[MetricDevice]

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!

[MetricDevice]

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.

[MetricDevice]

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.

[arctan]

Hi MetricDevice,
How do you modify mass and energy source in continuous phase?

[MetricDevice]

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.

[arctan]

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

[MetricDevice]

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.

[Sowmi]

Originally Posted by MetricDevice

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.

Hi Metric device
I am also facing the same problem and your UDF helped me to correlate new nusselt calculation. Thanks for sharing.

[ArikGuyz]

Originally Posted by arctan

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

Hello. Did you manage to add energy source to continuous phase considering the temperature change implemented through custom law.

It has been a while since this post created. But I hope I can get an answer. Thank you.