Fluid Dynamics

Fluid Dynamics

  • Michiel Gunsing added an answer:
    Has anyone worked on Hydrodynamics in Bubble Column Reactor, if so how do you measure gas hold-up, bubble dia and bubble l velocity, please help ?

    I am working on Bubble column of inner dia 16 cm of completely transparent glass.

    Michiel Gunsing · Martime Research Institute

    Have a look at:


  • Ph. Reynier added an answer:
    What are different forms of burnett equations(I mean different versions of it!)?

    I know one form of them as dQ/dt +dE/dx +dF/dy=0 where Q,E,F are 4X1 matrices.

    Ph. Reynier · Ingénierie et Systèmes Avancés

    Burnett equations are obtained using a Chapman-Enskog expansion of Boltzmann equations. Then you need a closure to solve the Burnett equations. For Navier-Stokes the closure is the Stokes relation, for Burnett you can not use it. As a consequence  there are as many sets of Burnett equations than ways to close them.

  • Ergin Bayrak added an answer:
    How to do optimum refrigerant distributor design?

    I have some problem at evaporator such as flow side non-uniform distribution. I want to design a new distributor in detail. Normally I have been using nozzle type distributor but I don't ensure desirable pressure drop and thereby distribution. ( It is clear from thermocouple result which is located circuit outlet and capacity reduction both). As a result, this design isn't easy due to two phase flow in distributor. I want to learn your advices and opinions. Thanks.

    Ergin Bayrak · Gebze Institute of Technology

    This study is quite important for me in terms of experimental approach. Thanks a lot Dear Sir.

  • Asghar Bohluly added an answer:
    How do I get rid of spurious currents in two-phase immiscible fluid flows problems?

    I am solving two phase immiscible fluid flows problem using least squares based meshless method. Spurious currents are being generated near the wall. How to get rid of it. Is  it an issue due to this particular method. 

    Asghar Bohluly · NAMROOD CO.

    In my point of view, the height function (Proposed by Ashgriz et. al.) is an artificial method although it could solve some part of the problem.

  • Sasaki Hirokazu added an answer:
    How can I visualize Temperature distribution using TSP?

    I am a master(M1) student of mechanical engineering.My major is the fluid dynamics,plus,my research subjects is heat transfer engineering in turbulent flow using TSP measurement.To visualize Temperature distribution,I use a single reflex camera as a light detector.

    I have a question about conversion procedure from RAW pictures to TIFF pictures.

    I use SLR camera to get  surface temperature/pressure image and get images as RAW.When I do post processing,it is needed to convert raw to tiff. To convert RAW Image to TIFF Image,I use 「stellar image 7」as a  image processing software. I tried to convert RAW images to TIFF images in a variety of conditions,but intensity of TSP didn't decrease ideally as temperature rise .In addition,I confirmed intensity decrease  in the previews.
    Judging from what mentioned above,I think conversion procedure has something wrong.Could you tell me how to convert raw to tiff if you please?
    (for example:white balance R:G:B=?...etc.)

    Sasaki Hirokazu · Iwate University

    Thank you for your valuable feedback.

    I use a TSP consisted of  Ru(phen),polymer,ethanol.

    I made a TSP by mixing these substance.

  • A. J. Roberts added an answer:
    Please. help! Is there any method to solve this nonlinear PDE using similarity?

    I stumbled upon equation j and l in my research.

    I found some books related to fluid dynamics, it says solution to j is the formula k

    (it didn't give the procedure, just solution)

    as you can see j and l looks similar. and similar boundary condition and mass balance.

    Assuming that solution to j is k, Is there any method to solve l and get the formula of h2?

    I tried to solve j analytically by using separation of variables, but it gives second order nonlinear ODE; and I made Wolfram Alpha solve it. but still it didn't respond. 

    so I decided to circumvent reaching the solution by using the similarity

    A. J. Roberts · University of Adelaide

    Regarding the comment "It is likely that some of the assumptions use to derive its equations break down for very small t, where this solution becomes singular." True.  But for a range of similarity problems one can prove that the similarity solution emerges from quite general initial conditions---including ones that are within the domain of validity of the derivation of the equations.  That is, often the similarity solution is widely relevant irrespective of its notional singularity at time zero. 

    For one example of this see the paper   S. A. Suslov and A. J. Roberts. Similarity, attraction and initial conditions in an example of nonlinear diffusion. J. Austral. Math. Soc. B, 40(E):E1–E26, Oct. 1998. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/453.

  • Kourosh Hejazi added an answer:
    Anyone familiar with discrete analogues of k-e turbulence model?

    Dear colleges,
    I'm trying to solve Reynolds equations with k-e turbulence model by FDM (finite difference method). I discretized equations using locally one scheme of Samarskiy. Does anybody know where i can find some information about it? I mean how can i check myself? Is discrete analogues right or wrong

    Kourosh Hejazi · Khaje Nasir Toosi University of Technology

    Dear  Alexander,

    I looked at the paper. It has presented all the original equations and the normalized ones including the turbulence model that have been used in the model which I guess you have been through them and are clear for you. The numerical solution however has been briefly discussed on page 112 in the 3rd paragraph. If you have discretized the equations then this part would help to check your procedure otherwise you may use the relevant references there and that might be helpful.

    But from what I understood these are not your problems. You would like to check whether your code is working correctly. If this it the main reference you are using I would suggest you go through its tests and results provided therein to avoid digging other suitable data. Once you get good results from these tests you could further test your code with other sources.

    If you don't get good results in the first attempt, try to check whether the model without the turbulence model is working and then concentrate on the turbulence model.

  • Chris L Pettit added an answer:
    Can Bernoulli's equation properly be derived from the first principle of thermodynamics?

    Usually Bernoulli's equation is well known  as a first integral of Euler's equations which can be read in standard textbooks on fluid dynamics. Hence, this equation can be derived within the framework of mechanics, only.

    Recently, I got notice about a different approach which starts from the first principle of thermodynamics. Having spent much time in literature research, I only found some very short and imprecise-looking statements but no convincing precise derivation. Coming from fluid mechanics, it looks like a different world to me!

    Does anybody know about a precise derivation in literature? Can Bernoulli's equation deduced from the first principle at all?    

    Chris L Pettit · United States Naval Academy

    First, I assume you mean to discuss the **steady** form of the Bernoulli equation, as taught in introductory fluids courses and many introductory physics courses. The unsteady version applies under the same conditions as the steady version, except of course for the unsteady term.

    Second, I assume you wish to avoid going through some form of the momentum equation, such as N-S or Euler. The closest version I'm familiar with is the path followed in Chapters 2 and 3 of Zucker and Biblarz, "Fundamentals of Gas Dynamics", 2/e, Wiley, 2002. However, this path to Bernoulli clearly shows that you cannot get there without also imposing an equation of state (which means incompressible flow in this case) and invoking the 2nd Law of Thermodynamics (2LTD) to show that entropy generation must not occur if the usual form of the Bernoulli equation is to be obtained.

    Requiring a specific equation of state and 2LTD seems to invalidate the claim that it can be obtained through 1LTD only.

    Finally, I'm confused by the original statement that the Bernoulli equation is a product of mechanics only when obtained from the Euler equations by integration. The derivation requires an equation of state to connect pressure and density. The assumption of constant density is a thermodynamics assumption about the pressure which, for example, relates to our model of the flow work in the process.

  • Dario Gaitan added an answer:
    Why does adding glycerin to water increase the intensity of the light emitted through sonoluminiscence?

    I am playing with a SBSL setup and, testing different substances that I put in distilled water, I have seen that glycerine enhances the intensity of the SBSL. The oxygen from its composition should not affect this since it is required to degass the water in order to get a decent SBSL. Is the hydrogen that does the trick or the carbon?

    Dario Gaitan · University of Mississippi

    Dear Constantin - Using dissolved Ar in just about any liquid will increase the light intensity for any type of SL.  For SBSL, however, there is another factor that needs to be considered: bubble stability, which is controlled primarily by 3 parameters: Amount of gas content, type of gas, and water cleanliness.

    SBSL, in water and air, requires a 50% saturation or less. Otherwise, the bubble tends to grow by rectified diffusion and become unstable (break up and disappear; see attached paper by Holt & Gaitan).

    The type of gas makes a difference because normal (non-noble) gases decompose under the high temps during collapse and the products dissolve in the liquid, causing the bubble to shrink in size and disappear. In fact, when using air, the N2 and O2 will dissociate and produce other compounds that dissolve in the liquid. Only the 1% of Ar in air remains unchanged, accumulating inside the bubble (see attached paper by Lohse et al.)

    The other factor is the number of particles (dirt) in the water. Too many cause the bubble to be unstable and break up at lower acoustic amplitudes. The harder you can drive the bubble without breaking up, the brighter it will glow.

    If you’re having difficulty getting a stable SBSL bubble, it’s usually too much gas or too much dirt in the water.

    Hope this helps.

  • Mohamad Afifi added an answer:
    If you measure with a loadcell the weight of both a static hovercraft and one in motion, are the two measurements expected to be similar?

    For instance, if air would be blown downward from an object onto a loadcell, so that the object flies at a given height, the measurement of the air stream over the sensor should be giving the value of the supported weight. Now, is it possible that the measurement of a high frequency loadcell would be lowered in the case where the flying object is now moving at 100 km/h over the sensor? 

    Mohamad Afifi · Universiti Teknologi Malaysia

    No static weight will be more...as hoovercraft moves there will be aerodynamic forces acting on the body which will reduce the vertical force.

  • Mohamad Afifi added an answer:
    How do I measure an internal blockage in a large-diameter pipe externally?

    hello everyone,

    I want to know about the measuring the blockage inside the pipe from externally.

    Thank you  

    Mohamad Afifi · Universiti Teknologi Malaysia

    Do you want to detect or measure.....detect is easy , go and tap along the pipe and listen to the sound , where the sound generated is different there is something there., well if younwant to measure the extent of blockage ultra sonic thickness may help.

    If your pumping power goes up then the flow is restricted....use can use the technique

    8use by medical doctors to detect high blood pressure

  • Vipin Nair added an answer:
    Is it possible to have have laminar flow at Re = 10000 for flow of water through a circular pipe?

    Recently,i came to know that it is possible to have turbulent flow for Re less than 2300 in a circular pipe..but the flow will become laminar again as the disturbances vanish!!.

    Same way is it possible to have laminar flow(for a small time period) for Re =9000~10000..??? 

    Vipin Nair · Sardar Vallabhbhai National Institute of Technology

    and Mr. Jesse M Johns 

    Thank you very much for that link which you shared.It made everything crystal clear.

  • Larisa N Andreeva added an answer:
    Polymer brushes in shear flow
    Does anybody know any articles about experimental (!) investigations of (dens) polymer brushes in shear flow? I need 'shear rate' vs 'brush height' data, or something comparable to test a theory.
    Larisa N Andreeva · Russian Academy of Sciences

    Is it interesting for you the results for polymer brushes (comb-like, grafted, hairy- polymers) in solutions or for polymer melts? We studied Flow birefringence for comb-like and grafted polymers with different structures  in dilute solutions.

  • Tapan K. Sengupta added an answer:
    Do we need to induce unsteadiness via boundary and initial conditions in an unsteady flow simulation?

    Hello. Lets say I am using unsteady RANS to simulate my flow and I need to capture the periodic vortex shedding of a flow around a profile. For this, will my CFD code automatically capture the unsteadiness and provide a periodic solution of the vortex shedding or do I have to induce unsteadiness via Boundary / Initial conditions.

    Tapan K. Sengupta · Indian Institute of Technology Kanpur

    Cannot agree more than what Filippo stated! This is often taught often in management schools!!

  • Pascal GALON added an answer:
    Can anyone help me with finite volume discretization of NS equation on a non uniform rectangular grid?

    Hi, I am solving NS equations and trying to code them in Matlab for lid driven cavity. 
    I have solved the problem using FDM but I have very little experience with FVM.
    Can anyone help me with the discretization 

    Pascal GALON · Atomic Energy and Alternative Energies Commission

    An other interesting book you can download from this adress :

  • Jörg Ho added an answer:
    What is the torque ratio and speed ratio of a Twin input/ Single output gearbox?

    I want to do some calculations for two diesel engines drive a ship propeller through a gearbox. I want to know the speed reduction ratio, total inertia of the system, torque ratio, etc.

    I know that the power delivered at the propeller which rotates at 150 rpm will be equal to the sum of power of the two engines running at 750 rpm.

    P(load) = 2*p(eng)
    T(laod) * 150 = 2*750*T(eng)

    Is the speed reduction ratio is different from torque ratio ? is (2*750)/150 the correct reduction ratio ? or it is just 750/150 ?

    Also, to model the shaft dynamics, i will use the following equation:

    2*pi*Inertia of rotating parts*(dn/dt)= T(eng) - T(propeller) - T(friction)

    The total system inertia at the shaft = inertia of propeller including entrained water + shaft + gearbox + engine inertia*(reduction ratio^2) ???? 

    Many Thanks in advance

    Jörg Ho · Fachhochschule Südwestfalen

    Assuming same speed of both engines, same speed ratio and same orientation of the torque, the torque of both engines add up, meaning you are right.

  • Bruno Porto added an answer:
    Does anyone know of any research papers reporting hypersonic CFD studies with OpenFoam?

    I would like to know any practial use of OpenFoam at supersonic and hypersonic flows.

    Bruno Porto · Instituto de Estudos Avançados

    Grazie Franco!

    I'll follow those discussions, thank you very much.

  • Hazim Hashim Tahir added an answer:
    Does an anti-hermitian inverse Fourier transform have any physical meaning?

    In a hydroelasticity problem, I have used the temporal Fourier transform in order to solve the linear hydrodynamic equations. The system of interest consists of a solid particle moving close to an elastic membrane. Since the membrane shape depends on the history of the particle motion, a Fourier analysis is therefore needed. After resolution, I found that the interface elevation in the frequency space has a real odd part, and an imaginary even part. This means that the transformation is anti-hermitian, and the elevation back in the time space is purely imaginary. I think that this has no sense since the measured quantity should be real! Does anyone have an idea about how to explain that? Thank you!

    Hazim Hashim Tahir · Ministry of Science and Technology, Iraq

    Dear my Colleague,

    Good Day,

    For real-valued input data, however, the resulting DFT is hermitian—the real-part of the spectrum is an even function and the imaginary part is odd, such that X−k=Xk, where the bar represents complex conjugation. This means that all of the "negative" Fourier frequencies provide no new information. Both the k=0 and k=N/2 bins are real-valued, and there is a total of N/2+1 Fourier bins, so the total number of independent pieces of information (i.e. real and complex parts) is N, just as for the input time series. No information is created or destroyed by the DFT. please, see the attached website for detail.

  • Andre Pineau added an answer:
    What Experiments are available for the Richtmyer-Meshkov instability involving gas and Liquid ?

    The Richtmyer–Meshkov instability (RMI) occurs when two fluids of different density are accelerated. Many experiments can be found  in the litterature. I am interested by the Richtmyer-Meshkov Instability of a Liquid-Gas or Liquid-Liquid Interface to validate different numerical schemes recently implemented in the Fast transient Dynamic code Europlexus ( www-epx.cea.fr/ europlexus.jrc.ec.europa.eu/).

    Andre Pineau · ParisTech

    Sorry, but I nannot help you

  • Stephan C. Kaiser added an answer:
    Is there a way to calculate the variance of a measured sauter diameter?

    From the definition of Sauter mean diameter in the below link:


    Can we assume the variance to be in the following form?:

    variance = (d_64)^2 - (d_32)^2

    OR, if you are not too familiarized with the notation, see gif file below.


    Stephan C. Kaiser · Zurich University of Applied Sciences

    When comparing your measurements with a literature model, the R^2 should be at least a good starting point to assess the goodness of the fitting. If you compare the model predictions with the measurements in a parity plot (i.e. measured values vs. predictions), the plot should give you also some idea about systematic deviations - for example, if your Sauter diameter is well-predicted for one surface tension, but the prediction fails for a second surface tension. Furthermore,  I recommend to look at the deviations between replicate measurements, if you have some, (e.g. expressed by the standard deviation) and to compare it with the deviations from the model predictions (i.e. is the deviation/agreement statistically significant related to the measurement reproducibilty?).

    Good luck.



  • Sita Drost added an answer:
    Does anyone know the Oldroyd-B fluid Prandtl number ranges?

    I am searching for the Oldroyd-B fluid Prandtl number ranges.

    Can anyone help me?

    Thanks for your cooperation

    Sita Drost · Delft University of Technology

    Hi Navid,

    Can you give some more background for your question? The Oldroyd-B fluid is a model, so its Prandtl number range depends on the model parameter values.


  • Michel Arrigoni added an answer:
    According to which mechanism do cavitation bubbles enhance atomization characteristics?

    Are there any analytical equations or theories that relate the final droplet's SMD to the mechanism by which cavitation bubbles improve the spray emerging from plain orifice nozzles into still air?

    Michel Arrigoni · ENSTA Bretagne

    Atomization is also governed by the Weber number versus Reynolds. There is a paper written by Chauvin et al in physics of fluids in 2011 I think.

  • Claus Fütterer added an answer:
    What are the best methods for droplet generation?
    What is the best method to produce uniform droplets in microchannels? Pneumatic pressure, syringe pumps? Is pressure control really better than syringe pumps? If yes, why? Please help me to understand better.
    Claus Fütterer · Biophysical Tools

    Dear Martin,

    indeed you are right. I added a syring pump simulator giving the response time as a function of channel, tubing and syringe size:  http://biophysical-tools.de/p2cs-syringe-pump-comparison-calculator/

    The slowing down of the reaction time is dramatic for microchannels, however, for large channels the difference is of less importance.

    We (collaborators and me) currently are investigating the possibilities of droplet formation, we keep you informed...

    Cheers. Claus

  • Avraham Hirschberg added an answer:
    How can I find exact solution for two-phase shock-tube problem?


    In papers regarding two-phase flow, the authors compare their results to exact solution for the shock-tube problem.

    How should one derive the exact solution if each phase has its own equation of state (stiffened gas e.o.s) and volume fraction?

    Avraham Hirschberg · Universiteit Twente

    The "exact" solution assumes initial conditions with on the high pressure side pure liquid water and at the low pressure side a perfect gas. The solution is an expansion fan in the water, which can be calculated using a linearised theory (because of the limited compressibility, we have an acoustical behaviour) and in the gas a shock wave (which you can calculate using the Rankine Hugoniot shock adiabatic). The final solution is found because at the contact between the two phases the pressure should be continuous. So this is not a "two phase solution), but two single phase solutions glued to each other at the contact surface.

  • Josef Chmelar added an answer:
    Which one of the SAFT EOSs is good for modeling both vapor and liquid phases?

    I do calculations with sPC-SAFT EOS for CO2/H2O system. It performed good for liquid but the results of vapor phase were not good.

    Josef Chmelar · Contipro


    The PC-SAFT calculations in general strongly depend on the parameterization. If you optimized some of the parameters (e.g., kij or those of the polar term) based on liquid data, you can get less accurate results for the vapour phase.



  • Karl Toppler added an answer:
    Does the archimedes principle give the exact density of an irregular shaped material?

    I prepared a porous tungsten sample by microwave sintering at 1550 C and 2hr soaking time. I measured the density of it with archimedes principle, but I have a doubt that is it really give the exact density

    Karl Toppler · Australian Nuclear Science and Technology Organisation

    Assuming that you do not have "closed porosity" you can use ISO5017:2013 or AS1774.5:2014 where by you weigh your sample dry  and then use a vacuum chamber to evacuate your sample and then introduce water such that it is completely saturated when measured wet...

  • Diana Kvaratskhelia added an answer:
    In fluid dynamics 2d boundary conditions of velocity are given at rectangular domain , How can I get the value of the velocity at the grid points?

    solving incompressible  2d Navier-Stokes equation

    Diana Kvaratskhelia · M. Nodia Institute of Geophysics, Iv. Javakhishvili Tbilisi State University

    On the rigid boundaries sharing sea from land, components of current velocity,  normal to the boundary surface are equal to zero; on the liquid boundaries connecting the sea with the  Strait and the River, values of velocityis given on the basis of experimental data.

  • Andriy O. Bori(y)syuk added an answer:
    Do you know of experimental data for the dynamics of an atomizing liquid jet?

    We have developed some physical-mathematical models for the dynamics of a round full-cone high-speed atomizing liquid jet. Here "high-speed" means above 30 m/s or so (ideally above 50 m/s). The assumption is that it is a turbulent two-phase fluid flow comprised of a mixture of liquid droplets and a entrained gas in dynamic equilibrium, and being described by a mean axial velocity and a composite density. With this we can derive an expression for the dynamic pressure of the free jet as a function of the distance from the nozzle.

    In order to validate the above model, I am in need of data for the axial velocity, liquid/gas ratio or composite density and if possible impact pressure of the liquid jet, all mean values or radial distributions as a function of distance from the nozzle.

    Any help would be highly appreciated as I have not been able to find appropriate data and if you contribute your own unpublished data and/or are willing to make some custom experiment for this purpose we can collaborate for the upcoming paper about this topic.

    Any doubt about the required data/model, please ask! Thank you in advance!

    Andriy O. Bori(y)syuk · National Academy of Sciences of Ukraine

    You can try to find the data of your interest here


    Best wishes

  • Vasuki Shankar added an answer:
    Is anyone familiar with Ultrasonic flow measurements?

    Hey, I have 2 pairs of PZT crystals (Piezoelectric) fixed to a tube in which water flows. The Transit time, or time from input transmitter (>500 KHz) to output receiver is to be measured. The time Along the flow is smaller and time Against the flow is larger. This time difference gives Velocity.

    1. When I give a Sine input to both the Tx, I am getting the same phased output at Rx, Without any delay, or sometimes a sudden unmeasurable change of phase.

    2. This happens for a pulse also

    (The tubes are of resin and steel and have thick walls)

    Vasuki Shankar · Visvesvaraya Technological University

    Thank you all for your guidance. 

    I could implement the Ultrasonic flow meter using PZT crystals. Please feel free to ask me, and I will be privileged to share all I know

About Fluid Dynamics

Fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids (liquids and gases) in motion.

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