Science method

Numerical Simulation - Science method

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In ABAQUS, I want to model a bent tube with varying thicknesses and diameter (continuous linear function) from one end to the other. I have attached a sketch with the question for better understanding.
Later I want to hydroform it into an even more complicated shape, therefore meshing, surface definition, and boundary condition definition are important. It is not a challenge for modeling tools like SolidWorks, CATIA or ProE but importing part from there is a mess and even if somehow import is successful, meshing, surface interaction definition, and BC definition is problematic. Therefore, it would be great if I can directly model it in ABAQUS.
I tried 3D/Shell deformable sweep command but it only asks for a sweep geometry at then sweeps the geometry along the defined path continuously, while I want to vary the thickness and diameter linearly.
Is there a possibility to do that?
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Hello Faisal,
for the generation of the geometry, you might use an array of planes, on each of them you can define the circle of the mid section of your tube as a planar wire ("Create wire: planar") and then connect all of them using the loft function (Create shell: loft).
For the thickness, you can use the analytical field for the shell thickness while you define your section.
I hope it helps.
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Hi,
I am working on numerical simulation of ultrasonic wave propagation through an elastic medium without any defect. I calculated the velocity of wave by using time and distance relationship. But when i used model with void or crack, i got less time to detect the first wave, while it should be longer as there is hole in model and wave propagation through it should be more. Can anyone help me out this problem i.e. how wave velocity is calculated in the model with defect.
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I am trying to slove the standard rayleigh lamb frequency equation in isotropic plate using the newton Rapson method ( FORTRAN code ) but I am not able to capture all the root of the equation and modes, even not getting how to generate the data for plotting the dispersion curves... Kindly , please help.
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I am trying to model excavation procedure of tunnel (D-shaped) in Abaqus (CAE). I have obtained the RF1 and RF2 from an independent analysis as given in Abaqus example (Abaqus example problem guide/1.1.11 Stress-free element reactivation). Now, my problem is that how to apply those concentrated forces ((2n+1)*2) on corresponding nodes?... Because, in my model total number of nodes (2n+1) on tunnel periphery are 129 (in the abaqus example, there are only 13 nodes). And, its changing with each trial/variation of mesh size.
So, how should I apply the concentrated forces?
i) one by one clicking each node, creating each node a set and then applied the loads from load module ? (it's tedious/repetitive. I don't want to do it) or
ii) Doing some editing in *.inp file? (But, when I tried with following format, ABAQUS is simply neglecting my edited lines:
*CLOAD
node number, direction, magnitude) or
iii) writing ULOAD subroutine?
Please clear my doubts.
Thanks in advance.
Regards,
Dipaloke
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So your input file looks like something like this ? (CLOAD statements for each node ?) :
*CLOAD
node number, direction, magnitude
*CLOAD
node number, direction, magnitude) or
*CLOAD
node number, direction, magnitude) or
...
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How can some one detect hidden attractors via numerical simulations?. What does localization of attractor mean?.
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Localization means discovering a region in the phase space, where the attractor is located. Usually, such a region lies in the basin of attraction. So, any point from the region tends to the attractor that allows to numerically compute it. Since for hidden attractors, their basins of attraction do not intersect with unstable manifolds of equilibria, one should develop an intuition for discovering such attractors. There are many developed approaches.
I recommend the following two surveys.
  1. Dudkowski D., Jafari S., Kapitaniak T., Kuznetsov N.V., Leonov G.A., Prasad A. Hidden attractors in dynamical systems. Phys. Rep. 637 1--50 (2016).
  2. Leonov G.A., Kuznetsov N.V. Hidden attractors in dynamical systems. From hidden oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractor in Chua circuits. Int. J. Bifurcat. Chaos. 23(01) (2013) 1330002.
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Recent numerical simulations show that the inner part of the disk seems to oscillate in presence of a Large scale magnetic field or when the disk is in MAD state. So, can we correlate this sort of behaviour with the variability of the source?
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Strong Magnetic field inside the compact object plays the crucial role for understanding the variable x-ray burst. Change in internal structure due to the presence of superfluidity, superconductivity and external accretion also are responsible for this variable x-ray burst. What I understand that we have to consider these three first and then to compare with the simulation where the effect is changing, finally we will be able to understand what is actually going on.
Simulation can help us to know the magnitude of possible change and its location to find out inside the compact object.
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I need to do numerical simulations such as phase plots, bifurcation diagrams, parametric basins of attraction, and Lyapunov exponent diagrams. I already have the fixed points though.
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With regard to Numerical Simulation, I have something to offer. But, what type of Differential Equations are included in the model ? is it ODE, stiff ODE or PDE and of what order?, what is the form of the DE? is it delay , fussy, Wave/Heat etc?. Let see the model maunwala@gmail.com
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I have started learning FEM from scratch. I want to apply it to do numerical simulation of solidification in ANSYS? Where and how to start learning ANSYS?
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You can start watching Youtube videos when you learn how to simulate you can start the simulation yourself and when you have problems you can ask questions here or on this site https://forum.ansys.com/
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How can I numerically solve coupled polynomial or transcendental equations using MATHEMATICA?
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What do you mean with coupled polynomial? The answer depends con the number of independent variables, the degree and the domain (integers, real or complex). I programm un Maple, Mathematica and Matlab. For nonlinear search of roots, I prefer the last one. It's very fast and accurate.
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I have read many publications using FE model to study interfacial behaviour. And Few of them considered matrix viscoelastic effect in the studies. I seems that most authors avoid to discuss about this.
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Follow
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I have a lab combustor on which I did some experiments and obtained some flashback data in terms of equivalence ratio at various flow conditions. i want to simulate the reacting flow field at those flashback data points.
Please help me with some literature which can help me perform those simulations using ANSYS Fluent 18.
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Currently, I am working on the development of Efficient Computational Reduction Methods for Hydrogen GT Combustion for flashback predictions. We are able to develop a methodology for predicting flashbacks using detailed kinetic simulations and progressing towards the development of fast computational processes for industrial applications, but the results are still not available in the public domain. You contact me directly, I can guide you in this regard.
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Honchos, is there any simulation software that can simulate the formation process of fault and the development of fracture zone and fissure zone after the formation.
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Dear
Have you tried Ansys?
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i had done some work about the debris flow through the experiment and numerical simulation using PFC3D.the particle velocity cloud figure of particle flow could't be well displayed to the reader.
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This is a good question.
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Hello Everybody,
My objective is to model the stress-relief mechanism of a clayey meter scale experiment.
Please, share published material and your suggestions for such a small scale experiment.
Thanks  
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This is a good question.
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Paleomagnetic studies show that the South China block was moving northward continuously from 300 to 260 Ma and has experienced an overall ∼27° clockwise rotation since then (Huang et al., 2018) ,and assuming a stationary Emeishan mantle plume, so if I want to do a numerical simulation of the geodynamics of the Emeishan mantle plume based on the above conditions. How can I do it?
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Hello dear;
I didn't research on Paleomagnetic studies, but i know 2 methods in order to behavioral study between two things. K-means clustering and Artificial Neural Network (ANN). you can read this combination method in this paper :
good luck
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Higher-order basis function (HOBF) settings are ignored when are used in conjunction with planar multilayer substrates in FEKO. Does anyone know how can i activate a similar setting?
Thanks in advance
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Thank you so much Dr. Smrity Dwivedi for the PDFs.
I have solved the problem without using higher-order basis functions!
Regards
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My field of expertize is in CFD and not in climatology. But I would start a discussion about the relevance of the numerical methods adopted to solve physical models describing the climate change.
I am interested in details in physical as well as mathematical models and the subsequent numerical solution.
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Thank you for the very thoughtful remarks. I know the literature mentioned in your note and I admire the style and depth of these books. In many ways, the book "Big Breasts and Wide Hips" connects in my perception with Marquez's "One Hundred Years of Solitude" due to a subtle and mysterious surrealism.
Regarding the Nobel prize examples from your comment, I would like to suggest an article in The Atlantic:
(I disagree with some of the opinions above but the paper is very interesting).
As far as my philosophy is concerned, I see a big role for the models of a continuum which, in the present mathematical form, were introduced by Euler in the 1750s. I also think that we can considerably improve our numerical weather prediction models, but I also share some of your skepticism about very long-term digital projections.
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Hello everyone.
I was looking for some literature on translational dynamics of particles (irrespective of their shape) in viscous sublayer, and unfortunately did not find any useful information. It is well known that, particles move faster than the fluid in the buffer layer but, the question is do they move faster or slower than the fluid in the viscous sublayer?
I would appreciate if someone can direct me towards some published research articles (both numerical simulations and experimental).
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I think you should first fix the size of particles and also flow Reynolds number. And simply by doing an experiment on flat plate using particle image velocimetry technique your question will be answered.
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I need to simulate Electrical double layer (EDL) in comsol to achieve more accurate results for my parallel microchannel. the fluid is water and channel is made of glass. it seems that for modeling EDL in comsol I should Couple Laminar flow, Electrostatics and transport of dilute species physics. but I cant do this.. What should I Do? is there any kind of tutorial media for this topic?
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There is some useful information in the link below:
Best
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Dear colleagues,
I am developing a reactor model and it is required that I employ thermal conductivity, heat capacity and diffusivity as properties that change with temperature. Most COMSOL examples seem to specify these properties as fixed parameters rather than as a variable. Could you describe to me how this can be achieved in COMSOL? References to specific pages in the COMSOL user guide or COMSOL tutorials/blog that explain this will also be appreciated.
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@nnaubo, the comsol software uses the Fourier equation to compute the thermal properties and you know there are different solutions of the Fourier equations. So in setting up your heat transfer model for the task at hand, you will have to decide which of the measurement methods you want to adopt I. E. Steady OR transient and which parameters of the solved Fourier equation you want to track I. E. Temperature and time dependent or other parameters. In computing the thermal properties, you will equally have to provide some of the other experimental variables like cross sectional area and the likes depending on your design
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I have run a simulation of a number of planets and smaller particles. The main integration went all right but after converting data to orbital elements, the output files (.aei) are completely empty. Any thoughts?
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No experience with Hg code here. There are many paper and dissertations using ChaNGa to work on planetary/solar system questions.
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I asked this a while ago, but decided to dig a little deeper before asking again. When using the Abaqus JH1/JH2/JHB Johnson-Holquist models for brittle materials, the FS (Failure strain) element removal threshold value is extremely important to ensure the simulation matches experiments, yet in practically all of the studies I have looked into, none of them have reported this FS value despite its major significance.
In the Abaqus documentation, FS was given as 0.2 for SiC. Subsequent studies on alumina have claimed that this FS value needed to be adjusted for accuracy, but then never reported it (e.g. Liu et al. 2015; Khan et al., 2021; Guo et al. 2020; Goda & Girardot 2021).
If anyone can shed some light about what this FS value is meant to be and how to obtain it experimentally or analytically, I would love to understand it better. Thank you!
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Hi Zherui,
FS is a parameter that provides flexibility on correlating numerical with experimental results. I reproduced the formulation of plastic strain in the attached file, as one can see the FS value depends on the values of D_1 and D_2 and the negative hydrostatic pressure strength, T.
If one is confident with the remaining parameter values, then an acceptable strategy for deciding on FS value would be to minimise the error between experimental and numerical results based on multiple references. In the case of impact, the ballistic limit, projectile velocity-time profile and residual projectile velocity for instance.
Please consider [1] for a comprehensive analysis of the effects of FS.
For HDCs, FS=0.6 was previously used yielding satisfactory results for the ballistic limit and residual velocity and FS=1.5 for DoP.
In addition, FS=3.0 was used in [2] to validate Johnson and Holmquist [3] cases,
successfully reproducing the JH results.
Hope my answer helped.
Regards,
Theo
  1. : https://apps.dtic.mil/sti/pdfs/ADA357607.pdf
  2. : Implementation and Validation of the Johnson-Holmquist Ceramic Material Model in LS-Dyna
  3. JOHNSON, G.R. AND HOLMQUIST, T.J., (1994) “An improved computational constitutive model for brittle materials”, High-Pressure Science and Technology – 1994, American Institute of Physics
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I am working on Numerical Simulation for Cold Crack prediction in additive manufacturing and looking for a way forward to do FEM simulation with ABAQUS. Generally, cold cracks produced in the presence of hydrogen so I wonder if there is a straightforward solution for hydrogen diffusion or crack prediction with FEM. Thank you in advance
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Rakesh Kumar from Imperial College London may help you out.
Vishal Singh, IIT Ropar, India may also be helpful to you.
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Hello!
I'm making a series of numerical simulations which the response is a curve of a determined variable along time, for exemple, y(t).
Basically, I have 5 parameters of control which I need to vary to obtain an response on my response variable. For exemple, I need to test three different particle diamenter and three different Reynolds number and obtain 6 curves to my response variable, which is a curve in the form y(t), which t is time.
I know that experiment design can help me with it. But I do not understand how can I correlate a curve as a function of time, and not an specific value. Most book exemples I was able to find correlate an specific value and I was not able to extrapolate from that.
Not sure if I was clear enough, but can someone help me with that?
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Maybe you can alernatively consider the recursive least squares algorithm (RLS). RLS is the recursive application of the well-known least squares (LS) regression algorithm, so that each new data point is taken in account to modify (correct) a previous estimate of the parameters from some linear (or linearized) correlation thought to model the observed system. The method allows for the dynamical application of LS to time series acquired in real-time. As with LS, there may be several correlation equations with the corresponding set of dependent (observed) variables. For the recursive least squares algorithm with forgetting factor (RLS-FF), adquired data is weighted according to its age, with increased weight given to the most recent data.
Application example ― While investigating adaptive control and energetic optimization of aerobic fermenters, I have applied the RLS-FF algorithm to estimate the parameters from the KLa correlation, used to predict the O2 gas-liquid mass-transfer, while giving increased weight to most recent data. Estimates were improved by imposing sinusoidal disturbance to air flow and agitation speed (manipulated variables). The proposed (adaptive) control algorithm compared favourably with PID. Simulations assessed the effect of numerically generated white Gaussian noise (2-sigma truncated) and of first order delay. This investigation was reported at (MSc Thesis):
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I am working on FEM Simulation of Crack Susceptibility in PBF additive manufacturing. Perhaps, Could not find a way to evaluate residual stress threshold value for crack prediction through numerical simulation. I look forward to your answers
Regards,
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plasticity induced crack closure (PICC) concept and three dimensional (3D) finite element method (FEM) were used to study the effect of compressive residual stress field on the fatigue crack growth from a hole. Furthermore, a new methodology on the basis of a correction factor was presented to increase the PICC precision. The result obtained was compared to two dimensional (2D) FEM, superposition method and Liu’s experimental data. To simulate the elasto-plastic behavior of the material, isotropic hardening was assumed and the Von-Mises yield criterion was implemented. A 3D mesh was built using eight-node hexahedral elements and one half of the specimen was modeled. The simulation results were fairly well correlated with experimental data. Furthermore, the 3D elasto-plastic FEM predicted a slightly smaller fatigue life than a 2D plane stress FEM. Applying the modified PICC method reduces the 3D FEM fatigue life prediction errors.
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In my paper, I simulated a PSC with different HTLs. The Jsc of different configurations were close to each other. However, the QE curves for the inorganic HTLs overlapped, except for organic HTLs. What can be the reason for the fluctuation of QE curves regardless of the close values of Jsc?
The same phenomenon happened in figure 4 of DOI: 10.1016/j.rinp.2020.103707, but there was no explanation. It will be much helpful for me if you kindly suggest me some references regarding this with your valuable comment.
I am attaching the QE curves for different HTLs and the Jsc table of my paper herewith. The arXiv preprint link of my paper is .
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Hope you are well!
The optical properties of the HTL can change while the effect of these changes on the short circuit current remains small because the HTL is chosen such that its absorption coefficient is small and also its thickness is much smaller than the absorber thickness. So, the most incident radiation is absorbed by the absorber layer not by the either the HTL or the ETL.
Please follow the papers:
Best wishes
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When planning and designing buildings, and urban environments, especially cities with many high-rises, simulating airflow is an important tool for studying how the city’s layout might affect expected temperatures, among other things. Other areas of use include modeling and predicting wind load on buildings to study Fluid-Structure Interaction(FSI). The local climate around a building in an urban environment can differ significantly from the more general weather data often used in the computation. Consequently, local wind and temperature conditions affect heating and cooling as energy requirements for buildings. However, there is still a stumbling block. Existing simulations use extremely simplified geometric descriptions of the urban environment, which results in poor computational precision. (The photo has been taken from Chalmers university of technology.)
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The answer depends on a scale of your problem. In some application there is a lot of emphasis on representation of the extremely fine details. Please see for example
In the end, it all depends on the capacity of your computer and the ability to digitize complex structures.
For a problem shown in your figure, you can represent the effect of a missing structure by appropriate parameterization of the surface roughness.
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Does anyone know how to plot the equilibrium point, stability region of a nonlinear cancer model? Please let me know and send me the code.
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kindly check your mail
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Dear All,
I am working on numerical analysis of the Friction Stir Welding (FSW) process using Abaqus. The model compressed of johnson cook flow model, ALE Adoptive Remesh to avoid distortion problem, Mass scaling to increase computational efficiency, Temperature-dependent material properties, modified columns law with the temperature-dependent friction coefficient, a shoulder to pin ratio of 3, assumed tilt angle as 0 in the present case, and trying to simulate the Plunging, Dwell, and welding phase of FSW.
Plunging, Dwell is happening as expected. However, on entering the welding phase, the material retrieves aren't taking place and leave a dent, as shown in the attached file in all cases of different rpm and travel speed. This looks like permanent deformation of material without material retrieval during the process. Kindly suggest relatable suggestions on how possibly these issues can be solved using Abaqus... I really appreciate any help you could provide.
#FSW #Abaqus #Friction Stir welding #ALE
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I modeled the FSW process using both ALE and CEL approaches. You need to specify a failure criterion, e.g., Johnson-Cook damage model. If you do so, you will notice a significant decrease in reaction force values - more realistic values. Also, you will achieve what you want.
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I would like to consider corrosion in a column in my numerical simulation in ABAQUS? Can I just decrease the stiffness to simulate the corrosion? or any change in mechanical properties?
Is there any reference or paper or guideline about numerical simulation of corrosion specially in the steel or RC columns?
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Dear Hadi,
FEM using 2D or 3D stochastic model could be numerical simulation studying the effect of corrosion on stress concentration.
This might be useful for you. Just check this article.
Ashish
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I would like to know if the SUPG method has any advantages over the least squares finite element method?
Thank you for your reply.
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Dear Zmour,
It can be better in term of diffusion convection reaction. My opinion is little different, the least-squares method has better control of the streamline derivative than the SUPG.
Ashish
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I am interested to perform spectral analysis of a structure under random waves. could anyone suggest me a book or an example that starts from wave spectrum (such as
JONSWAP spectrum , P-M etc) to RAO. A complete example from formulation to numerical evaluation.
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I submited a manuscript to Communications in Nonlinear Science and Numerical Simulation, and would like to list the reviewers in this journal.
Thank a lot .
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Dear Yamina Soula and Marc R Roussel in our field of research, virtually all renowned journals ask for ca. 3-5 suggested reviewers during the online submission process. Ideally these should not come from the same institution or have been co-authors of previous publications. Many journals also offer the possibility to oppose certain reviewers, e.g,. colleagues who are direct competitors in the same area of research.
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I'm performing a cryogenic turning process.
The temperature are recorded from the thermal imaging camera.
Can I use these temperature values to simulate the flow characteristics and behaviour of the cryogenic coolant?
Is this an acceptable thesis?
Thank you in advance.
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Interesting question. Fluent provides you platform for using different input boundary conditions. But it requires a proper meshing and validation of the experimental results. You somehow have to formulate a process of extracting the input boundary conditions from the IR image.
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As you might know, the centrifugal compressors can experience surge at low flow rates.
Surge detection is possible using experimental measurements and/or numerical simulations.
In the numerical simulation, the compressor's outlet pressure or mass flow rate starts to oscillate as the flow rate gets closer to the surge margin.
Is there any quantitative criteria for the amplitude of oscillations at which the flow rate can be considered as the surge margin? In other words, how mush oscillations are allowed in the safe operation of a centrifugal compressor?
Thanks
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I would think a dynamical model (with nonlinearity) should be constructed to see if the oscillations are stable or unstable and if their amplitude (LCO) can exceed an allowed value
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I would like to estimate the fatigue life of the composite through numerical simulation. please help me with how to write code for low cycle fatigue in Abaqus.
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Sorry Ehasan, I have not written the code.
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High fidelity simulations create an enormous amount of data that can mimic real-world values with excellent accuracy with modern tools and much of this is discarded as "too sanitized" for use in deep learning. But in cases where datasets are very lopsided, such as when a true positive is hard to obtain or rare to observe but true negatives are abundant, isn't sanitized synthetic positive data better than nothing?
In my current project, using an FEM model of the brain/skull system we are using the simulations of head impacts to supplement data from athletes who wear smart mouth guards in an attempt to gather important statistics for early concussion detection. This extra source of true positives has helped improve the overall performance of the ML platform that analyses signals coming from the mouth guards, but it isn't a perfect solution.
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I would like to be provided with the articles that you think simulated heat and mass transfer of droplets in condensation in the most accurate way. I am interested more in the simulations containing both fluid and vapor phases. Please recommend articles with numerical simulations, not analytical approaches.
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Here is one paper and some figures. I have more stuff, like mass transfer from nitrogen bubbles into water and cloud/droplet interactions. The mathematics are similar.
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Hi all,
I am dealing with quasi-static compression simulations on topology-optimized lattice structures using the Abaqus Explicit solver.
By the way, I have not modeled material failure model for several reasons and the material model I've used includes Johnson-cook plastic parameters for AM-SS316L. Now here is my question:
How important and effective is modeling material failure in this case? does it effectively change the stress-strain (force-displacement) curves trend?
If yes, what is your suggestion for material failure model of SS316L in Abaqus? Is there any easier way rather than finding J-C damage parameters for SS316L?
It would be great if anyone can help me to find these parameters.
Regards,
Mohsen
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Hi, SLM-ed SS316L does not need damage model. Based on numerous experiences working with the compression of SS316L lattices no fracture will occur even up to densification. In addition, bulk SS316L (cylinder) sample does not even fracture up to 80 % compressive strain. A solely bilinear or multilinear plasticity model will work for SS316L.
If you are interested in damage model for a less ductile metal, such as Ti64, high strength steel etc, you can consider the Johnson-Cook damage model nontheless. If you are not planning to obtain them experimentally, you can reference them easily from various lattice papers.
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Dear all,
I encountered some problems when using the ABAQUS CDP model. Could you please give me some suggestions?
I did a monotonic uniaxial test using a single 3D solid element (C3D8R) and the CDP model. As shown in the picture attached, if tension damage is defined the maximum principle stress vs maximum principle strain relation shows strain hardening compared to the input data, while the stress and strain curve matches the input value if tension damage was not introduced. This is kind of strange as material damage should not have an effect on the stress and strain relation under monotonic loading.
Moreover, when the plane stress element (CPS4R) is used, the stress and strain relation is identical for cases with and without damage as it should.
I have also attached the input files for both the 3D and 2D models. I will be grateful if you could give me some advice.
Regards,
Delon
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Hi Lei! It would be better to share the material and damage model you are using in this study, instead of inp file. These are the two key points to suggest/comment.
Best Regards!
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For simulating a time periodic flow, I increased simulation times up to 100s and use adaptive time steps.
But I didn't get desire result...I checked simulation setup several times...I don't know why CFX results are different from Analytical solution?
CFX simulation take about 20 days.
*may be by increase the simulation time get a better result!
what do you think?
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Hi, I entered the equations for a CPVT collector in ees and linked the model to TRNSYS to use in my simulations, the inputs (ambient temperature, atmospheric pressure and wind speed) are given to the model by Type109-TMY2, but the input for radiation (beam or total) is given zero and causes the model to not work properly. Does anyone know how to fix this? (The TMY2 file has no problem and works well with other components)
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you can contact Mr Essaid El Kennassi to help in this question
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I am trying to simulate the time-dependent corrosion of underground concrete structures. I'm looking for easy-to-use software that can handle such models. I know that common numerical simulation software (such as ANSYS and ABAQUS) can be used for this purpose. However, I am looking for a more straightforward and simple simulation tool specifically developed for such models.
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You can use FNCorrosion software for analysis.
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I am looking for FEM framework for cold cracks prediction in additive manufacturing. How to establish numerical criteria?
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Muhammad Qasim Zafar , these problems are common and fundamental, so you can find them in welding theory books and molybdenum welding guidelines. Good luck!
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With the limited ability of personal computers, it is often impossible to do numerical calculations because it involves a very large number of cells, for example, with 10 million cells. This problem is usually experienced when facing problems with large geometric sizes. What do we do to reduce the number of cells in a numerical simulation, but give good results?
Dear respective researchers, please give your reply for this case.
Thank you very much for your reply and contributions.
Kind regards,
Nazar
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Thank you very much for your reply and valuable contributions...🙏👍
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Since the unfortunate appearance of COVID-19, there has been a massive number of mathematical models based on the SIR or SEIR models. A perusal of these has shown that the models are mainly numerical simulations to predict the course of the outbreak under varying conditions. Would an understanding of the disease dynamics be improved if equilibria or bifurcation analysis was incorporated?
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Nice discussion...👍
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FEM, FTDT, MOM and BEM which method do you prefer and do use in your field?
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Subrat Sahu , you want apply FDTD to what kind of equations (Maxwell, elasticity, Navier-Stokes, ...) ?
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To analyze the thermal stratification of solar hot water storage tanks using numerical simulations, is it possible to apply the turbulence model? What are the parameters of using the model?
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In my opinion, it depends on the model that you are going to develop. Turbulence is a 3D phenomenon caused by inlet jet mixing, plume entrainment, heat losses, etc. Using CFD, of course, you can model the turbulence. However, it is not the case for one-dimensional models since temperature gradient is only considered in axial direction, but turbulence should also be considered in radial and angular directions. Followings are papers that give some hints to solve this issue:
I hope this reply helps!
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to which limit of acceptable error between numerical work and experimental work for validation
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The answer depends on several factors. For numerical solutions that are relatively new, difficult, and are related to engineering problems, differences of up to 30% are sometimes still acceptable....
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I'm training to make a numerical simulation for differents poisson's ratio which are varied between [0 0.1 0.2 0.3 0.4 0.5]. I need the references that contain their densities and young's modulus.
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you can visit from my publication
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Hi,
I would like to do the numerical simulation of an automobile catalytic converter and for that I need some input data such as viscosity, temperature, velocity &... of the exhaust gas. does anyone have access to this data to help me.
Thanks
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Dear Hessam Keshavarz,
The numerical model for the simulation may require a time independent formulation (time scale of channel flows) which can be used to describe the gaseous flow in order to calculate heat source terms for a transient heat conduction equation for the solid. Input data required.
The two-dimensional flow field of the fluid can be solved through the model and input data are required.
(1) Inlet (velocity, temperature, density, species mass fractions)
(2) Wall conditions (axial temperature profile) the two-dimensional flow field of the fluid can be solved.
(3) The material properties (density ρ, heat capacity Cp and thermal conductivity λ) are functions of the local temperature and material (monolith, insulation and canning) and can also be specified as functions of the direction.
(4) Different adsorption sites on the metallic catalyst surface, as surface reactions are considered between NO, CO, and O2 only for the kinetic data of the mechanism may be considered.
(5) The parameters of the catalyst used, e.g., metal composition and loading, dispersion, viscosity etc.
(6) Thermal capacities and insulation, varying design parameters, as geometry changes, variations in engine out emissions etc.
Ashish
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I´m working in a numerical simulation of the deformation of a thiourethane during annealing (stress relief) but at this moment I dont know the mechanical properties of the base material, so i want to use the shear and elastic modulus from DMA tests, it could be correct?
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Yea why not, for example in FEA method you can populate those data you measured and do the same tests.
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I can´t obtain the same results in Fresnel coeficients of a materials with complex refraction index (bi-layer dielectric thin-film) with angular incidence.
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Finite Element method is suitable for complex problems. If you have problem and used both methods to solve the problem, the answer should be same with small error. Further, You may have a complicated problem with no available analytical solution, Then you, must go to the finite elements methods. The question is how to validate your results ?. You need then to validate your FE results using experimental analytical results.
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Hi, I'm modeling shear critical beams, some of them have stirrups and some don't. I got excellent results for the specimens without stirrups and low load capacities for those with stirrups. It looks like adding the stirrups didn't have any effect at all.
I then realized that if I load only the reinforcement (without the beam) the stirrups move independently from the rebars, looks like they are not connected.
How can I connect them properly? I tried using tie interaction but it didn't work as I expected.
Thank you in advance,
Sálvio.
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I have a question about the modeling of rebars. When you assign the coordinates of the longitudinal rebars and stirrups, you input the coordinates of the center of the reinforcement, don't you? In other words there is a gap between stirrups and Longitudinal bars. It means if your Longitudinal bars' diameter is 16 mm and your stirrups' diameter is 10 mm. There should be a gap of 8+5=13 mm in between your reinforcement. Then, when you assign their diameters in property section, Abaqus itself would modify it and connect them together?
Am I right?
I would be grateful if respond my uncertainty and doubt.
Regards.
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Particularly i am having confusion in deciding boundary condition for swirl part.
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Thanks all of you for the discussion.
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I would like to characterize p-type semiconductor/Metal shottky barrier to study the activation energy Ea of the SC defects. Is there a way to make C(V) or C(F) by numerical simulation tool?
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Dear professor
You can use SCAPS software.
Regards.
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Is there anyone to guide me on how to find a reference geometry of the nasal cavity to validate numerical simulations?
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Hi Dear Mohamad,
you can refer to below link as a good guidance/start point:
You can also refer to my previous publications in this regard.
BR
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I am working on an algorithm that receives 4 pulsating inputs to produce two continuous outputs. A numerical model that enables numerical simulation is all that I have in hand. However, the practical value of the system can't be assured unless a stability analysis can be conducted. My question is: how to assess such algorithm stability while I don't have a dynamic model of the algorithm in the frequency domain?
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Hi Dr. Chak,
Thank you for your answer. It will be highly appreciated if you can support further (if possible, please examine the attached Simulink file in Matlab208A format).
My algorithm (the block with light-blue background) receives three-phase bipolar signals in addition to a fourth slowly changing positive signal. The frequency of the three-phase signal can change between zero to a known upper bound (changing rate is limited to a known limit as well). The algorithm's objective is to continually track the phase angle of the input three-phase signals. By stability is meant, the algorithm can keep tracking of the phase angle of the input signals infinitely!
The process within the algorithm is highly nonlinear and as I said only the Simulink numerical model is available (attached)
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I want to numerically simulate a planar solar thermophotovoltaic in matlab. As I searched, could not find complete and detailed formulation for this work. Does anyone have a complete reference or give me a detailed energy balance for the components?
also is it better using simulink platform or writing a detailed code?
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I am working on Mathematical Modelling project and looking to using some mathematical tools that they are widely used in cancer models.
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Just to back up Matija's response, have a look at the 'History Matching' papers from Vernon, Goldstein and Williamson (2010 onwards is a good date, although there is a seminal paper from 1997 by Craig et. al.). That stream of work is currently being applied to just about everything going. Also consider work on 'Bayesian Calibration' for good examples of general techniques (although beware this is now being shunned in high-dimensional / large input spaces)
Those search terms in Google Scholar (or look at the researchers I follow on my page + who they follow / co-author with etc...), will give you a great overview of applying mathematical models to general problems.
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Hi all,
I am attempting to implement 3D finite difference (FD) beam propagation method (BPM) based on alternate-direction implicit (ADI) method.
Does anybody know about how to implement or the formulation of transparent boundary condition (TBC) in 3D FD-BPM based on two step ADI method?
Any suggestions or advice would be appreciated,
Thank you!
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Dear Onur,
I am also trying to solve the waveguide propagation problem using x,y, and z co-ordinates using FDBPM. Could you please share your matlab code which might serve as a starting point for me.
Thanks in advance.
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I am performing a simulation of a system that involves a lot of random variables. The response of this system varies each time I run the simulation. It is always non-asymptotically stable though, as it eventually fluctuates around the equilibrium point with a variant magnitude (of the fluctuation) each time.
The attached figure illustrates how two different runs of the same simulation can look like.
I would like to have an automated function that calculates the fluctuation magnitude and the settling time each run, from the time response.
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I don't know if I got your point. Maybe you don't need a complex algorithm for your case. For example:
function [Ast,Tst]=func(T,Err)
%%
%The inputs T and Err are two vectors.
Ts=10;%Assume it is stable after T=Ts and Ts is much greater than Tst(the settling time).
Ts_index=sum(T<Ts)+1;
Err=abs(Err);
Emax=max(Err(Ts_index:end));%This maybe the amplitude(Ast) you need;
Ast=(1+0.01)*Emax(1);%Emax maybe a vector,
Tst_index=sum(Err>Ast);
Tst=T(Tst_index);
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A new Phenomenon in Nature: Antifriction
Otto E. Rossler
Faculty of Science, University of Tuebingen, Auf der Morgenstelle 8, 72076 Tuebingen, Germany
Abstract
A new natural phenomenon is described: Antifriction. It refers to the distance-proportional cooling suffered by a light-and-fast particle when it is injected into a cloud of randomly moving heavy-and-slow particles if the latter are attractive. The new phenomenon is dual to “dynamical friction” in which the fast-and-light particle gets heated up.
(June 27, 2006, submitted to Nature)
******
Everyone is familiar with friction. Friction brings an old car to a screeching halt if you jump on the brake. The kinetic energy of a heavy body thereby gets “dissipated” into fine motions – the heating-up of many particles in the end. (Only some cars do re-utilize their motion energy by converting it into electricity.) But there also exists a less well-known form of friction called dynamical friction. It differs from ordinary friction by its being touchless.
The standard example of dynamical friction is a heavy particle that is repulsive over a short distance, getting injected into a dilute gas of light-and-fast other particles. The heavy particle then comes to an effective halt. For all the repelled gas particles that it forced out of its way in a touchless fashion carried away some of its energy of motion while getting heated-up in the process themselves – much as in ordinary friction.
In the following, it is proposed that a dual situation exists in which the opposite effect occurs: “antifriction.” Antifriction arises under the same condition as friction – if repulsion is replaced by attraction. The fast particles then rather than being heated up (friction) paradoxically get cooled-down (antifriction). This surprising claim does not amount to an irrational perpetual-motion-like effect. Only the fast-and-light (“cold”) particle paradoxically imparts some of its kinetic energy onto the slow-and-heavy “hot” particles encountered.
A simplified case can be considered: A single light-and-fast particle gets injected into a cloud of many randomly moving heavy-and-slow particles of attractive type. Think of a fast space probe getting injected into a globular cluster of gravitating stars. It is bound to be slowed-down under the many grazing-type almost-encounters it suffers. The small particle will hence be “cooled” rather than heated-up as one would naively expect in analogy to the repulsive case.
The new effect is going to be demonstrated in two steps. In the first step, we return to repulsion. This case can be understood intuitively as follows: On the way towards equipartition (which characterizes the final equilibrium in the repulsive case as is well known), the light-and-fast particles – a single specimen in the present case – do predictably get heated up in their kinetic energy. In the second step, we then “translate” this result into the analogous attraction-type scenario to obtain the surprising opposite effect there.
First step: the repulsive case. Many heavy repulsive particles in random motion are assumed to be traversed by a light-and-fast particle in a grazing-type fashion. A typical case is focused on: as the light-and-fast particle starts to approach the next moving heavy repellor while leaving behind the last one at about the same distance, the new interaction partner is with the same probability either approaching or receding-from the fast particle’s momentary course. Whilst there are many directions of motion possible, the transversally directed ones are the most effective so that it suffices to focus on the latter. Since the approaching and the receding course do both have the same probability of occurrence, a single pair already yields the main effect: there is a net energy gain for the fast particle on average. Why?
In the approaching subcase the fast particle gains energy, and in the receding subcase it loses energy. But the two effects are not the same: The gain is larger than the loss on average if the repulsive potential is assumed to be of the inversely distance-proportional type assumed. This is because in the approaching case, the fast particle automatically gets moved-up higher by the approached potential hill gaining energy, than it is hauled-down by the receding motion of the same potential hill in the departing case losing energy. The difference is due to the potential hill’s round concave form as an inverted funnel. The present “typical pair” of encounters thus enables us to predict the very result well known to hold true: a time- and distance-proportional energy gain of the fast lighter particle as a consequence of the “dynamical friction” exerted by the heavy particles encountered along its way. Thus, eventually an “equipartition” of the kinetic energies applies.
Second step: the attractive case. Everything is the same as before – except that the moving potential hill has become a moving potential trough (the funnel now is pointing downward rather than upward). The asymmetry between approach and recession is the same as before. Therefore there is a greater downwards directed loss of energy (formerly: upwards directed gain) in the approaching subcase than there is an up-wards directed gain of energy (formerly: downwards directed loss) in the receding subcase. The former net gain thus is literally turned-over into a net loss. With this symmetry-based new result we are finished: Antifriction is dual to dynamical friction, being valid in the case of attraction just as dynamical friction is valid in the case of repulsion.
Thus a new feature of nature – antifriction – has thus been found. The limits of its applicability have yet to be determined. It deserves to be studied in detail – for example, by numerical simulation. It is likely to have practical implications, not only in the sky with its slowed-down space probes and redshifted photons [1), but perhaps even in automobiles and refrigerators down here on earth.
To conclude, the fascinating phenomenon of dynamical friction – touchless friction – was shown to possess a natural “dual”: antifriction. A prototype subcase (a pair of representative encounters) was considered above in either scenario, thereby yielding the new twin result. Practical applications can be expected to be found.
I thank Guilherme Kujawski for stimulation. For J.O.R.
Added in proof: After the present paper got finished, Ramis Movassagh kindly pointed to the fact that the historically first paper on “dynamical friction,” written by Subrahmanyan Chandrasekhar [2] who also coined the term, actually describes antifriction. This fact went unnoticed because the smallest objects in the interactions considered by Chandra were fast-moving stars. Chandra’s correctly seen energy loss of these objects therefore got classified by him as a form of “friction” suffered in the interaction with the fields of other heavy moving masses. However, the energy loss found does actually represent a “cooling effect” of the type described above: antifriction. One can see this best when the cooling is exerted on a small mass (like the above-mentioned tiny space probe traversing a globular cluster of stars). While friction heats up, antifriction cools down. Thus what has been achieved above is nothing else but the re-discovery of an old result that had been interpreted as a form of “friction” even though it actually represents the first example of antifriction.
References
[1] O.E. Rossler and R. Movassagh, Bitemporal dynamic Sinai divergence: an energetic analog to Boltzmann’s entropy? Int. J. Nonlinear Sciences and Numerical Simul. 6(4), 349-350 (2005).
[2] S. Chandrasekhar, Dynamical friction. Astrophys. J. 97, 255-263 (1943).
(Remark: The present paper after not being accepted by Nature in 2006 was recently found lingering in a forgotten folder.)
See also: R. Movassgh, A time-asymmetric process in central force scatterings (Submitted on 4 Aug 2010, revised 5 Mar 2013, https://arxiv.org/abs/1008.0875)
Nov. 23, 2019
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Hello Mykhailo and Otto,
The point I was trying to make in my last message was that all real systems experience some type of dissipation wherein energy is degraded to heat. For solids in mechanical contact with one another, dissipation arises from friction, specifically dynamic friction, when there is relative motion of two solid surfaces. In a moving fluid (liquid or gas), dissipation arises due to either shear viscosity in the case of tangential forces or bulk viscosity in the case of normal forces. The term 'friction' should only be used where it is directly applicable.
One can, of course, say that the viscosity of real fluids produces a "friction-like" dissipation, but this use of the term 'friction' is by analogy and it suffers from the logical fallacy of false equivalence as viscosity and friction arise from different root causes. Consider an incandescent light bulb. The electric current through its tungsten filament only produces a small amount of visible light, the majority of the applied electrical energy is converted directly to heat. The dissipation in the incandescent bulb arises from imperfections in the metal crystal lattice due to things such as defects, grain boundaries, interstitial and substitutional impurities, etc. These imperfections give rise to what one might call "friction-like" behavior, but the dissipation is obviously not caused by asperities as in the case of friction between solids.
Otto, with respect to the system discussed in your original question, it is still not clear to me that your use of the term 'friction' is appropriate. Does a space probe moving through a globular cluster of stars really experience friction or antifriction? Would it not be more appropriate to speak about the effective mass of the space probe changing due to the long range fields it experiences? Plus, I am still hazy about where and how the dissipation or anti-dissipation arises given that the forces acting on the space probe are probably conservative.
Regards,
Tom Cuff
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I am looking for statistical models (or results of relevant numerical simulations) to estimate the number of different types of contacts between particles in a powder mixture. The simplest case would be a mixture of particles of type A and B, both spherical and of same uniform size.
The goal would be to calculate the number of A-A, B-B and A-B contacts per unit volume.
More complex cases would include size and shape distributions (which may or may not differ between the components) and mixtures with more than two components.
Any relevant references are highly appreciated! Thanks in advance.
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Hi Jan!
I'm not sure there is an answer to this since the problem as written depends on the exact packing state of the bed, which is presumably unknown at a particle level. I suggest that you make the additional assumption that the bed is entirely random and the the contacts are quite soft (you need this because otherwise the number of contacts is extremely sensitive to tiny particle positional errors).
If you allow those simplifications, then assuming the bed is large enough, you can make some progress by assuming that each particle has a coordination number determining its number of nearest neighbours. Each one of these then has a x% chance of being either A or (100-x) of being B depending on your concentration ratio, so you can construct a probability distribution for the distribution of A and B surrounding each particle. Then you can propagate this through the bed and see how/if it converges (you only need to do a 1D chain since the bed is random).
If you wanted to improve this then you would need to look at probability distributions of coordination numbers as a function of PSD and other particle properties. Standard DEM simulations routinely produce such data, although it is probably not published in an accessible form.
Pretty much all bets are off for hard, non-spherical particles...
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I am currently working on post-earthquake retrofitting of non-ductile and ductile RC frames experimentally...is it possible to numerically simulate them in SAP2000? How would I retain the damaged frame in SAP2000 for retrofitting?
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I have prepared the damaged model in SAP2000 by splitting the member where the damage has occurred. The stiffness has been reduced up to the point of failure. Now how should i retrofit keeping in view the splitted parts of member.
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I have modelled a transient flow in a microchannel in ANSYS FLUENT using 100 timesteps. I want to export the velocity at each node in excell format for all timesteps simutaneusly. Although using the export command i can only do it for each time step individually . Please advice me how to extract velocity for all timesteps simultaneusly in excell format (does not matter if there is a diferent excell file for each timestep).
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Hi, I'd like to add something which I did to extract the Fluent transient simulation results from CFDpost. I understand it's a late reply, but maybe it'll be of use to somebody.
First, I defined a plane in CFDpost. In CFD post (select standalone, otherwise 'play session' option won't be available if opened from ANSYS workbench). Now, go to 'new session' under the tab 'session' and create one. Now, click on start recording under the session tab, and do the operations required (like go to export, select the variables to be exported, define the filename etc...), such that this operation has to be carried out for n timestep solutions. Now, stop recording and open the session file. you may edit the session file (written in perl language) to loop these operations for 'n' timesteps. That's all!!!
If somebody is in a hurry and needs the edited session file, here it is... (not the entire txt, but only required modifications). I had 1000 timesteps and hence i=00001 to 01000 (first line).
!for $i ("00001" .. "01000"){
>load filename=C:/Users/.../Fluent/SYS-13-18-$i.dat.gz, force_reload=\
true
EXPORT:
...
END
>export
!}
END
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Sometimes we hear somethings on stiffness problem of solution for chemical reaction modeling.
There is an option in Fluent software to figure it out.
Have you guys used it so far? tell us when and why did you use it?
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As Pierre Mandel kindly mentioned, when characteristic scales of your problem are very far (orders of magnitude) you see Stiff Differential Equations (ODE or PDE), It means you have small stability region or it means you have second or third order "Bifurcation" which needs a very high order numerical solution schemes and small time (discretization in general) steps.
There are two types of stiff problems in modeling advection-diffusion-reaction (ADR):
- If you model single specie, when time scale of Peclet number and Damkohler number are very different, you have an stiff ADE (or ADR, or transport equation), you can solve it either by implicit solver or small time steps, or dual time step, or other numerical tricks.
- If you have multi-rate mass transport and your species are internally related (reactive transport), you cannot solve this problem with small time step. Mathematically you have to get integral of infinity and you are always unstable. Those problem can only be solved with implicit solvers (all species in one shot!)
If you need more information on this topic, a very good and classic source for learning is this book chapter:
Approaches to modeling of reactive transport in porous media
Carl I Steefel, Kerry TB MacQuarrie Publication date: 1996/1/1 Reviews in Mineralogy and Geochemistry Volume 34 Issue 1 Pages 85-129 Publisher GeoScienceWorld
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There are some Computational fluid dynamic numerical simulations available like John Hopkins CFD numerical simulations database is available to use. Is that can be used for Astrophysics purposes?
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[I am not the right person to answer your question but this might help]
Two kind of CFD methods are more popular in Computational Astrophysics, compared to Mechanical/ Chemical/Civil engineering CFD, and there are solid reasons for that:
1) Smooth Particle Hydrodynamics (SPH) method. It is developed in first place for astrophysics and due to its Lagrangian nature it can tackle questions of astrophysics very nice.
2) Spectral Methods (I do not mean spectral FEM, I mean methods such as Chebyshev polynomials spectral method): Those methods are of very high order and they are computationally effective and suitable for "large" domains of astrophysics, on one hand; On the other hand, in astrophysics we are not dealing with odd and dynamic geometries of the domain and this fact eliminates one of the main limitation of spectral methods.
Hope it helps,
Kaveh
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Guys, Sometimes after initializing the problem in Fluent and triggering the calculate button, a residual/residuals start from a big non-zero magnitude. For instance, to me, it in many cases happens for some convection-diffusion equation when I'm simulating combustion. Interesting point is that the results looks ok and have good agreement with experimental results. In this page:
It's said that:
"For most problems, the default convergence criterion in ANSYS FLUENT is sufficient. This criterion requires that the scaled residuals defined by Equation 26.13-4 or 26.13-9 decrease to 10-3 for all equations except the energy and P-1 equations, for which the criterion is 10-6."
As it is said, the residuals need DECREASE TO 10-3. Then it means that it doesn't matter from where the residual starts, it should finally decrease to 10-3.
  1. Am I right?
  2. What's your opinion?
Another question:
3. Why does it happans? (I mean why does the residual start from a non-zero magnitude?) and How to figure it out?
I've attached two screenshots of the residual of a project for instance.
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In my honest opinion there are many situations where this statement from the ANSYS Fluent manual is rather misleading, if not even wrong. In particular in CFD simulations with strong heat and mass transfer almost the entire physics, material parameters and thermodynamics is bound to a veery good convergence of the energy equation. In my opinion a scaled residual (RMS Res) of 10^-3 for the energy equation usually leads to rather physically wrong fluid temperatures (i.e. large errors in comparison to the real physics) with the corresponding consequences for the accuracy of the overall simulation.
The CFD best practice is:
1) define meaningful, local and sensitive physical target quantities (e.g. a temperature profile or a distribution of a certain sensitive species of your mixture).
2) run a series of CFD simulations on a reasonable resolved mesh (not the coarsest one) with systematically refined (and reached !!) convergence criterion, i.e. RMS Res<10^-3, <10^-4, <10^-5. And so forth, if still there is not yet a convergent trend.
3) Make a comparison of your sensitive target quantities from this series of investigations. If the target quantities do NOT change anymore significantly (in the range of your wanted error level of the simulation), than you have found your convergence criterion to which you need to converge own all of your following simulations.
Any other explanation or strategy is not leading to realiable CFD results i my opinion. You can read this strategy in the ERCOFTAC Best Practice Guidelines for Industrial CFD and in the ASME Standard for CFD Simulations and Heat Transfer. And once it is an European and American standard approach, I think we should strive to fulfill it, doesn't we as responsible engineers?
Best regards,
Dr. Th. Frank.
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Please if anybody can help me by looking at the information below and tell me if I am on the right track;
Total simulation time = the number of time steps* time step size
for example:
time step size= 5e-6 sec ;
number of time steps= 1000 ;
Then: ∆t=Total simulation time= 5e-3 sec.
>>The Nyquist criterion states that a periodic wave can be correctly reconstructed when the sampling frequency is greater than double the highest frequency component in the phenomenon. >>
Considering the maximum desired frequency for acoustic simulation to be 2000 Hz, we would have:
the minimum wavelength would be λ_min= c⁄f_max =343⁄2000=0.1715 m and accordingly, for good simulation, we need at least 10 elements for the minimum wavelengths, so, the maximum element size would be:
∆x=Minimum element lenght=λ_min⁄10= 0.01715 m or 17.15 mm
Now considering CFL condition for convergence:
C=∆t∑u/∆x ≤1 or ∆t≤16.6 μsec
So, if we set the maximum mesh size equal to 10 mm and the time sep size equal to 5 μsec, then we should not worry about the simulation.
But the questions here are:
1- What are the relationship between Nyquist criteria (in signal processing) and appropriate total simulation time for acoustic numerical simulation?
2- Can we say that the lowest valid frequency after the solution would be two times of 1/∆t? which in this example would be 2*(1/5e-3)= 400 Hz.
So, the simulation would be valid for the frequency range of 400 to 2000 Hz. is this conclusion correct?
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the lowest frequency corresponding the the wavenumber k=1 leads to estimate the total time for the period T according to
f=2*pi*k/T evaluated for k=1 -> 20=2*pi/T -> T=pi/10=0.314 s
Be careful that this is a physical period of time after that the solution has correlated. If you have some numerical transient from initial arbitrary condition you need to wait some time (the solution must forget the initial condition) before starting to compute T.
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Hi everyone.
I have built three 2D plane strain model in Abaqus, each model was applied dynamic concentrated forces (1 MHz, last 10 microsecond), which are equivalent, at point A as shown in the figure named 'resultant decomposed force', and the results were the displacement of Rayleigh wave in the far field (at point B) on the free surface.
Except for the forces are different, everything else for the three models are the same, the results should be the same since the forces are equivalent. However, the results are not the same, results of force 2 and 3 are the same, results of force 1 is different.
The results for force 1, 2, 3 can be found in the attached pictures. I have no idea why the results are not the same. Does the synthesis and decomposition of forces not apply to dynamics?
Would you please help me, thank you a lot.
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You are most welcome Wang Chuangyong . I hope it helps. Have a very nice day.
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Guys,
I'm reading this Article:
You can download it from here:
Please take a look at Fig. 8. I'm trying to export the exprimental data of the velocity profiles in this graph. Both X and Y axises are normalized(non-dimensionalized). Y is normalized by H and there is no problem to me(just need to multiply it by H) but X axis is strange to me. Anybody could explain it to me that how is this graph drawed? I just want to export the exprimental data but don't know how to dimensionalize the X axis.