direct metal oxidation furnace (dmo-2) aet-cw-ae-32lucie.ericandlucie.com/resume/reports/structural...

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.

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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


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


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.

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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


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.

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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.

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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.


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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.

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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).

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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.


8,858 mm2 (13.73 in2) and is


Watts.


5,413 mm2 (8.39 in2) and is


Watts.

Figure 8. Heat losses from “chimney effect.”

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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%

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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


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.

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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 2 on the Motor side is assigned 374 Watts.

• Heater Section 2 on the Calciner side is assigned 374 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-

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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


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)

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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


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


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


Figure 14. Thermal model, temperature distribution.

Figure 15. Thermal model, thermal distribution on the furnace walls (interior view).

22


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

23


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.

24


Figure 17. Motor side thermocouple comparison.

25


Figure 18. Calciner side thermocouple comparison.

26


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.

27


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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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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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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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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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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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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Figure 28. Von Mises stress due to vacuum loading, exterior view.

Figure 29. Total deformation due to vacuum loading, interior view.

34


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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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

36


Figure 31. Von Mises stress due to combined loading, interior view.

Figure 32. Von Mises stress due to combined loading, exterior view.

37


Figure 33. Total deformation due to combined loading, interior view.

Figure 34. Total deformation due to combined loading, exterior view.

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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.

39


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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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

41


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.

42


Appendix B: Combined Model Mesh Comparison Cont’d

Figure 37. Displacement for coarse mesh.

Figure 38. Displacement for fine mesh.

43


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)


45

Figure 40. Oxidizer Heat Rejection to Water (No Direct Heating of Calciner).

direct metal oxidation furnace (dmo-2) aet-cw-ae-32lucie.ericandlucie.com/resume/reports/structural...

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