The stakes around digital prototyping are particularly high for RND, which was spun off from a larger company about five years ago. Key engineering and management talent in the larger firm’s custom machinery division parlayed more than 15-plus years of experience in the field and put it to work as a much smaller operation, with a plan to scale as required through the use of a contract workforce. Being a more compact organization presents its own share of challenges, however. RND is obviously highly focused on conservation of resources. Moreover, the firm cannot always match the engineering breadth of larger manufacturers, nor does it have a stable of on-staff assemblers and machinists to backstop the engineering and design process. For these reasons, RND committed to a digital prototyping and simulation strategy not only to help compensate for those perceived limitations but also to give it a competitive edge.

The classic manufacturing practice for this segment is heavily reliant on physical prototyping and, as a result, significant manpower. Manufacturing giants such as Procter & Gamble, Johnson & Johnson, and Coca-Cola turn to firms like RND to design and build custom equipment for assembly, inspection, pharmaceutical processing, robotics, and materials handling. Projects can range in size from million dollar–plus automated work cells to semiautomatic, operator-assisted devices small enough for a tabletop.

Typically, companies will build a series of prototypes of the custom automation equipment, make changes and revisions, and then issue a short production run in the late-stage development cycle to ensure that the end result is the optimal design. Some large firms take a design only part of the way, relying on the preproduction assembly and machining process to fine-tune physical prototypes and work out any manufacturing kinks before settling on a final product.

From its inception, RND was committed to altering that lengthy, physical prototype–centric workflow. RND knew it had to reduce the number of late-stage design revisions and, more important, minimize any “cutting of metal” beyond the official start of production to keep its costs in check. Despite the unique design characteristics of the different machinery it produces, it boiled down to a common design challenge across all RND projects: Get the design right the first time without incurring all the time and expense associated with cutting metal and the rest of a protracted physical prototyping cycle.

Simulating the Robot

The first step on the path to digital prototyping was standardizing a set of tools, in this case, Autodesk Inventor three-dimensional (3D) computer-aided design (CAD). One of the most significant changes to the RND workflow came via the simulation capabilities of the tool. Using Autodesk Inventor, RND engineers got a jump on tolerance analysis, the process of making sure that assemblies and parts of the machinery fit together properly without causing any interference. Before the software, engineers would make assumptions, do intricate hand calculations, and possibly invoke simplifications to the design to guard against common configuration problems such as linkages that bind or deflecting plates. Machinists and assemblers would take the physical prototypes to a shop floor and mimic the movement of robots to uncover possible interferences or other problems with the operation. With the software, that manual trial-and-error process is performed digitally, and engineers can simply query properties such as the mass moment of inertia as opposed to doing hand calculations to gain very quick access to the figures they need.

Simulating the motion of robots in 3D has other benefits in terms of saving time and cost. Traditionally, engineers would have to remake parts, adjust the wiring, and even drill holes in the final stages—all in the service of getting the physical prototypes to the proper fit and function. Today, with a digital prototyping process in place, RND avoids those extra material and labor costs, and when parts hit the floor, they bolt together properly without any issues the majority of the time. In addition, the digital prototyping strategy has facilitated reuse, not necessarily of specific parts and assembly designs but of motion analysis tests and processes that have been proved out with digital prototyping and can be applied to other robots and automation projects.

Being able to finesse robot designs via simulation, not through the production of multiple physical prototypes, also has helped RND meet customers’ increased demands for more streamlined automation equipment. In the past, engineers typically would err on the side of increasing machinery size to accommodate new features and functions. Today, with the new processes, RND is able to optimize designs via 3D simulation and meet customers’ calls for smaller equipment, even mobile models, whenever possible.

Crossing Cultural Boundaries

Because RND was an upstart and knew from the beginning that it needed an agile strategy to be competitive, selling management on the benefits and return on investment of an investment in digital prototyping was not an issue. However, there were cultural obstacles to overcome. Engineers accustomed to a physical prototyping process initially had trouble adapting to digital simulation and were skeptical about trusting results from the software. There was also pushback from engineers who resisted spending time early in the cycle using software to refine designs as opposed to going straight to the prototype stage and possibly nailing the proper configuration right out of the gate.

In all cases, time and training helped overcome engineers’ resistance. Giving staffers the time to master the digital prototyping software and processes was a critical aspect of getting them on board, as was proving out the benefits of the new approach with real-world examples and analysis of specific cost and time savings. After all, RND has made it a mission to take customers “from concept to reality.” Arming its own people with the right information helped it do the same thing for the new digital prototyping strategy.

The need to reduce the cost of the enclosure material for direct fired heaters or power boilers prompted this study, whose purpose was to determine whether significant cost savings could be achieved if the structural enclosures of such heaters employed steel-reinforced concrete construction rather than steel plate and structural steel construction. The article indicates the manner in which mechanical and thermal stresses in such internally heated structures can be determined and provides a proposed design for structures of this type. Material costs are provided, assuming the use of standard reinforcing steel wire mesh with a maximum wire size of ¼ inch diameter, 4-inch by 4-inch mesh openings, and conventional concrete with a design compressive strength of 4000 to 5000 PSIG. The tensile strength of the mesh wires is assumed to be 20,000 to 30,000 PSI, and the transverse or structural strength of the concrete is assumed to be 10% of its compressive strength, or 500 PSIG for 5000-PSIG concrete.

Design of a Direct Fired Process Heater or Power Boiler Enclosure

Figure 1 shows the general arrangement of a tubular direct fired process heater or power boiler enclosure, and Figure 2 shows a vertical longitudinal section at the center line of the heater. Both drawings provide details of the heater components. The figures do not show the details of the internal hardware, which consists of banks of horizontal or vertical tubular heat transfer elements on two diameter centers situated at either sidewall, supported by alloy steel tube supports fastened to the outer concrete walls. A sufficient thickness of insulation—about 12 inches behind the tubes and attached to the concrete wall—is provided so that the hot and cold surfaces of the concrete outer wall are exposed to acceptable temperatures. Because of the void space between the tubes, the hot face of the refractory insulation can reach high temperatures: about 1200°F in the case of the process heater and 550°F in the case of the power boiler. In both cases it is assumed that heat is generated by burners firing upward, with the burners situated in the closure plate at the bottom of the lowermost enclosure. That enclosure, which is referred to as the radiant section, consists of an internally insulated cavity bounded by the side and end walls, a top closure plate with a central rectangular opening, a bottom closure plate with openings to accommodate the burners, and tubular heat transfer elements at either sidewall within the cavity. The uppermost enclosure, which is referred to as the convection section, consists of an internally insulated cavity bounded by side and end walls, the closure plate at the top of the radiant section, a closure plate with a rectangular opening at the top of the cavity, and closely spaced horizontal and vertical rows of tubular heat transfer elements contained within the cavity. A stack for venting flue gas is located above the top opening in the top closure plate of the convection section.

The average temperature of the combustion product flowing from top to bottom of the radiant section is approximately 1500°F. Flue gas passing through the convection section is at a somewhat lower temperature than that in the radiant section, averaging approximately 800°F, and the combustion product gases leaving the convection section and entering the stack are at an even lower temperature: usually less than 1000°F. Because of the variation in combustion product gas temperature in these sections, horizontal and vertical expansion joints must be provided to accommodate the differences in movement between sections to avoid excessive stress to and damage of the enclosure.

For further details, refer to Figures 1 and 2; the numbered items in those figures are defined in Table 1.

Figure 1: General Arrangement of a Tubular Direct Fired Process Heater or Power Boiler Enclosure

Figure 2: Vertical Longitudinal Section at the Heater Center Line.

Table 1
Mechanical Design Data

1. Bottom support, 40 feet long × 8 feet high × 12 feet wide × 8 inches thick
2. Radiant section, 40 feet long long × 24 feet high × 12 feet wide × 8 inches thick, fabricated from five shop-assembled panels that are 8 feet wide × 12 feet high
3. Convection section, 40 feet long ×16 feet high × 6 feet wide × 8 inches thick
4. Stack, cross-section 6 feet long × 60 feet high × 8 inches thick
5. Three peripheral platforms with tread 2.5 feet wide and rail 3.5 feet high × 8 inches thick
6. Platform supports
7. 2 feet wide × 24 feet high radiant section tube access openings
8. 3 feet wide × 5 feet high radiant section access openings at each end
9. 3 feet wide × 5 feet high peripheral support access openings at each end
10. [not labeled]
11. Horizontal field joint for the bottom of the vertical shop-fabricated panels, consisting of alternating projections and spaces, with the spaces providing for clearance between vertical mesh projections at the bottom of the upper panels and the top of the lower panels. As in all field joints, wire mesh plates are provided at either side of the wire mesh projections to maintain mesh continuity at the joints before concrete is applied to fill the joints
12. Lower closure plate for bottom of radiant section, with openings for burner installation
13. Upper closure plate for radiant section, 40 feet long × 12 feet wide × 8 inches thick with an opening 8 feet wide × 36 feet long
14. Horizontal, peripheral expansion joints consisting of a continuous double layer of friction-lowering slide plates provided between bottom support section and radiant section, the radiant section and convection section, and the convection section and the stack
15. Vertical field joint (see item 11)
16. Four corner posts, 3 feet long × 3 feet wide × 8 inches thick
17. T bracket
18. Radiant section end panel, 12 feet wide × 24 feet high
19. Radiant section side panel, 40 feet wide × 24 feet high
20. Flexible expansion joints
21. Horizontal field joint

Calculation of Thermal Stress for a Process Heater or Power Boiler

Thermal stress can increase the stress in the reinforcing steel and concrete composite wall of a direct fired process heater or power boiler significantly because of the relatively high temperatures to which the inner surface of the concrete wall is exposed and the temperature difference between the inner and outer surfaces of the wall.
The power boiler is assumed to have the same general configuration as the process heater but differs in that the power boiler has so-called membrane-type vertical tubular surfaces, or surfaces with closed spaces between tubes, so that the temperature of the membrane wall and the hot insulation surface behind it can be assumed to be equal to that of the steam-water mixture inside the tubes: about 550°F, corresponding to a steam pressure of 1000 PSIA. It will be shown that this significantly reduces the thermal stress in the outer concrete wall if free expansion has not been provided for.

The thermal stresses can be calculated in the manner described below, and the stress that is calculated can be added to the mechanical stress caused by wind loads and weight loads to arrive at a figure for total stress, which must be sufficient to avoid permanent damage to the concrete or steel that constitutes the enclosure.

Of importance is the finding that the stress in the steel and concrete outer wall caused by the temperature gradient across the wall can be reduced very significantly and perhaps eliminated by accommodating thermal expansion of the wall through the use of properly placed and designed expansion joints. A conservative design would be one that assumes maximum design stresses in steel and concrete that are based on the sum of both the mechanical stress and the thermal stress. A much less conservative design would be one that considers maximum design stress equal to the thermal or mechanical design stress only.

The equations in Table 2 were used to calculate the tensile stresses that are developed in the composite wall of the enclosure as a result of the temperature gradient across the wall when allowance has not been made to allow for free expansion.

Table 2
Equations for Calculating Thermal Stress in an Internally Heated Steel-Reinforced Concrete Enclosure

Calculated and physical property data for the process heater and power boiler based on these equations are summarized in Table 3.

Table 3
Data for Calculating Thermal Stress in a Concrete Wall Reinforced with Steel Wire Mesh

Calculation of Combined Thermal and Mechanical Stress

Based on the preceding equations and data, the maximum calculated strain, e/L, at 110°F, the temperature differential at the hot face of the wall, is 0.000759 inch/inch. The strain decreases linearly from the hot face to the cold face so that the concrete and steel strain and the thermal stress at any point in the wall from hot face to cold face stress are determinable.

The net mechanical stress generated in the steel and concrete of the enclosure wall can be said to be equal to the thermal stress, as calculated by the Equations and Data of Tables 2 and 3, when used in combination with the Equations and Data of Table 4. The mechanical stress is based on a maximum wind pressure of 30 PSF acting in a horizontal direction at the radiant wall. The wind pressure and the thermally generated stresses generated by the temperature differential in the walls causes transverse bending of the wall and tensile and compressive stress in the steel and concrete at either face of the wall. The distance separating the steel wire mesh planes is 6 inches. With such an arrangement the wall can resist wind – propagating tensile and compressive stress regardless of whether the wind impinges at right angles to one wall or the wall opposite. The Equations of Tables 2 and 4 are based on the configuration of the radiant wall, but comparable calculations can be used to evaluate stresses in the convection section and stack.

Table 4
Equations for Calculating Thermal and Mechanical Stress

Mm = mechanical moment caused by 30-PSF wind pressure, lb.-inch
Lw = height of radiant wall, inches.
Wp = wind pressure, lbs./square foot
Rstl. = center-to-center distance between wire mesh plane and neutral axis, inches
Rconc. = center-to-center distance between concrete area and neutral axis, inches
Aw = radiant wall area, square feet
Astl. = area of wires in steel wire mesh planes, square inches
Aconc. = area of concrete, square inches
(Stl) = Ss = stress in steel, PSI
(Sconc) = Sc = stress in concrete, PSI
St-t = thermal stress in wires of mesh under tension, PSI
St-c = thermal tensile stress in wires of mesh under compression, PSI
Es = steel modulus of elasticity = 30 million PSI
Ce = thermal coefficient of expansion = (6.9)(10)^-6 , inches/inch-deg. F
(Deg.F)h = 96.3°F = temperature difference of steel and concrete at hot face
(Deg.F)c = 13.7°F = temperature difference of steel and concrete at cold face

Table 5 provides a summary of the calculations of tensile and compressive stress in steel and concrete.

Table 5
Summary of Calculated Tensile and Compressive Stresses in Steel and Concrete, thousand PSI

Conclusions

Because of the wall temperature differential defined and shown in this article, the hot face of any wall in the heated enclosure will increase in length by an amount greater than the cold face, causing the wall to bow inward. If there were no restraints on the wall, there would be no stress in the wall as a result of the bowing that occurs. However, the weight of the structure above and below the wall creates end moments that oppose wall bowing. Initially, the net result is that the steel and concrete are stressed in tension at both the hot and cold faces, whereas at the end, the steel and concrete are stressed in tension at the hot face and in compression at the cold face. The initial concrete stress in tension is high enough to cause cracking at both the hot and cold faces since the tensile stress at these locations exceeds the tensile strength of concrete, which is about 500 PSI. Cracking resulting from tensile stress failure of concrete is not uncommon in concrete beams used in steel-reinforced concrete structures, but this does not interfere with their use in their intended load-bearing service. The same could be said about the use of reinforced concrete for internally heated structures.

Despite the fact that cracking occurs at both the inner and outer surfaces of the internally heated enclosures, air infiltration should be minimal because once cracking occurs, further widening of the cracks will not occur. Coating of the external surfaces with a commercially available elastic compound such as one that would be used for the expansion joints therefore would be desirable.

The steel-reinforced concrete structure provides a material cost advantage relative to a conventional structural steel structure, as follows:

References

1. American Institute of Steel Construction. Steel Construction Manual, 5th ed. New York: AISC, 1949.
2. Seely, F. B. Resistance of Materials, 3d ed. New York: Wiley, 1952.

Description of Solution

The estimation of the nonboiling two-phase flow heat transfer coefficient, regardless of flow pattern, gas-liquid combination, and pipe inclination angle, is accomplished by using the following general heat transfer correlation (see the article on the Knovel website by Ghajar and Tang, Estimations of Heat Transfer in Nonboiling Two-Phase Flow with a General Correlation):

The flow pattern factor (F_p) and inclination factor (I*) are given as follows:

The liquid phase heat transfer coefficient (hl) is calculated by using the Sieder and Tate¹ correlation:

The value of the void fraction (α) is calculated by using general void correlation (see the article on the Knovel website by Ghajar and Tang, A General Void Fraction Correlation in Two-Phase Flow for Various Pipe Orientations) proposed by Woldesemayat and Ghajar²:

The two-phase distribution coefficient (C0) and gas drift velocity (ugm) in meters per second (m/s) are given as follows:

The general void correlation is applicable for horizontal to upward vertical pipe orientations. However, in cases in which the two-phase flow is in upward vertical pipe, the use of the void fraction correlation of Rouhani and Axelsson³ is expected to provide more accurate results (see the article on the Knovel website by Ghajar and Tang, Void Fraction Correlations for Vertical Upward Two-Phase Flow in Pipes). When the correlation by Rouhani and Axelsson³ is used, the two-phase distribution coefficient (C0) and gas drift velocity (ugm) are calculated as follows:

Application in Air and Silicone Flow in a Vertical Pipe
A two-phase bubbly flow of air and silicone is transported in an 11.7-mm-diameter vertical pipe. Liquid silicone such as Dow Corning 200 Fluid 5 CS is used primarily as an ingredient in cosmetic and personal care products because of its low surface tension (σ = 19.7 × 10-3 N/m), high spreadability, nongreasy soft feel, and subtle skin lubricity characteristics. The two-phase flow has a gas mass flow rate (ṁg) of 1.89 × 10-5 kg/s and a liquid mass flow rate (ṁl) of 0.907 kg/s, and the system pressure (Psys) is 250 kPa. The gas phase consists of air with density (ρg) of 1.19 kg/m³, dynamic viscosity (μg) of 18.4 × 10-6 kg/m•s, and Prandtl number (Prg) of 0.71. The liquid phase consists of liquid silicone with thermal conductivity (kl) of 0.117 W/m•K, density (ρl) of 913 kg/m3, dynamic viscosity (μl) of 45.7 × 10-4 kg/m•s, and Prandtl number (Prl) of 64. The dynamic viscosity (μs) of liquid silicone evaluated at the pipe surface temperature is 39.8 × 10-4 kg/m•s. The following example calculation illustrates the use of the general two-phase heat transfer correlation to predict the two-phase heat transfer coefficient (htp) for this flow.

From the measured gas and liquid mass flow rates, the quality (x) and the superficial gas (Vsg) and liquid (Vsl) velocities can be calculated as x = 2.084 × 10-5, Vsg = 0.1477 m/s, and Vsl = 9.24 m/s. The void fraction (α) is calculated by using the correlation of Rouhani and Axelsson³ (Equations 5, 8, and 9): α = 0.01295 where C0 = 1.2 and ugm = 0.1423 m/s. From the superficial gas and liquid velocities and void fraction, the gas (Vg) and liquid (Vl) velocities can be calculated as Vg = Vsg / α = 11.41 m/s and Vl = Vsl / (1 – α) = 9.361 m/s.

The flow pattern factor (Fp) and inclination factor (I*) for the vertical pipe (θ = 90°) are calculated by using Equations 2 and 3 to be Fp = 0.9873 and I* = 63.16. The liquid-phase heat transfer coefficient (hl) is calculated by using Equation 4 to be hl = 3248 W/m²•K where Rel = 21739. Using the general two-phase heat transfer correlation (Equation 1), the two-phase heat transfer coefficient is estimated to be htp = 3589 W/m²•K. Compared with the measured two-phase heat transfer coefficient of 3480 W/m²•K of Rezkallah4 in similar flow conditions, the general two-phase heat transfer correlation overpredicted the measured value by only 3.1%.

Application in Air and Gas-Oil Flow in a Vertical Pipe
A two-phase flow of air and gas-oil is being transported through a 70-mm-diameter vertical pipe. The two-phase flow has a gas mass flow rate (ṁg) of 0.077 kg/s and a liquid mass flow rate (ṁl) of 10.2 kg/s, and the system pressure (Psys) is 200 kPa. The liquid phase consists of domestic-grade gas-oil with dynamic viscosity (μl) of 39.2 × 10-4 kg/m•s, density (ρl) of 835 kg/m3, surface tension (σ) of 25 × 10-3 N/m, and Prandtl number (Prl) of 60. The gas phase consists of air with dynamic viscosity (μg) of 18.2 × 10-6 kg/m•s, density (ρg) of 2.5 kg/m³, and Prandtl number (Prg) of 0.71. The following example calculation illustrates the use of the general two-phase heat transfer correlation to predict the two-phase heat transfer coefficient to the liquid phase heat transfer coefficient ratio (htp/hl).

From the measured gas and liquid mass flow rates, the quality (x) and the superficial gas (Vsg) and liquid (Vsl) velocities can be calculated as x = 0.00749, Vsg = 8.0 m/s, and Vsl = 3.17 m/s. The void fraction (α) is calculated by using the correlation of Rouhani and Axelsson³ (Equations 5, 8, and 9): α = 0.5906 where C0 = 1.199 and ugm = 0.1532 m/s. From the superficial gas and liquid velocities and void fraction, the gas (Vg) and liquid (Vl) velocities can be calculated as Vg = Vsg/α = 13.55 m/s and Vl = Vsl / (1 – α) = 7.743 m/s.

The flow pattern factor (Fp) and inclination factor (I*) for the vertical pipe (θ = 90°) are calculated by using Equations 2 and 3 to be Fp = 0.4416 and I* = 1602. Using the general two-phase heat transfer correlation (Equation 1), the value for htp/hl can be calculated to be htp/hl = 1.75. Compared with the measured value of htp/hl = 1.65 by Dorresteijn5 in similar flow conditions, the general two-phase heat transfer correlation overpredicted the measured value by 6.1%.

Application in Air and Water Flow in a Horizontal Pipe
A two-phase slug flow of air and water is transported through an 18.6-mm-diameter horizontal pipe. The liquid phase is water with thermal conductivity (kl) of 0.6046 W/m•K, dynamic viscosity (μl) of 9.33 × 10-4 kg/m•s, density (ρl) of 999 kg/m³, surface tension (σ) of 0.0723 N/m, and Prandtl number (Prl) of 6.52. The dynamic viscosity (μs) of water evaluated at the pipe surface temperature is 8.40 × 10-4 kg/m•s. The gas phase is air with dynamic viscosity (μg) of 18.3 × 10-6 kg/m•s, density (ρg) of 1.19 kg/m3, and Prandtl number (Prg) of 0.71. The flow has a gas mass flow rate (ṁg) of 9.51 × 10-4 kg/s and a liquid mass flow rate (ṁl) of 0.661 kg/s, and the system pressure (Psys) is 200 kPa. The following example calculation illustrates the use of the general two-phase heat transfer correlation to predict the two-phase heat transfer coefficient (htp) for this flow.

From the measured gas and liquid mass flow rates, the quality (x) and the superficial gas (Vsg) and liquid (Vsl) velocities can be calculated as x = 0.00144, Vsg = 2.941 m/s, and Vsl = 2.435 m/s. The void fraction (α) is calculated by using the correlation of Woldesemayat and Ghajar² (Equations 5, 6, and 7): α = 0.5034 where C0 = 1.044 and ugm = 0.2298 m/s. From the superficial gas and liquid velocities and void fraction, the gas (Vg) and liquid (Vl) velocities can be calculated as Vg = Vsg/α = 5.842 m/s and Vl = Vsl/(1 – α) = 4.903 m/s.

The flow pattern factor (Fp) is calculated by using Equation 2 to be Fp = 0.4978. The liquid-phase heat transfer coefficient (hl) is calculated by using Equation 4 to be hl = 12340 W/m²•K where Rel = 68820. Using the general two-phase heat transfer correlation (Equation 1), the two-phase heat transfer coefficient is estimated to be htp = 8848 W/m²•K. Note that for the horizontal pipe (θ = 0°), the inclination factor is I* = 1. Compared with the measured two-phase heat transfer coefficient of 9079 W/m²•K of Franca and associates6 in similar flow conditions, the general two-phase heat transfer correlation underpredicted the measured value by only 2.5%.

Application in Air and Water Flow in a 5° Inclined Pipe
A two-phase flow of air and water is transported through a 27.9-mm-diameter 5° inclined pipe. The liquid phase is water with thermal conductivity (kl) of 0.5787 W/m•K, dynamic viscosity (μl) of 13.4 × -4 kg/m•s, density (ρl) of 999.6 kg/m³, surface tension (σ) of 0.0744 N/m, and Prandtl number (Prl) of 9.74. The dynamic viscosity (μs) of water evaluated at the pipe surface temperature is 12.6 × 10-4 kg/m•s. The gas phase is air with dynamic viscosity (μg) of 17.7 × 10-6 kg/m•s, density (ρg) of 2.38 kg/m3, and Prandtl number (Prg) of 0.71. The flow has a gas mass flow rate (ṁg) of 7.73 × 10-3 kg/s and a liquid mass flow rate (ṁl) of 0.494 kg/s, and the system pressure (Psys) is 250 kPa. The following example calculation illustrates the use of the general two-phase heat transfer correlation to predict the two-phase heat transfer coefficient (htp) for this flow.

From the measured gas and liquid mass flow rates, the quality (x) and the superficial gas (Vsg) and liquid (Vsl) velocities can be calculated as x = 0.01541, Vsg = 5.313 m/s, and Vsl = 0.8084 m/s. The void fraction (α) is calculated by using the correlation of Woldesemayat and Ghajar² (Equations 5, 6, and 7): α = 0.7112 where C0 = 1.178 and ugm = 0.2594 m/s. From the superficial gas and liquid velocities and void fraction, the gas (Vg) and liquid (Vl) velocities can be calculated as Vg = Vsg/α = 7.470 m/s and Vl = Vsl/(1 – α) = 2.799 m/s.

The flow pattern factor (Fl) and inclination factor (I*) for the inclined pipe (θ = 5°) are calculated by using Equations 2 and 3 to be Fp = 0.3375 and I* = 9.921. The liquid-phase heat transfer coefficient (hl) is calculated by using Equation 4 to be hl = 4764 W/m²•K where Rel = 31306. Using the general two-phase heat transfer correlation (Equation 1), the two-phase heat transfer coefficient is estimated to be htp = 3687 W/m²•K. Compared with the measured two-phase heat transfer coefficient of 3700 W/m²•K by Ghajar and Tang7 in similar flow conditions, the general two-phase heat transfer correlation underpredicted the measured value by only 3.5%.

Summary and Wider Applicability of Results
The practical illustrations presented in this article involved the estimation of heat transfer coefficients in nonboiling two-phase flows in pipes with diameters ranging from 11.7 to 70 mm for horizontal, inclined, and vertical pipe orientations. In addition, these practical illustrations included two-phase flow with different gas-liquid combinations. In these practical illustrations, the use of the void fraction correlations to estimate void fractions in two-phase flow was shown. Since void fraction is a hydrodynamic parameter, the correlations are applicable to both boiling and nonboiling flows. These illustrations show the versatility of the general heat transfer correlation, and the calculated results were verified with measured values. In addition to its applicability for a wide range of nonboiling two-phase flows, the general two-phase heat transfer correlation can be utilized as a tool to compare results from computational fluid dynamics (CFD) and computational heat transfer analysis.

References
1.    Sieder, E. N., and Tate, G. E. Heat Transfer and Pressure Drop of Liquids in Tubes. Industrial & Engineering Chemistry, vol. 28, no. 12, pp. 1429–1435, 1936.

2.    Woldesemayat, M. A., and Ghajar, A. J. Comparison of Void Fraction Correlations for Different Flow Patterns in Horizontal and Upward Inclined Pipes. International Journal of Multiphase Flow, vol. 33, no. 4, pp. 347–370, 2007.

3.    Rouhani, S. Z., and Axelsson, E. Calculation of Void Volume Fraction in the Subcooled and Quality Boiling Regions. International Journal of Heat and Mass Transfer, vol. 13, no. 2, pp. 383–393, 1970.

4.    Rezkallah, K. S. Heat Transfer and Hydrodynamics in Two-Phase Two-Component Flow in a Vertical Tube. Ph.D. thesis, University of Manitoba, Winnipeg, Canada, 1987.

5.    Dorresteijn, W. R. Experimental Study of Heat Transfer in Upward and Downward Two-Phase Flow of Air and Oil through 70-mm Tubes. Proceedings of the 4th International Heat Transfer Conference, Paris and Versailles, France, vol. 5, B5.9, 1970.

6.    Franca, F. A., Bannwart, A. C., Camargo, R. M. T., and Gonçalves, M. A. L. Mechanistic Modeling of the Convective Heat Transfer Coefficient in Gas-Liquid Intermittent Flows. Heat Transfer Engineering, vol. 29, no. 12, pp. 984–998, 2008.

7.    Ghajar, A. J., and Tang, C. C. Importance of Non-Boiling Two-Phase Flow Heat Transfer in Pipes for Industrial Applications. Heat Transfer Engineering, vol. 31, no. 9, pp. 711–732, 2010.

Although having a blank canvas to work on has given Optimal Energy an opportunity to develop processes that are lean and more efficient than those of many of its established automotive original equipment manufacturer (OEM) competitors, it also has required the company to go back to the drawing board and revisit fundamental vehicle design principles. That has posed a challenge for Optimal Energy as it aims to accelerate development cycles and introduce the Joule electric car to the market in a timely fashion.

The solution was to put systems and processes in place that would allow the company to leverage deep automotive domain expertise and talent spread around the globe while practicing concurrent engineering in a highly disciplined way. Because the disparate global team has access to “a single version” of design data, the vehicle’s diverse modules and components—not to mention the manufacturing facilities that will be used to produce the car—can be architected simultaneously without encountering any of the lag time or error-prone data translation that typically occur when distributed development teams leverage separate systems and employ a more serial engineering process.

Optimal Energy, a privately owned South African company founded in 2005, has a clear vision in mind. Its goal is to deliver world-class solutions for urban transport by creating an electric vehicle industry in South Africa and expanding globally from there. The vehicles are to have a high degree of local content, meaning that 60% or more of various sourced components are to be produced in South Africa and that the cars will be built in South Africa by local workers. The Joule, Optimal Energy’s first model, is slated for availability in the South African market in 2013 with a global expansion planned for 2014. Unlike many electric vehicles, which are quite small, the Joule will have ample room space with its five-seater design along with a top speed of 135 km/h and a nominal range of 300 km on a single charge.

A Global Team of Partners

Because Optimal Energy is developing the Joule from scratch, it is not locked into particular packaging configurations or ergonomic setups like most car companies, which typically reuse a core set of packaging as a basis for a new vehicle launch, including newer electric offerings. As a result, the Optimal Energy design team is free to explore fresh concepts, such as rethinking how a person sits in the vehicle, and experimenting with novel ways the user would interact and communicate with the car.

Although this design freedom is liberating, it also presents a challenge in light of the time constraints to get the Joule to market. Optimal Energy does not have its eye on being first out the door, but an aggressive schedule is critical because the development program must be completed in the time it might take an established OEM to retrofit an existing vehicle design for the electric market. To establish some sort of headway, Optimal Energy decided early on to focus internally on its core intellectual property and domain expertise—the drive system, the energy storage system, and the software controls for the Joule—and outsource design of the components outside its specialty area to key partners. For example, a German manufacturing partner is working on the mechanical aspects of the vehicle and the battery is being designed in a joint venture with a Korean firm.

Although these outside firms provide the deep automotive domain expertise to jump-start Optimal Energy’s fledgling development process, the far-flung nature of the engineering team can make collaboration a struggle. Even at the onset of the project, eight or nine systems were employed to manage the different aspects of the Joule, and it was challenging to keep everyone on the same design page, let alone ensure that all parties were working off the same data. The existing process also did not do much to alleviate the possibility of design miscues since individual components for the Joule were being handled by different teams that were using nonintegrated systems and the engineering process was being conducted on a serial basis.

A Big-Picture Approach

Two years into the development effort, the team made a case for taking a bigger-picture approach. Since the company was early in its life cycle, it was determined that no system or process was so entrenched that it could not be modified—or scrapped, if necessary—to yield better results. The engineering team decided to trade up the existing nonintegrated systems in favor of a single Product Lifecycle Management (PLM) platform that could serve as a central repository for all information related to the development of the Joule. Such a decision ensures that all data—from the initial design requirements to the maintenance documentation needed to service and support the vehicle once it is available in the field—will be housed in the same platform, with collaborative technologies delivering easy access to team members regardless of their geographic location.

A key consideration was to choose a PLM system and provider that had deep automotive domain expertise, balancing the desire to take advantage of a clean-slate design while keeping time-to-market considerations a priority. The team determined that Dassault Systemes’ CATIA computer-aided design (CAD) package, ENOVIA PLM platform, and DELMIA manufacturing software best met that criteria, especially since many core design partners already were using the Dassault software platform.

In fact, one of the primary decisions keeping the Joule effort on course was to model the engineering processes around the out-of-the-box processes defined by the Dassault PLM suite whenever possible. Once again, the team weighed the benefits of starting fresh or relying on proven automotive domain expertise to give it a head start. In critical areas such as engineering change orders (ECOs), for example, it was more efficient to use proven practices rather than taking the time to customize the software and reinvent new ways of working. The rationale was that precious development time was better spent on refining and optimizing Optimal Energy’s core intellectual property and electric designs than on doing a custom engineering software deployment.

This approach is working for a number of reasons. Because the team hails from different industries and different companies, there was no emotional attachment to a particular set of design tools and thus little pushback in getting members to embrace new software. Because Optimal Energy is a start-up with little to no process in place, there were few, if any, change management issues related to adopting new engineering processes. Finally, the decision to go with an already entrenched development platform kept training to a minimum while ensuring that the far-flung Joule team was “speaking the same design language.” These are all important steps in avoiding design miscues that can hamper a development project.

Perhaps most important factor is that the single, integrated PLM platform is paving the way for Optimal Energy to fully embrace concurrent engineering despite the fact that the team is globally dispersed. Without such an approach, it would be impossible to hit the aggressive delivery targets and compete with established OEMs that already have a foundation in place to take ownership of the nascent electric vehicle market.

Cities and campuses often transfer utilities between buildings through buried tunnels. The energy forms involved may be steam piping, water, or electrical buses. Each of these forms may have parasitic energy loss, heating both air in the tunnel and subsequently the ground external to the tunnel. Calculation of these losses may be important to design. Clearly, losses can be minimized with insulation but will never be zero, and over the long run the losses can be significant. In some locales there are regulatory limits to temperature rise in the earth above. Additionally, there may be limits on the air temperature rise in the tunnel related to maintenance personnel access or equipment. Forced ventilation may be needed.

Textbooks1,2 provide solutions to each of the elements of this situation. A general model is described with a closed solution to the heat transfer with the surroundings and the temperature increase of ventilation flow, given the thermal properties of the materials and the dimensions of the design.  Figure 1 illustrates the problem to be solved.

Figure 1: Solution to Problem of Heat Transfer

This problem may involve a buried tunnel or a vault that may contain piping through which steam or a heated fluid is pumped. Alternatively, the vault could contain electrical conductors, which generate heat from resistive losses. This is the most general case. Piping or conductors may simply be buried without any encasement. In the case of a tunnel, there may be forced convection of air to provide cooling for materials or for maintenance. The air temperature will increase in the direction of flow. There may be no airflow, in which case heat is transmitted though the walls, into the surrounding earth, and hence to the environment. The internal temperatures will rise until there is equilibrium between the heat generated and the heat transferred. This solution encompasses such cases through specification of the appropriate overall U-value.

The Adiabatic Case

For reference, first consider the simple relation for the adiabatic case. In this case, there is the assumption of no heat transfer through the soil. Air flows though a closed duct or tunnel with heat being added at a uniform rate q per unit length. The expression for the temperature increase ΔT is the classic flow thermal energy relation:¹

ΔT = q*L/(F*Cp)

where:

q = rate of heat loss from pipe, watts/m
L = tunnel length, m
F = air mass flow rate, kg/s
Cp= specific heat of air, joules/kg

This equation is generally valid for any fluid and any set of consistent units.  For example, consider a tunnel with a length of 600 m   and steam piping with heat loss through the pipe’s walls and insulation of 1320 W/m.  Airflow rates at near atmospheric pressure typically are given in volumetric units, such as cubic meters per minute. Conversion to mass flow rate requires multiplication by the density and, if needed, conversion from minutes to seconds.  For an airflow of 500 m³/min at a density of 1.2 kg/m³, the air mass flow rate is about 10 kg/s.  The specific heat of air is about 1005 J/kg-K.   From the equation above, the adiabatic dry air temperature rise would be 79°C. If the inlet air temperature were 15°C, outlet air would be 94°C.

Heat Transfer through Tunnel Walls and Soil

When the ambient temperatures of the surrounding soil or at ground level are different from the air temperature inside the tunnel, energy will flow via that route at a rate dependent on the temperature difference and the thermal properties of the intervening materials. The overall resistivity (or its inverse, conductivity) can be calculated from the resistivities of the individual materials in the same manner as a resistive electrical circuit. The general computational process to obtain U is described in most textbooks.¹

Calculation of Resistivity through Tunnel Walls and Soil

The total resistivity is the sum of the resistivity of the component material in the heat path. This is shown in Figure 2.

FIGURE 2: Total Resistivity

The overall or total thermal resistance is therefore:

Rtotal = Rwall surf +  Rwall + Rsoil + Rsurf

Additional terms can be added if known. The overall conductivity U is then 1/R.

Correlations for most of the terms above are well known.1,2 Values for Rsoil are more difficult to estimate. The heat transfer mode is conduction, just as occurs through the tunnel walls. However, values for soil resistivity vary widely with soil composition and moisture
content.  Reference 2 is one source of values for different soils. This situation is referred to in the classical heat transfer literature as a “semi-infinite” boundary condition problem. One common practice for buried objects is to define a shape factor S related to the standard heat conduction relationship as follows:

Q = k*(A/L)*ΔT = S*k*ΔT

so that the shape factor S replaces the ambiguous term (A/L). Exact solutions are available for simply shaped objects such as a circular pipe (cylinder). Factors for many other shapes have been determined. These factors take into account the dimensions of the object as well as the depth of burial.

Closed Form Solution for Tunnel

As discussed above, an important task is to determine the overall value of the thermal resistivity from inside the tunnel to the surroundings.  However, once this is done and assuming it is a constant over the length of the tunnel, one can write a differential equation for the tunnel air temperature as a function of tunnel length and solve it formally. The derivation begins with a simple energy balance on a volume of air in a differential length of tunnel dL.  In words, Energy in + energy added = energy out + energy transferred through walls.

Substituting suitable expressions for each term and algebraically simplifying, the resulting differential equation is

dT/dx + (PU/mcp)T = (P U Tamb + dqgen/dx)mcp

where:

T = local tunnel air temperature
P = perimeter of tunnel
U = 1/R = overall thermal conductivity from pipe to surface
Tamb= ambient temperature
Tin = inlet air temperature at x = 0 (boundary condition)
m = mass flow rate of tunnel air
cp = specific heat of the tunnel air

The term (dqgen/dx) is the heat generation rate per unit length in watts per meter and is assumed to be constant in this derivation.

The solution³ to this equation is

T = (Tamb + (1/PU)(dqgen/dx)) + C e-(PUx/mcp)

where C = ((Tin – Tamb) – 1/PU))(dqgen/dx)

This equation is exact for the assumptions made, but of course the result is strongly dependent on the correctness of the property values that define U. In the limit, as R becomes very large (U → 0), the computed result will be the same as the adiabatic solution given previously. This expression is also valid if heat generation is zero or if the ambient temperature is higher than the tunnel air
temperature.

Example Calculations:

Assume district heating in a buried concrete tunnel. The parameters assumed are as follows:

Table 1 summarizes these values.

Table 1 Cases and Comments

References

1. Incropera, F.P., and DeWitt, D.P.  Fundamentals of Heat and Mass Transfer, 5th ed. New York: Wiley, 2002.

2. ASHRAE Handbook. Fundamentals, 2005 ed. Atlanta: ASHRAE.

3. Rainville, E.D. Elementary Differential Equations, 2d ed. New York, Macmillan, 1958.

Skylight removed from a roof after a 14 year old boy working on roofing repairs fell through
to a concrete floor 12 feet below.  He died of his injuries. (NIOSH 2004 report)

Those measurements provided strong support for a slow degradation process since the mechanical strength of older skylight covers showed sharply reduced strength over time.  This was consistent with peer-reviewed publications in the scientific literature as well as general information on the weathering of acrylic polymers. We conclude that more effort should be expended to reduce the consequences of this degradation process, especially by informing engineers of the extent of the problem.

PMMA is an excellent choice for applications that require transparent properties, such as skylights, automobile taillights, rigid contact lenses, and acrylic paints.  There are many varieties of this polymer in commercial use, and they vary in molecular weight, copolymer composition, stabilizer additives (especially ultraviolet stabilizers), and colorants.  However, they all consist mainly of a repeat unit with a methyl ester side group and a methyl group positioned along a saturated carbon-carbon chain.  Although this structure provides great stability in many adverse environments, the materials undergo slow degradation when exposed to heat, light, and moisture, all of which are common on rooftops in Florida.  At a high enough temperature, the polymer will “unzip” to form a monomer, and this reaction can be used to recover monomer in high yield from polymer.  The ceiling temperature (polymer in equilibrium with monomer) is relatively low at 220°C, and a very small amount of monomer is formed at slow rates at lower temperatures.  Light generally passes through this transparent polymer, but some ultraviolet (UV) light is absorbed and causes chemical changes such as cleavage of chemical bonds.  That cleavage leads to loss of side groups as well as main chain cleavage and is revealed by the decrease in molecular weight of thin films exposed to sunlight.  For thick sheets such as skylights, the molecular weight normally is reduced to a larger extent on the side facing the sun. Main chain cleavage forms radicals that can recombine and reverse the loss of molecular weight, but the presence of oxygen will allow a photooxidation reaction to occur that locks in the molecular weight loss.   Moisture can hydrolyze the ester bonds and release methanol.  This process is accelerated in the presence of heating or UV light or when acids or bases are present.

The net result of these changes is a slow progression of surface damage toward the center of the sheet, with more porosity on the side facing the sun.  Indeed, we have seen exactly this type of change on a cross section of a PMMA skylight that has been on a roof for over a decade (see Figure 1).

In terms of preventing falls through a skylight, the basic OSHA rules were designed for glass skylights.  Those structures were generally flat and brittle and thus required a “covering” to protect people on the roof.  The rules for the covering were designed largely to prevent falls through the glass underneath and basically consisted of “the ability to support a 200 pound weight applied perpendicularly to the covering at any point.”  For the 1/8-inch or ¼-inch sheets used to make skylights, this was no problem to achieve for new sheets of plastic.  This meant that any skylights (or covering) installed more than met the standard, and there are films of weights bouncing off new skylights that show an elastic bending deformation with full recovery of shape.  How do the mechanical properties of the plastic skylights compare to this when they have been sitting on a roof for over a decade?

We examined several batches of skylights that had been removed from a building’s roof for replacement after being on the roof for about 12 to 15 years.  They were translucent, and some had been painted to limit the amount of heat transferred to a building.  Three skylights of each type (painted and unpainted) were used, and five large pieces were cut from the sides and the center.  The center pieces were a bit thinner because of the way they are molded, but this was not a large difference and could be corrected for in calculating tensile strength in pounds per square inch (psi) of cross section. The ASTM D638M-91a method was followed for tensile testing.  Each section was cut into seven rectangular blanks (1 inch by 6.5 inches) with a band saw, and those sections were filed and sanded down to remove any surface cracks or obvious imperfections such as nicks.  Some of the blanks had significant visible damage upon microscopic examination and were discarded before testing. Final sanding was done with wet 400-grit sandpaper.  These sections were conditioned for at least 48 hours at 25°C and 52% relative humidity before being tested in an Instron tensile tester, using manual grips.  The gauge length was set at 3 inches, and the speed at 0.2 inches/minute.  Tensile strength and elongation at break were measured, and averages with standard deviations were calculated to compare with values for new material.  The results are shown in Table 1.

Figure 1: Cross Section of a PMMA Skylight. SEM photographs of fractured, sun-exposed skylight
(scale bars at 20 u for side images, and 2 mm for central image).

Table 1. Tensile Strength and Elongation at the Break of a Skylight

Where:
EB = Elongation at break, percent
EB(sd) = elongation at break, standard deviation
TS = mean tensile strength, psi
TS(sd) = tensile strength, standard deviation.

The mechanical testing showed a very much weakened material after exposure to the elements in Florida for about 12 to 15 years.  This is exactly what one would expect from the scientific literature but may not be appreciated by some workers on rooftops.  If one examines the area under a stress-strain curve, which is roughly the energy needed to cause a fracture, one can estimate that it takes less than a third of the value needed for a new unit.  The true reduction in strength is probably much greater since the tensile specimens had the rough surface removed by sanding.  This was where most of the damage occurred, and it also would be a site for stress concentration and fracture initiation.  It is likely that the impact strength also would be reduced sharply.  Many such skylights remain on homes and businesses in sunny climates and can be very unsafe.  One solution to the problem is to require safety screens.  In fact, OSHA does require such protection, but the regulation seems widely ignored, perhaps because the material can be safe when installed and does not become brittle until it ages.

This represents a common materials engineering consideration: Replacing a metal or glass part with a plastic part requires understanding of the new material and use conditions.  Often the new part is more fracture-resistant and cheaper to manufacture in a complex shape, but the properties may change unacceptably with time.  One only has to walk through a parking lot and look at automobile headlights to see how the plastics that have replaced glass no longer are as optically clear as they were when a car was new.

Acknowledgement:  The electron micrographs were taken by the Major Analytical Instrumentation Center at the University of Florida. Dr. Dow Whitney and Dr. Chris Sakezles helped with the mechanical property measurements.

For more information on Professor Batich and polymethylmethacrylate skylights, please read his interview on K Exchange.

Statement of the Problem
Researchers have made considerable efforts to develop void fraction correlations for vertical upward two-phase flows. Currently, dozens of void fraction correlations for different flow patterns are available in the literature. Although Woldesemayat and Ghajar¹ have proposed a general void fraction correlation that is robust and suitable for various flow patterns, gas-liquid combinations, and pipe inclination angles, that correlation has a minor drawback. From the point of view of a general void fraction correlation, their correlation has been verified to be reliably accurate when compared with experimental data obtained from various sources with different experimental facilities. However, when engineers are dealing specifically with vertical upward two-phase flow, other correlations are available to provide predictions with an improvement in accuracy. Since vertical upward two-phase flows are relatively common in industry, void fraction correlations that can provide the greatest degree of accuracy need to be sorted out.

Description of Solution
A comprehensive comparison of more than 50 void fraction correlations with a total of 1,208 experimental data points compiled from 10 independent sources for gas-liquid combinations and pipe diameters has yielded two correlations that deliver excellent results.² The first correlation was proposed by Nicklin and associates,³ and the other by Rouhani and Axelsson.4 Both correlations were based on the drift flux model and have the following expression:

The two-phase distribution coefficient (C0) and gas drift velocity (ugm) are given as follows:

Nicklin and associates³:

Rouhani and Axelsson4:

where the subscripts l and g refer to the liquid phase and the gas phase and:
C0 = two-phase distribution coefficient
D = tube diameter, m
g = gravitational acceleration, m/s²
ugm = gas drift velocity, m/s
Vsg = superficial gas velocity, m/s
Vsl = superficial liquid velocity, m/s
x = flow quality
α = void fraction
ρ = density, kg/m³
σ = surface tension, N/m

Description of Results
The correlations by Nicklin and associates³ and Rouhani and Axelsson4 were validated and compared with a total of 1,208 experimental data points. The experimental data were compiled from various sources with different experimental facilities, which included various gas-liquid combinations and pipe diameters (ranging from 12.7 to 76.0 mm) for vertical upward flow. The results of the comparison of void fraction correlations with experimental data are summarized in Table 1. Although that table indicates that the correlation by Nicklin and associates³ has predicted more data points within the error bands of ±15% and ±20% than has the correlation by Rouhani and Axelsson,4 further scrutiny has indicated that the Nicklin and associates correlation did not perform as well in the range of 0.8 to 1.0 void fraction. The Rouhani and Axelsson correlation, in contrast, was found to perform satisfactorily for the entire range of void fraction (0 < α < 1).

Figures 1 and 2 show the comparison of the Rouhani and Axelsson and Nicklin and associates correlations with the entire experimental database of 1,208 data points. Figure 1 shows that the Rouhani and Axelsson correlation performed satisfactorily for the entire range of void fraction, with a slight tendency toward underprediction in the range of 0.8 to 1.0. By contrast, Figure 2 shows that the Nicklin and associates correlation conspicuously underpredicted the experimental data in the range of 0.8 to 1.0. Hence, the Nicklin and associates correlation is expected to work satisfactorily, possibly with better accuracy than the Rouhani and Axelsson correlation, in the 0.0 to 0.8 range. The Rouhani and Axelsson correlation, however, is expected to perform satisfactorily for the entire void fraction range (0 < α < 1).

Figure 1: Comparison of Void Fraction Correlation by
Rouhani and Axelsson4 with 1,208 Experimental Data Points

Figure 2: Comparison of Void Fraction Correlation by
Nicklin and associates³ with 1,208 Experimental Data Points

Table 1: Results of the Correlations When
Compared with All 1,208 Experimental Data Points

Wider Applicability of Results
The void fraction correlations shown in Equations (1) to (3) are applicable for estimating void fraction of vertical upward two-phase flow in pipes, which may include boiling and nonboiling flows. Vertical upward two-phase flows are used in offshore exploration for oil and gas. Offshore oil fields are being developed in deeper water, where vertical pipelines are used for transporting oil and gas from the seabed to the floating production vessel. In such cases, accurate void fraction results are important in the estimation of pressure drop of the two-phase flow in the pipelines. Another possible application of the void fraction correlations is in the membrane bioreactors (MBRs) used in the wastewater treatment process. A technique to reduce fouling on the membrane surface involves gas sparging, in which gas is injected to generate a gas-liquid two-phase cross-flow (typically slug flow).5 Slug flow induces an increase in surface shear stress, thus removing the fouling layers. In ozonation systems, void fraction is an important parameter in analyzing the influence of the ozone mass transfer on water treatment. Other wider applications in vertical upward two-phase flows can be found in nuclear reactor technology and pumping systems for vertical geothermal wells.

References
1. Woldesemayat, M. A., and Ghajar, A. J. Comparison of Void Fraction Correlations for Different Flow Patterns in Horizontal and Upward Inclined Pipes. International Journal of Multiphase Flow, vol. 33, no. 4, pp. 347–370, 2007.
2. Godbole, P. V. Study of Flow Patterns and Void Fraction in Vertical Upward Two-Phase Flow. M.S. thesis, Oklahoma State University, Stillwater, 2009.
3. Nicklin, D. J., Wilkes, J. O., and Davidson, J. F. Two-Phase Flow in Vertical Tubes. Chemical Engineering Research and Design, vol. 40, pp. 61–68, 1962.
4. Rouhani, S. Z., and Axelsson, E., Calculation of Void Volume Fraction in the Subcooled and Quality Boiling Regions. International Journal of Heat and Mass Transfer, vol. 13, no. 2, pp. 383–393, 1970.
5. Psoch, C., and Schiewer, S. Long-Term Study of an Intermittent Air Sparged MBR for Synthetic Wastewater Treatment. Journal of Membrane Science, vol. 260, no. 1–2, pp. 56–65, 2005.

In recent years, HSEI twin-screw extruders have moved beyond their roots in plastics and made their way into a growing number of pharmaceutical and nanotechnology applications. As a more advanced alternative to batch mixing, HSEI machines are enabling pharma users to create sophisticated new dosage forms by compounding active pharmaceutical ingredients with polymers.  In the nanotechnology world, HSEI twin-screw extruders incorporate functional nanoparticles into the next generation of aerospace, electronics, and packaging materials.

Despite their outward differences, the pharmaceutical and nanotechnology applications have something in common from a compounding standpoint. Both rely on material feedstocks that are typically available in very limited quantities and are breathtakingly expensive, sometimes costing many thousands of dollars per gram. These two factors create a problem for traditional HSEI twin-screw extruders: Machines designed for production environments that measure output in thousands of hourly kilograms will not be much help in developing materials measured in grams. The solution to this problem of scale has for years been the use of various laboratory-size extruders that comfortably process as little as 0.5 kg per hour.

Unfortunately, lab-size extruders have had problems when it comes duplicating the technical characteristics of full-scale HSEI machines, in part because the feed mechanism and process section design of production-sized twin screws do not scale down easily.

Over the last year, however, Leistritz engineers have worked around the problems of scale to come up with a new lab-size twin-screw extruder design. This “nano” extruder features mechanical design and process innovations that allow it to mimic the technical capabilities of traditional HSEI twin-screw machines without leaving precious quantities of developmental materials behind in the hopper.

Here’s a closer look at the design of this nano-scale compounding hardware and how it can make a difference in the efficient development of new drugs and nanotech materials.

Twin-screw Extrusion Fundamentals

Before diving into the details of the nano-scale machine, let’s start with an overview of twin-screw technology fundamentals, which will help put some of the intrinsic differences between production and nano-scale extrusion in context.

Production HSEI twin-screw extruders and many small-scale models share a basic construction philosophy. They consist of segmented screw and barrel elements that can be configured to the job at hand. These modular screw elements are assembled onto a motor-driven shaft capable of rotating the screws with high torque forces, imparting energy into the material to be processed. The modular barrel elements that enclose the screws feature internal cooling bores for tight thermal control.

When corotated within the barrel, the screw elements exhibit pumping and self-wiping actions. The specific compounding tasks performed by the extruder depend on the lineup of screw elements. For example, elements in machine’s process section can be tailored specifically for mixing or for devolatilization. Discharge elements downstream in the process section typically build and stabilize pressure (Figure 1 shows typical screw segments and functions).

Figure 1. Pressure Gradient in a Twin-Screw Extruder

The free volume available within the process section is directly related to the ratio of the screw’s outside diameter to its inside diameter (OD/ID) or, put differently, the ratio of the diameter around the screw flights to the screw’s root diameter. The torque-limiting factor in twin-screw extruders depends on the diameter of the screw shaft and the cross-sectional geometry of the shafts. For example, deeper screw flights result in more free volume but less torque because the deep flights reduce the screw shaft’s diameter.

Based on the use of a symmetrical splined shaft, an OD/ID ratio of approximately 1.55/1 historically has been considered to offer the best balance of torque and volume. In recent years Leistritz has developed new asymmetrical splined screw shafts that result in a more favorable volume-torque balance and potentially higher throughput rates. These asymmetrical shafts offer OD/ID ratios of 1.66/1 without sacrificing torque.

Conventional HSEI twin-screw extruders are starve fed with less material than the screws can handle at any specific time. Their output rate is determined by one or more feeders metering combinations of pellets, liquids, powders, and fibers into the process section. The rpm of the HSEI screw remains independent from the feed rate and is set to optimize compounding efficiencies.

By controlling pressure gradients with the barrel, starve feeding allows different fillers and other ingredients to be fed sequentially into downstream barrel sections. Sequential feeding is the key to many of the high-tech polymer compounds on the market today.

Nano Compounding: A New Mind-set

In high-volume production runs, the free volume, torque, and starve-feeding parameters are designed as a system with an eye toward maximizing throughput rates while maintaining product quality. A different mind-set and methodology are required in compounding pharmaceutical and nanotech materials. In these applications, the goal is to minimize the waste of rare, expensive materials while effectively evaluating the extrusion process and providing a route for future scale-up.

In many ways, this mind-set is uncharted territory that required a rethinking of the extruder’s process section design and feeding system. What Leistritz engineers came up with is a twin-screw extruder with segmented 16-mm OD screws and a 1-mm flight depth. Its 1.2/1 OD/ID ratio results in a free volume of approximately 1 cc/diameter. Called the Nano 16, this extruder is intended for the evaluation of samples in batches as small as 20 grams.

Figure 2: Micro-Plunger Feeder Mated to a Nano 16 Twin-Screw Extruder

Instead of the bilobed elements commonly used on larger machines, the Nano 16 employs trilobed screw elements to facilitate low-volume processing and mixing with the smaller OD/ID ratio.

Figure 3: Nano 16 Trilobal Screws

Figure 4: Micro 18 Bilobal TSE with 1.5/1 OD/ID

Figure 5: Nano 16 Trilobal TSE with 1.2/1 OD/ID

The same gearbox is used for the Nano 16 as for the larger Micro 18-GL Micro 18-mm HSEI twin-screw extruder. This design choice allows an 18-mm process section to be mated to the gearbox, providing a clear scale-up path to a 1.5/1 process section similar to those found on larger production machines.

One of the unique aspects of the Nano 16 is the way it simulates the starve-feeding mechanism normally used in production-scale twin-screw extrusion. Instead of conventional metering feeders, the Nano 16 uses a tiny patent-pending “micro-plunger” to meter small amounts of materials with nearly full utilization of the sample. This micro-plunger consists of a motor-driven piston within a stainless-steel tube that mates to the bottom of the Nano 16’s feed barrel.  A closed-loop Vector gearmotor drives the piston, allowing samples of 20 to 100 cc to be metered accurately into the barrel.

As with the starve-feeding mechanism on larger machines, the Nano 16 feed screw elements are designed to convey the materials at a higher rate than is being delivered by the micro-plunger. Thus, the combination of the Nano 16 twin-screw extruder and the micro-plunger feeder replicates the staging of unit operations and the shear-imparting mechanisms of production-scale twin-screw extrusion equipment.

Nano Extrusion Trials

To validate the Nano 16 design, a series of trials were performed to compound the pharmaceutical polymer hypromellose acetate succinate (HPMCAS) with 40% of a poorly soluble drug and a trace amount of an U.S. Food and Drug Administration (FDA)-approved blue color pigment. The objective was to demonstrate the viability of the extrusion process by using a very small sample with minimal waste. Also, the choice of a poorly soluble active ingredient was important because poor solubility is a barrier to usage for many new drugs.

All materials were premixed and metered by the Nano 16’s micro-plunger feeder. The trials used a 25:1 length/diameter process section, and the screw design included flighted, kneading, and shear-inducing elements.  An atmospheric vent and a low-volume strand die attachment were also part of the test system.

Tests were performed at feed rates of 2, 4, and 8 cc/min and under different run conditions. A feed rate of 2 cc/min translated to approximately 120 g/h, 4 cc/min to 240 g/h, and 8 cc/min to 480 g/h. The batch size selected for the premix was 50 grams, of which 44 grams of the sample was collected and usable for evaluation purposes. Approximately 6 grams of material was lost as follows: 1 gram at the extruder/plunger interface, 2 to 3 grams on the screws, and 2 grams in the die/front end.    Temperature profiles and screw rpm were selected on the basis of experience with similar formulations, and PC-based controls and data acquisition allowed for detailed analysis of the run conditions.

On the output end of the machine, the compounded material was cooled in an air-quenched annular chamber and cut into 1-mm pellets by a dual-drive strand pelletizer. The pellets then were milled into a powder and compressed into tablets for dissolution rate and solubility testing according to pharmaceutical standards.

The results (Figure 2) indicated the superiority of extrusion to process this poorly soluble active pharmaceutical ingredient compared with traditional “dry mixing” batch operations. The active ingredient was transformed from a crystalline to an amorphous structure during processing, and most of the drug was dissolved after 20 minutes. Without extrusion, this particular active ingredient might not have been a candidate for additional development.

Figure 6: Solubility Results from Dissolution Testing

Subsequent scalability tests were performed on larger extruders, including 2 kg/h runs on an 18-mm HSEI twin-screw and 6 kg/h runs on a model with 27-mm screws. Similar results were obtained on both larger machines, confirming the viability of the Nano 16 as an initial screening device.

In summary, traditional HSEI twin-screw extrusion technology has both similarities to and differences from the pharmaceutical mixing process. For most commodity products, the goal is to increase throughput rates. The discovery of cutting-edge drugs and advanced materials, however, requires machines that minimize the waste of costly developmental materials while providing an assessment of extrusion viability. With its new take on feeding and process section design, the 16-mm Nano meets both requirements.

This article examines methods for determining the droplet displacement that results from thermocapillary pumping in a closed microchannel. Thermocapillary pumping (TCP; see Figure 1) occurs when variations of surface tension and differences between contact angles at both ends of a droplet or liquid film contribute to an effective pressure difference across the liquid.

The droplet calculations described here have practical utility for the design and operation of microdevices, such as micro heat engines, actuators, sensors and lab-on-a-chip technology, that rely on accurate control of droplet motion within microchannels.

The droplet is positioned between two air pockets in a closed circular microchannel. There is a uniformly distributed cyclic heat source around the droplet. During heat input, thermocapillary forces induce fluid motion from left to right. Heat transfer to one end of the droplet leads to temperature variations within the liquid. The purpose of this article is to determine the displacement of a droplet, when subjected to a cyclic heating source.

Solution Procedure

The microchannel is modeled in two sections: the droplet/substrate region (on the left side) and the droplet/air region (on the right side). The two regions are assumed to be a quasi one-dimensional semi-infinite region. Each region is assumed to have its own heat source so that the heat transfer on the right and left sides are equal. The heat transfer between the substrate and the environment is neglected because only the axial direction is considered in this analysis. During the heating cycle, the pressure from the air on the right side of the channel opposes both the frictional force from within the droplet and the air force from the air pocket on the left side. The resultant force can be written as

Using the ideal gas law:

where A is the cross sectional area of the channel, m is the mass of air, R is the universal gas constant, V is the volume, and T is the temperature. The frictional force on the droplet is determined on the basis of the following reduced form of the Navier-Stokes equation, using the Poiseuille flow assumption:
The thermocapillary force on the droplet is then determined based on changes in the internal pressure of the droplet, as follows:

where G = 4 for a circular microchannel, and θ is the contact angle. The change of surface tension σ is estimated based on the temperature change across the droplet, σ = A – BT , where A = 0.07583N/m and B = 4.177×10-4 N/mK for water.

The net force on the droplet is then estimated as:

The change in pressure across the channel is the force per unit cross sectional area of channel:The velocity and displacement of the droplet can then be determined by integrating the equation of motion of the droplet, thereby yielding:

where mdroplet is the mass of the droplet, and u° and x° are the velocity and displacement at the previous time step.

Results and Discussion

The droplet motion in the channel is analyzed for a 16 μm microchannel, to observe the effects of heat input on the displacement of a droplet (see Table 1 for problem parameters). Figure 2 shows a comparison between the predicted results (based on the model in previous section) and the measured data. The speed of the droplet after the initial heat input to the channel is rapid, but decreases once the effect of back pressure from the opposite end of the closed channel increases. The initial speed of the droplet over a period of 2.3 seconds is about 13 μm/s. Once the droplet reaches a uniform velocity, the displacement is predicted accurately by the model.

However, during the transition period between the initial acceleration and the subsequent stage of uniform velocity, the model overpredicts the droplet displacement because the droplet motion has not yet reached a uniform velocity.

Conclusions

The difference in thermocapillary pressure across the droplet generates droplet motion within a closed microchannel. The effect of the pressure change can activate a membrane at the end of the microchannel, to generate electricity via piezoelectric materials. The displacement of the droplet shows that the microchannel also can be used as either a micro pump or an actuator.

The first step in the redesign program was determining what needed to change. A steering committee with representation from engineering, manufacturing, marketing, and business leadership spent weeks trying to determine what was required from a product standpoint to deliver radical improvements in both product performance and product economics. As a result of that collaboration, the team established aggressive new targets around robustness and reliability in addition to the goal of cutting the parts count and labor costs nearly in half. Once the “what” was clearly defined, the team needed to figure out how to accomplish its competitive new charter. It turned to a robust development approach coupled with DFMA methodology and a software toolset from Boothroyd Dewhurst Inc. and set out on the redesign course.

The robust development approach was essential because Hypertherm’s plasma cutting systems, used by factories and machine shops in shipbuilding, automobile work, construction, and metal fabrication, are exposed to the harshest conditions—from temperature extremes to physical impacts and vibrations. A key design goal was to ensure that any new products would work consistently in all sorts of environmental conditions without requiring customers to do any fine-tuning to ensure reliability. At the same time, the team wanted to configure the products in a manner that would ensure easy serviceability in case of problems. To achieve those stringent quality objectives, the engineering team turned to robustness surrogate testing, an accelerated cycle of design, build, test, break, and fix that mimicked the way customers might break a machine in the field. By performing this process as part of the early design regimen, Hypertherm engineers aimed to avoid the kinds of design miscues that lead to the most common failures and quality issues.

There were a couple of key challenges related to the robust development approach. The first was prioritizing failure modes, since there were thousands of things that could go wrong with any single product yet it was feasible to tackle only a handful of those things in a single design program. There was also the issue of creating the test surrogate. It was easy to break a product quickly, but breaking it in the manner in which it commonly fails in the field was a completely different story. For example, simply accelerating the stress on a cutting torch to achieve a particular failure rate would not provide the appropriate context for optimizing the design; instead, the team had to understand the failure mode in relation to the customer experience and replicate it in that exact fashion. By leveraging internal domain expertise, analytics, and good old-fashioned experimentation, the team was able to zero in on the right failure modes to provide a starting point for the new design. Finally, there was a need to change the engineers’ mind-set away from placing blame on customers for misusing the tool and breaking a “good design” to recognizing that a design might not be robust enough to stand up to the rigors of in-the-field use.

Taking Cost Out of the Equation

In addition to adopting robust design principles, Hypertherm began a campaign to make DFMA an integral part of the product development process in a wholesale effort to reduce its development and manufacturing costs. DFMA, a suite of software, and a development methodology pioneered by Boothroyd Dewhurst guided the engineers through a process to reduce part count and improve assembly with the overall goals of lowering costs and increasing reliability. DFMA would complement already existing lean and Six Sigma quality programs, along with voice-of-the-customer initiatives, as part of Hypertherm’s multiyear effort to bolster product performance, reduce costs, and achieve overall manufacturing efficiencies.

The team started the DFMA journey with one of its simplest plasma cutting products, leveraging the software to evaluate the unit part by part and document the assembly process step by step. From the software, the team generated three key Pareto charts (cost, part count, and assembly time) that established a baseline from which it could measure its success and zero in on the parts and processes in which there was the greatest opportunity for improvement.

Although the approach appears relatively straightforward, the process is quite involved and requires discipline on the part of the engineers. Depending on the complexity of the product being evaluated, it could take a team weeks or even longer to go through the rigorous and detailed exercise of counting every single part and evaluating the assembly strategy—and that was just for the baseline product, not for potential redesign work. Convincing individual engineers that the benefits of the DFMA approach outweigh the commitment it takes to learn and perfect the process has been an ongoing struggle. Hypertherm addressed some of these obstacles by giving the engineering team the tools, time, and training it needed to learn DFMA principles and by making the engineers—not the manufacturing group—responsible for meeting the aggressive cost reduction targets.

The real aha moment came when the engineers finally understood their designs and opened a window into the tangible opportunities for improvement, whether it was eliminating parts redundancies or seeing how a different design approach could eliminate parts such as fasteners and connectors altogether. Once the team bought into DFMA’s power, its members began to see their designs and the whole design process in a completely different light. Nearly eight years into the redesign effort, Hypertherm engineers now perform DFMA as a standard part of the design process and view the goal of parts reduction and design for assembly as their responsibility, not the domain of manufacturing. This has been a major shift for the engineering team and a key enabler for Hypertherm to achieve its aggressive performance and economic goals.

Today, Hypertherm’s metal-cutting products use about half the parts of previous versions, and the company is on course for consistently achieving a 50% cut in production costs. Product performance is up and warranty costs are down, with an 80% decrease per unit from 2002 to 2010. Although lean manufacturing and Six Sigma quality concepts continue to play a key role in Hypertherm’s strategy, it is the engineering team’s back-to-basics makeover around DFMA that has turned out to be the standout initiative fueling the company’s product success.