Simulation of Transient Temperature and Clearance after Shutdown of Aeroengine Based on CFD and FEA Coupled Models

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Introduction
Te fow patterns within the engine dictate the heat transfer intensity, subsequently impacting the temperature distribution of the engine components.As a result, studying the fuid fow patterns within the engine is crucial, with computational fuid dynamics (CFD) being the predominant method.Researchers have conducted studies at both component and whole engine levels.Negulescu and Pftzner developed a system using tubeless vortex reducers to achieve deswirl via the CFD method [1].By using CFD tools, the model with tubeless vortex reducer shows an increase in the relative swirl from 0.85 to 1.4 at the entry of nozzles of the vortex reducer which has a good agreement with the test data.Aidarinis and others used CFD to analyze airfow in the aeroengine front-bearing chamber [2].Che and others utilized CFD for the whole engine basin simulation [3], after a more detailed analysis of the fuid, and due to the cavity efect, the actual thrust of the entire engine is signifcantly reduced by up to 30%, and the specifc fuel consumption (SFC) is noticeably increased, with a maximum increase of up to 55%.Conan and Savarese [4] and Innocenti et al. [5] applied CFD to assess bleed airfow in the aeroengine.Yan and others employed the CFD unsteady method to simulate the inlet temperature distribution of the turbine [6], and the unsteady simulation using CFD has been efectively utilized to capture the fow pattern in the turbine stage.It was predicted that in the presence of hotspots at the turbine inlet, the highest temperature nonuniformity along the radial direction increased by 0.02 on the vane and 0.05 on the blade.Otter and others used CFD for aeroengine exhaust system simulation [7].Research has shown that the error between the thrust coefcient, bypass discharge coefcient, and core discharge coefcient obtained from the threedimensional CFD method and the experimental data is only 0.03%, 0.37%, and 0.31%, which fully demonstrates the accuracy of the CFD method.Chen and others conducted numerical simulations on the entire aeroengine, employing the CFD time-marching through-fow method to analyze the engine's fow feld and performance [8] and research shows the CFD result and experimental deviations of the entire engine are not greater than 7%, which meets the accuracy requirements for engineering applications.Zhang and others predicted the compressor stage characteristics via 3D CFD numerical simulations, achieving surge boundary prediction and stability expansion of multistage compressors [9].Sun and others simulated the three-dimensional fow in the vortex cavity, as well as the temperature feld and stress distribution of the turbine disc using CFD [10].Sun and others utilized CFD and FEA coupling methods to study the engine's secondary air system [11].Te completion of the thesis involved the coupled calculation of the CFD-FEA model focusing on the low-pressure turbine disk cavity.Te author believes that the FEA method is a practical engineering approach with a high efciency and accuracy.However, FEA results are dependent on a large database and engineering experience.Te CFD-FEA coupled method is currently a costly analysis tool, but it fully utilizes the accurate fow solutions of CFD and the temperature and stress results characteristics of FEA.It remains a promising direction for the future.Illingworth and others performed three-dimensional fow heat transfer coupling simulations on the engine's preswirl system, analyzing the fow and heat transfer conditions under maximum take-of conditions [12].Tis article presents a coupling code developed based on Fluent software, and applies it to the preswirl system of the Trent 500 model.With the help of the code, the twodimensional axisymmetric CFD model coupling, and the three-dimensional CFD model coupling took 34 hours, and 14 days, respectively.Although the coupling time is still relatively long, the precision gains brought by the CFD-FEA coupling model are still very appealing.
Finite element analysis (FEA) is a technique used to determine the degrees of freedom (DOF) by breaking down solid objects into multiple small elements and then evaluating the DOF of each element through interpolation.Numerous simulations of temperature, stress, and deformation of aeroengine components have been carried out by scholars using the FEA method.For instance, Qu et al. undertook a simulation analysis of the mechanical properties of the engine main bearing under high-temperature conditions and provided a life analysis of the main bearing [13] and based on the simulation results, the stress in the contact area of the bearing's steel ball is approximately 28 times that of the stress in other noncontact areas.Jinhua et al. performed a temperature feld simulation of a turbine disc based on the FEA method and compared the impact of coupling the temperature feld with the air system on the calculation result [14].And it has been demonstrated that fuid thermal calculation method has enhanced the accuracy of simulation.Compared to the uncoupled calculation results, the maximum error of the coupled calculation results with experimental data has been reduced by 10 K. Cao and Han conducted a thermal-solid coupling simulation based on the FEA method for the turbine disc and blade to obtain actual clearance values of the high-pressure turbine blade tip at the front edge and rear edge, guiding the structural design of the high-pressure turbine [15], and based on the detailed simulation FEA calculation of the heat transfer and deformation coupling model, it is found that the blade of a certain engine should ensure a cutting angle of 19.77′ to maintain a uniform clearance value at the leading and trailing edges of the blade under thermal conditions.Juethner et al. utilized a FEA model to simulate the thermal bending of the rotor under operational conditions [16].Sun et al. combined fnite element analysis with computational fuid dynamics (CFD) to complete temperature feld simulation of rotor parts [17].Tis study proposes a coupling acceleration algorithm for the CFD-FEA coupling method.Tis method treats the heat transfer process as a transient process and computes the CFD model and exchanges data at certain time points throughout the transient history.Tis approach accelerated the simulation by 1.4 and 3.1 times in two test cases, respectively.Tis method also provides signifcant inspiration for the simulation in this study.Papanikos et al. carried out stress and deformation analysis and calculations based on the three-dimensional fnite element simulation for the dovetail connection position of the engine rotor disc [18].
Based on a review of the literature, extensive simulations and analyses of engine performance under operating conditions have been conducted using FEA or CFD methods.However, research on fuid fow and heat transfer after the engine shuts down is limited.Only a small number of studies exist, such as Shaojie's et al. simulation of the natural cooling process of a rotating disc cavity after shutdown based on a 2D axisymmetric model [19].It is important to note that due to limitations of the model, the true thermal conduction process and circumferential nonuniformity of airfow after shutdown are not fully refected.Shuguang et al. analyzed and determined the location of a low-pressure turbine block based on a measured clearance value [20] and the survey points out that the engine was found at the #5 bearing, with a radial clearance smaller than the designated minimum value of 0.1 mm, resulting in the rubbing.Kanike et al. used a fnite element model in Ansys to simulate and predict temperature for analyzing the heat soak phenomenon at the bearing location after shutdown [21].
It is crucial to analyze the fuid fow and heat transfer following shutdown for several reasons.Once the engine is shutdown, efcient cooling fow within the engine ceases, potentially causing the temperature of components to exceed those during operation due to the heat soak phenomenon.Tis poses a greater risk to the engine's internal components after shutdown than during operation.In addition, the transient clearance of seals during natural cooling following shutdown is essential, as startup strategies heavily rely on it to facilitate quick restarts without stator-rotor rubbing.Furthermore, the fow and heat transfer dynamics after shutdown difer signifcantly from those under operating conditions, warranting an in-depth study based on a comprehensive engine model.Tis article introduces a comprehensive fuid-solid coupling CFD model primarily utilized for examining the fow characteristics of fuid inside the engine after shutdown.It also presents a 2D fnite element model for calculating the Using these two models, the article proposes a coupling simulation strategy to improve simulation accuracy by incorporating fow parameters such as the mass fow rate in the main fow channel and in the secondary air system cavities as boundaries for the fnite element model.Tis strategy not only leverages the efciency of 2D FEA models but also ensures high accuracy, as the CFD model ofers reliable fow patterns.Te schematic diagram of the CFD-FEA coupling strategy is shown in Figure 1.

CFD Model and Validation.
A reliable fuid fow simulation is essential to accurately simulate the postshutdown engine temperature.Te temperature of engine components greatly infuences the surrounding airfow, resulting in an uneven distribution of air temperature.As hot air rises and cold air sinks, a temperature distribution is gradually formed, with upper components being hot and lower components being cold.Terefore, a fuid-solid coupling model is indispensable to capture the intense interaction between the fuid and solid components.
To guarantee the legitimacy of the model, this article constructs a 3D solid domain and 3D fuid domain in the CFD model, as depicted in Figure 2. Te solid domain encompasses the entirety of engine components such as the fan, boost stage, ten-stage high-pressure compressor and blades, two-stage high-pressure turbine and blades, seven-stage lowpressure turbine and blades, core module cover, and nozzle.Te fuid domain encompasses the fuid within the main fow channel, the fuid within the secondary cavity, and the ambient environment outside the engine.Te model has been simplifed to a certain extent, such as the transformation of the seal structure into a narrow slit, the simplifcation of blades into fat plates, and the omission of internal structures such as air ducts and accessories inside the core module cover.Te bearing now only includes the outer surface of the oil cavity, disregarding internal details.Te thermal contact resistance between components is not considered, and the heat is fully conducted between the adjacent components.
Te given partial view of solid and fuid meshes are shown in Figures 3 and 4, as it is not easy to identify the entire grid.Te solid domain grid consists of 24.08 million elements, while the fuid domain grid comprises 347 million elements.Te simulation is performed using CFX software and the convergence criterion is set to an RMS value of 1e − 7. Te natural cooling process of the engine after shutdown is a highly complex process, with fow at diferent locations and diferent times that may be turbulent or laminar.Tis article assumes turbulent fow and uses the SST turbulence model for solving the process.Subsequently, in the FEA model, the heat transfer coefcient is set to match the simulated temperature values with the experimental values, thereby reducing the impact of fow uncertainty.
Te open boundary type is set for the outer cylindrical surface of the fuid domain, with reference pressure set to 0 Pa and operating temperature set to 293.15 K. Te other surface of the fuid domain is set to solid-fuid interface boundary type, which can be explained by equation (1).Te normal component of heat fux q can be calculated by static temperature gradient ∇T of fuid and λ fluid is the thermal conductivity of the fuid.Tis heat fux is the same as the fux at the boundary of the solid domain which can be determined by the heat transfer coefcient h and the diference between local reference temperature and solid temperature.Also, h is determined by the CFX solver which has no efect on the accuracy of the solution.
After shutdown, the fuid pattern can be predominantly characterized by a radial natural cooling fow driven by temperature diferentials, which are largely separate from each cavity.Under operating conditions, the airfow is typically driven by shear force, Coriolis force, and other factors.Te cooling air from the compressor exchanges heat with the solid surface through forced convection through holes and labyrinth seals, ultimately reaching the main fow channel.Using the 5 th disc cavity of the compressor as an example, a comparison of natural convection fow and    Shock and Vibration 3 operating condition fow is shown in Figures 5 and 6.Te scales in the fgures represent the nondimensional fow velocity in the disc cavity as V nd .Te defnition of V nd is provided in equation ( 2), where V loc denotes the local fow velocity, and V max represents the maximum fow velocity on the section plane.
Te simulation object of this article is a certain engine.Termocouples 1-3 are positioned on the outer casing of the high-pressure compressor entraining cavity, while thermocouples 4 and 5 are situated on the outer casing of the interstage load-bearing frame and the rear sealing structure.Termocouple 6 is located near the #5 bearing' outer surface, specifcally on the labyrinth seal.Tese thermocouples are used to verify the accuracy of the CFD model by comparing the test data with the simulation results, following a six-hour data acquisition period postengine shutdown after a running test.
Te CFD model's accuracy is depicted in Figure 7. Te temperature diference is represented by equation ( 3).For each thermocouple, the maximum diference is less than 6%.T CFD and T EXP represent simulation temperature results and test data.All temperature units are in Kelvin.
Te diference may be attributed to the simplifcation of structures, including accessories and the active clearance control system entraining tube in the core module.Tis simplifcation could infuence the airfow pattern and in turn impact the temperature of the outer casing.In addition, the initial temperature distribution of the CFD model might not perfectly align with the real engine.Nevertheless, it is estimated that this diference will have a maximum impact on deformation of not more than 0.2 mm.Tis level of accuracy in the interested seal clearance meets the requirements for simulation.Hence, the CFD model demonstrates sufcient accuracy and precision for simulating fow and heat transfer after shutdown.

FEA Termal Model of Whole Engine.
Based on highperformance simulation power, the 20-hour natural cooling simulation took almost 2 weeks.Tis method is not acceptable for structure design or optimization.To efciently calculate the transient temperature and seal clearance, a 2D FEA thermal model was created using Ansys APDL, as shown in Figure 8. Te model is meshed with axisymmetric elements, except for plane elements with thickness for discrete structures.Te FEA model consists of 41769 elements, which is only 1% of the solid domain grid in the CFD model.
Te fow path is designated as entering from the fan through the high-pressure compressor, high-pressure turbine, low-pressure turbine, and nozzle as depicted in Figure 8.According to the CFD result, an intriguing observation is that the fuid in the fow path forms two streams with opposite fow directions.Stream 1 initially fows from the combustor back to the compressor, while stream 2 fows from the combustor to the nozzle through the turbine.Te velocity vector is illustrated in Figures 9 and 10.
Consequently, a 1D fuid fow network is simulated in the fow path, starting from the combustor and fowing to both sides.Te heat transfer coefcient is set between the streamline and the surface, as well as the fow rate and the inlet temperature of the network.
Te other boundary type is a single-node thermal equilibrium cavity, also known as a thermal void.Te thermal void assumes that there is sufcient heat exchange between the surrounding solid wall and the fuid node.Tis boundary should only be used where the fuid temperature is uniform.Te thermal void boundary is used for all secondary fow cavities outside the main fow passage.For each thermal void boundary, the corresponding heat transfer coefcient is set.
Te fgure displays the schematic boundary diagram in Figure 11.
Te concept of fow network boundary is described in equation ( 4), while the thermal void boundary is delineated in equation ( 5): where T is the temperature K; HTC is the heat transfer coefcient W/(m 2 •K); A is the heat transfer area m 2 ; Q is the input power W; m is the mass fow rate kg/s; c is the heat capacity J/(kg•K); f is fuid; s stands for solid; and j represents node j of the fnite element.4

Shock and Vibration
Surface elements in APDL were utilized to facilitate heat transfer between the fuid and solid.In addition, appropriate heat transfer coefcients (HTCs) need to be applied.Based on the results from CFD and previous experience, HTCs are typically categorized into four types: the frst type pertains to the core module, the second relates to entraining cavities, the third is associated with the fow path, and the fourth is linked to disc cavities.Specifcally, each type of HTC after shutdown represents 12.5%, 0.2%, 1%, and 1.25% of the value of the ground idle condition.

Results of CFD Simulation.
A 20-hour natural cooling simulation was conducted after the engine shutdown, based on a CFD model.Typically, the actual engine shutdown process can be divided into two stages: the rotor speed gradually decreasing to 0 rpm in the frst stage and a complete stop in the second stage.In the frst stage, in addition to natural convection, there may be a certain forced convection due to rotor speed.To simplify the simulation, this study only focuses on the second stage.Te temperature distribution under the ground idle condition is used as the initial feld of the solid domain, while the initial temperature of the fuid domain is solved by the CFX steady solution, as shown in Figure 12.Te nondimensional temperature T nd is determined using equation ( 6), where T loc represents the local temperature and T max represents the maximum temperature of the initial feld.

Shock and Vibration
As depicted in Figure 12, the air temperature distribution within the core module exhibits noticeable unevenness.Te upward movement of hot fuid leads to the formation of a hot air trend at the top and cold air at the bottom, which proves challenging to replicate using the 2D simulation model.Equation ( 7) is utilized for determining the nonuniformity of the circumferential air temperature in the core module, denoted as θ.Here, T max and T min represent the highest and lowest circumferential temperatures of a specifc section and T denotes the average value.For instance, considering the temperature of the core module near the casing corresponding to the ffth-stage outer ring of the lowpressure turbine, the nonuniformity during downtime is 26%, while the maximum is 31% during the natural cooling process, as depicted in Figure 13.
After the shutdown, there is still some airfow through the main fow path.Te velocity reaches its maximum at the outlet of the nozzle.Te contour of the initial velocity is depicted in Figure 14.Te maximum velocity in the fow path is approximately 1.9 m/s, while the velocity in the secondary air cavity is generally less than 0.1 m/s.Terefore, the temperature change of the fuid in the fow path is much more pronounced and cannot be disregarded while the temperature of the fuid in the secondary air cavity is relatively uniform.

Results of the FEA Model.
In order to assess the consistency between the FEA model and the CFD model, we compare the initial temperature feld of the solid.
Te deviation between the FEA result and the CFD result is demonstrated at specifc locations.As depicted in Figure 15, the deviation at each location is below 2%.
Te initial fuid temperature feld also impacts the transient temperature of the component after shutdown.As indicated in Table 1, the CFD result column depicts the average fuid temperature at a specifc section.Te FEA result represents the fuid temperature from the results of the 1D fow network in the FEA model, and all temperature values have been nondimensionalized.Te maximum deviation is less than 5%.Hence, the temperature of the main fow fuid based on the FEA model also aligns well with the CFD result.
Te temperature distribution of the HPC (high-pressure compressor) inlet section is depicted in Figure 16.Te fuid with a relatively high temperature accumulates at the highradius location, while the cold fuid accumulates at the lowradius location.However, based on the CFD result, the axial velocity in the fow path is primarily infuenced by the hightemperature fuid.As a result, the fuid temperature in the 1D fow network closely aligns with the temperature of the high-radius airfow rather than the average value.Tis is the reason why maximum deviation occurs at the inlet section of the HPC.
During the natural cooling process, the engine typically experiences its highest and lowest circumferential temperatures at the 12 o'clock and 6 o'clock directions.To address this issue, the article conducts a simulation to depict the temperature distribution in the 12 o'clock direction, which signifes the highest temperature of the engine.
Te FEA model was utilized to compute transient temperature over a span of 20 hours following engine shutdown.Te FEA calculation results at specifc locations were chosen for comparison with the CFD simulation results, in order to validate the FEA model.
Te deviation in simulation between the FEA result and CFD result, T dev , is calculated using equation (8).T FEA represents the temperature result of the FEA model, and T CFD stands for the temperature result of the CFD model.Based on the locations where thermocouples 1-6 are installed, as mentioned in Section 2.1, a comparison of the temperature calculation results of FEA and CFD is shown in Figure 17.Te maximum value of deviation is less than 5%.Te diference is primarily caused by the limitations of the 2D FEA model, which is incapable of simulating the circumferential distribution of fuid.In addition, the FEA model is unable to simulate the circumferential heat conduction.
To provide a more detailed comparison between the FEA model and the CFD model, we carried out additional comparisons at diferent locations.Figure 18 illustrates the schematic diagram of the honeycomb (referred to as location 1) and the labyrinth seal at the rear of the second stage disc of the high-pressure turbine (location 2).
Te temperature deviation between location 1 and location 2 in the FEA and CFD models is depicted in Figure 19.Te maximum deviation is approximately around 3.5% half an hour after shutdown.
Te temperature variation in the outer casing of the 4 th stage (location 3) and 7 th stage (location 4) entraining cavity as well as the outer casing of the interstage load-bearing frame (location 5) are illustrated in Figure 19   Shock and Vibration 7 shutdown due to the gradual increase in temperature difference, resulting in positive deviation.Subsequently, as the temperature diference decreases gradually, the deviation becomes negative.Te maximum deviation is less than 5.8%.
Te temperature diference between the compressor's 5 th disc bottom (position 6) and the labyrinth disc bottom (position 7) is illustrated in Figure 21.Te maximum deviation is still less than 5%.8

Shock and Vibration
In general, the maximum deviation between the transient calculation results of the FEA model and the temperature results of the CFD model simulation is less than 6% at locations 1 to 7. Terefore, the FEA result demonstrates a strong agreement with the CFD temperature result.In comparison to developing a solid domain model in CFD, the FEA model ofers signifcant computational cost savings with only 1% of the grid quantity and merely 0.2% of the computational time.For the specifed engine, the fuid network and thermal void boundary with appropriate HTC as discussed in Section 2.2 can be a common method for transient temperature after shutdown.Hence, the subsequent analysis of the clearance changes after the shutdown will be conducted based on the FEA model.

Result of Temperature Simulation and Clearance Calculation after Shutdown.
After the engine is shutdown, the temperature of parts near the main fow channel decreases rapidly, and the heat is gradually conducted from the disc rim and outer ring to the low-radius and lowtemperature locations inside the engine, such as the bore of the disc and bearing.Tis is known as the heat soak phenomenon.Due to the efect of heat conduction, the temperature of those locations will gradually start to rise, and it can even exceed the temperature at the time of shutdown, before decreasing back to the ambient temperature.Taking the 6th stage of the compressor's rotor disc and the compressor discharge pressure (CDP) labyrinth disc as examples, the temperature curves of the rim and bore after shutdown are depicted in Figure 22.Te  Shock and Vibration temperature of the 6th disc bore rises from 0.504 to 0.557 in 1.3 hours, and the temperature of the CDP labyrinth disc bore rises from 0.694 to 0.732 in 0.7 hours.Meanwhile, the temperature of both disc rims decreases rapidly after shutdown, as the heat has been conducted to lowertemperature components such as bores and bearings within the engine.Similarly, the outer surface temperature of bearing #4 gradually increases under the efect of heat soak, as depicted in Figure 23.It reaches its peak value approximately four hours after shutdown.Consequently, this increase in temperature could potentially lead to oil coking if not addressed promptly.
Due to insufcient cooling airfow, the temperature of the casing also increases initially.Te transient temperature curves of the casing are illustrated in Figure 24, with the peak temperature being reached within just 50 minutes.Te temperature at this time point imposes a more rigorous condition for core module accessories.Te stator's temperature typically decreases faster than the rotor's after reaching its peak, leading to a gradual reduction in sealing clearance, which may even fall below the design requirement.Without a comprehensive analysis of the clearance change after shutdown, there is a signifcant risk of rotor-stator rubbing during the hot startup.
Taking the seal between location 1 and location 2 as an example, the transient temperature after shutdown is illustrated in Figure 25: the temperature of location 1 rises from 0.63 to 0.68, and the temperature of location 2 rises from 0.63 to 0.70 due to heat soak.Subsequently, as natural cooling progresses, the temperature of components decreases.Te temperature change rate on the stator exceeds that on the rotor, whether it rises or drops.
Te nondimensional transient clearance between positions 1 and 2 is depicted in Figure 26.With the stator's much higher temperature, the clearance gradually increases to its Another location susceptible to rotor-stator rubbing is the seal labyrinth of the #4 bearing.Its nondimensional transient clearance after shutdown is displayed in Figure 27.Similar to the trend in Figure 26, the clearance frst increases, and then gradually decreases to a minimum value before returning to the cold state value.
It is clear that the labyrinth's clearance initially increases due to the stator's temperature rising more rapidly than the rotor's.Subsequently, with better cooling and a relatively smaller heat capacity, the stator also cools down faster than the rotor, causing the clearance to reach a minimum.After a sufcient period of time, the temperatures of the stator and rotor reach ambient temperature, and the clearance ultimately returns to the cold state value.It is worth noting that all the transient simulations in this article are based on the ground idle condition which is not that of a high temperature.If the engine shuts down from larger operating conditions, with much more intense natural convection, the seal clearance will change much more rapidly which brings greater risk for a hot startup.

Conclusions
Tis article has conducted a 20-hour natural cooling transient simulation using a fuid-solid coupling CFD model of a complete engine.A 2D FEA model has been created to efciently simulate clearance.Te main conclusions that can be drawn from this work are as follows: (1) Te CFD results efectively support the study of the heat soak phenomenon.Te temperature deviation between the CFD model simulation and the thermocouple data is less than 6%, which can be attributed to a maximum of 0.2 mm deformation diference, occurring only in the case with the largest radius.Tis deviation has basically no impact on the clearance value for the interested seal labyrinth, which is typically located at a low radius.Terefore, the CFD model demonstrates sufcient accuracy in simulating conditions after engine shutdown.
(2) Te 2D FEA model aligns well with the results from the CFD.It exhibits a relatively accurate maximum 6% temperature deviation compared to the CFD results.Te FEA model can be used to simulate the transient temperature and labyrinth clearance after the engine shuts down.With only 1% of the elements compared to the solid domain in the CFD model, the FEA model saves almost 99.8% of simulation time, making it a more practical method in engineering.HTC after shutdown can be categorized into four types, and for the specifc engine, each type of HTC can have specifc proportions compared to that of the underground idle condition, as discussed in Section 2.2.To some extent, the FEA model can be run without the input of the CFD model, making it a common method for analyzing transient temperature and clearance after shutdown.(3) Te temperature of components near the main fow path decreases rapidly after shutdown, while the temperature of locations such as the disc bottom, bearing, and outer casing increases to a certain extent initially.Te temperature of the compressor 6th disc bore rises from 0.504 to 0.557 in 1.3 hours, and the temperature of the CDP disc bore varies from 0.694 to 0.732 in only 0.7 hours.Te temperature of the #4 bearing outer surfaces rises from 0.608 to 0.653.In addition, with the heat soak phenomenon, the temperature of the case also rises and reaches its peak value within only 50 minutes.Te peak temperature after shutdown should be taken into consideration as a more stringent condition for those locations.(4) Te transient temperature change of components after the engine shuts down causes the clearance to initially increase before decreasing to a minimum.Te nondimensional minimum clearance of locations 1 and 2 can be 0.8 times its cold state value, occurring approximately 7 hours after the engine shuts down.Te nondimensional minimum clearance of the labyrinth seal of the #4 bearing is 0.976 about 10 hours after shutdown.It is crucial to develop a quick hot-startup strategy in order to avoid stator-rotor rubbing.
Te CFD coupling method is an efective and fundamental approach for simulating the intense coupling of fow and heat transfer efects.However, when using a commercial solver, modifying the solver equations is challenging, and adjusting the model based on experimental data are even more difcult.In addition, CFD modeling typically requires signifcant time for meshing and solving.Moreover, CFD usually cannot provide support for testing the efectiveness of optimizations, since it involves unacceptable model-building work.On the other hand, an FEA model ofers a cost-efective solution with a smaller mesh quantity and shorter solution times, making it easier to modify the model by adjusting input parameters such as HTC.Furthermore, it efciently supports subsequent structural optimization.However, building an FEA Shock and Vibration 13 model requires prior knowledge of the fow pattern and characteristics, for which assistance from CFD is usually necessary.
To summarize and compare the CFD and FEA models, Table 2 outlines their individual strengths and weaknesses in several aspects as follows: cost of computation, accuracy of the model, and modifcation of the model.

2
Shock and Vibration transient temperature and seal clearance values during the natural cooling process to enhance simulation efciency.

Figure 1 :
Figure 1: Schematic diagram of the CFD-FEA coupled method.

Figure 2 :
Figure 2: Schematic diagram of the engine model.

Figure 3 :
Figure 3: Partial view of mesh in the solid domain.

Figure 4 :
Figure 4: Partial view of mesh in the fuid domain.

Figure 7 :
Figure 7: Diference between CFD simulation and test data.

Figure 8 :
Figure 8: FEA model of the whole engine.

Figure 11 :
Figure 11: Schematic diagram of the boundary of the FEA model.

Figure 16 :
Figure 16: Temperature distribution at HPC inlet section.

Figure 17 :
Figure 17: Deviation between FEA and CFD results at the locations of 1-6 thermocouples.

Figure 19 :
Figure 19: Deviation of temperature of locations 1 and 2.
. Te variation curves from location 6 to location 7 are displayed in Figure 20.Te results indicate that constant HTC in the FEA model slightly overestimated the natural cooling efect after

Table 1 :
Comparison of initial fuid temperature.

Table 2 :
Comparison of CFD and FEA models.