As of this writing, the economizer has been built, pressure tested and installed in the prototype vehicle. Its performance as a heat exchanger has not yet been tested. Described herein is the theoretical modeling, design and fabrication of the economizer units. Future plans include rigorous road testing to verify the model and to identify possible modifications for a second-generation economizer.
The economizer is required to vaporize and, if possible, superheat liquid nitrogen at mass flow rates of up to 300 g/s. It must not produce excessive pressure drop on either the tube- or shell-side fluids. The economizer must also be safe in both normal operations and during an accident.
For the design of the economizer, a variant of the shell-and-tube heat exchanger has been employed. The tube-side fluid is the incoming liquid nitrogen and the shell-side fluid is the exhaust from the expander. To examine the theoretical limitations on the performance of the economizer, conservation of energy can be applied as shown in Eq. 1.
For steady state operation, , so the tube-side outlet conditions can be specified by
To calculate the maximum theoretical performance, assume that the outlet temperature of the shell-side gas is equal to the saturation temperature of the tube-side fluid (~120 K). If the exhaust pressure and temperature of the nitrogen gas is 3 bar, and 270 K respectively, then the maximum enthalpy at the tube-side exit of the economizer, hmax, is 140 kJ/kg, corresponding to a temperature of 155 K. This equates to over 47 kW of steady state heat transfer at the maximum mass flow of 300 g/s, and is 35 K above the saturation temperature of the tube-side fluid. This calculation provides the figure of merit for the performance of the economizer, the heat transfer effectiveness:
where h1 is -18 kJ/kg and ?hmax is 158 kJ/kg. If more than 50% of maximum performance can be attained (i.e.: ?econ > 0.5), then this should allow the ambient-air heat exchanger to be designed for single phase flow.
Constraints: Due to limited space in the vehicle, the economizer must necessarily be of compact design. As shown in Fig. 7, the two economizer shells are situated in the center of the cargo deck, toward the front of the vehicle. The installation of a second dewar is planned for behind the driver’s seat, so the diameters of the two shells are constrained to be such that they can accommodate this addition. Even though the vehicle is of rugged construction and has good weight bearing capability, low mass components are installed where possible.
Configuration: A shell-and-tube heat exchanger is an obvious choice for compact, yet highly effective duty. The configuration chosen for the economizer is shown in Fig. 8. Though welding is the joining process of choice for tube-to-manifold connections in industrial scale heat exchangers, the available aluminum tubing had a wall thickness of 0.7 mm. This is a difficult size to weld, particularly when using aluminum and when joining to a considerably more massive manifold. This led to the use of compression fittings. Because each tube end has to be accessible to a wrench, the fittings are widely spaced on the manifold, as shown in Fig. 11.
Fig. 11: Manifold showing hole pattern.
Due to this geometric constraint, the tube density for straight tubing is lower than optimum. To increase the length of tube per fitting, a multiple double-back configuration, shown in Fig. 12, was adopted. Each individual tube doubles back on itself four times between the inlet and the outlet, to give five 0.5 m lengths. Each tube has three passes that are in counterflow with the shell-side fluid and two that are in parallel. To achieve an even greater density, each tube was intertwined with its neighbor before installation. There are two economizer units, with 16 tubes in each, totaling 90 m of 6.35 mm diameter tubing. This gives an overall heat transfer area of 1.8 m2.
Fig. 12: Economizer unit showing double-back tube configuration.
Within the shells, the tubes are supported by twelve 3.2 mm rubber disks, or baffles, also shown in Fig. 8 and Fig. 12. These baffles form a seal with both the shell wall and the tubes themselves. Because they have flow passages cut on alternating sides, the baffles also serve to direct the shell-side gas over the tubing in a cross-flow pattern.
Materials and Fabrication: The manifolds are constructed of aluminum 2024-T6 and the tubing is aluminum 6061-T6. Aluminum, besides being readily available, has the advantages of low density, high conductivity, high yield strength at cryogenic temperatures, and excellent machinability. All fittings are either NPT or compression, and are made of aluminum, for comparable thermal expansion. Each shell is constructed of 25.4 mm thick, high-density polyethylene. The inlet, outlet and relief nipples are fused to the main body of the shell.
Structural Integrity: Each economizer is secured to the deck of the vehicle with two nylon straps wrapped around each shell. The shells themselves are pressure rated by the manufacturer to 8.5 bar. The shells are also equipped with one relief valve each, set at a gauge pressure of 4 bar. The aluminum tubing is pressure rated by the manufacturer to near 500 bar.
Each of the four manifolds is designed to withstand an internal pressure of 27 bar, at 77 K. Utilizing the plate bending correlations of Timoshenko, and the yield strength for low-temperature aluminum given by Scott, a factor of safety of 6.7 was obtained. Modifying this result with the ligament efficiency factor given by Harvey for perforated plate stiffness, the final safety factor for the manifolds is 3.4.
When the economizer is operating, the shell will be pressurized to 3 bar. The manifolds will experience a differential pressure of 2 bar acting outward. Because of this, the economizers will see tensile forces in the axial direction of up to 6670 N during normal operations, and 21,600 N in the event of a catastrophic blow-by of the valving in the expander. To counter this, each economizer manifold is retained in place by aluminum brackets bolted together with two 1.9 cm threaded rods.
A model was developed for the performance of the economizer, to serve as a design tool. This enabled informed decision-making about such geometric parameters as tube length, number of passes, number of baffles, etc. Pressure drop was not considered as one of the design variables because a blow-down system is being used. It takes no energy and very little additional mass to offset pressure drop in the tube-side of the economizer. For this reason, pressure drop correlations were not included in the model, however, the capability to include them at a later date is built in.
The unique flow arrangement of this heat exchanger does not lend itself to analysis by the ?-Ntu method. Therefore, thermodynamic and heat transfer performance calculated numerically, using a finite differencing scheme. To model the economizer, both the shell-side and tube-side variables were discretized, according to the scheme shown in Fig. 13.
Fig. 13: Element numbering for one economizer tube.
The following assumptions were made in the modeling of the economizer:
* Thermodynamic equilibrium between fluid phases.
* Even flow distribution. There are 32 tubes and two shells, but only one of each is modeled.
* Steady-state operation.
* Fully developed flow.
* Adiabatic shell wall. This is also conservative because heat transfer from the air to the shell-side fluid will increase performance.
* Zero radiation.
* Zero axial conduction.
Across each element of the economizer, an energy balance is performed. That is,
Note that for this element numbering system, the flow is left-to-right for passes 1, 3 and 5 and right-to-left for passes 2 and 4. For two-phase flow, the heat equation can be written
For single phase flow, enthalpy is a function of temperature, which is found using a log-mean temperature difference method:
for j = 1,3,5 (6)
for j = 2,4 (7)
where P is the perimeter and L is the element length. is the average overall heat transfer coefficient:
The tube-side fluid is often of ambiguous phase, so equations of state for the thermodynamic variables are not useful. Instead, a nitrogen properties database is used, where the inputs are the pressure and either the bulk temperature or enthalpy, depending on the phase. The external heat transfer coefficient is evaluated using the Churchill and Bernstein correlation for cylinders in crossflow. The internal heat transfer coefficient for single phase flow is evaluated using Gnielinski’s formula. For two-phase flow, the heat transfer coefficient is found via Kandikar’s correlation.
Results found for the design cruise mass flow of 60 g/s are given in Fig. 14. The shell-side temperature, as well as the tube-side quality as a function of the non-dimensional span are shown. The specific enthalpy at the economizer outlet is 92.3 kJ/kg, giving a heat transfer effectiveness of ?econ = 0.72.
Fig. 14: Quality and temperature profiles through the economizer.
The thermodynamic performance, ?, of the economizer is inversely dependent on the mass flow. To examine why this occurs, note that for this heat exchanger, the shell-side resistance to heat transfer dominates. That is, for any element
The external heat transfer coefficient scales as , so
This behavior is displayed by the solid line in Fig. 15. This shows the decreasing value of ?econ, along with the resulting increase in the exit temperature of the shell-side fluid vs. mass flow. The variability in the curve is an artifact of the finite convergence criterion used in the heat transfer simulations and does not reflect any physical phenomena.
Fig. 15: Economizer effectiveness vs. mass flow.
The calculated performance of the economizer meets the original criteria of ?econ ; 0.5 for the majority of its operational envelope, but falls short of the requirement at high mass flows, which will typically occur only in transient bursts. Thermal transients for sub-ambient heat exchangers generally work in favor of performance, so a partial offset of this decrease in effectiveness is expected. To determine whether this is true requires extensive road testing, which was not possible as of this writing because construction on the test-bed vehicle was still in progress.