CN108533525B - Calculation method of enthalpy rise coefficient of pre-swirling air intake of centrifugal impeller based on maximum flow coefficient - Google Patents

Abstract

A calculation method of pre-swirling air enthalpy coefficient of centrifugal impeller based on the maximum flow coefficient: determine the design requirements of the centrifugal impeller; given the characteristic constant of the fluid medium and the geometric constant of the centrifugal impeller; calculate the outlet tangential velocity ratio of the centrifugal impeller; Set the initial enthalpy coefficient; calculate the Mach number of the machine; set the initial relative Mach number of the centrifugal impeller inlet cover; calculate the relative axial flow angle of the centrifugal impeller inlet cover; calculate the relative Mach number of the centrifugal impeller inlet cover; judge the centrifugal impeller inlet Whether the relative error between the relative Mach number of the wheel cover and the set initial centrifugal impeller inlet wheel cover relative Mach number is less than the set value; calculate the ratio of the diameter of the centrifugal impeller inlet wheel cover to the centrifugal impeller outlet diameter; calculate the enthalpy coefficient; judge the enthalpy Whether the relative error between the coefficient and the set initial enthalpy rise coefficient is smaller than the set value. The invention can accurately and quickly calculate the enthalpy rise coefficient of the large-flow centrifugal impeller under any pre-swirl inlet angle, and the produced centrifugal impeller has large flow and compact structure.

Description

Calculation method of enthalpy rise coefficient of pre-swirling air intake of centrifugal impeller based on maximum flow coefficient

technical field

The invention relates to a method for calculating the enthalpy-rise coefficient of an arbitrary pre-rotation inlet angle of a centrifugal impeller. In particular, it relates to a method for calculating the enthalpy rise coefficient of the pre-swirled air of a centrifugal impeller based on the maximum flow coefficient.

Background technique

Centrifugal compressors are widely used in aero-engines, ground gas turbines, automobile and ship turbochargers, petrochemical compressors, and play an irreplaceable role in the fields of national defense and civil industry. Centrifugal impeller is the core component of centrifugal compressor, and its accurate thermodynamic calculation and design method is a key technology. Accurate calculation of centrifugal impeller enthalpy coefficient is the basis for breaking through this key technology. For a centrifugal impeller with a given machine Mach number, there is a quantitative relationship between the enthalpy rise coefficient and the total pressure ratio and isentropic efficiency. Accurate estimation of the enthalpy rise coefficient is crucial to the design of the centrifugal impeller. At present, in most thermal calculations and designs of centrifugal impellers, the enthalpy rise coefficient is specified as a constant, or only the geometric influence of the impeller outlet (slip factor) is considered, which leads to a large deviation between the calculated enthalpy rise coefficient and the actual value. Moreover, the existing studies only focus on the condition of axial intake, without considering any pre-swirl intake, and the influence of geometric constraints on the enthalpy rise coefficient is also not considered. In fact, for a given impeller speed, it is mainly determined by the geometry of the impeller outlet (blade sweep angle, etc.) under the condition of axial intake, and it is also related to the geometry of the impeller inlet (blade leading edge shape factor, aerodynamic throat area, etc.). Therefore, a method for calculating the enthalpy-rise coefficient that fully considers various influencing factors is proposed. Obtaining an accurate enthalpy-rise coefficient is an urgent task in the thermodynamic calculation and design technology of centrifugal impellers.

Contents of the invention

The technical problem to be solved by the present invention is to provide a method for calculating the thermal properties of the centrifugal impeller (isentropic efficiency, total pressure ratio, etc.) .

The technical solution adopted in the present invention is: a method for calculating the enthalpy rise coefficient of the pre-rotation air intake of the centrifugal impeller based on the maximum flow coefficient, comprising the following steps:

1) Determine the design requirements of the centrifugal impeller, including: isentropic efficiency η, total pressure ratio ε, flow coefficient φ;

2) The characteristic constants of the fluid medium and the geometric constants of the centrifugal impeller are given respectively;

3) Calculate the outlet tangential velocity ratio of the centrifugal impeller

4) Set the initial enthalpy rise coefficient μ ₀ ;

5) Calculate the Mach number M _u2 of the machine;

6) Set the relative Mach number M _w1,0 of the initial centrifugal impeller inlet cover;

7) Calculate the relative axial flow angle β _1s of the centrifugal impeller inlet wheel cover;

8) Calculate the relative Mach number M _w1 of the centrifugal impeller inlet wheel cover;

9) Determine whether the relative error between the relative Mach number _{Mw1 of the centrifugal impeller inlet wheel cover and the set initial centrifugal impeller inlet wheel cover relative Mach number Mw1,0 is} less than 1%, if yes, execute the next step, otherwise return to step 6), Use the dichotomy method to reset the relative Mach number M _w1,0 of the initial centrifugal impeller inlet cover;

10) Calculate the ratio of the centrifugal impeller inlet wheel cover diameter D _1s to the centrifugal impeller outlet diameter D ₂ :

11) Calculate the enthalpy coefficient μ;

12) Determine whether the relative error between the enthalpy rise coefficient μ and the set initial enthalpy rise coefficient μ ₀ is less than 1%, if yes, μ is the desired enthalpy rise coefficient, and end; otherwise return to step 4) adopt the dichotomy method to reset the initial enthalpy Lifting coefficient μ ₀ .

Step 2) The characteristic constants of the fluid medium are: gas constant R and adiabatic index γ; the geometric constants of the centrifugal impeller; including: shape factor k, centrifugal impeller outlet radial velocity ratio Radial flow angle β ₂ at the outlet of the centrifugal impeller, pre-rotation angle α ₁ at the inlet of the centrifugal impeller, number of blades z, and specific enthalpy ratio σ.

The formula for calculating the shape factor k is: Among them, D _1h is the diameter of the centrifugal impeller inlet hub, and D _1s is the diameter of the centrifugal impeller inlet hub.

The formula for calculating the specific enthalpy ratio σ is: Among them, h _tot is the total work of the centrifugal impeller, and h _th is the work of the rim of the centrifugal impeller.

Step 3) is to calculate the outlet tangential velocity ratio of the centrifugal impeller using the Stodola formula as follows:

In the formula, is the radial velocity ratio at the exit of the centrifugal impeller, and _β2 is the radial airflow angle at the exit of the centrifugal impeller.

Step 5) is to use the following formula to calculate the Mach number M _u2 of the machine:

In the formula, γ is the adiabatic exponent, η is the isentropic efficiency, ε is the total pressure ratio, and μ ₀ is the initial enthalpy rise coefficient.

Step 7) is to use the following formula to calculate the relative axial flow angle β _1s of the centrifugal impeller inlet wheel cover

In the formula, α ₁ is the pre-rotation angle of the centrifugal impeller inlet, M _w1,0 is the relative Mach number of the initial centrifugal impeller inlet cover, and γ is the adiabatic index.

Step 8) is to use the following formula to calculate the relative Mach number M _w1 of the centrifugal impeller inlet wheel cover

In the formula, M _u2 is the Mach number of the machine, γ is the adiabatic index, M _w1,0 is the relative Mach number of the initial centrifugal impeller inlet cover, β _1s is the relative axial flow angle of the centrifugal impeller inlet cover, and α ₁ is the centrifugal impeller inlet Pre-rotation angle, k is the shape factor, φ is the flow coefficient.

Step 10) The ratio of the diameter of the centrifugal impeller inlet wheel cover to the diameter of the centrifugal impeller outlet is as follows:

In the formula, _Mw1 is the relative Mach number of the centrifugal impeller inlet cover, _β1s is the relative axial flow angle _of the centrifugal impeller inlet cover, α1 is the pre-rotation angle of the centrifugal impeller inlet, η is the isentropic efficiency, and _μ0 is the initial enthalpy Lift coefficient, γ is the adiabatic index, and ε is the total pressure ratio.

Step 11) is to adopt the following formula to calculate the enthalpy coefficient μ

where σ is the specific enthalpy ratio, is the outlet tangential velocity ratio of the centrifugal impeller, γ is the adiabatic index, M _w1 is the relative Mach number of the centrifugal impeller inlet cover, β _1s is the relative axial flow angle of the centrifugal impeller inlet cover, and α ₁ is the centrifugal impeller inlet pre-rotation angle , k is the shape factor, is the ratio of the diameter of the centrifugal impeller inlet wheel cover to the diameter of the centrifugal impeller outlet, and M _u2 is the Mach number of the machine.

The method for calculating the enthalpy-rise coefficient of pre-swirling air intake of the centrifugal impeller based on the maximum flow coefficient of the present invention considers any pre-swirling intake angle, and popularizes the traditional method that only includes axial air intake; at the same time, the method of the present invention includes the maximum flow rate Coefficient assumptions, the designed centrifugal impeller has the advantages of large flow and compact structure; the calculation expressions are all dimensionless and universal. The beneficial effect produced by the method of the present invention is that the enthalpy rise coefficient of the large-flow centrifugal impeller under any pre-swirl inlet angle can be accurately and quickly calculated, which lays a foundation for the evaluation of the performance of the existing impeller or the development of a new impeller.

Detailed ways

The method for calculating the pre-rotation enthalpy rise coefficient of the centrifugal impeller based on the maximum flow coefficient of the present invention will be described in detail below in conjunction with the embodiments. It should be noted that this embodiment is descriptive and does not limit the protection scope of the present invention.

The method for calculating the enthalpy-rise coefficient of pre-swirling intake air of the centrifugal impeller based on the maximum flow coefficient of the present invention considers any pre-swirl intake angle, introduces the design concept of the maximum flow coefficient, and provides a calculation method of the enthalpy-rise coefficient in a dimensionless form; finally according to Centrifugal impeller design conditions, given the specific steps of calculation of enthalpy coefficient.

The method for calculating the enthalpy rise coefficient of pre-swirled intake air of the centrifugal impeller based on the maximum flow coefficient of the present invention specifically includes the following steps:

1) Determine the design requirements of the centrifugal impeller, including: isentropic efficiency η, total pressure ratio ε, flow coefficient φ;

2) The characteristic constants of the fluid medium and the geometric constants of the centrifugal impeller are respectively given; where,

The characteristic constants of the fluid medium are: gas constant R and adiabatic index γ; the geometric constants of the centrifugal impeller; including: shape factor k, centrifugal impeller outlet radial velocity ratio Radial flow angle β ₂ at the outlet of the centrifugal impeller, pre-rotation angle α ₁ at the inlet of the centrifugal impeller, number of blades z, and specific enthalpy ratio σ.

The formula for calculating the shape factor k is: Among them, D _1h is the diameter of the centrifugal impeller inlet hub, and D _1s is the diameter of the centrifugal impeller inlet hub.

The formula for calculating the specific enthalpy ratio σ is: Among them, h _tot is the total work of the centrifugal impeller, and h _th is the work of the rim of the centrifugal impeller.

3) Calculate the outlet tangential velocity ratio of the centrifugal impeller is to use the Stodola formula to calculate the outlet tangential velocity ratio of the centrifugal impeller as follows:

In the formula, is the radial velocity ratio at the exit of the centrifugal impeller, and _β2 is the radial airflow angle at the exit of the centrifugal impeller.

4) Set the initial enthalpy rise coefficient μ ₀ ;

5) Calculate the Mach number M _u2 of the machine; the following formula is used to calculate the Mach number M _u2 of the machine:

In the formula, γ is the adiabatic exponent, η is the isentropic efficiency, ε is the total pressure ratio, and μ ₀ is the initial enthalpy rise coefficient.

6) Set the relative Mach number M _w1,0 of the initial centrifugal impeller inlet cover;

7) Calculate the relative axial flow angle β _1s of the centrifugal impeller inlet wheel cover; it is the best β _1s obtained based on the assumption of the maximum flow coefficient; specifically, the following formula is used to calculate the relative axial flow angle β _1s of the centrifugal impeller inlet wheel cover, which is Implicit format, using iterative evaluation:

In the formula, α ₁ is the pre-rotation angle of the centrifugal impeller inlet, M _w1,0 is the relative Mach number of the initial centrifugal impeller inlet cover, and γ is the adiabatic index.

8) Calculate the relative Mach number M _w1 of the centrifugal impeller inlet wheel cover; the relative Mach number M _w1 of the centrifugal impeller inlet wheel cover is calculated by the following formula:

In the formula, M _u2 is the Mach number of the machine, γ is the adiabatic index, M _w1,0 is the relative Mach number of the initial centrifugal impeller inlet cover, β _1s is the relative axial flow angle of the centrifugal impeller inlet cover, and α ₁ is the centrifugal impeller inlet Pre-rotation angle, k is the shape factor, φ is the flow coefficient.

9) Determine whether the relative error between the relative Mach number _Mw1 of the inlet wheel cover of the centrifugal impeller and the set initial Mach number _Mw1,0 of the inlet wheel cover of the centrifugal impeller is less than 1%. The dichotomy resets the relative Mach number M _w1,0 of the initial centrifugal impeller inlet cover;

10) Calculate the ratio of the centrifugal impeller inlet wheel cover diameter D _1s to the centrifugal impeller outlet diameter D ₂ : The ratio of the centrifugal impeller inlet wheel cover diameter to the centrifugal impeller outlet diameter is as follows:

In the formula, _Mw1 is the relative Mach number of the centrifugal impeller inlet cover, _β1s is the relative axial flow angle _of the centrifugal impeller inlet cover, α1 is the pre-rotation angle of the centrifugal impeller inlet, η is the isentropic efficiency, and _μ0 is the initial enthalpy Lift coefficient, γ is the adiabatic index, and ε is the total pressure ratio.

11) Calculate the enthalpy rise coefficient μ; the following formula is used to calculate the enthalpy rise coefficient μ

12) Determine whether the relative error between the enthalpy rise coefficient μ and the set initial enthalpy rise coefficient μ ₀ is less than 1%, if yes, μ is the desired enthalpy rise coefficient, and end; otherwise return to step 4) adopt the dichotomy method to reset the initial enthalpy Lifting coefficient μ ₀ .

Specific examples are given below:

This example demonstrates the method of calculating the enthalpy coefficient in combination with the design process of an industrial transonic centrifugal impeller, wherein It is calculated according to the Stodola formula, that is, formula (1). The enthalpy coefficient is calculated by the following 12 steps:

1) Determine the design requirements of the centrifugal impeller: isentropic efficiency η = 0.87, total pressure ratio ε = 6, flow coefficient φ = 0.15

2) given constant k=0.85, R=287, γ=1.4, β ₂ =38, z=13, σ=1.07, α ₁ =30deg

3) Calculate according to formula (1)

4) Assume that the initial enthalpy rise coefficient μ ₀ =0.7

5) Calculate the Mach number M _u2 of the machine according to formula (2) = 1.65659

6) Suppose the initial M _w1,0 = 1.1

7) Calculate β _1s according to formula (3), the final result β _1s =45.33

8) Calculate M _w1 according to formula (4), and the final result M _w1 = 1.204528

9) Check M _w1 , and execute the next step if the iteration accuracy is satisfied, otherwise return 6) Correct M _w1,0

10) Calculate according to formula (5) final result

11) Calculate the enthalpy coefficient μ according to formula (6), and the final result μ=0.541745

12) Check the enthalpy rise coefficient μ, if it satisfies the iteration precision, the calculation is completed, otherwise return to 4) Correct μ ₀ .

So far, the maximum flow coefficient design centrifugal impeller arbitrary pre-rotation inlet angle enthalpy coefficient has been calculated, which can be used as the basis for the thermal calculation or new design of the centrifugal impeller.

Claims (10)

1. A centrifugal impeller pre-rotation air inlet enthalpy rising coefficient calculation method based on a maximum flow coefficient is characterized by comprising the following steps:

1) determining design requirements for a centrifugal impeller comprising: the isentropic efficiency eta, the total pressure ratio epsilon and the flow coefficient phi;

2) respectively setting a characteristic constant of the fluid medium and a geometric constant of the centrifugal impeller;

3) calculating the outlet tangential velocity ratio of a centrifugal impeller

4) Setting initial enthalpy rise coefficient mu₀；

5) Computing machine Mach number M_u2；

6) Setting relative Mach number M of inlet shroud of initial centrifugal impeller_w1,0；

7) Calculating the relative axial airflow angle beta of the inlet wheel cover of the centrifugal impeller_1s；

8) Calculating relative Mach number M of inlet wheel cover of centrifugal impeller_w1；

9) Judging relative Mach number M of inlet wheel cover of centrifugal impeller_w1Relative Mach number M of inlet shroud of initial centrifugal impeller set_w1,0If the relative error is less than 1%, executing the next step, otherwise, returning to the step 6), and resetting the initial centrifugal impeller by adopting a dichotomyRelative mach number M of port wheel cover_w1,0；

10) Calculating the diameter D of the inlet wheel cover of the centrifugal impeller_1sAnd diameter D of centrifugal impeller outlet₂The ratio of (A) to (B):

11) calculating an enthalpy rise coefficient mu;

12) judging the enthalpy rise coefficient mu and the set initial enthalpy rise coefficient mu₀If the relative error is less than 1%, if so, mu is the enthalpy rise coefficient to be obtained, and ending; otherwise, returning to the step 4) and resetting the initial enthalpy rise coefficient mu by adopting a dichotomy₀。

2. The method for calculating the enthalpy rise coefficient of pre-swirl intake air of a centrifugal impeller based on the maximum flow coefficient according to claim 1, wherein the characteristic constants of the fluid medium in step 2) are: a gas constant R and an adiabatic index γ; the geometric constant of the centrifugal impeller; the method comprises the following steps: shape factor k, centrifugal impeller exit radial velocity ratioRadial air flow angle beta at centrifugal impeller outlet₂Inlet prerotation angle alpha of centrifugal impeller₁The number of blades z, and the specific enthalpy ratio σ.

3. The method for calculating the enthalpy rise coefficient of pre-swirl intake air of a centrifugal impeller based on the maximum flow coefficient of claim 2, wherein the shape factor k is calculated by the following formula:wherein D is_1hIs the diameter of the inlet hub of the centrifugal impeller, D_1sIs the diameter of the inlet shroud of the centrifugal impeller.

4. The method for calculating the enthalpy-rise coefficient of pre-swirl intake air of a centrifugal impeller based on the maximum flow coefficient of claim 2, wherein the specific enthalpy ratio σ isThe calculation formula is as follows:wherein h is_totIs the total work of the centrifugal impeller, h_thIs the rim work of the centrifugal impeller.

5. The method for calculating the enthalpy rise coefficient of pre-swirl intake air of a centrifugal impeller based on the maximum flow coefficient of claim 1, wherein the step 3) is to calculate the outlet tangential velocity ratio of the centrifugal impeller by using the Strorado formulaThe following were used:

in the formula,is the radial velocity ratio, beta, of the centrifugal impeller outlet₂Is the centrifugal impeller exit radial airflow angle and z is the number of blades.

6. The method for calculating the enthalpy-rise coefficient of pre-whirling intake air of the centrifugal impeller according to claim 1, wherein the step 5) is to calculate the Mach number M of the machine by using the following formula_u2：

Where γ is the adiabatic index, η is the isentropic efficiency, ε is the total pressure ratio, μ₀Is the initial enthalpy rise coefficient.

7. The method for calculating the enthalpy-rise coefficient of pre-swirl inlet air of a centrifugal impeller according to claim 1, wherein step 7) is to calculate the relative axial air of the inlet shroud of the centrifugal impeller by using the following formulaFlow angle beta_1s

In the formula, alpha₁Is the inlet prerotation angle of centrifugal impeller, M_w1,0Is the relative mach number of the inlet shroud of the initial centrifugal impeller and gamma is the adiabatic index.

8. The method for calculating the enthalpy-rise coefficient of pre-swirl intake air of a centrifugal impeller according to claim 1, wherein the step 8) is to calculate the relative mach number M of the inlet shroud of the centrifugal impeller by using the following formula_w1

In the formula, M_u2Is the machine Mach number, gamma is the adiabatic index, M_w1,0Is the relative Mach number, beta, of the inlet shroud of the initial centrifugal impeller_1sIs the relative axial flow angle, alpha, of the inlet shroud of the centrifugal impeller₁Is the centrifugal impeller inlet prewhirl angle, k is the shape factor and phi is the flow coefficient.

9. The method for calculating the enthalpy rise coefficient of pre-swirl intake air of a centrifugal impeller according to claim 1, wherein the ratio of the diameter of the inlet shroud of the centrifugal impeller to the diameter of the outlet of the centrifugal impeller in step 10) is as follows:

in the formula, M_w1Is the relative Mach number, beta, of the inlet shroud of the centrifugal impeller_1sIs the relative axial flow angle, alpha, of the inlet shroud of the centrifugal impeller₁Is the prerotation angle of centrifugal impeller inlet, eta is the isentropic efficiency, mu₀Is the initial enthalpy rise coefficient, gamma is the adiabatic exponent, and epsilon is the total pressure ratio.

10. The method for calculating the enthalpy-rise coefficient of pre-swirl intake air of a centrifugal impeller based on the maximum flow coefficient of claim 1, wherein step 11) is to calculate the enthalpy-rise coefficient μ using the following formula

Wherein, σ is a specific enthalpy ratio,is the outlet tangential velocity ratio of the centrifugal impeller, gamma is the adiabatic index, M_w1Is the relative Mach number, beta, of the inlet shroud of the centrifugal impeller_1sIs the relative axial flow angle, alpha, of the inlet shroud of the centrifugal impeller₁Is the centrifugal impeller inlet prewhirl angle, k is the form factor,is the ratio of the diameter of the inlet shroud of the centrifugal impeller to the diameter of the outlet of the centrifugal impeller, M_u2Is the machine mach number.