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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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210
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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;
}