A Method for Batch One-Dimensional Design and Design Space Visualization of Radial Turbines

Abstract

The present invention relates to a method for one-dimensional batch design and design space visualization of a radial turbine, belonging to the technical field of turbomachinery design. On the premise of a fixed power and a fixed speed, the spatial structure design of the turbine is carried out by setting the ranges of the energy head coefficient and the flow coefficient. By carrying out the design in the coordinate space formed by different numerical combinations of the energy head coefficient and the flow coefficient under the premise of a certain power and a certain speed, an interval is taken for the energy head coefficient and the flow coefficient, and appropriate values are taken for this interval, so that all possible design points under the values of the energy head coefficient and the flow coefficient can be covered, and all the turbine geometric structures at a certain power and a certain speed can be obtained. That is, through the present invention, a large number of turbine geometric structures for different head coefficients and different flow coefficients can be designed under the conditions of the same power and the same speed.

Description

Technical Field

[0001] The present invention relates to the field of turbomachinery design, and specifically to a design method for radial turbomachinery using high-density fluid as the working medium. Background Art

[0002] Centrifugal turbines have the characteristic of continuously doing work on fluids, so they are widely used in power cycle equipment such as power generation. Among them, for small generators, radial turbines are mostly used because their manufacturing process is simpler than that of axial turbines. For air turbines and steam turbines using air and steam as the working medium, their design methods are all single design calculations, calculating a set of turbine parameters that meet the design standards, designing one point at a time, unable to design in batches, and unable to create more geometric data for reference. Most designers adjust the parameters based on experience. Moreover, air and water vapor are low-density fluids. If the working medium is replaced with a high-density fluid, such as supercritical carbon dioxide, compared with turbomachinery using low-density fluids as the working medium, at the same efficiency, the turbomachinery using high-density fluids as the working medium has a more compact structure and a smaller volume. However, there are not many practical cases for the turbine design in this advanced power cycle, and there is not much experience for all designers to accumulate. For novice designers, the subsequent adjustment of turbine design is very difficult. Therefore, a new turbine design method is needed, which can not only design all design schemes that meet the design requirements but also facilitate designers to obtain the subsequent modification directions.

[0003] Traditional turbine design is derived based on the flow rate Q through the turbine, or the output power P, and the initial pressure p0, initial temperature T0, and back pressure p2 entering the turbine, to obtain the geometric dimensions and structure of the turbine that meet the conditions, and then use computational fluid dynamics software (CFD) for aerodynamic and strength checks. Due to different experiences of different designers, using this method, for the same set of given inlet and outlet cycle parameters (Q, p0, T0, p2, P, etc.), a very large number of feasible blade parameter combinations will be obtained, such as different blade heights, installation angles, chord lengths at the inlet and outlet of the impeller, etc. That is, using these different blade parameter combinations, all can be adapted to the given cycle parameters. However, designers often only use the empirical formulas they are familiar with, and thus can only obtain one set of blade profile parameters, which is not comprehensive enough.

[0004] For example, for a turbine with a designed power of 100 kW, using traditional design methods, designers can only calculate one geometric structure in each design process. However, in actual applications, the blade heights at the inlet and outlet of the rotor impeller may obtain different values under the same turbine power and cycle conditions due to the adjustment of empirical coefficients. Moreover, different designers have different experiences, and when designing turbines with the same power and cycle parameters, the designed geometric structures will also vary slightly. For example, designers may set different tip clearances and blade angles for the turbine, but the design results all meet the design requirements. Traditional design methods cannot calculate all the geometric structures that meet the design requirements at one time, and are even less able to show the optimization path of the turbine at the preliminary design level. Summary of the Invention

[0005] In addition to the disadvantages that traditional design methods cannot design all turbine structures under the same power and cannot subdivide turbine structures, during the design process, they not only need to check the aerodynamic performance of the geometric structure, but also require designers to judge based on experience whether the geometric structure meets the requirements of manufacturing and processing. At the same time, designers also need to have rich experience and know which parameters to adjust to design a turbine with better operating conditions (such as more reasonable flow angles, farther from resonance, etc.). For beginners who are newly exposed to turbine design, it is very difficult to master design methods and control the evolution direction of turbine design dimensions. How can designers quickly find the geometric structure parameters (including rotors and stators) that meet the design requirements under the condition of knowing the design requirements and considering many factors such as manufacturing and processing, and then directly conduct aerodynamic performance analysis using the structure parameters, so as to reduce the design difficulty of the turbine, greatly accelerate the design speed of designers, and at the same time reduce the generation of turbine blade geometric structures that are difficult to process (beyond the processing limit).

[0006] Therefore, the inventor changed the traditional method that uses fixed power, fixed speed, and fixed energy head coefficient The turbine design method with the fixed flow coefficient ψ as the design parameter is changed to set the energy head coefficient and the flow coefficient range on the premise of fixed power and fixed speed to carry out the spatial structure design of the turbine. The traditional turbine design method can only calculate one turbine model, but the designed geometric model may not fully meet the design requirements through verification. However, the improved design method of the present invention designs the coordinate space formed by different numerical combinations of the energy head coefficient and the flow coefficient on the premise of a certain power and a certain speed, takes an interval for the energy head coefficient and the flow coefficient, and appropriately takes values for this interval, so that all possible design points under the values of the energy head coefficient and the flow coefficient can be covered, and all turbine geometric structures at a certain power and a certain speed can be obtained. That is, through the present invention, a large number of turbine geometric structures for different head coefficients and different flow coefficients can be designed under the same power and the same speed.

[0007] The technical solution of the present invention is as follows:

[0008] The first step of the present invention is to calculate the corresponding geometric structure of the turbine under the given power, speed, flow coefficient and energy head coefficient. First, the program performs the design calculation of the rotor, and then, according to the geometric structure parameters and aerodynamic characteristics of the rotor, separately designs and calculates the matching stator. In addition, the necessary information provided by the detailed geometric module can construct the turbine profile, so that the turbine loss can be estimated by using a mature loss model. Then, a feasibility check is carried out on the successfully calculated geometric structure to check whether its structure meets the processing requirements. The overall program design process is as Figure 1 shown. For supercritical carbon dioxide gas, the physical property parameters used in the program are calculated by the van der Waals equation.

[0009] Different from the traditional design method, this design method adds various combinations of the flow coefficient and the energy head coefficient, and differentiates them in the design space of the fixed power and speed by the flow coefficient and the energy head coefficient, so as to obtain the design of all turbine geometric structures under the fixed power and the fixed speed. In other words, for a given combination of power and speed, all geometric shapes that meet the combination requirements are calculated by the program for evaluation, and all geometric shapes are differentiated by the flow coefficient and the energy head coefficient.

[0010] A method for one-dimensional batch design and design space visualization of a radial turbine, comprising the following steps:

[0011] (1) Initial setting of parameters, including output power W out , rotor speed N, flow coefficient energy head coefficient ψ, and the definition of the flow coefficient is as follows:

[0012]

[0013] In Equation (1), U4 represents the circumferential velocity at the inlet of the turbine rotor, U4 = ωr4, where ω is the angular velocity of the turbine rotor and r4 is the blade radius at the inlet of the turbine rotor, i.e., the rotor inlet radius, and C m4 represents the radial component of the absolute velocity at the inlet of the turbine rotor;

[0014] The definition of the energy head coefficient is as follows:

[0015]

[0016] In Equation (2), C θ4 represents the circumferential component of the absolute velocity of the air flow at the inlet of the rotor; C θ6 represents the circumferential component of the absolute velocity of the air flow at the outlet of the rotor; Δh0 is the enthalpy drop of the fluid per unit volume discharged through the turbine and is a constant value; r 6t is the radius at the tip of the rotor blade at the outlet; r4 is the radius of the rotor blade at the inlet; preferably, in this program, the ratio of r 6t to r4 is set to 0.3;

[0017] (2) Conjecture the initial value of the total static efficiency. The conjectured value of the total static efficiency of the turbine for determining the output power can be obtained through the following formula:

[0018]

[0019] where, W out is the output power of the turbine, η ts is the conjectured value of the total static efficiency of the turbine at this output power, ρ is the density of the working fluid, is the volume flow rate inside the turbine;

[0020] (3) Rotor calculation

[0021] Input the designed values of the output power and rotational speed, and re-classify different turbines according to the combination of the flow coefficient and the energy head coefficient. It is necessary to input the set values of the flow coefficient and the energy head coefficient, and then set the conjectured value η of the total static efficiency ts as the judgment for terminating the loop. Using the input output power, rotational speed, flow coefficient, energy head coefficient, and total static efficiency as known, and also the turbine inlet pressure and inlet temperature, turbine volume flow rate, physical property parameters of the working fluid such as the isentropic exponent κ, and the environmental parameters in Table 2 given as the design requirements at the beginning. According to the calculation method of rotor design, first solve for the circumferential velocity U4 of the rotor blade according to Equation (2), then calculate the radial component and circumferential component of the absolute velocity at the inlet of the rotor according to Equations (1) and (2) respectively, and finally obtain the absolute velocity of the fluid at the inlet according to the triangle rule, i.e., Equation (4), to complete the calculation of the absolute velocity in the velocity triangle;

[0022]

[0023] According to obtain the absolute flow velocity angle α4 of the fluid at the rotor inlet; according to calculate the installation angle β4 at the rotor inlet;

[0024] According to the input parameters, i.e., the inlet total pressure and the design pressure ratio, calculate the pressure at the rotor outlet. Under the condition that the rotor outlet pressure and the rotor outlet enthalpy value are known, use the REFPROP thermodynamic parameter query software to query the rotor outlet total temperature under the corresponding conditions. In addition, other thermodynamic parameters under the corresponding state can also be found, including the outlet static pressure, the outlet static temperature, and the gas density; similarly, under the condition that the inlet total pressure and the inlet total enthalpy are known, obtain the gas density and temperature thermodynamic parameters at the inlet by calling the REFPROP thermodynamic parameter query software.

[0025] Calculate the rotor inlet blade radius from the formula U4 = ωr4, and then calculate the rotor outlet blade radius r according to the ratio of the set rotor outlet blade tip radius to the rotor inlet blade radius 6t , i.e., r 6t = r4a 46 , where a 46 represents the ratio of the rotor outlet radius to the rotor inlet radius. In the program, a 46 = 0.3;

[0026] The rotor inlet blade height b4 is obtained through Equation (5)

[0027]

[0028] where M represents the mass flow rate, which is input by the user, ρ4 represents the density of the working fluid at the rotor inlet, and its value is obtained by calling the REFPROP thermodynamic parameter query software, C m4 represents the radial component velocity of the absolute velocity at the rotor inlet, r4 represents the rotor inlet blade radius, t represents the rotor blade thickness, Z r represents the number of rotor blades. The rotor blade thickness t and Z r are set by the user. Preferably, the set values in this program are t = 5 mm and Z r = 9;

[0029] The radial component velocity of the absolute velocity at the rotor outlet is C m6 = C m4 / ξ, where ξ represents the ratio of the radial component velocity of the rotor absolute velocity. Preferably, ξ = 1.0 in the program design; the circumferential component velocity of the absolute velocity at the rotor outlet is C θ6 = 0;

[0030] The rotor outlet blade height, b6, is Figure 4 The corresponding expression in should be b6=r 6t -r 6h , r 6t is the radius of the rotor outlet blade tip, r 6h is the root radius of the rotor outlet blade. For the rotor outlet blade height b6, according to the principle of equal area, the implicit calculation of equation (6) is:

[0031]

[0032] Where S6 is the outlet area, and its calculation formula is C6 represents the absolute flow rate at the outlet, ρ6 represents the density of the working fluid at the outlet, and b θ represents the angle between the true blade at the rotor outlet and the meridian blade. The binary method is used to calculate and solve equation (7) b θ , its implicit formula is as follows:

[0033]

[0034] Among them, r 6rms Indicates the relative average value of the rotor outlet blade radius, C m6 represents the radial velocity of the rotor outlet flow rate, R represents the universal gas constant, T 04 represents the total temperature of the rotor inlet, and p4 represents the static pressure of the rotor inlet;

[0035] Figure 4 The calculation formula for the impeller axial length L is shown in:

[0036] L=b4+r4-r 6t (8)

[0037] To simplify the geometric model, the thickness of the blade is set to a constant value, the trailing edge thickness is 4% of the outlet blade height b6, and the gap between the front and rear cover plates of the rotor is ε r , ε b and ε a , whose value is 5% of the rotor inlet blade height b4, such as Figure 4 Shown: ε r is the outlet blade tip clearance, i.e. the distance between the rotor outlet and the front cover, ε b is the distance between the back of the rotor and the rear cover, ε a is the inlet tip clearance, i.e. the distance between the rotor inlet and the front cover;

[0038] like Figure 4 As shown in the figure, the rotor meridian length L ms Use the following formula to calculate

[0039]

[0040] where b4 is the height of the rotor inlet blade, and r 6t is the radius at the tip of the rotor outlet blade, and r 6h is the root radius of the rotor outlet blade.

[0041] Through the above process, the geometric design parameters of the rotor's meridional plane are accurately calculated, and the rotor meridional plane design parameters are as Figure 4 shown.

[0042] For the installation angle of the rotor blade at the outlet, that is, the angle β h at the root of the blade and the blade angle β t at the tip of the outlet blade, the two angles transition smoothly;

[0043] where

[0044]

[0045] where: U 6h represents the circumferential velocity at the root of the rotor outlet blade, and r 6h represents the root radius of the blade at the rotor outlet, and U 6t represents the circumferential velocity at the tip of the rotor outlet blade, and r 6t represents the tip radius of the blade at the rotor outlet, and C θ6 is the circumferential component of the absolute velocity at the rotor outlet;

[0046] Finally, the above β4, b4, r4, r 6t , b6, t, Z r , L, L ms , β h , β t , r 6h , ε b , ε r geometric parameters are obtained to complete the design calculation of the rotor;

[0047] (4) Stator calculation

[0048] First, determine the basic geometric structure. Compared with the rotor, the stator structure is simple. The height b s of the stator is a uniform height, and its height should be the height of the rotor inlet blade, that is, b s = b4; also, since the outlet of the stator is the inlet of the rotor, for the outlet radius of the stator, the stator airflow outlet angle α3 is the rotor airflow inlet angle α4, that is, α3 = α4. At the same time, for the stator, its stator installation angle is the same as the stator airflow angle;

[0049] The stator itself does not rotate, and a certain gap needs to be designed between the stator and the rotor to ensure that the structures of the stator and the rotor do not wear. The inlet radius of the rotor is r4, so the outlet radius of the stator r3 = r4 + δ r , where δ r represents the gap between the stator and the rotor, and its calculation formula is as follows:

[0050] δ r = 2b s α4 (12)

[0051] The inlet radius r1 of the stator is the same as that of the rotor and is obtained by setting the radius ratio, that is, r1 = r3a 13 , where a 13 represents the ratio of the inlet radius of the stator to the outlet radius of the stator. Preferably, a 13 = 1.25 is set in the program;

[0052] After obtaining the inlet radius and outlet radius of the stator, and after obtaining the number of stators set by the user, the lengths of the single flow channels at the inlet and outlet of the stator can be obtained, that is Figure 7 marked in and

[0053]

[0054] where Z s represents the number of blades of the stator; in this program, Figure 7 the chord length C of the blade marked in s is set to C s = b1; the calculation of the geometric dimensions of the stator is completed;

[0055] (5) Model evaluation, judge whether the total static efficiency converges. If it converges, feasibility inspection can be carried out. If it does not converge, update the total static efficiency;

[0056] Preferably, specifically, after obtaining the geometric structures of the stator and the rotor, the geometric structures are detected through aerodynamic performance, and its total static efficiency is calculated through the following formula;

[0057]

[0058] Compare the calculated value of the total static efficiency with the guessed value. If the difference between the calculated total static efficiency and the guessed value is greater than 0.01, it is considered that the calculation does not converge. Substitute the calculated total static efficiency into the rotor calculation process in step (3) for recalculation until the calculated total static efficiency is less than or equal to 0.01 compared with the value of the total static efficiency brought in last time, then confirm that the iteration converges. At this point, a set of design calculations for the flow coefficient and the energy head coefficient ends; return to step (1) to perform the calculations for the rotor and the stator for the next set of flow coefficient and energy head coefficient;

[0059] (6) Perform a feasibility check to determine whether the model is feasible. If it is feasible, write the appropriate output; if not, write the inappropriate output.

[0060] (7) End the loop.

[0061] (8) Plot all the turbine design points at a certain output power W out and a certain rotor speed N, mark the feasibility of the design scheme on the drawing, and draw the contour lines of the parameters.

[0062] Preferably, in step (3), the flow coefficient ranges from 0.1 to 0.4, the energy head coefficient ψ ranges from 0.7 to 1.1, and the value interval each time is 0.001.

[0063] If a computer is used to continuously substitute the flow coefficient and the energy head coefficient from 0 to 1, all the turbine structures within the range of 1×1 of the flow coefficient and the hydraulic coefficient at a certain power and speed can be obtained. However, research shows that when the flow coefficient ranges from 0.1 to 0.4 and the energy head coefficient ψ ranges from 0.7 to 1.1, the highest total static efficiency exists in the two-dimensional design space formed. Therefore, the computer is used to increase the flow coefficient from 0.1 to 0.4 and the energy head coefficient from 0.7 to 1.1 in steps of 0.001 respectively, which greatly reduces the computational amount of the computer and excludes the low-efficiency space.

[0064] Preferably, in step (5), the calculation results of each group of flow coefficient and energy head coefficient are represented by a coordinate point diagram, and each group of results is a coordinate point, and all the results are graphically displayed.

[0065] Preferably, in step (6), the criteria for the feasibility check include the following evaluation parameters and parameter ranges: the absolute flow velocity angle α4 of the fluid at the rotor inlet ranges from 66° to 78°, the relative flow velocity angle β4 of the fluid at the rotor inlet ranges from -40° to -20°, the Mach number M4 of the fluid at the rotor inlet ranges from <1, and its calculation formula is M4 = U4 / C, where C represents the local speed of sound, the ratio r4 / r of the rotor inlet radius to the rotor outlet tip radius 6t ranges from ≥1.42, the ratio r 6h / r 6t of the rotor outlet blade root radius to the rotor outlet tip radius ranges from ≥0.4, the rotor blade inlet height b4 ranges from ≥0.9 mm, the rotor inlet radius r4 ranges from ≥10 mm, the iteration residual v i ranges from ≤1.0%, and the elastic stress σ r ranges from <0.9σ Y, the overall static efficiency η of the turbine ts ranges from ≥50%, and the frequency f generated by rotor excitation r ranges from ≥2ω n ; σ Y is the material yield stress, and ω n is the natural frequency of the rotor trailing edge.

[0066] The efficiency and speed of all geometric structures calculated using this design method are guaranteed. However, due to manufacturing, structural constraints, and performance guidelines, there may be problems with the geometric structures designed. Therefore, geometric structures with design problems must be excluded through feasibility checks. The main parameters for evaluation are as described above, ensuring that the designed geometric structures comply with production specifications.

[0067] Preferably, in step (6), after the inspection, visual drawings will be drawn according to the inspection results; the IDs of the turbines will be classified. The geometric parameters of each turbine ID are calculated according to one-dimensional design. The calculation results will form a list, which includes the energy head coefficient and the flow coefficient. The calculation results of each group of flow coefficient and energy head coefficient are represented by a coordinate point diagram, and each group of results is a coordinate point; each coordinate point will be marked to show the designer whether the corresponding turbine under the coordinate point meets the design parameters. This is convenient for the designer to check whether their design results are within the appropriate design range of the turbine, and it can also facilitate the designer to directly find the design parameters of the turbine corresponding to the coordinates according to the requirements.

[0068] Further preferably, in step (8), the data in the list in step (6) is sorted. The turbine IDs with equal geometric parameters are grouped together, and the coordinates of the points with equal parameters are equivalently found. Then, an isocurve of the parameter at a certain value is drawn according to the coordinates. For example, when sorting the relative fluid velocity angle β4 at the rotor inlet, the turbine IDs with equal β4 are grouped into a list, which is equivalent to finding the coordinates of the points with equal β4. Then, an isocurve of β4 at a certain value is drawn according to the coordinates. For designers, they can judge according to the isocurve what geometric factors affect the energy head coefficient and the flow coefficient, and then modify the design scheme according to the changing trend. It can also let newbies who are just starting to design turbines know the influence of different parameters on the performance of the turbine. The drawing procedure of its design drawing is as Figure 2 shown.

[0069] To simplify the design factors and facilitate the operation of beginners in design, the present invention designs a visual design drawing to be generated after the calculation results are completed, as Figure 2As shown, the feasibility of all design points is marked on the graph for designers to directly check whether the designed turbine meets the design standards. Then, points with consistent geometric parameters in the graph are plotted as contour lines, and the contour lines are used to reflect the evolution direction of some parameters of the design points, facilitating designers to make corresponding adjustments. This method maximally "visualizes" the design space, eliminating the blind search for combinations of suitable head coefficients and flow coefficients. After visualizing the design range, it is easy to find better combinations of head coefficients and flow coefficients, which is beneficial to the optimization and improvement of the overall turbine design. The design drawing not only enables designers to judge whether the aerodynamic performance of the designed turbine meets the requirements but also allows for corrections based on the design drawing. Its detailed description is in specific cases.

[0070] The beneficial effects of the present invention are as follows:

[0071] The present invention improves the method of taking traditional power, rotational speed, energy head coefficient, and flow coefficient as fixed parameters and only designing one turbine geometric structure. It changes the fixed energy head coefficient and flow coefficient to cyclically input different energy head coefficients and flow coefficients to obtain the designs of all turbine geometric structures under fixed power and fixed rotational speed.

[0072] The visual design drawing directly generated by the program at a certain power and a certain rotational speed, with the energy head coefficient and flow coefficient as the distinguishing criteria, can help designers know whether the designed turbine can be produced and whether it meets the requirements.

[0073] The generation of the visual design drawing can help new designers with product design and reduce their dependence on traditional experience. The turbine geometric data behind each design node is generated simultaneously when the design drawing is produced, and designers can directly view the generated geometric data and use it directly, which is convenient and fast.

[0074] It plays a guiding role in the optimization research of the turbine geometric shape. From the design drawing, the variation law of the energy head coefficient or flow coefficient when a certain geometric element changes can be obtained. For example, if the inlet height of the rotor blade is increased, its flow coefficient will increase. Therefore, if the flow coefficient of the designed turbine is too large, it can first be improved by reducing the inlet height of the rotor blade. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 is the flow chart of the visual turbine design idea;

[0076] Figure 2 is the flow chart of the visual drawing plotting;

[0077] Figure 3 is the design scheme drawing of a 100kW, 160kRPM turbine, with the abscissa being the flow coefficient and the ordinate being the energy head coefficient;

[0078] Figure 4 It is a schematic diagram of the blade structure;

[0079] Figure 5 It is a schematic diagram of the trailing edge structure of the rotor;

[0080] Figure 6 It is the relationship between the bearing diameter and the rotational speed. The abscissa is the bearing diameter, and the ordinate is the rotational speed;

[0081] Figure 7 It is a schematic diagram of the stator structure. Specific implementation manners

[0082] The present invention will be further described below by way of examples in conjunction with the accompanying drawings, but not limited thereto.

[0083] Example 1

[0084] A radial turbine batch one-dimensional design method includes the following steps:

[0085] The first variable selected in the design should be the rotor speed (N). The rotor speed is restricted by the selection of bearings and the material of the rotor. In the selection of bearings, rolling bearings are recognized by most researchers as relatively durable bearings due to their earlier development and use. However, gas foil bearings can withstand rotational speeds up to 350 kRPM. Figure 6 Shows the relationship between the maximum diameter and the maximum rotational speed of commercially available bearings. Using Figure 6 data, considering the shaft diameter and the load borne by the shaft, two rotational speeds are selected for a turbine with an output power of 100 kW. The optimal rotational speed is 160 kRPM, and its safe rotational speed is 120 kRPM. Therefore, according to the relationship between the shaft diameter and the maximum bearing rotational speed in the Swann study, a design parameter of 160 kRPM is adopted for the 100 kW turbine design study.

[0086] In addition to the rotor speed (N), the output power (W out ) of the turbine is considered another important parameter. Different output powers correspond to different geometries. The change in the turbine geometry will affect the manufacturing of the turbine, the strength of the turbine blades, and more seriously, it will bring the problem of dynamic resonance. Existing research has shown that the design of the turbine can be parameter-normalized, and a specific speed parameter (N s ) is used to characterize the aerodynamic kinetic energy and performance. For example, for two different turbines, if their specific speed parameters (N s ) are the same, it indicates that the aerodynamic kinetic energy and performance of the two turbines are the same.

[0087]

[0088] If a turbine with an output power of 100 kW is to be designed, and at the same time its aerodynamic performance is to be the same as that of a 200 kW turbine, that is, to ensure that the specific speed parameters (N S ) are the same. Also, because during the cycle, the enthalpy drop (Δh0) of the fluid per unit volume discharged through the turbine is a constant value, the total static efficiency of the 100 kW output power turbine can be obtained through the following formula.

[0089]

[0090] Keeping a certain specific speed, there is the following relationship between the output power and the shaft speed.

[0091]

[0092] In actual engineering, designers will obtain the design requirements of a power of 100 kW and a speed of 160 kRPM. Designers first input the design values of the output power and speed into the program, but there are many turbine geometric structure schemes designed under this requirement. Therefore, different turbines are further distinguished according to the combination of the flow coefficient and the energy head coefficient. So, the set values of the flow coefficient and the energy head coefficient also need to be input into the program. For example, designers input the flow coefficient and the energy head coefficient as 0.3 and 1.0 respectively, and then set the guessed value η ts as the judgment for loop termination. Using the input power, speed, flow coefficient, energy head coefficient, and total static efficiency as known, and also the turbine inlet pressure and inlet temperature, turbine volume flow rate, entropy exponent κ of the working fluid's physical properties, and the environmental parameters in Table 2 given as the initial design requirements, according to the calculation method of rotor design, the computer calculates to obtain the geometric characteristics of the rotor and the inlet and outlet flow velocities of the rotor, completing the design calculation of the rotor. According to the geometric structure of the rotor, the stator is designed. The stator height is constant and equal to the inlet height b4 of the rotor blades; the blade angle is set to be the same as the absolute flow velocity angle α4 of the inlet fluid of the rotor. The inlet stagnation conditions and velocities are iteratively calculated according to the continuity equation. After obtaining the geometric structures of the stator and the rotor, the geometric structures are evaluated through aerodynamic performance, and the actual total static efficiency of the geometric structures is calculated and compared with the guessed value. If the difference between the calculated total static efficiency and the guessed value is greater than 0.01, it is considered that the calculation has not converged, and the calculated total static efficiency is brought into the rotor calculation process for recalculation until the difference between the calculated total static efficiency and the previously brought-in total static efficiency value is less than or equal to 0.01, then the iteration convergence is confirmed. At this point, a set of design calculations for the flow coefficient and the energy head coefficient ends, and each set of calculation results is Figure 3 each coordinate point in. For example, when the input turbine design power is 100 kW, the speed is 160 kRPM, the set flow coefficient is 0.28, and the energy head coefficient is 0.82, we can obtain Figure 3One of the coordinate points is A(0.28, 0.82), which is the sign of successful convergence of the program. It means that the turbine geometry with a power of 100 kW, a rotational speed of 160 kRPM, a flow coefficient of 0.28, and an energy head coefficient of 0.82 has been successfully calculated. The geometry and turbine characteristics calculated by the program, the geometry includes the inlet height b4 of the rotor blade, the root radius r 6h of the rotor outlet blade, the tip radius r 6t of the outlet, the distance ε between the back of the rotor and the rear cover plate b and the distance ε between the rotor and the front cover plate r . As described in Figure 4 , the turbine characteristics include the rotor vibration excitation frequency f r , the absolute flow velocity angle α4 of the fluid at the rotor inlet, and the relative flow velocity angle β4 of the fluid at the rotor inlet.

[0093] If a computer is used to continuously substitute the flow coefficient and the energy head coefficient from 0 to 1, all turbine structures within the range of 1×1 of the flow coefficient and the hydraulic coefficient at a certain power and rotational speed can be obtained. However, research shows that when the flow coefficient is in the range of 0.1 - 0.4 and the energy head coefficient ψ is in the range of 0.7 - 1.1, the highest total static efficiency exists in the two-dimensional design space formed. Therefore, the computer is used to increase the flow coefficient from 0.1 to 0.4 and the energy head coefficient from 0.7 to 1.1 in steps of 0.001 respectively. This greatly reduces the computational amount of the computer and excludes the low-efficiency space, thus forming a design space diagram with the flow coefficient as the abscissa and the energy head coefficient as the ordinate as shown in Figure 3 . Figure 3 Behind each coordinate point on it is a turbine geometry. Therefore, there are a total of 120,000 turbine geometries that meet 100 kW and 160 kRPM, differentiated by different flow coefficients and head coefficients. For the convenience of designers to see clearly, 1200 are marked in Figure 3 , and their aerodynamic performances all meet the requirements.

[0094] As shown in Figure 3 , not all design schemes meet the standards. Only a subset in the design space of the flow coefficient and the head coefficient ψ is feasible. This is the feasibility check in Figure 1 the flow chart, excluding the failed geometries due to manufacturing, structural constraints, and performance constraints of the guidelines. Screening is carried out through the feasibility check of each design point in Figure 3 to obtain a reasonable subset of the design. In this way, the former program for calculating the rotor and stator ensures the generation of correct fluid characteristics and turbine efficiency; the latter inspection standard ensures the production of turbines that meet the specifications within the capabilities of existing manufacturing technologies.

[0095] Manufacturing Standards: Manufacturing standards include manufacturing limitations, structural limitations, and vibration limitations, which are all caused by tool limitations and operating impacts. For example, the thermal expansion of metals can affect the actual produced shape. The manufacturing limitations were proposed by DeMiranda Ventura, based on a radial turbine machine, with the inlet height of the rotor blade set to 10 mm to ensure sufficient machining allowance for generating the blade geometry. The next constraint is the tip clearance ε at the rotor outlet r Compared with the inlet blade height b4, it is considered the minimum blade height. Considering the uncertainties due to manufacturing tolerances and thermal expansion during operation, the operating clearance is limited to about 0.1 mm. Therefore, to maintain an appropriate tip clearance ratio of less than 10%, the inlet blade height (b4) is limited to 0.9 mm. The structural constraint is achieved through the rotor elastic stress (σ r ) caused by centrifugal load and the material yield stress (σ Y ).

[0096]

[0097] Considering uncertainties and variations, a constraint limit of 0.9×σ Y was selected. In this embodiment, INCONEL IN718 was chosen as the rotor material because INCONEL IN718 has good heat resistance and corrosion resistance.

[0098] In addition, the rotor blades of the radial turbine are also subject to vibrations generated by the collision of the aerodynamics of the blades and the casing. To prevent rotor excitation from causing blade damage and fatigue failure, vibration constraints were designed. The main cause of vibration is the interaction between the nozzle guide vane and the moving blade, and the vibration frequency generated by the excitation is

[0099]

[0100] The most vulnerable and fluid-damage-prone part of the turbine is the trailing edge of the rotor blade. The vibration constraint is set by comparing the excitation frequency (f r ) and the natural frequency (ω n ) of the rotor trailing edge. The natural frequency of the system was calculated using the models proposed by Blevins and Plunkett

[0101]

[0102] In the formula, E, ρ, and υ are the elastic modulus, material density, and Poisson's ratio of the material, respectively. In addition, in this embodiment, the actual trailing edge thickness is designed to gradually thin out, as Figure 5 shown (t t=(t / 2)). The purpose of designing it into a cone is to reduce the trailing edge loss while ensuring the stiffness of the trailing edge.

[0103] Guideline standards: The criterion performance standards consist of flow characteristics constraints, geometric constraints, and operating constraints. The flow characteristics constraints are set to obtain the optimal ranges of the absolute flow velocity angle (α4) of the fluid at the rotor inlet and the relative flow velocity angle (β4) of the fluid at the rotor inlet. The absolute flow velocity angle (α4) of the fluid at the rotor inlet should be between 66° and 78°, and the relative flow velocity angle (β4) of the fluid at the rotor inlet should be set between -40° and -20°. To allow for design studies at the edges of the feasible space, these ranges are increased by 62° respectively.

[0104] For geometric constraints, according to Rohlik's research, the ratio of the rotor inlet radius to the rotor outlet tip radius r4 / r 6t should not be less than 1.42, and the ratio of the rotor outlet root radius to the rotor outlet tip radius r 6h / r 6t should not be less than 0.4.

[0105] In terms of operating limitations, the feasibility check criteria are shown in Table 1:

[0106] Table 1 Feasibility Check Criteria

[0107]

[0108]

[0109] After clarifying the design requirements and limitations, a visual turbomachinery design drawing is generated.

[0110] In addition to the design requirements, it is also necessary to know the design environment of the turbine. The environmental parameters are input into the rotor calculation section. For the working environment used in the present invention, it is a Brayton cycle with solar energy as the heat source, and the operating conditions of the turbine are fixed. The environmental parameters are shown in Table 2.

[0111] Table 2 Environmental Parameters

[0112] Symbol Design value Symbol Design value <![CDATA[p 04 > 20MPa Fluid <![CDATA[CO2]]> <![CDATA[T 04 > 560℃ <![CDATA[Z r > 9 <![CDATA[PR(p 04 / p6)]]> 2.22 <![CDATA[Z S > 11

[0113] where p 04 - Total pressure at the rotor inlet; T 04 - Total temperature at the rotor inlet; PR - Ratio of the total pressure at the rotor inlet to the static pressure at the rotor outlet (turbine design pressure ratio); Fluid - Type of working fluid in the turbine; Z r - Number of blades on the rotor; Z S - Number of blades on the stator.

[0114] Example 2

[0115] A one-dimensional design method for radial turbines in batches, the steps are as described in Embodiment 1, the difference is that:

[0116] After the setting values are set, run the drawing program, and its program flow is as Figure 2 shown. The turbine data table includes the IDs of the turbines, namely 0, 1, 2..., in the turbine data table, each ID has a row of data. For example, for the turbine with ID 0, it is located in the first row of the data table. For the turbine with ID 0, the flow coefficient energy head coefficient ψ, rotor blade inlet installation angle β4, speed parameter N s 、rotor inlet radius r4, rotor outlet blade root radius r 6h 、rotor blade inlet height b4, rotor blade outlet height b6, rotor trailing edge natural frequency ω n 、rotor elastic stress σ r 、vibration frequency f generated by excitation r 、rotor trailing edge natural frequency ω n . First, the user inputs their own evaluation criterion range. In the present invention, 11 criteria in Table 1 are used to evaluate the generated turbine schemes. However, due to limited legends, in Figure 2 only the results of the evaluation criteria of 6 parameters, namely rotor blade inlet height b4, rotor excitation generated frequency f r 、rotor inlet fluid absolute flow velocity angle α4, rotor inlet fluid relative flow velocity angle β4, ratio of rotor outlet blade root radius to rotor outlet tip radius r 6h / r 6t and ratio of rotor inlet radius to rotor outlet tip radius r4 / r 6t are shown. Then the program starts to gradually judge the geometric parameters of the turbine with ID 0. If all 6 evaluation criteria are met, the ID of the turbine is stored in the feasible design list. If any evaluation criterion is not met, its ID is stored in the list of non-compliant criteria, thus completing the evaluation of the geometric factors of the turbine with ID 0. Then, read the parameters that the user wants to draw. Enter the parameter for which you want to draw the contour line. In this embodiment, 10 parameters are randomly selected and input, which are respectively rotor inlet fluid absolute flow velocity angle α4, rotor inlet fluid relative flow velocity angle β4, rotor outlet fluid relative average flow velocity angle β 6rms 、speed parameter N S 、rotor inlet radius r4, rotor outlet blade root radius r6, rotor blade inlet height b4, rotor blade outlet height b6, rotor trailing edge natural frequency ω n 、ratio of rotor inlet radius to rotor outlet tip radius r4 / r 6t, each parameter can input the value to be read. For example, if the input is a list of the absolute flow velocity angle α4 of the rotor inlet fluid [78, 72, 66], it means to draw the contour lines of the absolute flow velocity angle α4 of the rotor inlet fluid with values of 78, 72, and 66 on the drawing. Find the geometric parameters of the absolute flow velocity angle of the rotor inlet fluid under the turbine with ID 0, and then compare it with 78. If the absolute value of the difference is less than a (the value of a in this invention is 0.1), it is considered that the turbine with ID 0 is located on the contour line of the absolute flow velocity angle of the rotor inlet fluid of 78. Store the ID of the turbine into the list of the absolute flow velocity angle 78 of the rotor, and then read other geometric parameters of the turbine with ID 0 for classification. After the classification of the geometric characteristics in ID 0 is completed, the ID is incremented, and the inspection of the turbine with ID 1 starts, and then the geometric characteristics of the turbine with ID 1 are classified. Finally, after the inspection and classification of all turbines are completed, an image is drawn for the classified list according to the subroutine in python. Among them, a scatter plot is drawn for the list generated by the inspection, and a contour line is drawn for the list with equal values taken out according to the geometric characteristics.

[0117] Running the program will automatically generate a visual design drawing, that is Figure 3 . Figure 3 The information contained in it is extremely large. First, for 100kW and 160kRPM, the design is carried out with a flow coefficient in the range of 0.1 - 0.4 and a head coefficient in the range of 0.7 - 1.1, with a span of 0.001. There are a total of 120,000 design schemes, that is Figure 3 Each coordinate point in it is a design scheme. Behind a design scheme, there are a series of geometric features, which are used for feasibility inspection. The finer the coordinate points are divided, the more design schemes there are. To ensure that the design drawing can be seen more clearly by the designer, 1200 points are selected with a span of 0.01. Connect the points with the same value of the same feature in Figure 3 into a line, which is called a contour line. Different contour lines represent different meanings. In Figure 3 , black and gray, as well as solid lines, dashed lines, and dotted lines with different lengths are used to distinguish the contour lines. Taking the black solid line as an example, it represents the contour line of the absolute flow velocity angle of the rotor inlet fluid. The points on the line, that is, various design schemes on the line, have the same designed absolute flow velocity angle of the inlet fluid. In Figure 3 , it can be seen that the direction of the line is diagonally upward to the right, and its value increases continuously from left to right. From the feasibility inspection table in Table 1, the range of the absolute flow velocity angle of the inlet fluid that meets the design requirements is 66° - 78°. Therefore, the turbine design schemes outside this range cannot be used. Among them, the designs that do not meet the requirements due to the absolute flow velocity angle of the inlet fluid are in Figure 3It is marked with "×" in the figure. In addition to the contour lines of the absolute flow velocity angle α4 of the inlet fluid in the figure, there are also the relative flow velocity angle β4 of the inlet fluid of the rotor, the average value β of the relative flow velocity angle of the outlet fluid of the rotor 6rms , the speed parameter N s , the inlet radius r4 of the rotor, the root radius r of the outlet blade of the rotor 6h , the inlet height b4 of the rotor blade, the outlet height b6 of the rotor blade, the critical frequency ω of the trailing edge of the blade n and the ratio r4 / r of the inlet radius of the rotor to the tip radius of the outlet of the rotor 6t of the contour lines. The ranges that meet the design requirements are given in Table 1. For the coordinate points that do not meet the absolute flow velocity angle α4 of the inlet fluid, use for marking. For the coordinate points that do not meet the excitation frequency f r , use "+" to represent. For the coordinate points that do not meet the relative flow velocity angle β4 of the inlet fluid of the rotor, the ratio r4 / r of the inlet radius of the rotor to the tip radius of the outlet of the rotor 6t and the ratio r of the root radius of the outlet blade of the rotor to the tip radius of the outlet of the rotor 6h / r 6t , use to represent. For the structures that fully meet the design requirements in Table 1, use "●" to represent. From Figure 3 , it can be seen that there is a sub-design space enclosed by a thick black solid line. All the coordinate points inside it meet the design requirements of 100 kW and 160 kRPM. At the same time, these geometric structures also meet the design and production requirements. This area is called the reasonable design area. It can be seen that the upper and lower boundaries of the reasonable design area are limited by the relative flow velocity angle (β4) of the rotor inlet, the left part is limited by the critical frequency (ω n ) of the trailing edge of the blade, and the right part is limited by the geometric factor of the inlet height (b4) of the rotor blade. Its visualization results provide more diverse design options for designers.

[0118] When designers want to design turbines with different powers and speeds, designers only need to change the input of the program. After the program ends, they will also get Figure 3 the same visualization design drawing. Designers then select the head coefficient and flow coefficient within the solid line according to their needs. After determining, input these two parameters into the program, and they can obtain the geometric structure parameters under this design parameter, which can be directly used for turbine production.

Claims

1. A method for one-dimensional batch design and visualization of the design space of a radial turbine, characterized in that, It includes the following steps: (1) Initial setting of parameters, including output power W out , rotor speed N, flow coefficient energy head coefficient ψ, The definition of the flow coefficient is as follows: In Equation (1), U4 represents the circumferential velocity at the inlet of the turbine rotor, U4 = ωr4, where ω is the angular velocity of the turbine rotor and r4 is the blade radius at the inlet of the turbine rotor, and C m4 represents the radial component of the absolute velocity at the inlet of the turbine rotor; The definition of the energy head coefficient is as shown below: In formula (2), C θ4 represents the circumferential component of the absolute velocity of the gas flow at the inlet of the rotor; C θ6 represents the circumferential component of the absolute velocity of the gas flow at the outlet of the rotor; Δh0 is the enthalpy drop of the fluid per unit volume discharged through the turbine and is a constant value; r 6t is the radius at the tip of the rotor outlet blade; r4 is the radius of the rotor inlet blade; (2) Conjecture the initial total static efficiency value. The conjectured value of the total static efficiency of the turbine for determining the output power is obtained through the following formula: Among them, W out is the output power of the turbine, η ts is the guessed value of the total static efficiency of the turbine at this output power, ρ is the density of the working fluid, is the volume flow rate inside the turbine; (3) Rotor calculation The design values of the input and output power and the rotational speed are used to further distinguish different turbines according to the combination of the flow coefficient and the energy head coefficient. It is necessary to input the set values of the flow coefficient and the energy head coefficient, and then set the guessed value η of the total static efficiency. ts As the determination for loop termination, using the input output power, rotational speed, flow coefficient, energy head coefficient, and total static efficiency as known, as well as the turbine inlet pressure and inlet temperature, turbine volume flow rate, entropy index κ of the physical properties of the working fluid, and environmental parameters given as design requirements at the beginning. According to Equation (2), the circumferential velocity U4 of the rotor blade is solved, and then according to Equations (1) and (2), the radial component velocity and circumferential component velocity of the absolute velocity at the rotor inlet are respectively obtained. Finally, according to the triangle rule, that is, Equation (4), the absolute velocity of the fluid at the inlet is obtained, completing the calculation of the absolute velocity in the velocity triangle. Through calculation, the geometric parameters β4, b4, r4, r 6t , b6, t, Z r , L, L ms , β h , β t , r 6h , ε b , ε r , where β4 is the installation angle at the rotor inlet, b4 is the height of the rotor inlet blade, r4 is the radius of the rotor inlet blade, r 6t is the radius of the rotor outlet blade, b6 is the height of the rotor outlet blade, t is the thickness of the rotor blade, Z r is the number of rotor blades, L is the axial length of the impeller, L ms is the meridional length of the rotor, β h is the angle of the blade at the blade root, β t is the blade angle at the tip of the outlet blade, r 6h is the radius of the blade root at the rotor outlet, ε b is the distance between the rotor back and the rear cover plate, ε r is the tip clearance of the outlet blade, and the design calculation of the rotor is completed; (4) Stator calculation The height b of the stator s is a uniform height, which is the height of the rotor inlet blade, i.e., b s = b4; the stator air flow outlet angle α3 is the same as the rotor air flow inlet angle α4, i.e., α3 = α4. At the same time, for the stator, its stator installation angle is the same as the stator air flow angle; The stator outlet radius r3 = r4 + δ r , where δ r represents the gap between the stator and the rotor, and its calculation formula is as follows: δ r = 2b s α4(12) The stator inlet radius is r1, and r1 = r3a 13 , where a 13 represents the ratio of the stator inlet radius to the stator outlet radius; After obtaining the stator inlet radius and the stator outlet radius, and after obtaining the number of stators set by the user, obtain the lengths of the single flow channels at the stator inlet and the stator outlet, that is and where Z s represents the number of blades of the stator; the chord length C s is set to have a length of C s = b1; the calculation of the geometric dimensions of the stator is completed; (5) Model evaluation. Judge whether the total static efficiency converges. If it converges, conduct a feasibility check. If it does not converge, update the total static efficiency; After obtaining the geometric structures of the stator and the rotor, detect the geometric structures, and calculate its total static efficiency through the following formula; where, Δh loss is the enthalpy drop due to losses. Compare the calculated value of the total static efficiency with the guessed value. If the difference between the calculated total static efficiency and the guessed value is greater than 0.01, it is considered that the calculation has not converged. Substitute the calculated total static efficiency into the rotor calculation process in step (3) for recalculation until the difference between the calculated total static efficiency and the previously substituted total static efficiency value is less than or equal to 0.01, then confirm that the iteration has converged. At this point, a set of design calculations for the flow coefficient and energy head coefficient is completed; return to step (1) to perform the calculations for the next set of flow coefficient and energy head coefficient on the rotor and stator; (6) Feasibility check. Judge whether the model is feasible. If it is feasible, write the appropriate output. If it is not feasible, write the inappropriate output; (7) End the loop; (8) Plot all the turbine design points when the output power is W out and the rotor speed is N, mark the feasibility of the design scheme on the drawing, and plot the contour lines of the parameters.

2. The method for one-dimensional batch design and design space visualization of a radial turbine according to claim 1, wherein In step (1), the ratio of r 6t to r4 is set to 0.

3.

3. The method for one-dimensional design in batch and visualization of design space of a radial turbine according to claim 1, characterized in that, In step (3), the methods for obtaining each geometric parameter are as follows: According to obtain the absolute flow velocity angle α4 of the fluid at the rotor inlet; according to calculate the installation angle β4 at the rotor inlet; According to the input parameters, namely the inlet total pressure and the design pressure ratio, calculate the pressure at the rotor outlet. Under the conditions that the pressure and the enthalpy value at the rotor outlet are known, query the total temperature at the rotor outlet and other thermodynamic parameters corresponding to the conditions, including the outlet static pressure, the outlet static temperature, and the gas density; Similarly, under the conditions that the inlet total pressure and the inlet total enthalpy are known, query and obtain the gas density and temperature thermodynamic parameters at the inlet; The rotor inlet blade radius is calculated by the formula U4 = ωr4, and then the rotor outlet blade radius r is calculated according to the ratio of the set rotor outlet blade tip radius to the rotor inlet blade radius. 6t ; The blade height b4 at the rotor inlet is obtained through Equation (5) Among them, M represents the mass flow rate, which is input by the user. ρ4 represents the density of the working fluid at the rotor inlet, and its value is obtained by calling the REFPROP thermophysical property query software. C m4 represents the radial component of the absolute velocity at the rotor inlet, r4 represents the blade radius at the rotor inlet, t represents the rotor blade thickness, Z r represents the number of rotor blades. The rotor blade thickness t and Z r are set by the user; The radial component of the absolute velocity at the rotor outlet is C m6 = C m4 / ξ, where ξ represents the ratio of the radial component of the rotor absolute velocity; the circumferential component of the absolute velocity at the rotor outlet is C θ6 = 0; The height of the rotor outlet blade, i.e., b6, b6 = r 6t - r 6h , r 6t is the radius of the tip of the rotor outlet blade, and r 6h is the root radius of the rotor outlet blade. For the height b6 of the rotor outlet blade, an implicit calculation is performed, i.e., Among them, S6 is the outlet area, and its calculation formula is C6 represents the absolute flow velocity at the outlet, ρ6 represents the density of the working medium at the outlet, and b θ represents the angle between the true blade and the meridional plane blade at the rotor outlet, and the bisection method is used to calculate and solve equation (7). θ , and its implicit formula is as follows: where r 6rms represents the relative mean value of the rotor outlet blade radius, C m6 represents the radial component of the rotor outlet flow velocity, R represents the universal gas constant, T 04 represents the total temperature at the rotor inlet, and p4 represents the static pressure at the rotor inlet; Calculation formula for the axial length L of the impeller: L = b4 + r4 - r 6t (8) The thickness of the blade is set to a constant value, and the trailing edge thickness is 4% of the outlet blade height b6. The clearances between the front and rear covers of the rotor are ε r , ε b and ε a , the value of which is 5% of the rotor inlet blade height b4, ε r is the outlet tip clearance, that is, the distance between the rotor outlet and the front cover, ε b is the distance between the back of the rotor and the rear cover, ε a is the inlet tip clearance, that is, the distance between the rotor inlet and the front cover; The meridian length L of its rotor ms is calculated using the following formula where b4 is the rotor inlet blade height, r 6t is the radius at the tip of the rotor outlet blade, r 6h is the root radius of the rotor outlet blade, For the installation angle of the rotor blades at the outlet, i.e., the blade angle β at the blade root h and the blade angle β at the tip of the outlet blade t there is a smooth transition between the two angles; Among them Where: U 6h represents the circumferential velocity at the root of the rotor outlet blade, r 6h represents the radius of the root of the blade at the rotor outlet, U 6t represents the circumferential velocity at the tip of the rotor outlet blade, r 6t represents the radius of the tip of the blade at the rotor outlet, C θ6 is the circumferential component of the absolute velocity at the rotor outlet.

4. The method for one-dimensional design in batch and visualization of design space of a radial turbine according to claim 3, characterized in that In step (3), set t = 5 mm, Z r = 9; Set ξ = 1.

0.

5. The method for one-dimensional batch design and design space visualization of a radial turbine according to claim 3, wherein In step (3), the flow coefficient ranges from 0.1 to 0.4, the energy head coefficient ψ ranges from 0.7 to 1.1, and the value span for each time is 0.

001.

6. The method for one-dimensional design of radial turbines in batches and visualization of the design space according to claim 1, characterized in that In step (4), set a 13 = 1.25 7. The method for one-dimensional design in batch and design space visualization of a radial turbine according to claim 1, characterized in that In step (5), the calculation results of each group of flow coefficients and energy head coefficients are represented by a coordinate point diagram, and each group of results is a coordinate point.

8. The method for one-dimensional design in batch and visualization of design space of a radial turbine according to claim 1, characterized in that In step (6), the criteria for feasibility check include the following evaluation parameters and parameter ranges: the absolute flow velocity angle α4 of the fluid at the rotor inlet ranges from 66° to 78°, the relative flow velocity angle β4 of the fluid at the rotor inlet ranges from -40° to -20°, the Mach number M4 of the fluid at the rotor inlet ranges from < 1, and its calculation formula is M4 = U4 / C, where C represents the local speed of sound. The ratio r4 / r of the rotor inlet radius to the tip radius of the rotor outlet 6t ranges from ≥ 1.

42. The ratio r 6h / r 6t of the root radius to the tip radius of the rotor outlet blade ranges from ≥ 0.

4. The inlet height b4 of the rotor blade ranges from ≥ 0.9 mm. The rotor inlet radius r4 ranges from ≥ 10 mm. The iteration residual v i ranges from ≤ 1.0%. The elastic stress σ r ranges from < 0.9σ Y . The total static efficiency η of the turbine ts ranges from ≥ 50%. The frequency f generated by rotor excitation r ranges from ≥ 2ω n ; σ Y is the material yield stress, and ω n is the natural frequency of the rotor trailing edge.

9. The method for one-dimensional design of radial turbines in batches and visualization of the design space according to claim 1, characterized in that, In step (6), after the inspection is completed, draw a visualization drawing according to the inspection results; Classify the IDs of the turbines. The geometric parameters of each turbine ID are calculated according to one-dimensional design. Form a list of the calculation results, which includes the energy head coefficient and the flow coefficient. The calculation results of each group of flow coefficients and energy head coefficients are represented by a coordinate point diagram, and each group of results is a coordinate point; Mark each coordinate point and show whether the corresponding turbine under the coordinate point meets the design parameters to the designer.

10. The method for one-dimensional design in batch and design space visualization of a radial turbine according to claim 1, characterized in that In step (8), organize the data in the list in step (6). Concentrate the turbine IDs with equal geometric parameters, equivalently find the coordinates of the points with equal parameters, and then draw the isoline of this parameter at a certain value according to the coordinates.

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