Novel Flexure Design for a High-Temperature Thermal Storage Vessel Coupled to a Free-Piston Stirling Engine

Abstract

A novel support flexure for a salt-based thermal energy storage (TES) vessel coupled to a solar dish Stirling engine was designed and analyzed via Finite Element simulations. During normal operation, the TES vessel experiences significant thermal expansion as a result of the high temperatures experienced. This leads to a large deformation and high thermal stress along with a large temperature gradient within the flexure. Eight flexures are arranged symmetrically around the circumference of the salt vessel. The designed flexures have an axial and circumferential section that allows for the vessel to expand in both the radial and axial directions. Additionally, the flexures can be stacked to increase the lateral rigidity to prevent the vessel from sagging under gravitational effects while still allowing for the desired axial flexibility. Because of the high temperatures experienced by the flexure, the superalloy Inconel 625 was used as the flexure material. In addition to a model of just a single flexure, a system scale model that included the flexures, a dummy engine, and the TES salt container was developed. The results of the analysis showed that the final flexure design meets the stress, deformation, and fatigues requirements. The chosen design is compact, simple, low-cost, and can potentially be used in other applications where a support structure experiences a high degree of thermal expansion.

INTRODUCTION

Owing to the increased concern over the detrimental environmental effects of burning fossil fuels coupled with their ever-dwindling supply has spurred renewed interest in clean sustainable alternatives. Of particular interest is that of solar energy for grid scale electrical power generation. The most promising method for converting solar radiation into useful power is via a concentrated solar power (CSP) plant. At a CSP plant, the incoming solar radiation is used to heat a working fluid within a thermodynamic cycle. Typically CSP plants are broken down into three categories based on the type of receiver used; power tower, though, and parabolic dish. A trough type receiver can achieve a concentration of around 75 suns at temperatures around 400 °C whereas a power tower receiver has a concentration of 800 suns at 560 °C. Although it is the least used receiver a parabolic dish type receiver has a concentration of 3000 suns at temperature nearing 750 °C [1–4].

While there are numerous examples in the literature of the various applications for planar springs or flexures, few account for thermal gradients within the flexure. Given the vast body of work on using FEA to design flexures, a new method was developed that incorporates thermally induced stresses that can occur in high-temperature applications such as those that occur in Stirling CSP applications. In addition to the inclusion of the thermal stress, the designed flexure needs to be laterally rigid while being radially compliant all at low cost. The proposed TES flexures were simulated at two levels: a single flexure with 1/16^th of the vessel and a system scale model that included flexures, the salt TES vessel, and a dummy engine. The results of this investigation extended the already documented FEA analysis of flexures to include thermal stresses.

Nomenclature

CSP Concentrating Solar Power

System Design

The TES system consists of a cylindrical salt vessel that is welded to the heater head of a 3 kW Infinia FPSE. The engine and TES vessel are fixed to the receiver dish frame at ambient temperature via flexure springs. These springs allow for certain axial engine case vibration and reduce the transmissibility of the vibrational forces of the Stirling engine. The flexure springs, as well as two operational Power Dish units without TES incorporated, are shown in Figure 1. For the new system design, the existing stainless steel 304 planar engines mount flexures are used as the support for the 3 kW engine. However, in contrast to the engine, one end of the storage vessel flexure is fixed to the hot vessel enclosure and therefore has an elevated temperature of ~650 °C during operation. Not only is stainless steel not suitable for use at this temperature, the existing planar engine flexures are too rigid in the radial direction to allow for the thermal expansion they will experience. Therefore, new flexures must be designed to support the TES salt container. The flexures will be designed to have (1) a relatively large lateral rigidity as to only allow small amounts of vessel sagging or tilting under gravitational effects; (2) the axial flexibility to allow for the axial vibrations resulting from the case motion of the engine assembly; (3) the stress field within the flexure will meet the stress, fatigue, and creep requirements; (d) low thermal conduction loss through the flexure mounting; (e) the flexures will be low cost, compact, geometrically simple, and easy to assemble. A design that has all of these attributes is difficult to achieve. Additionally, a major design obstacle is to reduce the high thermal stresses that result from the radial and axial thermal expansion of the storage container as well as the large temperature gradient along the flexure.

As the storage vessel-engine assembly is largely symmetric, a natural assumption is that several individual flexures of the same shape can be arranged circumferentially to obtain the desired effects. Multiple design concepts were studied and compared which included a bolted flexure design in which the axial and circumferential flexure comments are bolted together and a one where the TES vessel is hung within a frame using coil springs. Analysis showed that the bolted design yields excessively high stress near the bolting region resulting from the thermal expansion. For the hanging design, a suitable coil spring or low-k spacer that can work at 650 °C with a suitable lifespan could not be found. The current working concept that will be investigated is that of using a single-piece flexure design that has a section placed along the vessel’s axis and a section in the circumferential direction. It is expected that the axial section will allow for the vessel’s radial deformation, while the circumferential sections allow the vessel to expand thermally in the axial direction and will also provide the required axial compliance. By optimizing the dimensions of the flexure, one can obtain the required rigidity in the lateral direction or this can be accomplished by using stacked flexures.

Design criterion

Stress

Fatigue

Due to the case motion of the Stirling engine, the flexures undergo a high cycle fatigue. The number of pressure cycle required in the design is 1.5×10¹⁰ cycles based on an engine frequency of 60 Hz, 8 hr/day operation, and a 25 year lifetime. Additionally, the flexures experience a low cycle fatigue due to the variation in the secondary stress field during thermal cycling resulting from start-up and cool down. Assuming three starts per day, the load results in 27,000 cycles. The stress per cycle, S-N, curves for Inconel 625 are shown in Figure 4. Note that Figure 4 indicates that for Inconel 625, the high-temperature and room-temperature fatigue strength. S_a, is close for large N, N>10⁷. Therefore, Figure 3 can be used for the high cycle fatigue loading. The Goodman criteria were also used to account for the combined effects of mean loading and fatigue loading. For Inconel 625 sheet, axial load, Kt=1, S_a = 270 MPa for N=2.9×10⁴ and S_a = 135 MPa for N=1.5×10¹⁰. The fatigue loading a for Inconel 625 is presented in Table 1.

Figure 4 – Infinia S-N Curves for Inconel 625

Displacement

Results and discussion

The various flexure designs were analyzed using FEA within Ansys. First, the steady state temperature was analyzed and then used as the input to a structural analysis. A linear-elastic evaluation was used and therefore no plastic deformation of the material was considered. A simplified 1/16th model was first analyzed to provide information on the heat loss and spring constants in the axial, radial, and circumferential directions. After this, a system scale model that included an engine, salt container, TES flexures, and engine flexures was analyzed.

Analysis of Single Flexure

Thermal Analysis

Due to the symmetry of the system, a 1/16^th model that includes a single flexure without the Stirling engine was used for the initial model. For the thermal analysis, the boundary conditions were a temperature of 650 °C applied to the interior of the TES container and 22 °C applied to the fixed end of the flexure. Figure 5 shows the predicted steady state temperature distribution for both the L-shaped and inverted 7-shaped flexure designs. The temperature gradient within the inverted 7-shaped flexure is slightly smoother than that within the L-shaped flexure. The results showed that for the L-shaped flexure the conduction heat loss for a single flexure is 1.7 W, therefore the total heat loss is 27.2 W for the entire system and thus can be ignored. (this information isn’t in the final report for the chosen flexure and I don’t know how to calculate it.)

Structural Analysis

System Model

In order to obtain more accurate results, a system scale model that consists of the salt container, TES flexures, engine, and engine flexures was constructed. In this model, the TES vessel was welded to the heater head of the FPSE. In an effort in increase the lateral and radial rigidity, two TE s flexures were stacked together. It is believed that using stacked flexures will not change the stress field significantly as the majority of the stress is thermally induced but it will double the effective rigidity of the flexure. In the model, both the engine body and engine flexures were taken to be stainless steel 304, while the heater head was Inconel 625 due to the high-temperature requirements. It is expected that the system model will reveal the interactions between the engine and salt vessel flexures as well as provide more accurate stress and deformation results.

Thermal Analysis

As with the single flexure model, first, a temperature field was calculated. Only half of the engine was modeled due to symmetry. As with the previous model, the inside temperature of the TES vessel is set to 650 °C and the cold end of the Stirling engine body is 22 °C. The temperature distribution is shown in Figure 8. The predicted heat loss was 54.9 W.

Structural Analysis

Experiments

The flexures along with the TES solar power system are first going to be tested at the laboratory scale where a fuel combustor replaces the solar energy from the solar dish. After the laboratory scale testing, the system and flexures will be tested in a full-scale PowerDish. The result of the experimental testing will be compared to the values predicted by the simulations. The lab scale test rig setup is shown in Figure 12. Fabrication of the salt vessel flexures and the vessel engine system is ongoing.

Figure 12 – Laboratory scale experimental set up

Conclusions

Acknowledgments

References

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