Analysis of the correction process for the initial field iteration calculation of the stability analysis program

As the heart of aircraft, the performance requirements of aviation engines are increasing, and analyzing the aerodynamic stability of engines has become an essential part. The methods for analyzing the stability boundary of engines at home and abroad are also gradually improving. When using a domestic engine stability analysis program, it was found that the turbine drop pressure ratio changed during the calculation process, which was inconsistent with the initial given. This article focuses on this issue and analyzes the process of parameter correction during the calculation process by analyzing the parameter changes discovered during its use. This program ensures power balance and duct and bypass outlet static pressure balance. The calculation accuracy is improved through these correction processes.


Introduction
As the heart of aviation aircraft, the performance and stability of aviation engines directly determine the performance of the aircraft [1,2] .With the continuous improvement of aircraft performance, flight altitude, speed, and maneuverability continue to improve.But there are also accidents of forced landing or even falling due to engine failures.Among them, engine aerodynamic instability is the most serious type of engine failure.
The unstable state of the engine mainly includes rotational stall and surge.When the engine is running at a certain compressor speed, the maximum flow rate through the compressor is usually determined by the blockage of the compression system or a certain component of the engine; when reducing the flow rate of the compressor, the internal flow state deviates from the design state, ultimately leading to unstable flow in the compressor, resulting in rotational stall or surge.The consequences of compressor surge often lead to damage to engine components or the entire machine, and the stable boundary of the compressor is often referred to as the surge boundary.
In the US and European regions, the main method used in the 1960s and 1980s was still to isolate compressors for stability analysis.The mainstream one-dimensional model for compressor stability discrimination is the one-dimensional exciter cluster volume model developed by Kurt et al. in 1969, which is widely used for compressor performance calculation and stability analysis.In 1975, Carl et al. linearized the one-dimensional nonlinear model of the compressor developed by Kurt.Based on the Lyapunov first-order approximation theorem, the stability of the system was determined, and the simulation results were compared with the J85 engine test results, achieving good results.In the mid-1980s, Moore and Greitzer collaborated to develop a two-dimensional nonlinear model coupled with rotational stalls and surges.The proposal of this model has promoted the development of research on rotational stalls and surges in axial compressors.In the early 1990s, there was a wave of research on IOP Publishing doi:10.1088/1742-6596/2764/1/012035 2 active and passive suppression of rotational stalls and surges in the industry.Many scholars have simplified the M-G model from the perspective of harmonic analysis [4][5][6][7] , among which Simon [4] and Gysling [5] developed Lyapunov functions for stability analysis of compressed systems based on the second Lyapunov method.Catherine [7] further extended the application of Lyapunov functions in active control of rotating stalls and surges based on distributed nonlinear models.Burdett Daniel and Povey Thomas [3] used high-fidelity experimental data taken in several axial planes downstream of a cascade of engine parts, in order to provide guidance on the accuracy of each method in a relevant, practical application.
Many domestic scholars have also carried out relevant research work.In 1980, Tang et al. developed a one-dimensional physical model for compressors using the "excitation disk hysteresis volume" model instead of the "excitation disk volume" model [8] , and they used Lyapunov's first approximation theory to determine the instability boundary of isolated compressors.Subsequently, the application of the Lyapunov method for predicting the stable boundary of isolated compressor systems in China gradually matured.Qiao et al. developed a stable boundary prediction method for compression systems under simulated engine regulation using this method [9,10] .Zhang and Qiao et al. established a compressor unsteady aerodynamic response model.And derived the calculation formula for the unsteady aerodynamic response of the compressor [11] .Wang et al. developed a method for evaluating the aerodynamic stability of fan components in the overall environment of turbofan engines [12] .
To explore the reasons for the differences and similarities in the stable boundary of compressors in the environment of the entire machine and components, and to fill the cognitive gap in this field in China, a numerical simulation technology has been developed to calculate the surge boundary of gas turbine engines.This technology regards the entire gas turbine engine as a system, establishes a one-dimensional aerodynamic small disturbance model for the entire engine, and judges the instability point of the system based on Lyapunov's first approximation theory.It achieves stable boundary determination of compressor components under uniform intake in the entire engine environment and applies this method to turbojet, split exhaust, and mixed exhaust turbofan engines by using computational programs as carriers, making it a practical technique for predicting the surge boundary of compressed components during uniform intake in engine environments.
Zhao from Nanjing University of Aeronautics and Astronautics developed a comprehensive, userfriendly, and scalable aerodynamic stability analysis system based on VC++ software [13] , hereinafter referred to as the DISTF program.
The design concept of the aircraft engine aerodynamic stability analysis system is to construct a simulation system suitable for various types of engines and used to evaluate the impact of various stability reduction factors on engine aerodynamic stability.

The initial field calculation iteration process of DISTF program
This article edited the input file of the DISTF program and established a two-dimensional flow channel model of the engine, as shown in Figure 1.The hybrid turbofan engine was divided into 34 units along the axial direction and 8 units along the circumferential direction.Among them, the fan component was divided into a guide unit and a compressor unit; the high-pressure compressor components were divided into a guide unit, a compressor unit, and a loss unit, with the loss unit used to describe the outlet diffuser section; the high and low-pressure turbine components were divided into a guide unit and a turbine unit, respectively.The nozzle components are divided into two units, one to describe the total pressure loss as a loss unit and the other to describe the throttling characteristics of the tail nozzle unit.The DISTF program will first calculate the initial field parameters of the engine under undistorted conditions for subsequent distortion calculations.In the initial field calculation results, it was found that the comparison error between the parameters in front of the turbine and the design point parameters is relatively small, around 3%.However, there is a significant error between the pressure and temperature of the components behind the turbine and the design point parameters, and it was found that the turbine drop pressure ratio is different from the initially given drop pressure ratio.We conducted the following analysis on the correction phenomenon of the SSS program.
This calculation set the total inlet pressure of the engine to 101, 325 Pa, the total temperature to 288 K, and the outlet back pressure to 101, 325 Pa.The DISTF program iterated four times during the initial field calculation, and the calculated result after four iterations were used as the initial field value for subsequent distortion calculations.The calculation results of total pressure and total temperature are shown in Figure 2. Figure 2 shows that in multiple iterative calculations, the correction of the components in front of the turbine was very small, while the total pressure and total temperature after the turbine were corrected due to the correction of the drop pressure ratio.In this calculation example, the total pressure drop ratio under the original input state was selected, and the drop pressure ratios of the input high-pressure turbine and low-pressure turbine were 2.821 and 2.081.Table 1 shows the changes in the drop pressure ratio during several iterations.596175315 When calculating the steady-state operating point of the turbine unit, the reason for the correction of the drop pressure ratio is that the DISTF program will back-calculate based on the work consumed by the compressor, ultimately achieving a balance between the turbine work and the compressor work.From Table 1, it is found that the high-pressure turbine work decreases, and the total pressure at the outlet of the high-pressure turbine increases, resulting in a change in the drop pressure ratio.The correction formula for turbine parameters is as follows: Correction coefficient for total temperature ratio of turbine unit: Correction coefficient for total pressure ratio of turbine unit: Where  : the power consumption of the compressor corresponding to the turbine;  : the output power of the turbine;  * : total pressure ratio, total outlet pressure/total inlet pressure;  * : total temperature ratio, total outlet temperature/total inlet temperature.As shown in the table 2. In the correction process, the turbine work is gradually corrected based on the compressor work, ultimately making it equal to the consumed work of the compressor.This leads to changes in the total pressure and temperature at the turbine outlet, resulting in changes in the drop pressure ratio and temperature ratio.
To ensure the static pressure balance at the outlet of the internal and external culverts, the DISTF program will also modify the turbine state point parameters (total pressure ratio and total temperature ratio).The correction formula is as follows: Turbine unit corrected total pressure ratio: Where  * : total pressure ratio of the turbine;  * : total pressure at the outlet of the bypass;  * : total outlet pressure of the duct;  : number of turbine units.After iterative correction, the static pressure at the outlet of the duct and bypass can approach equilibrium to ensure the accuracy of the mixing calculation of the inner and outer culverts.
The initial calculation process will also modify the area of the inlet of the impeller mechanical components so that the flow coefficient reaches the artificially given value.For example, in the highpressure compressor section: compressor components, the system will modify them based on the flow coefficient given in the input file, as shown in Table 4.The given flow coefficient is 0.7845, and the flow coefficient calculated for the compressor inlet is 0.79055.Therefore, the inlet area (Sa) is modified, by modifying the outer diameter size (r2), and the area and outer diameter are slightly increased, so that the flow coefficient can reach the given value.Table 4 shows the corrections made during the first iteration calculation, which has already met the requirements, so no further corrections will be made in the following three iterations.Fans and turbines are the same.
This correction in the program is made to accurately select the working point of the compressor according to the given flow coefficient and to obtain the required pressure ratio when interpolating the corresponding compressor characteristic line.

Conclusion
At each stage of the engine development cycle, aerodynamic stability analysis is required to ensure that the available stability margin is greater than the total required stability margin.The accuracy of the analysis system plays an important role in evaluating engine stability margin.
The DISTF program uses several revisions during initial field calculations to achieve power balance between the compressor and turbine power, as well as static pressure balance at the outlet of the duct and bypass by correcting the drop pressure ratio.By modifying the inlet area of the turbomachinery components and adjusting the corresponding flow coefficient at the inlet, the accuracy of the calculation can be improved.However, it sacrifices the accuracy of the pressure and temperature of the turbine components, resulting in significant errors between these parameters and the design point parameters.However, since engine instability typically occurs in compression components, the error here is acceptable.

Figure 1 .
Figure 1.Schematic diagram of calculation site division for hybrid turbofan engines.

Figure 2 .
Figure 2. Distribution of total pressure and temperature inside the engine with different iterations.Figure2shows that in multiple iterative calculations, the correction of the components in front of the turbine was very small, while the total pressure and total temperature after the turbine were corrected due to the correction of the drop pressure ratio.In this calculation example, the total pressure drop ratio under the original input state was selected, and the drop pressure ratios of the input high-pressure turbine and low-pressure turbine were 2.821 and 2.081.Table1shows the changes in the drop pressure ratio during several iterations.Table1.Changes in drop pressure ratio and power with iteration times.

Table 1 .
Changes in drop pressure ratio and power with iteration times.

Table 2 .
Changes in parameters during the iteration process.
t : turbine work.

Table 3 .
Static pressure correction process at the outlet of internal and external culverts.As shown in the table 3.During the iteration process, the static pressure at the outlet of the bypass remains unchanged, and the duct outlet static pressure is corrected.This correction process will cause a

Table 4 .
Correction of compressor component area.