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Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
convection and radiation. The model was only used to “interpolate” experimental data to the entire
furnace so that thermal expansion of the vessel could be calculated. This approach cannot be used
for design, i.e. in the absence of experimental data. A design model must properly capture radiation
and convection effects.
A schematic of the furnace is shown in Figure 1. Equipment such as radiant heaters, ceramic
insulation, and metal shrouding are used to regulate the temperature. Control of heat rejection
within the furnace is provided by two water cooled flanges.
Figure 1. DMO-2 furnace.
Heaters, ceramic insulation, and metal shrouding affect heat transfer in the furnace. Panels
made of stainless steel shrouding are used to package six radiant heaters embedded in insulation
into a unit that can easily be mounted around the contours of the furnace. They are offset by a 25.4
mm (1-inch) air gap, as shown in Figure 2. The air gap influences heat transfer within the furnace
in three major ways.
2
Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
1) Radiant heaters are more efficient when placed 25.4 mm (1-inch) away from the furnace wall
because radiant energy warms the air along the wall and makes the temperature uniform.
2) Heat transfer is enhanced through the air gap by drawing air from an opening at the bottom of
the furnace and allowing it to travel along the furnace walls.
3) Heat loss from the system is observed from a “chimney effect” and is due to a lack of insulation
covering the air gap near the lid and the upper 38.1 mm (1.5-inches) of the furnace.
The “chimney effect” is described in greater detail in the Methodology section of this report. The
panels are necessary to insulate the furnace and protect the outside environment from the hazards
associated with high temperatures.
Figure 2. Equipment and design features.
The operation of the thermal control system involves signal processing of thermocouples, a
digital-to-analog converter (DAC), a personal computer (PC), LabView software, and radiant
heaters. The LabView software controls temperature data acquisition and provides feedback
control logic to regulate the furnace temperature through the radiant heaters. In the furnace,
thermocouples (TC) 2 and 4 are used to regulate temperature. They are located inside tubes
3
Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
welded to the interior panels of the furnace, protecting them from direct radiation and forced
convection effects (see Figure 2 ).
Water cooled flanges are a design feature to extract heat from locations where the furnace is
attached to the lid and calciner. The purpose of the water cooled flanges is to cool the furnace in
areas where O-rings are placed. An internal vacuum is maintained inside the furnace. Thermal
expansion of the O-ring material will initiate misalignment between the two parts and disrupt the
vacuum, as shown in Figure 3. A pumping system is used to circulate water through the flanges
and a mass flow meter is used to record the total flow rate from the main line in the system.
LabView provides data acquisition for the mass flow meter. Environmental conditions are
controlled inside of the furnace by regulating the flow of gas which promotes oxidation reaction.
The air inside of the furnace is heated due to radiation and forced convection from the gas mixture
pumped into the furnace.
Figure 3. O-ring Locations.
The purpose of this study is to evaluate the stresses on the furnace walls due to combined
thermal and pressure loading using a finite element computer software (ANSYS Workbench 10.0).
4
Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
In order to predict stresses accurately, a reasonable temperature profile is required. Convection and
radiation play an important role in establishing the temperature profile on the furnace walls by
heating air surrounding the furnace. One approach to predicting a realistic temperature profile
would be to develop a Computational Fluid Dynamics (CFD) model where convection and
radiation heat transfer mechanisms are explicitly modeled. Another approach to capture the
temperature profile of the furnace is to use a conduction-based model. This latter method was
selected and experimental data gathered during acceptance testing was used to adjust and validate a
simplistic thermal model. A structural analysis is then completed to evaluate combined stresses
and deflections due to thermal and pressure loading. Test data and finite element models are
described in further detail in the Methodology section of this report.
2.0 References
1. M. D. Keddy, H. E. Martinez, K. J. Fisher, and D. Wedman, “Acceptance Test Report for
the Direct Metal Oxidation and Calibration Furnace System (DMO-2),” Los Alamos National Laboratory, LA-CP 02-542, 2002.
2. M. Keddy, [electronic mail] to [Theresa Montoya], September 19, 2005.
3. H. E. Martinez, “Structural Stability of the DMO Furnace,” ESA-AET Internal
Document, June 2005. 4. Department of Defense, Structural Alloys Handbook Metals and Ceramics Information
Center, Battell, Columbus, Ohio, pp 8 to 69, 1989.
5. Drawing Package No. 90Y-220020, sheet 4-6, ESA-AET Technical Drawing Packet (Furnace Assembly), July 2002.
6. Drawing Package No. 90Y-220035, ESA-AET Technical Drawing Packet (6-inch Water
Cooled Flange), October 2002.
7. Dawing Package No. M-PM-F-0269, ESA-AET Technical Drawing Packet, 2002. 8. H. E. Martinez and D. Taylor, Direct Metal Oxidation Testing Set-Up Drawing, ESA-
AET Technical Drawing Packet. 9. F. P. Incropera and D.P. DeWitt, Fundamentals of Heat Transfer, John Wiley & Sons,
1981. 10. Y. A. Cengel, Heat Transfer A Practical Approach, The McGraw-Hill Companies, Inc.,
pp 179 to 201 and 416 to 425, 1998.
5
Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
11. W. Young and R. G. Budynas, Roark’s Formulas For Stress And Strain, 7th edition.,
McGraw-Hill, New York, pp 502 to 508, 2002.
3.0 Computer Program Disclosure Information Computer Program Not Used
Software Vendor Software Program (Name/Version) Verification Document SolidWorks Corporation PADT Microsoft
SolidWorks 2005 ANSYS Workbench 10.0 Excel 2003
4.0 Methodology
As mentioned in Section 1, a conduction-based model is created using ANSYS Workbench
10.0 to capture complicated heat transfer mechanisms such as convection and radiation. Thermal
data gathered during acceptance testing are used to adjust model parameters and to predict a realistic
temperature profile for the furnace. Stresses and deformations corresponding to the thermal loading
are then evaluated. Stresses and deformations due to pressure loading are also calculated using the
same model. Results from both studies are then combined to evaluate total stress and deformation.
The Test Report for the Direct Metal Oxidation Furnace System (DMO-2) is the source of
existing data from experimentation conducted by members of ESA-AET and NMT-15 [1]. Test data
such as heater power inputs, heat rejection to the water cooled flanges, and thermocouple
measurements were collected. Heater power inputs were obtained by measuring the voltage of
heaters in the oxidation furnace. This was done as a preliminary check before any experimentation
was conducted. Heat rejection to the water cooled flanges was determined with calorimetry. A
temperature differential gauge measured water temperature at the inlet and outlet of the piping
system and a mass flow meter measured the total flow rate of water for the system. The results were
recorded in LabView and were used to assess the amount of heat rejection into the water.
Thermocouple measurements were taken at various locations of the furnace, using either a
permanent fixture or a temporary means to collect data. Thermocouples that are a permanent fixture
of the furnace are situated inside a cylindrical housing welded to the inside panels of the furnace,
protecting them from direct radiation and forced convection effects. There are only two
thermocouples attached in this way, thermocouples 2 and 4 (TC2 and TC4, see Figure 2). They are
used by the feedback control system as a temperature control switch for the heaters. They are
located on the same side of the furnace wall and were used to calibrate the finite element model.
The remaining thermocouples were welded to exterior locations of the furnace, were never shielded
6
Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
from radiation and convection effects, and were a temporary means to collect data during acceptance
testing. Temperature measurements on the lid were recorded by thermocouples 19 and 20.
In the simplistic thermal model, two blocks of material are used to simulate the air inside the
furnace and the air from the “chimney effect.” A block of material is modeled inside the furnace to
represent the inside air. Another block of material surrounds the outside of the furnace to simulate
the air circulating inside the chimney passages. The conductivity of both blocks of material is set to
a large number of approximately 10 times the conductivity of copper, so the temperature would be
uniform.
Two contact layers of constant thickness function as an intermediate material to mimic heat
transfer between the furnace and the blocks of material used to simulate air, as depicted in Figure 4.
These contact layers were explicitly modeled since ANSYS Workbench 10.0 does not allow a user
to define a heat transfer convection coefficient between two surfaces. The thermal conductivity
assigned to each contact is very low and both contact layers are assigned the same value. The
conductivity of the two contact layers (one on each side of the furnace wall) were adjusted to match
the experimental temperature data recorded for thermocouples 2 and 4.
Figure 4. Furnace thermal model schematic.
7
Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
Boundary conditions are used throughout the thermal model to take into account the heat
losses through the water cooled components (calciner flange and lid), the heat losses through the
sides (“chimney effects”), and the heat loss through the lid by natural convection. Heat transfer
coefficients are applied on the water cooled flanges and on the furnace lid to simulate water cooling
and natural convection.
As mentioned in Section 1, an air gap at the top of the insulation panels near the lid creates a
“chimney effect” by drawing air from the bottom of the furnace. While the air travels along the
furnace walls towards the lid, the temperatures along the walls becomes more uniform. Based on
experimental data, the heat losses through this air gap is significant. Approximately half the input
power is lost from this region. To account for this heat loss, constant power loss is applied on the
upper surface of the “chimney” as shown in Figure 5. Boundary conditions are described in further
detail in the Design Inputs and Assumptions section of this report.
Figure 5. Heat loss from “chimney effect.”
Once a reasonable temperature profile is established, it is possible to calculate stresses and
deflections due to thermal loading. The model used in this analysis only includes the furnace itself.
8
Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
The temperature profile previously calculated serves as a boundary condition for the structural
calculations. The same model is then used to predict stresses and deflection from a vacuum loading
of 53,329 Pa (~7.7 psi). Since the vacuum pressure is lower than ambient pressure, a gauge pressure
of 47,996 Pa (~ 7 psi) is applied to the inside of the furnace. Finally, the solutions from both studies
are combined to yield a Von Mises equivalent stress value and the total deformation.
5.0 Design Inputs & Assumptions
Design inputs and assumptions used to set-up the thermal and the structural finite element
models are outlined in the following sections. Heater heat inputs and heat losses attributed to water
cooled flanges, natural convection of the lid, and “chimney effects” are summarized as well. Also
included are thermal and structural material properties. Note that the DMO-2 furnace is
symmetrical, so that only half of the actual geometry is modeled in this analysis.
5.1 Heater Power Inputs
During acceptance testing, the amount of power used to heat the furnace was measured by
Mike Keddy of ESA-AET [1]. He determined that the total power used by six heaters was 3,340
Watts by measuring the voltage contribution from each heater. Since half of the furnace geometry
is modeled, a total of 1,670 Watts are applied as continuous power inputs at various locations on
the furnace walls. Heater sections and their corresponding power inputs are shown in Figure 6.
• Heater Section 1 is assigned 204 Watts.
• Heater Section 2 on the Motor side is assigned 374 Watts.
• Heater Section 2 on the Calciner side is assigned 374 Watts.
• Heater Section 3 is assigned 718 Watts.
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Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
5.2 Heat Losses from Water Cooled Flanges
Heat rejection into the water cooling system was recorded by Mike Keddy [1 and 2]. A
temperature rise of 1.7°C in the water was recorded for a total flow rate of 204 grams per second
and corresponds to a heat loss of approximately 1,500 Watts. Standard textbook correlations are
used to calculate heat transfer coefficients for the water flowing through rectangular cooling
channels. The heat transfer coefficients applied to the water cooled flange near the lid and the 6-
inch water cooled flange are 2,200 W/m2°C and 3,700 W/m2°C, respectively (see Figure 7). The
water temperature is set to 20°C.
5.3 Heat Losses from Lid
Standard textbook correlations are used to derive heat losses resulting from natural convection
on the furnace lid. A heat transfer coefficient of 7 W/m2°C is assigned to the upper side of the lid,
while a heat transfer coefficient of 2 W/m2°C is assigned to the area underneath the flange near the
top of the furnace, as shown in Figure 7. Both are subjected to an ambient temperature of 20°C.
Heat transfer coefficients were not assigned to the vertical edge of the lid because heat losses from
this area are negligible.
Figure 6. Heater locations.
10
Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
Figure 7. Heat losses from the water cooled flange and lid.
5.4 Heat Losses from “Chimney Effect”
Out of 3,340 Watts dissipated by the heaters, about 1,500 Watts are rejected through the water
cooling system. The remaining 1,840 Watts in heat losses are shared by the “chimney effect” and
the heat lost through the lid by natural convection. To account for the heat lost through the
“chimney effect” a constant power loss of 920 Watts (i.e. 1,840/2) is initially applied on the upper
surface of the chimney (see Figure 8). However, this does not take into account additional heat
losses from the lid. To evaluate the heat losses through the lid, the model was run with the
parameters listed above. The analysis showed that approximately 66 Watts were lost through the
lid. As a result, the chimney losses were adjusted down to 854 Watts and were distributed along
the upper surfaces of the chimney. The heat losses were split between three different areas
(chimney 1, 2, and 3). The total area for chimney 1, 2, and 3 is 19,684 mm2 (30.51 in2).
11
Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
5.5 Vacuum Pressure
A vacuum of 53,329 Pa (~7.7 psi) is maintained inside the furnace while heated [1]. As a
result, a gauge pressure of 47,996 Pa (~7 psi) is assigned to the inside walls of the furnace in the
structural analysis. Note that atmospheric pressure at sea level 101,325 Pa (14.7 psi) is used to
calculate gauge pressure in the FE analysis. Using the atmospheric pressure at sea level yields a
more conservative gauge pressure as opposed to using the atmospheric pressure for Los Alamos,
NM (75,994 Pa. or 11 psi).
It should be emphasized that deflection measurements were collected for the furnace during
initial thermal cycling of the system at 600°C and a vacuum load of 1 atmosphere of pressure at
7,200 ft (75,994 Pa or 11 psi, Los Alamos, NM) [3]. The resulting gage pressure was therefore
smaller – 3 psi. However, because deflections caused by vacuum loading are insignificant
compared to deflections caused by thermal loading, these deformation test data can still be used for
comparison purposes.
Chimney Location & Power Loss
• Chimney 1 has an area of
5,413 mm2 (8.39 in2) and is
assigned a power loss of -206.5
Watts.
• Chimney 2 has an area of
8,858 mm2 (13.73 in2) and is
assigned a power loss of -441.1
Watts.
• Chimney 3 has an area of
5,413 mm2 (8.39 in2) and is
assigned a power loss of -206.5
Watts.
Figure 8. Heat losses from “chimney effect.”
12
Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
5.6 Material Properties
In the thermal analysis, temperature dependent properties are used for the furnace walls. The
thermal conductivity for AISI 304 Stainless Steel is listed in Table 1 and graphed in Figure 9 [4].
For all other parts, a constant thermal conductivity is assumed. The two contact layers (one on
each side of the furnace wall) are assigned a conductivity of 0.1 W/m°C, while the air inside of the
furnace and the air inside of the “chimney” passage are both assigned a conductivity of 4,000
W/m°C.
Table 1. AISI 304 Stainless Steel, temperature dependent thermal conductivity.
Temperature
°C
AISI 304
Stainless Steel
Thermal
Conductivity
CmW°
-73.15 12.6
126.85 16.6
326.85 19.8
526.85 22.6
726.85 25.4
926.85 28.0
1226.85 31.7
Figure 9. AISI 304 Stainless Steel, temperature dependent thermal conductivity.
Room temperature values for all thermo mechanical properties (i.e. Young’s modulus,
Poisson’s ratio, and coefficient of thermal expansion) are used for structural analyses. Properties
used for the structural models are listed in Table 2. Note that using properties at room temperature
to predict the stresses is a reasonable approximation as the properties change only slightly when the
temperature is increased to 600°C. The Young’s modulus decreased slightly with temperature (by
about 22.3% between 20°C and 649°C). The coefficient of thermal expansion increases by 9.6%
13
Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
between 0°C and 600°C. The Poisson’s ratio increases by 3.4% from room temperature to 600°C.
Table 2. AISI 304 Stainless Steel Material Properties
Value
Units
Young’s Modulus 153 GPa
Poisson’s Ratio 0.29 --
Thermal Expansion 1.87e-5 1/°C
6.0 Unverified Assumptions
No unresolved items and assumptions.
7.0 Model Verification (Added by Author)
See Main Calculation.
8.0 Main Calculation
The geometry for the DMO-2 furnace was recreated from drawing packages No. 90Y-
220020 and 90Y-220035 from ESA-AET files [5-7]. A Computer Aided Drafting (CAD) model of
the furnace assembly was created using SolidWorks 2005 and imported as a parasolid file into
ANSYS Workbench 10.0, a commercial finite element code.
8.1 Thermal Model 8.1.1 Geometry and Mesh
Inside the furnace, a block of material is used to simulate the inside air. Another block of
material 25.4 mm thick (1-inch thick) surrounds the outside of the furnace and is modeled to
simulate the air circulating inside the “chimney” passages. Two contact layers, 5.08 mm thick
(0.2-inches thick), are added to mimic heat transfer between the furnace and air circulating along
the outside walls. The contact layers were explicitly modeled because ANSYS Workbench 10.0
does not allow a user to define a convection coefficient between two surfaces. A schematic of the
14
Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
geometry used is shown in Figure 10.
Figure 10. Thermal model geometry.
Tetrahedral solid elements with 3 degrees of freedom per node (translation in X, Y, and Z
directions) are used throughout the model. The average element size is 12.7 mm. The thermal
model has a total of 138,306 nodes and 57,449 elements. Figure 11 shows the tetrahedral mesh.
Figure 11. Thermal model mesh.
15
Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
8.1.2 Loads and Boundary Conditions
Surface heat fluxes are applied to the outside of the furnace walls to simulate the heat
generated by the heaters. The total power used by the six heaters was 3,340 Watts and the relative
contribution of each heater was measured with a voltmeter during acceptance testing. Since half of
the furnace geometry is modeled, a total of 1,670 Watts are applied at four locations along the
furnace wall. Heater sections and their corresponding power inputs are represented in Figure 12.
• Heater Section 1 is assigned 204 Watts.
• Heater Section 2 on the Motor side is assigned 374 Watts.
• Heater Section 2 on the Calciner side is assigned 374 Watts.
• Heater Section 3 is assigned 718 Watts.
Figure 12. Heater locations.
A pumping system with a total flow rate of 208 grams per second or 1.1 gallons per
minute capacity was used to cool the DMO-2 unit and was measured by Mike Keddy of ESA-AET
[1 & 2]. The flow was divided between the upper water cooled flange and the 6-inch flange
connected to the calciner [8]. The flow rate in each diversion was never measured.
Standard correlations to characterize convective heat transfer for internal flows of non-
16
Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
circular geometries for turbulent flow were used [9]. The heat transfer coefficient is given by:
⎟⎠⎞
⎜⎝⎛
Dk4.05
4
PrRe=h 023.0 , (1)
where Re is the Reynolds number, Pr is the Prandtl number, h is the heat transfer
coefficient of water, D is the hydraulic diameter, and k is the thermal conductivity of water. The
Reynolds number is given by:
υVD
=Re , (2)
where V is velocity of water, D is the hydraulic diameter, and υ is the viscosity of water.
The hydraulic diameter is defined as:
PAD 4
= , (3)
where A is the area of flow and P is wetted perimeter. Table 3 and 4 show the heat
transfer coefficients for the water cooled flange in the lid and the 6-inch water cooled flange,
respectively. Flow rates between 0.33 and 1.1 gallons per minute are used to estimate the
corresponding heat transfer coefficients. The lower value for flow rate corresponds to the onset of
turbulent flow for each case. All the water properties used in this calculation are evaluated at
20°C. Mid-range values of 2,200 W/m2°C and 3,700 W/m2°C are selected for the water cooled
flange near the lid and for the 6-inch water cooled flange, respectively.
Note that the heat transfer coefficients listed above result in a slightly elevated flow rate,
predicting a flow rate of 1.43 gpm where the actual rate is only 1.1 gpm. However, since in the
final simulation analysis, the heat rejected through the cooling system is restricted to be 1500 W, in
agreement with experimental measurements, the additional flow rate does not significantly affect
the final analysis, as demonstrated by the close agreement with experimental values for the
thermocouple locations along the sides of the furnace (see section 8.1.3). The local heat transfer
coefficients related to the cooling system are only approximate though and the thermal profiles
near these systems are also approximations of the actual system conditions. Nevertheless, since the
walls of the furnace experience the highest thermally-induced stresses and therefore thermally-
induced strains, the plastic deformation seen in the finite element simulation is a reasonable
approximation of the actual behavior of the system.
17
Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
Table 3. Constants and parameters used to find the heat transfer coefficient for the water cooled flange near the lid.
Constants Symbol Value UnitsWater Reference Temperature T 20 °C
Water Temperature Rise ΔT 1.7 °CWidth w 15.7 mmHeight h 7.8 mm
Cross Sectional Area A 1.22E-04 m2
Perimeter P 4.70E-02 mViscosity ט 1.02E-06 m2
Prandtl Number Pr 7.060 --
Quantity Symbol UnitsFlow Rate Q 0.44 0.8 1.1 GPMVelocity V 0.23 0.41 0.57 m/s
Reynolds Number ReD 2323 4223 5806 --
Heat Transfer Coefficient h 1435 2316 2988 W/(m2°C)
Table 4. Constants and parameters used to find the heat transfer coefficient for the 6-inch water cooled flange.
Constants Symbol Value UnitsWater Reference Temperature T 20 °C
Water Temperature Rise ΔT 1.7 °CWidth w 12.7 mmHeight h 5.1 mm
Cross Sectional Area A 6.45E-05 m2
Perimeter P 3.56E-02 mViscosity ט 1.02E-06 m2
Prandtl Number Pr 7.060 --
Symbol UnitsQuantityFlow Rate Q 0.33 0.8 1.1 GPMVelocity V 0.32 0.78 1.08 m/s
Reynolds Number ReD 2304 5586 7681 --
Heat Transfer Coefficient h 2046 4154 5360 W/(m2°C)
18
Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
Heat is lost through the lid and the area underneath the water cooled flange by natural
convection. A closed-form analytical solution for free convection over a surface is calculated from
natural convection correlations for the average Nusselt number [10] as:
Nukhδ
=
( )
, (4)
where h is the heat transfer coefficient of air, k is the coefficient of thermal conductivity
of air, δ is the length of the object, and Nu is the Nusselt number.
The average Nusselt number is the dimensionless number representing the temperature
gradient of a surface. It is a function of the Rayleigh number, Ra, which is a measure of the
relative magnitude of buoyancy and viscous forces in the fluid. The Rayleigh number is given by:
2
3 Prυ
δβ ∞−=
TTgRa s , (5)
where g is the acceleration of gravity, β is the volumetric thermal expansion of air, υ is
kinematic viscosity of air, δ is the height of the plate, Ts is the surface temperature of the plate, and
T∞ is the temperature of the surrounding air. All fluid properties are to be evaluated at the film
temperature, Tf, defined by:
( )∞+= TTT sf 21 . (6)
Simple relationships for the average Nusselt number for various geometries are given in
Table 5 along with the range of Raleigh numbers in which the relation is applicable.
Table 5. Equations for heat transfer coefficients of a horizontally heated plate.
Position
Range of Ra
Nusselt Number
Horizontal plate with hot
surface facing up
104-107
107-1011
Nu= 0.54 Ra1/4
Nu= 0.15 Ra1/3
Horizontal plate with hot
surface facing down 105-1011 Nu= 0.27 Ra1/4
A summary of the variables used to calculate the free convection heat transfer coefficients
for the lid are listed in Table 6. The heat transfer coefficients were evaluated for a range of film
19
Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
temperatures. Mid-range values for the lid with heat face facing up is determined to be 7 W/m2°C
and the hot surface facing down is determined to be 2 W/m2°C. Heat transfer coefficients were not
assigned to the vertical edge of the lid because heat losses from this area are negligible.
Table 6. Heat transfer coefficients for the furnace lid.
Quantity Symbol Lid Flange Units
Reference Temp T 150 150 °C
Temperature of Surrounding T∞ 20 20 °C
Film Temperature Tfilm 358 358 K
Volumetric Thermal Expansion β 0.0028 0.0028 K-1
Height of Plate δ 0.3556 0.3556 m Acceleration of Gravity g 10 10 m/s
Rayleigh Number Ra 2.E+08 2.E+08 -- Nusselt Number Nu 87 18 --
Heat Transfer Coefficient h 7 2 W/m2°C
The heat rejected from the “chimney effect” is applied as a continuous heat loss in the
finite element model. The power losses from the “chimney effect” were determined by subtracting
the total power from the heaters, 3,340 Watts, from the heat rejected to the water cooled flanges,
1,500 Watts, to yield 1,840 Watts. The remaining power losses must be shared between the
“chimney effect” and the heat loss due to free convection of the lid. An iterative process was used
to vary the amount of heat lost from the “chimney effect.” Heat transfer coefficients were assigned
to the water cooled flanges and lids along with a continuous power input for the heaters. The value
for the “chimney effect” was varied until a resulting heat loss of 1,500 Watts was obtained from
the water cooled flanges. Since only half of the geometry is modeled, the boundary conditions are
adjusted for half symmetry. In the first iteration, 920 Watts of power was assigned as a continuous
power loss, however an energy balance showed that the amount of heat rejected to the water cooled
flanges was slightly lower than 1,500 Watts. As a result the “chimney” losses were adjusted down
to 854 Watts, resulting in a total of 1,708 Watts of power for the full furnace assembly. The heat
losses were adjusted based on the area on the upper side of the chimney.
20
Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
No symmetry boundary condition is needed along the furnace mid-plane since, by default,
surfaces on that plane are adiabatic. There is no heat transfer across the plane of symmetry as
shown in Figure 13.
Figure 13. No boundary conditions are needed on the symmetrical face of
thefurnace.
The thermal conductivity of the two contact layers was adjusted so that the temperatures
predicted by the model at thermocouples 2 and 4 match closely the experimental data. Better
agreement between the finite element model and the experiment is observed when the contact layer
is assigned a thermal conductivity of 0.1 W/m2°C. (The locations of thermocouples 2 and 4 are
shown in Figure 15.) In this case, the temperatures predicted by the model at thermocouples 2 and
4 are, respectively, 507°C and 588°C, compared to experimental data of 525°C and 600°C [1, pg.
15].
8.1.3 Results
Results of the thermal study are shown in Figure 14. As expected, the inside and outside
air layers have a uniform temperature due to their high conductivity. Hiding both the resistance
and bulk layers reveals the temperature profile on the furnace as shown in Figure 15 and 16. Heat
losses from the “chimney effect” and the water cooled flange cause a steep temperature gradient in
the upper half of the furnace.
21
Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
Figure 14. Thermal model, temperature distribution.
Figure 15. Thermal model, thermal distribution on the furnace walls (interior view).
22
Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
Figure 16. Thermal model, temperature distribution on the furnace walls (exterior view).
Table 7 shows a comparison between the temperatures predicted by the FE model and the
experimental data at thermocouple locations 2 and 4. Also listed in the table is the temperature
differential between the two thermocouples (TC 4-TC 2). The results of the finite element model
are within 8% of the experimental values and fall within an acceptable range.
Table 7. Temperatures at TC2 and TC4.
Thermocouple
Experimental *
(°C)
FE Model (°C)
Percent Difference
TC 2 525 507 3%
TC 4 600 588 2%
TC 4-TC 2 75 81 8%
Temperatures recorded during acceptance testing by exterior thermocouples placed
throughout the furnace are compared to temperatures predicted by the finite element model (see
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Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
Figure 17 and 18). A diagram listing the thermocouple locations are provided in the Acceptance
Test Report for the Direct Metal Oxidation and Calcination Furnace System (DMO-2) [1, pg. 6.].
Exact locations of the thermocouples are not known but can still be used as a basis for comparison.
Thermocouple data can be found in Appendix C. The exact locations of thermocouples 19 and 20
are unknown, however in the FE model the temperature was obtained at the center of the model
(see Figure 19). Several thermocouples are listed as “NA” which means that temperatures
corresponding to these thermocouples were either not collected in the experiment or not explicitly
modeled in the finite element model because of symmetry.
Good agreement between the FE model and the experimental data is observed for the
thermocouples attached to the sides of the furnace (1-16% difference). The temperatures predicted
by the finite element model on the lid are twice as high as the temperature recorded experimentally.
However, the sensitivity of thermocouples 19 and 20 was influenced by radiation and convection
effects and more data is needed to calibrate the temperature in the lid in the finite element model.
Overall, temperatures predicted by the model compares well with experimental data. Therefore,
the simple thermal model can be used to predict thermal induced stresses.
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Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
Figure 17. Motor side thermocouple comparison.
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Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
Figure 18. Calciner side thermocouple comparison.
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Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
Figure 19. Lid thermocouple comparison.
8.2 Structural Model
Two structural studies are performed to understand the effects of thermal and pressure
loading in the furnace. Solutions are then combined to predict overall stresses and deformations.
8.2.1 Model Geometry and Mesh
For both studies, only the furnace is modeled. The geometry of the furnace consists of
surfaces and solid bodies as shown in Figure 20. The walls of the furnace and the cylinder flange
stubs protruding from the walls are modeled as surfaces. The walls of the furnace are 4.83 mm
(0.19-inches) thick. Each surface is defined on the mid-plane of that particular part. The lid and
flanges are modeled as solid bodies.
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Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
Figure 20. Geometry used for structural model.
Tetrahedral solid elements with 3 degrees of freedom per node (translation in X, Y, and Z
directions) are used to mesh the solid bodies, while shell elements with 6 degrees of freedom per
node (translations and rotation in X, Y, and Z directions) are used to mesh the surfaces
corresponding to the flange stubs and the furnace walls. Contact conditions are defined at each
solid/shell element interface. The average element size is about 12.7 mm. The structural model
has a total of 10,329 elements and 18,361 nodes. Figure 21 shows the mixed solid/shell mesh.
Figure 21. Structural model mesh.
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Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
Note that, due to memory limitations, using a solid element model with enough nodes
through the wall thickness to capture the stress profile was not feasible. As a result, a mixed
solid/shell element model was developed.
8.2.2 Thermal Loading
8.2.2.1 Loads and Boundary Conditions
The temperature profile from the thermal analysis serves as a loading condition to predict
stresses and deformations due to thermal loading. An ANSYS routine is used to interpolate the
temperature profile of the solid model described in section 8.1.3 into the shell element model.
Boundary conditions are depicted in Figure 22. The furnace mid-plane is constrained in
the X direction (uX=0) as it is a symmetry plane. Two vertices are also constrained to prevent rigid
body motion. The vertex at the edge of the water cooled flange is pinned to constrain motion in the
Y and Z directions (uY=0 and uZ=0). The vertex at the edge of the motor flange is constrained in
the Y direction (uY=0).
Figure 22. Boundary conditions for structural model.
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Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
8.2.2.2 Results
The Von Mises stress and the deflections induced by thermal loading are shown in Figure
23 through 26. In each figure, a wire frame shows the undeformed furnace. The maximum stress
due to thermal loading is 1.035x103 MPa (150 ksi) but is attributed to singularities in the mesh due
to contact regions between the furnace walls and flange stubs. The scale is adjusted so that stresses
over 550 MPa are displayed in hot pink to easily distinguish singularities from actual stresses. A
maximum Von Mises stress of 550 MPa is observed in the corners near the lid and is compared to
the 0.2% yield strength of AISI 304 Stainless Steel at 648°C (207 MPa). The furnace exceeds the
0.2% yield strength by 2.7 times. The maximum deformation predicted by the finite element
model is 5.7 mm (0.22 in).
Figure 23. Von Mises stress due to thermal loading, interior view.
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Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
Figure 24. Von Mises stress due to thermal loading, exterior view.
Figure 25. Total deformation due to thermal loading, interior view.
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Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
Figure 26. Total deformation due to thermal loading, exterior view.
8.2.3 Vacuum Loading
8.2.3.1 Loads and Boundary Conditions
A gage pressure of 47,996 Pa (~ 7 psi) is assigned to the internal surface of the furnace as
a loading condition to predict stresses and deformations due to vacuum loading. The boundary
conditions used to restrain this model are identical to those used in the thermal loading case (see
section 8.2.2.1).
8.2.3.2 Results
Results from this analysis are depicted in a Von Mises stress and displacement plot, as
shown in Figure 27 through 30. Figure 27 and Figure 28 show the furnace deforming under the
vacuum load and the corresponding Von Mises stress levels. The wire frame shows the furnace
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Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
prior to deformation. The scale has been adjusted and regions with stresses higher than 88 MPa are
plotted in hot pink. The maximum Von Mises stress due to vacuum loading is approximately 88
MPa except for a minute area where the small flange stub meets the furnace wall on the calciner
side (see Figure 27). The maximum Von Mises stress is 2.4 times lower than the 0.2% yield
strength for AISI 304 Stainless Steel at 649°C (207 MPa). The stress due to vacuum loading is
almost one order of magnitude lower than the thermal induced stress. The maximum deformation
predicted by the FE model is 1.67 mm (0.07 in) for the coarse mesh, as depicted in Figure 29 and
Figure 30. Simple hand calculations for a plate subjected to a uniform pressure loading are shown
in Appendix A. Calculating maximum stress and deflections for a plate with all edges fixed and all
edges simply supported help to bound the problem. Using Roark’s formulas for stress and strain,
the stress at the center of the plate falls between 55.7 MPa (rectangular plate, 4 edges fixed) and
167 MPa (rectangular plate, 4 edges simply supported) [11]. Deflections fall between 0.76 mm
and 3.56 mm. The values predicted by the FE model fall within the same range.
Figure 27. Von Mises stress due to vacuum loading, interior view.
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Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
Figure 28. Von Mises stress due to vacuum loading, exterior view.
Figure 29. Total deformation due to vacuum loading, interior view.
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Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
Figure 30. Total deformation due to vacuum loading, exterior view.
8.2.4 Combined Loading
Results from the structural analysis for thermal and pressure loading are combined to
evaluate overall stresses and displacements. The resulting Von Mises stress and deformations are
summarized in Figures 31 through 34 and Table 8. As described in section 8.2.3, the scale for the
Von Mises plot was adjusted so that the stresses due to singularities at the contact areas (stresses
above 550 MPa) would be displayed in hot pink. The Von Mises stress is again maximum in the
corners near the top of the lid and is about 583 MPa (see Figure 31 and 32). It is about 2.8 times
larger than the 0.2% yield strength of AISI 304 Stainless Steel at 649°C (207 MPa). A maximum
deflection of 5.76 mm (0.23 inches) is predicted by the FE model, as shown in Figures 33 and 34.
Deflections of the furnace panels were measured experimentally after several thermal cycles at
600°C and 1 atmosphere of pressure at 7,200 ft (75,994 Pa. or 11 psi). Deflections of the order of
6.35 mm (0.25 inches) were recorded [3]. However, because deflections caused by vacuum
loading are insignificant compared to deflections caused by thermal loading, these deformation test
data can still be used for comparison purposes.
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Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
Note that the thermal and vacuum loadings were combined to give a rough idea of stress
and deflection levels. However, because the stress levels are above yield the furnace will undergo
plastic deformation and a non-linear analysis should be performed.
A mesh independence study was performed for the combined loading case between a
coarse mesh of 12.5 mm and a fine mesh of 5 mm for the combined loading model. The number of
elements was increased by a factor of 5.8% (from 10,329 elements to 60,631 elements). Changes
observed in maximum Von Mises stress and deflections did not exceed 17% (see Appendix B for
more information).
Table 8. Maximum Von Mises stress and results summary.
Thermal Loading
Vacuum Loading
Combined Loading
Maximum Von Mises
Stress
MPa
ksi
Compared to Yield Strength
550
79.8
Exceeded yield
by 2.7 times.
88
12.3
Below yield by
2.4 times.
583
91.4
Exceeded yield by
2.8 times.
Maximum Deflection
mm
in
5.74
0.23
1.67
0.07
5.76
0.23
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Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
Figure 31. Von Mises stress due to combined loading, interior view.
Figure 32. Von Mises stress due to combined loading, exterior view.
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Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
Figure 33. Total deformation due to combined loading, interior view.
Figure 34. Total deformation due to combined loading, exterior view.
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Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
9.0 Summary and Conclusions
A conduction-based model was created to capture the temperature profile of the DMO-2
furnace. Experimental data gathered during acceptance testing was used to adjust the thermal
model. Readings from thermocouples mounted on the outside of the furnace walls during
acceptance testing were compared to temperatures predicted by the finite element model. After
adjusting the model, percent difference varied between 1 and 16%, except for the lid where the
temperatures predicted by the FE model are much higher than the temperatures recorded
experimentally. However, the sensitivity of thermocouples located on the lid was influenced by
radiation and convection effects and more data is needed to calibrate the temperature in the lid in
the finite element model. Overall the temperature profile from the finite element model compared
well to experimental data, although it must be recognized that the thermal model used in this study
(conduction only) should only be seen as a semi-empirical tool to interpolate discrete temperature
measurements onto the vessel wall continuum, i.e. it most certainly is not appropriate for design
purposes.
A structural analysis was then completed to evaluate combined stress and deflection due to
thermal and pressure loading. First, the thermal profile attained from the previous analysis was
used as a thermal loading condition. A maximum Von Mises stress of 550 MPa and a maximum
deflection of 5.74 mm were predicted by the FE model under that load. Then, a gage pressure of -
47,996 Pa was applied to the interior of the furnace to simulate the partial vacuum load. This
pressure loading yielded a maximum Von Mises stress of 88 MPa and a maximum deflection of
1.67 mm. When combined, thermal and pressure loading together yielded a maximum stress of
583 MPa (which exceeds the 0.2% yield at 649oC by a factor 2.8) and a maximum displacement of
5.76 mm, which agrees well with deformations observed experimentally after several thermal
cycles.
Recommendations for future experimental tests set-up and data collection are listed below:
Check and record power inputs to the various heater sections before and during every test.
Use two differential temperature gauges to measure the inlet and outlet temperature of the cooling
flange near the lid and in the 6-inch water cooling flange.
Use two mass flow meters to measure the flow rate of water into the cooling flange near the lid and
the 6-inch cooling flange.
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Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
Shield thermocouples attached from the outside of the furnace from radiation and convection effects.
Implementation of these features will help with acquiring more reliable experimental results for
future DMO furnaces.
Finally, we want to emphasize again that the current finite element model is not intended
and should not be used to predict thermal and structural effects in future furnace designs because
the physics are far from fully captured with this simplistic conduction-only approach. Future
furnace design changes call for insulation to be placed around the entire furnace, which will
eliminate –or vastly reduce- the “chimney effect” causing a substantial change in heat transfer and
more heat rejected to the water cooled flanges. For design purposes, a Computational Fluid
Dynamic (CFD) code should be used to properly model the physics of radiation, convection, and
conduction of future furnace designs.
10.0 Attachments
Appendix A: Evaluation of Stresses and Deflections Caused by Vacuum Loading
Appendix B: Combined Model Mesh Comparison
Appendix C: Testing Information from Mike Keddy, ESA-AET Archives
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Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
Appendix A: Hand Calculations to Evaluate Stresses and Deflection Caused by Vacuum Loading [11]
Table 11.4 Formulas for flat plates with straight boundaries and constant thickness
1. Rectangular Plate; all edges simply supported, uniform pressure over entire plate.Quantity Symbol Value Unitslength a= 21.25 inwidth b= 12.95 in
thickness t= 0.19 in
pressure q= -6.96 lb/in^2Elasticity E= 2.80E+07 lb/in ^2
Therefore a/b 1.6 ∞β 0.5172 0.7500α 0.0906 0.1421δ 0.4910 0.2000
Answer:At center σmax=(βqb^2)/t^2)
σmax (lb/in^2) -16,722 -24,250~1.15e8 Pa ~1.67e8 Pa
ymax=(-αqb^4)/(Et^3)ymax (in) 0.09 0.14
2.29 mm 3.56 mm8. Rectangular Plate, all edges fixed, uniform pressure over entire plate.
a/b 1.6 ∞β1 0.4680 0.5000β2 0.2286 0.2500α 0.0251 0.0285
Answer:
At center of long edge σmax=(-β1qb^2)/t^2)
σmax (lb/in^2) 15,132 16,166~1.04e8 Pa ~1.11e8 Pa
At center σmax=(-β2qb^2)/t^2)σmax (lb/in^2)
7,391 8,083~5.09e7 Pa ~5.57e7 Pa
ymax=(αqb^4)/(Et^3)
ymax (in) 0.03 0.030.76 mm 0.76 mm
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Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
Appendix B: Combined Model Mesh Comparison
A mesh independence study was conducted for the combined model. The average mesh size
was decreased from 12.5 mm (coarse mesh) to 5 mm (fine mesh). As a result, the number of elements
was increased by a factor of 5.8 (from 10,329 elements to 60,631 elements). Stresses and deflections
were compared at several locations throughout the model (see Table 10, and Figures 35 to 38).
Table 9. Von Mises Stress comparison.
Coarse Mesh (MPa)
Fine Mesh (Mpa) Percentage Difference583.9 550.4 5.7% 264.7 268.8 1.6% 560.8 519.9 7.3% 317.2 264.5 16.6%
Table 10. Displacement comparison.
Course Mesh (mm) Fine Mesh (mm) Percentage Difference4.7 4.6 0.9%2.6 2.7 1.8%5.1 5.5 7.2%3.6 3.6 0.3%
Figure 35. Von Mises stress, coarse mesh. Figure 36. Von Mises stress, fine mesh.
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Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
Appendix B: Combined Model Mesh Comparison Cont’d
Figure 37. Displacement for coarse mesh.
Figure 38. Displacement for fine mesh.
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Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
44
Appendix C: Test Information from Mike Keddy, ESA-AET Archives Acceptance Test DMO-2 Furnace 03/22/02 output filename”03.22.02” Objectives: Heat up profile for Oxidizer. Cold start to operating temperature. Full Power (i.e., 208VAC , 30 amp circuit) Control: Honeywell 800 using “Config1b.fbd” this is the same program used in the previous runs w/ exception that Calciner is limited to 0% power from the 110 VAC Bus and Oxidizer is allowed 105% (i.e., the reverse of the previous run, “Cal_TempProfile032002.” Data Logging: Labview “New Furn Tst Hot (beta5)” 07:35 Start Data Logging 07:39 Baseline Temps around 14 - 15°C before applying heat, TC1 is faulty. Will proceed with test and fix this TC later. 07:50 Start Heating, Final setpoint at 600°C, initial demand at 105% 09:22 Power output throttled back to approx. 25% output. Process Value = 595°C. Set Point = 600°C. Calculated Power into water = 1584 Watts. 10:39 Shut down power, continue logging. 14:04 Stopped data logging
Figure 39. Temperature Profile of Oxidizer (No Direct Heating of Calciner)
Direct Metal Oxidation Furnace (DMO-2) AET-CW-AE-32
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Figure 40. Oxidizer Heat Rejection to Water (No Direct Heating of Calciner).