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Custom Nusselt Number for DPM

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Old   November 8, 2016, 03:54
Default Custom Nusselt Number for DPM
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Hannes
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Hello everyone,

I am doing some research on particle flow and particle heating in combustion environments. Ceramic particles (about 400 to 800 microns in diameter) are injected directly into a natural gas flame and heat up, I want to calculate the temperature over residence time using the discrete phase model.

The results look pretty good as a start but now I am facing a problem. I would like to customize the way fluent calculates the Nusselt number for the particles. Measurements show, that the particle temperature overshoots and I guess, that the Nusselt formulation by Kudryashev

Nu=0,664*squrt(Re)*Pr^(0.33)

or maybe a weighting between the latter Nusselt correllation and the formulation by Ranz and Marshall (which is default in Fluent) is more suitable.

I found the DEFINE_DPM_HEAT_MASS - UDF in the Fluent UDF manual but in this case, no evaporation, melting or other phase changes take place and I don't have multicomponent particles either.

Does somebody know how a UDF which is suitable for my case look like?

Thank you!
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Old   November 8, 2016, 04:48
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Alright, I guess I ran across the solution. The UDF looks like this:

--------------------------------------------------

/******* DPM LAW for droplet heating ********/
#define RO_AIR 1.225
#define RO_WATER 998.2
#define MU_AIR 1.7894e-05
#define CP_AIR 1006.43
#define CP_WATER 4182
#define K_AIR 0.0242
DEFINE_DPM_LAW(DropHeatLaw,p,ci)
{
real area, rel_vel, Re, Pr, HTC, delta_temp;
cell_t c = P_CELL(p);
Thread *t = P_CELL_THREAD(p);
area = 4.0 * M_PI * pow(P_DIAM(p),2.0);
rel_vel = sqrt(pow((P_VEL(p)[0] - C_U(c,t)),2.0) + pow((P_VEL(p)[1] - C_V(c,t)), 2.0));
Re = RO_AIR * P_DIAM(p) * rel_vel /MU_AIRů /* Reynolds number */
Pr = CP_AIR*MU_AIR/K_AIR; /* Prandtl number */
HTC = K_AIR * (2.0 + 0.6*pow(Re,0.5)*pow(Pr,1./3.))/ P_DIAM(p);
delta_temp = P_DT(p) * area * HTC * (C_T(c,t)-P_T(p))/(P_MASS(p)*CP_WATER);
P_T(p) = P_T(p) + delta_temp;
}

-----------------------------------------------

This is suitable for a 2D-case with constant material properties. I'm able to adapt this function for my needs. I've found it online in a PhD thesis.

Maybe this code helps somebody who is facing the same problem.
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Old   November 10, 2016, 12:35
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Hey everyone, right now I am getting really tired of troubleshooting, maybe it's just a simple mistake but I don't see it. What I am working on are particles which are injected into a flame, they heat up and fall through cold air afterwards where they are supposed to cool down.

Here is my UDF with the custom Nusselt corellation:

----------------------------------------------------------
#include "udf.h"
#include "math.h"
#include "dpm_types.h"
#include "dpm_laws.h"
#include "mem.h"
#include "dpm.h"
#include "materials.h"

DEFINE_DPM_LAW(HeatingSphere,p,c)
{
Thread *t0 = P_CELL_THREAD(p); //Pointer on Thread
real gastemp = C_T(c,t0); //Flue Gas Temperature
real eta = C_MU_L(c,t0); //Molecular Viscosity of the flue gas
real lambda = C_K_L(c,t0); //Thermal conductivity of flue gas
real rho = C_R(c,t0); //Density of flue gas
real cp = C_CP(c,t0); //Specific heat of flue gas

//calculation of the relative velocity
real rel_vel = sqrt(pow((P_VEL(p)[0] - C_U(c,t0)),2) + pow((P_VEL(p)[1] - C_V(c,t0)),2) + pow((P_VEL(p)[2] - C_W(c,t0)),2));


real Pr = eta * cp / lambda; //Prandtl
real Re = rel_vel * P_DIAM(p) * rho / eta; //Reynols

real Nu = 0.568 * pow(Pr,0.333333) * sqrt(Re) + 0.0104 * pow(Pr,0.3333333) * pow(Re,0.666666) + 1.7; //Custom Nusselt Correllation
real alpha = lambda * Nu / P_DIAM(p); //Heat Transfer Coefficient
real Area = 4.0 * M_PI * pow(P_DIAM(p),2); //Particle Surface

real massPartikel = P_MASS(p);
real partikeltemp = P_T(p);
real timestep = P_DT(p);
real sigma = 5.670367e-8; /* Stefan Bolzmann Konstante */
real G = C_STORAGE_R_XV(c,t0,SV_DO_IRRAD,0);
real T_radiation = pow(G/(4*sigma),0.25); //Radiation Temperature

Material *m = P_MATERIAL(p);
real epsilon = DPM_EMISSIVITY(p,m);//Particle Emissivity

real cpParticle = DPM_SPECIFIC_HEAT(p,P_T(p));


real dT = timestep * Area * ( alpha * (gastemp - P_T(p)) + epsilon * sigma * (pow(T_radiation,4) - pow(P_T(p),4) ) ) / (massPartikel * cpParticle);
P_T(p) = P_T(p) + dT;
}
-----------------------------------------------------------------


The calculation of Reynolds and Nusselt works pretty good, the calculated values look plausible. Particle Temperatures rise much faster and higher as I would expect.

Any ideas where the mistake might be?
Thank you!

Edit: There's one thing more. The particle specific heat is defined as a temperature dependend function, it works fine when I don't use the custom dpm heating law. But, after I activate the dpm law, the specific heat of the particles doesn't fit the particle temperatures anymore.
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Old   June 2, 2017, 05:43
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Hi MetricDevice,
How do you modify mass and energy source in continuous phase?
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Old   June 2, 2017, 06:38
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I almost forgot about this topic, sorry.

Here's the solution:
real Area = 4.0 * M_PI * pow(P_DIAM(p),2); //Particle Surface

I've made a really stupid mistake and calculated the particle surface area with the corresponding particle diameter, not with the radius. Sometimes, i could bang my head against the wall but whatever...

@arctan
There is no mass source, the energy source is implemented using the default function of Fluent.
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Old   June 2, 2017, 08:49
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In your solution, you mean:
real Area = 4.0 * M_PI * pow(P_DIAM(p)/2.0,2); //Particle Surface

Anyway, I'm writing my custom vaporization law (law 2) for evaporation of water droplet with DEFINE_DPM_LAW and I need to modify mass and energy terms in continuous phase. But I don't know how, may be with DEFINE_DPM_SOURCE? Any ideas?

What do you mean by "the energy source is implemented using the default function of Fluent."?

Thanks
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Old   June 2, 2017, 09:04
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I'd try DEFINE_DPM_HEAT_MASS; so far I haven't worked with evaporating droplets but I guess, that's the way to go.
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