ISFV14 - 14th International Symposium on Flow Visualization
June 21-24, 2010, EXCO Daegu, Korea
MASS TRANSFER- AND CFD-VISUALIZATION
IN HIGH-VISCOSITY AND NON-NEWTONIAN FLOW
IN REGULAR STRUCTURES
C. Schill*, G. Zheng**, P. Gschwind***
*now: Bühler AG, Pasta and Extruded Products, Uzwil, Switzerland
** now: FMP Technology GmbH, Erlangen, Germany
*** ILB, Food Process Engineering, University of Hohenheim, Germany
KEYWORDS:
Main subject(s): mass transfer visualization
Fluid: high-viscosity Newtonian and shear-thinning non-Newtonian fluids
Visualization method(s): Mass transfer, CFD
Other keywords: regular structures (plate heat exchangers, spacers)
ABSTRACT : Flow characteristics in regular structures (plate heat exchanger geometries,
spacers) have been investigated with a mass transfer method and CFD for high-viscosity as
well as Non-Newtonian fluids, extending the work done by Kottke and his co-workers in [1],[2].
The measuring method is based on convective mass transfer with a coupled chemisorption of
an anionic dye (Acidol-Blau 3 GX) to polyamide. The technique gives the mass transfer
distribution as color density distribution. The evaluation of the measurements is carried out with
image processing through a scanner. The CFD calculations were carried out with ANSYS-CFX.
Fig. 1 shows the geometrical parameters of the corrugated structure, typical for plate heat
exchanger geometry. This is investigated in the low-Reynolds number regime for dimensionless
a 11 and an angle of attack of 15
90°. A comparison
wavelengths /a between 4
= 30°, Re = 1 and a Newtonian 85% glycerolbetween CFD and experiment for /a = 10,
water-mixture is made. Secondary flows and an increase of mass transfer can be observed near
the ridge of the corrugation, as well as low mass transfer in the valleys of the corrugated duct.
Fluids showing a non-Newtonian flow behavior, i.e. a shear-thinning behavior, are investigated
experimentally with the mass transfer method, using a transparent shear-thinning liquid
(Methocel K 15M, n<1) for a variety of spacer-filled channels. Fig. 2 shows the geometrical
parameters for the spacer-filled channel, which are investigated for Reynolds-numbers Re
a 11, an angle of
between 0.1 Re 80, dimensionless wavelengths /a between 4
of 15
90° and n-values between 0.3
n
1. Comparisons with CFD
attack
calculations for creeping flow were performed. The calculated mass transfer in a single
diamond of a spacer filled channel for creeping flow is presented.
1
Fig. 1 Geometric parameters of corrugated
structures
ISFV14 – Daegu / Korea – 2010
Fig.2 Geometric parameters of spacer-filled
channels.
SCHILL, ZHENG, GSCHWIND
1 General Introduction
Regular structures have a number of applications in food technology. Regular corrugated structures in
crosswise orientation are a typical geometry used in plate heat exchangers to enhance heat transfer,
incite turbulence and guarantee mechanical stability (Fig.1). In membrane modules on the other hand,
e.g. ultrafiltration and electrodialysis, regular structures of cylinders in crossed arrays, so-called spacers
spacers, have several functions: on one hand, they are used as stabilisators (supporting nets) between
the membrane sheets, on the other hand they serve as turbulence promoters to homogenize and increase
the heat and mass transfer rates (Fig.2). In spiral-wound modules, they enhance wall shear stress and
promote eddy mixing, thereby reducing wall concentration polarization and fouling.
In this paper, flow characteristics in regular structures (e.g. plate heat exchanger geometries, spacers)
have been investigated with a mass transfer method and CFD for high-viscosity as well as NonNewtonian fluids.
For experimental flow visualization and for the determination of local and integral mass transfer
coefficients in Non-Newtonian media a measuring method for mass transfer is used, which was
developed in previous work for Newtonian media [1],[2]. It is based on convective mass transfer with a
coupled chemisorption of an anionic dye (Acidol-Blau 3 GX) to polyamide.
ANSYS CFX, a finite volume method (FVM) based commercial CFD code was used as the solver in
this work for CFD flow visualization and local mass transfer. For FVM numerical analysis, mesh
generation is used to decompose computational domains into finite volumes and the boundaries
replaced by a number of simple patches. Then for every volume, the governing equations (conservation
of mass, momentum and energy) are solved based upon an integral form of the partial differential
equations. As a mesh generator, ICEM CFD was used to generate mesh. In order to simulate the mass
transfer, an equation describing the concentration of the added species was solved simultaneously with
the Navier-Stokes equation.
2 Experimental and CFD Results
2.1 High viscosity flow in regular corrugated structures
Corrugated structures in crosswise orientation are composed of passages formed by corrugated layers
with opposite orientation of the corrugation lines. The main geometrical parameters of such structures
are the inclination angle , the wavelength , the amplitude a and the shape of the corrugation (Fig. 1).
This is investigated in the low-Reynolds number regime for dimensionless wavelengths /a between
/a 11 and an angle of attack  of 15
90°, see [3].
4
In the numerical simulations with ANSYS CFX the Navier-Stokes-, energy- and concentration
equation were solved. Fully developed, stationary, laminar, isothermal flow is assumed. Here the mass
transfer in single diamonds of the corrugated structure is calculated, assuming periodicity over flow
ISFV14 – Daegu / Korea – 2010
2
Mass transfer- and CFD-visualization in high-viscosity and non-Newtonian flow in regular
structures
length. The boundary layer is finely meshed, for a single diamond, all in all, ca. 800.000 knot points are
used. Figure 3 shows the region of computation. A diffusion coefficient of DAcidol = 5 10-5 m2/s is used.
Fig. 4 shows a comparison between CFD and experiment for /a = 10,
= 30°, Re = 1 and a
Newtonian 85% glycerol-water-mixture. Figure 4, left side, shows that the mass transfer on the front
side of the structure is better than in the trough of the structure. This is caused by an impingement of
the flow on the height of the structure, which leads to a higher mass transfer, shown by the greenyellow color and the corresponding higher Shx numbers in the CFD results. On the lee side of the
altitude lines and in the separation zones in the troughs of the structure the mass transfer is distinctly
lower, characterized by the blue color and the corresponding lower Shx numbers.
Fig. 3 Computational region
Fig. 4 Computed and experimental mass transfer
in a single diamond of cross-flow corrugated structures,
Newtonian flow, /a= 10, = 30°, Re =1.
The dimensionless Sh-number Shx is calculated as
( x ) dh
D Acidol
Sh x
c / n wall dh
c m c wall
(1)
The dimensionless Re-number for the corrugated structures,
Re h
w dh
(2)
is based on a hydraulic diameter of
dh
4 ai
k fi
2
ai
B
(3)
Experiments were carried out in a water channel. An 85% glycerol-water-mixture was used to achieve
a high viscosity flow, giving a dynamic viscosity of = 799 mPas (20°C). To the mixture an anionic
dye (Acidol-Blau 3 GX) as transferable reacting mass component is added in very small concentration.
ISFV14 – Daegu / Korea – 2010
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SCHILL, ZHENG, GSCHWIND
One of the walls is coated with a polyamide foil. The transferred dye is adsorbed and chemically bound
in the surface layer of the polyamide. The technique gives the local mass transfer distribution directly
as color density distribution (Fig.4, right side).
Flow direction here is from the left to the right. The white area without mass transfer is caused by the
contact point of the corrugated structures. Following this point, a streak with very low mass transfer is
observed. A warped line with low mass transfer can also be observed, both in computational and
experimental mass transfer.
The mass transfer for cross-wise corrugated structures in high viscosity fluid for different wavelengths
and inclination angles is shown in the following figure, (Fig.5).
Fig. 5 Visualization of mass transfer in corrugated structures, 5.5
Oa 10, 15
60°, Re = 1.
2.2 Non-Newtonian Flow in Spacer-filled channels
Numerous foods show a non-Newtonian flow behavior. The majority shows a shear-thinning behavior,
which is investigated here in detail. The aim of this work is to establish a method to analyze flow and
transport phenomena in various geometry for non-Newtonian media, extending the work done in [1],
[2].
As example for the Non-Newtonian flow, the flow and transport phenomena in rectangular channels
with spacers are analyzed, typical for membrane separation processes with viscous media and small
channel heights. The main geometrical parameters of these structures are the inclination angle , the
wavelength , the amplitude a and the shape of the spacer structure. Fig. 2 shows the geometrical
parameters for the spacer-filled channel.
They are investigated for Reynolds-numbers Re between 0.1 Re 80, dimensionless wavelengths O/a
between 4 Oa 11, an angle of attack M of 15
90° and n-values between 0.3 n 1.
ISFV14 – Daegu / Korea – 2010
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Mass transfer- and CFD-visualization in high-viscosity and non-Newtonian flow in regular
structures
In the experiments, a transparent shear-thinning liquid (Methocel K 15 M, n
material, which can be described with a modified power-law behavior (Eq.4).
m
0
⎛ ⎞
1 ⎜ 0⎟ &
⎝K ⎠
1) is used as working
(5)
1 n
Through a variation of the concentration of the added material as well as the temperature, the viscosity
can be adjusted in a wide range (Table 1), which is interesting for numerous foods. The viscosity is
measured with a rotational viscometer.
C
[wt%]
0
0.25
0.5
0.75
1
1.25
n
[-]
1
0.57
0.51
0.47
0.36
0.35
0
[Pas]
0.015
0.11
0.16
0.95
2.26
K
[kg/ms2-n]
0.001
0.27
0.87
1.52
8.10
14.29
Table 1 Modified power law rheological parameters for Methocel K15M in different concentrations.
The Reynolds-number here is calculated as a Non-Newtonian Reynolds-number for a modified powerlaw model with
w dh
R eM
0
(a
b )
(1
)
(6)
a*,b* being geometric correction parameters for the spacers, and * a so-called Reynolds correction
factor, see [6]. For a single diamond, the specific hydraulic diameter can be calculated to
dh,d
4 Vf
Sw
8
1
a
4
a
(7)
2
In Figure 6, the color intensity directly corresponds to the local transferred mass. Flow direction is from
the left to the right. The white areas without mass transfer are caused through the contact of the spacer
structure.
Fig. 6 Experimental wall mass transfer for spacer diamonds over flow length for Non-Newtonian flow,
/a = 11, = 60°, Re = 1, c = 0.5% Methocel.
ISFV14 – Daegu / Korea – 2010
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SCHILL, ZHENG, GSCHWIND
ANSYS CFX, a finite volume method (FVM) based commercial CFD code was used as the solver in
this work. For FVM numerical analysis, mesh generation is used to decompose computational domains
into finite volumes and the boundaries replaced by a number of simple patches. Then for every volume,
the governing equations (conservation of mass, momentum and energy) are solved based upon an
integral form of the partial differential equations. As a mesh generator, ICEM CFD was used to
generate mesh. To save computing time, the simulation was focused on single diamonds of the spacer
grid. Figure 7 shows the mesh for a single-diamond of the spacer-filled channel.
Figure 8 shows the calculated mass transfer in a single diamond of a spacer filled channel for creeping
flow for very low Re-number (Re = 10-5). Red corresponds to high mass transfer and blue to low mass
transfer. Mass transfer near to the contact lines is found to be very low. The ratio of this very low mass
transfer area was found to be a function of /a, not of the inclination angle . The smaller the
wavelength is, the larger the region with very low mass transfer.
Fig. 7 Computational domain of a
single diamond of a spacer-filled channel
Fig.8 Computed mass transfer for creeping flow in a
diamond of a spacer-filled channel, NonNewtonian flow, /a = 11 = 15°, Re = 10-5.
Three-dimensional flow visualization was carried out for the single diamonds under periodic interface
boundary conditions, which corresponds to fully developed laminar flow (Fig.9). Creeping flow was
simulated under low Reynolds number conditions to avoid flow separation. Flow strongly depends on
geometry parameters, (Fig. 9).
ISFV14 – Daegu / Korea – 2010
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Mass transfer- and CFD-visualization in high-viscosity and non-Newtonian flow in regular
structures
Fig. 9 Computed flow for single diamonds of a spacer-filled channel, 4
a
11, 15
60°.
Three basic flow types can be observed, a “corkscrew flow” in spacer with small inclination angles and
large wavelengths, “channel flow” for large inclination angles and small wavelengths, and an
intermediate “mixing flow” for in-between inclination angles and wavelengths, (Fig. 9), for higher Renumber Newtonian flow, see [4], [5].
ISFV14 – Daegu / Korea – 2010
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SCHILL, ZHENG, GSCHWIND
3 Nomenclature
A
A’
a
ai
a*
B
b
b*
c
D
dH
L
K
kfi
n
Re
Sh
Sf
Vf
w
projected surface area
developed surface area
amplitude
amplitude sine wave
geometric correction factor
duct width
transferred mass density
geometric correction factor
concentration
diffusion coefficient
hydraulic diameter
length of test section
fluid consistency
A’/A
flow index
Reynolds number
Sherwood number
free cross section
volume
mean flow velocity
Greek symbols
[m2]
[m2]
[m]
[m]
[-]
[m]
[g/m2]
[-]
[m2/s]
[m]
[m]
[kg/ms2-n]
[-]
[-]
[-]
[-]
[m2]
[m3]
[m/s]
&
m
mass transfer coefficient
Reynolds correction factor
shear rate
viscosity
apparent viscosity
viscosity
wavelength of the sine duct
wavelength of the spacer
viscosity
inclination angle
[m2/s]
[-]
[1/s]
[mPas]
[Pa s]
[mPas]
[m]
[m]
[m2/s]
4 References
1.
2.
3.
4.
5.
6.
Kühnel, W, Kottke, V., Visualization and determination of mass transfer at solid walls in fluid flow,
Int. Symposium on Fluid Control, Measurement and Visualization, Flucome, Toulouse, France 1994.
Kühnel, W. Experimentelle Methoden zur Sichtbarmachung und Messung des lokalen
Stoffübergangs an festen Wänden, Dissertation, University of Hohenheim, 1997.
Schill, C. Strömungs- und Transportvorgänge bei kleinen Reynoldszahlen in gekreuzten Strukturen
von Plattenwärmeübertragern, Dissertation, University of Hohenheim, 2010 (in press).
Zimmerer, C. Strömungs- und Transportvorgänge in Kanälen mit gekreuzten Gitterstrukturen,
Dissertation, University of Hohenheim, 1998.
Zimmerer, C, Gschwind, P, Gaiser, G and Kottke, V. 2002, Comparison of heat and mass transfer in
different heat exchanger geometries with corrugated walls, Experimental thermal and fluids Science
Vol. 26 (No. 2-4), pp 269-273, 2002.
Zheng, G. Neue Messtechniken für die Analyse der Strömungsvorgänge und des örtlichen
Stoffübergangs in nicht-Newtonschen Fluiden, Dissertation, University of Hohenheim, 2010 (in
press)
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ISFV14 – Daegu / Korea – 2010
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