3241results about "Gas-turbine engine testing" patented technology

The present invention discloses an aero engine bearing fault diagnosis method based on STFT-IncepNext, which includes the following steps: step 1: collect acceleration signals under various working conditions and fault conditions of the bearing as sample data; step 2: determine the number of sampling points of each sensor first, and perform data merging by permuting and combining data collected by sensors at different positions in the same time series, and then use short-time Fourier transform to convert the fused vibration signal into a time-frequency diagram; step 3: data preprocessing: divide into training set, test set and validation set according to fault type, and normalize the converted time-frequency diagram using average value and standard difference; step 4: build an IncepNext model, train and validate it; and step 5: use the trained IncepNext model to diagnose aero engine bearing faults and obtain a diagnosis result. The present invention can effectively identify aero engine bearing faults, can guarantee the fault identification rate, and has good accuracy.

The invention provides an equipment supervision data real-time analysis method and system, and the method comprises the steps: calculating an energy value of a frequency band corresponding to a sub-band signal, determining the energy characteristics of the surface roughness and dust deposition distribution uniformity of a blade in each sub-band in a square sum form, and generating energy distribution vectors which are arranged according to a frequency band sequence; performing time-frequency analysis on the vibration signal by using the acquired real-time rotating speed information of the gas turbine, identifying a frequency component corresponding to the eccentric distance value of the rotor and the vibration frequency offset, and determining the amplitude of the frequency component; according to the classification result and the real-time rotating speed information, the comprehensive influence index of the material density change rate and the ash deposition layer thickness difference is calculated, the fault early warning level is determined through a weighted average method, and an early warning signal is generated; and according to the change trend of the early warning signal and the blade edge wear degree, a random forest algorithm is adopted to predict a development curve of the vibration frequency offset in the future target time, and real-time equipment supervision analysis data are obtained.

An engine for aeromechanical instability abatement includes a sensor configured to capture data from rotating blades of the engine system, a airflow effector device, and an engine controller. The engine controller is configured to control the airflow effector device according to a nominal schedule, detect, based on a signal from the sensor indicating a vibration amplitude of the rotating blades within a frequency band, an incipient instability condition, in response to the incipient instability condition being present, determine a modified control parameter for at least one of the airflow effector device, and control the airflow effector device according to the modified control parameter, deviating from the nominal schedule.

The invention provides an aero-engine state monitoring method and device based on sound and vibration fusion and a computer readable storage medium, and relates to the technical field of aero-engine state monitoring. The method comprises the following steps: acquiring signals respectively acquired by a vibration sensor and a sound sensor; respectively intercepting a vibration signal low-frequency component and a sound signal high-frequency component based on the frequency response characteristic difference of the sensor; performing normalization processing on the intercepted signal to eliminate amplitude difference; constructing a transition region through an interpolation method, and splicing the continuous mixed frequency spectrum to obtain a sound-vibration fusion spectrum; and establishing a health benchmark based on the normal state fusion spectrum, and realizing abnormity monitoring and alarm through characteristic difference analysis. Advantages and characteristics of a low-frequency band of the vibration sensor and a high-frequency band of the sound sensor are fully utilized, frequency response limitation of a traditional single sensor is broken through, deep fusion of sound and vibration signals is achieved, the effective detection frequency range is remarkably widened, and accuracy and robustness of recognition of early faults such as aero-engine blade breakage are improved.

The invention discloses an instantaneous torque testing method of an aero-engine and a related system. The method comprises the following steps: dividing an engine shafting into three temperature zones, and applying acoustic excitation signals with different frequencies to obtain acoustic response signals; determining an operation phase point according to the rotating speed change rate to collect a torque response signal; acquiring inter-axis crosstalk signals to extract a response time difference and an amplitude ratio; collecting pressure field information and extracting spatial distribution and time domain evolution data; an instantaneous torque value is calculated from the signals and data. According to the technical scheme, the problem of torque signal transmission distortion caused by heterogeneous material interface stress wave reflection can be effectively solved, and the accuracy of instantaneous torque measurement is improved.

The invention discloses a physical information fused aero-engine residual life prediction method, and belongs to the field of neural network residual life prediction. The method comprises the following steps: acquiring sensor data of the whole process from engine simulation operation to fault, and performing standardization and windowing preprocessing; establishing a time-space dual-channel multi-layer perceptron model, extracting time dimension and feature dimension information of the signal, performing self-attention fusion with original data, completing mapping to a life prediction value, and calculating an error with a real life; establishing a physical information neural network model, learning a hidden partial differential equation among a predicted life value, time and a hidden state, and performing error calculation with an equation in an equilibrium state; and performing self-attention fusion with the life error to obtain comprehensive loss so as to continuously train the model until the error is minimum, and finishing final life prediction. Physical information is fused on the basis of the multi-layer perceptron, the complexity of the model is simplified, and the prediction precision of the residual life of the engine is improved.

The invention relates to a real-time monitoring method for asynchronous vibration stress of a blade based on a blade tip timing principle, which comprises the following steps of: obtaining at least six-order modal shape of the blade under the action of prestress by using finite element analysis, and then obtaining the actual vibration displacement of the blade to at least one blade tip timing probe by using a blade tip timing system; the change relation of the actual vibration displacement of the blade tip along with time is obtained, the actual vibration frequency of the blade, the actual vibration amplitude of the blade and the actual vibration pitch diameter of the blade corresponding to the actual vibration displacement of the blade tip are calculated, the actual modal shape of the blade is determined, and then the modal shape corresponding to the actual modal shape is used; and the maximum stress value and the position of the maximum stress under the asynchronous vibration condition of the blade are determined. According to the invention, the real-time monitoring of the vibration frequency, the vibration amplitude and the circumferential pitch diameter number of the blade can be realized, and the method is of great significance to the health early warning of the engine blade, the research of a fluid-solid coupling mechanism and the research of a vibration suppression method.

The invention relates to the technical field of combustion monitoring, and discloses a combustion instability boundary prediction system based on complex environment condition analysis, and the system comprises a multi-source sensing module, a data fusion module, an anti-interference processing module, an instability feature library, an intelligent decision engine and a digital twinborn body. A dynamic environment interference compensation mechanism is constructed, spectrum correction parameters are configured according to different environment working conditions during real-time prediction of a combustion instability boundary, the problem of spectrum distortion caused by environment disturbance on combustion dynamic parameters is eliminated in real time, spectrum interference deviation of a combustion measurement position can be automatically sensed and corrected, and real-time prediction of the combustion instability boundary is realized. The accuracy of combustion instability sensitive feature extraction is guaranteed, the instability early warning error is reduced, a flame pose real-time tracking system is deployed, fuel control parameter self-adaptive adjustment is triggered immediately when it is detected that the pose is abnormal, autonomous correction of the combustion instability feature recognition position is achieved, and it is guaranteed that the feature capture space is accurately positioned.

The invention discloses an aero-engine hybrid power test control system, and the system comprises a rapid switching device which is in circuit connection with an engine, a generator, a rectifier, and each load system. The emergency protection load system is in circuit connection with the rapid switching device; the first test system and the second test system are respectively used for collecting and storing state parameters of an engine and state data of a generator, a rectifier and each load system and transmitting the data to the electrical control system; the filter is used for suppressing electromagnetic interference; the control system is in circuit connection with the engine EEC and the electrical control system; the electrical control system is respectively in circuit connection with the EEC, the control system, the auxiliary equipment, the quick switching device, each load system and the like; according to the PROFINET system network, a PROFINET protocol is adopted to carry out rapid data exchange. According to the invention, systematic design is adopted, the defect of independent design is avoided, the test control reliability can be realized, and the test safety risk can be greatly reduced.

The invention provides an aero-engine small sample fault diagnosis method for agency attention enhancement diffusion, and belongs to the technical field of aero-engine gas circuit fault diagnosis. According to the method, the proxy attention is added on the basis of the DDIM, so that the sample generation can be accelerated, the sample generation quality is obviously improved, and no extra training is needed. Inputting a small amount of pre-processed collected sensor signal data into the agent attention enhanced denoising diffusion implicit model for data enhancement to generate high-quality sample data so as to make up for the deficiency of an original data set and improve the performance of the model under the condition of scarce data; the expanded data set is used as a training set, the original data set is used as a test set for model training, the test set is used for testing the performance and accuracy of the model after training is completed, and a final aero-engine fault diagnosis model is established. According to the method, the problem of insufficient data in fault diagnosis is solved, and the accuracy and robustness of the model are improved.

The invention discloses a gas turbine high-temperature component fault early warning method, which comprises the following steps: S1, constructing and training to obtain an early warning model of a gas turbine high-temperature component for monitoring the performance change trend of the gas turbine high-temperature component; and S2, predicting the time series data of the real gas turbine parameters at the current moment by using the early warning model, and then judging the abnormal condition of the high-temperature part of the gas turbine by comparing the residual quantity of a predicted value and an actual value and using a preset threshold value. According to the method, normal data and abnormal data can be effectively distinguished, the sensitivity of early warning of faults of the high-temperature parts is improved, the dynamic threshold judgment technology based on the sliding time window is added in the prediction and use process of the early warning model, the method can well adapt to dynamic changes of the data, dependence on historical data is reduced, and the prediction efficiency of the early warning model is improved. Compared with a traditional Gaussian hypothesis method, errors are not required to obey specific distribution, and the robustness of the model in the real-time operation process is also improved.

A method for monitoring a rotating machine in order to detect a fault in a bearing, the method including acquiring, from the rotating machine, a vibration signal measured by a vibration sensor; determining a first-order spectrogram by first-order cyclostationary analysis of the vibration signal using a delta transform and spectral standardisation; determining a second-order spectrogram by second-order cyclostationary analysis of the vibration signal using averaged cyclic coherence, a delta transform and spectral standardisation; and detecting a vibration signature of the fault in the bearing on the basis of the first-order spectrogram and the second-order spectrogram.

The invention provides a same-side input double-shaft compressor tester rotor concentricity reserving method, which belongs to aero-engine tests and comprises the following steps: determining thermal expansion displacement of an exhaust passage and a gear box support structure in a same-side input double-shaft compressor tester, according to the thermal expansion displacement and the axial distance, the thermal expansion displacement of the input flange of the biaxial compressor test piece and the thermal expansion displacement of the output flange of the gearbox are obtained through calculation, and then the estimated cold and hot state concentricity variation is obtained; according to the estimated cold and hot state concentricity variable quantity, the estimated cold state concentricity is calculated by taking the hot state concentricity as zero, and the rotor of the double-shaft compressor tester is arranged according to the estimated cold state concentricity; vibration measuring points and bearing temperature measuring points are arranged for testing, the operation state of the double-shaft compressor tester is judged through the vibration measuring points and the bearing temperature measuring points, and if the operation state meets the requirement, the estimated cold-state concentricity meets the requirement; and if the operation state does not meet the requirement, the estimated cold state concentricity is corrected.

The invention relates to a steam-jet pump system and a control method thereof, in particular to a variable-stage steam-jet pump system and a control method thereof, and solves the technical problems that an existing steam-jet pump system is difficult to realize switching of different working conditions and energy consumption is difficult to reduce. The variable-stage steam jet pump system comprises a gas collecting chamber and a gas jet pump unit connected with the gas collecting chamber, and the gas jet pump unit comprises a vacuum suction pipeline, a first-stage vacuum jet pump, a first-stage condenser, a second-stage vacuum jet pump, a second-stage condenser and a third-stage vacuum jet pump which are sequentially connected with the gas collecting chamber in the gas flow direction. The system further comprises a three-stage variable pump, a four-stage vacuum jet pump, a steam conveying unit and a cooling water conveying unit. The water supply reliability is greatly improved, and the long-time operation stability of the steam-jet pump system is guaranteed. According to the control method, ignition tests of engines with multiple thrust magnitudes and multiple working heights can be completed.

The invention provides a method for simulating bypass ratio regulation and control under the complete machine condition of a turbofan engine, and the method is realized based on a double-shaft compressor tester, and belongs to the field of aero-engine tests.The method comprises the steps that control parameters under the complete machine state are determined; determining the control precision of the test state control parameters of the double-shaft compressor tester; constructing a control module which stores an adjusting rule in a whole machine state and is used for enabling the rotating speed of the fan and the rotating speed of the high-pressure compressor to be in a linkage mode in the test process; the fan pressure ratio is monitored, an outer culvert throttling valve is adjusted, then an inner culvert throttling valve is adjusted, the high-pressure compressor pressure ratio is monitored at the same time, and finally the inner culvert throttling valve and the outer culvert throttling valve are adjusted at the same time, so that the high-pressure compressor pressure ratio and the fan pressure ratio meet the requirements; the state of the double-shaft compressor tester is kept stable, and compressor parameters are collected through an inner and outer culvert exhaust collection device; the rotating speed of the high-pressure compressor or the rotating speed of the fan is adjusted according to the rotating speed difference of the fan and the high-pressure compressor in the complete machine state, and parameters of the compressor are collected after stabilization.

The invention relates to the technical field of equipment fault diagnosis, and discloses a steam turbine vibration fault risk evaluation method and system.The method comprises the following steps that real-time data such as vibration, temperature, pressure and rotating speed of a steam turbine are collected through multiple sensors; the sensors comprise an accelerometer, a displacement sensor, a temperature sensor, a pressure sensor and a rotating speed sensor; the collected multi-source data is preprocessed, including de-noising, time synchronization and data standardization, to eliminate environmental noise and time difference between the data. The technical scheme based on multi-dimensional data acquisition and fusion is adopted, vibration sensors, temperature sensors, pressure sensors, rotating speed sensors and the like are arranged at key parts of a steam turbine, the running state of equipment is obtained in real time, multi-dimensional fusion and feature extraction are carried out on data, and the effects of comprehensive and real-time monitoring and early prediction of vibration faults of the steam turbine are achieved.

The invention provides a multivariable decoupling control method and system for an air inlet system of a high-altitude simulation cabin, and the method comprises the steps: firstly building a precombustion chamber cavity thermodynamic differential equation, and building a state equation in combination with a regulating valve first-order inertia model and an engine model; constructing a decoupling matrix by using a differential flatness theory, and converting a pressure and temperature coupling system into an independent control channel; monitoring a system state in real time by using an extended state observer, uniformly estimating internal and external disturbances as total disturbances, and generating a compensation signal; the model prediction controller performs rolling optimization on future time domain control quantity according to deviation between a set value and an actual value, generates an initial instruction in combination with the compensation signal, and converts the initial instruction into an independent valve control signal through a decoupling matrix; the high / low-temperature airflow mass flow is controlled through the opening degree of the adjusting valve, the engine model outputs actual parameters to form closed-loop feedback, and the controller updates the control quantity in each cycle. The multi-variable strong coupling, the dynamic disturbance and the model uncertainty are effectively overcome, the control precision and the parameter robustness are both achieved, and the complex working condition requirements are met.

The invention discloses a mechanical analysis method for flexible sleeve tooth connection considering three-dimensional friction force of a contact surface, which comprises the following steps of: firstly, dividing the flexible sleeve tooth connection into a plurality of shaft section infinitesimal elements along the axis direction, and simulating the contact behavior of a meshing tooth pair of each shaft section infinitesimal element by adopting a three-dimensional contact unit; wherein parameters of each contact unit are calculated according to geometric parameters and material parameters of the teeth. Summing the output results of all the contact units to obtain the relation between displacement and force or torque, and finally drawing a hysteresis loop and solving the rigidity and damping. According to the method, the non-linear rigidity can be calculated according to the size parameters of flexible sleeve tooth connection, a basis is provided for relatively accurately estimating the resonance rotating speed of the rotor system, and the method has important theoretical value and engineering significance for the safety design of the engine rotor system.

The invention relates to the technical field of aero-engines, in particular to an aero-engine thermal barrier coating working condition simulation experiment system which comprises a high-temperature thermal cycle module, a high-speed airflow scouring module, a high-pressure loading module, an atmosphere control module and a data monitoring and collecting module. The high-temperature thermal cycle module is used for realizing rapid heating and cooling so as to simulate a thermal environment; the high-speed airflow scouring module is used for generating high-speed airflow to simulate gas scouring; the coating performance can be accurately evaluated through the multi-working-condition high-precision simulation capability, research and development personnel can be assisted to optimize components and structures, coating defects and weak points can be rapidly and accurately found through strict working condition simulation in the aspect of quality detection, the product quality is guaranteed, the defective rate is reduced, and the method has good application prospects from cost benefit consideration. The test frequency and the part replacement cost caused by the coating problem in engine research and development are reduced, the research and development period is shortened, the performance and reliability of the aero-engine are greatly improved, the development of the aerospace industry is powerfully promoted, and a solid foundation is laid for advanced engine research and development.

The invention relates to a multi-dimensional high-resolution turbine blade heat-flow coupling field synchronous measurement method and system, and the method comprises the steps: obtaining a target spot image of known space distribution in a measurement space, and building a three-dimensional space mapping function; carrying out particle matching on the velocity field measurement original image based on a three-dimensional space mapping function, and reconstructing a three-dimensional particle trajectory by adopting a self-adaptive grid algorithm combined with machine learning to obtain a high-resolution three-dimensional velocity vector field; acquiring a temperature field measurement original image, performing three-dimensional space registration according to a three-dimensional space mapping function, further calculating voxel-level temperature distribution, and inverting a three-dimensional temperature field; and carrying out coupling analysis on the three-dimensional velocity vector field and the three-dimensional temperature field, and outputting a three-dimensional heat-flow coupling cloud picture. According to the invention, multi-dimensional and high-precision synchronous measurement of the temperature field and the velocity field in the complex flow field of the turbine blade is realized, the spatial resolution and dynamic response capabilities are remarkably improved, and a reliable experimental basis is provided for analysis and optimization of the cooling performance of the blade.

The invention discloses a creep test system of a turbine rotor blade film hole simulation piece and a test method of the creep test system. Comprising a clamping assembly used for fixing a test piece, a loading assembly used for applying a load to the test piece, a strain measuring assembly used for measuring the strain rate of the test piece, a heating assembly used for covering the test piece to form a heating channel, and a cooling assembly used for manufacturing and conveying cooling airflow to flow through the interior of the test piece, the strain measurement assembly is used for measuring the external temperature of the test piece and the internal temperature of the test piece, the control assembly is connected with the strain measurement assembly, the heating assembly, the cooling assembly and the temperature measurement assembly, and the heating assembly is used for manufacturing and conveying high-temperature airflow to flow through the heating channel so as to heat the outside of the test piece to a first set temperature; the cooling assembly is used for cooling the interior of the test piece to a second set temperature, and the heating assembly and the cooling assembly are used for forming a dynamic convection environment around the test piece.

The invention relates to the technical field of aero-engines, and discloses an aero-gas turbine engine complete machine stability margin evaluation method, which comprises the following steps of: analyzing physical characteristics and working principles of all parts of a gas turbine engine to construct an engine complete machine model, and constructing an engine experiment table to carry out an experiment; judging whether the compressor enters a surge state and recording experimental data, carrying out numerical simulation based on the constructed engine complete machine model and recording simulation data, comparing the simulation data with the experimental data, verifying the accuracy of the model, if so, constructing a surge boundary, and if not, optimizing the model. The method comprises the following steps: judging whether an engine has a stall hysteresis phenomenon or not in real time, generating a normal operation signal or a stall hysteresis signal, if the stall hysteresis signal is generated, updating a surge boundary, calculating a stability margin value of the engine based on the surge boundary, and evaluating the stability margin of the whole engine.

The invention discloses a rapid switching emergency protection system for an aero-engine test, and the system comprises a rapid switching unit which is used for rapidly disconnecting a DC load according to a switching instruction transmitted by a controller, and switching the DC load to an emergency protection load; the measuring unit is used for measuring signals such as engine gas turbine rotating speed, free turbine rotating speed, alternating-current voltage and current, direct-current voltage and current and the like; the controller is used for carrying out fault judgment on the system according to the measurement data acquired by the measurement unit and correspondingly sending a switching instruction to the rapid switching unit when a fault occurs; the monitoring system is used for monitoring and displaying parameters and operation states of the rectifier, the bus and the direct-current load system; and the emergency protection load is in circuit connection with the rapid switching unit and is used for providing the emergency protection load when the hybrid power system is in a large state and the load is suddenly lost. According to the invention, overspeed protection of a turboshaft engine hybrid power system test is realized, so that accidents such as breakage and flying-out of turbine blades are avoided.

Disclosed in the present application are a method and apparatus for acquiring the positions of measurement points of a combustion chamber of a turbine engine. By minimizing a condition number of a design matrix A, the minimum number of measurement points and an optimal measurement position are determined by using a global optimization algorithm. In the embodiments of the present application, on the basis of data of the minimum number of measurement points and an optimal measurement position that are determined, a temperature field of a turbine engine can be reconstructed, thereby solving the problems with respect to the low efficiency and high costs of conventional rotary-rake-based methods during combustion chamber measurement, and reducing the test cycle and cost during turbine engine development.

The invention discloses an engine fault detection method, device and equipment based on a single sensor and a medium, and relates to the technical field of fault detection. The method comprises the following steps: acquiring an eddy current original signal and an optical fiber pulse signal of the optical fiber eddy current composite sensor; the optical fiber eddy current composite sensor is installed at the position of an aero-engine casing. Calculating a blade radial displacement signal according to the eddy current original signal, and calculating a blade circumferential displacement signal according to the optical fiber pulse signal; filtering the blade circumferential displacement signal to obtain a target circumferential displacement signal; resampling the radial displacement signal of the blade to obtain a time sequence blade tip clearance signal; and engine blade fault information is determined according to the target circumferential displacement signal and the time sequence blade tip gap signal. Thus, the eddy current original signal and the optical fiber pulse signal are directly measured through the single sensor to detect faults, the transmission path is shortened, the diagnosis sensitivity and accuracy and the measuring point utilization rate are improved, and the sensor arrangement complexity is reduced.

The present disclosure relates to a system and method for adjusting a tool with a plurality of segments for inserting into a cavity of a machine. The method includes determining an initial alignment measurement of at least a portion of the tool; comparing the initial alignment measurement to a target alignment measurement to determine an adjustment amount; and adjusting at least one of the plurality of segments based on the adjustment amount. The tool includes a plurality of segments moveably coupled, where one or more of the plurality of segments comprises a unique dimensional measurement affecting a fit tolerance.

The invention provides an aero-engine blisk health monitoring method based on digital twinning, and provides an on-line damage identification and real-time monitoring method for the fatigue damage problem of an aero-engine blisk in a service state, and the fatigue damage problem of the aero-engine blisk in the service state is solved by integrating the digital twinning technology, the model correction technology and the non-contact laser vibration measurement technology. The damage identification, positioning, quantification and early warning of the blisk in a service state are realized, and the health state of the blisk is evaluated. The method has the advantages that the precise digital twin model of the blisk obtained through model correction provides a reference model for damage identification of the blisk; by establishing a blisk health monitoring system, feedback iteration among an engine control state, a digital twin model and online measurement parameters is realized, so that whether structural damage occurs or not is judged, the damage position is positioned, the damage degree is calculated, an alarm is given when the damage amount exceeds a limit value, the repair cost is reduced, and the flight safety is ensured.

The invention provides an aircraft engine air inlet channel detection system, and belongs to the technical field of aircraft engine air inlet channel detection. In order to solve the problems of low detection efficiency, reliability and safety of an aircraft engine air inlet channel, the invention provides an aircraft engine air inlet channel detection system, which comprises a carrying device, a detection robot and a control device, the carrying equipment is used for carrying the detection robot under the control of the control equipment and enabling the detection robot to be aligned with an inlet of an aircraft air inlet; the detection robot is used for moving in the air inlet channel under the control of the control equipment, and the detection robot comprises a mobile platform, and an engine blade shifting device, a mechanical arm and an image acquisition device which are sequentially arranged from the front end to the rear end of the mobile platform; and a detection device for detecting the interior of the pipeline is arranged at the tail end of the mechanical arm. According to the invention, the human input can be greatly reduced, the detection efficiency and reliability are improved, the human error risk is avoided, and the detection safety is improved.

This invention provides a three-dimensional testing device and method for measuring the fluctuation frequency of liquid films, belonging to the field of gas turbines and internal combustion engines. The method uses a laser generator to emit a continuous laser beam onto the surface of the liquid film, which is reflected. Two photodetectors are arranged in space to receive the laser signals reflected from the fluctuations of the liquid film in different directions. Throughout the fluctuation period, only one or two specific locations on the liquid film surface allow the photodetectors to receive the reflected laser signals. The photodetectors convert the laser signals into electrical signals. Using a computer, a fast Fourier transform is used to convert the electrical signals obtained from the photodetectors into frequency domain signals, thereby obtaining the fluctuation frequency of the liquid film at a single point in each fluctuation direction. This invention can measure the three-dimensional fluctuation frequency of liquid films ejected from nozzles such as centrifugal nozzles, pre-filming nozzles, and direct-fire nozzles. The measurement results can be used to analyze the initial atomization characteristics of the nozzles and guide the optimized design of the nozzles.