Fluid Dynamics

Fluid Dynamics

  • Jai Manik added an answer:
    How do I get Reynolds number, Froude number and Weber number from given Morton and Evotos numbers?

    Dear all

    I am facing a problem related to non-dimensioning bubbble rising process in a quiescent medium. Almost all papers have described only two parameter ( Morton and Evotos number) which describes the process. However, the way I non-dimensionalize the Navier-Stokes equation, I get 3 non-dimensional numbers viz. Reynolds number, Froude number and Weber number, all sitting in the denominator of diffusive fluxes, gravitational body force term and surface tension term respectively. Now how to get these 3 numbers out of two given numbers(Morton and Evotos)?

    Otherwise, please suggest the other method by which we can get only these two numbers, sitting in the Navier-Stokes equation.

    Any sort of help is highly appreciated.


    Jai Manik

    Thank you so much for taking interest in my problem. I am indebted to you all.

    Actually I am trying to validate a paper regarding oblique coalescence of two gas

    Numerical simulation of gas bubbles behavior using a three-dimensional
    volume of fluid method.

    Authors: M. van Sint Annaland, N.G. Deen, J.A.M. Kuipers

    Chemical Engineering Science(2005).

    They have performed their simulations by giving Morton, Weber and Reynolds number. However for defining Reynolds number their velocity scale is bubble terminal velocity, but in my case it:

    U=g^1/2 D^1/2

    and time scale:


    length scale:


    g= acceleration due to gravity,D=bubble diameter.

    So after non dimensionalising the N-S equation, I get Reynolds and Weber number. Although the Froude number will be 1, if we follow these scales.

    Now I am unable to convert their non-dimensional numbers into what I required.

    Sincere thanks



  • Daniel J Isaak added an answer:
    Measuring stream flow/velocity remotely: do any cost-effective options exist (loggers, drones)?

    I'm looking for advice on alternatives to measuring stream velocity and flow rates other than manual insertion of velocity meters. We are interested in tracking stream flows over time that our study populations of fish must deal with. However, because of the remote location of these streams, it is difficult to obtain data throughout the year. We use a variety of temperature loggers to measure temperature, and these work great. We are looking for a cost-effective way to measure stream flow/velocity remotely, across a large number (10-15) streams as well. any advice, suggestions are most welcome!

    Daniel J Isaak

    this recent EPA Report covers methodologies and instrumentation for flow gaging using inexpensive pressure transducer technology http://www.treesearch.fs.fed.us/pubs/46926

  • Peter Vernarsky added an answer:
    Can someone help with Archtube inflation and wind load applying via FSI in abaqus?

    can someone help me please with an FSI problem in ABAQUS. I try to model an inflation of tube and than apply wind load using the definition of wind velocity. There are some problems that I need to discuss. I can send or upload the .cae or .inp file. I use the definition of fluid cavity and cavity pressure boundary condition for inflation of the tube. The tube is modeled as shell using membrane elements. Fluid is modeled as basic CFD problem using the k-epsilon turbulence model. For example some of warnings that may causing the errors:
    1. The ratio of deformation speed to wave speed exceeds 1.0000 in at least one element.
    2. Distance function calculation has not fully converged.
    3. The PPE for pressure may not have fully converged

    Thank you for you help.
    Best regards

    Peter Vernarsky

    These are two separate processes but in interacted FSI model. At the time of 1s (for example) is the tube fully inflated, at time at 2s starts the wind flow. But the entire operation is in FSI interacted model.

    For a better idea I attach an image.

    The .cae file I will upload latter for other reasons.

  • Alexander P. Savencov added an answer:
    Why surface tension depends on area of tested liquid?

    I measure surface tension of water by Wilhelmy plate, capillary rise, and non-contact jet methods. When area of free liquid surface is less than approximately 0.04 m2 (20x20 cm = 400 cm2) the surface tension becomes less than 73 mN/m. The value of surface tension decreases during decreasing the free liquid surface. It takes a values of 50 mN/m or less. Why? I have not found an answer in books. They tell only about this fact.

    Alexander P. Savencov

    Pascal, but if I increase the liquid surfase, may the Langmuir effect appear?
    This observation was made during films of Langmuir investigation. Thanks. I know about this effect.

  • Patrick Schalbart added an answer:
    Is it possible to identify optimum refrigerant distributor geometry by building a water-vapor mixture test set-up?

    Hi Dear Colleagues,

    As you know, refrigerant two phase distribution at evaporator is big problem because of the fact that it can cause significant capacity reduction unless used optimum distributor. Thus, I am planning a experimental test rig but I'll use water- vapor mixture as refrigerant, merging this mixture at determined ratios and measuring the flow rate at outlet of each circuit. Does using water instead of refrigerant such as R404A give certain result? I would like to take your value opinions. Thanks    

    Patrick Schalbart

    Dear Ergin,

    I invite you to check out Patrick Leblay's work (https://www.researchgate.net/profile/Patrick_Leblay), and especially the following article:


    You can also download his PhD thesis (in French) with the following link:


    • Source
      [Show abstract] [Hide abstract]
      ABSTRACT: A methodology was developed to characterise the heat exchangers’ performance decrease due to two-phase flow maldistribution. It consists in measuring the spatial distribution of the local heat transfer coefficients with a rapid, non-invasive and fluid independent method. The method is based on the infrared (IR) thermography measurement of the temperature response to an oscillating heat flux. The amplitude of the measured temperatures is compared to the solution of an analytical model. The problem is solved iteratively to obtain the heat transfer coefficients. This method has been applied to evaluate the uneven phase distribution of an air-water mixture in a compact heat exchanger. The exchanger is composed of seven multiport flat tubes, a vertical downward header and horizontal channels. Experiments were performed for mass flux from 29 kg.m−2.s−1 to 116 kg.m−2.s−1 and for quality from 0.10 to 0.70.
      International Journal of Refrigeration 09/2014; 45. DOI:10.1016/j.ijrefrig.2014.05.015
  • Jack Tadjer added an answer:
    How can I determine fluid velocity in Eulers cavitation formula for hydrodynamic cavitator?

    I am wondering if velocity in formula means average velocity of fluid passing through cavitator, or velocity of fluid within the cavitator, between points with different pressure?

    Jack Tadjer

    There are many cavitation numbers depending on the purpose of research. If you want to define the incipient or end of cavitation, or cavitation threshold, or supercavitation, initial cavitation erosion or etc. and want to use data from previous studies, it is important to use the same cavitation number and to read the definition where the pressure difference and the speed is taken. In most cases you have to trust the selected cavitation number. Sometimes based on the experimental data (if published), it can make interesting conclusions or change cavitation number and propose new criteria.

    If you're doing research perhaps for ultrasonic cavitator you should know the pressure distribution and choose correct place for measurements of the pressure difference and the velocity.

  • Vemula Ramakrishna Reddy added an answer:
    Does anyone have knowledge on fluid dynamics stability?

    I wonder, if there are any simple principles that allow one to figure out if given steady-state solution of Euler or Navier-Stokes equations is stable? The general approach is to linearize equations around the given solution and solve eigenvalues problem -- looks much too complex. My intuition says, these equations are local, i.e. temporal evolution in each point depends only on the close vicinity of that point, so, solving eigenvalue problem in whole space is overkill. There must be some simple approaches that allow to check stability in a given point locally, so that if all points are stable -- the solution is stable in general.

    Can someone advice good review of works on fluid dynamics stability? 

    Vemula Ramakrishna Reddy

    introduction to Hydrodynamic Stability by Drazin will help you to get some general information o stability

  • Chirag Patel added an answer:
    How can I obtain NU number in finned surfaces for forced convection B.C?


    We have clear equation for free convection and finned surfaces. but how i can obtain NU an h in forced convection over a finned surface?

    Chirag Patel

    I have not expertise in this but i will suggest that you can calculate heat flux and from that applying newton's law of colling you can able to find out heat transfer coefficient and from that find out Nu. Same kind of work is done by my friend and he also not able to find out Nu in corrugated plate heat exchanger and he implemented as i suggested

    Hope this method works.

  • Ciprian G. Gal added an answer:
    Is there any recent work on droplet dynamics considering dynamic contact angle?

    When a water drop encounters a solid surface, a droplet is formed that consists of a sphere of water sectioned by the surface at a discreet, measurable contact angle. Several literature have been reported on this type of contact angle hysteresis. But everyone considered constant angle for analysis. Is there any paper where dynamic contact angle has been explained?

    Ciprian G. Gal

    You may start with the attached paper which discusses the problem with moving contact lines for two-phase fluids. It also includes the pertaining literature (on the rigorous mathematical analysis as well as computational/numerical work that has been performed in this connection). The link is


    • Source
      [Show abstract] [Hide abstract]
      ABSTRACT: We consider a well-known model for the study of the evolution of an incompressible binary fluid flow in a two or three-dimensional bounded domain, through the fluid velocity u and an order parameter φ. This model consists of a system of two evolution equations, namely, the incompressible Navier-Stokes equations coupled with a convective Cahn-Hilliard equation. The novelty is that the system is endowed with boundary conditions which account for moving contact line slip velocity. The existence of a suitable global energy solution is proven and the convergence of any such solution to a single equilibrium is also established.
  • Weidong Li added an answer:
    Why not directly solve PDE on cell interfaces to get accurate values and their evolution without depending on reconstruction?
    The most important technology in FVM is to reconstruct the variables at cell interfaces accurately. So why not directly solve PDE on cell interfaces to get accurate value and their evolution? Do you believe that it will be much accurate than the reconstruction method? We can directly solve PDE not only on the cell, but also on the cell interfaces. For example, in the UGKS presented by Xu and Huang and DUGKS presented by Guo et al., they solved the Boltzmann equation on cell interfaces.
    Weidong Li

    CE/SE is not solving the equations on cell interface. It use staggered mesh and use Taylor expansion with respect to time and space to obtain the variables on cell interfaces and then use the Cauchy-Kowalewski procedure to transfer the time related derivatives into the space derivatives. The CE/SE is compact and low dissipation. But it is still not satisfying.

  • Riahi Mehdi asked a question:
    How is the study of flow stabilty problem is important on the basis of Rayleigh's discriminant ? Especially in the case of pulsed flows ?

    On the basis of Rayleigh's discriminant I have studied the stabilty if pulsed flow in Maxwell fluid. Results obtained in this framework represent a good agreement to the numerical one. Furthermore, potentially unstable regions inside the gap can be shown.

  • Said Mekroussi added an answer:
    Why is Characteristic length for flow over flat plate taken as along flow but Diameter for flow inside a pipe?

    In reference to Nusselt number and Reynolds number calculation.

    Said Mekroussi

    Hey visite this


    A. Kulkarni, and S. Moeykens. Flow over a heated plate. Fluid Mechanics and Transport
    Process (Flow Lab 1.2), January 6, 2005.

  • Ron Reiserer added an answer:
    How to quantify mixing in microfluidics?

    I have a microfluidic device having five outlet channels, and two inlets. I am flowing two nutrients through the 2 inlets (eg: say YPD(c1) and SD(c2)). The two nutrients are mixed in different proportions in the five channels. Hence, I want to quantify this mixing for each channel, that is, I want to find out how much of each media is there (may be concentration ratio, c1:c2) in each of the five mixtures formed in the five output channels.

    Ron Reiserer

    Use fluorescein and DI water. Mix a high concentration as one input and clear DI as the other input. Image the fluorescence and quantify the ratio in each channel by the fluorescence intensity. You can even mix various concentrations for direct comparison. There may be some variation in the results with media if the viscosity of one is significantly different from the other. You could always do the same test with the fluorescein in the media. Just to check that your results are right, reverse the input or media with the fluorescein.

  • Murugan Thangadurai added an answer:
    Is turbulence intensity calculated with speed data from a one-directional hot wire anemometer meaningful?

    I am aware that turbulence intensity (TI) is defined as TI = uRMS/umean. However, I wonder if when not all x, y and z components of the velocity vector are available, which is the case when a one-directional hot wire anemometer is used, it is still possible to get some meaningful estimate of the TI? Is there such a thing as one-directional TI? Thank you!

    Murugan Thangadurai

    Turbulent flow is a random, 3 dimensional and highly dissipative flow with eddies (can be assumed as a vortex for simplicity ) of size varying from micro scales to  problem domain. In reality, you need to take into consideration of all three fluctuating components of the velocity. However, in some specific cases, the flow is assumed to be isotropic (fluctuations in all three direction is same which is exists when there is a equilibrium between the energy input and dissipation).  For example flow inside the wind tunnel test section is assumed as isotropic. I do not know your situation, so I cannot comment about the applicability of the single wire hot wire anemometry results.

  • Bastian Schmandt added an answer:
    How can I calculate time average Cd which is not in periodic steady state?

    i am simulating flow around bluff bodies and i got Cd v/s Time plot

    But i am not able to understand how to calculate time average Cd from it because it is not becoming steady state after so much of time.Ask

    I also attached picture of it if you want to look at that.

    Thanks in advance.


    I have uploaded correct Cd in below session so pleases look at that.

    Bastian Schmandt

    For presumably laminar flow at Re=100 I would expect a periodic signal with a clear shape and  frequency.

    In a study about losses in periodically unsteady flow i once had a similar problem with the transient simulation using the piso-algorithm in OpenFOAM. It could be solved by increasing the number of piso-corrector-loops.

  • ye Siang added an answer:
    Is it accuracy to simulate natural convection inside a duct without putting the duct in a large environment domain in Fluent?

    Is it accuracy to simulate the transient performance of natural convection inside an air duct without putting the duct in a large environment domain in Ansys Fluent? The square duct is vertical sitting and has pressure inlet and outlet. It use boussinesq approximation for air flow as temperature difference is small.Fixed heat flux is applied to one side of duct. The case is like Trombe wall. Many Thanks!

    ye Siang

    @Abdulmajeed Mohamad Thank you so much for your reply. I know there is pressure and temperature difference between inlet and outlet, however, the difference is very small in natural air convection. I have tired several times as I used same pressure and temperature at inlet and outlet in Fluent, the result seems reasonable and continuity is also converged. So I wonder if the result is accuracy?

  • Abhishek Kumar added an answer:
    What is the equation for primary/secondary wave speed in solids in 2D?

    I found on Wikipedia that the equation for primary/secondary wave speed in solids in 3D is

    C_{solid,p} = sqrt((K+4/3*G)/rho)

    C_{solid,s} = sqrt(G/rho)

    where K is the bulk modulus, and G is the shear modulus of the elastic material, and rho is the material density.

    1. How was this equation derived? A source of literature will be helpful.
    2. Is this equation the same in 2D?
    Abhishek Kumar

    These equations are derived for 1D wave propagation. For 2D wave propagation, even the radial damping should be taken into account to determine these velocities. Any standard textbook on Geotechnical Engineering can give you idea about the derivations.

  • Wei Zhong added an answer:
    How can I draw half pipe in FLOW3D?

    How can I import half pipe in .stl file to Flow3D.

    Wei Zhong

    Generally, we build our geometry in UG or other CAD softwares in the first and export it into a .stl file. In Flow3D V9.3, you just need import your available .stl file in the tab "Modelsetup->Meshing & Geometry->stl->add "

  • Mohamad Afifi 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.)

    Mohamad Afifi

    in film cooling I painted the surface with liquid crystals . It changes colour with temperatures....

  • Sujit K. Bose added an answer:
    When water is drained through sink, free vortex is formed due to Coriolis effect. How can I model this phenomenon mathematically?

    I am trying to find pressure and velocity distribution of irrotational vortices, and was able to find the equations at far from the vortex core, but I want to know what happens near the core where axial component of velocity exists. How to find circulation around the core? Is it related to rotation of earth? If so, then how? What are governing equations? Any guidance regarding it will be helpful.

    Sujit K. Bose

    I am afraid not. The toilet is too small a system compared to cyclones. If Coriolis force had to be taken in to account for every rotatory motion on earth, then all solutions of dynamical problems have to be revisited. See my text: Analytical Engineering Mechanics.

  • Shuang-Xi Guo added an answer:
    While doing CFD analysis using Fluent for unsteady 2D flow past cylinder, I'm getting very low values of lift coefficient; how do I correct it?


    have checked common areas of concern like 

    1) Reference values.

    2) Mesh quality.

    I m getting drag values spot on but i dnt know what is issue with lift coefficient

    Shuang-Xi Guo

    I agree with Lopes. The lift force should be vary periodically because of the vortex shedding, if the body is symmetric and in a infinite water. I guess that you mean that the maximum of the lift is much bigger than your experiment. If my guess is ture, I think that maybe your computational domain is not large enough. You can corrcet you computational domain as Adio told, and the boundary condition as slip one or Neumann boundary condition. Good luck.

  • Nur Hazirah Nohseth added an answer:
    How can I calculate the camber-% chord and thickness-% chord of an airfoil?

    I am trying to optimize the design parameters to enhance the lift force generated in airfoil. But, I am not able to calculate the camber-% chord and thickness-% chord. I intend to compare the variation of camber and thickness with lift and drag force by ANSYS Fluent (CFD). 

    Nur Hazirah Nohseth

    thanks!! i found the solution weeks ago. i did notice t/c change a little bit, buat only at the point value which not a significant change. anyhow, thanks for answering. by the way, since you're studying about an airfoil, did you calculate the value of Cd? since the equation containing Cd is a drag force equation and the equation consists Area parameter, how do you calculate the area of an airfoil? especially in my case, it's definitely a 3D airfoil with span. unfortunately, my leading edge span is a little shorter than my trailing edge span. any idea?

  • Kannan B T 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.

    Kannan B T

    Chinese journal of Aeronautics have one paper on Hypersonic flow using OpenFOAM based on densityTurbo solver

  • Nemish Kanwar added an answer:
    How can I calculate the maximum flow rate through a pipe when the velocity is not known?

    How I can calculate the maximum mass flow rate through a circular pipe with a inner diameter of 3 cm  when the velocity is not known? The working fluid is sample of breathe.

    Nemish Kanwar

    The mass flow rate(velocity) should be less than sonic velocity

  • Thomas Cermack added an answer:
    Will increasing shear, reducing pressure drop in a spin pack for a Power Law fluid reduce fiber swelling and decrease draw resonance?

    Polymer in question is Nylon 6,6. Looking to understand flow through spin pack and how changes in the design will affect fiber spinning.

    Thomas Cermack

    Thank you.  I have been studying as best I can the melt extrudant flow and the elongational flow. It seems a lot of the activity I have seen from the fibers can be linked to the extrudant flow instabilities.  This helped a lot and helped clear things up!

  • Zdravko Virag added an answer:
    Is this mesh refinement procedure correct?

    Hello, I am using the following coarse mesh of size 7. I am integrating using the control-volume approach in which I use difference between the fluxes at the edges of CV. As you can see that in the middle, I have three points for which I divided their control volume in four parts to have a refinement of factor 2. Apart from these 12 points, I have to had some ghost points which are required to provide fluxes at the edge of fine mesh points.

    After two integration on fine mesh (because r equals 2), I am averaging the fine mesh values and putting them in place of their respective underneath coarse mesh point. On some coarse points near to coarse-fine mesh interface, I use the procedure described here(http://www.sciencedirect.com/science/article/pii/0021999189900351) which is basically that I replace some coarse fluxes by the sum of fine mesh fluxes which are along the interface.

    This is not giving me the desired results even I broke down my code manually point-by-point i.e. for every point, I am writing precisely what happens to it.

    Please let me know if I am committing a mistake anywhere. Thanks!

    Zdravko Virag

    Dear Tanmay Agrawal,

    Your equation is unsteady convection-diffusion equation, which of parabolic type. Since you use explicit method (which is conditionally stable) you should satisfy a stability condition. A stability criterion of the diffusion equations in 2D case says

                dt < dx^2*dy^2/(2*lambda*(dx^2+ dy^2)

    If you are at the edge of stability, be aware that if you reduce your space steps dx and dy by factor 2, you should reduce your time step by factor 4.

    Also, the central differencing scheme (you use it) may introduce nonphysical oscillations into your solution if the local Peclet number is greater than two.

  • Alexandros Terzis added an answer:
    What is the relationship between average Nusselt number and Reynolds number?

    avg nusselt number              reynoldsno


  • Qi-hua Zhang added an answer:
    What is the appropriate B.C for the pressure poisson equation derived from Navier-Stokes Equations

    Hi everyone

    Suppose for the Navier-Stokes problem using FEM that the velocity field is known, and we want to solve the problem for the pressure field, what I'm doing is taking the divergence of the momentum equation so that I  get a Poisson equation on the pressure, in The weak form and after integration by parts, I get the boundary term which I can't deal with!

    my question is : what is the adequate B.C that I have to impose on the pressure for this problem ?

    Qi-hua Zhang

    hi Mourad Oulghelou, for incompressible fluid, the question is still not clearly understood from theoretical aspect. Unlike compressible fluid, the pressure difference makes sense in incompressible fluid. So commonly, Raffaele Salerno's opinion is a classic point of view, and many commercial CFD utilize this kind idea. Obviously, the detailed pressure exerted on the wall boundary is not known and not possible to find. So the boundary pressure value is commonly assigned the inner grid point value, which means the Neumann B.C. is applied. 

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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