Turbine-based ramjet combined engine and design method thereof

Abstract

The invention belongs to the technical field of design of turbine-based ramjet combination engines, and particularly relates to a turbine-based ramjet combination engine and a design method thereof. A turbine engine and a subsonic combustion ramjet engine are designed to be connected in parallel to intake air and share a thrust augmentation / ramjet combustion chamber; main advantages of a series-connection type turbine-based ramjet combination engine and a parallel-connection type turbine-based ramjet combination engine are integrated, and compared with the series-connection type turbine-based ramjet combination engine, mode selection valves can be arranged at inlets of an air inlet channel low-speed channel and an air inlet channel high-speed channel when the series-connection type turbine-based ramjet combination engine works in a ramjet engine mode; the high Mach number working reliability is good, the efficiency is high, compared with a parallel type turbine-based ramjet combined engine, a set of ramjet combustion chamber and a combined spray pipe channel are reduced, the weight can be reduced by 12%-15%, the mission load and transonic speed performance of an aircraft can be improved, and the control difficulty is reduced.

Description

Technical Field

[0001] The present application belongs to the technical field of turbine-based ramjet combination engine design, and specifically relates to a turbine-based ramjet combination engine and a design method thereof. Background Art

[0002] The turbine-based ramjet combination engine is an ideal power source for high-Mach number space vehicles. The maximum operating Mach number is 5. Ramjet engines within Ma5 use sub-combustion ramjet engines, and ramjet engines above Ma5 use dual-mode ramjet engines or scramjet engines. At present, the turbine-based ramjet combination engine within Ma5 mainly has two configurations: tandem turbine-based ramjet combination engine and parallel turbine-based ramjet combination engine.

[0003] In a tandem turbine-based ramjet combination engine, the turbine engine and the ramjet engine are coaxially connected in series, with a common inlet, a common turbine engine afterburner and a common ramjet combustion chamber (afterburner / ramjet combustion chamber), and a common nozzle. The airflow is compressed in a single-channel inlet and then split. The central airflow enters the turbine engine, and the outer ring airflow enters the ramjet engine through an annular ramjet duct. After the airflow burns in the turbine engine afterburner and ramjet combustion chamber, it expands and is discharged through the nozzle. When the tandem turbine-based ramjet combination engine works in ramjet mode, it is difficult to achieve the closure and sealing of the turbine engine channel, and the reliability of high Mach number operation is poor.

[0004] In a parallel turbo-ramjet combination engine, the turbine engine and the ramjet engine are connected in parallel, and the airflow enters the turbine engine and the ramjet engine respectively after being compressed by the dual inlet ducts, and then expands and discharges through the dual-channel nozzle. The parallel turbo-ramjet combination engine has two channels in parallel, and the overall height of the engine is relatively high and the weight is relatively large, which is not conducive to the space layout of the integrated flight and engine, and the controllability is poor.

[0005] This application is proposed in view of the above-mentioned technical defects. Summary of the invention

[0006] The purpose of the present application is to provide a turbine-based ramjet combined engine and a design method thereof to overcome or alleviate at least one aspect of the known technical deficiencies.

[0007] The technical solution of this application is:

[0008] A turbine-based ramjet combination engine, comprising a parallel combined air intake, a mode selection valve, an air intake low-speed passage, a turbine engine main engine, an air intake high-speed passage, a mixing flow device, an afterburner / ramjet combustion chamber, and a nozzle;

[0009] The inlet of the low-speed channel and the high-speed channel of the intake duct are connected to the outlet of the intake duct in parallel combination, and a mode selection valve is arranged at the inlet of the low-speed channel and the high-speed channel of the intake duct, and the mode selection valve can open or close the inlet of the low-speed channel and the high-speed channel of the intake duct, and adjust the relative opening of the inlet of the low-speed channel and the high-speed channel of the intake duct;

[0010] The inlet of the turbine engine main engine is connected to the outlet of the low-speed passage of the air inlet, and the low-speed passage of the air inlet, the turbine engine main engine and the high-speed passage of the air inlet are arranged in parallel;

[0011] The inlet of the mixing flow device is connected to the main engine of the turbine engine and the outlet of the high-speed channel of the air inlet;

[0012] The inlet of the afterburner / ramjet combustion chamber is connected to the outlet of the mixing flow device;

[0013] The nozzle is arranged at the outlet of the afterburner / ramjet combustion chamber.

[0014] According to at least one embodiment of the present application, the above-mentioned turbine-based ramjet combined engine has:

[0015] In turbine engine mode, the mode selection valve closes the inlet of the high-speed channel of the inlet;

[0016] In ramjet mode, the mode selection valve closes the inlet of the low-speed passage of the inlet;

[0017] In the intermediate conversion mode, the mode selection valve opens the inlet of the low-speed channel and the high-speed channel of the intake duct.

[0018] According to at least one embodiment of the present application, in the above-mentioned turbine-based ramjet combination engine, the nozzle is a single-sided expansion nozzle.

[0019] According to at least one embodiment of the present application, in the above-mentioned turbine-based ramjet combination engine, the high-speed channel of the inlet is circular or elliptical;

[0020] The flow mixing device comprises an internal high-speed channel and an internal low-speed channel, and the outlets of the internal high-speed channel and the internal low-speed channel are connected inside the flow mixing device and connected to the outlet of the flow mixing device;

[0021] The internal high-speed channel is an annular channel, and its inlet is connected to the outlet of the high-speed channel of the air inlet through a volute structure, serving as the outer duct inlet of the afterburner / ramjet combustion chamber. The inlet of the internal low-speed channel is connected to the outlet of the turbine engine main engine, and a variable area duct ejector structure is set at the outlet of the internal high-speed channel.

[0022] A method for designing a turbine-based ramjet combination engine is used to design the turbine-based ramjet combination engine, comprising:

[0023] Step 1: Task and requirements analysis:

[0024] Sort out aircraft requirements, clarify the aircraft mission requirements and constraints on power, and integrate the upstream and downstream requirements and constraints of the engine to clarify the input of engine design;

[0025] Step 2: Thermal cycle analysis:

[0026] Taking the turbine engine design point as the target and taking into account typical conditions, the thermal cycle parameter analysis of the turbine engine is carried out;

[0027] Taking the design point of the ramjet engine as the target and taking into account the typical state, the thermal cycle parameter analysis of the ramjet engine is carried out;

[0028] Step 3: Design point performance calculation:

[0029] Carry out design point performance calculations for turbine engines and ramjet engines;

[0030] Step 4: Main flow path design:

[0031] Design the main flow path of turbine engine and ramjet engine based on their design point performance and parameters;

[0032] Step 5: Typical state performance calculation:

[0033] Considering the aircraft requirements and the engine's own characteristics, the typical state performance calculation of the turbine engine and the ramjet engine is performed. If the typical state performance does not meet the aircraft requirements, repeat steps 1 to 5;

[0034] Step 6: Combined intake flow split ratio design:

[0035] The executable common working range is clarified, requiring that the total pressure at the outlet of the high-speed channel of the inlet duct Pcy2 is greater than or equal to the static pressure at the outlet of the low-pressure turbine of the main engine of the turbine Ps6 or the static pressure at the outlet of the outer duct of the main engine of the turbine Ps16;

[0036] According to the aircraft's power requirements, based on the performance of turbine engines and ramjet engines in the common working range, the combined intake flow is distributed, and the split ratio is optimized in combination with the performance calculation of the combined power common working range to determine the best split ratio of the combined intake flow in the executable common working range;

[0037] Step 7: Calculation of modal transition point performance:

[0038] Based on the optimal split ratio of the combined intake flow rate and the combined power and performance of each power unit within the executable common working range, the mode transition point is determined according to the inlet characteristics, the performance matching of the turbine engine and the ramjet engine within the mode transition range, the mixing device characteristics, and the afterburner / ramjet combustion chamber characteristics;

[0039] According to the matching of the inlet characteristics, the turbine engine and the ramjet engine characteristics, the modal transition point performance is calculated. If the modal transition point performance does not meet the aircraft requirements, repeat steps 1 to 7.

[0040] Step 8: Determine the design requirements of each component and system:

[0041] According to the performance calculation results of turbine engine and ramjet engine design point, typical state and mode transition point, the requirements for engine components and systems are proposed;

[0042] Step 9: Determine the overall performance concept plan:

[0043] The overall engine performance concept is formed by taking into account the aircraft mission requirements and constraints on power, the upstream and downstream requirements and constraints of the engine, the design points of the turbine engine and the ramjet engine, the typical state performance, and the modal transition point performance. If the overall engine performance does not meet the design requirements, repeat steps 1 to 9.

[0044] This application has at least the following beneficial technical effects:

[0045] Provided are a turbine-based ramjet combination engine and a design method thereof. The design is that a turbine engine and a ramjet engine are connected in parallel to share an air intake and an afterburner / ramjet combustion chamber, and the main advantages of a tandem turbine-based ramjet combination engine and a parallel turbine-based ramjet combination engine are combined. Compared with the tandem turbine-based ramjet combination engine, when working in a ramjet engine mode, a mode selection valve can be set at the entrance of a low-speed channel and a high-speed channel of the air inlet to close the low-speed channel of the air inlet, so as to achieve a closed and sealed turbine engine channel. The high Mach number working reliability is good and the efficiency is high. Compared with the parallel turbine-based ramjet combination engine, one set of ramjet combustion chambers and one combined nozzle channel are reduced, and the weight can be reduced by 12% to 15%, so that the mission load and transonic performance of the aircraft can be improved, and the control difficulty can be reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is a schematic diagram of a turbine-based ramjet combination engine provided in an embodiment of the present application;

[0047] Figure 2 It is a schematic diagram of a turbine-based ramjet combination engine design method provided in an embodiment of the present application.

[0048] In order to better illustrate the present embodiment, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of the actual product. In addition, the drawings are only used for illustrative purposes and should not be construed as limitations on the present application. DETAILED DESCRIPTION

[0049] In order to make the technical solution and advantages of the present application clearer, the technical solution of the present application will be described in further detail in detail and in detail with reference to the accompanying drawings. It can be understood that the specific embodiments described here are only partial embodiments of the present application, which are only used to explain the present application, not to limit the present application. It should be noted that, for the convenience of description, only the parts related to the present application are shown in the accompanying drawings, and other related parts can refer to the general design.

[0050] In addition, unless otherwise defined, the technical terms or scientific terms used in the description of this application shall have the usual meanings understood by those of ordinary skill in the art to which this application belongs. The words used in the description of this application to indicate orientation are only used to indicate relative directions or positional relationships. When the absolute position of the described object changes, its relative positional relationship may also change accordingly. The word "include" used in the description of this application indicates that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, but does not exclude other elements or objects.

[0051] In addition, it should be noted that, unless otherwise clearly specified and limited, the words "installation", "connection" and similar terms used in the description of this application should be understood in a broad sense. For example, the connection can be a fixed connection or a detachable connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium. Technical personnel in the field can understand its specific meaning in this application according to the specific circumstances.

[0052] A turbo-ramjet combination engine, such as Figure 1 As shown, it includes a parallel combined intake duct, a mode selection valve, an intake duct low-speed channel, a turbine engine main engine, an intake duct high-speed channel, a mixing flow device, an afterburner / ramjet combustion chamber, and a nozzle.

[0053] The inlets of the intake duct low-speed channel and the intake duct high-speed channel are connected to the intake duct outlet in parallel, and a mode selection valve is arranged at the inlets of the intake duct low-speed channel and the intake duct high-speed channel. The mode selection valve can open or close the inlets of the intake duct low-speed channel and the intake duct high-speed channel, and adjust the relative opening of the inlets of the intake duct low-speed channel and the intake duct high-speed channel.

[0054] The main inlet of the turbine engine is connected to the outlet of the low-speed passage of the air inlet, and the low-speed passage of the air inlet and the main turbine engine are located at the periphery of the high-speed passage of the air inlet.

[0055] The inlet of the mixing flow device is connected to the main engine of the turbine engine and the outlet of the high-speed channel of the air inlet.

[0056] The inlet of the afterburner / ramjet combustion chamber is connected to the outlet of the mixing flow device.

[0057] The nozzle may specifically adopt a single-sided expansion nozzle, which is arranged at the outlet of the afterburner / ramjet combustion chamber.

[0058] The turbine-based ramjet combination engine disclosed in the above embodiment has a turbine engine mode, a ramjet engine mode, and an intermediate conversion mode.

[0059] In the turbine engine mode, the mode selection valve closes the inlet of the high-speed channel of the inlet, and the airflow enters the turbine engine main engine through the parallel combined inlet and the low-speed channel of the inlet for combustion, and then enters the afterburner / ramjet combustion chamber through the mixed flow device for supplementary combustion, and is discharged through the nozzle expansion. The turbine engine mode is suitable for low Mach number flight, Ma0~Ma2.

[0060] In the ramjet engine mode, the mode selection valve closes the inlet of the low-speed channel of the inlet, and the airflow enters the mixing device through the parallel combined inlet and the high-speed channel of the inlet, and then enters the afterburner / ramjet combustion chamber for combustion, and is discharged through the nozzle expansion. The ramjet engine mode is suitable for high Mach number flight, Ma3~Ma5.

[0061] In the intermediate conversion mode, the mode selection valve opens the inlet of the low-speed channel and the high-speed channel of the inlet, and the airflow enters the parallel combined inlet, enters the main engine of the turbine engine through the low-speed channel of the inlet for combustion, and enters the mixing device through the high-speed channel of the inlet, mixes in the mixing device, enters the afterburner / ramjet combustion chamber for combustion, and is discharged through the nozzle expansion. The intermediate conversion mode is suitable for flights between low Mach numbers and high Mach numbers, Ma2~Ma3.

[0001] Taking into account factors such as the integrated layout with the turbine engine main engine, the inlet high-speed channel can be designed to be circular, elliptical or even irregular in shape.

[0002] The mixing flow device includes an internal high-speed channel and an internal low-speed channel. The internal high-speed channel and the internal low-speed channel outlets are connected inside the mixing flow device and connected to the outlet of the mixing flow device. The internal high-speed channel is an annular channel, and its inlet is connected to the outlet of the high-speed channel of the air inlet through a volute structure, serving as the duct inlet of the afterburner / ramjet combustion chamber. The inlet of the internal low-speed channel is connected to the outlet of the turbine engine main engine. A variable area duct ejector structure is provided at the outlet of the internal high-speed channel to adjust and balance the static pressure of the exhaust gas of the internal high-speed channel and the internal low-speed channel, and to balance the static pressure of the exhaust gas of the low-pressure turbine of the turbine engine main engine and the exhaust gas of the duct inlet.

[0003] The turbine-based ramjet combination engine disclosed in the above embodiment is designed to share a parallel intake and afterburner / ramjet combustion chamber for a turbine engine and a ramjet engine, and combines the main advantages of a tandem turbine-based ramjet combination engine and a parallel turbine-based ramjet combination engine. Compared with the tandem turbine-based ramjet combination engine, when working in the ramjet engine mode, the mode selection valve can be set at the inlet of the low-speed channel and the high-speed channel of the inlet to close the low-speed channel of the inlet, so as to achieve the closure and sealing of the turbine engine channel. The high Mach number working reliability is good and the efficiency is high. Compared with the parallel turbine-based ramjet combination engine, one set of ramjet combustion chamber and one combined nozzle channel are reduced, and the weight can be reduced by 12% to 15%, which can improve the aircraft mission load and transonic performance and reduce the control difficulty.

[0004] A method for designing a turbine-based ramjet combination engine is used to design the turbine-based ramjet combination engine disclosed in the above embodiment, such as Figure 2 shown.

[0005] Step 1: Task and requirements analysis.

[0006] Sort out aircraft requirements, clarify the aircraft mission requirements and constraints on power, and integrate the upstream and downstream requirements and constraints of the engine to clarify the input of engine design.

[0007] Step 2: Thermal cycle analysis.

[0008] Taking the turbine engine design point as the target and taking into account typical conditions, the analysis of thermodynamic cycle parameters such as turbine engine compression ratio, turbine pre-turbine temperature, afterburner temperature, etc. is carried out. Factors such as component technology, material process limitations, temperature constraints, cooling type and cooling air volume coefficient need to be considered.

[0009] Taking the design point of the ramjet engine as the target and taking into account the typical conditions, the analysis of thermodynamic cycle parameters such as the total pressure recovery coefficient and flow coefficient of the ramjet engine inlet, the combustion efficiency and outlet temperature of the ramjet combustion chamber, the nozzle thrust coefficient and the expansion ratio is carried out. Factors such as component technology, temperature constraints and the cold air volume coefficient need to be considered.

[0010] Step 3: Calculate design point performance.

[0011] Carry out design point performance calculations for turbine engines and ramjet engines.

[0012] Step 4: Main flow path design.

[0013] Based on the design point performance and parameters of turbine engines and ramjet engines, the main flow paths of turbine engines and ramjet engines are designed.

[0014] Step 5: Calculate the performance under typical conditions.

[0015] Considering the aircraft requirements and the engine's own characteristics, the typical state performance of the turbine engine and the ramjet engine is calculated. If the typical state performance does not meet the aircraft requirements, repeat steps 1 to 5.

[0016] Step 6: Design the combined intake flow split ratio.

[0017] The executable common working range is clearly defined, requiring that the total pressure at the outlet of the inlet high-speed channel Pcy2 is greater than or equal to the static pressure at the outlet of the low-pressure turbine of the main engine of the turbine engine Ps6 or the static pressure at the outlet of the outer duct of the main engine of the turbine engine Ps16.

[0018] According to the aircraft's demand for power, the combined intake flow is distributed based on the performance of the turbine engine and the ramjet engine in the common working range. The split ratio is optimized by combining the performance calculation of the combined power in the common working range to determine the best split ratio of the combined intake flow in the executable common working range.

[0019] Step 7: Calculate the performance of the modal transition point.

[0020] Based on the optimal split ratio of the combined intake flow, the combined power and the performance of each power unit within the executable common working range, the modal transition point is determined according to the inlet duct characteristics, the performance matching of the turbine engine and the ramjet engine in the modal transition range, the characteristics of the mixing flow device, and the afterburner / ramjet combustion chamber characteristics.

[0021] According to the matching of the inlet characteristics, the turbine engine and the ramjet engine characteristics, the modal transition point performance is calculated. If the modal transition point performance does not meet the aircraft requirements, repeat steps 1 to 7.

[0022] Step 8. Determine the design requirements for each component and system.

[0023] According to the performance calculation results of the design points, typical states and modal transition points of turbine engines and ramjet engines, requirements for engine components and systems are proposed.

[0024] Step 9: Determine the overall performance concept plan.

[0025] The overall engine performance concept is formed by taking into account the aircraft mission requirements and constraints on power, the upstream and downstream requirements and constraints of the engine, the design points of the turbine engine and the ramjet engine, the typical state performance, and the modal transition point performance. If the overall engine performance does not meet the design requirements, repeat steps 1 to 9.

[0026] The above embodiments disclose

[0027] The turbine-based ramjet combination engine design method disclosed in the above embodiment is used to design the turbine-based ramjet combination engine disclosed in the above embodiment. The description is relatively simple. For specific related matters, please refer to the relevant description of the turbine-based ramjet combination engine part. Its technical effects can also refer to the technical effects of the relevant parts of the turbine-based ramjet combination engine, which will not be repeated here.

[0028] So far, the technical solution of the present application has been described in conjunction with the preferred embodiments shown in the accompanying drawings. Those skilled in the art should understand that the scope of protection of the present application is obviously not limited to these specific embodiments. Without departing from the principles of the present application, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will fall within the scope of protection of the present application.

Claims

1. A turbo-ramjet engine, characterized in that: It includes parallel combined air intake, mode selection valve, air intake low-speed channel, turbine engine main engine, air intake high-speed channel, mixing flow device, afterburner / ramjet combustion chamber, and nozzle; The inlet of the low-speed channel and the high-speed channel of the intake duct are connected to the outlet of the intake duct in parallel combination, and a mode selection valve is arranged at the inlet of the low-speed channel and the high-speed channel of the intake duct, and the mode selection valve can open or close the inlet of the low-speed channel and the high-speed channel of the intake duct, and adjust the relative opening of the inlet of the low-speed channel and the high-speed channel of the intake duct; The inlet of the turbine engine main engine is connected to the outlet of the low-speed passage of the air inlet, and the low-speed passage of the air inlet, the turbine engine main engine and the high-speed passage of the air inlet are arranged in parallel; The inlet of the mixing flow device is connected to the main engine of the turbine engine and the outlet of the high-speed channel of the air inlet; The inlet of the afterburner / ramjet combustion chamber is connected to the outlet of the mixing flow device; The nozzle is arranged at the outlet of the afterburner / ramjet combustion chamber.

2. The turbo-ramjet combined engine according to claim 1, characterized in that: have: In turbine engine mode, the mode selection valve closes the inlet of the high-speed channel of the inlet; In ramjet mode, the mode selection valve closes the inlet of the low-speed passage of the inlet; In the intermediate conversion mode, the mode selection valve opens the inlet of the low-speed channel and the high-speed channel of the intake duct.

3. The turbo-ramjet combined engine according to claim 1, characterized in that: The nozzle is a single-sided expansion nozzle.

4. The turbo-ramjet combined engine according to claim 1, characterized in that: The high-speed channel of the air intake is circular or elliptical; The flow mixing device comprises an internal high-speed channel and an internal low-speed channel, and the outlets of the internal high-speed channel and the internal low-speed channel are connected inside the flow mixing device and connected to the outlet of the flow mixing device; The internal high-speed channel is an annular channel, and its inlet is connected to the outlet of the high-speed channel of the air inlet through a volute structure, serving as the outer duct inlet of the afterburner / ramjet combustion chamber. The inlet of the internal low-speed channel is connected to the outlet of the turbine engine main engine, and a variable area duct ejector structure is set at the outlet of the internal high-speed channel.

5. A method for designing a turbo-ramjet combination engine, for designing the turbo-ramjet combination engine according to claim 1, characterized in that: include: Step 1: Task and requirements analysis: Sort out aircraft requirements, clarify the aircraft mission requirements and constraints on power, and integrate the upstream and downstream requirements and constraints of the engine to clarify the input of engine design; Step 2: Thermal cycle analysis: Taking the turbine engine design point as the target and taking into account typical conditions, the thermal cycle parameter analysis of the turbine engine is carried out; Taking the design point of the ramjet engine as the target and taking into account the typical state, the thermal cycle parameter analysis of the ramjet engine is carried out; Step 3: Design point performance calculation: Carry out design point performance calculations for turbine engines and ramjet engines; Step 4: Main flow path design: Design the main flow path of turbine engine and ramjet engine based on their design point performance and parameters; Step 5: Typical state performance calculation: Considering the aircraft requirements and the engine's own characteristics, the typical state performance calculation of the turbine engine and the ramjet engine is performed. If the typical state performance does not meet the aircraft requirements, repeat steps 1 to 5; Step 6: Combined intake flow split ratio design: The executable common working range is clarified, requiring that the total pressure at the outlet of the high-speed channel of the inlet duct Pcy2 is greater than or equal to the static pressure at the outlet of the low-pressure turbine of the main engine of the turbine Ps6 or the static pressure at the outlet of the outer duct of the main engine of the turbine Ps16; According to the aircraft's power requirements, based on the performance of turbine engines and ramjet engines in the common working range, the combined intake flow is distributed, and the split ratio is optimized in combination with the performance calculation of the combined power common working range to determine the best split ratio of the combined intake flow in the executable common working range; Step 7: Calculation of modal transition point performance: Based on the optimal split ratio of the combined intake flow rate and the combined power and performance of each power unit within the executable common working range, the mode transition point is determined according to the inlet characteristics, the performance matching of the turbine engine and the ramjet engine within the mode transition range, the mixing device characteristics, and the afterburner / ramjet combustion chamber characteristics; According to the matching of the inlet characteristics, the turbine engine and the ramjet engine characteristics, the modal transition point performance is calculated. If the modal transition point performance does not meet the aircraft requirements, repeat steps 1 to 7; Step 8: Determine the design requirements of each component and system: According to the performance calculation results of turbine engine and ramjet engine design point, typical state and mode transition point, the requirements for engine components and systems are proposed; Step 9: Determine the overall performance concept plan: The overall engine performance concept is formed by taking into account the aircraft mission requirements and constraints on power, the upstream and downstream requirements and constraints of the engine, the design points of the turbine engine and the ramjet engine, the typical state performance, and the modal transition point performance. If the overall engine performance does not meet the design requirements, repeat steps 1 to 9.

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