# Energy equation terms for reacting flows

 User Name Remember Me Password
 Register Blogs Members List Search Today's Posts Mark Forums Read

 December 17, 2019, 02:59 Energy equation terms for reacting flows #1 New Member   Pavan Inguva Join Date: Dec 2019 Location: Singapore Posts: 7 Rep Power: 6 Hi! I am trying to implement a model for a single phase flow reaction with an energy equation to model non-isothermal effects. But the formulation of the energy equation in the system is something I am trying to figure out. The model thus far: Navier-Stokes: Species transport: Energy Equation: This is where I am a bit unsure. I have seen a formulation energy equation that accounts a term for "energy flux by molecular diffusion" (Froment & Bischoff) which is the last term in the equation below: But I am more familiar with the following formulation which has 1) transient term, 2) advective term, 3) diffusive term and 4) source term which would be the heat of reaction: So would the additional term (energy flux by molecular diffusion) be necessary for a good model for such a reactive flow problem.

 December 17, 2019, 06:20 #2 Senior Member     - Join Date: Jul 2012 Location: Germany Posts: 184 Rep Power: 14 The answer to your question depends on the problem you want to solve. Your heat flux due to species diffusion in your energy equation is a very simple approximation of Onsager reciprocal relations, namely the Dufour effect, based on non-equilibrium thermodynamics. What problem do you want to solve? Regards __________________ Check out my side project: A multiphysics discontinuous Galerkin framework: Youtube, Gitlab. Last edited by Eifoehn4; December 17, 2019 at 13:44.

 December 17, 2019, 12:48 #3 Senior Member   Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,732 Rep Power: 66 The diffusion of energy is more generally written as: where q is a generalized diffusive energy flux. For homogeneous media, q is only heat diffusion from Fourier's law: You can of course use, , to write it in terms of thermal diffusivity instead of thermal conductivity. For multi-component problems, there is diffusion of heat via concentration gradients, which is the last term in your equation. If you derive your energy equation assuming diffusion of heat is only via heat conduction/diffusion then you end up with: The source is a fudge factor because you didn't account for any possible chemical reactions or alternative forms of energy transport. Note that when the equation is written in this way, S is a temperature source. It's not even an energy source! If you properly derive an energy transport equation starting with conservation of total energy then you should get the more complicated looking thing you showed: The heat of reaction is contained in the term: The contribution of heat diffusion via temperature gradients vs species gradients depends on the problem. If the reaction is nearly isothermal, then species diffusion will dominate. If the reaction is highly exothermic, then thermal diffusion dominates. It may also be important to mention that these are the time-accurate equations (which means you are doing DNS, whether laminar or turbulent). If you do time/Reynolds-averaging, the contribution of turbulent transport also needs to be taken into account and this gets even more wonky. Last edited by LuckyTran; December 17, 2019 at 20:17.

 December 27, 2019, 02:35 #4 New Member   Pavan Inguva Join Date: Dec 2019 Location: Singapore Posts: 7 Rep Power: 6 Thanks for your really valuable insights regarding the Dufour effects. Fortunately it seems that neglecting the Dufour effect is not a bad assumption for many cases of reacting flows. For others' reference, I found that this book was great for outlining the derivation of the model equations and also discusses the Dufour effects with some detail: https://www.springer.com/gp/book/9783540686224.

 Tags energy balance, reacting flows, species tranport

 Thread Tools Search this Thread Search this Thread: Advanced Search Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are Off Pingbacks are On Refbacks are On Forum Rules

 Similar Threads Thread Thread Starter Forum Replies Last Post usv001 OpenFOAM Programming & Development 4 September 6, 2024 07:51 mohammad_kordo OpenFOAM Running, Solving & CFD 9 November 22, 2020 07:18 tangleiplus Fluent UDF and Scheme Programming 6 January 21, 2019 21:28 tatu OpenFOAM Running, Solving & CFD 5 February 19, 2013 08:19 yueroo FLUENT 2 April 3, 2001 22:11

All times are GMT -4. The time now is 11:02.

 Contact Us - CFD Online - Privacy Statement - Top