Fuel evaporation
 

I deal with injected fuel evaporation modeling. n-Heptane injected into air @T=293K (both of them). Chemical model of combustion initiated. The results are very strange, e.g. the droplets evaporate very quickly and achieve the temperature of 45K (i.e.-228C).

I think the problem is saturation pressure set in Droplet Properties (Psat=10e+5 Pa (?) ). The questions are: 1) what are the units of pressure? 2) where is the value of the saturation pressure used in the calculations? 3) at what temperature it should be given (i.e. initial, mean, etc.) and 4) what is the saturation pressure for my fuel?

The most confusing here is that in handbooks I found there is no saturation pressure given, but only the vapor pressure. Is this the same?

Thanks,

Julie

Re: Fuel evaporation
 

1) Pressure is in Pascals [Pa]. 2) The vapor pressure is used in the mass and heat transfer computations between the drop and the surroundings. 3) It should be computed according to the drop temperature in dropro.f. 4) The vapor pressure depends on the temperature.

What kind of injection velocities are you encountering ? Extremely high velocities would maybe lead to such low temperatures or very incorrect vapor pressure.

Re: Fuel evaporation
 

The velocities are about 150 m/sec.

Ossi, you say that the vapor pressure should be computed according to the drop temperature in dropro.f. But there is the saturation pressure value that I should supply in the Droplets Properties. The default value is 10e+5. I have performed the computations with the sat. pres. = 0.5e+5. It yelds better result, but the temperature is still incredibly low (~76 K).

May be there is a bug in dropro.f?

Thank you,

Julie

Re: Fuel evaporation
 

You have an example in dropro.f for n-dodecane how saturation pressure changes with temperature as well as latent heat of evaporation.

regards, Dragan

Re: Fuel evaporation
 

Thank you. I'll check that

Re: Fuel evaporation
 

The saturation pressure set for each droplet type is used as a default in case dropro doesn't return anything; the same applies to the other properties.

Re: Fuel evaporation
 

Hi, I guess your saturation pressure is wrong. I found this about Heptane. (http://webbook.nist.gov). You should probably have a look at this. Furthermore, the sat. pressure is very much dependent on temperature.

Antoine Equation Parameters

log10(P) = A - (B / (T + C))

P = vapor pressure (bar)

T = temperature (K)

Temperature (K) A B C Reference 299.07 - 372.43 4.02832 1268.636 -56.199 Williamham, Taylor, et al., 1945

Re: Fuel evaporation
 

Stefan,

Thank you for the answer. Can you tell me for what temperature range the Antoine equation is valid?

Regards,

Julie

Re: Fuel evaporation
 

I have tried this and it doesn't work. The pressure obtained by the equation is 4760 Pa @ T=293 K. The calculation just stops at the 3rd iteration.

Have any idea?

Julie

Re: Fuel evaporation
 

Hi,

You can use a few values of vapour pressure and derive some sort of function of temperature (eg. poynomial) as the input for your dropro. These are values I found in 'VDI-Wärmeatlas': 371,6 K - 101,3 kPa (this is the 'normal' boiling temperature); 380 K - 130 kPa; 400 K - 219 kPa; 420 K - 349 kPa; 440 K - 529 kPa; 460 K - 721 kPa; 480 K - 1094 kPa; 500 K - 1513 kPa; 520 K - 2046 kPa; 540,3 K - 2736 kPa. At the critical temperature (540,3 K), Heptane is gaseous at any pressure, so this value is quite important in the droplet property setup. Another possibilty to calculate the vapour pressure is this (again from 'VDI Wärmeatlas'):

ln p,sr=f0(Tr)+omega*f1(Tr),

where: p,sr=ps/pc (reduced vapour pressure) ps - vapour pressure pc - critical pressure (i.e. 27,4e+5 Pa for heptane) Tr=T/Tc (reduced temperature) Tc - critical temperature (i.e. 540,3 K for heptane) omega - acentric factor (i.e. 0,349 for heptane)

f0(Tr)=5,92714-(6,09648/Tr)-1,28862*ln(Tr)+0,169347*Tr**6

f1(tr)=15,2518-(15,6875/Tr)-13,4721*ln(Tr)+0,43577Tr**6

It's a bit of a monster but it worked alright for n-dodecan. Are there any ohter possible reasons for your problem? You could try and check the void fraction of your droplets (should be below 40% of the cell volume). Did you try to run your case without the chem. module (maybe with a high initial temperature to see if your droplets evaporate as expected)? Another thing that might cause you problems are thin wall layer cells.

Hope that helps.

Regards,

Volker

Re: Fuel evaporation
 

Volker,

Can you tell me what happens to the vapor pressure at 273K?

The problem is that I have to simulate droplets evaporation inside the vaporiser, so they are not suppose to evaporate before they hit the vaporizer's hot wall. However, in the model I build for today droplets evaporate far away before the wall...

Could you, please, explain me the sence of the void fraction in STAR-CD? I think I don't understand it properly. What means that it should be below 40% of the cell volume?

Thanks for the help,

Julie

Re: Fuel evaporation
 

I have checked the void fraction. It changes from 0.003 to 0.01. Is it ok?

Regards,

Julie

Re: Fuel evaporation
 

Hi,

May be the result depends upon number of droplets per parcel (i.e. total mass of drops per parcel)? What do you think?

Regards,

Julie

Re: Fuel evaporation
 

It's valid in the range 299.07 - 372.43 K, so your 293 K are not accounted for.

Re: Fuel evaporation
 

Have you tried that function to get an idea of the vapour pressure at 273 K? Anyway, it should be well below standard pressure. What did you use in dropro to define the vapour pressure? Have you defined the critical temperature? The void fraction is the fraction of the volume of a cell that is filled by droplets. The droplet model in Star does only work properly when the volume of the droplet is small compared to the cell volume, i.e. The user guide recommends a maximum fraction of 40%.

Volker

Re: Fuel evaporation
 

It should be better (with respect to accuracy) to have many parcels with only few droplets in them but that will result in longer CPU time. One more tip for droplet calculations. Try the Switches SW 70 (impl. treatment of dropl mass transfer source, don't use with ignition model), 71 (impl. treatm. of dropl. heat transf. source) and 199 (disable evaporation). Furthermore set the Rconstants RCONS 34 = 0.1 - 0.7 (Under-relaxation of coupling terms between disp. and cont. phase) and RCONS 185 = 1 (Gradient based interpolation of vel. for dropl. tracking, with this one you have to use the -3 option in starlink).

Hope that helps.

Volker

Re: Fuel evaporation
 

Hi!

The answers to your questions:

1) Q: Have you tried that function to get an idea of the vapour pressure at 273 K? Anyway, it should be well below standard pressure.

A: Yes, you are right. It is about 5 kPa and STAR does not want to perform any calculaions with this value.

2) Q: What did you use in dropro to define the vapour pressure? Have you defined the critical temperature?

A: I do not use dropro.f subroutine. All parameters defined as "Standard" at initial temperature (273 K).

Some new questions to you:

1) Is there any detailed description of Switches and Real Constants?

2) I have checked the void fraction. It changes from 0.003 to 0.01. Is it ok? Is there some "lower limit" for it?

Thank you,

Julie

Re: Fuel evaporation
 

Hi,

I think if you want to get any meaningful results for droplet evaporation you have to define the vapour pressure as a function of temperature (in dropro). You have to tell the code at which temperature-pressure couples heptane is going to evaporate. If you don't do that it will take the value you provide for the vapour pressure (under standard) and the droplet will evaporate whereever the pressure in your domain is below or equal that pressure regardless of the temperature (or maybe it will stop do anything sensible). If you use the standard value of 100 kPa and use the same pressure as your inlet pressure the droplets will evaporate as soon as they enter the domain. If you want to prevent boiling altogether just switch the boiling model off.

Your void fraction sounds ok (I don't know of any lower limit).

There is no description of the switches and constants to my knowledge, try and get in touch with Star.

Volker

Re: Fuel evaporation
 

Volker,

How did you got to know about the switches and constants, if tere is no description available?

Do you have an experience of writing any subroutines for the STAR? There are some functions, which I can not figure out where they are defined. (E.g. FUELFN(,,).)

May I ask what kind of work do you do?

Regards,

Julie

Re: Fuel evaporation
 

Julie,

I found out about those switches on a Star CD training course. The user guide says that they 'activate beta-level features in the code', so they will probably become properly documented and introduced in later releases of the code. I am not quite sure myself how that FUELFN works but apparently it works alright. If you don't trust these functions you can always include your own function. In this example you click on 'user' in that saturation pressure field and Star will set up the folder 'ufile' and copy the dropro into that folder. You will find a bit of sample code in dropro that gives you an idea how to set the thing up. I hope you are a little familiar with the joys of Fortran programming.

I am just getting involved with liquid fuel combustion myself (automotive industry).

Regards,

Volker