Numerical analysis of the hydraulic design of sugar evaporating

Transcription

Numerical analysis of the hydraulic design
of sugar evaporating crystallizers (vacuum pans)
Numerische Analyse der hydraulischen Bauweise von Verdampfungskristallisatoren
Luis F. Echeverri, Peter W. Rein and Sumanta Acharya
The effect of several design parameters of sugar evaporative crystallizers (vacuum pans), on the natural circulation of massecuite
has been studied using Computational Fluid Dynamics (CFD). For
the analysis, the flow within the crystallizers has been simulated
applying an Eulerian-Eulerian multiphase approach, solving the
conservation equations for both the liquid and vapor phases, and
incorporating relevant buoyancy and interphase force exchange
terms. This paper presents numerical results obtained in the analysis of the hydraulic design of the crystallizers, identifying design
features that contribute to increasing the circulation and enhancing
the performance.
Keywords: evaporating crystallizer (vacuum pan), natural circulation, CFD
1 Introduction
The circulation of massecuite is a key factor in the efficient performance of sugar evaporating crystallizers (vacuum pans), and
must be as high as practically possible to maximize heat transfer,
capacity, recovery, and sugar quality. However, the complexities
of the two-phase fluid flow and heat transfer phenomena involved,
and the difficulty in performing accurate experimental measurements have precluded a satisfactory understanding of this process.
As a result, the information available on massecuite circulation is
limited and often imprecise.
Although the basic mechanisms that govern the processes of boiling, buoyancy, and two-phase fluid flow have been extensively
studied, their combined behavior under high-viscosity conditions
in the complex geometry of sugar evaporating crystallizers makes
it difficult to understand the process and optimize the design. The
design of evaporating crystallizers has therefore been developed on
the basis of experience, identifying certain features which influence performance. Rein et al. (2004) presented a review of practical
operation and design aspects of evaporating crystallizers related to
the circulation of massecuite.
The developments in Computational Fluid Dynamics (CFD) and
computer processing capacity have resulted in accessible engineering tools for numerical analysis and optimization of complex
fluid systems, which have been used successfully in diverse industries. For the particular case of sugar processing, CFD has been
applied to optimization of the design of bagasse boilers (Mann et
al., 2005), juice clarifiers (Steindl, 2001; Chetty et al., 2002), and
evaporators (Steindl, 2003). The complex flow in sugar evaporat908
Der Einfluss verschiedener Auslegungsparameter von Verdampfungskristallisatoren auf den Naturumlauf des Magmas wurde mit
Hilfe der numerischen Strömungssimulation (Computational Fluid
Dynamics) untersucht. Für die Untersuchung wurde die Strömung
innerhalb des Kristallisators mit Hilfe des Euler-Euler-Mehrphasenmodells simuliert, das die Erhaltungsgleichungen sowohl für
die flüssige als auch für die Dampfphase löst sowie relevante Auftriebs- und Zwischenphasen-Austauschkräfte berücksichtigt. Vorgestellt werden die in der Untersuchung der hydraulischen Auslegung der Kristallisatoren erhaltenen numerischen Ergebnisse, die
die Parameter kenntlich machen, die zur Steigerung des Umlaufs
und zur Verbesserung der Arbeit beitragen.
Stichwörter: Verdampfungskristallisator, Naturumlauf, numerische
Strömungssimulation
ing crystallizers has been studied numerically by Bunton (1981),
Stephens (2002), Rein et al. (2004), and Echeverri et al. (2005,
2007), obtaining predictions that show possible flow patterns and
recirculation regions. However, the flow simulations have not been
applied to explore potential alternatives for improving the design
of the crystallizers.
This paper presents numerical predictions of the effect of several
geometric and operational parameters on the circulation rate in
sugar evaporating crystallizers. The simulations give a better understanding of the sugar crystallization process and the factors that
contribute toward enhancing circulation, and therefore the efficiency and the capacity of sugar crystallizers.
2 Numerical analysis
2.1 Simulation of the flow within sugar evaporating crystallizers
The flow in sugar evaporating crystallizers has been simulated using the commercial CFD code FLUENT. The Eulerian-Eulerian
multiphase approach has been applied using a strategy based on a
previous study developed with a lab-scale test rig (Echeverri et al.,
2005). Although three phases are strictly present during sugar crystallization (mother liquid + vapor + sugar crystals), the high viscosity of massecuites and relatively small size of sugar crystals make
it reasonable to assume that the liquid and solid phases move together, so a two-phase flow model is used (vapor and massecuite).
The numerical analysis has been performed for two-dimensional
Sugar Industry / Zuckerindustrie 132 (2007) No. 12, 908–919
planar and axisymmetric geometries that represented continuous
and batch crystallizers respectively. Parallel vertical channels were
used to represent the calandria tubes in continuous crystallizers,
while concentric annular rings were used to represent the tubes in
batch crystallizers. To approximate the complex mass and energy
interactions occurring during boiling in calandria tubes, vapor has
been injected along the corresponding computational domain with
mass source functions, which were defined based on experimental
measurements carried out by Rouillard (1985) in a single heated
tube test rig.
It is assumed that uniform evaporation takes place across the calandria. However, knowing that tubes with lower evaporation produce
less circulation, the flow distribution is expected to be smoother
than that experienced in practice. In the model, the vapor is injected
without any momentum, and rises due to its density difference with
the surrounding massecuite. The primary buoyancy is generated by
the difference between the liquid and vapor densities. The buoyancy forces caused by liquid temperature differences are assumed
negligible with respect to those caused by density difference between the phases; thus the system can be treated as isothermal,
avoiding the solution of the energy equation. The vapor is removed
at the top using an outflow boundary condition.
No information exists on the size of the bubbles in sugar evaporating crystallizers, or the appropriate drag coefficient correlation
that is applicable for high-viscosity flow in calandria tubes. For the
present analysis the bubbles have been assumed to be spherical gas
particles with the same size as the calandria tubes (LD ~100 mm),
since in high-void fraction gas-liquid regimes, such as the slug and
churn, the cross sectional area of the bubbles approaches the internal diameter of the channel. However, in reality a large dispersion
in size and shape of the bubbles is expected to occur as a consequence of boiling, which is impossible to consider in detail. A drag
correlation developed from tests under adiabatic continuous-flow
conditions1 is applied to model the interfacial momentum interaction in the non-adiabatic calandria tubes (Echeverri et al., 2007).
This interaction had to be reduced using a multiplicative correction factor (~0.5) to get agreement with field measurements under
non-isothermal conditions. The lowered momentum interaction
has been attributed to increased friction and intermittent vaporization as a consequence of thermo-hydraulic boiling instability in the
calandria tubes (geysering).
2.2 Design parameters of sugar evaporating crystallizers
studied
The numerical analysis of the design of sugar evaporating crystallizers has been performed by systematically studying the effect of
different design parameters on the flow, in an attempt to identify
optimum values that lead to improved circulation. The analysis has
focused mainly on continuous crystallizers, predicting numerically
the effect of the following design parameters:
– Massecuite head (H): Liquid level above the top calandria tube
sheet.
– Length of the heated calandria tubes (L).
– Downtake size: The relative size of the downtake is expressed
by the circulation ratio (CR), which relates the nominal upflow
area (calandria tubes) to the downflow (downtake) area.
– Geometry of the calandria-downtake wall: flat or rounded
(bowed calandria).
– Inclination of the top calandria plate.
– Inclination of the bottom calandria plate.
– Bottom: geometry and space below the bottom calandria plate.
For batch or discontinuous sugar evaporating crystallizers, a large
range of operational conditions is possible during each cycle as the
liquid level increases and the evaporation rate and physical properties of the massecuite change. This study presents preliminary
results obtained on the effect of the size of the downtake and the
shape of the bottom in batch evaporating crystallizers.
Rouillard (1985) studied the effect of several variables on the
evaporation in calandria tubes, and based on experimental results
developed an empirical correlation. In the numerical analysis presented here, the correlation proposed by Rouillard has been used
to consider the effect of changes in the massecuite level and the
length of the calandria tubes on the evaporation rate2.
2.3 Design criteria
The circulation of massecuite, defined here as the liquid downflow rate through the downtake, is chosen as the main criterion
for evaluation in the analysis. As in other convection processes,
the heat transfer in sugar evaporating crystallizers (vacuum pans)
improves as the circulation increases, and practical experience has
demonstrated that good circulation favors the crystallization rate,
the effective capacity of the crystallizers, and the quality of the
sugar produced.
The circulation period (τ) is defined as the ratio between the volume of massecuite and the circulation rate through the downtake,
indicating the average time required for each fluid particle, and
sugar crystal, to complete a circulation loop within the crystallizer.
The circulation period is particularly useful for comparison of design alternatives involving different massecuite volumes.
Apart from circulation, there are additional design constraints that
are also important from a technical and practical point of view, and
are taken into account in the present analysis:
– Accessibility: Enough space for inspection and maintenance is
required, particularly at the bottom. Based on existing designs
of sugar evaporating crystallizers it is assumed that a minimum
distance of 100 mm from the bottom tube plate is required for
access to the bottom of the calandria.
– Stagnant regions: It is undesirable to have stagnant or low-velocity regions, since this can result in crystal settling, encrustation and differential growth rates of the crystal. A minimum
velocity of 10 mm/s is defined as a critical value for comparison
purposes.
1
Multi-particle drag coefficient:
Ê 1
CDM = 3.6351◊ Á
LD3 ◊ g ◊ rLiquid
ÁË m Liquid
µ Viscosity (Pa · s)
LD Tube diameter (m)
ρ Density (kg/m3)
α Void fraction
Re Reynolds number
(
2
ˆ
rGas ◊ rLiquid ˜
˜¯
)
1.6286
◊
(1 – a )0.3951
Re1.7
Correlation developed by Rouillard (1985) for evaporation in calandria tubes:
 W) = 15.92 – 0.165 · wDS,MA – 0.0601 · Pabs + 0.0311 · qMA + 0.00639 · PSteam – 0.321 ·
ln(m
· L – 0.298 · H
m W
wDS,MA
Pabs
qMA
PSteam
L
H
Evaporation rate (kg/[h · m2])
Massecuite Brix
Absolute pressure (kPa abs)
Massecuite purity (%)
Steam pressure (kPa abs)
Tube length (m)
Massecuite head above calandria (m)
909
– Practicability: Simplicity in the design and manufacture are
valuable features, since they can affect significantly fabrication
and maintenance costs. It is assumed here that complicated configurations or geometries should be avoided unless they result in
a substantial improvement in performance.
– Discharge time: Particularly for batch crystallizers, the time that
is required for discharging the massecuite at the end of the strike
has some importance, since it contributes to the total duration
of the cycle, and therefore the capacity of the crystallizers. It is
considered here that the use of low slopes at the bottom must be
avoided (e.g. must have θ  17°).
3 Results and discussion
3.1 Continuous sugar evaporating crystallizers
3.1.1 Basis
The analysis of the hydraulic design of continuous sugar evaporating crystallizers is based on a commercial Fletcher Smith (TongaatHulett) unit installed at Enterprise sugar mill, USA, where field
measurements and numerical simulations of the flow have been
carried out previously (Echeverri et al., 2007). Figure 1 and Table
1 present the geometry and main design and operation parameters
considered as the starting point for the numerical flow simulations.
Fig. 1: Schematic representing the cross section of the continuous
sugar evaporating crystallizer studied
Table 1: Main design and operation parameters for continuous
A massecuite crystallization
Design
Gas phase
(vapor)
Liquid phase
(massecuite)
910
Massecuite volume (m3)
Heating surface (m2)
Footprint (m2)
Number of cells
Tube length L (mm)
Tube diameter LOD (mm)
Evaporation (kg/[h · m2])
Density ρG (kg/m3)
Viscosity µG (Pa · s)
Density ρL (kg/m3)
Viscosity µL (Pa · s)
160
1655
16.1 · 5.4
12
1400
101.6
18.5
0.20
1.10 · 10–5
1450
6.5
3.1.2 Effect of the liquid level above the top calandria plate in
continuous crystallizers
Table 2 presents the nominal massecuite head above the top calandria plate used in three horizontal continuous crystallizers currently
available in the market, indicating that relatively low massecuite
heads are normally used compared to batch crystallizers, where at
the end of the strike the massecuite level can reach values that are
3 to 6 times higher.
As the liquid level above the top calandria plate increases, the
hydrostatic pressure in the heated tubes increases, resulting in a
higher saturation temperature and a reduction in the driving temperature difference responsible for heat transfer. This well known
hydrostatic and thermodynamic effect makes low liquid heads attractive. However, experiments performed at lab-scale indicated
that below a certain critical height the flow resistance above the calandria becomes significant and causes poor circulation (Echeverri
et al., 2005).
Table 2: Liquid head above the top calandria plate and dimensions of heated tubes in continuous evaporating crystallizers
Design
Tongaat-Hulett
SRI
Honiron
Liquid head
H (m) Tube length
L (m) Tube diameter
LOD (m)
0.30
0.50–0.70
0.30
1.20–1.50
1.20–1.80
1.40–1.70
0.10
0.10–0.13
0.09–0.10
The effect of massecuite level has been studied numerically varying the liquid head above the top calandria plate within rational
limits (H = 0.3–1.1 m). Figure 2 presents numerical results on the
flow showing an increasingly complex situation above the calandria plate as the liquid level is increased. The simulations indicate
a vortex in the upper downtake region, which grows as the liquid
level increases and more room is available to extend its field, resulting in a larger recirculation of massecuite.
Figure 3 shows the predicted effect of the massecuite level on circulation, indicating an initial increase in terms of the superficial
liquid velocity in the calandria tubes (JL) as the liquid head is higher, this in spite of the reduction in evaporation that has been considered based on the correlation developed by Rouillard (1985). This
behavior is in agreement with results obtained at lab-scale, and is
attributed to the ‘bottle-neck’ effect or higher frictional resistance
above the top tube plate with low liquid heads as a consequence
of the reduced cross sectional area above the calandria. The result
suggests that the gain in circulation is significant up to H ~ 0.7 m.
A larger volume of massecuite is logically obtained as the liquid
level increases, and this results in higher circulation periods, which
indicate that the average time required for each fluid particle, and
sugar crystal, to complete a circulation loop within the crystallizer
is extended as the liquid level rises. Based on the numerical results it can be proposed that the massecuite level above the top
tube calandria plate should be around H ~ 0.6–0.8 m in continuous
evaporating crystallizers for A-massecuite. However, experimental
verification would be important before a definitive conclusion can
be drawn.
Fig. 2: Contours of void fraction and liquid velocity vectors numerically predicted for a
continuous A massecuite crystallizer with different liquid levels above the top tube plate
Fig. 3: Effect of the liquid head above the
top calandria plate on the circulation predicted numerically
continuous sugar crystallizer provided with calandria tubes of different length
Fig. 5: Effect of the length of the calandria tubes on the circulation in a continuous
sugar evaporating crystallizer predicted numerically
3.1.3 Effect of the length of calandria tubes in continuous
crystallizers
It has been established that batch evaporating crystallizers provided with short calandria tubes display higher heat transfer rates
than those with long tubes. Modern batch evaporating crystallizers
use tubes around L ~ 0.6–1.0 m in length, while in the past longer
tubes were employed. Table 2 presents the main dimensions of the
calandria tubes currently used in continuous evaporating crystallizers, illustrating that they are relatively long with respect to batch
applications.
Figure 4 presents numerical results on the two-phase flow in the
continuous crystallizer studied with tubes of different length,
showing higher massecuite velocities and higher void fractions at
the upper part of the tubes as tube length increases, this as a natural
consequence of the higher evaporation per tube.
Figure 5 illustrates the predicted effect of the length of the calandria
tubes, showing a progressive drop in heat transfer and an increase
in circulation in terms of the superficial liquid velocity (JL) as the
tubes are longer. However, the liquid velocity displays non-linear
behavior that indicates that the gains in circulation are progressively reduced as the length of the tubes increases. The circulation
period suggests an optimum in tube length around L ~1.0 m.
The number of tubes required and the length of the calandria would
logically increase as the tubes are shortened. Figure 6 presents the
estimated length of the calandria with respect to the length of the
911
Fig. 6: Estimated effect of the length of the heating tubes on the
length of the calandria of a continuous evaporating crystallizer
(vacuum pans)
heated tubes. The results obtained suggest that calandria tubes with
length between L = 1.0–1.2 m offer a reasonable compromise between circulation (Fig. 5) and size of the sugar crystallizer (Fig. 6).
The length of the calandria grows rapidly when shorter tubes are
considered, resulting in a vessel undesirably larger. On the other
hand, longer tubes affect the heat transfer efficiency and the reduction in calandria length drops off as the tube length increases.
consequence of the corresponding reduction in cross sectional
area. The vortex that is developed at the top corner of the calandria
is predicted to become larger as the downtake is wider, causing
undesirable massecuite recirculation and a low velocity region at
the calandria wall.
Figure 8 illustrates the predicted circulation with respect to the
size of the downtake, showing a critical value around ~ 0.50 m.
The use of a smaller downtake, corresponding to a circulation ratio
above CR  1.8, is predicted to be detrimental to circulation. On
the other hand, the use of a downtake larger than ~ 1.25 m gives no
advantage, because no further gain in circulation is observed, while
undesirable recirculation and low velocity regions are generated as
illustrated in Figure 7.
Based on the numerical results it is proposed that the continuous evaporating crystallizer studied should be constructed with a
downtake around 0.75–1.0 m, corresponding to circulation ratios
between CR ~ 0.9–1.2, which would result in maximum circulation
and limit the expansion of the vortex developed at the top of the
downtake.
3.1.5 Effect of rounding the calandria-downtake wall in continuous crystallizers
3.1.4 Effect of the downtake size or circulation ratio in continuous crystallizers
Continuous sugar evaporating crystallizers are normally provided
with a relatively large downcomer or downtake channel, resulting
in low circulation ratios (e.g. CR ~ 0.9), well below the maximum
value recommended for the design of batch evaporating crystallizers (CR  2.5). This is possible because of the continuous character
of the process, where having a small footing volume as in batch
crystallizers is not required.
Simulations of the flow in a continuous crystallizer with a downtake channel varying between 0.2–2.0 m in width have been performed. Figure 7 presents numerical results showing higher velocities within the downtake channel as its size decreases as a logical
In conventional evaporating crystallizers a vertical metallic wall
separates the massecuite within the downtake and the heating steam
within the calandria. This wall is normally rounded in continuous
applications (bowed calandria) in an attempt to favor the circulation
by reducing the changes in direction of the flowing massecuite.
Table 3 and Figure 9 present numerical results on the flow in a continuous evaporating crystallizer provided with a flat and a bowed
(rounded) downtake wall, showing minor differences between the
two flow fields. The use of the flat wall is predicted to give a circulation slightly higher (+ 0.2%), and this is explained by the larger
downtake cross sectional area obtained in this case. However, this
also results in a larger volume of massecuite that increases the circulation period.
Fig. 7: Contours of void fraction and liquid velocity vectors numerically predicted for
a continuous sugar evaporating crystallizer (vacuum pan) with different downtake size /
circulation ratios
912
Fig. 8: Numerically predicted effect of the
downtake size or circulation ratio on the circulation in a continuous sugar evaporating
crystallizer
The velocity vectors presented in Figure
9 show a low velocity region within the
downtake towards the calandria wall,
which is predicted to be less pronounced
when a rounded calandria-downtake wall
is used. Because of the effect on the size
of the low velocity region, and considering that the effect on the circulation rate
is almost negligible, it appears that a
bowed calandria is a desirable feature for
the design of continuous sugar evaporating crystallizers.
3.1.6 Effect of inclining the top
calandria plate in continuous
evaporating crystallizers
Fig. 9: Contours of void fraction, liquid velocity vectors, and low velocity areas numerically predicted for a continuous sugar evaporating crystallizer provided with flat and bowed
calandria wall
Table 3: Circulation numerically predicted for a continuous evaporating crystallizer
provided with a flat and a rounded calandria-downtake wall
Calandria downtake wall Flat
Rounded (radius 1.2 m)
Circulation
JL (m/s) Ratio
JL / JL,,max Circulation
period τ (s)
0.0644
0.0643
1.000
0.998
85.8
81.4
continuous evaporating crystallizer with different inclinations of the top calandria plate
Inclined or sloped calandria plates are
used sometimes in batch and continuous evaporating crystallizers in the belief
that they improve the circulation. In these
cases the tube plates are angled usually
between 10 and 25°.
Figure 10 presents numerical results on
two-phase flow in a continuous crystallizer with different inclinations of the top
calandria tube plate, covering a range of
slopes within 0° # θ # 30º. The veloc-
Fig. 11: Effect of the inclination of the
top calandria tube plate on the circulation
in a continuous evaporating crystallizer
predicted numerically
913
ity vectors presented indicate that the vortex developed at
the upper downtake tends to grow in size and strength as
the inclination of the top tube plate increases, resulting in
increased recirculation.
Figure 11 presents the predicted circulation for different
inclinations of the top tube plate, indicating that inclining
the plates up to θ ~ 10° has a minimal effect on the circulation, while further increases tend to reduce the circulation
rate. The numerical results have suggested that inclining
the top tube plate in continuous sugar evaporating crystallizers is unnecessary and does not lead to any significant
gain in circulation. The use of large slopes is predicted to
be unfavorable, this probably due to an increase in recirculation above the calandria and to the implicit use of longer
tubes, where the transfer of momentum between the vapor
and massecuite and the heat transfer tend to be less effective. Based on the flow simulations it appears that the top
tube plates of continuous evaporating crystallizers should
be horizontal.
Fig. 13: Effect of the inclination of the bottom calandria plate on the circulation in a continuous sugar evaporating crystallizer predicted numerically
3.1.7 Effect of inclining the bottom tube calandria
plate in continuous evaporating crystallizers
Figure 12 presents numerical results on the flow in a continuous evaporating crystallizer with different inclinations
of the bottom calandria tube plate (0° # θ # 30º). In this
case the geometry of the shell was adjusted for the different inclinations to keep the volume of the bottom section
constant.
Figure 13 presents the circulation rate that has been numerically predicted for different inclinations of the bottom tube plate, suggesting that inclining the plates up to
θ ~15° does not affect the circulation significantly, and
that further increases would have a slightly detrimental effect. Based on the flow simulations it is considered that
the bottom tube plates of continuous evaporating crystallizers should be horizontal.
Fig. 14: Geometric simplification of continuous evaporating crystallizers
for analysis of the effect of the bottom geometry applying single-phase
CFD modeling
3.1.8 Effect of the geometry of the bottom section of continuous evaporating crystallizers
Considering that only massecuite is present in the bottom of evaporating
crystallizers, it was possible to study the effect of the geometry of the bottom
applying single-phase modeling. For the numerical analysis the geometry
of the continuous crystallizer has been simplified restricting the computational domain to represent only the downtake and the bottom. Figure 14 presents
the section of the crystallizer studied and
the boundary conditions assumed. A mass
inlet boundary condition is used to introduce the circulating massecuite above the
top tube sheet, while outflow boundary
conditions are set in multiple locations
representing the entrance to the calandria
tubes. A frictionless wall is used at the top
to represent the free surface. The boundary conditions are set to represent the circulation measured in a full-scale continuous evaporating crystallizer (Echeverri et
al., 2007).
To compare different alternatives for the
bottom, the pressure drop between the inlet
and outflow boundary conditions is obtained
from the numerical flow simulations, which
corresponds to the frictional resistance of
the path conformed by the downtake and the
bottom. Attention is also given to areas of
Fig. 12: Contours of void fraction and liquid velocity vectors numerically predicted for a low velocity or stagnation, which are undesirable for the crystallization process.
continuous crystallizer with different inclinations of the bottom calandria tube plate
914
3.1.8.2 Separation between the bottom
calandria plate and the bottom
wall below the middle (LS)
The effect of the separation between the
bottom calandria plate and the bottom wall
at the middle of the crystallizer has been
studied defining an elliptical geometry
underneath the downtake and a straight
wall below the calandria. In the numerical
analysis the separation LS has been adjusted between 0.10 # LS # 0.40 m, while a
constant value of the separation LCB = 0.65
m was maintained.
Figure 16 presents the frictional pressure
drop that has been numerically predicted
Fig. 15: Effect of the separation between the bottom tube plate and the bottom wall (LCB) on
for different separations between the botthe frictional pressure drop in a continuous evaporating crystallizer predicted numerically
tom tube plate and the bottom wall, indicating a very small effect of this parameter
on
the
circulation
(<
2%).
Based on the numerical results it is proDifferent alternatives for the design of the bottom of continuous
evaporating crystallizers have been evaluated numerically, chang- posed this separation should be designed around LS ~ 0.1–0.2 m.
ing systematically the openings or separations between the bottom Increasing the opening above this range results in enlargement of a
calandria plate and the bottom wall below the corner (LCB) and the low velocity region that is produced at the corner of the bottom, as
middle (LS) of the calandria, parameters that are shown in Figure illustrated in Figure 17.
Different bottom geometries with openings within the ranges de14.
termined as favorable in previous analyses have been evaluated
numerically, observing a logical increase in friction as the bottom
3.1.8.1 Separation between the bottom calandria plate and section is narrower. The results indicate similar frictional pressure
drop for different geometries with comparable openings, suggestthe bottom wall (LCB)
An elliptical geometry of the bottom has
been considered initially, defined by two
concentric ellipses centered in the lower
corner of the calandria, one below the
downtake and one below the bottom tube
plate. The elliptical geometry guarantees
tangency automatically at the intersections
on the edges. Different openings between
the bottom calandria plate and the elliptical bottom wall were evaluated, covering a range between 0.25 # LCB # 1.0 m.
Figure 15 presents the frictional pressure
drop that has been predicted numerically
for different openings. Understandably, the
flow simulations indicate lower frictional
resistance as the opening of the bottom,
Fig. 16: Effect of the separation between the bottom calandria plate and the bottom wall on
and therefore the cross sectional area, are
the frictional pressure drop in a continuous evaporating crystallizer predicted numerically
increased.
Based on the numerical results it can be
proposed that the separation of the bottom must be around LCB ~
0.6–0.7 m. Reducing this opening below that range is predicted
to be detrimental to the circulation due to a rapid rise in frictional
resistance that is illustrated in Figure 15, while larger openings do
not seem to produce significant benefit. The result is consistent
with the effect of the downtake size presented earlier, where a critical value around ~ 0.50 m was determined using multiphase flow
modeling.
Fig. 17: Low velocity region numerically predicted for a continuous evaporating crystallizer with different separations between the
bottom tube plate and the bottom wall
915
ing that the shape of the bottom has a minimal effect on the circulation rate as long as it is not undersized. On the other hand, the
flow simulations show that correctly designing the geometry of the
bottom is important to prevent low-velocity or stagnant regions.
3.1.8.3 Practical aspects related to the geometry of the
bottom of continuous evaporating crystallizers
The continuous evaporating crystallizer used as the case study has
a shell geometry conveniently defined based on circular shapes, as
illustrated in Figure 18[a]. The smallest circle, in the middle of the
bottom simplifies fabrication, but causes some undesirable stagnation. The flow simulations have shown that bottom geometries
with comparable openings and without the rounding at the middle
display similar frictional pressure drop (Figure 18[b]), so the effect
on circulation would be practically negligible; while eliminating
the rounding in the middle of the bottom is predicted to reduce the
size of the low-velocity region at this point.
The stagnation point at the middle of the bottom could be reduced
further by rounding the corner as indicated in Figure 18[c], a
modification that would add complexity to the construction of the
crystallizer and is predicted to have a minimal effect on frictional
resistance.
Figure 19 presents numerical results on the two-phase flow in a
continuous evaporating crystallizer that combines design features
identified as desirable in the previous analyses. The simulations
show vigorous circulation and reduced low-velocity areas, and
suggested potential improvements in circulation up to 10% when
the length of the tubes is maintained at 1.4 m, and up to 24% if the
tubes are shortened to 1.0 m.
3.2 Batch evaporating crystallizers
3.2.1 Basis
A preliminary analysis of the hydraulic design of batch evaporating
crystallizers has been performed based on an 85 m3 A-massecuite
unit installed at Felixton sugar mill, South Africa. Figure 20 and
Table 4 presents the geometry and main design and operation parameters considered.
Fig. 18: Low velocity region and frictional pressure drop numerically predicted for a continuous evaporating crystallizer with different bottom geometries
Fig. 20: Schematic representing a batch
evaporating crystallizer
Table 4: Main design and operating parameters for batch A
massecuite crystallization
Fig. 19: Liquid velocity vectors and low velocity regions (in red)
numerically predicted for a continuous sugar evaporating crystallizer combining desirable design features
916
Nominal
Massecuite volume (m3)
Heating surface (m2)
Ratio downtake/calandria
Circulation ratio
Tube length L (mm)
Tube diameter LOD (mm)
85
516
2.87 / 6.95 (0.41)
2.57
737
101.6
Gas phase
(vapor)
Evaporation (kg/[h · m2])
Density – ρG (kg/m3)
Viscosity – µG (Pa · s)
25
0.20
1.10 · 10–5
Liquid phase
(massecuite)
Density – ρL (kg/m3)
Viscosity – µL (Pa · s)
Height above calandria (m)
1450
6.5
0.95
3.2.2 Effect of the downtake size or circulation ratio in batch
evaporating crystallizers
down-flow. Smith observed that good performance crystallizers
were constructed with a circulation ratio not larger than three,
and proposed this value as a design constraint, which was applied
The ‘circulation ratio’ concept was devised originally by Smith satisfactorily in many subsequent applications. The concept of
(1938) for coil batch evaporating crystallizers to describe the re- the circulation ratio was then extrapolated to the newer calandria
lation between the area available for the massecuite up-flow and crystallizers, and its value was normally around two in the 1950s
(Jenkins, 1958). Today it is considered that
the circulation ratio should not exceed 2.5
in batch evaporating crystallizers, but as
Jenkins described years ago, this parameter
“is still an empirical figure and simply expresses an area ratio which has been found
satisfactory in practice”.
In this analysis the effect of the size of the
downtake has been evaluated numerically
considering downtake channels varying
between 25–65% of the calandria diameter, and corresponding to circulation ratios
between 0.8–8.0. Figure 21 presents numerical results showing lower velocities in
the downtake as its size increases, logical
consequence of the larger cross sectional
area and the corresponding reduction in the
number of heating tubes or heat transfer
surface.
As in the case of continuous evaporating
crystallizers, a vortex is predicted at the top
corner of the calandria, which grows larger
as the size of the downtake increases and
can lead to significant recirculation (Fig.
batch evaporating crystallizer with different downtake size – circulation ratios
21[c]). For small downtake sizes, the predictions indicate an undesirable flow separation below the lower corner of the calandria (Fig. 21[a]), as well as significant velocity gradients near the downtake wall and
the bottom that suggest high shear stresses
and frictional resistance.
Figure 22 presents the circulation that has
been predicted for different downtake sizes
and circulation ratios, showing maximum
values when the downtake is about 37–41%
of the calandria diameter, corresponding to
circulation ratios around 2.5–3.2. The numerical predictions show reasonably good
Fig. 22: Numerically predicted effect of the downtake size and the circulation ratio on the
agreement with the circulation ratios that
circulation in a batch evaporating crystallizer
have been identified in practice as convenient throughout the years.
Figure 23 helps to explain the effect of the downtake, showing an
asymptotic increase in the heat transfer area as the circulation ratio
becomes larger and the cross section of the downtake is reduced.
The curves illustrate a compromise between heat transfer and frictional resistance as the size of the downtake increases. According
to these results, the use of circulation ratios higher than ~ 3.2 (small
downtakes) results in minor gains in heat transfer area, while the
friction in the downtake would be unnecessarily increased. On the
other hand, using circulation ratios below ~ 2.5 (large downtakes)
would result in a rapid and disadvantageous reduction in the heat
exchange area and capacity of the crystallizer.
Fig. 23: Effect of the circulation ratio on the downtake and heat
transfer areas
917
3.2.3 Effect of the geometry of the bottom
in batch evaporating crystallizers
Identifying the ideal bottom shape for batch sugar evaporating
crystallizers has been a major concern for a long time among sugar
technologists. It is considered that the bottom section should promote an even distribution of the massecuite across the calandria,
without restricting circulation or providing stagnant areas, and allow the discharge of massecuite by gravity within an acceptable
time (Rein et al., 2004).
Several alternatives for the design of the bottom of batch evaporating crystallizers have been evaluated numerically using the same
approach utilized previously for continuous crystallizers. An elliptical bottom has been considered initially, changing systematically
the opening between the bottom calandria plate and the bottom wall
towards the downtake (LCB). This separation has been varied covering a range between 0.14 # LCB # 1.4 m, corresponding to relative
values with respect to the external diameter of the calandria or the
body of the vessel between LCB/calandria diameter ~ 0.06–0.21.
Figure 24 presents the frictional pressure drop that has been predicted numerically, indicating lower frictional resistance as the
opening of the bottom and the cross sectional area increase. Based
on the numerical results it can be proposed that the separation of
the bottom must be around LCB ~ 0.7–0.9 m, corresponding to ratios
LCB/calandria ~ 0.10–0.13. Reducing the LCB opening below this
range is predicted to be detrimental to circulation due to a rapid
rise in frictional resistance. On the other hand, larger openings do
not seem to produce a significant benefit, while the footing volume
would be increased.
Figure 25 presents a bottom geometry based on the LCB separation
range identified as desirable (LCB ~ 0.7–0.9 m) and the minimum
Fig. 26: Bottom geometry for batch evaporating crystallizer using
flat walls
limit that has been considered (LS = 0.1 m). A flat bottom wall is
used below the calandria tube plate for convenience, which results
in inclination angles around 16.8° # θ # 20.9°. It is interesting to
note that these slopes show some agreement with values recommended in the literature, where it has been indicated that the bottom is normally constructed with a slope between 17° # θ # 25°
(van der Poel et al., 1998), although in the past it was proposed that
it does not need to exceed θ = 20° (Bosworth, 1959).
Figure 25 shows how the frictional pressure drop reduces and the
volume of the bottom increases as the slope of the bottom wall
increases, illustrating a compromise between friction and footing
volume that makes it difficult to establish optimum values. Combining the numerical results obtained here with practical experience, it can be proposed that the bottom should be constructed with
an inclination within 17° # θ # 21°. The
use of slopes in the upper range (e.g. 20° #
θ # 21°) seems a convenient and conservative alternative, favoring circulation and a
rapid discharge at the end of the boiling.
The bottom geometry below the downtake
presented in Figure 25 has been defined
based on geometrical considerations, with a
progressive change in the cross sectional area
as the massecuite moves from the downtake
to the bottom section below the calandria
tube sheet. Although an ideal smooth rounded bottom has been obtained, no significant
benefits are expected as a result of using this
elaborate shape, and therefore a simplification using a flat wall to approximate this
geometry seems appropriate as illustrated in
Fig. 24: Effect of the separation between the bottom tube plate and the bottom wall (LCB)
Figure 26.
on the frictional pressure drop in a batch evaporating crystallizer predicted numerically
4 Conclusion
Fig. 25: Effect of the bottom slope on the volume and friction in a batch crystallizer
918
The effect of several design parameters of
sugar evaporating crystallizers (vacuum
pans) on massecuite circulation has been
investigated numerically using multiphase
CFD simulations. The results indicated for
A-continuous crystallizers that using a liquid level above the top tube plate of H ~
0.6–0.8 m, a downtake corresponding to
circulation ratios between CR ~ 0.9–1.2, and
shorter tubes (e.g. L ~ 1.0 m) bring potential improvements in circulation and performance. No significant benefits in circulation are
predicted to result from the use of complicated geometries, such
as inclined calandria plates, or from the use of elaborate bottom
shapes, although care should be taken to avoid low-velocity regions
at the bottom. For batch evaporating crystallizers, the optimum size
of the downtake has been predicted to correspond to a circulation
ratio around CR ~ 2.5–3.0, in agreement with practical experience.
Geometrical constraints for the construction of the bottom in continuous and batch sugar crystallizers have been proposed from the
numerical analyses. The flow simulations have suggested potential
increases in circulation up to 10–24% by adjusting the design parameters studied, which result in enhanced efficiency and capacity
of evaporating crystallizers for sugar.
Acknowledgments
The financial support for this project from the Louisiana Board of
Regents (LEQSF2004-07-RD-B-01) is gratefully acknowledged.
Symbols
CR
Circulation ratio
H
Head / Height
J
Superficial velocity (or flux)
L
Length
P
Pressure
U
Velocity
µ
Viscosity
ρ
Density
τ
Circulation period
θ
Angle
Indices
D
Diameter
G
Gas
L
Liquid
Steindl, R.J. (2001): Development of the new generation SRI clarifier design.
Proc. Int. Soc. Sugar Cane Technol. 25, 80–85
Stephens, D.W. (2002). Studies on modeling circulation in sugar vacuum pans.
Ph.D. Thesis, James Cook Univ. Australia
Smith, N. (1938): Circulation in coil vacuum pans. Int. Sugar J. 40, 101–104
and 145–147
Analyse numérique de la conception hydraulique des
cristalliseurs à sucre par évaporation (appareils à cuire sous vide) (Résumé)
L’effet de plusieurs paramètres dans la conception de cristalliseurs à sucre par évaporation (appareils à cuire sous vide) sur la
circulation de la masse cuite a été étudié en utilisant le système
CFD (Computational Fluid Dynamics). Pour l’analyse, le flux à
l’intérieur des cristalliseurs a été simulé en appliquant l’approche
multiphase d’Euler-Euler en résolvant les équations de conservation pour les phases liquide et vapeur et en incorporant les termes
pertinents de poussée et d’échange de force à l’interphase. Cet
article présente les résultats chiffrés obtenus dans l’analyse de la
conception hydraulique des cristalliseurs en identifiant les particularités de conception qui contribuent à augmenter la circulation et
à améliorer les performances.
Análisis numérico del diseño hidráulico de evapocristalizadores de azúcar (tachos) (Resumen)
El efecto de varios parámetros del diseño de evapo-cristalizadores
de azúcar (tachos al vacío) sobre la circulación de la masa cocida
ha sido estudiado utilizando Dinámica de Fluidos Computacional
(CFD). Para simular el flujo dentro de los cristalizadores se aplicó el modelo multifase Euler-Euler, resolviendo las ecuaciones
de conservación para las fases líquida y gaseosa individualmente,
e incorporando términos relevantes de flotación e intercambio de
momento entre fases. Este articulo presenta resultados numéricos
obtenidos en el análisis del diseño hidráulico de evapo-cristalizadores de azúcar, identificando parámetros de diseño que podrían
ayudar a incrementar la circulación y mejorar el desempeño.
References
Bosworth, R. (1959): Evaporation and circulation in the crystallization process.
In: Honig, P. (Ed.): Principles of Sugar Technology. Vol. 2 Crystallization.
Elsevier, Netherlands, 371–393
Bunton, J.J. (1981): Natural convection, two-phase flow, and crystallization in a
vacuum pan sugar crystallizer. Ph.D. Thesis, Louisiana State Univ. USA
Chetty, S.; Davis, S.B.; Raghunandan, A.; Maharaj, S. (2002): A successful
modification to the Dorr 444 clarifier. Proc. S. Afr. Sugar Technol. Assoc.
76, 433–434
Echeverri, L.F.; Rein, P.W.; Acharya, S. (2005): Numerical and experimental
study of the flow in vacuum pans. Proc. Int. Soc. Sugar Cane Technol. 25,
212–221
Echeverri, L.F.; Rein, P.W.; Acharya, S. (2007): Measurements and CFD simulation of the flow in evaporating crystallizers. Sugar Industry 132, 817–823;
also in: Proc. Int. Soc. Sugar Cane Technol. 26
Jenkins, G.H. (1958): Heating surface arrangement and circulation in vacuum
pans. Proc. Qld. Soc. Sugar Cane Technol. 25, 199–207
Mann, A.P.; Dixon, T.F.; Plaza, F.; Joyce, A. (2005): Opportunities for improving the performance and reducing the costs of bagasse-fired boilers. Proc.
Int. Soc. Sugar Cane Technol. 25, 241–247
Poel, P.W. van der; Schiweck, H.; Schwartz, T. (1998): Sugar Technology. Verlag Dr. A. Bartens, Berlin
Rein, P.W.; Acharya, S.; Echeverri, L.F. (2004): Circulation in vacuum pans. J.
Amer. Soc. Sugar Cane Technol. 24, 1–17
Rouillard, E.E.A. (1985): A study of boiling parameters under conditions of
laminar non-Newtonian flow with particular reference to massecuite boiling.
Ph.D. Thesis, Univ. of Natal, South Africa
Steindl, R.J. (2003): Improved Roberts evaporator performance through circulation modeling with CFD. Proc. Aust. Soc. Sugar Cane Technol. 25, Paper
on CD – 14 p
Authors’ addresses: Dr. L.F. Echeverri, Audubon Sugar Institute,
LSU Agricultural Center, St. Gabriel, Louisiana, USA, and Louisiana State University, Department of Mechanical Engineering,
Baton Rouge, Louisiana, USA, e-mail: lechev1@lsu.edu; Dr. P.W.
Rein, Audubon Sugar Institute, LSU Agricultural Center, St. Gabriel, Louisiana, USA; Prof. S. Acharya, Louisiana State University,
Department of Mechanical Engineering, Baton Rouge, Louisiana,
USA.
919

Numerical analysis of the hydraulic design of sugar evaporating

Transcription

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