Design method of hydraulic turbine based on axial velocity and entropy increase analysis and hydraulic turbine

Abstract

This invention discloses a hydraulic turbine design method based on axial velocity and entropy increase analysis, and the designed hydraulic turbine. The design method includes: determining the inlet and outlet diameters of the flow channel based on given parameters; initially drawing the main dimensions of the impeller and creating an impeller axial projection diagram; determining the centerline of the flow channel, and then drawing multi-segment axial flow cross-sections in the flow channel; calculating the axial flow cross-section velocity of each segment of the flow channel; correcting the flow channel based on the velocity changes; calculating the entropy production of each segment of the flow channel; determining the entropy increase region based on the entropy production of each segment of the flow channel, and correcting the flow channel in the entropy increase region to reduce hydraulic losses; keeping the optimized impeller structural parameters unchanged, adjusting the area ratio parameter by adjusting the guide vane outlet axial width to further optimize the hydraulic turbine efficiency; finally, obtaining the various parameters of the optimized hydraulic turbine. The hydraulic turbine of this invention has relatively low hydraulic losses.

Description

Technical Field

[0001] This invention relates to the field of turbine technology, and in particular to a hydraulic turbine design method and a hydraulic turbine based on axial velocity and entropy increase analysis. Background Technology

[0002] In recent years, the country has attached great importance to energy conservation and emission reduction, and the development and improvement of liquid energy recovery and utilization technology is of great significance to energy conservation and emission reduction. In processes such as petrochemicals, oil processing, seawater desalination, and iron and steel metallurgy, there are large amounts of high-pressure liquids. Previously, these high-pressure liquids were discharged through pressure reducing valves or orifice plates, resulting in energy waste. With the development of liquid residual pressure energy recovery technology, these high-pressure liquids can now achieve energy recovery by performing work through hydraulic turbines.

[0003] For example, Chinese patent document CN111808644A discloses a method for energy recovery of rich liquor in the decarbonization process of a natural gas purification plant. This method includes a portion of the rich liquor from the bottom of the absorber entering a hydraulic turbine recovery pipeline for energy recovery, then being sent to a flash tank for flash regeneration. A second portion enters a first bypass pipeline, and a third portion enters a second bypass pipeline. After flow adjustment, the second portion is sent to the flash tank for flash regeneration. The energy from the hydraulic turbine is transferred to a motor-driven lean liquor circulation pump, which pressurizes the regenerated lean liquor before returning it to the absorber for recycling. The latter includes an absorber, a first high-pressure differential angle throttling valve, a second high-pressure differential angle throttling valve, a hydraulic turbine, a first lean liquor circulation pump, and a flash tank.

[0004] Improving the recovery efficiency of hydraulic turbines makes the selection of turbine type and the optimization design of its flow-through components particularly important.

[0005] Currently, most hydraulic turbines on the market use the pump reversal method. Their design and calculation can be found in Professor Guan Xingfan's "Modern Pump Technology Handbook," which proposes commonly used turbine design flow channel methods.

[0006] Currently, commonly used turbine design methods have the following drawbacks:

[0007] (1) Selection of hydraulic turbine: Generally, the conversion relationship between the performance parameters of the centrifugal pump when it is in forward and reverse rotation is used as a reference. However, it is difficult to select a reasonable conversion coefficient for the specific speed. The conversion relationship also varies greatly under different specific speeds. The operating conditions of the centrifugal pump and the converted turbine design are not well matched. It is only suitable for operating conditions with relatively stable flow and the operating range is relatively narrow, resulting in low turbine recovery efficiency and poor performance.

[0008] (2) Hydraulic design of internal turbine flow components: The widely used impeller flow channel design technology employs conformal mapping using a grid. The process involves determining the inlet and outlet diameters, calculating efficiency, initially determining and drawing the main impeller dimensions, drawing the impeller axial projection, streamlining, drawing the grid, drawing the axial section lines, drawing the wooden model, and completing the design. The hydraulic design process for these flow components is relatively complex, and the connections at the flow channel bends are not smooth, resulting in significant hydraulic losses. Summary of the Invention

[0009] This invention provides a hydraulic turbine design method based on axial velocity and entropy increase analysis, which results in hydraulic turbines with smaller hydraulic losses.

[0010] The technical solution of the present invention is as follows:

[0011] A hydraulic turbine design method based on axial velocity and entropy increase analysis includes the following steps:

[0012] (1) Determine the inlet and outlet diameters of the flow channel based on the given parameters, and draw the main dimensions of the impeller and the axial projection of the impeller.

[0013] (2) Determine the flow channel centerline on the initially drawn impeller axial surface projection diagram, and then draw the multi-segment axial surface flow cross section in the flow channel, dividing the flow channel into multiple segments with the axial surface flow cross section as the boundary.

[0014] (3) Calculate the axial flow velocity of each flow channel; based on the change of the axial flow velocity of each flow channel, correct the flow channel and make the flow channels smoothly connected.

[0015] (4) Calculate the entropy production of each flow channel segment; determine the entropy increase region based on the entropy production of each flow channel segment, and modify the flow channel in the entropy increase region to reduce hydraulic loss.

[0016] (5) Keep the impeller structure parameters optimized in steps (1)-(4) unchanged, adjust the area ratio parameter by adjusting the width of the guide vane outlet shaft surface, and further optimize the hydraulic turbine efficiency; finally, obtain the various parameters of the optimized hydraulic turbine.

[0017] The front and rear cover plates of the hydraulic turbine are arranged in parallel, and the front and rear cover plates and the impeller form multiple flow channels; the flow channels are centrally symmetrical about the central axis of the hydraulic turbine.

[0018] After determining the inlet and outlet diameters, initially drawing the main dimensions of the impeller, and creating the impeller axial surface projection, this invention utilizes an optimization method based on axial velocity to better smooth the connection between the flow channel bend and the leading and trailing edges, reducing hydraulic losses and improving the recovery efficiency of the hydraulic turbine. Combined with the entropy production analysis method based on the second law of thermodynamics, it accurately and quickly locates the energy loss in the flow path. Based on the energy transformation, it identifies the entropy-increasing areas on the axial flow cross-section. By expanding or shrinking the axial profile of the flow channel, an efficient flow cross-sectional shape is obtained. Finally, by adjusting the area ratio parameter, the goal of reducing hydraulic losses in the hydraulic turbine is ultimately achieved.

[0019] To refine the flow channel streamlines, preferably, in step (2), the flow channel is divided into at least 6 segments by the axial flow cross section.

[0020] Preferably, the principle for drawing multi-segment axial flow cross sections is as follows: the axial flow cross sections on the outer side of the flow channel have equal heights and lengths, the axial flow cross sections on the inner side of the flow channel gradually approach each other, and the axial flow cross sections are perpendicular to the centerline of the flow channel.

[0021] A further preferred method for drawing the axial flow section is as follows:

[0022] ① Draw the first axial flow section r0 at a distance l / n from the leading edge of the flow channel on the outer side of the flow channel, and make the first axial flow section r0 perpendicular to the centerline of the flow channel. Here, l is the length from the inlet to the outlet of the flow channel on the outer side of the flow channel, and n is the number of segments of the flow channel. The direction of the axial flow section velocity V0 of the first axial flow section r0 is perpendicular to r0.

[0023] ② Draw the second axial flow section r1 at a distance of 2l / n from the leading edge of the flow channel on the outside of the flow channel, and make the second axial flow section r1 perpendicular to the centerline of the flow channel; the direction of the velocity V1 of the axial flow section r1 is perpendicular to r1.

[0024] ③ Draw the remaining axial flow sections using the same method.

[0025] In step (3), the velocity V of the axial flow section is calculated according to the formula. m :

[0026]

[0027] In the formula, Q is the critical flow rate; d m b is the inlet diameter of the segmented flow channel section; m ψ is the inlet width of the segmented flow channel section; ψ is the blade inlet displacement coefficient; r m It is a cross-section of the axial surface through which water flows;

[0028]

[0029] In the formula, dm+1 d is the outlet diameter of the segmented flow channel section; m The inlet diameter of the segmented flow channel section; θ is the polar angle; This is the wrap angle of the flow centerline.

[0030] In step (3), the flow channel is corrected based on the change in the axial flow cross-sectional velocity of each segment, including: when the axial flow cross-sectional velocity of the next segment is greater than that of the previous segment... When the width of the next flow channel segment is increased, the axial flow velocity of the next segment is less than that of the previous segment. If so, then reduce the width of the next flow channel segment.

[0031] In step (4), the entropy production of each flow channel includes the entropy production caused by the average velocity and the entropy production caused by the flow channel wall.

[0032] The entropy production S caused by average velocity VD The calculation formula is:

[0033]

[0034] In the formula, V is the flow velocity;

[0035]

[0036] ρ is the fluid density; ε is the turbulent dissipation rate; T is the temperature;

[0037] Entropy production S caused by flow channel wall pro The formula for calculating W is:

[0038]

[0039] In the formula, τ is the wall shear force; v is the velocity vector; T is the temperature; and A is the wall area.

[0040] In step (4), the entropy increase region is determined based on the entropy production of each flow channel, and the flow channel in the entropy increase region is modified, including:

[0041] Based on the entropy production of each flow channel segment, determine the entropy increase in the local flow channel area;

[0042] In a flow channel region with increasing entropy, adjustment nodes are selected on the walls on both sides of the flow channel; if there is entropy increase, the local flow channel area is expanded by adjusting the nodes; otherwise, the local flow channel area is reduced by adjusting the nodes.

[0043] By calculating and analyzing the entropy increase of the internal and wall surfaces of the segmented flow channel using the entropy production formula, and by adjusting the curvature of the inner and outer flow channels using the node control method, the entropy production loss of each flow channel segment is reduced, thereby increasing efficiency.

[0044] Step (5) includes:

[0045] Define the area ratio coefficient Y = F3 / F2, where F3 is the cross-sectional area of ​​the guide vane outlet and F2 is the cross-sectional area of ​​the impeller inlet;

[0046] Keeping the impeller structure parameters optimized in steps (1)-(4) unchanged, the area ratio parameter is adjusted by adjusting the width of the guide vane outlet axial surface.

[0047] For upstream and downstream hydraulic matching, i.e. matching the guide vane outlet section with the impeller inlet section, the area ratio parameter is adjusted by changing the guide vane outlet axial surface width.

[0048] Preferably, the optimized area ratio parameter is no greater than 2.

[0049] The present invention also provides a hydraulic turbine designed according to the above design method.

[0050] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0051] The existing hydraulic design technology for flow channels uses conformal mapping with a grid, which is cumbersome and difficult to understand; the connection at the bend is not smooth enough, resulting in increased hydraulic losses. The design method of this invention is based on comparative analysis of the original design, which is relatively simple. It achieves an efficient flow cross-sectional shape through local analysis, ultimately reducing losses. Attached Figure Description

[0052] Figure 1 This is a flowchart illustrating the hydraulic turbine design method of the present invention.

[0053] Figure 2 This is a projection of the impeller shaft surface drawn based on given parameters;

[0054] Figure 3 A schematic diagram illustrating the method for drawing a multi-segmented axial water passage section;

[0055] Figure 4 A schematic diagram illustrating the adjustment of the curvature of the inner and outer flow channels using the node control method;

[0056] Figure 5 This is a schematic diagram of upstream and downstream hydraulic matching. Detailed Implementation

[0057] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be noted that the embodiments described below are intended to facilitate the understanding of the present invention and do not limit it in any way.

[0058] The hydraulic turbine joint design method based on axial velocity and entropy increase analysis of the present invention is used to determine the axial profile of a hydraulic turbine. Its basic principle is to correct the area of ​​the flow cross section by axial velocity, obtain the transition cross section shape by geometric drawing, analyze the parts with significant energy loss by entropy increase analysis, and finally obtain an efficient flow cross section shape by precise hydraulic control at the point.

[0059] The turbine has a front cover and a rear cover, which are parallel to each other. Multiple sets of flow channels are directly connected to the front and rear covers of the turbine. These channels are symmetrically distributed about the turbine's central axis, and the flow cross-section of each channel is trapezoidal. The overall design method is detailed in the appendix. Figure 1 As shown:

[0060] (1) Determine the impeller's basic flow channel axial surface: Determine the inlet and outlet diameters based on given parameters, preliminarily draw the main dimensions of the impeller, and draw the impeller axial surface projection diagram, such as... Figure 2 As shown;

[0061] (2) Method for drawing multi-segment water passage sections: After determining the flow channel centerline on the initially drawn impeller axial projection drawing, multi-segment water passage sections are drawn in the flow channel of the axial projection drawing, such as... Figure 3 As shown.

[0062] Method for drawing multi-segment water flow cross sections:

[0063] ① Determine the first water passage section r0 in the flow channel: The height h1 of the first water passage section is taken at 1 / 4 of the line segment at the leading edge of the flow channel (the leading edge of the flow channel is from the impeller inlet to the elbow part); the streamline r0 of the first water passage section is obtained by perpendicularly and parallelly to the impeller inlet width b1 at the leading edge of the flow channel centerline; the axial velocity V0 is perpendicular to the first water passage section r0.

[0064] ② Determine the second water passage section r1 in the flow channel: The height h2 of the second water passage section is the same as h1; the centerline of the flow channel is perpendicular to the direction to obtain the second water passage section r1; the direction of the axial velocity V1 is perpendicular to the second water passage section r1.

[0065] ③ Determine the third water passage section r2 in the flow channel: The height h3 of the third water passage section is the same as h1; the centerline of the flow channel is perpendicular to the direction to obtain the third water passage section r2; the direction of the axial velocity V2 is perpendicular to the third water passage section r2.

[0066] ④ Determine the fourth water passage section r3 in the flow channel: The height h4 of the fourth water passage section is the same as h1; the centerline of the flow channel is perpendicular to the direction to obtain the fourth water passage section r3; the direction of the axial velocity V3 is perpendicular to the fourth water passage section r3.

[0067] Based on the above method of dividing the multi-segment axial cross-section, multiple cross-sections are sequentially divided. To refine the streamlines, the cross-section in the flow channel projection diagram is divided into at least 6 segments. The overall flow channel segmentation shows that the cross-section height is equal at the outer bends, and the cross-section at the inner bends gradually approaches the outer bends (see reference). Figure 3 ).

[0068] (3) Calculation of axial velocity: Based on the above method, the cross-sectional velocity r of the water passage is divided into segments. m Obtain the velocity V of each axial surface segment m The formula is:

[0069] ①Inlet shaft surface speed:

[0070]

[0071] In the formula

[0072] Q—Critical flow rate;

[0073] d m —Inlet diameter after segmentation;

[0074] r m —Axial surface water passage section;

[0075] b m —Inlet width after segmentation;

[0076] ψ—blade inlet displacement coefficient;

[0077] ② Axial surface water passage section:

[0078]

[0079] In the formula

[0080] d m+1 —Outlet diameter after segmentation;

[0081] d m —Inlet diameter after segmentation;

[0082] θ — polar angle;

[0083] —Cross-flow centerline wrap angle;

[0084] (4) Analysis method of axial surface velocity:

[0085] The axial flow cross-sectional velocity V calculated based on the above formula is... m Through different segments of axial flow section r m The velocity comparison analysis above determines the change in flow velocity within the flow channel. When the velocity of the next segment exceeds that of the previous segment... In this case, the width of the flow channel, i.e. the curvature of the two-sided flow channel, needs to be adjusted to correct the original flow channel and make it smoothly connected. (5) Entropy production calculation and analysis method:

[0086] The entropy production analysis method based on the second law of thermodynamics is used to quickly assess the hydraulic losses on the axial surface. Within this flow channel system, the entropy production area continuously increases with constant movement, resulting in entropy increases at certain locations. The entropy production formula is used to calculate and analyze the entropy increases within and on the walls of the segmented axial flow cross-section. The curvature of the inner and outer flow channels is adjusted using the nodal control method (e.g., ...). Figure 4 As shown, this reduces the entropy loss of each flow channel section, thereby increasing efficiency.

[0087] The specific method for controlling the node is as follows:

[0088] ① Using the entropy production formula, with the above-defined axial cross-sections as the dividing line, different cross-sections r are analyzed. m The flow channels and walls are calculated and compared using formulas, and the entropy increase in local flow channels is judged based on the calculated values.

[0089] ② Selecting Nodes: Based on the entropy increase region determined by the above calculations, select the required nodes on both sides of the flow path within this region. A positive entropy production calculation value indicates entropy increase; the larger the value, the greater the degree of disorder in entropy increase. There is no fixed point to determine this.

[0090] ③ Based on the entropy increase analysis, stretch the nodes in regions with entropy increase to expand the local flow channel area, and conversely, shorten the nodes to reduce the flow channel area.

[0091] Entropy production calculation:

[0092] The entropy production rate caused by average velocity:

[0093]

[0094] In the formula

[0095] ρ — density;

[0096] ε—Turbulent dissipation rate;

[0097] T – Temperature;

[0098] The entropy production S caused by the average velocity VD for:

[0099] Where V is velocity;

[0100] Entropy production near the wall:

[0101] Where A is the wall area;

[0102] In the formula

[0103] τ—wall shear force;

[0104] v — velocity vector;

[0105] T – Temperature;

[0106] (6) For upstream and downstream hydraulic matching, i.e., matching of the guide vane outlet section with the impeller inlet section, see attached... Figure 5 As shown, the area F3 of the guide vane outlet and the area F2 of the impeller inlet are defined with an area ratio coefficient Y = F3 / F2. With the impeller structural parameters unchanged, the area ratio parameter is adjusted by changing the width of the guide vane outlet axial surface using the node control method described in (5) above, so that the maximum deviation of the optimized model parameter area ratio Y' is 2. A node is also set at the guide vane outlet; adjusting the node changes the guide vane outlet width, i.e., increases the outlet area F3.

[0107] As the flow channel space inside the guide vane increases, the velocity of the fluid inside the flow channel decreases, and the low-velocity zone inside the flow channel becomes larger. As a result, the impact loss and friction loss inside the guide vane also decrease, increasing the area ratio and improving turbine efficiency.

[0108] The embodiments described above provide a detailed explanation of the technical solutions and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, additions, and equivalent substitutions made within the scope of the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for hydraulic turbine design based on the analysis of meridional velocity and entropy increase, characterized in that, Includes the following steps: (1) Determine the inlet and outlet diameters of the flow channel based on the given parameters, and preliminarily draw the main dimensions of the impeller and draw the axial projection of the impeller. (2) Determine the flow channel centerline on the initially drawn impeller axial surface projection diagram, and then draw the multi-segment axial surface flow cross section in the flow channel. Divide the flow channel into multiple segments with the axial surface flow cross section as the boundary. The principle for drawing the multi-segment axial surface flow cross section is: the axial surface flow cross section on the outside of the flow channel has the same height and length, the axial surface flow cross section on the inside of the flow channel approaches each other successively, and the axial surface flow cross section is perpendicular to the flow channel centerline. (3) Calculate the axial flow velocity of each flow channel segment; based on the change in axial flow velocity of each flow channel segment, correct the flow channel and ensure smooth connection of each flow channel segment, including: when the axial flow velocity of the next segment is greater than that of the previous segment... When the width of the next flow channel segment is increased, the axial flow velocity of the next segment is less than that of the previous segment. If so, then reduce the width of the next flow channel segment; (4) Calculate the entropy production of each flow channel segment separately. The entropy production of each flow channel segment includes the entropy production caused by the average velocity and the entropy production caused by the flow channel wall. Entropy production due to average velocity S VD The formula for calculating is: In the formula, V is the flow rate; is the fluid density; is the turbulent dissipation rate; T is the temperature; Entropy production by channel wall surface The calculation formula is: wherein is the wall shear stress; is the velocity vector; T is the temperature; A is the wall area; The entropy increase region is determined based on the entropy production of each flow channel segment. The flow channel in the entropy increase region is then modified to reduce hydraulic losses, including: Based on the entropy production of each flow channel segment, determine the entropy increase in the local flow channel area; In the flow channel region where entropy increases, adjustment nodes are selected on the walls on both sides of the flow channel; if there is entropy increase, the local flow channel area is increased by adjusting the nodes; otherwise, the local flow channel area is decreased by adjusting the nodes. (5) Keep the optimized impeller structure parameters of steps (1)-(4) unchanged, adjust the area ratio parameter by adjusting the width of the guide vane outlet shaft surface, and further optimize the hydraulic turbine efficiency; finally, obtain the various parameters of the optimized hydraulic turbine.

2. The method for hydraulic turbine design based on the analysis of the velocity of the generatrix and entropy increase according to claim 1, characterized in that, In step (2), the flow channel is divided into at least 6 segments by the axial flow cross section.

3. The method for hydraulic turbine design based on the analysis of the velocity of the generatrix and entropy increase according to claim 1, characterized in that, The method for drawing the axial flow section is as follows: ① On the outer side of the flow channel, at a distance from the leading edge of the flow channel l / n Draw the first axial flow section r0 at point [location], and make the first axial flow section r0 perpendicular to the centerline of the flow channel. l The length from the inlet to the outlet of the flow channel outside the channel. n The number of segments in the flow channel; the direction of the velocity V0 of the axial flow section r0 of the first segment is perpendicular to r0; ② At a distance of 2 meters from the leading edge of the flow channel on the outer side of the flow channel l / n Draw the second axial flow section r1, and make the second axial flow section r1 perpendicular to the centerline of the flow channel; the direction of the velocity V1 of the second axial flow section r1 is perpendicular to r1. ③ Draw the remaining axial flow sections using the same method.

4. The hydraulic turbine design method based on axial velocity and entropy increase analysis according to claim 1, characterized in that, In step (3), the velocity V of the flow section across the axial surface is calculated according to the formula m : In the formula, The critical flow rate; d m This refers to the inlet diameter of the segmented flow channel section; This refers to the inlet width of the segmented flow channel section; The blade inlet displacement coefficient; It is a cross-section of the axial surface through which water flows; In the formula, This refers to the outlet diameter of the segmented flow channel section. The inlet diameter of the segmented flow channel section; Polar angle; This is the wrap angle of the flow centerline.

5. The method for hydraulic turbine design based on the analysis of the velocity of the generatrix and entropy increase according to claim 1, characterized by the fact that, Step (5) includes: Define the area ratio coefficient Y = F3 / F2, where F3 is the cross-sectional area of ​​the guide vane outlet and F2 is the cross-sectional area of ​​the impeller inlet; Keep the impeller structure parameters optimized in steps (1)-(4) unchanged, and adjust the area ratio parameter by adjusting the width of the guide vane outlet shaft surface.

6. A hydraulic turbine, characterized in that The hydraulic turbine was designed according to any one of claims 1-5.

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