Method for obtaining internal flow rate of twin-spool turbofan engine and its overall environment

Abstract

The application provides a method for obtaining internal flow in a double-rotor turbofan engine under an overall environment, and belongs to the technical field of aero-engine testing. The method comprises: carrying out a flow characteristic measurement test on key throttling elements of an air system at a part level to obtain flow characteristics; using all the key throttling elements of the air system for core engine testing, and carrying out core engine testing to obtain core engine test parameters; calculating a throat conversion flow of a high-pressure turbine guide vane after reaching a critical rotating speed according to the core engine test parameters; using the core engine for overall testing, and carrying out overall testing to obtain overall test parameters; and calculating an initial value of the throat conversion flow of the high-pressure turbine guide vane under an overall state according to the overall test parameters, and iteratively calculating an absolute value of a relative difference between the initial value and a fixed value to obtain internal flow in the overall test.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of aero-engines, and particularly relates to a dual-rotor turbofan engine and an internal flow rate acquisition method under an overall environment of the dual-rotor turbofan engine. BACKGROUND

[0002] With the deepening of the research on the overall performance of an aero-engine, the accurate evaluation of the internal flow rate of a dual-rotor turbofan engine under the overall condition of the engine has gradually become one of the problems to be solved, especially for the state in which the engine speed exceeds a certain value to approach the design speed. At this time, the accurate evaluation of the internal flow rate will directly affect the evaluation results and the optimization improvement direction of the overall performance.

[0003] Since the internal flow rate cannot be directly measured in the overall test, in the prior art, the compressor component characteristics are obtained according to the test results of the compressor components, including the compressor operating line simulating the overall throttling state, i.e., the relationship among the compressor pressure ratio, the flow rate and the compressor corrected speed, and then the compressor inlet flow rate, i.e., the internal flow rate, is calculated according to the compressor corrected speed, the compressor inlet temperature and the pressure measurement results in the overall test. However, since the compressors used in the compressor component test and the overall test are not the same compressor, the states of the components are different, and at the same time, the inlet throttling simulation is used in the compressor component test, which will cause the twist deformation angle of the rotor blade to be smaller than that in the overall environment, and the fan outlet flow field, temperature and pressure are not simulated in the compressor component test, the inlet flow conditions and the overall environment are different, and the working states of the compressor blades, guide vanes and adjusting mechanisms and the overall environment are different.

[0004] The above factors will cause the internal flow rate obtained by the existing method to be greatly deviated from the actual result, and affect the accurate evaluation and optimization improvement of the overall performance. SUMMARY

[0005] The purpose of the present application is to provide an internal flow rate acquisition method under the overall environment of a dual-rotor turbofan engine, so as to solve or alleviate at least one problem in the background art.

[0006] The technical solution of the present application is: an internal flow rate acquisition method under the overall environment of a dual-rotor turbofan engine, the method comprising:

[0007] Step S1, determining the key throttling elements of the air system of the dual-rotor engine, carrying out a flow rate characteristic measurement test of the key throttling elements of the air system at the component level, and obtaining the flow rate characteristics of all the key throttling elements of the air system;

[0008] Step S2, using all the key throttling elements of the air system for core engine test;

[0009] Step S3: Conduct the core machine test in step S2 to obtain the core machine test parameters, including the core machine physical flow W. 25 Core compressor bleed air volume W 引气 Core engine high-pressure turbine guide vane throat front displacement W 排气 The total pressure at the core engine compressor outlet (P3), the total temperature at the core engine compressor outlet (T3), the total pressure at the core engine main combustion chamber outlet (P4), and the mass flow rate of fuel at the core engine inlet (W) are all related to the core engine compressor. fin and calorific value H f ;

[0010] Step S4: Calculate the equivalent flow rate at the throat of the high-pressure turbine guide vane based on the core machine test results. In the formula, W4 represents the physical flow rate at the throat of the high-pressure turbine guide vane. T4 is the total temperature at the throat of the high-pressure turbine guide vane, and T4 is the enthalpy of the combustion gas at the throat of the high-pressure turbine guide vane. The function, i.e. Where H3 is the enthalpy of the compressor outlet airflow, which is a function of the total temperature T3 at the core compressor outlet. ;

[0011] When the core machine's converted speed exceeds the critical speed of the high-pressure turbine guide vane At that time, the converted flow rate at the throat of the high-pressure turbine guide vane is a constant value, that is const is a constant value;

[0012] Step S5: Use the core unit from step S3 for whole-machine testing;

[0013] Step S6: Conduct the overall machine test as described in step S5 to obtain the overall machine test parameters, including the compressor bleed air volume during the overall machine test. High-pressure turbine guide vane throat front displacement Total pressure at compressor outlet and compressor outlet total temperature Total pressure at the main combustion chamber outlet Fuel mass flow rate and calorific value ;

[0014] Step S7: The core machine's calculated rotational speed exceeds the critical rotational speed of the high-pressure turbine guide vane. Based on the principle that the equivalent flow rate at the throat of the high-pressure turbine guide vane remains constant, the design speed of the high-pressure turbine guide vane is given for the whole machine test. Initial value of physical flow rate at the core machine inlet Based on the test parameters obtained in step S6 and the calculation method in step S4, the initial value of the converted flow rate at the throat of the high-pressure turbine guide vane during the whole machine test is obtained. ;

[0015] Calculating the initial value of the equivalent flow of the high-pressure turbine guide vane throat The absolute value of the relative difference from the value const in step S4 , adjusting the initial value of the physical flow of the core engine inlet until the absolute value of the relative difference is less than a predetermined value, at which time the core engine inlet flow is the internal flow at the design speed of the dual-rotor turbofan engine;

[0016] Step S8, given the initial value of the physical flow of the core engine inlet at any speed of the engine greater than the critical speed of the high-pressure turbine guide vane in the whole machine test , repeating step S7 to obtain the internal flow at any speed of the engine greater than the critical speed of the high-pressure turbine guide vane .

[0017] Further, the key throttling elements of the air system include the compressor intermediate stage bleed air pipeline, the turbine pre-rotation nozzle, and the turbine air-cooled blade.

[0018] Further, in the core engine test of step S3, the core engine inlet flow is warmed and pressurized to simulate the total temperature and total pressure of the fan outlet in the whole machine environment, and a disturbance device is arranged at the core engine inlet to simulate the pressure field of the fan outlet in the whole machine environment.

[0019] Further, in the core engine test of step S3, the process of obtaining the physical flow W 25 of the core engine is as follows:

[0020] The pressure boundary layer in the inlet flow pipeline is measured by using a measurement rake with densely arranged measurement points near the wall surface in the core engine inlet flow pipeline, so as to obtain the physical flow W 25 of the core engine inlet.

[0021] Further, in the core engine test of step S3, the process of obtaining the core engine compressor bleed air amount W 引气 and the core engine high-pressure turbine guide vane throat pre-exhaust amount W 排气 is as follows:

[0022] Temperature and pressure measurement points are arranged at the inlet and outlet positions of the key throttling elements of the air system, the core engine test air system bleed air amount and exhaust amount are calculated according to the temperature and pressure measurement results at the inlet and outlet of the key throttling elements of the air system and the obtained flow characteristics of the key throttling elements of the air system, and the core engine test air system bleed air amount and exhaust amount are the core engine compressor bleed air amount W 引气 and the core engine high-pressure turbine guide vane throat pre-exhaust amount W 排气 .

[0023] Furthermore, in the core engine test in step S3, the process of obtaining the total pressure P3 at the core engine compressor outlet and the total temperature T3 at the core engine compressor outlet is as follows:

[0024] An arc-shaped total pressure measuring rake is used at the compressor outlet to cover measuring points at different radial heights of a blade passage, thereby obtaining the total pressure P3 at the core compressor outlet.

[0025] The total outlet temperature T3 of the core compressor is obtained by inserting a thermocouple inside the blade passage.

[0026] Furthermore, in the core machine test in step S3, the process of obtaining the total pressure at the throat of the high-pressure turbine guide vane is as follows:

[0027] Based on the simulation results of the main combustion chamber flow field, static pressure measurement points were selected on the inner wall of the main combustion chamber flame tube to obtain the total pressure at the throat of the high-pressure turbine guide vane.

[0028] Furthermore, in the core engine test in step S3, the mass flow rate W of the core engine inlet fuel is obtained. fin The process is as follows:

[0029] The volumetric flow rate W of the fuel at the core engine inlet was measured using a volumetric flow meter. fin体积 The fuel density ρ was obtained by measuring the physical properties of the fuel in the oil depot. f Temperature T f and calorific value H f Measure the inlet fuel temperature T of the core engine. fin ;

[0030] Based on the relationship between fuel temperature and density, a curve is constructed showing the relationship between the core engine inlet fuel density and fuel density ρ. f Temperature T f and core engine inlet fuel temperature T fin relational formula Thus, the density of imported fuel in the core engine is obtained;

[0031] The mass flow rate of the core engine inlet fuel is obtained based on the core engine inlet fuel density. .

[0032] Furthermore, the process of obtaining the whole machine test parameters in step S6 is the same as the process of obtaining the core machine test parameters in step S4.

[0033] In addition, this application also provides a dual-rotor turbofan engine, wherein the intrinsic flow rate of the dual-rotor turbofan engine under the overall engine environment is determined by any of the above-described methods for obtaining the intrinsic flow rate of the dual-rotor turbofan engine under the overall engine environment.

[0034] The method for obtaining the internal flow provided by the application is based on actual measurement test data under the whole machine environment, and can realize accurate acquisition of the internal flow under the high speed state of the whole machine (after the high pressure turbine guide reaches the critical state), which is of great significance for realizing accurate evaluation of the performance of the whole machine and formulating optimization improvement measures. BRIEF DESCRIPTION OF DRAWINGS

[0035] In order to more clearly illustrate the technical solutions provided by the application, the drawings will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the application.

[0036] Figure 1 The figure is a schematic diagram of the method for obtaining the internal flow of the dual-rotor turbofan engine under the whole machine environment of the application.

[0037] Figure 2 The figure is a schematic diagram of the flow characteristic of the turbine pre-rotation nozzle of an embodiment of the application.

[0038] Figure 3 The figure is a schematic diagram of the fan outlet pressure field in the whole machine environment simulated by adding the disturbance device of an embodiment of the application.

[0039] Figure 4 The figure is a schematic diagram of the pressure measurement in the flow tube in an embodiment of the application.

[0040] Figure 5 The figure is a schematic diagram of the pressure measurement at the outlet of the compressor in an embodiment of the application.

[0041] Figure 6 The figure is a schematic diagram of the flame tube wall surface static pressure measurement in an embodiment of the application. DETAILED DESCRIPTION

[0042] In order to make the purpose, technical solutions and advantages of the embodiments of the application more clear, the technical solutions in the embodiments of the application will be described in more detail below with reference to the drawings in the embodiments of the application.

[0043] In order to realize accurate acquisition of the internal flow under the high speed state of the dual-rotor turbofan engine under the whole machine condition (after the high pressure turbine guide reaches the critical state) so as to more accurately evaluate the performance of the whole machine, the application provides a method for obtaining the internal flow under the high speed state of the dual-rotor turbofan engine under the whole machine condition, which is based on the existing internal flow acquisition process and provides an accurate acquisition method for the main parameters (including air system gas consumption, core machine test inlet flow, compressor outlet pressure, main combustion chamber outlet pressure, fuel flow, etc.) required for internal flow acquisition, thereby improving the accuracy of the internal flow under the whole machine environment.

[0044] As Figure 1As shown, the method for obtaining the internal flow rate of a dual-rotor turbofan engine under whole-machine conditions provided in this application includes the following process:

[0045] Step S1: Identify the key throttling elements of the air system of the dual-rotor engine, conduct flow characteristic measurement tests at the component level of the key throttling elements of the air system, and obtain the flow characteristics of all key throttling elements of the air system.

[0046] The key throttling elements of a twin-rotor engine's air system can be determined by calculating the sensitivity of engine performance, such as thrust, fuel consumption, and turbine inlet temperature, through aero-engine overall performance software (e.g., GasTurb). These key air system throttling elements typically include the compressor intermediate stage bleed air duct, turbine pre-swirl nozzles, and turbine air-cooled blades.

[0047] For all critical throttling components of the air system that will be used in subsequent core engine and complete engine tests, such as the compressor intermediate stage bleed air line, turbine pre-swirl nozzle, and turbine air-cooled blades, component-level flow characteristic measurement tests were conducted on these critical air system throttling components to obtain their flow characteristics. This is to improve the accuracy of the assessment of air system bleed and exhaust volumes in subsequent core engine and complete engine tests. Figure 2 The diagram shown is a schematic diagram of the flow characteristics of a turbine pre-swirl nozzle in one embodiment of this application.

[0048] Step S2: Use all the key air system throttling elements from Step S1 for core engine and complete engine assembly and testing to ensure the consistency of the technical status of the key air system throttling elements in the flow characteristic test, core engine test and complete engine test, and improve the accuracy of the air system exhaust and desiccation volume assessment in the subsequent core engine and complete engine tests.

[0049] Step S3: Conduct core machine experiments using the core machine from step S2. The experiment process includes:

[0050] 1) such as Figure 3 As shown, the airflow at the core machine inlet is heated and pressurized to simulate the total temperature and total pressure at the fan outlet in the whole machine environment. A turbulence device is added at the core machine inlet to simulate the fan outlet pressure field in the whole machine environment.

[0051] 2) such as Figure 4 As shown, a measuring rake 11 with denser measuring points close to the wall is used in the core machine inlet flow line 12 to measure the pressure boundary layer in the inlet flow line 12, thereby obtaining the core machine inlet physical flow W. 25 The above process can increase the physical flow rate W at the core machine inlet. 25 Measurement accuracy;

[0052] 3) Arrange temperature and pressure measuring points at the inlet and outlet of the key throttling element of the air system. Based on the temperature and pressure measurement results at the inlet and outlet of the key throttling element of the air system, and the flow characteristics of the key throttling element of the air system obtained in step S1, calculate the bleed and exhaust volumes of the air system during the core engine test. The bleed and exhaust volumes of the air system are the core engine compressor bleed volume W. 引气 and the core engine high-pressure turbine guide vane throat front displacement W 排气 ;

[0053] 4) such as Figure 5 As shown, an arc-shaped total pressure measuring rake is used at the compressor outlet to cover measuring points at different radial heights of a blade channel to obtain the total pressure P3 at the core compressor outlet. The above process can improve the measurement accuracy of the total pressure P3 at the core compressor outlet. The total temperature T3 at the core compressor outlet can be measured using the conventional technique of thermocouple insertion.

[0054] 5) such as Figure 6 As shown, based on the flow field simulation results of the main combustion chamber, a static pressure measurement was performed at a location on the inner wall of the main combustion chamber flame tube to obtain the total pressure at the outlet of the core engine's main combustion chamber. The total pressure at the outlet of the main combustion chamber of the core engine This refers to the total pressure at the throat of the high-pressure turbine guide vane;

[0055] 6) The volumetric flow rate W of the fuel at the core engine inlet is measured using a volumetric flow meter. fin体积 The fuel density ρ was obtained by measuring the physical properties of the fuel in the oil depot. f Temperature T f and calorific value H f Measure the inlet fuel temperature T of the core engine. fin Based on the relationship between fuel temperature and density, the fuel density at the core engine inlet was calculated. Thus, the mass flow rate of the imported fuel in the core engine is obtained. .

[0056] Step S4: Based on the core machine test results in Step S3, calculate the equivalent flow rate at the throat of the high-pressure turbine guide vane. The physical flow rate at the throat of the high-pressure turbine guide vane Total temperature at the throat of the high-pressure turbine guide vane Enthalpy of gas at the throat of the high-pressure turbine guide vane The function, i.e. ,in The enthalpy of the compressor outlet airflow is the unit of enthalpy, which is the total temperature at the compressor outlet. The function, i.e. ;

[0057] When the core machine's converted speed exceeds the critical speed of the high-pressure turbine guide vane When the core engine speed is less than the design speed, the high pressure turbine guide vane throat flow rate is constant because the high pressure turbine guide vane reaches a critical state, i.e. , where const is a constant.

[0058] Step S5: The core engine in step S3 is used for the whole engine assembly and test to ensure that the core engine hardware and test technology state in the whole engine test is consistent with that in the core engine test in step S3, and the consistency of various test parameters of the core engine is ensured.

[0059] Step S6: The whole engine in step S5 is used to carry out the whole engine test, to obtain the compressor bleed air flow rate and the high pressure turbine guide vane throat front exhaust flow rate , the compressor outlet total pressure and the outlet total temperature , the main combustion chamber outlet total pressure (i.e. the high pressure turbine guide vane throat total pressure), the fuel mass flow rate and the heat value . The process or technical scheme for obtaining the above parameters is consistent with that in step S3.

[0060] Step S7: When the core engine conversion speed exceeds the critical speed of the high pressure turbine guide vane , the high pressure turbine guide vane throat flow rate is constant, the core engine inlet physical flow rate initial value is given when the high pressure turbine guide vane design speed in the whole engine test is given , the initial value of the high pressure turbine guide vane throat conversion flow rate in the whole engine test is calculated according to the test parameters obtained in step S6 and the calculation method in step S4 , the absolute value of the relative difference between the initial value of the high pressure turbine guide vane throat conversion flow rate and the constant value const in step S4 is adjusted , the core engine inlet physical flow rate initial value is adjusted until the absolute value of the relative difference is less than a predetermined value (for example, 0.1% in this application), i.e. the core engine inlet flow rate at this time is considered to be the content flow rate at the design speed of the dual-rotor turbofan engine. S8, the core engine inlet physical flow rate initial value is given when the engine speed in the whole engine test is greater than the critical speed of the high pressure turbine guide vane , and step S7 is repeated, so as to obtain the content flow rate at any speed greater than the critical speed of the high pressure turbine guide vane.

[0061] S8, the core engine inlet physical flow rate initial value is given when the engine speed in the whole engine test is greater than the critical speed of the high pressure turbine guide vane , and step S7 is repeated, so as to obtain the content flow rate at any speed greater than the critical speed of the high pressure turbine guide vane.

[0062] ​​​The method for obtaining connotation flow under the whole machine environment provided in the application is based on actual measurement test data under the whole machine environment, and can realize accurate acquisition of connotation flow under the whole machine condition in a high speed state (after the high pressure turbine guide reaches a critical state), which is of great significance for realizing accurate evaluation results of the whole machine performance and formulating optimization improvement measures.

[0063] The above merely provides a specific implementation of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can easily think of changes or replacements within the technical scope disclosed in the present application, which shall be covered within the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.

Claims

1. A method for obtaining the internal flow rate of a twin-spool turbofan engine in an overall engine environment, characterized in that, The method comprises: Step S1, determining the air system key throttle elements of the dual-rotor engine, carrying out flow characteristic measurement test of the air system key throttle elements at the part level, and obtaining the flow characteristics of all the air system key throttle elements; Step S2, using all the air system key throttle elements for core engine test; Step S3, obtaining core engine test parameters from the core engine test in step S2, wherein the core engine test parameters include core engine physical flow W 25 , core engine compressor bleed air amount W 引气 , core engine high pressure turbine guide vane throat front exhaust amount W 排气 , core engine compressor outlet total pressure P3 and core engine compressor outlet total temperature T3, core engine main combustion chamber outlet total pressure P4, and core engine inlet fuel mass flow W fin , and heat value H f ; Step S4, calculating the high-pressure turbine guide vane throat equivalent flow rate according to the core engine test result , wherein W4 is the high-pressure turbine guide vane throat physical flow rate, , T4 is the high-pressure turbine guide vane throat total temperature, and the high-pressure turbine guide vane throat total temperature T4 is a function of the high-pressure turbine guide vane throat gas unit enthalpy , that is, , wherein H3 is the unit enthalpy of the compressor outlet airflow and is a function of the core engine compressor outlet total temperature T3, that is, ; When the core engine speed exceeds the high pressure turbine guide vane critical speed , the high pressure turbine guide vane throat flow rate is constant, i.e. , const is constant; Step S5, using the core engine in step S3 for whole engine test; Step S6, conducting the whole machine test in step S5 to obtain the whole machine test parameters, the whole machine test parameters including the bleed air amount of the compressor in the whole machine test , the pre-throat exhaust amount of the high-pressure turbine guide vane , the total pressure at the outlet of the compressor , and the total temperature at the outlet of the compressor , the total pressure at the outlet of the main combustion chamber , the fuel mass flow , and the heat value ; Step S7, according to the core engine conversion speed exceeds high pressure turbine guide critical speed the principle of the high pressure turbine guide throat conversion flow when the high pressure turbine guide design speed in the whole machine test the core engine import physical flow initial value , according to the test parameters obtained in step S6 and the calculation method in step S4, obtain the high pressure turbine guide throat conversion flow initial value in the whole machine test ; Computing high pressure turbine guider throat flow rate initial value Absolute value of relative difference with the value const in step S4 , adjusting core engine inlet physical flow rate initial value Absolute value of relative difference Less than a predetermined value, at this time the core engine inlet flow rate Is the inner content flow rate when the design rotating speed of the dual-rotor turbofan engine Step S8, the engine speed is greater than the high pressure turbine guide critical speed in the whole machine test The core machine inlet physical flow initial value at any speed Repeat step S7 to obtain the internal flow at any speed when the engine speed is greater than the high pressure turbine guide critical speed ​ 2. The method of claim 1, wherein The air system key throttle elements comprise compressor intermediate stage bleed air pipeline, turbine pre-rotation nozzle, and turbine air-cooled blade.

3. The method of claim 2, wherein, In the core engine test of step S3, the inlet airflow of the core engine is heated and pressurized to simulate the total temperature and total pressure of the fan outlet in the whole engine environment, and a disturbance device is arranged at the inlet of the core engine to simulate the pressure field of the fan outlet in the whole engine environment.

4. The method of claim 3, wherein In the core machine test in step S3, the core machine physical flow W is obtained 25 The process is as follows: In the core engine import flow pipeline, the wall surface measurement point is encrypted to measure the pressure boundary layer in the import flow pipeline, so as to obtain the core engine import physical flow W 25 .

5. The method of claim 3, wherein In the core engine test in step S3, the core engine compressor bleed air amount W 引气 and the core engine high-pressure turbine guide vane throat front exhaust air amount W 排气 The process is as follows: The temperature and pressure measuring points are arranged at the inlet and outlet positions of the key throttling element of the air system, the air system bleed air amount and the exhaust amount in the core engine test are calculated according to the temperature and pressure measurement results of the inlet and outlet of the key throttling element of the air system and the obtained flow characteristics of the key throttling element of the air system, and the air system bleed air amount and the exhaust amount are the core engine compressor bleed air amount W 引气 and the pre-throat exhaust amount of the core engine high-pressure turbine guide vane W 排气 .

6. The method of claim 3, wherein In the core engine test of step S3, the process of obtaining the total pressure P3 of the core engine compressor outlet and the total temperature T3 of the core engine compressor outlet is as follows: An arc total pressure measuring rake is used at the outlet of the compressor to cover measuring points at different radial heights of a cascade passage, so as to obtain the total pressure P3 of the core engine compressor outlet; The total temperature T3 of the core engine compressor outlet is obtained by inserting a thermocouple into the cascade passage.

7. The method of claim 3, wherein In the core engine test of step S3, the process of obtaining the total pressure of the high-pressure turbine guide vane throat is as follows: According to the simulation results of the main combustion chamber flow field, the total pressure of the high-pressure turbine guide vane throat is obtained by selecting the positions of static pressure measuring points on the inner wall surface of the main combustion chamber flame tube for static pressure measurement.

8. The method of claim 3, wherein, In the core engine test in step S3, the core engine inlet fuel mass flow rate W fin is obtained. The volumetric flow meter is used to measure the volume flow W of the fuel into the core engine fin体积 The fuel density p f , temperature T f and heat value H f are obtained by measuring the physical properties of the fuel in the oil depot fin The fuel temperature T fin into the core engine is measured According to the relationship between the fuel temperature and the density, a relational expression of the core engine inlet fuel density with respect to the fuel density p f , the temperature T f , and the core engine inlet fuel temperature T fin is constructed , so as to obtain the core engine inlet fuel density; According to the core engine inlet fuel density, the core engine inlet fuel mass flow is obtained .

9. The method of claim 3 to 8, characterized in that, The process of obtaining the whole engine test parameters in step S6 is the same as the process of obtaining the core engine test parameters in step S4.

10. A dual-spool turbofan engine characterized by, The internal flow of the dual-rotor turbofan engine in the whole engine environment is determined by the internal flow acquisition method of the dual-rotor turbofan engine in the whole engine environment according to any one of claims 1 to 9.

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