Conclusion and Recommendations

206

Chapter 9 Conclusion and Recommendations

9.1 Conclusions

The aim of the research was to investigate experimentally and via simulation the

processes of pulse combustion drying. Since pulse combustion drying technology

consists of pulse combustion and drying techniques, a through investigation of pulse

combustion and its drying process was carried out. The key conclusions about these

two processes are summarized as follows.

A CFD model for a mechanically-valved pulse combustor was developed with

simple inflow conditions. The combustion process in the combustor was simulated to

understand the basic dynamics of flame structure, flow-chemistry interaction and the

resulting pulsation. Parametric studies were carried out for different operating

conditions and flapper settings to examine the cause-effect scenario between the

dynamics of the flapper valve and pulsating combustion. Numerical results were found

to be in broad agreement with experimental observations.

A small-scale pulse combustor was operated successfully with increased life of the

flapper valve. The small combustor used a curved flow passage for fuel/air mixing and

a flapper valve as the inlet; this is a unique design. Some thermal and dynamic

parameters such as gas pressure wave, exhaust gas and velocity were measured and

compared with data for a conventional size pulse combustor.

Impinging jets of PC exhaust for drying paper sheets were studied experimentally

and the drying performance evaluated. Flow behavior within the PC impingement zone

was simulated using a CFD model. For PC impingement to enhance paper drying, it

was found that (1) Under a single free pulse jet, the optimal drying occurs at about 3

times the diameter of the tailpipe; (2) At a low impingement height, convection near

Conclusion and Recommendations

207

the stagnation point is governed by the impinging jet flow, accompanied with a high

paper surface temperature and fast drying rate; outside of this region, the impinging

vortex is the dominant influence, where the drying rate is relatively low.

PC spray drying of NaCl aqueous solution was investigated experimentally and

numerically. Liquid atomization in a pulsating jet was carried out and the droplet

diameter distribution was measured. Numerical results provided detailed information

about the intensely turbulent pulsating flow pattern, gas temperature and humidity

distribution as well as heat and mass transfer characteristics in the drying chamber.

High drying rates and short drying times were observed in this drying process. The

effect of gas pulsation on drying performance was also evaluated.

Gas-particle flow behaviors in a cylindrical spouted bed were predicted using a

two-fluid modeling approach. The numerical results were noted to be in good

agreement with the published experimental data (He, et al, 1994a and b). Parametric

studies were carried out for different operating conditions such as gas jet velocity,

particle density and size and for the special case of a pulsating spouting jet. It was

found that bubbles may be generated in the bed with an unsteady gas jet, causing flow

instabilities and that the high frequencies of pulse combustors contribute to reducing

such instabilities. Gas-particle flow behavior in a three dimensional spout-fluid bed

was also investigated utilizing the above two-fluid model. Some typical phenomena

observed in spout-fluid beds were correctly predicted, i.e. the bubble formation,

surface disturbance, etc. It was found that flow instabilities develop in the spout-fluid

bed. The mechanisms leading to instabilities were discussed based on the numerical

results.

A drying model for mass and heat transfer between gas and particles was

incorporated into the two-fluid model to investigate the drying characteristics of grains

Conclusion and Recommendations

208

in the cylinder spouted bed dryer. The particle moisture, mass transfer rate distribution,

etc in the bed were predicted and discussed. The drying model can be used to study PC

spouted bed drying process later when a high temperature, pulsating spouting gas jet

was applied.

The results obtained from this study contribute to a better understanding of pulse

combustion and PC drying processes. The CFD model for pulse combustion can be

used as a design, analysis, and optimization tool for a flapper valve-coupled to a pulse

combustor. Investigation of pulse combustion spray drying and impingement process

contribute to a deeper understanding of pulse combustion drying. Knowledge obtained

in investigation of spouted bed dryer may contribute to a fundamental understanding of

PC spouted bed drying of particles, leading to improved design of such dryers

9.2 Recommendations

Some recommendations for future work are summarized as follows:

1. The combustion process is a complex one which involves numerous chemical

reactions. A multiple step chemical reaction model may be more suitable to

simulate the pulse combustion process than the one-step model used in this study

of pulse combustion. When a multiple step reaction model is incorporated, the

CFD model can simulate chemical reactions involving emission of gaseous

pollutants such as NOx, CO, etc. Thus, the model can contribute to the

understanding of why fewer gaseous pollutants are generated in the pulse

combustion processes as reported in the literature.

2. Experimental /numerical tests on use of renewable fuels such as bio-diesel and

bio-gas in pulse combustors are desirable. Renewable fuels are of major research

interest due to the decreasing supply and increasing cost of oil.

3. To design dryers with impinging jets of PC exhaust for drying of paper sheets,

Conclusion and Recommendations

209

both modeling and experimental studies are needed to examine drying kinetics of

the material and its effects on product quality before definitive conclusions can be

drawn about its industrial applications. Parametric studies on nozzle geometries,

arrays of PCs, etc, are suggested for future works.

4. Numerical results on PC spray drying of solutions should be validated

experimentally. The CFD model for the drying process can then be improved, if

needed.

5. For spouted bed drying of grains, only one drying process is simulated here. It is

suggested that more parametric studies will be carried out to achieve a deeper

understanding of PC spouted bed drying. Also, the numerical results need to be

validated experimentally.

6. More work should be done on the atomization process of liquid materials in a

pulsing jet. Effects of viscosity, gas velocity oscillation etc on particle size

distribution, can be studied experimentally. Such data are needed for efficient

design of PC-spray dryers.

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Appendices

220

Appendices

Appendix A: Gas property variations with temperature and composition The empirical correlations used in this study for specifying the thermodynamic and

transport properties of combustion gas are listed in Table A-1

Table A-1 Temperature and composition -dependent properties of gas species

A1+A2T+A3T2+A4T3+A5T4 Physical properties A1 A2 A3 A4 A5

Cp 365.26 2.5482 -0.0037 2e-06

-2e-06 7e-08 -4e-11 1e-14 CO2 k -0.0013 4e-05 7e-08 -2e-11

Cp 1609.791 0.7405 -9.1298e-06 -3.814e-08 4.8023e-12

-4.4189e-06 4.6876e-08 -5.3894e-12 3.2029e-16 4.9192e-22 H2O k -0.00797 6.8813e-05 4.49045e-08 -9.01e-12 6.1733e-16

Cp 811.1803 0.4108345 -1.7507e-04 3.7576e-08 -2.9736e-12

7.8794e-06 4.9249e-08 -9.8515e-12 1.5274e-15 -9.4257e-20 O2 k 0.003922 8.0812e-05 -1.3541e-08 2.2204e-12 -1.4161e-16

Cp 938.899 0.301791 -8.1092e-05 8.2639e-09 -1.5372e-13

7.4733e-06 4.0837e-08 -8.2446e-12 1.3056e-15 -8.1779e-20 N2 k 0.004737 7.2719e-05 -1.1220e-08 1.4549e-12 -7.8717e-17

RTPM /= (ideal gas)

Cp

=i j jii

pii

pY

CYC

,

=i j jii

ii

Y

Y

,

Gas

fuel

mixture

k

=i j jii

ii

Y

kYk

,

21

2

41

21

,

18

1

+

+

=

j

i

i

j

j

i

ji

M

M

M

M

Appendices

221

Appendix B Discrete Droplet Model

In principle, there are two theoretical approaches to characterize the impact on a

second phase (particles/ droplets), which is dispersed in the continuous phase (gas

mixture): Euler-Lagrangian modeling and Euler-Euler modeling. Lagrangian model is

used in this study, which is called Discrete Droplet Model available in Fluent.

B-1 Particle tracking

The Euler-Lagrangian approach is used to trace the particle trajectories by solving the

force balance by considering the particle inertia with the forces acting on the particle,

and the equation can be written (for the axial x direction) as

p

px

pxxD

px gvvF

dt

dv

)()( ,

, += (B-1)

In Equation (B-1), a set of assumptions has been made: (1) the particles are spherical;

(2) the particle/air mixture is dilute, so interactions between particles can be ignored;

(3) each particle is considered as a point mass and does not influence the fluid flow

pattern; and (4) the drag force is the only interaction force. Where the term FD(v - vp) is

the drag force per unit particle mass and

24

Re182

D

pp

D

C

dF

= (B-2)

Here, Re is the relative Reynolds number, which is defined as

vvd pp Re (B-3)

The drag coefficient, CD, can be taken from

2Re

3

Re

21

aaaCD ++= (B-4)

Where a1, a2, and a3 are constants (Walton, 2000).

The trajectory equation of droplets is updated by,

Appendices

222

pvdt

dx= (B-5)

The droplet trajectory is updated each time the droplet enters a neighboring cell along its

path. Two-way coupling allows interaction between both phases by including the

effects of the particulate phase on the fluid phase.

B-2 Heat and mass transfer between droplet and gas

Because heat and mass transfer between droplets and continuous phase is very

complex, several heat and mass relationships are employed in this thesis, based on

FLUENT. During calculation, the droplet temperature was regarded uniform for small

droplet diameter.

While the particle temperature is less than the vaporization temperature, Tvap, and

after the volatile fraction, fv,0, of a particle has been consumed, that is,

Tp < Tvap and mp (1-fv,0) mp,0

droplets are only heated and no evaporation happens. A simple heat balance to relate the

particle temperature, Tp(t), to the convective heat transfer is used

)()( 44 RRppppp

pp TATThAdt

dTcm += (B-6)

The heat transfer coefficient, h, is evaluated using the correlation of Ranz and Marshall

(Ranz and Marshall, 1952):

3/12/1 PrRe0.2 dp

ak

hdNu +==

(B-8)

Where, mp = particle diameter (m); Ap=droplet surface area (m2); cp=heat capacity of the

droplet (J/kgK); T=local temperature of the hot medium (K); k = thermal

conductivity of the continuous phase (W/m-K); Red = Reynolds number based on the

particle diameter and the relative velocity; Pr = Prandtl number of the continuous phase.

p = the emissivity of droplet; =constant; R = radiation temperature, 4/1

4

I

,

Appendices

223

where I is the radiation intensity.

When the temperature of the droplet reaches the vaporization temperature, Tvap, and

continuing until the droplet reaches the boiling point, Tbp, droplets begin to evaporate.

During this period, the rate of vaporization is governed by gradient diffusion, i.e.

)( ,, = isici CCkN (B-9)

Where Ni = molar flux of vapor (kgmol/m2-s); kc = mass transfer coefficient (m/s); Ci;s =

vapor concentration at the droplet surface (kgmol/m3); Ci; = vapor concentration in the

bulk gas (kgmol/m3). Ci;s and Ci; are defied as

p

psat

siRT

TpC

)(, = (B-10)

=

RT

pXC

op

ii , (B-11)

Where Psat= the saturated vapor pressure at the droplet temperature (Pa); R = the

universal gas constant; Xi =the local bulk mole fraction of species i; Pop =the operating

pressure (Pa); T = the local bulk temperature in the gas. The mass transfer coefficient

in Equation B-9 is calculated from a Nusselt correlation:

3/12/1

,

Re6.00.2 ScD

dkNu d

mi

pc

AB +== (B-12)

Where Di;m = diffusion coefficient of vapor in the bulk (m2/s); Sc = the Schmidt

number (miD ,

)

The mass balance of single particle is computed as

ip NM =& (B-13)

The mass transfer between the droplet and the hot gas is computed simply as

=

=n

i

iNM1

& (B-14)

The heat transfer between the droplet and the hot gas is updated according to the

heat balance as follows

Appendices

224

)()( 44 PRppfgp

pp

p

pp TAhdt

dmTThA

dt

dTcm ++= (B-15)

Where hfg= latent heat (J/kg); dt

dm p= rate of evaporation (kg/s)

The third period, called droplet boiling, is applied to predict the convective boiling of

a discrete phase droplet when the temperature of the droplet has reached the boiling

temperature, Tbp, and while the mass of the droplet exceeds the non-volatile fraction, (1

-fv;0):

bpp TT and opovp mfm ,, )1( >

When the droplet temperature reaches the boiling point, a boiling rate equation is

applied Walton, 2000:

[ ]

+

+=

)()(

Re23.0122)( 44PRpp

d

fgp

pTTT

dp

k

hdt

dd

(B-16)

Where Cp, = heat capacity of the gas (J/kgK); p = droplet density (kg/m3); k =

thermal conductivity of the gas (W/mK).

Finally, the heat lost or gained by the particle as it traverses each computational cell

appears as a source or sink of heat in subsequent calculations of the continuous phase

energy equation.

Appendix C: UDF programs used in this study

C-1: UDF for the movement of the flapper (Chapter 3)

#include

#include "udf.h"

#if !RP_NODE

# define UDF_FILENAME "udf_loc_velo"

/* read current location and velocity from file */

static void

Appendices

225

read_loc_velo_file (real *loc, real *velo)

{

FILE *fp = fopen(UDF_FILENAME, "r");

if (fp != NULL)

{

float read_loc, read_velo;

fscanf (fp, "%e %e", &read_loc, &read_velo);

fclose (fp);

*loc = (real) read_loc;

*velo = (real) read_velo;

}

Else

{

*loc = 0.0;

*velo = 0.0;

}

}

/* write current location and velocity in file */

static void

write_loc_velo_file (real loc, real velo)

{

FILE *fp = fopen(UDF_FILENAME, "w");

if (fp != NULL)

{

fprintf (fp, "%e %e", loc, velo);

fclose (fp);

}

else

Message ("\nWarning: cannot write %s file", UDF_FILENAME);

}

#endif /* !RP_NODE */

DEFINE_ON_DEMAND(reset_velocity)

{

#if !RP_NODE

real loc, velo;

read_loc_velo_file (&loc, &velo);

write_loc_velo_file (loc, 0.0);

Message ("\nUDF reset_velocity called:");

#endif

}

DEFINE_CG_MOTION(valve, dt, cg_vel, cg_omega, time, dtime)

{

Appendices

226

#if !RP_NODE

Thread *t = DT_THREAD (dt);

face_t f;

real force, loc;

#endif

real velo;

FILE *fb = fopen("valvemovement.txt", "a");

real kk=CURRENT_TIME;

/* reset velocities */

NV_S (cg_vel, =, 0.0);

NV_S (cg_omega, =, 0.0);

if (!Data_Valid_P ())

return;

#if !RP_NODE

/* compute force on piston wall */

force = 0.0;

begin_f_loop (f, t)

{

real *AA;

AA = F_AREA_CACHE (f, t);

force += (F_P (f, t)-0.0 )* AA[0];

}

end_f_loop (f, t)

# if RP_2D

if (rp_axi)

force *= 2.0 * M_PI;

# endif

read_loc_velo_file (&loc, &velo);

/* compute change in velocity */

{

real dv = dtime * force / 0.000209583;

if (loc0)

{

dv=0.0;

Appendices

227

loc=0.00050;

velo=0.0 ;

}

velo += dv;

loc += velo * dtime;

}

Message ("\nUDF valve: time = %f, x_vel = %f, force = %f, loc(m)= %f\n",

time, velo, force, loc);

write_loc_velo_file (loc, velo);

fprintf( fb, "%+12.4e %+12.6e %+12.6e %+12.6e\n", kk, velo, force, loc );

fclose(fb);

#endif /* !RP_NODE */

#if PARALLEL

host_to_node_real_1 (velo);

#endif

cg_vel[0] = velo;

}

C-2: UDF for the Gidaspow drag force model (Chapter 7)

***************************************************************/

/* UDF for customizing the drag law in Fluent */

/***************************************************************/

#include "udf.h"

#define pi 4.*atan(1.)

#define diam2 1.41e-3

DEFINE_EXCHANGE_PROPERTY(custom_drag, cell, mix_thread, s_col, f_col)

{

Thread *thread_g, *thread_s;

real x_vel_g, x_vel_s, y_vel_g, y_vel_s, abs_v, slip_x, slip_y,

rho_g, rho_s, mu_g, reyp, cd,

void_g, vfac, fi_gs, k_g_s, k_g_s_eg, k_g_s_wy;

/* find the threads for the gas (primary) */

/* and solids (secondary phases) */

thread_g = THREAD_SUB_THREAD(mix_thread, s_col);/* gas phase */

thread_s = THREAD_SUB_THREAD(mix_thread, f_col);/* solid phase*/

/* find phase velocities and properties*/

x_vel_g = C_U(cell, thread_g);

y_vel_g = C_V(cell, thread_g);

x_vel_s = C_U(cell, thread_s);

y_vel_s = C_V(cell, thread_s);

slip_x = x_vel_g - x_vel_s;

Appendices

228

slip_y = y_vel_g - y_vel_s;

rho_g = C_R(cell, thread_g);

rho_s = C_R(cell, thread_s);

mu_g = C_MU_L(cell, thread_g);

/*compute slip*/

abs_v = sqrt(slip_x*slip_x + slip_y*slip_y);

void_g = C_VOF(cell, thread_g);/* gas vol frac*/

/*compute reynolds number*/

reyp = rho_g*abs_v*diam2/mu_g;

/*compute Cd*/

if(reyp

Appendices

229

rho_s = C_R(cell, thread_s);

mu_g = C_MU_L(cell, thread_g);

/* compute slip */

abs_v = sqrt(slip_x*slip_x + slip_y*slip_y);

A1=rho_g*abs_v;

A2=A1*diam2;

reyp =A2/mu_g;

/*define mass diffusivity of vapor in air */

if (C_T(cell, thread_g)1.0)

{

xnow = C_VOF(cell, thread_s)*C_YI(cell, thread_s, 1);

}

xban = 0.05;

/* compute mass_transfer_rate */

if ( xnow > C_VOF(cell, thread_s)*xban )

{

gset=0.002*exp(0.0479*C_T(cell, thread_s));

csat = gset/(UNIVERSAL_GAS_CONSTANT*C_T(cell, thread_s));

MMC =18*kc*(csat-cgas)*AS*C_VOF(cell, thread_g)*C_VOF(cell, thread_s);

MM=MMC;

DD=7.2E-08;

temp=39.4783509*2500.0*DD*(xnow - C_VOF(cell, thread_s)*xban)/diam2;

MMD = temp*C_VOF(cell, thread_g)/diam2;

if (MMD < MMC)

Appendices

230

MM=MMD;

}

else

MM=0 ;

if (C_T(cell,thread_s)< 330.0)

{

MM=0.0;

}

if (MM>0.1)

{

C_CENTROID(x, cell, thread_s);

x1=x[0];

x2=x[1];

Message( "There is a big mistake: %12.6e,%12.6e, %12.6e\n", x1,x2,MM);

Message( "%12.6e %12.6e %12.6e %12.6e %12.6e %12.6e %12.6e\n",

x_vel_g, y_vel_g, x_vel_s, y_vel_s, rho_g, rho_s, mu_g);

Message( "%12.6e %12.6e %12.6e %12.6e %12.6e %12.6e %12.6e\n",

reyp, C_T(cell, thread_g),diff, scht, Nu, kc, xi);

Message( "%12.6e %12.6e %12.6e %12.6e %12.6e %12.6e %12.6e\n",

C_P(cell, thread_g), cgas,xnow, gset, csat, MM, C_VOF(cell, thread_g));

}

return MM;

}