[zhangyan]

Hi everyone,
I want to simulate combustion in Internal Combustion Engine with LES.
Now I am trying to implement some SGS models to my code.
But I found many SGS models are suited for incompressible problems.

Fortunately, I found several compressible SGS models:

compressible SGS models:
	compressible Smagorinsky:
	[1] Yoshizawa A. Statistical theory for compressible turbulent                                                             
	shear flows, with the application to subgrid modeling[J]. Physics                 
	of Fluids(1958-1988), 1986, 29(7):2152–2164.
	dynamic(Germano)-compressible Smagorinsky:
	[2] Moin P, Squires K, Cabot W, et al. A dynamic subgrid-scale                
	model for compressible turbulence and scalar transport[J].                
	Physics of Fluids A: Fluid Dynamics, 1991, 3(11):2746. DOI:                
	10.1063/1.858164.
	dynamic(Lilly)-compressible Smagorinsky:
	[3] Martín M P, Piomelli U, Candler G V. Subgrid-Scale Models for                
	Compressible Large-Eddy Simulations[J]. Theoretical & 
	Computational Fluid Dynamics, 2000, 13(5):361–376.

I know these compressible SGS models can be used to simulate
compressible problems.
Unfortunately, most of SGS models are incompressible version:

incompressible SGS models:
	Smagorinsky:
	[1] Smagorinsky J. General circulation experiments with the primitive equations: I. the basic experiment*[J]. Monthly weather review, 1963, 91(3):99–164.
	K-eqn:
	[2] Yoshizawa A, Horiuti K. A statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation of turbulent flows[J]. Journal of the Physical Society of Japan, 1985, 54(54):2834–2839.
	dynamic(Germano) Smagorinsky:
	[3] Germano M, Piomelli U, Moin P, et al. A dynamic subgrid-scale eddy viscosity model[J]. Physics of Fluids A: Fluid Dynamics (1989-1993), 1991, 3(7):1760–1765.
	dynamic(Lilly) Smagorinsky:
	[4] Lilly D K. A proposed modification of the Germano subgrid‐scale closure method[J]. Physics of Fluids A Fluid Dynamics, 1992, 4(4):633.
	dynamic-K-eqn:
	[5] Kim W-W, Menon S. A new dynamic one-equation subgrid-scale model for large eddy simulations[J]. AIAA, Aerospace Sciences Meeting and Exhibit, 33 rd, Reno, NV, 1995.
	dynamic-Lagrangian:
	[6] Meneveau C, Lund T S, Cabot W H. A Lagrangian dynamic subgrid-scale model of turbulence[J]. Journal of Fluid Mechanics, 1996, 319:353–385.
	I don't know:
	[7] Menon S, Yeung P K, Kim W W. Effect of subgrid models on the computed interscale energy transfer in isotropic turbulence[J]. Computers & Fluids, 1996, 25(2):165–180.
	WALE:
	[8] Nicoud F, Ducros F. Subgrid-scale stress modelling based on the square of the velocity gradient tensor[J]. Flow, turbulence and Combustion, 1999, 62(3):183–200.
	dynamic structure--1:
	[9] Pomraning E, Rutland C J. Dynamic one-equation nonviscosity large-eddy simulation model[J]. AIAA journal, 2002, 40(4):689–701.
	dynamic structure--2:
	[10] Chumakov S G, Rutl C J. Dynamic structure subgrid‐scale models for large eddy simulation[J]. International Journal for Numerical Methods in Fluids, 2005, 47(8‐9):911–923.

Question is:
I don't know whether these incompressible models can be used to simulate
compressible problems.

[FMDenaro]

One of the main difference is in the isotropic term related to div v, for compressible flows you need to supply a model for both isotropic and deviatoric terms.

Have a look here http://www.springer.com/us/book/9789048128181

[zhangyan]

Originally Posted by FMDenaro

One of the main difference is in the isotropic term related to div v, for compressible flows you need to supply a model for both isotropic and deviatoric terms.

Have a look here http://www.springer.com/us/book/9789048128181

Thank you Sir,
I am a first-year graduate student， and I am just start my research.
After reading some papers, I found many people simulate combustion in the internal combustion engine with an incompressible SGS model.
I don't know why.
I think a compressible SGS model is necessary in such simulation.

[FMDenaro]

it depends on the choice of a low-Mach model

[zhangyan]

Originally Posted by FMDenaro

it depends on the choice of a low-Mach model

But I never heard Mach number in the cylinder of engine, except for air intake port of engine.
I think the compressibility in the engine is related to the reaction.
Reaction causes the big variation of density.
As far as I know, we didn't mention Mach number in the cylinder combustion simulation.
So, which kind of SGS models should I choose?
Maybe incompressilbe model is OK. But compressible model is better. Do I understand this correctly?

[FMDenaro]

Originally Posted by zhangyan

But I never heard Mach number in the cylinder of engine, except for air intake port of engine.
I think the compressibility in the engine is related to the reaction.
Reaction causes the big variation of density.
As far as I know, we didn't mention Mach number in the cylinder combustion simulation.
So, which kind of SGS models should I choose?
Maybe incompressilbe model is OK. But compressible model is better. Do I understand this correctly?

well, no...for the flow in the cylinder you have a fully compressible case...

if you search in google you will find a lot of papers. Try with "LES" and "in-cylinder" words

[zhangyan]

Originally Posted by FMDenaro

well, no...for the flow in the cylinder you have a fully compressible case...

if you search in google you will find a lot of papers. Try with "LES" and "in-cylinder" words

As I mention above, I have found several papers about LES simulation in cylinder simulation, and they all used incompressilbe models.
Such as:

[1] Jhavar R, Rutland C J. Using Large Eddy Simulations to Study Mixing Effects in Early Injection Diesel Engine Combustion[J]. 2006. DOI: 10.4271/2006-01-0871.
[2] Som S, Senecal P K, Laboratory A N, et al. Comparison of RANS and LES Turbulence Models against Constant Volume Diesel Experiments[J]. 2012.
[3] Som S, Longman D E, Luo Z, et al. Simulating Flame Lift-Off Characteristics of Diesel and Biodiesel Fuels Using Detailed Chemical-Kinetic Mechanisms and Large Eddy Simulation Turbulence Model[J]. Journal of Energy Resources Technology, 2012, 134(3):189–206.

I didn't mean any offense to these authors.
Now I'm quite confused!

[FMDenaro]

Some studies are related to the valve flowing, without any compression/expansion phase. In such case you can adopt the incompressible model. But if you consider the movement of the piston the compressible effects are relevant.

[zhangyan]

Originally Posted by FMDenaro

Some studies are related to the valve flowing, without any compression/expansion phase. In such case you can adopt the incompressible model. But if you consider the movement of the piston the compressible effects are relevant.

So, if I want to simulate combustion in engine, I'd better choose the SGS model ,like this :


And,

Am I correct now ?

[FMDenaro]

If you have combustion I suppose that the SGS model enters into the other equations... for low-Mach model the density variation term can be coupled.

I never worked personally on LES of combustion I suggest following the literature (have a look to the book of Sagaut for reference), your flow problem is often found in the SAE literature

[zhangyan]

Originally Posted by FMDenaro

If you have combustion I suppose that the SGS model enters into the other equations... for low-Mach model the density variation term can be coupled.

I never worked personally on LES of combustion I suggest following the literature (have a look to the book of Sagaut for reference), your flow problem is often found in the SAE literature

Thank you very much!
I have bought that book recently.
And I will read it carefully.