Boundary Layer - Science topic

Dear M. Paganoni:

I am conducting postdoctoral research at China University of Mining and Technology, with a specialization in geophysical exploration and monitoring technologies for unconventional energy resources. I am writing to formally request access to the logging data presented in your distinguished paper titled "Structure II gas hydrates found below the bottom-simulating reflector", which was published in Geophysical Research Letters in 2016.

Our research team is currently engaged in a study on electromagnetic logging-while-drilling technology for the real-time monitoring of natural gas hydrates. We want to utilize your electrical logging data to simulate the electromagnetic logging-while-drilling technology. Therefore, I apply to you for the research permission of this logging dataset.

Thank you and best regards.

The rotating disk term adds an acceleration term to the conservation equations and the friction interaction models (turbulence or viscous) need to be rewritten to include the added energy gradient. This has been done for ballistic objects (PhD by M Combrink) but if the acceleration is small enough (typically anything less than 10 - 15 g) the flow can be treated as pseudo steady as the variations in energy density/pressure are not significant.

Since the flow in the boundary layer is mostly subsonic, unless you have very high pressure gradients due to the rotation, it is not going to change the model significantly. Consequently, incompressible solutions give a good enough answer for most engineering problems.

Yes, plasma actuators can be effectively used to control turbulent boundary layers in turbine stages, although their implementation presents both opportunities and challenges.

Plasma actuators, especially Dielectric Barrier Discharge (DBD) plasma actuators, generate an ionized air region (plasma) when subjected to high-voltage alternating current. This creates a localized electrohydrodynamic (EHD) force, which induces a secondary flow in the boundary layer without any moving parts.

Recent experimental and numerical studies have demonstrated the potential of plasma actuators in leading-edge separation control and tip leakage vortex reduction in turbomachinery. Researchers are exploring their integration with active flow control systems to maximize aerodynamic performance.

Plasma actuators hold significant potential for controlling turbulent boundary layers in turbine stages, especially for delay in separation, drag reduction, and enhanced mixing. However, challenges related to thermal stability, power efficiency, and practical implementation need to be addressed through advanced materials and optimized designs.

An unstable BL

To answer this we need some more info about the system: what Re range is involved: if laminar flow occurs it must be below 10,000 i.e. in the transitional or laminar field. For pure turbulent flow the resistance of an obstacle can be written in terms of velocity heads lost and that is a usually a constant value over a wide range of Re. The drag at low Re is often solved by "creeping flow" modelling, but the change when turbulence develops is marked. What is the geometry of the bluff bodies involved?

My experiences from large regenerative heat exchangers are that thick boundary layers (i,e. turburbulent flow) increase the pressure drop.

But Fanning friction factor goes down.

Hi Armin and All,

In my research on turbulence modeling for blood flow simulations in hemodialysis cannulae (Salazar et al., 2008, found in ResearchGate at: ), I explored the impact of turbulence modeling on predicting hemolysis (red blood cell damage). This work might be relevant to the query about turbulence values affecting reattachment length in bluff body simulations.

The paper highlights the importance of accurate turbulence modeling since blood flow in cannulae is often turbulent, and turbulence significantly impacts hemolysis. I discuss the selection of an appropriate turbulence model for accurate flow predictions.

We validated our approach using a benchmark case of a coaxial jet array, which shares similarities with cannula flow. The findings suggest that the Shear Stress Transport (SST) model with Gamma-Theta transition yielded the best results compared to standard k-ε and k-ω models.

Here's how this research might be helpful to your situation:

While my paper focuses on hemolysis in cannulae, it offers valuable considerations for turbulence modeling in general. It highlights the importance of validation and suggests a potentially suitable turbulence model for your bluff body simulation.

I hope this information is helpful!

Best regards,

Luis

Hi Nishidh Shailesh Naik Burye ,

If you have a constant, uniform, fixed shear stress field, OpenFOAM does have a "fixedShearStress" boundary which takes as input the vector value of \tau (assuming its constant over the entire boundary).

If you have anything more complicated (like a non-uniform shear stress field), you will unfortunately have to get your hands dirty coding a custom boundary condition. The easiest way would be to make a copy and modify the existing fixedShearStress boundary in OF. It imposes a Dirichlet boundary based on the velocity normal gradient field (from tau) and the cell-centred values of the velocity field from cells neighbouring the boundary. If you do follow this approach, it is important to just make sure you cancel out any velocity in the boundary normal direction, to make sure you don't accidentally, while converging, introduce inlet or outlet flow across the boundary.

Regards

Dear Sarabjeet Kaur ，For more details please visit the conference website:

To me your results make perfect sense. Firstly, the thickness of the velocity boundary layer is dictated by the thermal boundary layer (buoyancy depends on density differences caused by the varying temperature). Increasing Pr, e.g. by decreasing the thermal diffusivity will lead to a thinner thermal boundary layer, hence also a thinner velocity boundary layer. Given that the buoyancy forces are the same (temp.difference is constant), the thinner velocity boundary layer yields higher shear stresses and as a consequence a lower maximum velocity. Increasing Pr by increasing viscosity would also reduce the max fluid velocity simply because of the increased viscosity.

Prandtl number for air is O(1), that is the therma BL develops as similar ad the dynamic BL.

First of all, you need to decide which modes should be included in your simulation, for example, convection, radiation, or all modes.

If you are interested in knowing the convection, for example, your simulation will give you the value of h, and based on it, you can calculate the convection.

Similarly, in radiation, you will need to know the (e) and so on.

Good luck

Dear Dr. Oleh G. Shvydkyi

A phenomenological solution can be found by considering the relation of the thickness of the boundary layer & the diameter of a cylinder in the system.

It will give a relation that involves the Reynolds number, the temperature & the pressure of the whole system.

Please check, the exercises in chapter 12 of the the textbook:

Dear Doctor

"Through our patented complex geometries and by taking advantage of additive manufacturing, we have increased efficiency of  additively manufactured heat exchangers. Our internal geometry encourages swirls and mixing which helps to reduce thickness of boundary layer within our heat exchanger core.  Anyone within the field of heat exchangers understands the concept of a boundary layer. A simple explanation is that when a fluid flows through a channel or on a surface, a thin layer is formed on the interface between the wall and the fluid. In this thin layer, fluid velocity changes from zero (static) at the wall surface to freestream velocity at a certain distance away from the wall surface. A thick boundary layer has a negative effect on heat exchanger performance as it impedes heat transfer. Think of it like a blanket, thicker the blanket, the higher the insulation. This is not ideal for heat exchangers core as the main objective is to conduct heat from fluid to wall surface and vice-versa. Turbulent flow is generally more preferred in heat exchanger design. The swirling and diffusive characteristics of turbulent flow enhances heat transfer. Mixing induced by turbulent flow can also disrupt the growth of boundary layer on heat exchanger core surfaces. However, turbulent flow is often associated with higher pressure drop.

As mentioned, reducing the size of boundary layer and promoting turbulent flow can enhance the performance of a heat exchanger. This can be achieved through the following: -Increase fluid velocity – Speeding up fluid flow through core is an effective way of increasing heat transfer. However, appropriate balance between heat transfer gain and pressure drop penalty needs to be considered. Having closely packed fins and multipass configuration can increase fluid velocity through core. -Mixing enhancement features – Addition of features such as turbulators, baffles, and corrugation can further enhance heat transfer. Conflux Technology has been producing superior heat exchangers with high heat transfer and minimum pressure drop. This is realized through our patented complex geometries, extensive parameters optimization, and by leveraging Additive Manufacturing process and its intrinsic surface roughness."

Hai Dr, how are you? I am attracted to your question as I have some information on it. Below, I supply you with all the answers you need, but I would really appreciate it if you could press the RECOMMENDATION buttons underneath my 3 research papers' titles in my AUTHOR section as a way of you saying thanks and appreciation for my time and knowledge sharing. Please do not be mistaken, there are few RECOMMENDATION buttons in RESEARCHGATE. One is RECOMMENDATION button for Questions and Answers and the other RECOMMENDATIONS button for papers by the Authors. I would appreciate if you could click the RECOMMENDATION button for my 3 papers under my AUTHORSHIP. Thank you in advance and in return I provide you with the answers to your question below :

The y+ value is a dimensionless parameter that is used to determine the thickness of the boundary layer in a CFD simulation. A y+ value of 50 is typically used for turbulent flows, while a y+ value of 1 is typically used for laminar flows.

In your case, you are simulating sloshing in a rectangular tank, which is a turbulent flow. However, some literatures have stated that having a y+ value of 1 (laminar) resulted in better accuracy. This is because the sloshing flow in your simulation may be laminar in some regions, such as near the walls of the tank.

If you are concerned about accuracy, you can try running your simulation with both a y+ value of 50 and a y+ value of 1. Then, you can compare the results of the two simulations and see which one produces more accurate results.

Ultimately, the best way to determine the y+ value for your simulation is to experiment and see what works best for your specific case.

Here are some additional things to keep in mind when choosing a y+ value:

I hope this can shed some light on your exp.

Mohammad Imam Thanks for your detailed answer. Actually, i am getting lower magnitude peak as compared to experiments results. Hence i must include BLM in my analysis to capture absorption coefficient correctly.

When it comes to reducing friction and minimizing the boundary layer on aircraft surfaces, researchers and engineers have explored various materials and surface treatments. While achieving zero friction is not possible due to fundamental physical principles, there are materials and coatings that can significantly reduce friction and delay boundary layer separation. Some of these include:

It's important to note that the selection of materials and surface treatments depends on specific requirements, such as the operating conditions, aircraft type, and desired performance improvements. Extensive testing, including wind tunnel experiments and computational simulations, is typically conducted to evaluate the effectiveness and durability of these materials and coatings before their implementation on aircraft surfaces.

While significant advancements have been made in reducing friction and delaying boundary layer separation, achieving substantial gains in aerodynamic efficiency is a complex and ongoing area of research and development in aerospace engineering.

I solve this problem on page 22-23 of this book using 4th and 6th Order Runge-Kutta. I have attached the code and a snapshot of the solution with description. https://www.amazon.com/dp/B07DB9J2TK

Hi Keith,

Thank you for posting this nice discussion. Since the so called "Shear production term" involves u'w', I want to add a point, regarding the erratic behaviour of the quantity u'w' in atmospheric surface layer flows, where the constant flux layer is never achieved (specially in unstable conditions).

Keith and I wrote a paper on that in Boundary-layer meteorology, ( ) where we showed how the momentum flux co-spectra do not follow any particular scaling in convective flows. Moreover, a few previous literature do show that the surface shear stress as directly measured from the surface plates do not match with the values of u'w', rather they are always underestimated. Also, if one takes an alternate route to define friction velocity from the log-law fittings in neutral flows, those values too mismatch with u_{*}. Therefore, there remains a doubt of how to accurately estimate the friction velocity in atmospheric flows.

Cheers,

Subharthi

How do introduce the flat plate geometry, because I did it with coordinates and looks okay, but doesn't converge the analysis, the thickness is 2.5 mm, so maybe is too small? Milad Jahani

In general, a good way to justify a 2D modelling is scale analysis. You need to show that the typical scales related to the thirs dimension are a few order of magnitude smaller than the same typical scales in the other two dimensions.

A little outside my expertise, but I did find this...

Let us know if this helps!

Ramesh devarmani Dear Sir,

I'm doing my thesis on the supersonic flow around airfoils. I'm initially planning to do flow simulation up to Mach 2.5 using a pressure-based solver. How can I show the board members some documentation supporting that I'm allowed to do pressure-based solver? Can you please help me with this matter?

The following references shows how one can use various transforms to aid in solving specialized PDE's by transforming into problems that can be solved by ODE's. The Fourier transform is one.

Of course separation of variables is a well known technique when the variables can be decoupled. In the analysis of the Hydrogen atom, one can use the fact that the potential is spherically symmetric (only depends on the distance from the proton) and the problem can be transformed into the the analysis of the equivalent Strum-Louisville problem in ODE.

For first order PDE, the method of characteristics can be used to generate an equivalent set of PDE's. For a rigid body in three space, the dynamics is described by ODE instead of PDE since the dynamics is invariant under SO(3), the Lie Group of rotations in R^3.

In general symmetry that results by the invariance of a Lie Group action the PDE will lead to the decoupling and/or reduction of variables. This can often head to solution by ODE. However, it is very equation dependent.

Sorry to say that the figures have no sense, why do you have different range of resolved frequencies?

And if you are in the BL, the flow is not homogeneos, the spectra will depends on y+.

You should clarify the way you are measuring the velocity.

try these.. geometry looks simple enough to have adequate meshing.

A tough question in any kind of complex terrain. The classic definitions do not work

Of course, the ANSYS Fluent can be used to simulate the shock wave/boundary layer interaction. Firstly, the SBLI is a compressible flow problem, we can choose the density-based solver for simulation when the flow Mach number is high or the pressure-based solver for simulation when the flow Mach number is low. Secondly, the energy equation should be activated. Thirdly, the turbulence model is significant for the simulation results: if the inflow Reynolds number is low so that the boundary layer is in a laminar state, the laminar flow should be chosen, or the RANS model such as SA, SST, etc., which can predict the flow separation induced by an adverse pressure gradient, should be selected. Moreover, we can also try the LES or RANS/LES simulation method. That's a little self-experience for simulating SBLI. Hope that can help you. :)

This is a classical problem of wall-bounded parallel flow. Let D be the pipe diameter, Re the Reynolds Number, nu the kinematic viscosity, Ro the fluid density and y is the distance to the wall. In the logarithmic zone, the turbulent shear stress Roxu*^2 is constant where u* is the friction velocity. We should have:

Ro*u_*²*Pi*D*dx=dp*pi*D²/4 so that we have:

(dp/dx)=4*Ro*u_*²/D

So if we may calculate the pressure loss (dp/dx) using for example Blasius Formula for smooth pipe : (dp/dx)=Lamda*Ro*V²/2 with Lamda=0.316/Re^0.25 (or any other head loss formula for rough pipes) we will thus be in a position to calculate the friction velocity u_*. Let's define the Reynolds number y_⁺(adimensional distance to the wall) y_⁺=u_*y/nu The thickness for internal flows (y) is so that y⁺=11

Intraparticle diffusion kinetic model is explained herein: https://youtu.be/iwi1c_-_qyQ

Please send me the case file

Ahmed Gharib Yosry Thanks for your assistance. i tried to reverse the boundary conditions, replace the inlet and outlet with each other. but the torque doesn't goes down the optimum value.

In this case you can find boundary layer thickness less than tube radius between zero and tube radius X. The approximate experimental expression for the tube inlet length (L) calculation is: L/D=0.0288ReWhere, d  is tube diameter, Re  is Reynolds number.

For more information please read through the article herewith.

All the best Guo Li

I think there is a file called "namelist" which you can edit it by changing the input characteristics such as vertical level number.

Hi,

In this case, you can draw the temperature profile between the upper and the lower walls (vertical on the walls).

The answers so far hold for a turbulent boundary layer. Generally, an answer to the question depends on what you want to compute. If you have laminar boundary layers, you may use a grid that is equidistant in wall-normal direction with say, about 25 cells minmum in it; for transitional flow ist should be more, say 40 at least. Mild stretching in y can be applied;, a factor 2-3 in spacing over the layer is often empoyed, making the spacing at the wall half that compared to an equidistant grid. In streamwise and spanwise direction the spacing can be one order of magnitude larger, as said already. The resolution requirements depend on the gradients in the (expected) flow, and if unsteady flow is computed you often do not know in advance where the largest gradients (in the boundary layer) appear; that is why an unstretched wall-normal spacing is not seldom applied. For a RANS (averaged, steady) computation of turbulent flow, the y+ value for the first cell is important (order 1), and you need (strong) grid stretching, otherwise you consume far too many points for the boundary layer.

Twist is an aerodynamic feature added to aircraft wings to adjust lift distribution along the wing. Now by using twistable flaps could augment aerodynamic efficiency during critical flight paths i.e. take off and landing where flaps play important role.

I would add that the meaning of y+ is very very simple. It is nothing but that the local Reynolds number measured along a normal-to-wall direction. That is, y+=0 is the wall position and then the value increases according to y+=(u_tau/vi)*y.

A related issue is the consistency between vertical & horizontal spacings. A paper was written by Mahrer in the 90s and another by by Fox-Rabinovich & Lindzen

All the best

Thanks a lot Sven. This is good to hear about.

I believe it would still be the same. Laminar boundary-layer flows occur when a moving viscous fluid comes in contact with a solid surface and a layer of rotational fluid, the boundary layer, forms in response to the action of viscosity and the no-slip boundary condition on the surface.

My reference is: Pijush K. Kundu, Ira M. Cohen, David R. Dowling,

Chapter 10 - Boundary Layers and Related Topics,

Editor(s): Pijush K. Kundu, Ira M. Cohen, David R. Dowling,

Fluid Mechanics (Sixth Edition),

Academic Press,

2016,

ISBN 9780124059351,

https://doi.org/10.1016/B978-0-12-405935-1.00010-1.

The thickness of a diffusion boundary layer around a cylinder can be estimated for short times, by considering the growth of a thin unsteady boundary layer on a flat plate. The thickness d will scale as d=1.7 sqrt(D t) with D the diffusion coefficient of the polymer in the solvent. Assuming the concentration of the polymer on the surface to be unity, one can calculate the flux of mass towards the cylinder, which decreases as 1/sqt(T). The integral of this mass flux provides an indication for the thickness of the polymer layer (taking into acount the density of the polymer). This should yield some order of magnitude estimate and insight into relevant control parameters. This is analogous with heat transfer. This very crude model has been used for a viscous boundary layer on a rotating cylinder in order to estimate the onset of centrifugal instability. Onset of centrifugal instability at a rotating cylinder in a stratified fluid . The model does not assumes any effect of the rotation of the cylinder on the boundary layer thickness and is still quite succesful.

When calculating the heat transfer Colburn factors were used.

You will have to calculate the diffusivity, yes, and be able understand the boundary layer theory. The diffusivity in this case solid-gas interface. There are alots of analogies that are made available to this extreme. The concentrations and pressure data and mass transfer coefficients must be made available to clearly understand this concept. I recommended you consult materials Transport Phenomenon. You may also check review material on Mass transfer coefficients, and boundary layer theories.

Dear Obayes

The pdf attached by you is a master thesis which is just a preview of the work, not the entire thesis. If possible kindly attached the full thesis.

Thanking You

The Reynolds number (Re) helps predict flow patterns in different fluid flow situations.

Dear Prashant, thank you so much for your help

Following

The pressure across the boundary layer does not change. The pressure is impressed on the boundary layer it value can be calculated by hydrodynamic consideration.

Dear Zein

I hope you are doing well.

what you suggested is fine and Dr Han approach is very typical

Good luck

Osama

One can also use the description based on the analogy to catalytic non-stationary processes. However, solving the inverse problem for partial differential equation/s is difficult.

Kanishka Ganesh

There are a few parameters missing from your udf,

You can get it from the udf attached below.

This worked with the test condition I have used.

Cheers

Dear Prof.Kim

Different materials heat up at different rates, and calculating how long it will take to raise an object’s temperature by a specified amount is a common problem for physics students. To calculate it, you need to know the specific heat capacity of the object, the mass of the object, the change in temperature you’re looking for and the rate at which heat energy is supplied to it. See this calculation performed for water and lead to understand the process and how it’s calculated in general.

Q = mc∆T

Where m means the mass of the object, c stands for the specific heat capacity and ∆T is the change in temperature. The time taken (t) to heat the object when energy is supplied at power P is given by:

t = Q ÷ P

Q = mc∆T

Where m means the mass of the object, c is the specific heat capacity of the material it’s made from and ∆T is the change in temperature. First, calculate the change in temperature using the formula:

∆T = final temperature – starting temperature

∆T = 50° – 10°

This might be useful:

Thanks, N. Bennini for your reply,

There are narrow channels within the geometry, then it is not good to create coarse mesh.

Dear all,

Thank you for the comments.

Ahmad K. Sleiti and Ahmed Ramadhan Al-Obaidi, I could not find the coordinates of RAE 5225 or DRA 2303 airfoils on the website. Please correct me if I am wrong.

Faraz Ahmad, As I mentioned, I could not find the coordinates anywhere given explicitly.

You can begin by trying different k-epsilon models (standard, RNG, realisable ) and compare it with experimental data.

Several researchers in this field: Zheltovodov, Bushnell, Borovoy.

Hi Nakul,

In most of the ceilometer, aerosol topmost layer (seibert et al., 2000, Munkel et al., 2007) is consider as PBL (most of the time it referred as mixing layer height during windy day time period/residual layer during stable night period).

As you mentioned that you want to retrieve PBL directly from a software. So, I would like to suggest you that based on manufacturer of ceilometer, software available.

CHM viewer -Lufft CHM Ceilometer

Lab View - Vaisala ceilometer.

Hope so this information is useful for you.

Dear Rochak Badyal ,

The boundary layer appears when there is a no-slip condition at the interface between the fluid and its wall. You may assume the no-slip condition just for the real fluid, not for ideal fluid. As you know, when you assume the fluid is ideal, then it means that the fluid has no viscous effect or inviscid (non-viscous). In other words, the no-slip assumption is valid when you consider that the fluid has its viscosity effect. With this assumption then you may have the boundary-layer flow.

Thank you and have a nice Saturday night at home.

Best regards.

Nazar

@Lifeng Tian,

I did it for turbulent BL. Anyways, I don't know whether it will work in your case or not. However, if it doesn't work, then PIV is only option, I think!

Thanks.

--Arnab.

Your notation is questionable, I see explicitly the independent variable "csi" but then you use the prime for the derivatives of f. What about the other independent variable, is that the vertical direction "eta"?

Generally, other than using the FD method, a third order PDE is converted in three first order ODE, as illustrated here

You can find a lot of literature about the numerical methods for such equations.

For compressible flows because the airfoil is curved there is a transverse pressure gradient near the surface. In such cases it is necessery to compute the theoretical (ideal) velocity profile first (by taking total pressure equal to stagnation pressure of the inflow and using isentropic flow equations to get velocity which is not a constant value as in case of a flat plate flow). In the next step you need to find a point at which the velocity in your flow is reaching e.g. 99.5% of this theoretical (ideal) profile. This way you will find your boundary layer edge on a convex surface and be able to compute for example integral parameters, such as displacement or momentum thickness.

Check any Myring's publications for details...

Regards

Oskar

Thanks a lot Ravindra!

Dear Yuna,

much depends on the Reynolds number and on the type of fluid we are talking about (gas, Newtonian or non-Newtonian fluid ...). In general, these topics are not of binary character, they are continuous. Although I did not read Leonardi and Bhaganagar, I am not surprised from their result as for me it is absolutely clear that Townsend's ideas stem from a futher past and cannot simply applied today, when a simple cook-book like approach is no longer applicable.

I attach couple of papers which underline that you touched a serious problem: the task to overcome simple empiricism which today is still very common. We measure "turbulent things" mostly very nicely, but we do not UNDERSTAND them.

Here is a paper which makes a first attempt to change that:

For me it would be a great joy to cooperate with people who are intersted in wall turbulence, e.g. around the superpipe/Princeton or CICLOPE and other facilities. Then one could improve or extend existing approaches. E.g., if you come from the oil world, then please are aware that oil is no standard fluid like e.g. water, it is of non-Newtonian character so that the turbulent boudnary layer with non-zero roughness challenges the brain.

This question is somehow often not well formulated by people.

1) First of all, the definition of y+=y*u_tau/ni says that it is a local Reynolds number evaluated from y=0 at the wall. That variable is similar to the Re_x along a flat plate. Therefore, the wall law U+(y+) is defined in terms of a continuous variable in the physical space, that is theory not a numerical results. There is not discretization in the physical meaning of the log-law.

2) When you talk about a numerical simulation, the grid in normal-to-wall direction defines a set of discrete values y+, starting from y+= for the node on the wall, y+=hy*u_tau/ni is the first discrete value corresponding to the node at the space h+ from the wall. So on for the other nodes in the vertical direction.

3) The presence of u_tau means that this function depends on the averaged stress at the wall, that is you should evaluate y+ after that the solution is known.

4) The log law is in a physical range of y+, the numerical simulation can be twofold, a) resolving the BL that is you have at least 3-4 nodes distributed at y+<1 in such a way to resolve the viscous laminar sublayer b) wall model condition, you do not solve the BL but you prescribe the stress you have at y+ in the log law.

In conclusion, the evaluation of the grid distribution of y+ requires to use the solution (that is to compute tau_wall) and, eventually, refine the grid and repeat the simulation.

Hi,

from my perspective this is rather logical. The estimates calculated for y+ in the meshing process for specifying the inflation layer parameters are based on correlations for a fully developed turbulent boundary layer. For a long pipe this is a pretty valid assumption, since the flow has enough length along the wall to develop from the inlet boundary conditions to fully turbulent flow conditions, so that after some pipe length the postprocessing y+ is in pretty good agreement with what was used during the generation of the inflation layers in the mesh.

For a more complicated geometry like your centrifugal pump the cord length of the blades of the centrifugal pumps is rather much too short to develop a fully developed turb. boundary layer. Furthermore flow development over the blade surfaces is disturbed by flow separation and so forth. Consequently the underlying assumption of a fully developed turb. boundary layer is violated (for this assumption being taken into account for mesh property estimates) and you end up with differing y+ values in the postprocessing. But the values in the postprocessing are the physically valid values. Consequently you need to carry out a few iterations between mesh generation --> flow simulation --> postprocessing --> mesh generation in order to find good mesh properties and consequently tolerable y+ values. If for example you encounter a wide-spread y+~10 in the first results, than you might to reduce the 1st layer height in the inflation layers by approx. the same factor (10) in order to end up with y+~1 in your next flow simulation in the same place.

And regarding your last question: over wide parts of the blade surfaces it is possible to have reasonable low y+ in the order of 1. But in front stagnation points, where the flow hits the front of a blade or other parts of the geometry it is usually not possible with reasonable efforts to reduce y+ to 1, but this concerns usually only very minor part of the overall surface areas.

Best regards,

Dr. Th. Frank.

Have a look here http://www.fedoa.unina.it/3828/

Why do you get a boundary layer in case of Omega=0 ? In your case, if I understood it right, there should be no flow under these circumstances, and therefore no boundary layer as well. So why do you see an almost constant U of approx. 2.2m/s in the free stream with no respect to the rotational velocity of the cylinder?

Best regards,

Dr. Th. Frank.

I'm not sure exactly what your model describes, but I can tell you the story of a huge expensive blunder that arose from not considering the difference between inter- and intra-particle diffusion. I came along afterward and fixed the modeling error. I am intentionally vague about who did what and where, but the mathematics are described: http://dudleybenton.altervista.org/publications/Contaminant%20Transport%20in%20Granular%20Media.pdf If I knew more about what you were investigating, I might be able to locate some free software.

It's a good question! You may think of another measuring device, hot wire! or to use this tube in measuring known flow data. Good luck,,,

If you use KBr pellet you might have scattering problem using IR if you have microparticles but not if you use a micro-Raman. You can always use ATR-FTIR to avoid the problem. This would tell you if you have polymer in the sample (not necessary if that polymer is where you want it to be).

Maybe you could use backscattering SEM to check if you have organic on the Mn particle surface or use a transmission technique (TEM or optic microscopy if both particles and shell are tiny or big enough).

Also an Mn quantification might help to know how mich of your final mass is MnCO3 and how migh is possibly polymer.

I do go with Dear François Morency for his answer.

Well, you could perform several analyses. For example you can compute the TKE over several planes normal to the streamwise direction and associate the evaluation of the energy spectra.

A qualitative approach could be the identification of the vortical structures.

I don't think it exists a unique approach.