Use of Sensible Enthalpy in FDS

[Tom]

Hi.

What is the reason for the use of the of sensible enthalpy in the energy equation and not total enthalpy? The FDS Tech. Ref. Guide says that (total enthalpy) = (internal energy) + ((pressure) / (density)) due to the low Mach number approximation. For low Mach flow, does kinetic energy disappear in the total enthalpy equation, leaving behind what is essential the sensible enthalpy equation? 

[Randy McDermott]

The point of the sentence in the tech guide that the low-Mach number approximation let's you write

e = h - pbar/rho

is that you can use pbar (the background thermodynamic pressure) instead of the local pressure p.  This is just the definition of enthalpy.  If you want to add k (kinetic energy) to both sides you can.

Beyond that, conversion of h to h_s is just a matter of taking the chemical enthalpy into account.  In low-Mach LES the kinetic energy is implicitly solved from the momentum equation.  Dot the resolved velocity vector into the momentum equation and you get resolved K.  See Eq. (4.14).

On Thu, Apr 5, 2018 at 4:17 PM, Tom <tbbc...@gmail.com> wrote:

Hi.

What is the reason for the use of the of sensible enthalpy in the energy equation and not total enthalpy? The FDS Tech. Ref. Guide says that (total enthalpy) = (internal energy) + ((pressure) / (density)) due to the low Mach number approximation. For low Mach flow, does kinetic energy disappear in the total enthalpy equation, leaving behind what is essential the sensible enthalpy equation? 

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[Tom]

Hi Randy.

How my question came about (What is the reason for the use of the of sensible enthalpy in the energy equation and not total enthalpy ?) is from what I read in general CFD and in the FDS Tech. Ref. Guide. 

What I see in the energy equation used in general CFD is that it contains total enthalpy, being comprised of both internal energy and kinetic energy (u, J, Yeoh, G, & Liu, C 2012). The energy equation is derived in terms of total energy and then expressed in terms of total enthalpy. In the energy equation provided by (D.A. Anderson, J.C. Tannehill, and R.H. Pletcher. 1984) it is expressed in terms of sensible enthalpy as in FDS, having been derived priorly in terms of internal energy. 

Basically, why the difference? 

Reference

Tu, J, Yeoh, G, & Liu, C, Computational Fluid Dynamics: A Practical Approach, Elsevier Science & Technology, London, 2012

D.A. Anderson, J.C. Tannehill, and R.H. Pletcher. Computational Fluid Mechanics and Heat Transfer. Hemisphere Publishing Corporation, Philadelphia, Pennsylvania, 1984

On Thursday, April 5, 2018 at 11:30:53 PM UTC+2, Randy McDermott wrote:

The point of the sentence in the tech guide that the low-Mach number approximation let's you write

e = h - pbar/rho

is that you can use pbar (the background thermodynamic pressure) instead of the local pressure p.  This is just the definition of enthalpy.  If you want to add k (kinetic energy) to both sides you can.

Beyond that, conversion of h to h_s is just a matter of taking the chemical enthalpy into account.  In low-Mach LES the kinetic energy is implicitly solved from the momentum equation.  Dot the resolved velocity vector into the momentum equation and you get resolved K.  See Eq. (4.14).

On Thu, Apr 5, 2018 at 4:17 PM, Tom <tbbc...@gmail.com> wrote:

Hi.

What is the reason for the use of the of sensible enthalpy in the energy equation and not total enthalpy? The FDS Tech. Ref. Guide says that (total enthalpy) = (internal energy) + ((pressure) / (density)) due to the low Mach number approximation. For low Mach flow, does kinetic energy disappear in the total enthalpy equation, leaving behind what is essential the sensible enthalpy equation? 

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[Randy McDermott]

I don't have Tu's book, but is sounds like it is aimed at compressible flows.  There, one probably has some advantage of solving for (h + k) because the quantity is conserved across a shock wave.  If the transfer between k and h is significant, like when the Space Shuttle re-enters the atmosphere at Mach 25 and the k dissipation does directly to increase h, then it is convenient to couple them.

If you strictly want to account for every last joule of energy, then the correct energy equation contains both thermal and kinetic.  But the dissipation of kinetic energy may be negligible, as in a low-Mach flow (when wind goes around a tree branch, the wake flow doesn't increase significantly in temperature as the eddies die down).  To get to the thermal energy equation, as we do, and as Anderson does, you simply subtract off the kinetic energy equation (as I said below, this equation is independently derived from contracting the velocity with momentum).

What I think may be confusing you is the cavalier use of the words "total energy".  To be more precise, you can break down the energy into: thermal + kinetic.  Then you can break down the thermal into: sensible + chemical.  It is possible that we (FDS authors) have somewhere used "total" to mean sensible + chemical.  If so, please point that out.

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[Tom]

Thank you for the feedback. It addresses both compressible and incompressible flow. Anderson makes use of the term "total energy" as do some other texts, I don't think it ever gets mentioned with FDS. Do you know of any further text that I can read that addresses the simple subtraction of the kinetic energy?

Again, I'm very thankful for all your feedback.

[Randy McDermott]

Ron Panton, "Incompressible Flow", 2nd ed Wiley, 1996.  See chapter 5.9 on the energy equation.

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[Tom]

Thank you.