CN107366634B - A kind of compressor blade row loss calculation method - Google Patents

Abstract

The invention discloses a method for calculating the loss of a compressor cascade. Through the method for evaluating the loss of a compressor cascade proposed by the present invention, it can be roughly judged and calculated due to various vortex consumption and boundary layer friction in the compressor cascade. The size and proportion of various losses can be used to judge the main loss source in the compressor cascade, so as to provide theoretical guidance for the grasp of the flow mechanism in the compressor and the flow control in the compressor cascade later.

Description

A Calculation Method of Compressor Cascade Loss

technical field

The invention belongs to the field of impellers, and in particular relates to a method for calculating the loss of a compressor cascade.

Background technique

In a compressor cascade, a strong lateral flow is generated at the end wall due to the pressure difference between the blade pressure face and the adjacent suction face and the low velocity characteristics of the end wall fluid. Coupled with the induction of the horseshoe vortex at the leading edge and the complex wall shearing effect in the corner area of the end wall, the channel vortex in the channel will continue to grow and develop, and an obvious separation line will be generated on the suction surface of the blade, which will induce the generation of concentrated shedding vortex. This leads to the accumulation of the low-velocity zone in the corner zone and then extends to the entire leaf span. Especially in the case of a large angle of attack, the channel vortex involves a wider range, and the accumulation in the low-velocity region is more serious, resulting in severe angular separation. Due to the mutual shear between the viscous vortices, a large energy consumption is caused, and an obvious loss concentration area appears. At the same time, the corner separation phenomenon will not only reduce the efficiency of the cascade, but also induce the stall phenomenon of the whole stage compressor due to the separation of the corner region, and then lead to the surge problem. Therefore, in order to design a high-performance and high-efficiency compressor, it is necessary to conduct relevant research on and control the loss of corner separation in the cascade.

At present, the evaluation of the corner area of the cascade is mainly focused on the loss coefficient loss method based on the total pressure. The definition of loss is as follows:

In the formula, pt and p respectively represent the total pressure and static pressure, and Loss is constructed with reference to the static pressure and dynamic pressure in the middle of the inlet blade, that is, the subscripts in and m represent the data of the position of the inlet blade.

The current general method is to characterize the loss in the channel through the loss distribution cloud image of a certain section or the circumferential average data of the loss along the span direction, and it is considered that the loss is small where the absolute value of loss is small. However, there are two disadvantages in this method. First, the loss estimated by the total pressure shows the continuous accumulation of losses, that is, the air flow continuously flows through the entire cascade from the cascade inlet until it passes through the measurement point. However, it cannot characterize the loss due to the viscosity of the airflow in a certain volume unit. Second, this method can only roughly characterize the size of the loss, but since there are mainly channel vortices, corner vortices, concentrated shedding vortices, and wake low-energy areas in the compressor cascade channel, and the loss is mainly concentrated in some In this region, the pure loss coefficient method cannot combine the loss with the vortex structure in the channel. Therefore, it is necessary to improve the existing cascade loss analysis method.

Contents of the invention

The technical problem to be solved by the present invention is: the purpose of the present invention is to solve the current situation that the current analysis method of the internal loss of the compressor cascade is not perfect. Therefore, a kind of analysis of the loss of the compressor cascade based on the volume fraction of different regions is proposed. method, through this method, the loss of each area of the space can be accurately calculated, and at the same time, this method is combined with the vortex structure in the compressor, which can accurately calculate and distinguish the channel vortex, corner vortex, and near-wall shear. The size of the loss in different areas such as the cutting action area. In addition, this method is different from the conventional method based on total pressure loss. This method is directly based on the dissipation function, and its loss is only related to the deformation and shear strength at this position, and there is no problem of loss accumulation.

The technical scheme of the present invention is: a kind of compressor cascade loss calculation method, comprises the following steps:

Step 1: For the region between the starting point of the leading edge of the cascade and the end point of the 40% chord length behind the trailing edge of the cascade, the vortex field area is calculated according to the positive and negative values of the axial vorticity, the position of each separation line and attachment line, and the wall distance The division is divided into channel vortex area, suction/pressure surface angular vortex area, concentrated shedding vortex area, trailing edge shedding vortex area, near-wall friction loss area and other areas. The division is defined as follows:

Channel vortex area: located in the entire channel, close to the end wall, the axial vorticity is negative, and the spanwise height is between the end wall and the separation line of the channel vortex;

Friction loss area near the wall: located at the end wall, where the suction surface of the blade is close to the wall, and where the pressure surface of the blade is close to the wall, the distance between the walls is on the order of millimeters, and the axis vorticity is positive;

Angular vortex area on the suction/pressure surface: located at the junction of the blade suction/pressure surface and the end wall, the axial vorticity is positive; the spanwise height is between the end wall and the angular vortex separation line, and the circumferential area is from the blade root to the between the attachment lines of the angular vortex;

Trailing edge shedding vortex area: located in the wake area behind the trailing edge, the spanwise position is located in the area where the axial vorticity is positive between the concentrated shedding vortex and the angular vortex;

Concentrated shedding vortex area: in the area from the leading edge to the trailing edge of the cascade, after the separation line of the suction surface of the blade, close to the middle part of the blade in the span direction, and above the passage vortex, the axial vorticity is positive;

Other areas: 40% of the chord length from the leading edge to the trailing edge of the blade other than the areas described above

set area;

Step 2: Carry out loss integration for the regions divided in Step 1: Carry out the volume integral of the corresponding regions for the dissipation function, calculate the loss of each region, and obtain the loss generated by each vortex structure.

Invention effect

The technical effect of the present invention is that: through the compressor cascade loss evaluation method proposed by the present invention, it is possible to roughly determine and calculate the size and result of various losses due to various vortex consumption and boundary layer friction in the compressor cascade. The proportion can be used to judge what is the main loss source in the compressor cascade, so as to provide theoretical guidance for the grasp of the flow mechanism in the compressor and the flow control in the compressor cascade later.

Description of drawings

Fig.1 Contour map of LOSS distribution at 40% chord length behind the cascade trailing edge

Fig.2 Contour diagram of axial vorticity distribution at 20% chord length position of cascade leading edge and schematic diagram of partition

Fig.3 Contour diagram of axial vorticity distribution at 50% chord length position of cascade leading edge and schematic diagram of partition

Fig.4 Contour diagram of axial vorticity distribution at 20% chord length behind the cascade trailing edge and schematic diagram of partitions

Explanation of reference signs:

For Figure 1: A-Compressor cascade blade B-Compressor cascade hub C-Blade leading edge D-Blade trailing edge E-Blade trailing edge 40% axial position section

For Figure 2-4: 1-corner vortex area on suction surface 2-corner vortex area on pressure surface 3-near end wall friction loss area 4-friction loss area near suction surface 5-friction loss area near pressure surface 6-channel vortex area 7 -Concentrated shedding vortex area 8-Tailing edge shedding vortex area 9-Vorticity compensation area 10-Others

area

Detailed ways

First, it should be noted that the dissipation function defined as:

In the formula, μ refers to the dynamic viscosity, Indicates the gradient of the velocity component in the direction of v _i in the direction of j, such as Indicates the gradient of the velocity component v _x in the y direction

Through the Euler method, the size of the dissipation function of a tiny unit in the flow field area can be calculated, and the loss due to the deformation and expansion of the tiny unit, shear deformation and other viscous factors can be obtained. At the same time, by integrating the specific area of space with the help of the dissipation function, the loss due to fluid viscosity in this area can be calculated. Then, divide the flow field area according to the different types of loss, and use the dissipation function to perform volume integration on this area, then you can distinguish and obtain the loss size caused by different areas and different loss types in the flow field. By comparing the loss size, the main loss source in the flow field can be obtained, which provides a theoretical basis for the subsequent disclosure of the cascade flow and flow control mechanism. Then, the difficulty of the problem is transformed into how to divide the cascade flow field area.

Past studies have shown that the loss in the channel of the compressor cascade is mainly the friction loss area near the wall and the secondary flow loss caused by the strong shear in the different vortex structures in the channel. Therefore, the present invention mainly aims at the compressor cascade. The inner vortex structure features divide the cascade flow channel area. The flow field area considered in the present invention is from the leading edge of the blade cascade to the position of 40% of the chord length behind the trailing edge. Because the area before the leading edge of the cascade is a steady flow section, the loss is relatively small, and the flow field in the area after 40% is seriously mixed, and each vortex system cannot be well identified. Therefore, the present invention only considers the 40° from the leading edge to the trailing edge % chord length of the flow field area.

The current common compressor cascade vortex structure model believes that the compressor cascade mainly includes leading edge horseshoe vortex, channel vortex, corner vortex on suction/pressure surface, concentrated shedding vortex on blade surface, and trailing edge shedding vortex. Considering that the horseshoe vortex only affects the leading edge area of the cascade, and the vortex structure is small, the influence of the horseshoe vortex is ignored in the division of the area affected by the vortex, that is, the channel vortex, the suction/pressure surface angular vortex, and the concentrated shedding of the blade surface The vortex structures of the vortex and the trailing edge shedding vortex divide the cascade flow path into the above-mentioned vortex-affected areas and other areas. At the same time, since there is also a large friction loss in the near-wall area near the hub of the cascade and the blade wall, it also needs to be separated. Finally, the flow field area is divided into the following areas: channel vortex area, suction/pressure surface angular vortex area, concentrated shedding vortex area, trailing edge shedding vortex area, near-wall friction loss area and other areas. The criteria for judging and distinguishing each region mainly include: the positive and negative axial vorticity, the position of each separation line and attachment line, and the wall distance. The characteristics of each region are as follows;

1. Channel vortex area: located in the entire channel, close to the end wall side, with the widest range of influence, the axial vorticity is negative, and its spanwise position can be roughly judged by the channel vortex separation line on the suction surface. For the introduction of the separation line and the attachment line below, I will not go into details here, and you can refer to the relevant literature of Alexander Hergt (Heydorn A, et al.Effects of Vortex Generator Application on the Performance of a Compressor Cascade[J].Journal of Turbomachinery,2012,135(2):021026.)

2. Near-wall friction loss area: located near the end wall and blade suction pressure surface, the wall distance is on the order of millimeters, which can be constrained by the wall distance, and the axis vorticity is positive. Therefore, the present invention considers that the region where the wall distance is less than a certain value and the vorticity is positive is the boundary layer region. (except the corner vortex area)

3. Angular vortex area on the suction/pressure surface: from the leading edge to the trailing edge of the cascade, limited to the junction of the suction/pressure surface and the end wall of the blade, from the leading edge of the cascade to the trailing edge within 40% of the chord length exist. The upper limit of its spanwise height can be judged by the separation line of the suction/pressure surface close to the trailing edge area, and the influence distance at the end wall can also be judged by the attachment line on the end wall. Axial vorticity is positive. In the region of 40% chord length from the trailing edge of the cascade to the rear of the trailing edge, due to the loss of the binding of the blade wall, the impact position will change, but the change is small. Since the angular vortex area and the boundary layer area in the region from the leading edge to the trailing edge of the cascade overlap, the influence of the boundary layer can be ignored in this area, and it is divided into the angular vortex area. Therefore, the present invention considers the region where the axial vorticity is positive in the corner region of the cascade and the extension of the corner region behind the trailing edge to be the corner region of the suction/pressure surface.

4. Concentrated shedding vortex area: in the area from the leading edge to the trailing edge of the cascade, after the separation line of the blade suction surface, close to the middle part of the blade in the span direction, and above the channel vortex, the axial vorticity is positive. From the trailing edge of the cascade to the 40% chord length region behind the trailing edge, its influence area gradually expands, spanwise above the trailing edge shedding vortex, and finally merges with the trailing edge shedding vortex. Therefore, the present invention considers the region where the axial vorticity is positive in the middle of the blade after the separation line of the blade suction surface and behind the blade trailing edge to be the concentrated shedding vortex region.

5. Trailing edge shedding vortex area: Located in the wake area behind the trailing edge, the spanwise position is located in the area where the axial vorticity is positive between the concentrated shedding vortex and the angular vortex.

6. Other areas: the area of 40% of the chord length from the leading edge to the rear of the trailing edge of the blade other than the areas described above.

Through the above analysis, the flow path of the cascade can be divided into the above 6 regions by the three indicators of the positive and negative axial vorticity, the position of each attachment line and separation line, and the wall distance. However, the vortex structure cannot be accurately distinguished only by the positive and negative values of the axial vorticity alone, that is, for example, in the boundary layer region, even if there is no obvious vortex structure in this region, it still has a certain axial vorticity. Therefore, in actual operation, the region cannot be divided solely by the positive or negative of the axial vorticity, but a threshold should be set to shield the interference of the region with a small vorticity. The threshold value can be set between 1% and 10% of the magnitude of the axial vorticity. For example, when the considered axial vorticity in the cascade passage of the compressor is between 10 ³ -10 ⁴ , the threshold may be set to be 100s ^-1 . That is, for the above analysis, the positive axial vorticity means that the axial vorticity is greater than 100s ^-1 , and the negative axial vorticity means that the axial vorticity is less than -100s ^-1 . Therefore, other regions include the regions where the vorticity moment confrontation in the flow field is less than 100s ^-1 . At the same time, due to the vorticity characteristics, in the region with a large vorticity, a vorticity compensation region with a different vorticity direction will be formed nearby, such as the negative vorticity region near the shear region of the pressure surface, and the corner vortex The vorticity is negative region and the vorticity is negative region near the concentrated shedding vortex after the trailing edge. The existence of the vortex compensation area is also the reason why the vortex cannot accurately represent the actual position of the vortex, but the vortex can roughly reflect the distribution of the vortex. Since vortex does not necessarily exist in these vortex compensation areas, and because its influence range is small, these areas are combined into other areas.

With the help of the above area division criteria, the loss caused by various vortex clusters and boundary layers in the compressor cascade can be obtained through the integral calculation of dissipation in different areas, and by comparing the loss of each area Size, which is a measure of the main source of losses within the compressor cascade.

Figure 1 shows the contour map of the loss distribution of the compressor cascade and the 40% chord length after the trailing edge of the blade. Since the rectangular cascade is symmetrical along the 50% span direction, Fig. 1 only shows the cascade Half-height range, and the description of the cascade height below is for the half-height cascade, that is, the spanwise position range of the half-height cascade is 0-100% spanwise position .

Figure 2-4 shows the contour map and partition diagram of the axial vortex distribution of the equal axial section in the cascade passage of a certain compressor. Figure 2 is the section at 20% of the axial chord length of the cascade, Figure 3 is the section at 50% of the axial chord length, and Figure 4 is the section at 20% of the chord length behind the trailing edge. (Because the contours are dense, considering the clarity, the size data of the axial vorticity contours are not marked, and the positive and negative values of the values can be supplemented by the distribution cloud map of the axial vorticity)

From Fig. 2 and the corresponding axial vorticity distribution nephogram, it can be found that there is a large range of negative axial vorticity at the deflected end wall, that is, the channel vortex region. In the position where the wall distance is small, that is, there is a positive axial vorticity area close to the end wall and the blade suction surface, that is, the friction loss area near the wall surface, which is divided into three parts, namely, near the end wall, near the blade suction surface and the pressure surface area. There is a small positive vorticity area in the corner area, that is, the corner vortex area on the suction/pressure surface. There is no concentrated shedding vortex area and trailing edge shedding vortex area at this position. Figure 3 adds the concentrated shedding vortex area in the middle of the blade on the basis of Figure 2 . The corner vortex is constrained near the separation line and attachment line in the corner area, while the concentrated shedding vortex is located behind the separation line on the suction surface, and the spanwise position of the channel vortex is limited to the separation line of the channel vortex on the suction surface. In Fig. 4, the position of the concentrated shedding vortex rises upwards, and a new trailing edge shedding vortex area is generated between the concentrated shedding vortex and the corner vortex, and a vortex compensation area appears near the suction surface of the concentrated shedding vortex. In addition, the angular vortices on the suction pressure surface are merged into one angular vortex region in Fig. 4 . Therefore, it can be considered that the influence area of each vortex cluster can be roughly distinguished through the three indicators of the positive and negative axial vorticity, the position of each separation line and attachment line, and the distance from the wall surface in the above method.

After the area division is completed, it is necessary to perform loss integration on the divided areas to calculate the loss of each area. The integration method can directly use the CFD post-processing software to perform volume integration on the divided area. Since it is a routine operation, it will not be repeated here.

Example 1

In order to verify the practicability of the invention, for a certain high-load axial flow compressor cascade, aiming at its +5 degree angle of attack, the method is applied to solve the loss in the cascade, and the structure finds the loss in each region The integral size is shown in Table 1 below.

It can be found from the analysis that since the channel vortex occupies the largest volume, its corresponding loss percentage is also the largest. Therefore, for the cascade, the channel vortex is the source of its loss. To improve the efficiency of the cascade, attention should be paid to suppressing Development of channel vortices within channels. Secondly, it can be found that although other regions occupy a larger volume ratio, the flow in this region is closer to the mainstream, so the corresponding loss is smaller, which is consistent with previous research conclusions.

Claims (1)

1. A compressor cascade loss calculation method, is characterized in that, comprises the following steps: Step 1: For the region between the starting point of the leading edge of the cascade and the end point of 40% of the chord length behind the trailing edge of the cascade, the vortex field area is calculated according to the positive and negative values of the axial vorticity, each separation line, the position of the attachment line, and the wall distance Divide into channel vortex area, suction/pressure surface angular vortex area, concentrated shedding vortex area, cascade trailing edge shedding vortex area, near-wall friction loss area and other areas. The division is defined as follows: Channel vortex area: located in the entire channel, close to the end wall, the axial vorticity is negative, and the spanwise height is between the end wall and the separation line of the channel vortex; Near-wall friction loss area: located at the end wall, where the suction surface of the blade is close to the wall, and where the pressure surface of the blade is close to the wall. The wall distance near the wall is on the order of millimeters, and the axis vorticity is positive; Angular vortex area on the suction/pressure surface: located at the junction of the blade suction/pressure surface and the end wall, the axial vorticity is positive; the spanwise height is between the end wall and the angular vortex separation line, and the circumferential area is from the blade root to the between the attachment lines of the angular vortex; Cascade trailing edge shedding vortex area: located in the wake area behind the cascade trailing edge, the spanwise position is located in the area where the axial vorticity is positive between the concentrated shedding vortex and the corner vortex; Concentrated shedding vortex area: in the region from the leading edge of the cascade to the trailing edge of the cascade, after the separation line of the suction surface of the blade, close to the middle part of the blade in the direction of the blade span, and above the channel vortex, the axial vorticity is positive; Other areas: 40% of the chord length from the leading edge of the blade to the trailing edge of the cascade except the areas described above set area; Step 2: Carry out loss integration for the regions divided in Step 1: Carry out the volume integral of the corresponding regions for the dissipation function, calculate the loss of each region, and obtain the loss generated by each vortex structure.