[CFD] The Energy Equation for Solids and Fluids in CFD

[@sreekar443]

So far well-explained mate. My friend suggested me this vid. Guess I 'll forward it to the whole class.

[@fluidmechanics101]

Thats fantastic! Yes definitely forward it to the class if you think they will find it useful

[@akshayghorpade8624]

Thank you Dr. Aidan wimshurst Your lectures help a lot in developing solvers of openFoam. The kind of explanation you give is remarkable. Thank you for making our lives easy by covering these topics in so much detail.🎉

[@zaidrehman21]

Best playlist I found till now... Concise 👌🏼👍🏼👏🏼

[@gagank9199]

@19:58 in the video -why are we neglecting kinetic and potential terms for the incompressible flows? (I don't think they are negligible terms)

[@pavelmaksimov3850]

This is absolutely brilliant!

[@scientium8770]

Hey Aidan, Thank You very much for this amazing lecture!! I had a doubt... Isn't internal energy equal to "c_v * T" rather than "c_p * T", which is instead for enthalpy?? Then why are we using "c_p * T" for internal energy here?? If anyone can help, please do...

[@MrDuonghuong1991]

Thanks for the videos, can you make some videos about chemical reactions and combustion??

[@Pakhavar]

Thank you man. Stay safe and blessed.

[@Thonix94]

is there a divergent missing in eqn 13?

[@ahmedx89]

thank you for this amazing lecture

[@alejandropiquero5193]

Hi Aidan! First of all, I would like to say thank you for all the incredible effort you are putting into this channel and all the useful material provided. Hands down one of the best resources out there for anyone starting out with CFD like myself. One question arises from my side after watching the video: say you are modelling a liquid flow in which you are accounting for the temperature dependence of its properties (density, viscosity, thermal conductivity and specific heat). What would be the energy equation to be used here according to you? Despite being a liquid per definition an "incompressible fluid", if we follow a fluid parcel along its pathline in this context its density wouldn't be constant due to the temperature dependence (i.e. D(rho)/Dt =/0) ... so strictly speaking we would have a compressible flow (correct me if I'm wrong). Could we however neglect the variations in density with temperature (since these are much lower in comparison with those of a compressible fluid at high Mach numbers) and still assume an incompressible flow? (D(rho)/Dt = 0 --> divergence of U = 0). All the best, Alejandro

[@fluidmechanics101]

Hi Alejandro, yes you are correct! you would want to use the full form of the energy equation (rho E) being inside the differential operators. This is the same formulation as the compressible formulation, even though the flow is not compressible. Really the full form can be thought of as ‘the form when density variations are significant’. If you are using ANSYS Fluent, you wont need to worry, as Fluent uses the full form by default. If you are using OpenFOAM I would choose your solver carefully. If you are using CFX, i would choose the ‘total energy’ form of the equation. To be honest, using the full form wont slow down the solution that much and you wont have to worry about incorrect modelling or missing a term! Better to be safe than sorry i think 😊

[@alejandropiquero5193]

@@fluidmechanics101 Got it! Thank you for the quick response Aidan! Keep up the good work and definitely looking forward to seeing more from your content.

[@javierconesa1952]

Hi Aidan! Thanks a lot for all the videos you make, they are such an incredible help for us! In this case, in which Fluent solves the full energy equation, how is the conduction term treated? Since the specific heat depends on the temperature, the relation between T and e is not proportional. So, is the heat flux treated as a source term when Fluent solves the energy equation, computed from a suposed value of T? So then, once the value of e is obtained, the value of T is updated and Fluent recalculates the equation with this new value. Or would it be possible to solve the energy equation in terms of T? Thanks!

[@rafaortwein6646]

Super useful.

[@yongtuition]

Have you made any video on how to incorporate radiation into CFD? Such as a radiative-convection model. Thanks.

[@fluidmechanics101]

Yes! Check out the Surface to Surface radiation model video or the discrete ordinates model video ☺️

[@mohammedouallal2]

Enthalpy = Cp.T Enthalpy (Tolal energy) = kinetic + internal + potential

[@bi_block_inbleau4105]

for the 20/23 page, where is the terme -grad(Up) at the left of the =?

[@ramkumars2329]

hi. it is a well explained talk.. thank you!.. by the way, i wrote few codes for solving incompressible flows and would like to go for compressible one.. could u plz make a talk that shows on how to solve for compressible flow field, algorithm used etc..?..

[@nikan4now]

Good work but two important things: 1. The first equation needs to incorporation the contribution of work 2. e=CvT (not Cp) and ONLY for callorifically perfect gasses

[@abhayminachi6020]

Bro Your videos are too good🙌🙌🙌🙌. Please make a video on pressure based and density-based solver.

[@fluidmechanics101]

Yes! Pressure based solver should be coming later this year 😃

[@abhayminachi6020]

@@fluidmechanics101 : Thanks a lot bro

[@mostafaelshafie6889]

Thanks, sir. How can I define buoyancy force in COMSOL?

[@goodday276]

Tnx for good tutorials Aidan what software do you use for drawing the pictures and writing the formulas?

[@fluidmechanics101]

I make all the pictures in inkscape and make the equations in latexit. Once you have made the equations as vector images (pdf) you can insert them into your pictures in inkscape so that the fonts match 👍 all the software is open source so you can use it yourself

[@goodday276]

@@fluidmechanics101 thank U so much my friend

[@shuchang769]

Hi, is there any problem with eq. 2? I think it should be e=CvT and h=CpT. Thanks for the videos. It helps a lot.

[@fluidmechanics101]

Ah yes! Well spotted. This is a typo. It should be e = cvT. The reason for the confusion is that cp and cv are practically identical for liquids. Hence, we only really use the energy equation in terms of temperature when we have an incompressible liquid flow, say water. However, for gases, we use the energy equation in the form of e or h (if incompressible) or total energy (if compressible), so this typo shouldnt make a difference and the later equations still stand. I will correct the first few slides and upload a part 2 video! Thanks for spotting the error!

[@shuchang769]

@@fluidmechanics101 Thanks, this makes it more clear, and it did not affect the derivation after. Will you cover some about species transport equations? It also have several assumptions and different versions. Your videos always make things clear. Really like them.

[@fluidmechanics101]

Yes definitely. Species transport can be confusing, especially with some codes using volume fraction, others using mass fraction. Im going to take some time and pull together the best video i can for everyone, as it is definitely a confusing topic :)

[@idreeskhan1629]

i'm confused sir in OpenFoam user Guide when the are writing dive discritization schemes how they (page123-124 version 7) take.first please explaine what is the difference b/w advection, convection , diffusion Laplacian.and which one term represent which one ( advection, convection , diffusion Laplacian,) in naviar stocks equation.

[@fluidmechanics101]

If you have a watch of my video ‘the finite volume method in CFD’ that should help you understand a lot better 😊 alternatively, you can check out my fundamentals course on my website, which will explain everything to you from first principles! Check it out: www.fluidmechanics101.com/shop

[@fluidmechanics101]

Sorry got the url wrong! www.fluidmechanics101.com/pages/shop.html

[@srijithms1]

But combustion model non pre-mixed, pressure based solver in supersonic flow is used..It's compressible flow !!

[@engineeringarts4509]

Thanks Dr. Aidan for your sharing. According to the 1st thermodynamics law, dQ = dU + dW, where U is the internal energy of the system. In yr eq 1, the heat flux is balanced out the internal energy of the system but the works done by the system to resist the fluid motion is NOT included. May I know if I misunderstood it? Thanks.

[@fluidmechanics101]

Yes, this was a slight error in the talk which i have not had time to correct yet. Well spotted 👍

[@engineeringarts4509]

@@fluidmechanics101 Thanks for your reply, Dr. Aidan. I like yr channel!

[@idreeskhan1629]

sir i,m confused what is the difference b/w trnsport equation and naviar stockes equation.plz explane in detail

[@fluidmechanics101]

Navier-Stokes equations are transport equations for momentum. Transport equations are a general type of equation that describe the transport of a physical quantity (temperature, momentum, turbulence) through a physical space. I hope this makes a bit more sense now!

[@ahmedbalushi5161]

Hi, if I have a solid bar surrounded with gas and the gas only flowing due to the natural convection around the bar and i want to find the temperature gradient across bar cross-section. What i need to do in CFD models? Is same concept explained here to be followed? In ansys fluent possible?

[@fluidmechanics101]

Yes it is possible. You will need to set this up as a Conjugate Heat Transfer calculation in ANSYS Fluent (mesh the solid and the fluid). Maybe send ANSYS support an email to help you get started?

[@ninesstea3215]

Hello Aidan, thank you so much for the explanation! I just have one question: how to get from equation 13 to 14? I try to do the dot product (along with a funny integration-like business *facepalm*) but I do not reach the expression in 14.

[@fluidmechanics101]

Yes, this is quite tricky! Start by taking the dot product of the entire equation with U. Then use equation 12 to simplify and try and get K inside the brackets. Only the terms on the left hand side simplify. The right hand side terms just stay as the dot product 😊

[@ninesstea3215]

Ooh, I see. Thanks!

[@idreeskhan1629]

Fluid Mechanics 101 Thanks sir, other what is the difference b/w advection term and diffusion term in momentum equation?

[@fluidmechanics101]

The advection term in the momentum equations is non linear, as it contains UU (velocity squared). The diffusion term is linear and contains the stabilising effect of viscosity 👍 there are many differences but these are the main ones

[@idreeskhan1629]

@@fluidmechanics101 but sir what is the difference between advection and convection

[@jungtaemin1639]

Shouldn't the inernal energy be e = Cv * T? Cp * T is the enthalpy

[@fluidmechanics101]

Yes you are right. This is a very old video and hopefully I will redo it one day!

[@knnfatima9]

Brilliant