CN114034489A - Gas turbine engine ground starting acceleration time calculation method - Google Patents
Gas turbine engine ground starting acceleration time calculation method Download PDFInfo
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Abstract
The invention belongs to the technical field of gas turbine engines, and particularly relates to a method for calculating the ground starting acceleration time of a gas turbine engine, which comprises five steps: the ground starting process of the gas turbine engine is divided into three stages; and the ignition speed is given by the designern 1Estimated value of, disengaged speed of rotationn 2Estimated value of (2) and slow speedn id The value of (d); step two: acquiring parameters in a calculation, reference or estimation mode; step three: to ignition rotational speedn 1Balancing the rotation speedn p And disengagement rotational speedn 2Judging the rationality of the operation; step four: respectively calculating torque, resistance torque and torque generated by a turbine of the gas turbine engine acted on by a starter at different rotating speeds in the starting process; step five: and calculating the rotor speed response and the starting time in the starting process. By turning on ignitionThe input estimated parameters such as speed, balance rotating speed, throw-off rotating speed and the like realize rationality judgment, repeated iteration modification of the input parameters can be avoided, and further the calculation efficiency is improved.
Description
Technical Field
The invention belongs to the technical field of gas turbine engines, and particularly relates to a method for calculating the ground starting acceleration time of a gas turbine engine.
Background
A gas turbine engine is a power machine that converts the chemical energy of a fuel into mechanical or kinetic energy. The main working processes of the gas turbine engine are: the air compressor continuously sucks air from the atmosphere and compresses the air; the compressed air enters the combustion chamber, is mixed with fuel sprayed into the combustion chamber and then is combusted, so that high-temperature gas is generated, the high-temperature gas flows into the turbine and the spray pipe to expand and do work, one part of the expansion work generated by the gas is used for driving the compressor to rotate, and the other part of the expansion work is used for outputting outwards, so that power is provided for airplanes, ships, vehicles or generators.
Since the advent of gas turbine engines, gas turbine engines have been widely used in various fields such as energy, aviation, and marine applications due to their advantages of large thrust-to-weight ratio/power-to-weight ratio, quick start, and the ability to use a variety of fuels. The level of gas turbine engine development and manufacture also reflects the level of national science and technology and military strength. The ground starting process is one of the important working processes of the gas turbine engine, and the calculation of the ground starting acceleration time and other related parameters is an essential important link for the design of a starting system.
The process of the gas turbine engine accelerating from zero rotational speed to the slow vehicle rotational speed at ground level is referred to as the ground start process. During the ground starting process of the gas turbine engine, the auxiliary belt rotation acceleration must be carried out by means of an external power source, namely, a starting system is utilized to drive a rotor of the gas turbine engine to rotate. In the design phase of the starting system, the starting time and speed response process of the gas turbine engine must be calculated in order to determine key design parameters such as the power of the starter, the transmission ratio of the transmission mechanism and the like.
At present, the starting time and the rotating speed response process of a turbine in the ground starting process of a gas turbine engine are generally calculated by an approximate method, parameters such as ignition rotating speed, balance rotating speed, disengagement rotating speed, slow turbine torque, transmission ratio and the like need to be estimated or calculated before calculation, and then calculation is carried out based on the parameters, so that the acceleration time of the ground starting is calculated. When a certain parameter is input unreasonably, the estimated values of all the parameters cannot be substituted to obtain a calculation result, at the moment, designers need to try again to modify the estimated parameters, and repeat iteration until the ground starting acceleration time can be calculated, the parameter estimated values are judged by experience, the error rate is high, a large amount of time and experience are wasted, the efficiency is low, and meanwhile, the requirements on the experience and skill of the designers are high.
Disclosure of Invention
The invention provides a method for calculating the ground starting acceleration time of a gas turbine engine, which aims to solve the problems that the calculation result cannot be obtained and the input parameters are repeatedly and iteratively modified due to unreasonable parameter setting in the conventional gas turbine engine ground starting acceleration time calculation technology and realize the rapid calculation of the ground starting acceleration time of the gas turbine engine.
The technical scheme adopted by the invention is as follows:
a gas turbine engine ground start acceleration time calculation method comprising the steps of:
the method comprises the following steps: the ground starting process of the gas turbine engine is divided into three stages; and the ignition speed is given by the designern 1Estimated value of, disengaged speed of rotationn 2Estimated value of (2) and slow speedn id Value of (the slow speed)n id Is a determined value, which varies from gas turbine engine to gas turbine engine); in the first stage, the gas turbine engine is accelerated from zero speed to ignition speedn 1(ii) a Second stage, the gas turbine engine is rotated by ignition speedn 1Accelerating to starter disengaging speedn 2(ii) a In the third stage, the gas turbine engine is started by a starterDisengagement rotational speedn 2Accelerating to slow speedn id ；
Step two: acquiring parameters in a calculation, reference or estimation mode; the parameters include equilibrium rotational speedn p Slow vehicle state turbine torqueM T,id Gas turbine engine rotor mechanical efficiencyη m Gas turbine engine rotor moment of inertiaJStarting system transmission ratioiStarter maximum powerP CT,max And coefficient of starterc；
Step three: based on disengagement speedn 2The principle that the torque generated by the turbine is larger than the resistance torque; to ignition rotational speedn 1Balancing the rotation speedn p And disengagement rotational speedn 2Judging the rationality of the operation;
step four: respectively calculating torque, resistance torque and torque generated by a turbine of the gas turbine engine acted on by a starter at different rotating speeds in the starting process;
step five: and calculating the rotor speed response and the starting time in the starting process by using the torque calculated in the fourth step and the parameters in the first step and the second step.
In addition or as an alternative to the above: in the third stage, the gas turbine engine reaches an equilibrium speedn p While the starter continues to bring the gas turbine engine rotor to a higher disengagement speedn 2Is disengaged, the third stage gas turbine engine rotor is brought together by the starter motor and the turbine of the gas turbine engine itself.
In addition or as an alternative to the above: in the second step, the ignition speedn 1Balancing the rotation speedn p And disengagement rotational speedn 2The three parameters are obtained in a pre-estimation mode, and when the rationality of the three parameters accords with the following formula, the pre-estimation values of the three parameters have the rationality;
in addition or as an alternative to the above: in the fourth step, the torque of the starter acting on the rotor of the gas turbine engine at different rotating speeds is calculated:
output torque of starterM CT And the speed of the startern CT The relationship of (c) is reduced to a linear relationship:
in the formula,M CT,0the torque is the torque of the starter at zero rotating speed;cis a torque constant of the starter, and is related to the type of the starter;
power of starterP CT, And the speed of the startern CT The relationship of (1) is:
according to the formula, the torque and the rotating speed of the starter are in a quadratic convex function relationship, and the maximum power of the starter is obtainedP CT,max ：
The torque of the starter at zero speed can be obtained by the above formulaM CT,0With maximum power of starterP CT,max The relationship of (1) is:
starter maximum power may be determined during an initial design phase of a gas turbine engine starting systemP CT,max And then the torque constant of the starter is determined by the designer according to experiencecThen, can confirm according to the above formulaTorque at zero starter speedM CT，0 (ii) a Therefore, the relation between the rotating speed of the starter and the torque of the starter is obtained, namely the torque characteristic of the starter per se;
the output shaft of the starter is connected with a rotor of the gas turbine engine through a transmission system; gas turbine engine starting system gear ratio ofiNamely, it is considered that: speed of startern CT And gas turbine engine rotor speed driven by starternRatio of (A) to (B) being equal toiThus, the torque characteristics of the starter acting on the gas turbine engine rotor are:
wherein,M CT ’ torque acting on the gas turbine engine rotor for the starter.
In addition or as an alternative to the above: in the fourth step, the resistance torque under different rotating speeds is calculated:
introducing gas turbine engine rotor mechanical efficiencyη m To calculate the drag torque during the rotor start-upM Z ：
Wherein,M C the torque required to drive the compressor in rotation,M acc to burn the drag torque of the oil accessory system,M m in order to mechanically resist the frictional resistance torque,η m mechanical efficiency for gas turbine engine rotors;
taking the slow-speed vehicle state as a reference state, calculating resistance torques of different rotating speeds in the starting process, and calculating the resistance torque according to the turbine torque in the slow-speed vehicle stateM T,id And resistance torqueM Z The principle that the resistance torque of equal and different rotating speeds is in direct proportion to the square of the rotating speed is adopted, and the slow vehicle is calculated by the following formulaFollowing rotational speednResistance torque ofM Z ：
Wherein:
wherein,M C,id for driving the compressor at slow speedn id The torque required for rotation.
In addition or as an alternative to the above: in the fourth step, when the torque generated by the turbine in each stage is calculated and the first stage combustion chamber is not ignited, the torque generated by the turbine is 0.
In addition or as an alternative to the above: in the fourth step, when the torque generated by the turbine in each stage is calculated, in the second stage of the starting process, the total temperature of the turbine inlet is kept at the maximum value, namely, the total temperature does not change greatly, the torque generated by the turbine can be considered to change linearly along with the rotating speed, and different rotating speeds are calculated according to the following formulanTorque generated by the lower turbineM T ：
Balance the rotational speedn p The torque generated by the turbine just drives the rotor to rotate, and at the momentM T = M Z Combined with ignition rotational speedn 1Time of flightM T = 0, constant in the above formulac 1Andc 2comprises the following steps:
in addition or as an alternative to the above: in the fourth step, when the torque generated by the turbine in each stage is calculated, in the third stage of the starting process, the total temperature change of the turbine inlet is larger than that in the second stage, but the relation between the torque generated by the turbine and the rotating speed is still approximate to a linear relation by the conventional method, so that errors are brought to the calculation result; torque to be generated by the turbineM T The change along with the rotating speed is simplified into a quadratic polynomial relationship, and different rotating speeds are calculated according to the following formulanTorque of turbineM T ：
When in usen = n 2 When the temperature of the water is higher than the set temperature,
and the derivatives on the left and right sides are equal; and whenn = n id When the temperature of the water is higher than the set temperature,M T = M Z constant in the above formulac 3、c 4Andc 5comprises the following steps:
or:
in addition or as an alternative to the above: constant numberc 1、c 2、c 3、c 4Andc 5byaValue, ignition speedn 1Balancing the rotation speedn p And disengagement rotational speedn 2And slow vehicle speedn id Determining; wherein,athe value being the speed of rotation of the gas turbine engine in a slow-running staten id And turbine torqueM T,id Calculated to obtain the ignition rotating speedn 1And disengagement rotational speedn 2The rotational speed is directly selected and balanced by the designern 2It is determined empirically by the designer; at the ignition rotation speedn 1And disengagement rotational speedn 2 Under certain conditions, different balance rotating speed values can influence the relation between the torque and the rotating speed generated by the turbine in the second stage and the third stage in the starting process; if the input ignition rotating speed, the balance rotating speed and the disengagement rotating speed are unreasonable, in the third stage of the acceleration process, the torque generated by the turbine is smaller than the resistance torque, the rotor cannot be accelerated continuously, and the corresponding starting process calculation cannot be continued, namely the calculation result cannot be obtained; thus, when the rotor accelerates to the disengagement speedn 2The torque generated by the turbine should be greater than the drag torque:
namely:
will be constantc 1Andc 2substituting the formula:
due to the fact thata>0, further development ofThe method is simple and available:
due to the fact thatn p <n 2 Thus:
namely:
therefore, the ignition speedn 1Balancing the rotation speedn p And disengagement rotational speedn 2The rationality of these three parameters is judged by the above formula.
In addition or as an alternative to the above: step five, calculating and obtaining the rotor acceleration at any time in the starting process of the gas turbine engine
：
Wherein,Jrotational inertia of a gas turbine engine rotor; and calculating according to the formula by a time advancing mode to obtain the rotating speed response of the gas turbine engine in the starting and accelerating process, and further obtaining the starting and accelerating time.
The invention has the beneficial effects that: in the existing method for calculating the acceleration time of the ground starting process of the gas turbine engine, a plurality of parameters such as ignition rotating speed, balance rotating speed, disengagement rotating speed, slow vehicle starting resistance torque, transmission ratio and the like need to be set or estimated, and then calculation is carried out; some artificially estimated parameters cannot judge the estimated reasonability, and when a certain parameter is unreasonably set, a calculation result cannot be obtained, so that designers need to try again to modify the input parameters and iterate repeatedly, and the working efficiency is seriously influenced; according to the scheme of the invention, the reasonability judgment of the estimated parameters such as the ignition rotating speed, the balance rotating speed, the disengagement rotating speed and the like is realized, the accuracy of the estimated parameters is improved, and the calculation efficiency is further improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below.
FIG. 1 is a flow chart of a gas turbine engine ground start acceleration time calculation evaluation;
FIG. 2 is a schematic illustration of a process torque at ground level of a gas turbine engine as a function of rotational speed;
FIG. 3 is a calculated torque characteristic of a starter acting on a gas turbine engine rotor, a drag torque characteristic, and a turbine generated torque characteristic;
FIG. 4 is a calculated rotor speed response for starting from zero speed to creep speed;
fig. 5 shows the characteristics of the torque resistance and the torque generated by the turbine at the same ignition rotational speed and the same disengagement rotational speed, respectively, and at different equilibrium rotational speeds.
Detailed Description
The technical solutions in the embodiments will be described clearly and completely with reference to the accompanying drawings, and the described embodiments are only a part of the embodiments, but not all embodiments, and all other embodiments obtained by those skilled in the art without creative efforts will belong to the protection scope of the present solution based on the embodiments in the present solution.
Example 1
As shown in fig. 1, the present embodiment designs a method for calculating a ground start acceleration time of a gas turbine engine, including the following steps:
the method comprises the following steps: as shown in FIG. 2, the process of ground starting a gas turbine engine is divided into three phases and the ignition speed is given by the designern 1And is disengaged from the rotary shaftSpeed measuring devicen 2Estimated value of (2) and slow speedn id The value of (d); in the first stage, the gas turbine engine is accelerated from zero speed to ignition speedn 1(ii) a Second stage, the gas turbine engine is rotated by ignition speedn 1Accelerating to starter disengaging speedn 2(ii) a Third stage, the gas turbine engine is de-rotated by a startern 2Accelerating to slow speedn id ；
Step two: acquiring parameters in a calculation, reference or estimation mode; the parameters include equilibrium rotational speedn p Slow vehicle state turbine torqueM T,id Gas turbine engine rotor mechanical efficiencyη m Gas turbine engine rotor moment of inertiaJStarting system transmission ratioiStarter maximum powerP CT,max And a torque constant of the starterc；
Step three: based on disengagement speedn 2The principle that the torque generated by the turbine is greater than the drag torque of the gas turbine engine rotor; to ignition rotational speedn 1Balancing the rotation speedn p And disengagement rotational speedn 2Judging the rationality of the three parameters, and acquiring the three parameters in an estimation mode; in the third stage, the equilibrium rotation speed is reachedn p While the starter continues to bring the gas turbine engine rotor to a higher disengagement speedn 2Only disengaged, the third stage gas turbine engine rotor is jointly rotated by the starter and the turbine of the gas turbine engine;
based on disengagement speedn 2The ignition speed based on the principle that the torque generated by the turbine is greater than the resistance torquen 1Balancing the rotation speedn p And disengagement rotational speedn 2When the parameters are reasonably set, the following formula should be met:
in the formula：n 1Is the ignition rotating speed,n p For balancing the rotating speed,n 2For disengaging the rotational speed;
step four: respectively calculating torque, resistance torque and torque generated by a turbine of the gas turbine engine acted on by the starters at different rotating speeds in the starting process;
step five: and calculating the rotor speed response and the starting time in the starting process by using the torque calculated in the fourth step and the calculation parameters in the first step and the second step.
In the scheme, the designer can adjust the ignition rotating speedn 1Balancing the rotation speedn p And disengagement rotational speedn 2Slow speed of vehiclen id Slow vehicle state turbine torqueM T,id Gas turbine engine rotor mechanical efficiencyη m Gas turbine engine rotor moment of inertiaJStarting system transmission ratioiStarter maximum powerP CT,max And a torque constant of the startercAfter the parameters are set and input, the set ignition speed is setn 1Balancing the rotation speedn p And disengagement rotational speedn 2The three parameters are subjected to rationality judgment, so that the set parameters do not need to be checked back after the rotating speed response time and the starting time cannot be calculated, and the calculation efficiency can be effectively saved. In addition, the software system capable of implementing the above steps can be performed along the flow shown in fig. 1, and the rationality of parameter setting can be judged without the final result of calculating the rotational speed response and the starting time, so that the time can be saved and the efficiency can be improved.
Example 2
In the step flow of embodiment 1, in step four, the torque acting on the rotor of the gas turbine engine by the starter at different rotation speeds, the drag torque, and the torque generated by the turbine are calculated.
Wherein the torque acting on the gas turbine engine rotor by the starter at different rotational speeds is calculated:
output torque of starterM CT And the speed of the startern CT The relationship of (c) is reduced to a linear relationship:
in the formula,M CT outputting torque for a starter;M CT,0the torque is the torque of the starter at zero rotating speed;cthe torque constant of the starter is related to the type of the starter.
Power of starterP CT And the speed of the startern CT The relationship of (1) is:
in the formula:P CT power for a starter;M CT outputting torque for a starter;n CT the rotating speed of the starter;M CT,0the torque is the torque of the starter at zero rotating speed;cis a torque constant of the starter, and is related to the type of the starter;
according to the formula, the torque and the rotating speed of the starter are in a quadratic convex function relationship, and the maximum power of the starter is obtainedP CT,max ：
In the formula:P CT,m the maximum power of the starter;M CT,0the torque is the torque of the starter at zero rotating speed;cis a torque constant of the starter, and is related to the type of the starter;
the torque of the starter at zero speed can be obtained by the above formulaM CT,0With maximum power of starterP CT,max The relationship of (1) is:
in the formula:P CT,max the maximum power of the starter;M CT,0the torque is the torque of the starter at zero rotating speed;cthe torque constant of the starter is related to the type of the starter.
Starter maximum power may be determined during an initial design phase of a gas turbine engine starting systemP CT,max And then the torque constant of the starter is determined by the designer according to experiencecThe torque at zero starter speed can then be determined according to the above equationM CT,0(ii) a Therefore, the relation between the torque of the starter and the rotating speed of the starter is obtained, namely the torque characteristic of the starter per se;
the output shaft of the starter is connected with a gas turbine engine rotor through a transmission system; gas turbine engine starting system gear ratioiNamely, it is considered that: speed of startern CT And gas turbine engine rotor speed driven by starternRatio of (A) to (B) being equal toiThus, the torque characteristics of the starter acting on the gas turbine engine rotor are:
in the formula:M CT ’ torque acting on the gas turbine engine rotor for the starter;M CT,0the torque is the torque of the starter at zero rotating speed;cis a torque constant of the starter, and is related to the type of the starter;ito start the system gear ratio;nis the gas turbine engine speed.
Calculating resistance torque at different rotating speeds:
introducing gas turbine engine rotor mechanical efficiencyη m To calculate the drag torque of the starting processM Z ：
In the formula,M C torque required to drive the compressor to rotate;M acc is the fuel accessory system resistance torque;M m in order to mechanically resist the frictional resistance torque,η m mechanical efficiency for gas turbine engine rotors;M Z is the drag torque of the starting process.
Taking the slow-speed vehicle state as a reference state, calculating resistance torques of different rotating speeds in the starting process, and calculating the resistance torques according to the rotating speed of the slow-speed vehiclen id Torque of the turbineM T,id And resistance torqueM Z The principle that the resistance torque of equal and different rotating speeds is in direct proportion to the square of the rotating speed is adopted, and the following formula is utilized to calculate the rotating speed below slow speednResistance torque ofM Z ：
In the formula:M Z resistance torque for the rotor starting process;M C,id for driving the compressor at slow speedn id Torque required for rotation;η m mechanical efficiency for gas turbine engine rotors;ngas turbine engine rotor speed;n id the slow vehicle rotating speed;M T,id at a slow speedn id Lower turbine torque;athe ratio of the square of the slow vehicle state turbine torque and the slow vehicle rotating speed;
wherein:
in the formula:athe ratio of the square of the slow vehicle state turbine torque and the slow vehicle rotating speed;M T,id at a slow speedn id Lower turbine torque;n id the slow vehicle speed.
Then there are:
in the formula:M Z resistance torque for the rotor starting process;athe ratio of the square of the slow vehicle state turbine torque and the slow vehicle rotating speed;ngas turbine engine rotor speed.
Calculation of the torque produced by the turbine during the various starting phases:
in the first stage, when the combustion chamber is not ignited, the torque generated by the turbine is 0.
In the second stage, the total temperature of the turbine inlet is kept at the maximum value, namely the total temperature is not changed greatly, the torque generated by the turbine can be considered to be changed linearly along with the rotating speed, and different rotating speeds are calculated according to the following formulanTorque generated by the lower turbineM T ：
In the formula:M T torque generated for the turbine;ngas turbine engine rotor speed;c 1andc 2the different constants are determined by ignition speed, balance speed, slow speed and turbine torque calculation of slow state.
Balance the rotational speedn p The torque generated by the turbine just drives the rotor to rotate, and at the momentM T = M Z Combined with ignition rotational speedn 1Time of flightM T = 0Constant in the above formulac 1Andc 2calculated according to the following formula:
in the formula:c 1andc 2the constant values are different constants and are determined by the ignition rotating speed, the balance rotating speed, the slow vehicle rotating speed and the turbine torque calculation of the slow vehicle state;athe ratio of the square of the slow vehicle state turbine torque and the slow vehicle rotating speed;n 1is the ignition rotational speed;n p to balance the rotational speed.
In the third stage, the total temperature change of the turbine inlet is larger than that in the second stage, but the relation between the torque and the rotating speed generated by the turbine is still approximate to a linear relation by the conventional method, so that errors are brought to the calculation result; torque to be generated by the turbineM T The change along with the rotating speed is simplified into a quadratic polynomial relationship, and different rotating speeds are calculated according to the following formulanTorque of turbineM T ：
In the formula:c 3、c 4andc 5the constant values are different constants and are determined by the ignition rotating speed, the balance rotating speed, the disengagement rotating speed, the slow vehicle rotating speed and the turbine torque calculation of the slow vehicle state;M T is the turbine torque;nis the rotor speed.
When in usen = n 2 When the temperature of the water is higher than the set temperature,
and the derivatives on the left and right sides are equal; and whenn = n id When the temperature of the water is higher than the set temperature,M T = M Z constant in the above formulac 3、c 4Andc 5calculated according to the following formula:
or:
in the formula:c 1、c 2、c 3、c 4andc 5the constants are respectively different constants and are determined by the ignition rotating speed, the balance rotating speed, the disengagement rotating speed, the slow running rotating speed and the turbine torque calculation of the slow running state;athe ratio of the square of the slow vehicle state turbine torque and the slow vehicle rotating speed;n id the slow vehicle rotating speed;n 2to disengage the rotational speed.
The results of the calculation of the torque characteristics on the engine rotor, the drag torque characteristics, and the torque characteristics generated by the turbine are shown in fig. 3.
Step five, calculating and obtaining the rotor acceleration at any time in the starting process of the gas turbine engine
：
In the formula:
is the rotor acceleration;M CT ’ torque acting on the gas turbine engine rotor for the starter;M T torque generated for the turbine;M Z resistance torque for the rotor starting process;Jfor gas turbine engine rotor moment of inertia。
The rotational speed response of the gas turbine engine during the starting acceleration process is calculated according to the above formula by the time advancing method, and further the starting acceleration time is obtained, and the result is shown in fig. 4.
Example 3
To further illustrate the ignition speed described in step three of example 1n 1Balancing the rotation speedn p And disengagement rotational speedn 2The parameters conform to a calculation formula; this example, in conjunction with the calculation conclusions in example 2, makes the following deductions:
constants in example 2c 1Andc 2byaValue, ignition speedn 1Balancing the rotation speedn p And disengagement rotational speedn 2Determining; wherein,athe value is determined by the turbine torque of the gas turbine engine slow running and the slow running rotating speed, and the ignition rotating speed and the disengagement rotating speed are directly selected by a designer; the firing speed and the trip speed are determined primarily by the starting specifications and the characteristics of the gas turbine engine itself. The ignition rotating speed is selected according to the test result of the combustion chamber part and the reference of other thrust or power and the engine with equivalent flow, and the ignition rotating speed is 10-20% of the highest rotating speed; the disengagement speed is selected according to starting technical requirements, starter power and engine drag torque characteristics, and is 50% -60% of the maximum disengagement speed. The balance rotating speed is determined by designers according to experience; as shown in fig. 5, at the ignition rotation speedn 1And disengagement rotational speedn p Under certain conditions, different balance rotating speed values can influence the relation between the torque and the rotating speed generated by the turbine in the second stage and the third stage in the starting process; if the input ignition rotating speed, the balance rotating speed and the disengagement rotating speed are unreasonable, in the third stage of the acceleration process, the torque generated by the turbine is smaller than the resistance torque, the rotor cannot be accelerated continuously, and the corresponding starting process calculation cannot be continued, namely the calculation result cannot be obtained; thus, when the rotor accelerates to the disengagement speedn 2The torque generated by the turbine should be greater than the drag torque:
namely:
will be constantc 1Andc 2substituting the formula:
due to the fact thata>0, further simplified to obtain:
due to the fact thatn p <n 2Thus:
namely:
in the formula:
torque generated by the turbine when the starter is disengaged;
the resistance torque of the rotor when the starter is disengaged;n 1is the ignition rotational speed;n p to balance the rotational speed;n 2for disengaging the rotational speed;ais the ratio of the turbine torque in the slow state to the square of the slow speed.
Therefore, the ignition speedn 1Balancing the rotation speedn p And disengagement rotational speedn 2The rationality of these three parameters is judged by whether the above formula is satisfied.
The above examples are merely for clearly illustrating the examples and are not intended to limit the embodiments; and are neither required nor exhaustive of all embodiments. And obvious variations or modifications of this technology may be resorted to while remaining within the scope of the technology.
Claims (10)
1. A method for calculating the ground start acceleration time of a gas turbine engine, characterized by: the method comprises the following steps:
the method comprises the following steps: the ground starting process of the gas turbine engine is divided into three stages; and the ignition speed is given by the designern 1Estimated value of, disengaged speed of rotationn 2Estimated value of (2) and slow speedn id The value of (d); in the first stage, the gas turbine engine is accelerated from zero speed to ignition speedn 1(ii) a Second stage, the gas turbine engine is rotated by ignition speedn 1Accelerating to starter disengaging speedn 2(ii) a In the third stage, the gas turbine engine is de-rotated by the startern 2Accelerating to slow speedn id ；
Step two: acquiring parameters in a calculation, reference or estimation mode; the parameters include equilibrium rotational speedn p Slow vehicle state turbine torqueM T,id Gas turbine engine rotor mechanical efficiencyη m Gas turbine engine rotor moment of inertiaJStarting system transmission ratioiStarter maximum powerP CT,max And coefficient of starterc；
Step three: based on disengagement speedn 2The principle that the torque generated by the turbine is larger than the resistance torque; to ignition rotational speedn 1Balancing the rotation speedn p And disengagement rotational speedn 2Judging the rationality of the operation;
step four: respectively calculating torque, resistance torque and torque generated by a turbine of the gas turbine engine acted on by a starter at different rotating speeds in the starting process;
step five: and calculating the rotor speed response and the starting time in the starting process by using the torque calculated in the fourth step and the parameters in the first step and the second step.
2. The gas turbine engine ground start acceleration time calculation method of claim 1, characterized in that: in the third stage, the gas turbine engine reaches an equilibrium speedn p While the starter continues to bring the gas turbine engine rotor to a higher disengagement speedn 2Is disengaged, the third stage gas turbine engine rotor is brought together by the starter motor and the turbine of the gas turbine engine itself.
3. The gas turbine engine ground start acceleration time calculation method of claim 1, characterized in that: in the second step, the ignition speedn 1Balancing the rotation speedn p And disengagement rotational speedn 2The three parameters are obtained in a pre-estimation mode, and when the rationality of the three parameters accords with the following formula, the pre-estimation values of the three parameters have the rationality;
4. the gas turbine engine ground start acceleration time calculation method of claim 1, characterized in that: in the fourth step, the torque of the starter acting on the rotor of the gas turbine engine at different rotating speeds is calculated:
output torque of starterM CT And the speed of the startern CT The relationship of (c) is reduced to a linear relationship:
in the formula:M CT,0the torque is the torque of the starter at zero rotating speed;cis a torque constant of the starter, and is related to the type of the starter;
power of starterP CT And the speed of the startern CT The relationship of (1) is:
according to the formula, the torque and the rotating speed of the starter are in a quadratic convex function relationship, and the maximum power of the starter is obtainedP CT,max ：
The torque of the starter at zero speed can be obtained by the above formulaM CT,0With maximum power of starterP CT,max The relationship of (1) is:
starter maximum power may be determined during an initial design phase of a gas turbine engine starting systemP CT,max And then the torque constant of the starter is determined by the designer according to experiencecThe torque at zero starter speed can then be determined according to the above equationM CT,0(ii) a Therefore, the relation between the rotating speed of the starter and the torque of the starter is obtained, namely the torque characteristic of the starter per se;
the output shaft of the starter is connected with a rotor of the gas turbine engine through a transmission system; gas turbine engine starting system gear ratio ofiNamely, it is considered that: speed of startern CT And gas turbine engine rotor speed driven by starternRatio of (A) to (B) being equal toiThus, the torque characteristics of the starter acting on the gas turbine engine rotor are:
in the formula:M CT ’ torque acting on the gas turbine engine rotor for the starter.
5. The gas turbine engine ground start acceleration time calculation method of claim 4, characterized in that: in the fourth step, the resistance torque under different rotating speeds is calculated:
introducing gas turbine engine rotor mechanical efficiencyη m To calculate the drag torque during the rotor start-upM Z ：
Wherein,M C the torque required to drive the compressor in rotation,M acc to burn the drag torque of the oil accessory system,M m in order to mechanically resist the frictional resistance torque,η m mechanical efficiency for gas turbine engine rotors;
taking the slow-speed vehicle state as a reference state, calculating resistance torques of different rotating speeds in the starting process, and calculating the resistance torque according to the turbine torque in the slow-speed vehicle stateM T,id And resistance torqueM Z The principle that the resistance torque of equal and different rotating speeds is in direct proportion to the square of the rotating speed is adopted, and the rotating speed below slow speed is calculated by using the following formulanResistance torque ofM Z ：
Wherein:
in the formula:M C,id for driving the compressor at slow speedn id The torque required for rotation.
6. The gas turbine engine ground start acceleration time calculation method of claim 5, characterized in that: in the fourth step, when the torque generated by the turbine in each stage is calculated and the first stage combustion chamber is not ignited, the torque generated by the turbine is 0.
7. The gas turbine engine ground start acceleration time calculation method of claim 6, characterized in that:
in the fourth step, when the torque generated by the turbine in each stage is calculated, in the second stage of the starting process, the total temperature of the turbine inlet is kept at the maximum value, namely, the total temperature does not change greatly, the torque generated by the turbine can be considered to change linearly along with the rotating speed, and different rotating speeds are calculated according to the following formulanTorque generated by the lower turbineM T ：
Balance the rotational speedn p The torque generated by the turbine just drives the rotor to rotate, and at the momentM T = M Z Combined with ignition rotational speedn 1Time of flightM T = 0, constant in the above formulac 1Andc 2comprises the following steps:
8. the gas turbine engine ground start acceleration time calculation method of claim 7, characterized in that: in the fourth step, when the torque generated by the turbine in each stage is calculated, in the third stage of the starting process, the torque generated by the turbine is calculatedM T The change along with the rotating speed is simplified into a quadratic polynomial relationship, and different rotating speeds are calculated according to the following formulanTorque of turbineM T ：
When in usen = n 2 When the temperature of the water is higher than the set temperature,
and the derivatives on the left and right sides are equal; and whenn = n id When the temperature of the water is higher than the set temperature,M T = M Z constant in the above formulac 3、c 4Andc 5comprises the following steps:
or:
9. the gas turbine engine ground start acceleration time calculation method of claim 8, characterized in that: constant numberc 1、c 2、c 3、c 4Andc 5byaValue, ignition speedn 1Balancing the rotation speedn p And disengagement rotational speedn 2And slow vehicle speedn id Determining; wherein,athe value being the speed of rotation of the gas turbine engine in a slow-running staten id And turbine torqueM T,id Calculated to obtain the ignition rotating speedn 1And disengagement rotational speedn 2The rotational speed is directly selected and balanced by the designern 2It is determined empirically by the designer; at the ignition rotation speedn 1And disengagement rotational speedn 2 Under certain conditions, different equilibrium rotational speedsn p Will have an effect on the relationship between the torque and speed generated by the turbine during the second and third stages of the starting process; if the input ignition rotating speed, the balance rotating speed and the disengagement rotating speed are unreasonable, in the third stage of the acceleration process, the torque generated by the turbine is smaller than the resistance torque, the rotor cannot be accelerated continuously, and the corresponding starting process calculation cannot be continued, namely the calculation result cannot be obtained; thus, when the rotor accelerates to the disengagement speedn 2The torque generated by the turbine should be greater than the drag torque:
namely:
will be constantc 1Andc 2substituting the formula:
due to the fact thata>0, further simplified to obtain:
due to the fact thatn p <n 2 Thus:
namely:
therefore, the ignition speedn 1Balancing the rotation speedn p And disengagement rotational speedn 2The rationality of these three parameters is judged by the above formula.
10. The gas turbine engine ground start acceleration time calculation method of claim 8, characterized in that: step five, calculating and obtaining the rotor acceleration at any time in the starting process of the gas turbine engine
：
Wherein,Jrotational inertia of a gas turbine engine rotor; and calculating according to the formula by a time advancing mode to obtain the rotating speed response of the gas turbine engine in the starting and accelerating process, and further obtaining the starting and accelerating time.
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