A method for predicting gas ingress for high-speed compressible flow

Abstract

The present application relates to the technical field of aero-engine, in particular to a gas invasion prediction method suitable for high-speed compressible flow, which converts the complex gas invasion problem into the cold gas supply total pressure problem, and can determine whether the gas invasion phenomenon exists by calculating the total pressure margin coefficient. The method has the advantages of being suitable for compressible flow conditions, and being suitable for the rim seal design and safe operation; the total pressure discriminant can not only predict the gas invasion condition, but also obtain the minimum supply pressure of the seal.

Description

Technical Field

[0001] The present invention relates to the technical field of aero-engines, and in particular to a method for predicting gas intrusion suitable for high-speed compressible flow. Background Art

[0002] With the continuous development of aircraft engines, the temperature before the turbine has risen sharply. When high-temperature combustion gases flow through the gap between the turbine rim and the seal, they can intrude into the disc cavity, eroding the turbine disc and affecting the safe, stable operation and service life of the aircraft engine. To prevent this, a cooling air stream is typically drawn from the high-pressure compressor to prevent gas intrusion and cool the turbine disc. If the flow rate of this cooling air stream is too low, it will be difficult to prevent gas intrusion. If the flow rate is too high, it will increase the turbine's aerodynamic losses, thus affecting the efficiency of the turbine stage. Therefore, it is crucial to distribute the appropriate cooling air flow to the rim seal structure.

[0003] During aircraft engine design and operation, it is crucial to be able to predict the presence of gas intrusion based on mainstream and cold air conditions. The Mach number of the airflow in an aircraft engine turbine cascade is very high, typically within the compressible flow range. Existing gas intrusion prediction models are primarily based on low-speed, incompressible flow conditions, which differ from the high-speed, compressible flow conditions found in aircraft engines. Consequently, they provide inaccurate predictions of gas intrusion under actual aircraft engine operating conditions.

[0004] Therefore, in order to better predict the gas intrusion situation of the aircraft engine turbine, the present invention proposes a gas intrusion prediction method suitable for high-speed compressible flow. Summary of the Invention

[0005] To address the aforementioned technical issues, the present invention primarily addresses the existing inaccurate prediction of gas intrusion conditions under real-world aircraft engine operating conditions. This invention provides a gas intrusion prediction method suitable for high-speed, compressible flow. This method transforms the complex gas intrusion problem into a cold air supply total pressure problem. By calculating the total pressure margin coefficient, the presence of gas intrusion can be determined. This method is advantageous in that it is applicable to compressible flow conditions. Using the total pressure discriminant, it can both predict gas intrusion conditions and determine the minimum seal supply pressure, providing valuable information for rim seal design and safe operation.

[0006] The first object of the present invention is to provide a method for predicting gas intrusion in high-speed compressible flow, which is used to predict gas intrusion in real compressible flow of an aircraft engine, comprising:

[0007] Obtain the static pressure distribution of the guide vane cascade flow channel outlet in a single cycle, as well as the total pressure and static pressure of the cold air inside the rim seal;

[0008] Obtain the maximum static pressure and average static pressure of the mainstream at the guide vane cascade outlet according to the static pressure distribution;

[0009] The circumferential Mach number of the airflow inside the rim seal is obtained based on the total cold air pressure and static pressure inside the rim seal;

[0010] The cooling air supply pressure coefficient is obtained based on the total cooling air pressure of the inner ring of the wheel rim seal, the maximum static pressure and the average static pressure of the mainstream at the outlet of the guide vane cascade;

[0011] The cold air outflow loss coefficient is obtained based on the circumferential Mach number of the airflow inside the rim seal, the total pressure and static pressure of the cold air inside the rim seal, and the maximum static pressure and average static pressure of the mainstream at the guide vane cascade outlet.

[0012] Obtain the total pressure margin coefficient based on the cold air supply pressure coefficient and the cold air outflow loss coefficient;

[0013] Determine whether there is gas intrusion based on the total pressure margin coefficient.

[0014] In one embodiment, whether gas intrusion occurs is determined based on the total pressure margin coefficient, including: when the total pressure margin coefficient is greater than or equal to 0, there is no gas intrusion; otherwise, there is gas intrusion.

[0015] In one embodiment, the cold air outflow loss coefficient is obtained according to the following steps:

[0016] The effective outflow pressure of the cooling air is obtained based on the circumferential Mach number of the airflow inside the wheel rim seal, the airflow adiabatic index, and the cooling air static pressure inside the wheel rim seal.

[0017] The total pressure loss of the cold air outflow is obtained based on the total pressure of the cold air in the inner ring of the wheel rim seal, the maximum static pressure of the mainstream at the outlet of the guide vane cascade, and the effective outflow pressure of the cold air.

[0018] The cold air outflow loss coefficient is obtained based on the total pressure loss of the cold air outflow and the average static pressure at the guide vane cascade outlet.

[0019] In one embodiment, the calculation formula for the effective outflow pressure of cold air is as follows:

[0020]

[0021] Where, Indicates the effective outflow pressure of cold air; Indicates the static pressure of the cold air inside the wheel rim seal; r 1 represents the inner ring radius of the wheel rim seal; r 2 represents the outer ring radius of the wheel rim seal; Ma θ,c is the circumferential Mach number of the cooling air inside the rim seal; Represents the adiabatic index.

[0022] In one embodiment, the calculation formula for the total pressure loss of the cold air outflow is as follows:

[0023]

[0024] Where, Indicates the total pressure loss of the cold air outflow; Indicates the effective outflow pressure of cold air; Indicates the total pressure of cold air inside the wheel rim seal; Indicates the maximum static pressure of the mainstream at the guide vane cascade outlet.

[0025] In one embodiment, the calculation formula of the cold air outflow loss coefficient is as follows:

[0026]

[0027] Where, Indicates the cold air outflow loss coefficient; Indicates the total pressure loss of the cold air outflow; Average static pressure at the guide vane cascade outlet.

[0028] In one embodiment, the calculation formula of the cold air supply pressure coefficient is as follows:

[0029]

[0030] Where, Indicates the cooling air supply pressure coefficient; Indicates the total pressure of cold air inside the wheel rim seal; P g,max Indicates the maximum static pressure at the guide vane cascade outlet, P g,avg It represents the average static pressure at the outlet of the guide vane cascade.

[0031] In one embodiment, the calculation formula of the total pressure margin coefficient is as follows:

[0032]

[0033] Where, Indicates the total pressure margin factor; Indicates the cooling air supply pressure coefficient; Indicates the cooling air outflow loss coefficient.

[0034] In one embodiment, the static pressure distribution of the guide vane cascade flow channel outlet in a single cycle, as well as the total cold air pressure and static pressure of the rim seal inner ring are obtained by measuring with a pressure measuring element in a rim seal test.

[0035] A second object of the present invention is to provide a gas intrusion prediction system applicable to high-speed compressible flow, comprising:

[0036] The data acquisition module is used to obtain the static pressure distribution of the guide vane cascade flow channel outlet in a single cycle, as well as the total pressure and static pressure of the cold air in the inner ring of the rim seal; obtain the maximum static pressure and average static pressure of the mainstream at the guide vane cascade outlet based on the static pressure distribution; and obtain the circumferential Mach number of the airflow in the inner ring of the rim seal based on the total pressure and static pressure of the cold air in the inner ring of the rim seal;

[0037] The data processing module is used to obtain the cooling air supply pressure coefficient based on the cooling air total pressure of the inner ring of the wheel rim seal, the maximum static pressure and the average static pressure of the mainstream at the outlet of the guide vane cascade; obtain the cooling air outflow loss coefficient based on the circumferential Mach number of the airflow in the inner ring of the wheel rim seal, the cooling air total pressure and the static pressure of the inner ring of the wheel rim seal, and the maximum static pressure and the average static pressure of the mainstream at the outlet of the guide vane cascade; and obtain the total pressure margin coefficient based on the cooling air supply pressure coefficient and the cooling air outflow loss coefficient;

[0038] The intrusion prediction module is used to determine whether there is gas intrusion based on the total pressure margin coefficient.

[0039] The present invention has at least the following beneficial effects:

[0040] The present invention provides a method for predicting gas intrusion suitable for high-speed compressible flow. The method first obtains the static pressure distribution of a single cycle at the outlet of the guide vane cascade flow channel, as well as the total pressure and static pressure data of the inner ring of the rim seal. The data is further processed to calculate the cold air supply pressure coefficient and the cold air outflow loss coefficient. The cold air supply pressure coefficient is determined by the total cold air pressure of the inner ring of the seal, the maximum static pressure of the mainstream at the guide vane cascade outlet, and the average static pressure at the guide vane outlet. The cold air outflow loss coefficient is determined by the total cold air outflow pressure loss and the effective cold air outflow pressure. The total pressure margin coefficient is calculated based on the total pressure discriminant formula, and the presence of gas intrusion is determined. When the total pressure margin coefficient is greater than or equal to 0, there is no gas intrusion. Otherwise, there is gas intrusion. In addition, the total pressure margin coefficient can be assumed to be 0 and reversely calculated to obtain the minimum cold air supply pressure. The method of the present invention can be used to predict the presence of gas intrusion or to obtain the minimum supply pressure when designing the rim seal. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 This is a flow chart of the gas intrusion prediction method applicable to high-speed compressible flow conditions provided by the present invention.

[0042] Figure 2 Schematic diagram of the wheel rim sealing model structure.

[0043] Figure 3 A flow chart for obtaining the minimum cooling air supply pressure for promoting the present invention.

[0044] Figure 4 is the rotational Mach number Ma φ =0.00, the corresponding relationship curve between the sealing efficiency of the inner ring of the rim seal and the total pressure margin coefficient.

[0045] Figure 5 is the rotational Mach number Ma φ =0.18, the corresponding relationship curve between the sealing efficiency of the inner ring of the rim seal and the total pressure margin coefficient.

[0046] Figure 6 is the rotational Mach number Ma φ =0.36, the corresponding relationship curve between the sealing efficiency of the inner ring of the rim seal and the total pressure margin coefficient.

[0047] Figure 7 is the rotational Mach number Ma φ =0.56, the corresponding relationship curve between the sealing efficiency of the inner ring of the rim seal and the total pressure margin coefficient. DETAILED DESCRIPTION

[0048] In order to illustrate the technical means and effects adopted by the present invention to achieve the predetermined purpose of the invention, the following is a detailed description with reference to the embodiments.

[0049] The present invention addresses existing gas intrusion prediction methods, which are typically derived from incompressible flow theory and therefore have poor applicability under high-speed compressible conditions. The present invention provides a gas intrusion prediction method more suitable for the actual compressible flow conditions of aircraft engines. This method converts the complex gas intrusion problem into a cold air supply total pressure problem, and can determine whether gas intrusion is present by calculating the total pressure margin coefficient. The advantage of this method is that it is applicable to compressible flow conditions. The total pressure discriminant can not only predict gas intrusion but also determine the minimum seal supply pressure, which is beneficial for rim seal design and safe operation.

[0050] To achieve the above purpose, see Figure 1 As shown, a gas intrusion prediction method suitable for high-speed compressible flow is used to predict the gas intrusion of real compressible flow in aircraft engines, including:

[0051] S1. Obtain the static pressure distribution of the guide vane cascade flow channel outlet in a single cycle, as well as the total pressure and static pressure of the cooling air in the inner ring of the rim seal;

[0052] The static pressure distribution of the guide vane cascade flow channel outlet in a single cycle, as well as the total cold air pressure and static pressure of the rim seal inner ring are obtained by measuring with a pressure measuring element in a rim seal experiment.

[0053] In this embodiment, the total pressure and static pressure of the inner ring of the rim seal are obtained by a pressure measuring element, which is a total pressure and static pressure probe. Figure 2 As shown, the specific positions in the rim sealing structure include the guide vane cascade outlet position, the rim inner ring position and the pressure measuring point positions involved.

[0054] S2. Obtain the maximum static pressure and average static pressure of the main flow at the guide vane cascade outlet according to the static pressure distribution;

[0055] The circumferential Mach number of the airflow inside the rim seal is obtained based on the total cold air pressure and static pressure inside the rim seal;

[0056] In this embodiment, the dimensionless radius position of the inner sealing ring is r / b =0.98. Among them, r is the radius, b is the maximum radius of the turbine disk.

[0057] The calculation formula for the circumferential Mach number of the inner ring of the wheel rim seal is as follows:

[0058]

[0059] Where, is the circumferential Mach number of the inner ring of the rim seal; is the total circumferential pressure of the inner ring of the rim seal; P c is the static pressure of the cold air in the inner ring of the rim seal; γ is the adiabatic index.

[0060] S3. Obtain the cold air supply pressure coefficient based on the total cold air pressure of the inner ring of the wheel rim seal, the maximum static pressure and the average static pressure of the mainstream at the outlet of the guide vane cascade;

[0061] The calculation formula of the cooling air supply pressure coefficient is as follows:

[0062]

[0063] Where, Indicates the cooling air supply pressure coefficient; Indicates the total pressure of cold air in the inner ring of the wheel rim seal; P g,max Indicates the maximum static pressure at the guide vane cascade outlet, P g,avg It represents the average static pressure at the outlet of the guide vane cascade.

[0064] S4. Obtain the cold air outflow loss coefficient based on the circumferential Mach number of the airflow in the inner ring of the rim seal, the total pressure and static pressure of the cold air in the inner ring of the rim seal, and the maximum static pressure and average static pressure of the mainstream at the outlet of the guide vane cascade;

[0065] The cold air outflow loss coefficient is obtained according to the following steps:

[0066] The effective outflow pressure of the cooling air is obtained based on the circumferential Mach number of the airflow inside the wheel rim seal, the airflow adiabatic index, and the cooling air static pressure inside the wheel rim seal.

[0067] The calculation formula of the effective outflow pressure of cold air is as follows:

[0068]

[0069] Where, Indicates the effective outflow pressure of cold air; Indicates the static pressure of the cold air inside the wheel rim seal; r 1 represents the inner ring radius of the wheel rim seal; r 2 represents the outer ring radius of the wheel rim seal; Ma θ,c is the circumferential Mach number of the cooling air inside the rim seal; Represents the adiabatic index.

[0070] S5. Obtain the total pressure loss of the cold air outflow based on the total pressure of the cold air on the inner ring of the wheel rim seal, the maximum static pressure of the mainstream at the outlet of the guide vane cascade, and the effective outflow pressure of the cold air;

[0071] The calculation formula of the total pressure loss of the cold air outflow is as follows:

[0072]

[0073] Where, Indicates the total pressure loss of the cold air outflow; Indicates the effective outflow pressure of cold air; Indicates the total pressure of cold air in the inner ring of the wheel rim seal; Indicates the maximum static pressure of the mainstream at the guide vane cascade outlet.

[0074] S6. Obtain a cold air outflow loss coefficient based on the total pressure loss of the cold air outflow and the average static pressure at the guide vane cascade outlet.

[0075] The calculation formula of the cold air outflow loss coefficient is as follows:

[0076]

[0077] Where, Indicates the cold air outflow loss coefficient; Indicates the total pressure loss of the cold air outflow; Average static pressure at the guide vane cascade outlet.

[0078] S7. Obtaining a total pressure margin coefficient based on a cold air supply pressure coefficient and a cold air outflow loss coefficient;

[0079] The calculation formula of the total pressure margin coefficient is as follows:

[0080]

[0081] Where, Indicates the total pressure margin factor; Indicates the cooling air supply pressure coefficient; Indicates the cooling air outflow loss coefficient.

[0082] The presence of gas intrusion is determined based on the total pressure margin coefficient; when the total pressure margin coefficient is greater than or equal to 0, there is no gas intrusion; otherwise, there is gas intrusion.

[0083] The present invention can be further promoted to obtain a suitable total pressure of cold air supply in the wheel rim sealing design. The specific process is as follows: Figure 3 As shown in the figure, the specific method is as follows: The total pressure loss coefficient is determined in the same way as the total pressure margin coefficient described above. Assuming the total pressure margin coefficient is 0, since the total pressure loss coefficient can be obtained from the above process, the cooling air supply pressure coefficient can be obtained by reverse calculation using the formula, and then the cooling air total pressure is obtained, which determines the minimum total supply pressure when gas intrusion occurs.

[0084] In order to illustrate a gas intrusion prediction method applicable to high-speed compressible flow provided by the present invention, it is described with reference to the accompanying drawings.

[0085] See also Figures 4-7 As shown in the figure, the corresponding relationship between the sealing efficiency of the inner ring of the wheel rim seal and the total pressure margin coefficient under different rotational Mach numbers is shown. Figure 4 Shows the rotational Mach number Ma φ =0.00, the corresponding relationship curve between the sealing efficiency of the inner ring of the rim seal and the total pressure margin coefficient; Figure 5 Shows the rotational Mach number Ma φ =0.18, the corresponding relationship curve between the sealing efficiency of the inner ring of the rim seal and the total pressure margin coefficient; Figure 6 Shows the rotational Mach number Ma φ =0.36, the corresponding relationship curve between the sealing efficiency of the inner ring of the rim seal and the total pressure margin coefficient; Figure 7 Shows the rotational Mach number Ma φ =0.56, the corresponding relationship curve between the sealing efficiency of the inner ring of the rim seal and the total pressure margin coefficient; Figures 4-7 The sealing efficiency of the inner ring of the rim seal is measured by a high-speed rim seal test bench. The total pressure margin coefficient is obtained according to the method provided by the present invention.

[0086] The rotational Mach number is defined as follows:

[0087]

[0088] ω is the rotational angular velocity of the turbine disk, b is the maximum radius of the turbine disk, γ is the adiabatic index, R is the gas constant, T For static temperature.

[0089] Depend on Figures 4-7 It can be seen that when the total pressure margin coefficient is greater than or equal to 0, the sealing efficiency of the inner ring of the rim seal is basically maintained above 0.99, indicating that there is no gas intrusion in the disc cavity at this time. Therefore, the method provided by the present invention can well predict whether there is gas intrusion. Although the total pressure margin coefficient is less than 0 in some operating conditions, the sealing efficiency is still close to 1. This is because the cold air supply pressure coefficient is calculated based on the maximum pressure at the guide vane cascade outlet in the judgment criteria. Therefore, if the cold air supply pressure coefficient is too small, the total pressure margin coefficient is too small. It can be seen that when designing the rim seal, the designed cold air total pressure obtained by reverse deduction using the method provided by the present invention may be higher than the minimum cold air total pressure that can just prevent gas intrusion, and thus safer.

[0090] The present invention provides a gas intrusion prediction system applicable to high-speed compressible flow, comprising:

[0091] The data acquisition module is used to obtain the static pressure distribution of the guide vane cascade flow channel outlet in a single cycle, as well as the total pressure and static pressure of the cold air in the inner ring of the rim seal; obtain the maximum static pressure and average static pressure of the mainstream at the guide vane cascade outlet based on the static pressure distribution; and obtain the circumferential Mach number of the airflow in the inner ring of the rim seal based on the total pressure and static pressure of the cold air in the inner ring of the rim seal;

[0092] The data processing module is used to obtain the cooling air supply pressure coefficient based on the cooling air total pressure of the inner ring of the wheel rim seal, the maximum static pressure and the average static pressure of the mainstream at the outlet of the guide vane cascade; obtain the cooling air outflow loss coefficient based on the circumferential Mach number of the airflow in the inner ring of the wheel rim seal, the cooling air total pressure and the static pressure of the inner ring of the wheel rim seal, and the maximum static pressure and the average static pressure of the mainstream at the outlet of the guide vane cascade; and obtain the total pressure margin coefficient based on the cooling air supply pressure coefficient and the cooling air outflow loss coefficient;

[0093] The intrusion prediction module is used to determine whether there is gas intrusion based on the total pressure margin coefficient.

[0094] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for predicting gas intrusion in high-speed compressible flow, characterized in that: Used for prediction of gas intrusion in real compressible flows in aerospace engines, including: Obtain the static pressure distribution of the guide vane cascade flow channel outlet in a single cycle, as well as the total pressure and static pressure of the cold air inside the rim seal; Obtain the maximum static pressure and average static pressure of the mainstream at the guide vane cascade outlet according to the static pressure distribution; The circumferential Mach number of the airflow inside the rim seal is obtained based on the total cold air pressure and static pressure inside the rim seal; The cooling air supply pressure coefficient is obtained based on the total cooling air pressure of the inner ring of the wheel rim seal, the maximum static pressure and the average static pressure of the mainstream at the outlet of the guide vane cascade; The cold air outflow loss coefficient is obtained based on the circumferential Mach number of the airflow inside the rim seal, the total pressure and static pressure of the cold air inside the rim seal, and the maximum static pressure and average static pressure of the mainstream at the guide vane cascade outlet. Obtain the total pressure margin coefficient based on the cold air supply pressure coefficient and the cold air outflow loss coefficient; Determine whether there is gas intrusion based on the total pressure margin coefficient; The cold air outflow loss coefficient is obtained according to the following steps: The effective outflow pressure of the cooling air is obtained based on the circumferential Mach number of the airflow inside the wheel rim seal, the airflow adiabatic index, and the cooling air static pressure inside the wheel rim seal. The total pressure loss of the cold air outflow is obtained based on the total pressure of the cold air in the inner ring of the wheel rim seal, the maximum static pressure of the mainstream at the outlet of the guide vane cascade, and the effective outflow pressure of the cold air. The cold air outflow loss coefficient is obtained according to the total pressure loss of the cold air outflow and the average static pressure at the guide vane cascade outlet; The calculation formula of the effective outflow pressure of cold air is as follows: Where, Indicates the effective outflow pressure of cold air; Indicates the static pressure of the cold air inside the wheel rim seal; r 1 represents the inner ring radius of the wheel rim seal; r 2 represents the outer ring radius of the wheel rim seal; Ma θ,c is the circumferential Mach number of the cooling air inside the rim seal; represents the adiabatic index; The calculation formula of the total pressure loss of the cold air outflow is as follows: Where, Indicates the total pressure loss of the cold air outflow; Indicates the effective outflow pressure of cold air; Indicates the total pressure of cold air inside the wheel rim seal; Indicates the maximum static pressure of the mainstream at the outlet of the guide vane cascade; The calculation formula of the cold air outflow loss coefficient is as follows: Where, Indicates the cold air outflow loss coefficient; Indicates the total pressure loss of the cold air outflow; Average static pressure at the guide vane cascade outlet; The calculation formula of the cooling air supply pressure coefficient is as follows: Where, Indicates the cooling air supply pressure coefficient; Indicates the total pressure of cold air in the inner ring of the wheel rim seal; P g,max Indicates the maximum static pressure at the guide vane cascade outlet, P g,avg represents the average static pressure at the outlet of the guide vane cascade; The calculation formula of the total pressure margin coefficient is as follows: Where, Indicates the total pressure margin factor; Indicates the cooling air supply pressure coefficient; Indicates the cooling air outflow loss coefficient.

2. The method for predicting gas intrusion in high-speed compressible flow according to claim 1, characterized in that: Whether there is gas intrusion is determined based on the total pressure margin coefficient, including: when the total pressure margin coefficient is greater than or equal to 0, there is no gas intrusion phenomenon; otherwise, there is gas intrusion phenomenon.

3. The method for predicting gas intrusion in high-speed compressible flow according to claim 1, characterized in that: The static pressure distribution of the guide vane cascade flow channel outlet in a single cycle, as well as the total cold air pressure and static pressure of the rim seal inner ring are obtained by measuring with a pressure measuring element in a rim seal experiment.

4. A prediction system for the gas intrusion prediction method applicable to high-speed compressible flow according to claim 1, characterized in that: include: The data acquisition module is used to obtain the static pressure distribution of the guide vane cascade flow channel outlet in a single cycle, as well as the total pressure and static pressure of the cold air in the inner ring of the rim seal; obtain the maximum static pressure and average static pressure of the mainstream at the guide vane cascade outlet based on the static pressure distribution; and obtain the circumferential Mach number of the airflow in the inner ring of the rim seal based on the total pressure and static pressure of the cold air in the inner ring of the rim seal; The data processing module is used to obtain the cooling air supply pressure coefficient based on the cooling air total pressure of the inner ring of the wheel rim seal, the maximum static pressure and the average static pressure of the mainstream at the outlet of the guide vane cascade; obtain the cooling air outflow loss coefficient based on the circumferential Mach number of the airflow in the inner ring of the wheel rim seal, the cooling air total pressure and the static pressure of the inner ring of the wheel rim seal, and the maximum static pressure and the average static pressure of the mainstream at the outlet of the guide vane cascade; and obtain the total pressure margin coefficient based on the cooling air supply pressure coefficient and the cooling air outflow loss coefficient; The intrusion prediction module is used to determine whether there is gas intrusion based on the total pressure margin coefficient.

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