank you.

For anyone who is facing such problem. While modeling cavitation, a cavitation limit has to be defined. We can define it in input file. Once the input file is saved, it has to be run from abaqus command. Abaqus/CAE can not rut the file.

A gel is a two-phase system: dispersant/external phase is a solid and dispersed/internal phase is a liquid. Size of liquid particles range roughly from 1 to 1000 nm. The gel migth flow (non-newtonian fluid), depending on the relative proportion of phases. During flow, cavitation may occur, governed mainly by the liquid phase vapour pressure, which is highly dependent on temperature. Again, you’ll have to find/develop a gel using a liquid of very low vapor pressure, so as to minimize the chances of cavitation.

Dear sir,

I had this problem many times so I open the CFD POST individually and load the FLUENT results, this will make all of results important to the CFD POST and you can run FLUENT many times in different boundary conditions l.

Note that you have to export the results by (case and data) from the FLUENT program.

Hello Elisabet,

This question showed up in my home feed and I found it interesting. So let me take a crack at it.

I know that hydrodynamic cavitation occurs when local pressure decreases below vapor pressure of the liquid at that temperature. Generally, this phenomenon is associated with high speed flows of incompressible or slightly compressible liquids. I googled and found that the JEG-3 cells you are using are stored in liquid nitrogen. So I think this phenomenon might have something to do with the gas being used. I again googled and found saturated N2's vapor pressure at different temperatures (https://www.bnl.gov/magnets/staff/gupta/cryogenic-data-handbook/Section6.pdf). I says that at temperatures lower than STP or room temperature, the vapor pressure is significantly greater than 1 atm. Thus the local pressure (assuming 1 atm) satisfies the condition for cavitation to occur resulting in the pictures you have posted. From the pics it seems that liquid N2 were hidden in the channels (?) where cavitation was seen.

My follow up questions / comments are:

1. Is my assumption about storage in liquid nitrogen correct?

2. Are the cells completely thawed when kept outside? How do you judge complete thawing?

3. Cavitation results in small bursts of these gas bubbles as the local pressure increases around the bubble. Will this potentially damage the cells you are trying to observe?

4. What is the length scale of the cells we are looking in the picture. I do not have a biology background so please pardon my lack of knowledge.

I hope my reasoning makes sense and this answer is helpful. I will be happy to hear or discuss what the experts have to say.

Regards,

Pranab

which model did you use for 3 phase flow, and which software are you using for you modeling?

- By increasing the diameter of the impeller eye can add less space for liquid to boil or vaporize.

- By adding a impeller inducer. Pump inducers are designed to prevent significant cavitation by adding a smoother inlet for pumped liquids or materials.

Hello, Ziming Zhu 

I'm not an expert in turbulence also, but i guessed several reasons which can lead to behaviour, described by you. So i can't say which turbulent viscosity ratio more realistic, but i can ask you to change intensity at inlet whithout changing ratio. And if results are same for both cases then the reason in eddy viscosity ratio.

Regarding Q.2 - yes, you need time varying B.C. Also, if you have initial velocity internal field with value, equal to inlet, then flow "hits" the hydrofoil with dynamic pressure rho*w*w/2 and this can create large pressure drop and vapor generation term, Try to increase velocity field from 0 to 2.1m/s.

Such a large pressure drop across a valve is destructive to  the valve with vibration, ultrasound, erosion, and recoil. Unstable control and excess noise are the common complaints.

Best remedy is to let down in two stages or more, one setting a down stream pressure and the other setting a flow through. To avoid interference I prefer a spring operated pressure control and an instrument operated flow control. This is a common configuration that usually contains a safety pressure relief valve to protect down stream against failures. 

Other remedies are possible. The petroleum industry uses calibrated chokes to deliver small flow at high pressure drop. They are just precisely made short lengths of metal cylinders with a small passage drilled and machined  through the center.

If you had more flow a work engine might be possible.

Hello, 

I would like to recomend this book:

The structure close to the trailing edge could be physical, but the rest are spurious. Looks a bit like it could be in proximity to a mesh coarsening if you have a refinement wedge around the foil?

Hi Bavan

For more information I suggest

CAVITATION AND BUBBLE DYNAMICS book by Christopher Earls Brennen

http://caltechbook.library.caltech.edu/archive/00000001/00/bubble.htm7/8/2003 3:53:57 AM

With regards

Thanks

Hi Atreyee,

Thanks for your answer. You are right but i have something to add. Negative pressure doesn't always mean a signature of liquid gas coexistence. A liquid in metastable state may also show negative pressure in simulation. Any-ways I wanted to know  about how to calculate exact cavitation line not the liquid-gas spinodal line.

Thanks again

If you are looking for physical rig to observed the formation of cavitation in journal bearing, then you can construct your journal bearing from tranparent materials such as perspex or any tranparent materials that willnot be corroded or reactive to the lubricant.. Your rig should allow for variable ecentricity and rpm. You need only to construct the lower journal from transparent material. With high speed camera and some form of computer imaging  you should be able to observe the formation of cavities in the lubricant. 

Dear Robinson,

   I hope these links be useful and helpful for your request. 

Best Luck.

- Analysis on Cavitation Performance in Multi-Stage Centrifugal Pump Based on Cavitation Model (http://www.scientific.net/AMR.317-319.414)

For the following, I assume that you mean the threaded replaceable tips. Then there are three considerations for renewing sonication tips -

1. Frequency. As the eroded material is removed, the frequency of the ultrasonic stack will increase. Ultrasonic power supplies (generators) typically have a frequency band within which they will operate properly. This will depend on the design of the power supply. However, you should typically expect at least +/-1% of the nominal operating frequency (e.g., +/- 200 Hz at 20 kHz) or more. You can get the exact spec from the equipment manufacturer although the equipment may still operate well outside the specified band. You can simply remove tip material until the frequency falls outside this band at which point the power supply should no longer start due to its internal protection circuitry.

2. Amplitude. As the frequency increases the output amplitude may change. If the amplitude is critical then you should measure the amplitude with a new tip. Then when the renewed tip is installed the amplitude should be adjusted via the power supply to get the desired amplitude. These measurements can be taken in air.

3. Heating. You should be able to run a new tip for some time (say 30 seconds) in air without appreciable heating of the tip. If you run the same test with a renewed tip and find appreciable heating then this means that the stiffness across the tip's surface is not adequate to support the tightening load. Then the renewed tip should be discarded.

If you are making your own tips then you can try machining the tips somewhat longer than normal to give extra wear length. The frequency will then be below nominal (for instance 19.8 kHz instead of 20 kHz). However, the added weight will put additional stress on the tip-horn joint so you should avoid this method if you find any extra heating at this joint.

You can find such data in Table 1 of this paper:

S. A. Mohammadein and K. G. Mohamed, Growth of a gas bubble in a supersaturated and slightly compressible liquid at low Mach number, Heat and mass transfer 47 (12), 1621-1628, (2011)

I can also help you to find any missed data.

Mostly micro cavity chains , which are nothing but growing vacancy clusters  are observed along those grain boundaries subjected to the applied uniaxial tensile stresses, and  aligned  almost normal to the direction of the stress axis. Theoretically one can't image to have creep strain without having applied stress unless one deals with the relaxation stage that takes place after one  turns off the applied stress.  With the acception of   high temperature Herring-Nabarro creep,  there is a large amount  of dislocation climb  occurs due to the vacancy flow to the compression sides of  the dislocations having edge or mixed characters.  This  temperature dependent  process especially enhanced very much under the applied high stresses, and the creep rate shows almost  sin- hyperbolic dependence  on the stress. (Barrett & Nix). 

P = ωΤ . Lower number of blades means lower angular mass i.e torque. If the speed remains the same, then the output power should be lower. Something has to change. Either the speed, or the power. If the speed remains the same, then the turbine produces less power, it is "weak" and it will  "see" more motion resistance i.e cavitation. If the power remains the same, then the speed will be higher for a lower number of blades, but higher speed leads to cavitation. 

Dear Matevz, late answer, just joined RG.

The volume dynamics is very well captured with RP, thus RP should work for midly deformed bubbles. This is the case for gamma>1.5 near a surface, the jet forms only in the late phase prior collapse. The rebound with jet can't be captured with RP, because you loose energy during the impact (water hammer pressure) and the formation of a vortex ring. Thus the question remains, RP better for smaller than larger bubbles? It works very well for small (SL type bubbles) and for large ones (under water explosions), yet when the bubble is too large, buoyant effects can came in as the pressure head between top and bottom is large and the oscillation time is larger, thus more time to develop instabilities. My guess therefore is that RP is good for volume dynamics for gamma>1.5 and sufficiently small bubbles.

Hi,

we did quite a number of experiments in the recent years to address specifically these questions. We have not worked with tropical trees, but I think the processes are quite generic (see or global review paper in Nature Choat et al 2012). 

There is actually two questions:

1- Are trees able to refill embolised vessels? There is a lot of confusion in the literature on this point because many previous observations are biased by faulty methodologies. X-ray micro-CT is probably the most reliable technique available today to study these processes and we have used it intensively recently (through Synchrotron facilities, or with our lab based systems). So far, our conclusion is that trees can refill embolised vessels only if they can generate positive root pressures. In other words, we have not been able to confirm the so called 'novel' refilling with these robust techniques. This means that embolism can be reversed only when transpiration is null (at night) and when soil is fully hydrated. I've seen this phenomenon on temperate trees only during spring on few species. A point that should be made clear is that cavitation is not routine in trees. Cavitation forms only under extreme drought conditions, typically after stomata have closed and leaves loos their turgor. We have never been able to confirm daily cycles of embolism/refiling with our new technologies (micro-CT). 

2- Are trees able to recover once embolism has formed? How resilient are they ? We have addressed this question experimentally by exposing trees so increasing levels of drought, measuring embolism and quantifying mortality. We have data for about 10 species and if we can generalize from this small data set we can say that the lethal level of embolism is around 90% for angiosperms and 50% for gymnosperms. Above these levels tree never recovered (=death). Below, they were able to regrow, but their growth was impaired and they would have eventually die in the field (less competitive).

There is of course a lot of experiments that need to be done to confirm these preliminary conclusions. The real world is probably more nuanced and several species probably behave different (especially in the tropics!). However, the key point is that you should be extremely critical about the methods you use and it is essential to confirm your findings with robust techniques such as micro-CT. Very sadly there is a lot of confusion in the literature, so please do not bring more confusion ! 

Here is a list of recent papers from our group addressing these questions. You can find them here on Resarchgate or on my website: http://herve.cochard.free.fr/publi.htm

Torres-Ruiz JM, Jansen S, Choat B, McElrone A, Cochard H, Brodribb TJ, Badel E, Burlett R, Bouche PS, Brodersen C, Li S, Morris H, Delzon S. 2015 Direct X-ray microtomography observation confirms the induction of embolism upon xylem cutting under tension. Plant Physiology 167: 40-43.

Cochard H, Delzon S, Badel E. 2015 X-ray microtomography (micro-CT): a reference technology for high-resolution quantification of xylem embolism in trees. Plant Cell and Environment. 38: 201-206

Martin-StPaul N K, Longepierre D, Huc R, Delzon S, Burlett R, Joffre R, Rambal S, Cochard H. 2014 How reliable are methods to assess xylem vulnerability to cavitation? The issue of “open vessel” artifact in oaks. Tree Physiology 34: 894-805.

Torres-Ruiz JM, Cochard H, Mayr S, Beikircher B, Diaz-Espejo A, Rodriguez-Dominguez CM, Badel E, Fernández, JE. 2014 Vulnerability to cavitation in Olea europaea current-year shoots: more support to the open-vessel artefact with centrifuge and air-injection techniques. Physiologia Plantarum. 152: 465-474 doi: 10.1111/ppl.12185

Delzon S, Cochard H. 2014 Recent advances in tree hydraulics highlight the ecological significance of the hydraulic safety margin. New Phytologist. 203: 355–358 doi: 10.1111/nph.12798

Cochard H, Delzon S 2013. Hydraulic failure and repair are not routine in trees. Annals of Forest Science 70: 659-661

Urli M, Porté A, Cochard H, Guengant Y, Burlett R, Delzon S 2013. Xylem embolism threshold for catastrophic hydraulic failure in angiosperm trees. Tree physiology 33: 672–683

Cochard H, Badel E, Herbette S, Delzon S, Choat B, Jansen S 2013. Methods for measuring plant vulnerability to cavitation: a critical review. Journal of Experimental Botany 64: 4779-4791

Barigah ST, Charrier O, Douris M, Bonhomme M, Herbette S, Ameglio T, Fichot R, Brignolas F, Cochard H 2013. Water stress-induced xylem hydraulic failure is a causal factor of tree mortality in beech and poplar. Annals of Botany 112:1431-1437

Choat B, Jansen S, Brodribb TJ, Cochard H, Delzon S et al 2012. Global convergence in the vulnerability of forests to drought. Nature 491: 752–755

Brodribb TJ, Cochard H 2009. Hydraulic failure defines the recovery and point of death in water stressed conifers. Plant Physiology 149: 575-584

Dear Khawar,

I suggest that you go to the online service of "Zhang Lab On-line Service System", they can help you.

Good luck,

Regards

Abel

Dear Dr. Thornber and Dr. Bensow,

Thank very much for your answers.

Hi again,

A cavitation bubble normaly consists of combination of dissolved gas (O2, N2 etc..) and vapour. (For further explanation, you can look at 1st and 2nd chapters of Brennen's book 1995)

Mostly, i am interested in the numerical simulation of cavitation based on bubble dynamics models. Therefore, i could say that, due to easy treatment, most of cavitation models based on bubble dynamics ignores the dissolved gas and assumes only vapour inside of cavitating bubbles. Thats, why physically we assume that when the pressure in the local region falls below the Pv (vaporisation pressure) bubbles (which are already existed inside liquid) start to grow up. This phenomena is called as cavitation. In other words, the small micro bubbles are already dispersed inside liquid, which result in the phase change by growing up within low pressure region.

Hope it helps for you.

Baris. 

I complete Mr Bicer's answer : the bubble collapse is due to inertial phenomena and lead sometimes to implosion which results in the splitting of the main bubble in various smaller ones tha t can have the size of a spray particle.

Regards!

Thanks Franco,

As you said, i already used blockMesh and refineMesh utulities and solved problem. I saw that if you just check mesh quality by typing only checkMesh, you cant see this message. On the other hand, It is just seen in the case of typing checkMesh -allTopology -allGeometry, and found that it is ignorable.

Thanks for your answer.

Baris

I believe that steam turbines should only be taken from service and dismantled for overhaul if there is a good economical or technically compelling reason.  I recall two machines that operated for 17 years before overhaul.   A close watch was kept on internal condition by regular performance and vibration  monitoring. OEM advice should of course be taken into account if they have experience of any particular issue with similar designs or components. 

To speed up the outage period, steam forced cooling can enable a turbine to be stopped inside a day rather than taking a few days by natural cooling.  Air forced cooling has been used to further reduce cooling time but that needs some equipment and minor turbine modification 

Dear James F Peters, the answer of this question you could find in Sov. Phys. JETP 01/1990; 70(6):997 - 1002.

Dear James F Peters, and Sergey Sukhinin the answer of this question you could find in Sov. Phys. JETP 01/1990; 70(6):997 - 1002.

Dear James F Peters, and Sergey Sukhinin I'll give the answer with all explanations and drawings after one answer another my question.

Dear colleagues, I would like to ask the Bible question connected with numbers. Can seem that this question is far from interests of pure scientists, but my researches showed that all scientists anyway faced this question therefore I couldn't ignore it. For everything two "bad" numbers are known. The first is "13", the unhappy number or "baker's dozen", and the second is "666", this number of an animal or the devil. From here question: "How in old editions of the book of the Bible pages 13 and 666 were numbered?"

Sincerely yours,

Alexander

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