Fluid Dynamics

Fluid Dynamics

  • Tarik Ömer Oğurtani added an answer:
    How does the presence of corners affect the 3D boundary integral equation?

    It is well known that corners require a special treatment in the 2D boundary integral equaiton. The factor 1/(2pi) appearing in the equation should be replaced by 1/(2 alpha), where alpha is the corner angle (see the problem 2.6.4 in the book of Pozrikidis on the boundary integral methods for viscous flows). Here I am concerned with a 3D viscous flow problem where the geometry is composed with several planes that form sharp edges. Right now, I am excluding those nodes from the computation but I get dubious results. I wonder if the nodes at the corner need a special treatment as well. Any help will be highly appreciated. Thank you in advance.

    Tarik Ömer Oğurtani · Middle East Technical University

    The edges and corners create troubles  in the Greens function solutions  of Laplace and elastic  problems in Boundary Element methods when one applies Dirichlet and Neumann boundary conditions.  Which generate integral equations first and second kinds, respectively. The proofs of existence for these two kinds of integral equations met in theory of elasticity are similar to those in Laplace based cases (EM, solutions of electrostatic field, solution of steady state heat flow in interconnect lines ) there are important differences in the surface and functional smoothness requirements, and  in the interpretation of the integral appeared on Neumann BC.  Boundary S  must now be a Lyapunov surface and traction vector should be Hölder continuous, and the Cauchy principal value of the integral   must be taken....

    All my work last 15 years went by  handling very sophisticated practical problems ( surface instabilities, electromigration, grain boundary grooving, quantum dots etc.)  using our home-made coded  indirect boundary element method, which uses simplest and more accurate linear elements  that can easily by pass the corners and edges. For the time integration of course one has to utilize the simplest technique, which is Euler integration scheme (exception:Thermal stress problem) since one has constantly varying  linear element lengths from one time step to another. For the time varying thermal stress gradient evaluations, we had to  use body forces as well without too much difficulties. 

    Best Regars

  • Paulo R. de Souza Mendes added an answer:
    Experiments with non-Newtonian fluids?

    In your opinion what are the best fluids  to use to experiment with non-Newtonian fluid.
    I look for a shear-thinning fluid (without viscoelasticity).
    I am also looking for a viscoelastic fluid (without elongational properties).
    I want to work at room temperature.
    Transparent fluids are desirable
    The maximum shear rate is 1000 s-1

    Paulo R. de Souza Mendes · Pontifícia Universidade Católica do Rio de Janeiro

    Dear Albert,

    Gels while flowing above the yield stress are generally shear thinning and have very little elasticity. Below the yield stress they are of course viscoelastic solids. Carbopol solutions are an example, and are transparent. Probably the extensional non-Newtonian effects are also negligible above the yield stress.


  • Olivier Louisnard added an answer:
    How can I model the rupture of an emulsion (W / O) with surfactant solution using ANSYS?

    I would like to model the breakdown of a W / O emulsion but not as introducing the action of surfactant at the interface of two fluids.

    Olivier Louisnard · École des Mines d'Albi-Carmaux

    Emulsion rupture shares some similarity with spinodal decomposition, so that you might use Cahn-Hilliard equation. I don't know however if you can implement that on ANSYS.

  • Morton Litt added an answer:
    How to calculate maximum pressure sustain by a cylindrical tube which is closed at one end?

    I have an acrylic cylindrical tube which is closed at one end and other end applying fluid pressure. 

    Morton Litt · Case Western Reserve University

    This depends on the nature of the pressure. If it is intermittent, that is relatively simple. Any pressure is transmitted to the cylinder surface which much hold it. The measured pressure is also the force per unit area on the cylinder surface.  If we know the area of a cylindrical section, we can calculate the total force. This is then divided by the cross-sectional area (wall thickness times the section width). If the result is as large as the breaking strength of the polymer, the tube will fail rapidly. 

    For continuous pressure, the polymer will fail eventually at much lower force. There are many old papers (pre 1970)  relating the stress on acrylics to failure time.

  • How does pressure and velocity vary in a pipe with constant diameter and fully developed flow?

    The gauge pressure between the two sections is desired to be 0 and the pumps are centrifugal pumps. There is also head loss due to friction.

    What I want to know is how velocity and gauge pressure vary along the suction and discharge lengths of the pipe. And also how the gauge pressure can be made zero at the intersection after exiting the first pump

    Maddali V S Murali Krishna · Chaitanya Bharathi Institute of Technology

    The application of Bernoulie's equation solves this problem at suction point and delvivery point of the pump. Fluid always flow from  higher energy to lower energy.

  • Lucky Tran added an answer:
    How does Fluent calculate the variables that are not mentioned in boundary conditions?

    In Fluent, when pressure outlet boundary condition is mentioned, we are usually mentioning only the value of the pressure at that boundary, but it is also necessary that even velocity should be mentioned at that boundary due to the very basic elliptic nature of NS equations. Or in other words boundary of the domain should be completely closed for the variables to be found. So how does fluent calculate the other variables at that location internally? (For steady state case)

    Lucky Tran · University of Central Florida

    You need to consider that the equations being solved are the discretized Navier-Stokes and not the continuous Navier-Stokes. The values at the boundaries (or cell faces of volumes adjacent to boundaries) are computed based on the discretization schemes selected. Depending on particular schemes, the convective fluxes at downstream faces can be computed entirely from upstream information (i.e. purely upwind schemes). I know this doesn't completely explain why not all information is needed, but I hope it helps.

  • Francesca De Serio added an answer:
    Does anyone know the modern technique for measuring velocity profiles along water column in a wave flume?

    I would like to measure the vertical velocity profile along water column in a wave tank, where the water depth is quite shallow, approximately 10 cm. Under this circumstance, what is the best option to obtain the velocity profile? Thanks.

    Francesca De Serio · Technical University of Bari, Italy

    If the walls of the wave tank are transparent you can also use LDA or PIV. Even if some LDA suitable for underwater use are also available now. They have higher acquisition frequencies with respect to ADVs, which could be useful for turbulent analysis for example.

  • Giovanni Maria Carlomagno added an answer:
    Should we stop using the phrase "secondary flow" in fluid mechanics?

    From my point of view the phrase "secondary flow" was coined in a time where real three-dimensional flows could not be calculated. The one dimensional approximation (Bernoulli-equation) was the "primary flow" and to account for the fact that most of the flows are three dimensional a secondary flow in certain cross sections was superimposed, as for example in a 90 degree bend.In these cross sections then closed streamlines are shown - which never will be path- lines of particles, even for steady flows (where stream- and pathlines are the same). In fact the flow is three dimesional with stream- and pathlines spiraling through the flow field. This, nowadays can be calculated (and measured) as the three dimensional flow that it is - and the idea of a "secondary flow" should be abendoned - or not ?

    Giovanni Maria Carlomagno · University of Naples Federico II


    I can mention at least two examples of secondary flows in straight channels.

    The first one concerns channels with angled ribs, attached at the opposite walls of a square straight channel, such as those used to cool from the inside vanes of a gas turbine.

    The rib angle causes the formation of secondary flows in the form of two counter-rotating vortices in the channel cross section.
    In fact, the main (primary) flow close to the ribbed walls, entrapped by the ribs, is accelerated towards one of the unribbed walls. The two (top and bottom) secondary flows after licking this wall merge and go back, via the duct central zone, to the other unribbed wall so as to practically generate a jet that impinges onto the latter wall.
    This secondary flow causes colder fluid to be pumped from the channel centre towards the ribbed heat exchanging walls, making heat exchange more efficient.

    The other example regards, e.g., a smooth rotating square channel directed along a radius, such as that to cool from the inside a turbine rotor blade.

    Besides enhancing buoyancy forces, the channel rotation gives rise to Coriolis forces in the internal flow that completely changes the flow field and, consequently, the distribution of the local heat transfer coefficient with respect to a static (non-rotating) smooth channel. For a rotating channel, it is common usage to call leading the wall that goes ahead and trailing the one that follows.
    For a radially outward flow, the Coriolis force produces a secondary flow, in the plane perpendicular to the main flow direction, having the form of a pair of counter-rotating vortices. The secondary flow pushes the fluid particle in the centre of the channel towards the trailing wall, then along the sidewalls and finally to the leading wall. With respect to the non-rotating smooth channel, these secondary flows enhance convective heat transfer coefficients at the trailing wall with respect to those at the leading wall.
    When the flow is reversed, i.e. radially inward flow, one has only to change the role played by the leading wall with that of the trailing one and vice versa.

    I think that, in both cases, it is difficult not to consider the in-plane (channel cross section) motion as a secondary flow with respect to the main (primary) flow along the channel axis.

    Regards to all

  • Amin Ebrahimi added an answer:
    Is there anyone who has taken a course in Microfluidics?
    If so what were the materials in the class? I mean any sources including books, notes and so on.
    Amin Ebrahimi · Ferdowsi University Of Mashhad

    These books may help you.

    "Microflows and Nanoflows - Fundamentals and Simulation" by George Karniadakis, Ali Beskok and Narayan Aluru.

    "Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices", by Brian J. Kirby

  • N.C. Markatos 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!

    N.C. Markatos · National Technical University of Athens

    Alex is right.

    Now if you want to make computer runs and you need an initial estimate for say inlet boundaries you may start with the "1-d" wire value and then perform a couple of more runs with say + and - 20/% and see if there is any change.I bet it will not be if your wire has measured in the predominant flow direction!

  • Marc Schmieger 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)

    Marc Schmieger · Fraunhofer Institute for Biomedical Engineering IBMT

    @William: exactly what I proposed but with an good explanation.

  • Sávio Edisson added an answer:
    Is the value of residual of Navier-Stokes equations on the boundaries Zero ?


    A happy new year for all the readers.

    I am confused if the residual of the Navier-Stoke equations is zero or not on the boundaries. Especially on the Dirichlet boundary.

    This also brings me to the question that the defined boundary conditions (Dirichlet conditions) should they satisfy the NS equations ?

    I am of the opinion that if lets say velocity is prescribed on the boundary, the solution to NS equations will formulate a pressure field which together with the given velocity will satisfy the NS equations, and vice-versa with pressure Dirichlet boundary condition. Please comment and correct if I am wrong.

    Also how can this be explained for Neumann boundary conditions ?

    Sávio Edisson · Instituto Tecnológico de Aeronáutica (ITA)

    The residual is calculated where the equations are discretized. Although you can discretize the boundaries of your problem, it is not usual. So, the residual at the boundaries is not calculated and only the residual at the field is importante to evaluate the convergence of the solver.

  • Aaron Altman added an answer:
    How can I measure curvature in a beam under bending using particle image velocimetry?

    I want to measure moment-curvature diagram in a beam under bending using particle image velocimetry

    Aaron Altman · University of Dayton

    I agree with David,

    You can add markers on your beam and use the PIV cross-correlation algorithms to show movement of your markers, but you could also just use MatLab's (or similar code) to do the cross-correlation without using a PIV code. 

    If the bending is going to be large enough you could even use markers and overlay the deflected and undeflected images and input them into the freeware PlotDigitizer and manually measure the distances between the markers to derive the deflections.

    If you want even greater accuracy you could employ photogrammatic techniques using cameras in a stereo arrangement.  Something you can do for your problem with a stereo PIV setup, especially if you are only concerned with 2d bending and deflection.

    I guess it all depends on what degree of accuracy you are looking for.

  • Stephan Schmidt added an answer:
    We want to write the code to calculate the rate of energy dissipation in vortexes?

     For this, we need to:
    1. Detect total number of vortexes
    2. Compute the precise boundary of each vortex (streamline that circumscribed the vortex)
    3. Calculate dissipation rate for the cells inside this boundary (or boundaries)
    the question is step1 and step 2.

    Stephan Schmidt · Helmut-Schmidt University

    Dear Yahya,

    it would helpful to get more information about your topic, i.e., do you want to performa an instantaneous simulation or the evaluation of a time-averaged flow field such as your attached picture.



  • Dmitry Kovriguine added an answer:
    How can the reflected waves at the end of a numerical wave tank be absorbed?

    I am now working on the establishment of a numerical wave tank. Could anyone give me an overall introduction about the methods to absorb reflected waves?

    Dmitry Kovriguine · Russian Academy of Sciences. Industrial Eng. Institute. Nizhniy Novgorod

    Sure, Xue-Nong Chen. Though the second case needs to tune the same impedance, or wave resistance, between the boundary and wave guide.   

  • Bachir Achour 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.

    Bachir Achour · Biskra University, Algeria

    Dear Aya,

    The direct calculation of the discharge Q in pipe (Pressurized pipe) can be done using a simple relationship, provided the absolute roughness, the energy slope, the pipe diameter and the kinematic viscosity are given. Please find in attached file this relationship, especially Eq. (27) along with Eq. (23).

    Best regards

    Prof. Bachir ACHOUR

  • Mohamad Afifi added an answer:
    What is the importance of performance curve of pumps in industry?
    What are the applications of performance curve of pumps in industry which are doing in the lab test setup?
    Mohamad Afifi · Universiti Teknologi Malaysia

    yes some manufacturer have faciliteis to test pump or you can test when installed.

  • Arifah Ali added an answer:
    Can ANSYS predict wave resistance coefficent (Cw)?

    I am working with numerical simulation using CFX on predicting resistance component of catamaran. From my literature review, CFX just only predict Pressure Force and Frictional Force. Pressure Force is total of Wave  Resistance and Viscous Pressure Resistance. Is there any way I can predict the component of pressure force? I know the most suitable way is doing Cw prediction in SHIPFLOW but my model is a complex design hull and it is not easy doing the prediction with SHIPFLOW.

    Arifah Ali · Universiti Teknologi Malaysia

    Thank you for all the answers.

    I will try to use the form factor to estimate the resistance component.

  • Michael Nazarkovsky added an answer:
    Does zeta potential value vary with colloid size in the same solution?

    If there are two different sizes of colloids (10 nm and 1 um) in the same solution (the same conditions such as the same pH, etc),  the 10-nm colloid and 1-um colloid have the same zeta potential?

    Simply say, in one solution(DI-water) + two different sizes gold particles, the gold colloids have different zeta potential values due to the size difference? 

    Michael Nazarkovsky · Chuiko Institute of Surface Chemistry, Kiev, Ukraine

    Sehr geehrter Herr Dr. Sobisch,

    Yes, causa et effectus are interchanged in these terms but I considered z-potential as a visible indication of particles size, you see.

    Vielen Dank für Ihre Bemerkung.



  • Ronny Rives Sanz added an answer:
    Is reynolds number valid for different cross sections of pipe?

    For a circular cross section if reynolds number is less than 2000 it is laminar flow,

    is the same range applicable for a pipe with rectangular cross section (5by8mm)?

    If not how to calculate reynolds number for the rectangular cross section?

    Any info will be great help.

    Ronny Rives Sanz · Instituto Superior de Tecnologías y Ciencias Aplicadas

    Reynolds is defined as   speed*density*characteristic length/dynamic viscosity. In the case of a cylinder,  the diameter is the characteristic length. This length can be calculated for the different cross sections as 4*wet area/perimeter.

  • Ming He added an answer:
    What value of gamma should be given in the equation of state (Tait equation) for oil?

    There is a well-known equation of state between pressure and density of fluid written as P=B[(rho/rho0)^gamma-1]. Gamma in the equation is different for each material, e.g. water=7.
    I am recently working on sunflower oil dynamic simulating. But I couldn't find what value of gamma should be taken. What I have merely known is that 10 is a suitable value of gamma for castor oil. But I'm not sure whether the value could be used in sunflower oil simulating.

    Could anyone provide me some information on the value of gamma for different materials.

    Thank you very much!

    Ming He · Dalian University of Technology

    I think I have got what I need.
    According to the following work:
    Rostocki, A.J., Tefelski, D.B. and Ptasznik, S., 2009. Compressibility studies of some vegetables oils up to 1 GPa. High Pressure Research. 29(4):721-725.
    The value of gamma of sunflower oil is equal to 12.66.

  • Chen Flyer Xi added an answer:
    How to guarantee the convergence of nonlinear Parabolized Stability Equations (NPSE) ?

    When marching downstream to a distance, my NPSE (for compressible flow) code will fail to converge. I have neglected dp/dx which is believed to be the remaining elliptic term. 

    Chen Flyer Xi · Peking University

    Your suggestion above is very helpful. I very appreciate it. 

    I do use an implicit Euler marching scheme and include the mean-flow distortion. In fact, the mean-flow distortion seems to be  hard to converge. I'll read thest two papers immediately. 

    Thanks again.

  • Yuri Mendez added an answer:
    Is there an exact analytical solution of the Stokes equations for the fluid flow between two divergent planes?

    I would like to know whether exact analytical solutions exist for the fluid flow between two planes with a linearly increasing height, when the convective term is zero (please see the attached image). The flow is pressure driven flowing in the x direction (the gravity effect is neglected). Unlike a plane Poiseuille flow, the component w pointing toward the wall does not vanish. The geometry is infinite along the y direction. That is to solve for the two unknown velocities u and w, both are functions of x and z. Any hints / references would be highly appreciated. Thank you.

    Yuri Mendez · Geoseismic: Geotechnical Engineering

    Your little problem is a lot to think about. To give you something you may think about, Poiseuille may do something for you at a point where the plates are very close together so that the viscous term control the motion. Actually, maybe not. The pressure gradient can not be constant along any distance as the pressure loss varies (and have to) along the direction of the fluid.  Solving exactly seems unlikely. Remember that in the essence you are trying to compute shear stress across an expansion of a given geometry so that you have to decide on your geometry model and how the stresses are computed across that geometry up to the boundary at the wall. Thinking of it in the per square meter basis may help. So think of 1 meter perpendicular to the paper and 1 m of surface (boundary wall). Your geometry model may do something for you and assume that if the space between walls get to be about a couple of milimeters wide (in water) your relationship is meaningless and need to start assuming that you need to include the momentum terms. This is my 2 cents.

    This is not to say that I know the answer, it is to say, where the math could aim to try to solve the problem.  Good luck though.

  • A. Doudou added an answer:
    Is there is an easy way to predict turbulence in a flowing suspension under high pressure?

    Is there a simple way to predict turbulence in a dilute suspension of spherical particles (say ~ 10% w/v) which are travelling in a tube under very high pressures (> 8000 psi) but low flow rates (ca. 3-4 mL/min)? Is it possible to predict (just an estimate) Reynolds number if we know the particle diameter, tube diameter, and viscosity of the continuous medium rather than the suspension itself?


    A. Doudou · Mutidisciplinary Faculty of Nador, Université Mohammed Premier, Morocco

    Maybe You should do measurements with PDPA or LDV. Those techniques are intrusive so that they don't affect the flow and they aren't affected with the flow conditions.

  • What would be the effect on hydration radius of ions (say Na+ and Cl-) if I increase salt concentration (NaCl) in a fixed volume of water (say 50 ml)?

    I am curious to know If I keep on increasing concentration of NaCl...how 'number of water molecules per ion' varies for positive (Na+) and negative (Cl-) ions?

    Shaban Ahmed Ali Abdel-Raheem · Assiut University

    I hope to find your answer in the attached paper

  • Milan Jirsák added an answer:
    How can one accurately model a 1/35.5 scale wing in a 'low speed' wind tunnel?

    I have modeled the full sized kite in ANSYS-Fluent and now wish to use wind tunnel testing in order to validate the CFD results. The issue is that using 'Dimensional Analysis' I still come up with a model that requires the Reynold's number to be equal (Re_prototype=Re_model).

    Does this mean that with a scale of 1/35.5, & CFD wind speed of 10 m/s, I must run the wind tunnel air speed at (35.5 x 10 m/s) i.e. 355 m/s in order to achieve equivalent Reynold's numbers?

    The actual 'projected span' of the prototype is (7.096 m) & the max model size is (0.2 m), therefore I can't alter the scaling. Any help would be appreciated.

    Milan Jirsák · Výzkumný a zkušební letecký ústav, a.s.

    It is not possible to use excessive experimental wind velocity to attain equivalent Re-number (when the Mach number  exceed, say 0,3) as the compressible effects modify considerably flow field. Scaling about 35 is evidently too small (e.i. you employ too small wind tunnel for CFD results validation. Tip strips are not enough reliable to ensure effective Re-mumber too (more than by one order). See special literature on wind tunnel technique with examples. Each method recommended here is acceptable within certain boundaries only.

  • Mohamad Afifi added an answer:
    What's the best method to visualize the vortex structure in a boundary layer?

    I recently simulated the early-stage of the transition of the flat-plate boundary layer. I have tried to plot the vortex lines but the results are something messy. I wonder is there some simple methods to clearly show the vortex structure?

    Mohamad Afifi · Universiti Teknologi Malaysia

    Try schlieren or shadow graph method

  • Alexander A. Proussevitch added an answer:
    Does anybody know the density of water steam at high P(>10MPa) and T(>1273 K)?

    I need to know the density of water steam in the Temperature interval 1273 K-1873 K and Pressure interval 0.1-300 MPa. I didn't find anything for pressures higher than 10 MPa and temperatures higher than 1273 K. Any suggestions?

    Alexander A. Proussevitch · University of New Hampshire

    Looking forward to seeing your surface tension paper published!- It is very interesting and needed subject. Best wishes with your research.

  • Mohamed Balbaa asked a question:
    I need a reference for Hugoniot parameters for Inconel 718?

    I want to find the 3 hugoniot parameters ( C, S, Gamma0) for Inconel 718

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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