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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
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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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References
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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;
}