A method for determining the mid-camber line of a low-speed simulated blade profile

Abstract

The present invention provides a method for determining the camber line of a low-speed simulated blade profile, comprising the following steps: determining the average airflow angle of a low-speed blade profile at any axial position x; superimposing the derailment angle along the high-speed blade profile at any axial position x as the initial derailment angle and the average airflow angle of the low-speed blade profile at any axial position x, to obtain the preliminary camber line angle of each axial position of the low-speed blade profile; adjusting the preliminary camber line angle of each axial position of the low-speed blade profile according to a first convergence condition, to obtain the camber line angle of each axial position of the low-speed blade profile that reaches the first convergence condition; establishing a geometric blade profile according to the camber line angle of each axial position of the low-speed blade profile, obtaining the derailment angle of the low-speed blade profile by numerical simulation means, and judging whether the relative error between the derailment angle of the low-speed blade profile and the initial derailment angle reaches the second convergence condition. The present invention can quickly determine the camber line of a low-speed blade profile by using a calculation method using the average airflow angle.

Description

Technical Field

[0001] The invention relates to the technical field of impeller machinery, and in particular to a method for determining a mid-camber line of a low-speed simulated blade profile. Background Art

[0002] Low-speed simulation test is a test technology that uses low-speed flow to simulate high-speed flow. In current low-speed simulation tests, most of the design parameters including the median arc line, maximum thickness, and leading edge shape are adjusted based on the experience of designers through numerical simulation software. In low-speed simulation tests, the high-speed blade profile and low-speed blade profile flows are required to be similar, so the loading law determined by the median arc line should also have a corresponding physical correspondence. At present, the determination of design parameters for low-speed simulation tests usually relies on the experience of designers, and the corresponding relationship cannot be modeled, resulting in unclear iteration direction, a large number of iterations, and a large workload. Especially for the low-speed simulation of the compressor stage, which contains dozens of blade profiles, repeated iterations will take up a lot of time for designers. Summary of the invention

[0003] In view of the shortcomings of the prior art, the present invention provides a method for determining the mid-arc line of a low-speed simulated blade profile. By utilizing the calculation method of the average airflow angle, the mid-arc line of the low-speed blade profile can be quickly determined, avoiding excessive manual intervention and saving computing and labor costs.

[0004] The present invention achieves the above technical objectives through the following technical means.

[0005] A method for determining a low-speed simulated blade profile mid-camber line comprises the following steps:

[0006] S01: Determine the total pressure loss coefficient ω along the high-speed blade at any axial position x according to the high-speed blade x and the static pressure lift coefficient Cp of the high-speed blade along the path at any axial position x x ;

[0007] S02: Determine the average airflow angle α of the low-speed blade at any axial position x according to the following formula x , the formula is as follows:

[0008]

[0009] Where:

[0010] α x is the average airflow angle of the low-speed blade at any axial position x;

[0011] α1 is the average airflow angle at the inlet of the low-speed blade;

[0012] s xis the circumferential width of the low-speed blade at any axial position x, obtained by superimposing the thickness distribution of the initial low-speed blade mid-arc;

[0013] s1 is the circumferential width of the blade at the inlet of the low-speed blade profile;

[0014] S03: Determine the derailment angle Δγ along the path at any axial position x according to the high-speed blade profile x , the derailment angle Δγ of the high-speed blade at any axial position x x As the initial derailment angle and the average airflow angle α of the low-speed blade at any axial position x x Add them together to get the preliminary camber angle of each axial position of the low-speed blade;

[0015] S04: adjusting the preliminary camber angles at each axial position of the low-speed blade profile according to the first convergence condition, to obtain the camber angles at each axial position of the low-speed blade profile that meets the first convergence condition;

[0016] S05: Establish a geometric blade profile according to the mid-arc angles of each axial position of the low-speed blade profile, obtain the derailment angle of the low-speed blade profile by means of numerical simulation, and judge whether the relative error between the derailment angle of the low-speed blade profile and the initial derailment angle meets the second convergence condition: if the second convergence condition is not met, the initial derailment angle in S03 is replaced by the derailment angle of the low-speed blade profile, and return to S03 until the second convergence condition is met; if the second convergence condition is met, the mid-arc angles of each axial position of the low-speed blade profile obtained in S04 are used as the final mid-arc angles of each axial position of the low-speed blade profile.

[0017] Further, the specific adjustments in S04 are as follows:

[0018] Establish a preliminary low-speed blade profile based on the preliminary mid-camber angles at each axial position of the low-speed blade profile, and recalculate s x , determine the recalculated s x Compared with the previous calculation s x Whether the relative error of meets the first convergence condition: If not, s will be recalculated x Replace the s in S02 x , return to S02 until the first convergence condition is reached; if the first convergence condition is reached, the mid-camber angles of the low-speed blade profiles at each axial position that reaches the first convergence condition are obtained.

[0019] Furthermore, the first convergence condition is that the recalculated s x Compared with the previous calculation s x The relative error is less than 0.01%.

[0020] Furthermore, the second convergence condition is the derailment angle of the low-speed blade and the derailment angle Δγ along the high-speed blade at any axial position x xThe relative error is less than 0.01%.

[0021] A low-speed simulated blade profile is designed using a method for determining a mid-camber line of a low-speed simulated blade profile.

[0022] The beneficial effects of the present invention are:

[0023] 1. The method for determining the mean camber line of the low-speed simulated blade profile of the present invention can quickly determine the mean camber line of the low-speed blade profile through the calculation method of the average airflow angle, avoiding excessive manual intervention and saving calculation cost and labor cost. Taking a first-stage compressor (including a rotor and a stator) as an example, it is generally necessary to perform a low-speed simulation design of 20 primitive blade profiles, which previously took 2-3 days of manual iteration to complete. The present invention can shorten the design time by about 80%.

[0024] 2. The method for determining the mid-arc line of a low-speed simulated blade described in the present invention can obtain a mid-arc line that meets the design requirements by adjusting the mid-arc line angles of each axial position of the low-speed blade through the first convergence condition and the second convergence condition. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0026] Figure 1 The present invention is a flow chart of the method for determining the mid-camber line of a low-speed simulated blade profile.

[0027] Figure 2 Dimensionless bending angle distribution diagram of high and low speed blade profiles in an embodiment of the present invention.

[0028] Figure 3 It is a dimensionless velocity comparison diagram of the high and low speed blade profiles and blade surfaces in an embodiment of the present invention.

[0029] Figure 4 It is a comparison diagram of the high and low speed blade angle of attack-total pressure loss characteristics in an embodiment of the present invention.

[0030] Figure 5 Schematic diagram of the blade profile in an embodiment of the present invention. DETAILED DESCRIPTION

[0031] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments, but the protection scope of the present invention is not limited thereto.

[0032] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0033] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "axial", "radial", "vertical", "horizontal", "inner", "outer" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first" and "second" are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "multiple" is two or more, unless otherwise clearly and specifically defined.

[0034] In the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be an indirect connection through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0035] like Figure 1 As shown, the method for determining the camber line of a low-speed simulated blade profile according to the present invention comprises the following steps:

[0036] S01: Determine the total pressure loss coefficient ω along the high-speed blade at any axial position x according to the high-speed blade x and the static pressure rise coefficient Cp along the high-speed blade at any axial position x x ;

[0037] S02: Determine the average airflow angle α of the low-speed blade at any axial position x according to the following formula x , the calculation process is as follows:

[0038] The low-speed blade flow is generally incompressible. According to the flow balance equation, for any axial position x,

[0039] v1s1cosα1=v x s x cosα x (1)

[0040] in:

[0041] v1 is the speed at the inlet of the low-speed blade;

[0042] v x represents the velocity at any axial position x;

[0043] α1 is the average airflow angle at the inlet of the low-speed blade;

[0044] α x is the average airflow angle of the low-speed blade at any axial position x;

[0045] s1 is the circumferential width of the blade at the inlet of the low-speed blade profile;

[0046] s x is the circumferential width of the low-speed blade at any axial position x, such as Figure 5 shown.

[0047] The static pressure rise coefficient along the high-speed blade at any axial position x can be expressed as:

[0048]

[0049] Where P represents the static pressure rise, ρ represents the gas density, P x is the static pressure rise at any axial position x, and P1 is the static pressure rise of the blade at the inlet. The low-speed simulation process implicitly contains the constraint of keeping the total pressure loss coefficient of the high-speed and low-speed blades the same. Therefore, according to the incompressible energy equation, we have:

[0050]

[0051] Among them, P1 * is the total pressure of the blade at the inlet, ω x is the total pressure loss coefficient along the process, and when it is substituted into formula (2), we have

[0052]

[0053] Combined with formula (1), the average airflow angle α of the low-speed blade at any axial position x can be obtained: x The satisfied relationship is:

[0054]

[0055] Among them, Cp xIt can be obtained from the high-speed blade profile, and α1 is obtained by the low-speed simulation design criterion constraint; the initial low-speed blade profile mid-camber is determined by the dimensionless bending angle distribution of the high-speed blade profile, and s is obtained by superimposing the initial low-speed blade profile mid-camber thickness distribution. x ,ω x From the high-speed blade profile, these four parameters are all known quantities, so α can be calculated x .

[0056] S03: Determine the derailment angle Δγ along the path at any axial position x according to the high-speed blade profile x , the derailment angle Δγ of the high-speed blade at any axial position x x As the initial derailment angle and the average airflow angle α of the low-speed blade at any axial position x x Add together to get the initial camber angle of each axial position of the low-speed blade, that is, the initial camber angle of each axial position of the low-speed blade = Δγ x +α x ;

[0057] S04: adjusting the preliminary camber angles of each axial position of the low-speed blade according to the first convergence condition, and obtaining the camber angles of each axial position of the low-speed blade that meets the first convergence condition; the specific adjustment is as follows: establishing a preliminary low-speed blade according to the preliminary camber angles of each axial position of the low-speed blade, and recalculating s x , determine the recalculated s x Compared with the previous calculation s x Whether the relative error of meets the first convergence condition: If not, s will be recalculated x Replace the s in S02 x , return to S02 until the first convergence condition is reached; if the first convergence condition is reached, the mid-camber angles of the low-speed blade profiles at each axial position that reaches the first convergence condition are obtained.

[0058] S05: Establish a geometric blade profile according to the mid-arc line angles at each axial position of the low-speed blade profile, obtain the derailment angle of the low-speed blade profile by means of numerical simulation, and judge whether the relative error between the derailment angle of the low-speed blade profile and the initial derailment angle meets the second convergence condition: if the second convergence condition is not met, the initial derailment angle in S03 is replaced by the derailment angle of the low-speed blade profile obtained, and return to S03 until the second convergence condition is met; if the second convergence condition is met, the mid-arc line angles at each axial position of the low-speed blade profile obtained in S04 are used as the final mid-arc line angles at each axial position of the low-speed blade profile, and the mid-arc line of the low-speed blade profile can be obtained through the mid-arc line angles at each axial position of the low-speed blade profile.

[0059] Example

[0060] A high-speed blade profile of a high-pressure compressor is selected, and the parameters are shown in Table 1. The dimensionless bending angle distribution of the mid-camber line of the blade profile is as follows: Figure 2 As shown, the mid-camber line is a typical front-loaded blade shape.

[0061] Table 1 Comparison of high-speed blade profile and low-speed simulated blade profile parameters

[0062] Leaf Type High speed cascade Low speed cascade Chord length / m 0.04386 0.13815 Entrance 0.5 0.15 Import geometry angle 66.6 68.0 Exit geometry 45.6 42.7 Consistency 1.14689 1.14689 Aspect ratio 3 3

[0063] S01: The characteristic line of the high-speed blade and the dimensionless velocity distribution on the blade surface at the reference angle of attack are calculated using numerical simulation software. The static pressure rise, total pressure loss and along-the-path distribution of the high-speed blade are extracted, and the derailment angle is used as the initial derailment angle.

[0064] S02: Determine the average airflow angle α of the low-speed blade at any axial position x according to the following formula x , the formula is as follows:

[0065]

[0066] Where:

[0067] α x is the average airflow angle of the low-speed blade at any axial position x;

[0068] α1 is the average airflow angle at the inlet of the low-speed blade;

[0069] s x is the circumferential width of the low-speed blade at any axial position x, obtained by superimposing the thickness distribution of the initial low-speed blade mid-arc;

[0070] s1 is the circumferential width of the blade at the inlet of the low-speed blade profile;

[0071] S03: Determine the derailment angle Δγ along the path at any axial position x according to the high-speed blade profile x , the derailment angle Δγ of the high-speed blade at any axial position x x The average airflow angle α with the low-speed blade at any axial position x x By superposition, the preliminary camber angle of each axial position of the low-speed blade is obtained;

[0072] S04: Establish a preliminary low-speed blade profile based on the preliminary mid-camber angles of each axial position of the low-speed blade profile, obtain the initial low-speed blade profile mid-camber, and recalculate s based on blade profile parameters such as blade profile thickness distribution. x , iterate to twice s x The relative error is 0.01%, that is, the mid-arc angle of each axial position of the low-speed blade profile that meets the first convergence condition is obtained; in this process, all calculations are performed by program without complex calculations, and the convergence time is less than 1 second.

[0073] S05: Establish a geometric blade profile according to the mid-camber angle of each axial position of the low-speed blade profile, calculate the flow field information of the low-speed blade profile using numerical simulation software, extract the derailment angle of the low-speed blade profile, and determine whether the relative error between the derailment angle of the low-speed blade profile and the initial derailment angle is less than 0.01%: if not less than 0.01%, replace the initial derailment angle in S03 with the derailment angle of the obtained low-speed blade profile, return to S03 until it is less than 0.01%, and then obtain the mid-camber angle of each axial position of the low-speed blade profile. In the embodiment, this process takes about 3-5 iterations to complete.

[0074] The dimensionless bending angle distribution of the mid-arc obtained by the two convergence conditions is as follows: Figure 2 As shown in the figure, compared with the high-speed blade, the front loading degree is enhanced. The final blade is calculated using numerical simulation software, and the angle of attack-loss characteristics of the low-speed simulated blade and the dimensionless velocity distribution of the blade surface at the reference angle of attack are extracted. The dimensionless velocity distribution of the blade surface at the reference state of the high-speed and low-speed blade is compared. Figure 3 As shown, the angle of attack-total pressure loss characteristics are as follows Figure 4 As shown in the figure, the dimensionless velocity distribution of the blade surface is consistent and the total pressure loss is basically the same at the positive angle of attack, indicating that the low-speed blade profile determined by the method for determining the camber line of the low-speed simulated blade profile described in the present invention simulates the high-speed blade well. The iterative process of the present invention greatly saves time compared to the original manual iteration.

[0075] It should be understood that although this specification is described according to various embodiments, not every embodiment contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

[0076] The series of detailed descriptions listed above are only specific descriptions of feasible embodiments of the present invention. They are not intended to limit the scope of protection of the present invention. All equivalent embodiments or changes that do not deviate from the technical spirit of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for determining the mid-camber line of a low-speed simulated blade profile, characterized in that: The steps include: S01: Determine the total pressure loss coefficient ω along the high-speed blade at any axial position x according to the high-speed blade x and the static pressure rise coefficient Cp along the high-speed blade at any axial position x x ; S02: Determine the average airflow angle α of the low-speed blade at any axial position x according to the following formula x , the formula is as follows: Where: α x is the average airflow angle of the low-speed blade at any axial position x; α1 is the average airflow angle at the inlet of the low-speed blade; s x is the circumferential width of the low-speed blade at any axial position x. The initial low-speed blade mid-camber is determined by the dimensionless bending angle distribution of the high-speed blade. The initial low-speed blade mid-camber superimposed thickness distribution is used to obtain s x ; s1 is the circumferential width of the blade at the inlet of the low-speed blade profile; S03: Determine the derailment angle Δγ along the path at any axial position x according to the high-speed blade profile x , the derailment angle Δγ of the high-speed blade at any axial position x x As the initial derailment angle and the average airflow angle α of the low-speed blade at any axial position x x Add them together to get the preliminary camber angle of each axial position of the low-speed blade; S04: adjusting the preliminary camber angles at each axial position of the low-speed blade profile according to the first convergence condition, to obtain the camber angles at each axial position of the low-speed blade profile that meets the first convergence condition; S05: Establish a geometric blade profile according to the mid-camber angles of each axial position of the low-speed blade profile, obtain the derailment angle of the low-speed blade profile by means of numerical simulation, and judge whether the relative error between the derailment angle of the low-speed blade profile and the initial derailment angle meets the second convergence condition: if the second convergence condition is not met, replace the initial derailment angle in S03 with the obtained derailment angle of the low-speed blade profile, and return to S03 until the second convergence condition is met; If the second convergence condition is met, the camber line angles at each axial position of the low-speed blade obtained in S04 are used as the final camber line angles at each axial position of the low-speed blade.

2. The method for determining the mean camber line of a low-speed simulated blade profile according to claim 1, characterized in that: The specific adjustments in S04 are as follows: Establish a preliminary low-speed blade profile based on the preliminary mid-camber angles at each axial position of the low-speed blade profile, and recalculate s x , determine the recalculated s x Compared with the previous calculation s x Whether the relative error of meets the first convergence condition: If not, the recalculated s x Replace the s in S02 x , return to S02 until the first convergence condition is reached; if the first convergence condition is reached, the mid-camber angles of the low-speed blade profiles at each axial position that reaches the first convergence condition are obtained.

3. The method for determining the mean camber line of a low-speed simulated blade profile according to claim 2, characterized in that: The first convergence condition is the recalculated s x Compared with the previous calculation s x The relative error is less than 0.01%.

4. The method for determining the mean camber line of a low-speed simulated blade profile according to claim 1, characterized in that: The second convergence condition is that the relative error between the derailment angle of the low-speed blade profile and the initial derailment angle is less than 0.01%.

5. A low-speed simulated blade profile, characterized in that: A low-speed simulated blade profile designed using the method for determining the mid-camber line of a low-speed simulated blade profile as described in any one of claims 1 to 4.

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