Ke-xin Wang Lei Zhao Li-min Gao Dong Zhang Yi-bo Yu

（School of Power and Energy,Northwestern Polytechnical University）

Abstract：Inlet distortion is one of the main factors for the degradation of aerodynamic performance and stability margin of the compressor in practical operation.Due to the change of the inlet shape and the large amount of inhalation of the body Boundary Layer,the ducted thrust fan of the Boundary Layer Ingestion(BLI)propulsion system inevitably works in the intake distortion condition.In this paper,the ducted thrust fan in a BLI propulsion system is taken as the research object.The influence of radial and circumferential total pressure distortion on the inlet section of the ducted thrust fan caused by boundary layer suction and inlet shape is studied by steady single channel and fullloop numerical simulation.The influence law of distortion intensity and distortion range of the two types of distortion patterns of the distortion map is analyzed emphatically.The results show that:(1)the greater the range and intensity of the radial total pressure distortion are,the more affected the performance of the ducted thrust fan is;(2)The aero-dynamic performance decline amplitude of the ducted thrust fan increases with the increase of the intensity of the circumferential total pressure distortion;The transmission law of the circumferential total pressure distortion intensity along the inlet and outlet of the fan is almost the same.Different working conditions have influence on the attenuation degree of the circumferential total pressure distortion in the ducted thrust fan,and the attenuation range of the circumferential total pressure distortion in the design working condition is the largest.

Keywords：Ducted Thrust Fan;Radial Total Pressure Distortion;Circumferential Total Pressure Distortion;Aerodynamic Performance

0 Introduction

In recent years,the environmental problems brought by the air transport industry have been received more and more attention with the increasingly busy air traffic.However,the potential of energy saving,emission reduction and noise reduction of aircraft with classical aerodynamic layout and propulsion system of pod-like architecture tends to the limit,and the above development goals cannot be achieved.In order to achieve the development goals proposed by NASA[1],the existing aircraft propulsion systems must be comprehensively improved.The Boundary Layer Ingestion (BLI)propulsion system has gradually attracted extensive attention of scholars due to its significant advantages in structural weight,environmental protection,safety and economy.

As early as 1947,A M O Smith et al.[2]first proposed the concept of Boundary Layer Ingestion (BLI),that is,a large number of fuselage or wing boundary layers enter the air inlet (the thickness may be as high as 30% of the inlet height of the air inlet).It flows through the fan,becomes the working fluid of the engine,and participates in the propulsion method of doing work to generate thrust [3].In 2011,Plas et al.[4]of the University of Cambridge,UK.by comparing the working principles of the traditional propulsion system and the BLI propulsion system,theoretically proved that the BLI propulsion system has significant advantages that the traditional propulsion system is incomparable to.With the maturity of numerical techniques,a large number of researchers have adopted numerical studies [5,6]to further analyze the flow mechanism of the BLI effect,proving the potential advantages of the BLI propulsion system.

Although the BLI propulsion system has obvious advantages over the traditional propulsion system in terms of propulsion efficiency,the BLI intake port continuously absorbs a large number of boundary layers.After the buried S-shaped channel,the total pressure distortion at the outlet of the intake port is significantly enhanced,and it also brings problems that cannot be ignored for the performance and stability of the BLI ducted thrust fan [7-9].For example,the massflow is reduced and the total pressure recovery coefficient of the inlet section is slight,and the inlet of total pressure distortion is serious.In the BLI propulsion system,the front flow disturbance of the ducted thrust fan is significantly enhanced,and the axial velocity distribution of the fan intake air flow changes greatly,which makes the fan work under unstable working conditions for a long time,and makes various performance indicators (pressure ratio,efficiency etc) degradation[10-11].

In order to evaluate the influence of the distortion caused by the BLI inlet on the aerodynamic performance of the fan/compressor,Plas et al.[4]conducted numerical calculations on a boundary layer ingestion s-curve inlet and the whole of its subsequent components.They found that the boundary layer suction can reduce fuel consumption by several percentage points,and the development of distortion in the duct is the main reason for the reduction of the overall performance of the fan.Gunn et al.[12]found that although the BLI propulsion system can reduce fuel consumption,the fan must be designed to operate continuously and stably in the case of severe air intake distortion compared with the traditional propulsion system.Ferrar et al.[13]simulated the distorted flow field at the outlet of the intake port through a distortion net,and their results showed that the intake distortion would cause change of the relative angle of attack of the fan blade inlet,which would further lead to complex mechanical responses and reduce efficiency.Masakil et al.[14]found in the study of the impact assessment of boundary layer ingestion on axial flow fans,under the same corrected flow rate,the total pressure ratio of the fan when the radial total pressure is distorted in intake is higher than that of the fan when uniform intake is used.

Liu Lei et al.[15]carried out an integrated numerical simulation of the buried S-shaped air intake and single-stage fan,and found that compared with uniform air intake,the air intake distortion formed by the development of the buried air intake will significantly reduce the performance of the ducted thrust fan.Ning et al.[16]analyzed the flow structure in the intake port with and without boundary layer inhalation by using numerical simulation methods and experiments.They found that compared with the inhalation without boundary layer,there is a large low pressure area at the bottom of each section of the intake port,the secondary flow is significantly stronger,the swirl distortion is significantly increased,and the total pressure recovery coefficient of the BLI intake port is reduced by 4%.Wei et al.[17]used steady and unsteady CFD numerical simulation methods to simulate and analyze the overall characteristics and flow field characteristics of the intake duct and fan components when the inlet suctions the boundary layer of different heights.They found that with the increase of the suction thickness of the inlet boundary layer,the total pressure deficit of the fan inlet distortion zone increased,the flow coefficient decreased,and the relative airflow angle increased,but the extent of the distortion zone did not increase significantly.

Scholars have done a lot of research on the performance of fans in BLI propulsion systems under distortion conditions,but more focus on the effect of air intake distortion caused by BLI on the flow field of ducted thrust fans.The development law of the strong total pressure distortion formed by the development of the BLI inlet in the ducted thrust fan and the degree of influence of different distortion intensities on the performance of the fan are still unclear.Therefore,in view of the total pressure distortion caused by the BLI inlet,the effects of radial and circumferential total pressure distortion on the aerodynamic performance of the ducted thrust fan were studied.The research work has guiding significance for the development and design of the ducted thrust fan in the BLI propulsion system,and is helpful for the wide application of the BLI propulsion system in the future aircraft.

1 Materials and Methods

1.1 Classification of Total Pressure Distortion and Calculation of Distortion Index

1.1.1 Classification of total pressure distortion

The total pressure distortion is mainly caused by the disturbance of the flow before the intake port and inside the intake port.For example,the intake of ground vortices during take-off,the separation of the inlet lip during high angle of attack maneuvers,the interference of the boundary layer and the shock wave of the inlet during supersonic flight,or the intensification of the separation flow at the raised parts of the fuselage,etc.

According to the classification of distortion parameters,the flow field distortion can be mainly divided into total pressure distortion,total temperature distortion,swirl distortion,static pressure distortion,plane wave and compound distortion,etc[18].According to the current research,there are mainly total pressure distortion and swirl distortion before the inlet of the ducted thrust fan in the BLI propulsion system.Among them,the total pressure distortion is the main factor that causes the high cycle fatigue of the fan blades,and has the most prominent impact on the aerodynamic performance of the fan [19-21].Figure 1 shows the different forms of total pressure distortion classified according to different spatial locations.

Fig.1 The form of inlet total pressure distortion

1.1.2 Calculation of radial total pressure distortion index

The radial distortion index mainly considers the inhomogeneity of the total pressure distribution along the radial direction.The radial inhomogeneity of the total pressure on the Aerodynamic Interface Plane(AIP) is quantitatively described by the range of the radial low pressure area where the total pressure on the section is less than the average total pressure on the surface and the relative magnitude of the region deviating from the average total pressure on the surface.The radial distortion index includes the radial distortion intensity and the extent of the low pressure area.

Usually,the entire AIP interface is divided intoNequalarea torus,as shown in Figure 2.

Fig.2 N torus of equal area

The radial distortion index primitive is defined as the difference between the surface average pressure and the ring average pressure divided by the surface average pressure[22],and the radial distortion intensity of any torusican be expressed as:

In the formula,(Pav)iis the average total pressure of the torusi,PF,avis the average surface pressure.They are defined as:

The radial total pressure distortion index of the entire surface can be expressed as:

IDRT(r/R) is expressed as the radial total pressure distortion of the low pressure area near the shroud,wherer/Rrepresents the extent of the low pressure area occupying the section.

1.1.3 Calculation of circumferential total pressure distortion index

The circumferential total pressure distortion is based on the torus,and is represented by the distortion intensity and distortion range.The range of the circumferential low pressure area where the total pressure on the section is less than the average total pressure on the surface is denoted by Δθ.The circumferential total pressure distortion index primitive is defined as the average value of the pressure deficit in the low pressure area on each ring [22],and the circumferential total pressure distortion index primitive is calculated by dividing the section intoNequal-area torus,as shown in Figure 3 shown.

Fig.3 Schematic diagram of circumferential total pressure distortion

The circumferential distortion primitive of any torusican be expressed as:

where (Pav,low)iis the average total pressure of the part of the torusiin the low pressure region,which is defined as:

The circumferential total pressure distortion indexIDC(Δθ)of the entire torus can be expressed as:

1.1.4 Analysis of total pressure distortion at AIP interface in BLI propulsion system

The structure of a typical BLI propulsion system is shown in Figure 4,and the total pressure distortion map of the AIP interface of the air inlet and the ducted thrust fan in a BLI propulsion system is shown in Figure 5.

Fig.4 Schematic diagram of BLI propulsion system

Fig.5 The total pressure distortion map

The high total pressure area on the AIP interface of the BLI propulsion system is mainly located in the middle of the section(areaA),and the low total pressure area mainly appears in three locations: the first is the near-wall area of the outer diameter of the AIP interface.This part of the low total pressure fluid is mainly related to the development of the boundary layer.The second is located at the bottom of the section (areaB),where the lower half of the AIP interface has been occupied by the low total pressure fluid.In addition,a pair of smaller paired vortices appeared at the positionsC1andC2on both sides of the cross-section,resulting in an obvious low total pressure area at the positionsC1andC2.It can be seen that in a BLI propulsion system,there are both radial and circumferential total pressure inhomogeneities on the AIP interface,and the distortion range and distortion intensity are more severe than those of the traditional propulsion system.

Select the representative sector area of the total pressure distortion map of the AIP interface,and apply the calculation formula of the radial total pressure distortion index defined in Section 1.1.2.It is calculated that the radial low pressure range occupies 30% of the radius of the AIP interface,and the radial total pressure distortion intensity isIDRT(0.3)=8%.The distribution of the average total pressure in the area along the radial direction is shown in Figure 6.

Fig.6 Radial distribution diagram of AIP interface total pressure

Applying the calculation formula of the circumferential total pressure distortion index defined in Section 1.1.3 to the total pressure distortion map of the AIP interface,it is calculated that the circumferential extent of the low pressure area is Δθ=130.9°,and the circumferential total pressure distortion intensity isIDC(130.9°)=3.65%.The distribution of the average total pressure on the AIP interface along the circumferential direction is shown in Figure 7.

Fig.7 Circumferential distribution diagram of AIP interface total pressure

1.2 Parameters of the Ducted Thrust Fan

The ducted thrust fan is a single-stage transonic axial fan,as shown in Figure 8.The fan inlet diameter is 500mm,the rotor tip rim speed is 399m/s,and the blade tip relative Mach number is 1.29.Among them,the number of rotor blades is 22,and the number of stator blades is 34.The rotor tip clearance is 0.61mm.The detailed design point parameters are shown in Table 1.

Fig.8 Geometric model of the ducted thrust fan in a BLI propulsion system

Tab.1 Design point parameters of the ducted thrust fan in a BLI propulsion system

1.3 Numerical Simulation Method and Its Accuracy Verification

NUMECA software has been recognized by the industry for its advantages of high speed,high precision and good reliability when simulating the flow field of subsonic or transonic impeller rotating machinery and other related problems.In order to study the effect of total pressure distortion on the aerodynamic performance of a ducted thrust fan in a BLI propulsion system,the EURANUS solver of NUMECA was used to solve the steady-state Reynolds time-averaged NS equ ation.The spatial discretization scheme adopts the second-order central difference,and the turbulence model adopts the S-A model.

The accuracy of the selected numerical simulation method is verified before the numerical simulation calculation of the ducted thrust fan is carried out.NASA Rotor67 [23]is a typical low aspect ratio axial flow transonic fan rotor with more detailed and complete experimental data.The experimental data comes from the results measured by the laser measurement technology published by Strazisar A J et al[24]in 1989.Therefore,this paper selects NASA Rotor67 as the test object,as shown in Figure 9.

Fig.9 NASA Rotor67 geometric model

In order to ensure the full development of the inlet and outlet flow fields,the inlet and outlet extension sections of the computational domain are set to be 1.5 and 2 times the blade chord length respectively.Figure 10 shows the schematic diagram of the experimental measurement site and the numerical calculation area of this paper.The corresponding section is intercepted according to the position of the measurement site in Figure 10,and "Mass-Flow Weighted Average" is selected to calculate the total temperature and total pressure of the two measurement sites respectively.

Fig.10 Schematic diagram of numerical calculation area and experimental measurement station

The subscript of measurement station 1 is 1,and the subscript of measurement station 2 is 2,then the pressure ratio and efficiency of the rotor can be described by the following formulas respectively:

In formula（9）,κis the specific heat ratio of the working fluid(ideal air).

After the calculation,the numerical simulation characteristic curves of NASA Rotor67 are compared with the experimental characteristic curves,as shown in Figure 11.

It can be seen from the figure that the numerical calculation results of the efficiency characteristic curve and the pressure ratio characteristic curve are almost consistent with the experimental results,and the overall trend is the same.

Figure 12 shows the 90% span relative Mach number cloud map of the S1 flow surface at the rotor peak efficiency point.It can be seen from Figure 12 that the relative Mach number distribution of the calculated and experimental results at 90% span is in good agreement with the peak efficiency condition.This shows that the numerical calculation software can accurately simulate the details of the flow field.

Fig.11 The verification of the accuracy of numerical calculation results

Fig.12 The 90% span relative Mach number cloud map of the S1 flow surface at peak efficiency point

To sum up,it can be considered that the numerical simulation method in this paper meets the accuracy requirements of numerical calculation.

In the study of the influence of radial total pressure distortion on the aerodynamic performance of the ducted thrust fan,a single-channel computational grid was used for numerical calculation,the two side walls were set as periodic boundary conditions,and the dynamic/static interference in the numerical simulation was mixed plane method.When studying the circumferential total pressure distortion,the grid model adopts the full-channel calculation grid for numerical calculation,and the dynamic/static interference is processed by the frozen rotor method.

The working fluid is the ideal gas.In the setting of boundary conditions,the total temperature and total pressure are given at the inlet boundary,and the intake direction is axial.The rotor’s hub and blade are set to rotate and the rest are stationary.The outlet boundary is given different outlet static pressures to obtain different working points of the ducted thrust fan.In the calculation,the adjustment step of the outlet static pressure is 1000Pa,and the throttling situation during the experiment is simulated by gradually increasing the static pressure.When approaching the stall point,the adjustment step is 100Pa.When the difference between the inlet and outlet flow is less than 0.5%,and the performance convergence curve develops smoothly,the calculation is considered to converge.When the calculation results diverge,it is considered that the ducted thrust fan reaches the stall condition.

1.4 Mesh Independence Verification

The IGG and Autogrid5 modules in NUMECA are used for mesh division.The blade channel mesh adopts the O4H multi-block mesh partition technology,the O-shaped mesh is used around the blade,and the H-shaped mesh is used for the front and rear extension positions.The mesh is refined towards the solid wall.In order to verify the mesh independence,6 grid configurations of 0.34 million,0.54 million,1 million,1.86 million,2.97 million and 3.95 million were set,of which 1.86 million mesh configurations are shown in Figure 13.

The aerodynamic performance of the ducted thrust fan under different mesh configurations is calculated at the same static pressure point.The calculation results are shown in Figure 14.It can be seen that when the mesh volume of the ducted thrust fan is greater than 1.86 million,the massflow and efficiency of the ducted thrust fan are almost unchanged,and the 1.86 million mesh has met the grid independence requirement.Therefore,1.86 million grids were selected for follow-up research in single-channel numerical calculation.

2 Results and Discussion

2.1 Influence of Radial Total Pressure Distortion on Aerodynamic Performance

2.1.1 The radial total pressure distortion map of inlet

Distortion intensity and distortion range are important parameters for evaluating total pressure distortion.To study the effect of radial total pressure distortion on the aerodynamic performance of the ducted thrust fan under different distortion intensities,the distortion range needs to be kept the same.According to the total pressure map ofIDRT(0.3)=8%above,on the premise that the distortion range remains unchanged and the average total pressure is equal to the uniform intake,by adjusting the total pressure values of the high pressure area and the low pressure area,IDRT(0.3)=6% andIDRT(0.3)=10% of the radial total pressure distribution are obtained,as shown in Figure 15.

In order to study the influence of the radial total pressure on the aerodynamic performance of the ducted thrust fan under different distortion ranges of the radial total pressure,the distortion intensity of the total inlet pressure must be kept the same.However,it is difficult to accurately adjust the distortion range on the premise of ensuring the distortion intensity.Therefore,this paper adopts a simplified method to obtain the radial total pressure distortion map in different distortion ranges by giving the pressure value and range of the low pressure area without changing the distortion intensity.Figure 16 shows the radial total pressure distortion map of the same distortion intensity and different distortion ranges obtained by the above method.

Fig.13 Schematic diagram of mesh scheme of the ducted thrust fan

Fig.14 Mesh independence verification

Fig.15 Radial total pressure distortion map of different distortion intensities

Fig.16 Radial total pressure distortion map with different distortion ranges

2.1.2 The influence of radial total pressure distortion intensity on aerodynamic performance

Figure 17 shows the efficiency characteristic curve and pressure ratio characteristic curve of the ducted thrust fan under different radial total pressure distortion intensities.The peak efficiency of the ducted thrust fan is 88.92% when the air intake is uniform.The radial total pressure distortion does not change the changing trend of the efficiency characteristic curve.However,under the influence of radial total pressure distortion,the peak efficiency of the ducted thrust fan will decrease to a certain extent.

It can be seen from Table 2 that when the distortion index is small,the effect of radial total pressure distortion on the efficiency of the ducted thrust fan is not obvious.WhenIDRT(0.3)=6%,the peak efficiency of the ducted thrust fan decreases by 1.77% compared with the uniform intake.With the increase of the distortion index,the degree of radial total pressure distortion affecting the efficiency of the ducted thrust fan also increases accordingly.Under the conditions ofIDRT(0.3)=8% andIDRT(0.3)=10% distortion intensities,the peak efficiency of the ducted thrust fan decreased by 3.1%and 4.69%,respectively,compared with the uniform intake condition.

In addition,it can be clearly seen from the characteristic curve of the ducted thrust fan that when the radial total pressure distortion occurs at the inlet,the stable working range of the ducted thrust fan is significantly narrowed,and as the distortion index increases,this trend becomes more and more obvious.In order to quantitatively describe the influence of radial total pressure distortion on the stability of ducted thrust fans,the calculation formula of stability margin is introduced:

In the formula,m0and π0are the massflow and total pressure ratio at the highest efficiency point,andmsand πsare the massflow and total pressure ratio at the stall point.

Fig.17 Characteristic curves of the ducted thrust fan under different distortion intensities

Tab.2 Influence of different radial total pressure distortion intensity on aerodynamic performance of the ducted thrust fan

According to Equation 10,the stability margin of the ducted thrust fan under different radial total pressure distortion indices is calculated as shown in Table 3.It can be found that the larger the distortion index is,the narrower the stable working range of the ducted thrust fan is.The radial total pressure distortion has a great influence on the stability margin.Compared with the uniform intake,the stability margin loss of the ducted thrust fan is 16.49% under the condition ofIDRT(0.3)=10%.The larger the radial total pressure distortion index is,the greater the influence of the radial total pressure distortion on the stability margin of the ducted thrust fan is.The fan is more likely to enter unstable conditions such as surge condition or rotating stall condition.

2.1.3 The influence of radial total pressure distortion range on aerodynamic performance

Figure 18 shows the curves of the efficiency and pressure ratio of the ducted thrust fan as a function of massflow under three radial total pressure distortion inlet conditions with the same distortion intensity and different distortion ranges.

Fig.18 Characteristic curves of the ducted thrust fan in different distortion ranges

Tab.3 Influence of different radial total pressure distortion intensity on stability margin of the ducted thrust fan

The following conclusions can be drawn from the figure:

1)The radial total pressure distortion range is an important factor affecting the working stability margin of the ducted thrust fan.When the radial total pressure distortion occurs at the inlet of the ducted thrust fan,the working stability margin of the ducted thrust fan is obviously narrowed.

2)When the distortion range is small,the effect of radial total pressure distortion on the peak efficiency of the ducted thrust fan is almost negligible.It can be seen from Table 4 that in the 5%Rdistortion range,the peak efficiency of the ducted thrust fan is only reduced by 0.09% compared to the uniform intake.When the radial distortion range is large,that is,under the condition of 20%Rdistortion range,the influence of radial total pressure distortion on the peak efficiency of the ducted thrust fan begins to increase,and the peak efficiency of the ducted thrust fan is reduced by 1.31% compared with the uniform intake air.

3)When the radial total pressure distortion occurs at the inlet of the ducted thrust fan,the plugging point will shift to the left,and the massflow at the plugging point will decrease.And with the increase of the distortion range,the influence of the radial total pressure distortion on the massflow at the plugging point also increases accordingly.

Tab.4 Influence of different radial total pressure distortion range on aerodynamic performance of the ducted thrust fan

2.2 Influence of Circumferential Total Pressure Distortion on Aerodynamic Performance

2.2.1 The circumferential total pressure distortion map of inlet

In the study of the effect of circumferential total pressure distortion on the performance of the ducted thrust fan,the inlet of the ducted thrust fan is divided into 22 sector areas according to the number of rotor channels.According to the analysis results of the total pressure distortion map of the AIP interface in theBLIpropulsion system in section 1.1.4,and on the premise of ensuring the same range as the previous AIP interface circumferential total pressure distortion range,8 channels are selected as low pressure areas to create distortion range that is 130.9°.By adjusting the numerical value of the low pressure region,the distortion maps of different circumferential total pressure distortion intensity are obtained,as shown in Figure 19.In the numerical calculation of the circumferential total pressure distortion,the full ring channel mesh must be used for calculation.The single-channel mesh is copied to generate a full-ring channel mesh,and the number of mesh is 26.6 million.

Fig.19 The inlet total pressure maps of three kinds of circumferential total pressure distortion intensities

2.2.2 Influence of circumferential total pressure distortion intensity on aerodynamic performance

Figure 20 shows the effect of different circumferential total pressure distortion intensities on the aerodynamic performance of the ducted thrust fan.It can be seen from the figure that:

1)The effect of the circumferential total pressure distortion on the efficiency curve of the ducted thrust fan is similar to that of the radial total pressure distortion,and the overall efficiency curve moves to the lower left.With the increase of the circumferential total pressure distortion intensity,the peak efficiency of the ducted thrust fan shows a downward trend.

2)The effect of the circumferential total pressure distortion on the total pressure ratio of the ducted thrust fan is different from that of the radial total pressure distortion.Compared with the uniform intake,when the intake condition is the circumferential total pressure distortion,the pressure ratio characteristic curve of the ducted thrust fan moves to the lower left as a whole.And the greater the circumferential total pressure distortion intensity is,the greater the pressure ratio loss of the ducted thrust fan is.

3) Combining with the table 5,it can be seen that the greater the circumferential total pressure distortion intensity,the more the stability margin of the ducted thrust fan decreases.When the circumferential total pressure distortion intensity reaches 10%,the stability margin of the ducted thrust fan decreases by 18.25%,and its margin is only 2.01%.It can be seen that the circumferential total pressure distortion intensity has a great influence on the stability margin of the ducted thrust fan.

Fig.20 Characteristic curves of the fan under different circumferential total pressure distortion intensities

Tab.5 Influence of distortion intensity of circumferential total pressure on stability margin

2.2.3 The variation law of circumferential total pressure distortion along the axial direction with different intensities

In order to verify the development law of the circumferential total pressure distortion along the axial direction in the ducted thrust fan under different inlet conditions of circumferential total pressure distortion intensities.The inlet conditions of the ducted thrust fan are selected asIDC(130.9°)=6%,IDC(130.9°)=8%andIDC(130.9°)=10%,and the design operating points are compared.In order to explain the variation law of circumferential total pressure distortion along the axial direction in the ducted thrust fan,Figure 21 shows the numerical calculation area of the ducted thrust fan when the circumferential total pressure distortion is studied in this paper.Figure 22 and Table 6 show the development of the circumferential total pressure distortion along the axial direction under different distortion intensities.

Fig.21 Numerical calculation area of the ducted thrust fan

Fig.22 Axial development of total pressure distortion with different distortion intensities

Tab.6 Circumferential distortion index along the axial position under distorted intake conditions %

Combining Figure 22 and Table 6,the following conclusions can be drawn:

1) Under different distortion intensities,the transmission law of circumferential total pressure distortion in the ducted fan is almost the same.

2) During the axial development of the circumferential total pressure distortion in the ducted thrust fan,the distance from the inlet to the fan inlet cap has the largest decrease in the distortion index,and the greater the distortion intensity,the greater the decrease.In the distance from the intake cap to the leading edge of the rotor,the circumferential total pressure distortion index starts to increase under the three distortion conditions.And the greater the circumferential total pressure distortion intensity at the fan inlet,the faster the circumferential total pressure distortion index growth in this distance.From the leading edge of the rotor to the leading edge of the stator,if the intensity of inlet circumferential total pressure is greater,the distortion intensity after passing through the rotor is also greater.

3)The total pressure distortion index at the outlet of the ducted fan gradually decreases for the three intake conditions with different circumferential total pressure distortion intensity,and the corresponding circumferential total pressure distortion index at the outlet is 1.33%,1.07% and 2.21%,respectively.

When the circumferential total pressure distortion develops along the axial direction in the ducted thrust fan,the distortion intensity is weakened to a large extent,but the weakening effect is not linear.

2.2.4 Variation law of circumferential total pressure distortion along the axial direction at different operating points

Aiming at the condition ofIDC(130.9°)=8% intake air,the variation law of the circumferential total pressure distortion in the ducted thrust fan along the axial direction in the near-plugging condition,the near-stall condition and the neardesign condition is studied respectively.Figure 23 shows the variation of the circumferential total pressure distortion intensity at different positions along the axial direction in the ducted thrust fan.

Fig.23 The axial development of total pressure distortion in different working conditions

It can be seen from Figure 23 that the propagation law of the circumferential total pressure distortion intensity along the axial direction is different under different working conditions:

1)From the inlet to the front of the intake cap(Z=-0.13m),the intake distortion intensity under the three working conditions decreases in the same trend;

2)From the air intake cap to the leading edge of the fan rotor (Z=-0.01m),compared with the design condition and the near-plugging condition,the circumferential total pressure distortion intensity in the near-stall condition increases from 4.12% to 5.43%.The near-stall condition has the largest enhancement;

3) From the rotor to the leading edge of the stator(Z=0.11m),the distortion intensity of the near-stall condition and the near-design condition both decreased,and the distortion intensity of the near-plugging condition continued to increase.

4) After passing through the stator (Z=0.21m),the distortion intensity of the near-plugging condition increases the most;from the back of the stator to the exit of the calculation area,the distortion intensity of the three working conditions shows a downward trend,and the design condition decreases to 1.07%.The design condition has the largest decrease.

Figure 24 shows the circumferential distribution of the total pressure of the ducted thrust fan in front of the intake cap (Z=-0.13m) along each section of the axial direction.It can be seen that the circumferential distribution range of the circumferential total pressure distortion is basically unchanged from the inletZ=-0.25m,no matter it is near-stall condition or near-plugging condition.Under the two working conditions,the total pressure in the low-pressure area is increased,and the total pressure in the high-pressure area is reduced,resulting in a decrease in the total pressure distortion intensity in the front section of the intake cap.

Fig.24 The total pressure at different axial positions in front of the air intake cap is distributed along the circumferential direction

Air continues to flow from the intake hood to the front section of the rotor.Figure 25 shows the circumferential total pressure distribution in the front section (Z=-0.01m) of the rotor inlet under near-plugging and near-stall conditions.At this section,the value of total pressure fluctuates obviously and regularly along the circumferential angle,so that the circumferential total pressure distortion begins to increase under different working conditions.

After that,the airflow flows from the leading edge of the rotor(Z=-0.01m)through the rotor channel and flows out of the rotor (Z=0.11m).Due to the high speed rotation of the rotor,the circumferential mixing is intensified after the airflow passes through the rotor.Figure 26 shows the circumferential distribution of the total pressure at different axial positions of the ducted thrust fan under near-stall conditions.It can be seen from the figure that in the near-stall condition,compared with the total pressure distribution of the front section of the rotor,the average total pressure of the rotor outlet section increases significantly,and the total pressure begins to become uniform along the circumferential direction.Therefore,the distortion strength of the circumferential total pressure at the rotor outlet section (Z=0.11m) is weakened in the near-stall condition.

Fig.25 The circumferential total pressure distribution of the rotor section under near plugging and near stall conditions before inlet

Fig.26 The total pressure at different axial positions nearstall conditions is distributed along the circumferential direction

It can be seen from Figure 27 that in the near-plugging condition,although the average total pressure of the rotor outlet section increases,the phenomenon of high-low total pressure fluctuates obviously along the circumferential angle.Therefore,the circumferential total pressure distortion strength increases in the near-plugging condition on this section.

Fig.27 The total pressure at different axial positions is distributed along the circumferential direction under the nearplugging condition

Fig.28 Cloud diagram of total pressure distribution of each section along axial direction behind stator under near-stall condition

Fig.29 Cloud diagram of total pressure distribution of each section along axial direction behind stator under nearplugging condition

Figure 28 and 29 are the cloud diagrams of the total pressure distribution of each section along the axial direction at the rear of the stator under near-stall and near-clogging conditions,respectively.It can be seen that as the airflow flows from the back of the stator(Z=0.21m)to the outlet(Z=0.3m),the average total pressure of the high-pressure fluid near the hub begins to weaken,and the average total pressure of the low-pressure fluid near the rim begins to increase .The high-low pressure fluid still mixes in the circumferential direction at this distance,and its total pressure inhomogeneity decreases continuously along the axial direction.Therefore,the circumferential total pressure distortion intensity decreases gradually from the back of the stator to the outlet,no matter it is near-plugging condition or near-stall condition.

3 Conclusions

The research results of radial total pressure distortion show that:

1)Radial total pressure distortion reduces peak efficiency,maximum total pressure ratio,and stability margin of the ducted thrust fan.The greater the distortion intensity is,the greater the decline in the aerodynamic performance of the ducted thrust fan is.WhenIDRT(0.3)=10%,the peak efficiency of the ducted thrust fan decreases by 4.69%.

2) When the distortion range is small,the radial total pressure distortion has little effect on the aerodynamic performance of the ducted thrust fan.With the increase of radial distortion range,the influence degree of radial total pressure distortion on the performance of ducted thrust fan increases gradually.When the distortion range isIDRT(0.05)=8%,the peak efficiency loss is 0.09%,and when the distortion range isIDRT(0.2)=8%,the peak efficiency loss is 1.31%.The efficiency loss of the ducted thrust fan is nearly 15 times different.Therefore,when the distortion range is large,the adverse effect of radial total pressure distortion on the ducted thrust fan must be considered.

The research results of circumferential total pressure distortion show that:

1)The circumferential total pressure distortion will deteriorate the aerodynamic performance of the ducted thrust fan,which is reflected in the decrease of peak efficiency,maximum total pressure ratio and the stability margin.

2)The attenuation amplitude of the circumferential total pressure distortion at the fan outlet is not much different under different distortion intensities.However,different working conditions have an impact on the decay speed of the circumferential total pressure distortion in the ducted thrust fan.Under the design condition,the circumferential total pressure distortion decay rate is the largest.Under theIDC(130.9°)=8% design condition,the total pressure distortion intensity at the fan outlet is attenuated by 1.07%.

4 Acknowledgement

This work is suppored by the high performance computing power and technical support provided by Xi'an Future Artifical Intelligence Computing Center.