INTRODUCTION
Dr Robert Stirling initially discovered Stirling engines back in 1816 [1]. A Stirling engine is an ideal cycle, like a Carnot Cycle. It operates on a four-stage cycle, as shown in Figure 1 [2]. To start with, in stage (1→2) the expansion of gas in the cylinder at a constant temperature in the hot end body takes place. Stage (2→3); at constant volume, the temperature is transferred from high temperature areas to lower temperatures, hot end to cold end. Stage (3→4); compression at constant cold temperature takes place. Finally, in stage (4→1);
the gas returns to a higher temperature at constant volume. The cycle keeps working as long as the high temperature input is available, which is the driving force of the engine [2]. Additionally, some researchers are
currently studying the feasibility of using solar radiation principals to power Stirling engines for green energy with no environmental impact [3], which can be applied to small-scale applications, and studied for large-scale everyday used engine, to eliminate the use of fossil fuels [4]. This research focuses on identifying the best primary location to place different geometry types of Fins on a Stirling Engine to enhance the heat transfer within the system. In addition, different geometry types of fins are analyzed and determined according to their effectiveness in enhancing the heat transfer of a Stirling Engine, including an annular type, a conical type, and a rectangular type, in which the identified best geometry, based on results and comparisons, would be selected and ran through a placement location analysis to find the best possible location to add the fins. Nevertheless, Received: 9 September 2022, Accepted: 31 October 2022, Published: 31 December 2022, Publisher: UTP Press, Creative Commons: CC BY 4.0
HEAT TRANSFER ENHANCEMENT IN STIRLING ENGINE USING FINS WITH DIFFERENT CONFIGURATIONS AND GEOMETRIES
Ahmad Ramahi, Hasan Hamdan, Sharul Sham Dol*
Department of Mechanical Engineering, Abu Dhabi University, Abu Dhabi, United Arab Emirates
*Email: [email protected] ABSTRACT
The temperature difference across a Stirling engine cylinder is one of the main factors contributing to the power output and efficiency. Stirling engine is a heat engine that operates through expansion and compression cycles through different fluid temperatures. In addition, the engine was noted to have three different configurations, which include the alpha, beta, and gamma types, which are discussed in work. This study aims to investigate the effect of adding various fin geometries on different engine cylinder locations to simulate and visualize heat transfer enhancement across the cylinder. The various configurations were simulated through the ANSYS Fluent commercially available CFD model, which was used to simulate the temperature difference on the hot and cold ends of the tested fins. A validation model of mesh element sizing was also implemented to determine the accuracy of the achieved numbers.
Moreover, Fusion360 was used to 3D design different geometries, including annular, conical and rectangular fins.
Furthermore, lastly, validation of the obtained simulated results was conducted to monitor the accuracy of the simulation through two different methods. An effectiveness of 8.17 was obtained through the simulation for annular fins; in addition, it was found that annular fins achieved the best temperature distribution among the selection of geometries and configurations simulated, which was recorded as 223°C for the hot end and 40°C for the cold end.
Keywords: CFD, simulation, fins effectiveness, fins efficiency, stirling engine, heat transfer
the paper proceeds to confirm the accuracy of the results through a mesh sensitivity analysis and a sample theoretical calculation section. Enhancing the power output through the maximization of the temperature
difference across the Stirling engine is the main aim of this paper.
Figure 1 PV diagram of a Stirling engine [2]
LITERATURE REVIEW
Dol et al. conducted a numerical CFD analysis on circular cylindrical and rectangular cantilevers to investigate the effects of aspect ratio and geometry on the flow dynamics on the free end [5]. It was found that tip effects were not related to the aspect ratio, while they are connected to 2D and 3D for cylindrical cantilevers and 3D and 4D for rectangular flat cantilevers [5].
Additionally, it was noted that the velocity defect was
stronger and more noticeable in the flat plate case compared to the cylindrical circular, suggesting strong vortical activity in the flat case [5], as shown in Figure 2.
Additionally, research done by Dol et al. show the use of a flexible cylindrical circular agitator, where the wake and turbulence were analyzed and quantified, and the results show a better turbulence production capability in comparison to the rigid agitator counterpart [6].
Figure 2 The instantaneous turbulent kinetic energy contour at the plane of symmetry at T=2s for (1) Circular Cylindrical Cantilever, (2) Rectangular Flat Plate, where (a) AR=3, (b) AR=5, (c) AR=7 [5]
Nevertheless, Dol et al. investigated the intensity of vortices behind a Flexible Vortex Generator (FVG) numerically using Fluid-Structural Interaction (FSI) simulation [7]. The study showed that vortices generated by FVG were more intense than those created by Rigid Vortex Generators (RVG), where the performance of FVG in turbulence transport was noted to suggest better turbulent transport for better heat transfer [7]. This concluded that the use of FVG showed positive results in implementation through the heat transfer process of heat exchangers.
Similarly, Dol et al. continued their investigation on the FVGs and their applications in heat exchangers [8].
In this study, both FVGs and RVGs performance have been compared through use in heat exchangers and analyzed through ANSYS CFD [8]. Similar to the previous research, the study showed that FVGs perform better in generating stronger vortices and have superior turbulence formation due to the stronger turbulence production at the boundary layer (Figure 3), meaning better heat transfer through better energy mixing [8].
All of these studies can be used to improve heat flux in
Figure 3 Velocity contours of flow on (1) RVG, (2) HFVG and heat exchanger specified iso-surface [8]
Figure 4 Assembly of stirling engine [4]
Stirling engine applications. The research of FVGs and RVGs is continued by Dol, where the authors in [9] in which the strength of wake structures behind a flexible vortex generator was investigated numerically, where the circulation was stronger than the rigid counterpart, further confirming the enhanced ability of turbulence generation by using FVGs.
Moreover, Yunus et al. designed a rhombic drive Beta- type Stirling engine, which consisted of hot and cold cylinder walls, thermal insulation separating both ends, outlet pipes, displacer piston, power piston and flywheel [10]. Figure 4 displays the cross-sectional view of the design and locations of the components provided by Yunus et al. [10]. In addition, the researchers also provided considerable geometry dimensions, as shown in Table 1.
Figure 5 Stirling engine detailed dimension [11]
Table 1 Specifications of β-type stirling engine [4]
Specifications
Engine type Beta-type Stirling Engine
Swept volume 75 cc
Displacer length 78 mm
Piston length 40 mm
Displacer diameter 36 mm
Piston diameter 38 mm
Displacer stroke length 16 mm
Piston stroke length 16 mm
Displacer rod diameter 12 mm
Furthermore, Maheswaran et al. provided a detailed dimensional analysis of the design of their Stirling engine, as shown in Figure 5 [11]. Their design aimed
Table 2 Dimension and nomenclature of rhombic drive [11]
Components Label Nomenclature Dimension (mm)
Total Length Lt 283
Displacer cylinder bore bdc 37.5
Displacer piston length ld 65
Displacer piston bore bd 31.2
Regenerator length l R 32.5
Power piston length Lpt 150
Power piston cylinder bore Bp 31.25
Displacer piston yoke shaft lys 250
Power piston yoke 2dp 60
Displacer piston yoke 2dd 60
Connecting rod length Lp=Ld=L 42.5
Crank offset radius R 13.75
Spur gear pitch diameter 2Rg 100
Displacer yoke distance Ldt 315
Piston displacement Yp 170.66
Displacer displacement Yd 274.2
to resolve the energy in rural areas that is not attained by conventional energy resources. It is noted that Table 2 is the dimensional reference for our design.
Different Layouts of Stirling Engine
Alpha α, Beta β and Gamma γ are the three categories that create different types of Stirling engines. These categories are mainly differentiated depending on the way the cylinders are connected and the components included within the design [12].
1. α type
As shown in Figure 6, the alpha type layout includes two power pistons attached on two separate ends connected by a series method with a heater, regenerator, and cooler. Means of expansion and compression between the fluids from hot and cold ends are carried out between the chambers [2].
Figure 6 Alpha type [2]
2. β type
The beta layout is the first type of Stirling engine, initially designed and discovered by Dr Stirling back in 1816 [12]. This layout of the Stirling engine includes only one power piston responsible for the compression and expansion cycles, unlike the alpha type, which includes two power pistons on both ends. Moreover, the transfer of fluid between the hot end and cold end of the Stirling engine is the responsibility of the displacer, which acts like a piston, as shown in Figure 7 [2].
Figure 7 Beta type [2]
3. γ type
One major difference between the design of the beta type and the gamma type Stirling engines is that the piston and displacer are placed on different cylinders, as shown in Figure 8. This design provides a lower compression ratio but is mechanically simpler [2].
Figure 8 Gamma type [2]
Yunus et al. [10] analyzed the different types of Stirling engines and compared them using a decision matrix and considered important aspects such as efficiency, engine size, ideal dead space, popularity, maintenance, manufacturability, material cost, noise output, power density and sealability. The outcome of the comparison between the different types of Stirling engines in the decision matrix resulted in identifying that Beta type Stirling engine is the most suitable [10].
METHODOLOGY
To satisfy the problem statement, it is required to simulate the heat transfer performance of a beta type Stirling engine under different fin placements, configurations, and geometries. Thus, it was concluded that a proper simulation through ANSYS Fluent with a design that follows the referenced dimension should be done. This would provide results that would then be validated in the validation section.
Boundary Conditions
To run the simulation on ANSYS Fluent, specific boundary conditions had to be placed to ensure effective results. First, five bodies were identified in the geometry section, as shown in Figure 9: hot end, cold end, displacer, cover, and domain. The boundary condition for the hot and cold end were defined to be 500 K and 300 K, respectively, as stated by Mukhtar et al.
[13]. Additionally, the hot end boundary condition was defined as fixed in the simulation to simulate a constant heat source, while the cold end was free to change to
be used as a performance metric of the different fin geometries and configurations. Moreover, for the convection on the cover body, a value of W
25 ––––– m2 x K was achieved by assuming the speed of air to be 2 m/s, which is evident equated as [14],
h=12.12-1.16v+11.6v –– 2 1
where h the convective heat is transfer coefficient and v is the speed of airflow.
Figure 10 Stirling engine configuration Geometry
The geometry was done using Fusion360 and imported into ANSYS DesignModeler. Figure 10 demonstrates the designed geometry, which consists of a cover that includes the fins, the hot end space, the cold end space, a displacer between the two spaces, and an environment that contains the entire geometry and simulates room conditions for the cylinder. Also, the geometry was divided into quarters or halves, based on symmetry, to reduce the overall size of the mesh and allow the simulation to run faster. Figure 9 shows the Fusion360 design with a summary of the dimensions used.
Figure 9 Geometry and dimensions of part of the engine and fins (in cm) (1)
SIMULATION SETUP
The simulations were run through ANSYS Fluent CFD, one of the most used software to analyze CFD and thermal problems. To start, three main simulations were done to compare the optimal fin placement on the engine’s cylinder in three different locations which are the hot end, cold end, and the entire length scale.
The fin used was the annular fin due to its simple geometry and popularity. The mesh was optimized as best as possible. The number of elements and nodes for the hot end simulation was 1033080 and 272418, respectively, while for the cold end (Figure 11), the number of elements and nodes was 306187 and 80770, respectively, lastly for the length scale run, the elements and nodes were 975488 and 241220 respectively. The lower element and node count for the cold end simulation is explained in the coming sections.
After conducting the three simulations for the fin location comparison, the best location was taken, which is the cold end, and two more runs were done for two different geometries. This was done to determine the optimal shape of the three options, annular, rectangular, and conical, as well as the best feasible fin location and layout on the cylinder.The results of all runs are shown in the coming sections. There are four more runs that have not been mentioned, the first of the four is a no-fin run, where the simulation was conducted on the cylinder with no fins, and the other
three runs are done on the same configuration of the cold end the annular simulation, but with different mesh quality, to validate the results obtained based on mesh quality, the result of these mesh validation runs will be discussed in the validation section.
The fluent setup is simple and easy to explain. The simulation type selected was transient and the model used and applied was the energy equation alone. The material used for the cover was steel, with the program default properties shown in Table 3.
Table 3 Material properties
Steel Material Properties (ANSYS Fluent)
Density ––– kg
m3 8030
Specific Heat ––––– J kg x k
502.48
Thermal Conductivity W –––––
m x K 16.27
The fluid chosen was the air with generic properties.
The solid material was assigned to the cover, while the fluid was assigned to the environment and the insides of the cylinder. Moreover, the boundary conditions were assigned to all wall contact regions related to the cold end, hot end, and cover. Then the simulation was run for 2000 steps in program seconds. All runs had the same setup.
RESULTS
The results were obtained through ASNYS CFD Post, visualized as temperature and flux contours. This section will summarize the results obtained for the multiple simulations done to further show the best Figure 12 Length scale simulation mesh
Figure 11 Cold end figure simulation mesh
available fin configuration and geometry out of the selected alternatives.
Fin Location Simulation Results and Discussion After running the simulation for different placements, the following results were obtained.
Table 4 Results of fin location simulation Fin Type/Location
Temperature at Point (Hot End) (°C)
Temperature at Point (Cold End) (°C)
No Fins 224.9 90
Annular (Hot End) 185 70
Annular (Length Scale) 200 50
Annular (Cold End) 223 40
The results were obtained as contours from ANSYS CFD Post, with the ability to use a probe for the temperature, which were used for the validation part, however, in this table, an average temperature was recorded through the contours over a certain area. As shown in Table 4, the results show that the cold end placement kept the hot end temperature at 496 K, which is very close to the optimum 500 K temperature, and the cold end temperature was cooled and kept at 313 K, which is close to the room temperature required temperature. In comparison to the other fin locations, we can evidently see that the hot end temperature was being cooled and lowered down; this is not favorable as we need to keep or increase the temperature difference between the end as best as possible to increase the power output of the engine, hence what is shown in the table in our case, does lower the efficiency of the engine. Similarly, for the cold end temperature of the other placements, we can see the temperature rising above the required room temperature, thus decreasing the temperature difference and lowering the engine efficiency. This is the reason the cold end fin placement was chosen for the following analysis step.
Fin Geometry Simulation Results and Discussion The following results were obtained when we compared the annular fins to the rectangular and conical fins.
Table 5 Fin geometry analysis results Fin Type/Location
Temperature at Point (Hot End) (°C)
Temperature at Point (Cold End) (°C)
Annular (Cold End) 223 40
Rectangular (Cold End) 215 48
Conical (Cold End) 225 132
As evident in Table 5, the results show that using the chosen two types of geometries in comparison to the annular fins, the annular type still shows better temperature distribution values. Where in the cold end, the conical type recorded 405 K, which is the highest cold end temperature value recorded in all alternatives, while the rectangular type showed a small increase in the cold end temperature, and a small decrease in the hot end temperature. However, this concludes that the annular fin type placed on the cold end of a Stirling engine cylinder would give the best temperature difference and better efficiency than the other geometries and locations observed through the simulation.
DISCUSSION
To validate the result obtained from the simulations, two main validation methods were introduced in this section; the first one is the theoretical calculation, in which calculations for the fin effectiveness of the best recorded alternative will be done to check the accuracy of the ANSYS Simulation. Additionally, mesh validation analysis results were discussed to show the difference in results with different mesh cases and the sensitivity of the mesh quality with the result contours.
Mesh Validation Analysis
A mesh validation analysis were conducted to further validate the results of annular cold end simulation and
check the possibility of error that occurred through the setup. In this analysis, one would change the mesh parameters for a higher or lower number of elements.
Two additional simulations were done to compare the main simulation results; the first simulation increased the number of elements from 306187 elements to 500419 elements, then the second simulation increased the number of elements from 500419 to 789848 elements. The results are summarized in Table 6.
Table 6 Results of mesh validation
Fin Type/Location
Temperature at Point (Hot End) (°C)
Temperature at Point (Cold End) °(C) Annular (Cold End)
-300k elements- 214 39
Annular (Cold End)
-500k elements- 223 40
Annular (Cold End)
-790k elements- 223 133
As evident in Table 6, the results show close temperature results on the hot and cold ends. However, the results started to vary and change once the mesh number of elements increased above 500419 to 789848 elements, where the temperature at the cold end was abnormal when compared to the other simulations, as shown in
other compared simulations. As stated by Sosnowski et al., refining and improving the mesh quality contributes entirely to the accuracy and stability of the model [15], thus, it would be advised to increase the simulation time for cases with higher mesh quality.
Theoretical Calculation
Efficiency and Corrected Length
A sample calculation to achieve the value of effectiveness for the annular fin is shown below using the corrected length of a fin method [16]. To start with the value of ξ was calculated to determine the fin efficiency:
η_fin. Figure 8 shows the annotated dimensions of the designed annular fins, and units were converted to meters for the purpose of unifying the calculations.
where ξ is a fin efficiency factor, Lc is the corrected length, k is the thermal conductivity and Apis the surface area.
Moving on,
= 2.08 r2c
––– r1
0.0325
= –––––––––
0.01562511
where r2cis the corrected radius and r1 is the inner radius.
Using Figure 14 the value of ηfin was denoted to be approximately 0.8 [16].
Figure 13 Mesh Validation Analysis on 3 Different Numbers of Elements
To calculate ξ; the value of k was taken from the ANSYS Fluent database,
ξ = Lc x = (0.029375)
= 0.5079 (2)
h kAp–––
–3 2
1 2–
( )
––––––––––––––– 25 –– 21 (16.72)(0.00014688)3
2–
( )
Figure 13. This was because the simulation required more than 2000s to converge, while the simulations with less elements and nodes converging quickly. This is why the value of the temperature at the cold end was abnormal, where the simulation did not satisfy the convergence criteria. So, to conclude this section, the simulation with 500419 elements was taken as a refined simulation with less potential errors than the
Figure 14 Fin Efficiency vs ξ [16]
(3)
The value of Qfin was calculated as:
Q ̇fin=ηfin Afin (Tb ― T∞ )=5 W
Q unfin=πDS=0.2513 W
where Qfin is the fin rate of heat transfer, Qunfin is the rate of heat transfer for the unfinned part of the cylinder, Afin is the fin area, Tb is the body temperature of the cylinder, T∞ is the ambient temperature of the cylinder, D is the cylinder diameter and S is the spacing between the number of fins.
15 fins were used across the cylinder, hence:
Q total,fin=n(Q fin+Q unfin ) = 78.7695 W
where n is the number of fins available across the cylinder. Lastly,
Q no fin=hAb (Tb ― T_∞ )=13.375 W εannular fin= Qtotal,fin
–––––––––
Qno fin = ––––––––– 78.769513.375 = 5.889
where εannular fin is the effectiveness of annular fins.
In comparison with the simulation results, the effectiveness was found to be 8.17189, which was found while comparing the unfinned simulation contours, and the annular cold end finned contours. This value was found by comparing the maximum flux value evident in Figure 15, multiplied by the respective areas.
Figure 15 Heat flux contours on finned and unfinned bodies
Simulation Physics
Multiple simulations were conducted in order to carefully understand the effect of fins on the heat transfer properties of Stirling engines and to obtain results that are as systematically accurate as possible.
The boundary conditions were set to be almost similar to a real-life model of the engine, where the hot end
temperature was set for a value in the range of values found in literature, while the cold end temperature was defined as the room temperature. Moreover, the hot end temperature was specified as fixed, similar to a heat source, while the cold end temperature was free to change to see the heat flow from the expansion to the compression areas. Nevertheless, the cover, or the cylinder surface, was given a convection boundary condition, with the convection heat transfer coefficient value correlated through an assumed value of airflow speed over the cover, which was and 25 m/s and 2 , respectively.
The results obtained for the cold end annular fin simulation, specifically the 500,000-element mesh simulation, in comparison to the un-finned simulation, show that the temperature of the cold end area was kept at 40°C for the finned simulation, and 90°C for the un-finned simulation, even the other types of fins showed a lower cold end temperature than the one recorded in the un-finned analysis. And as earlier mentioned, to enhance the heat transfer and the efficiency of the engine, a higher temperature difference must be achieved during operation to increase the overall power output, as studied and noted by Sowale et al. in their research [17]. The mentioned temperature value recorded for the un-finned analysis on the cold end was obtained due to the fact that the system was unable to remove the stored heat inside of it as compared to the finned system, where the finned geometry was able to remove the stored heat in the cold end in a quicker manner, enhancing the heat transfer process, and in turn, would continuously ensure that the system produces the optimal power output as long as the wind is flowing over the fins to remove the generated heat through convection. This higher temperature difference was evidently noticed throughout the different simulations while compared to the un-finned environment.
For the case of the heat flux results, comparing the cold end finned analysis to the un-finned analysis again and obtaining the values from the contours, as seen in Figure 15, the heat flux for the cold end finned simulation was roughly -100 w
––– m2 , where the negative sign shows that heat is being removed from the system, and for the un-finned analysis, the heat flux was noted to be roughly -4 w
––– m2 , this shows evidently that the –––––W m2 x K ––m s
(4) (5)
(6)
(7) (8)
system is dumping less heat out of the cold end due to the body’s inability to dump more heat out faster than the heat flowing from the hot end, thus not holding the optimal temperature for the case of the un-finned analysis, while for the finned case, the system is having a better performance of dumping heat out of it to hold the best noted cold end temperature out of the other simulations.
It is, in the end, to be noted that there are more types of unexplored fin geometries and solutions that can enhance the heat performance of Stirling engines, however using fins showed good results in obtaining the best required temperature distribution for higher engine power output.
CONCLUSION
In conclusion and to sum up, a study was conducted on the impact of applying fins of different configurations and geometries on a cylinder of a Stirling engine to enhance the power output through maximization of the temperature difference. It was noted that the annular fins applied on the cold end section of the cylinder showed better temperature results than the other alternatives of location and geometry, which is reflected in the results section. Where the temperature of the cold end area with the annular fins is noted to be 40 degrees Celsius in comparison to the 90 degrees temperature for the un-finned design, the other geometries and location placements are also noted and mentioned in Tables 4-5, which noted the noticeable difference in temperatures, allowing us to clearly choose the annular fin design placed on the cold end section of the engine cylinder. Moreover, some validations were applied through a mesh analysis to study the change in results with the change in the mesh number of elements. The selection of annular fins was noted to be common sense in different literature based on power generation analysis, with no support or fact around the effectiveness of the annular fins in comparison to other geometries and placement studies; thus our research clearly proves the effectiveness of the selected fins in comparison to other types and placements, through the means of simulation. In the end, future work is recommended to include and study the effect of radiation on the Stirling engine to cover up all aspects of heat transfer.
Additionally, it is advised to study the effects of flow mechanics and wall shear stress on the heat transfer
quality, which contributes to adding more heat to the Stirling engine. Nevertheless, it would further improve the study if a dynamic mesh motion was applied to simulate the motion of the displacer and piston bodies for an approximate actual representation of the real-life engine. This is supported by the future experimental studies to be conducted to strongly support the completed simulations.
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