Design method of subsonic and equal diameter axial flow reaction supercritical carbon dioxide expander

Abstract

The application provides a subsonic equal diameter axial flow reaction supercritical carbon dioxide expander design method, which is reasonable in design, simple in method, can greatly improve the design speed of the carbon dioxide expander, and can select the corresponding scheme. Unlike the high-temperature turbine method of the traditional water unit steam turbine, the design method is convenient and fast, starts from the mass flow and axial velocity, quickly determines the blade first stage and last stage height through the calculation of the meridian flow area, so that the scheme selection and one-dimensional design of the carbon dioxide high-temperature turbine can be quickly performed, and the method is more suitable for the carbon dioxide high-temperature expander with small enthalpy drop and large flow.

Description

Technical Field

[0001] This invention relates to the field of supercritical carbon dioxide cycle power generation technology, specifically to a design method for a subsonic, constant-diameter axial-flow reaction supercritical carbon dioxide expander. Background Technology

[0002] With the development of power generation technology in recent years, research has shown that supercritical carbon dioxide can replace water vapor as the working fluid in generator sets. Within a certain power range, it has advantages such as high cycle efficiency, compact equipment structure, and low initial investment in infrastructure. Therefore, supercritical carbon dioxide cycle power generation system is a very promising power generation method.

[0003] In supercritical carbon dioxide power generation technology, the generator is mainly driven by a high-temperature gas expander. Therefore, the aerodynamic design performance of the carbon dioxide high-temperature gas expander directly determines the overall cycle efficiency of the generator set. Since the carbon dioxide high-temperature gas expander has the characteristics of small enthalpy drop and large flow rate, the traditional steam turbine design method of water turbine units cannot be directly applied to the carbon dioxide turbine design. Furthermore, the aerodynamic design of the carbon dioxide high-temperature gas expander in the existing technology is relatively complex, so it is not possible to quickly select a solution, which affects the large-scale application of supercritical carbon dioxide power generation. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a design method for a subsonic, constant-diameter, axial-flow reaction supercritical carbon dioxide expander. The design is reasonable and the method is simple, which can greatly improve the design speed of the carbon dioxide expander and the selection of corresponding solutions.

[0005] This invention is achieved through the following technical solution:

[0006] Design methods for subsonic, medium-diameter axial-flow reaction supercritical carbon dioxide expanders, including:

[0007] Based on the properties of carbon dioxide and the local Mach number limit of the expander, the maximum absolute velocity of the working fluid at the outlet of the last stage stator of the expander is determined, and then the absolute velocity of the working fluid at the outlet of the stator at the middle diameter is calculated according to the optimal diameter-to-height ratio.

[0008] Based on the absolute velocity of the working fluid at the stationary blade outlet and the selected optimal speed ratio of the expander, the airflow angle at the blade inlet and outlet is determined, and then the absolute velocity of the meridional direction at the mid-diameter is calculated.

[0009] Based on the meridional absolute velocity and the expander inlet and outlet state parameters, the first-stage inlet area and the last-stage outlet area are obtained;

[0010] Based on the blade height-efficiency curve and the optimal diameter-efficiency curve, the first and last stage blade heights and median diameters are determined, thereby determining the meridional channel dimensions.

[0011] Based on the airflow angles at the inlet and outlet of the blades and the absolute velocity of the meridional diameter, the flow coefficient and stage load coefficient are obtained, thereby determining the total number of stages of the expander;

[0012] The optimal medium-diameter blade consistency was selected based on the blade consistency-efficiency relationship curve, and the number of blades was calculated.

[0013] Calculate the outlet airflow angles of the stationary and moving blades at each stage based on the number of blades, determine the blade installation angles of the stationary and moving blades, and then calculate the design parameters of each section of the blade tip, blade root, and middle part based on the selected flow pattern and chord span distribution law; thus completing the design of the subsonic constant diameter axial flow reaction supercritical carbon dioxide expander.

[0014] Optional design constraints may also include the following:

[0015] The velocity triangles of each stage of the blades are equal, and the mean diameter and the absolute velocity of the mean diameter meridion are both constants.

[0016] Optionally, the determination of the maximum absolute velocity of the working fluid at the outlet of the last stage stator of the expander, based on the properties of carbon dioxide and the local Mach number limitation of the expander, is specifically based on the following formula.

[0017] Ma = c 2max / vs<0.8,

[0018] Where Ma is the local Mach number, c 2max is the maximum absolute velocity of the working fluid at the outlet of the last stage stator of the expander, and vs is the local speed of sound.

[0019] Optionally, the expander design method is characterized by the following method for calculating the absolute velocity of the working fluid at the stator outlet at the mid-diameter according to the optimal diameter-to-height ratio:

[0020] According to the optimal diameter-to-height ratio of a reaction turbine, θ = d a / l b Distribution interval [θ] min ,θ max ] Calculate the absolute velocity c of the working medium at the outlet of the stationary blade at the middle diameter. 2a =c 2max *θ min / (θ min +0.5);

[0021] Where, d a The mean diameter, l b For leaf height, c 2max This is the maximum absolute velocity of the working fluid at the outlet of the final stage stationary vane of the expander.

[0022] Optionally, the calculation of the absolute velocity of the meridional direction at the median diameter is specifically performed using the following formula.

[0023] c m,a =c 2a *cosα2,

[0024] Among them, c m,a c is the absolute velocity of the median meridian. 2a α1 represents the absolute velocity of the working medium at the outlet of the stationary blade at the mid-diameter, and α2 represents the absolute airflow angle at the outlet of the stationary blade.

[0025] Optionally, the area of ​​the primary inlet is determined using the following formula:

[0026] A l,3 =v l,3 / v f,1 *A f,1 ,

[0027] Among them, A f,1 and v f,1 A represents the inlet area and specific volume of the primary stator blades. l,3 and v l,3 This indicates the outlet area and specific volume of the final stage moving blade.

[0028] The outlet area of ​​the final stage moving blade is determined by the following formula, A l,3 =qv l,3 / c m.a .

[0029] Optionally, the flow coefficient and the stage load coefficient are determined using the following formulas:

[0030]

[0031]

[0032] Among them, u a α1 represents the circumferential velocity of the mid-diameter, and α2 and α3 represent the absolute airflow angles at the blade inlet and blade outlet, respectively.

[0033] Optionally, the total number of stages of the expander is determined by the following formula:

[0034]

[0035] Where, Δh s For the isentropic enthalpy drop of the expander, η s It is isentropic efficiency.

[0036] Optionally, the number of blades is determined using the following formula:

[0037] z b =πd a / s a ,

[0038] Among them, z b Indicates the number of blades, s a Indicates the median pitch.

[0039] Compared with the prior art, the present invention has the following beneficial technical effects:

[0040] This invention discloses a rapid design method for a subsonic, constant-diameter, axial-flow reaction-type supercritical carbon dioxide expander, which differs from the traditional high-temperature turbine method for steam turbines in water-cooled units. The design method is convenient and quick. Starting from the mass flow rate and axial velocity, the height of the first and last stages of the blades is quickly determined by calculating the meridional channel area. This allows for rapid scheme selection and one-dimensional design of high-temperature carbon dioxide turbines, and is more suitable for high-temperature carbon dioxide expanders with small enthalpy drop and large flow rate. Detailed Implementation

[0041] The present invention will be further described in detail below with reference to specific embodiments. These descriptions are for explanation purposes only and are not intended to limit the scope of the invention.

[0042] This invention relates to a design method for a subsonic, constant-diameter, axial-flow reaction-type supercritical carbon dioxide expander.

[0043] First, based on the local Mach number limit of the working fluid, determine the maximum absolute velocity of the working fluid at the outlet of the last stage stator, and then calculate the absolute velocity of the working fluid at the outlet of the stator at the middle diameter according to the optimal diameter-to-height ratio.

[0044] Secondly, based on the absolute velocity of the working fluid at the stator outlet and the selected optimal speed ratio of the expander, the airflow angles at the blade inlet and outlet are determined, and then the absolute velocity of the working fluid in the meridional direction at the mid-diameter is calculated. Based on the meridional absolute velocity and the expander inlet and outlet state parameters, the first-stage inlet area and the last-stage outlet area are obtained.

[0045] Next, based on the blade height-efficiency curve and the optimal diameter-efficiency curve, the first and last stage blade heights and median diameters are determined, thereby determining the meridional channel dimensions;

[0046] Then, based on the airflow angles at the inlet and outlet of the blades and the absolute velocity of the meridional diameter, the flow coefficient and stage load coefficient are calculated, thereby determining the total number of stages of the expander; the optimal mid-diameter blade consistency is selected based on the blade consistency-efficiency relationship curve, and the number of blades is calculated.

[0047] Finally, the airflow angles at the outlets of the stationary and moving blades at each stage are calculated to determine the blade installation angles of the stationary and moving blades. Then, based on the selected flow pattern and the chord span distribution law, the design parameters of each section of the blade tip, blade root, and middle part are calculated to complete the design of the subsonic constant diameter axial flow reaction supercritical carbon dioxide expander.

[0048] In this paper, the variables are set as follows: Ma represents the Mach number, h represents the static enthalpy of the working fluid, c represents the absolute velocity of the working fluid, vs represents the local speed of sound, θ represents the diameter-to-height ratio, d represents the diameter, l represents the blade height, α represents the absolute airflow angle, v represents the specific volume, q represents the mass flow rate, and u represents the circumferential velocity. ψ represents the flow coefficient, η represents the stage load coefficient, z represents the efficiency, and s represents the number of blades.

[0049] The subscripts are as follows: s represents the isentropic parameter, a represents the median diameter parameter, b represents the blade parameter, m represents the meridional plane parameter, f represents the first-stage parameter of the blade, and l represents the last stage parameter of the blade; 1 represents the stationary blade inlet, 2 represents the stationary blade outlet or the moving blade inlet, and 3 represents the moving blade outlet.

[0050] The specific implementation process is as follows:

[0051] 1) In the design of a constant diameter axial flow expander, the velocity triangles of each stage of the blades are equal, and d a = constant, c m,a = constant, α2=β3, α3=β2, α1=α3, where d a c is the mean diameter. m,a Here, α is the absolute velocity along the mid-meridian, β is the absolute airflow angle, and β is the relative airflow angle. Based on the properties of carbon dioxide and the local Mach number constraint for subsonic expanders, Ma = c. 2max / vs<0.8, determine the maximum absolute velocity c at the tip of the final stage stator vane of the expander. 2max According to the optimal diameter-to-height ratio θ = d of a reaction turbine a / l b Distribution interval [θ] min ,θ max ] Calculate the absolute velocity c of the working medium at the outlet of the stationary blade at the middle diameter. 2a =c 2max *θ min / (θ min +0.5), where d a The mean diameter, l b For the leaves.

[0052] 2) Based on the relationship between the speed ratio and efficiency of the reaction-type axial flow expander, select the optimal speed ratio x1 = u a / c 2a Determine the circumferential velocity u at the mid-diameter a Given the absolute airflow angles α1 and α2 at the inlet and outlet of the stationary blades, the absolute meridional velocity c at the mid-diameter is... m,a =c 2a *cosα2 and the final stage exit area A l,3 =q m v l,3 / c m.a It can be calculated using a formula.

[0053] 3) Based on the expander inlet and outlet state parameters and the mid-diameter meridional velocity c m,a Then the area of ​​the primary entrance can be determined by A. l,3 =v l,3 / v f,1 *A f,1 Sure.

[0054] 4) Based on the leaf height-efficiency curve l b -η, diameter-to-height ratio efficiency curve θ-η, first-stage inlet blade height l b,f,1 Final stage outlet blade height l b,l,3 , median diameter d a The rotational angular velocity ω can be obtained from the formula d a =l b θ and ω a =2u a / d a Calculated.

[0055] 5) From the formula and Calculate and determine the flow coefficient and the load factor ψ.

[0056] 6) Through the formula Calculate the total number of stages in the expander, where Δh s For the isentropic enthalpy drop of the expander, η s It is isentropic efficiency.

[0057] 7) Based on the optimal aspect ratio r sc Through formula b a =l b / r sc Calculate the chord lengths of the stationary and moving blades at each stage.

[0058] 8) Based on the relationship curve between blade consistency and efficiency (loss), σ-η(h) loss Select the optimal medium diameter blade consistency σ. a Then, by formula s a =b a / σ a Calculate the blade pitch and z-axis. b =πd a / s a Calculate the number of blades.

[0059] 9) According to the formula Calculate the airflow lag angle at the stator blade exit, where 'a' is the distance from the airfoil's maximum camber point to the leading edge. This refers to the absolute airflow angle at the stator blade outlet under design conditions. Let α be the airfoil bending angle. Using the airfoil parameters of the moving blade instead of the data in the above formula, the lag angle δ3 of the airflow at the moving blade exit can be calculated using the same method. Then, the installation angles at the static and moving blade exits can be obtained from the formula α. 2sm =α 2m -δ2 and β 3sm =β 3m -δ3 is determined, and the installation angles of the stationary and moving blade inlets can be determined by formula α. 1sm =α 1m -i c1 and β 2sm =β 2m -i c2 Determined, where i c This refers to the angle of attack at the blade inlet.

[0060] Then, based on the selected flow pattern and the chord span distribution law, the design parameters of each section of the blade tip, root and middle part are calculated; finally, the design of the subsonic constant diameter axial flow reaction supercritical carbon dioxide expander is completed.

Claims

1. A design method for a subsonic, constant-diameter, axial-flow reaction-type supercritical carbon dioxide expander, characterized in that: include, Based on the properties of carbon dioxide and the local Mach number limit of the expander, the maximum absolute velocity of the working fluid at the outlet of the last stage stator of the expander is determined, and then the absolute velocity of the working fluid at the outlet of the stator at the middle diameter is calculated according to the optimal diameter-to-height ratio. Based on the absolute velocity of the working fluid at the stationary blade outlet and the selected optimal speed ratio of the expander, the airflow angle at the blade inlet and outlet is determined, and then the absolute velocity of the meridional direction at the mid-diameter is calculated. Based on the meridional absolute velocity and the expander inlet and outlet state parameters, the first-stage inlet area and the last-stage outlet area are obtained; Based on the blade height-efficiency curve and the diameter-efficiency curve, the first and last stage blade heights and median diameters are determined, thereby determining the meridional channel dimensions; Based on the airflow angles at the inlet and outlet of the blades and the absolute velocity of the meridional diameter, the flow coefficient and stage load coefficient are obtained, thereby determining the total number of stages of the expander; The optimal medium-diameter blade consistency was selected based on the blade consistency-efficiency relationship curve, and the number of blades was calculated. Calculate the outlet airflow angles of the stationary and moving blades at each stage based on the number of blades, determine the blade installation angles of the stationary and moving blades, and then calculate the design parameters of each section of the blade tip, blade root, and middle part based on the selected flow pattern and chord span distribution law; complete the design of the subsonic constant diameter axial flow reaction supercritical carbon dioxide expander. The maximum absolute velocity of the working fluid at the outlet of the last-stage stator of the expander is determined based on the properties of carbon dioxide and the local Mach number limitation of the expander, specifically using the following formula. Ma= / v s ,and Ma <0.8, in, Ma The local Mach number, This represents the maximum absolute velocity of the working fluid exiting the final stage stator of the expander. v s The speed of sound is the local speed. The specific method for calculating the absolute velocity of the working medium at the stator outlet at the mid-diameter according to the optimal diameter-to-height ratio is as follows. Based on the optimal diameter-to-height ratio of reaction turbines Distribution range Calculate the absolute velocity of the working fluid at the outlet of the stationary blade at the median diameter. ; in, d a The mean diameter, l b For Ye Gao, This is the maximum absolute velocity of the working fluid at the outlet of the last stage stator vane of the expander. In the design of a constant diameter axial flow expander, the velocity triangles of each stage of the blades are equal, and , , in The mean diameter, The absolute velocity of the median meridian. The absolute airflow angle, This is the relative airflow angle.

2. The design method for a subsonic, constant-diameter axial-flow reaction supercritical carbon dioxide expander according to claim 1, characterized in that, It also includes the following design constraints, The velocity triangles of each stage of the blades are equal, and the mean diameter and the absolute velocity of the mean diameter meridion are both constants.

3. The design method for a subsonic, constant-diameter axial-flow reaction supercritical carbon dioxide expander according to claim 1, characterized in that, The absolute velocity of the meridional direction at the median diameter is calculated using the following formula. ， in, The absolute velocity of the median meridian. The absolute velocity of the working fluid at the outlet of the stationary blade at the mid-diameter section. α 2 represents the absolute airflow angle at the stator blade outlet.

4. The design method for a subsonic, constant-diameter axial-flow reaction supercritical carbon dioxide expander according to claim 1, characterized in that, The area of ​​the primary entrance is determined using the following formula. ， in, and This indicates the inlet area and specific volume of the primary stilling blades. and This indicates the outlet area and specific volume of the final stage moving blade; The outlet area of ​​the final stage moving blade is determined by the following formula. .

5. The design method for a subsonic, constant-diameter axial-flow reaction supercritical carbon dioxide expander according to claim 1, characterized in that, The flow coefficient and the stage load coefficient are determined using the following formulas. ， ， in, Indicates the circumferential velocity of the mean diameter circle. and These represent the absolute airflow angles at the blade inlet and blade outlet, respectively.

6. The design method for a subsonic, constant-diameter axial-flow reaction supercritical carbon dioxide expander according to claim 1 or 5, characterized in that, The total number of stages of the expander is determined by the following formula. ， in, For the isentropic enthalpy drop of the expander, It is isentropic efficiency.

7. The design method for a subsonic, constant-diameter axial-flow reaction supercritical carbon dioxide expander according to claim 1 or 5, characterized in that, The number of blades is determined using the following formula. ， in, Indicates the number of blades. Indicates the median pitch.

Images