Design method of two-stage high-speed axial propeller pump for shallow water working condition

Abstract

The application discloses a design method of a two-stage high-speed axial propelling pump suitable for a shallow water working condition, and the two-stage high-speed axial propelling pump comprises a primary-stage impeller and a secondary-stage impeller, and is specifically implemented according to the following steps: according to the actual lift of the primary-stage impeller and the actual lift of the secondary-stage impeller, the actual design lift of the underwater vehicle in the design working condition is determined through a water jet propelling pump thrust and vehicle resistance balance equation; the cascade of the primary-stage impeller and the secondary-stage impeller is respectively designed by using a lift method, the section shape of the primary-stage impeller and the secondary-stage impeller is taken as an airfoil, the best airfoil shape in terms of anti-cavitation performance is selected, parameters in the actual design lift of the underwater vehicle in the design working condition are corrected according to the fluid dynamic characteristics of the airfoil, and the design of the two-stage axial pump impeller is completed; the two-stage axial pump for the underwater vehicle in the shallow water high-speed working condition can be quickly and efficiently designed, and the anti-cavitation performance requirement is met.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of underwater vehicle parameter design, and particularly relates to a design method of a two-stage high-speed axial flow propelling pump suitable for a shallow water working condition. BACKGROUND

[0002] The underwater vehicle is a new type of underwater unmanned platform, which can be applied to underwater execution of submarine war and anti-submarine war, anti-mine war, intelligence collection, target attack and the like, greatly expands the combat space of the surface and underwater combat system, and is an underwater combat equipment developed by major naval countries in the world.

[0003] With the development of military confrontation technology, higher performance requirements such as high speed, long range and strong concealment are put forward for the underwater vehicle. As the mainstream propeller of the underwater vehicle at present, the contra-rotating propeller is mature in technology and high in efficiency, but has the disadvantage that the rotating speed of the contra-rotating propeller is limited by cavitation and erosion phenomenon in the shallow water condition, and cannot meet the high speed thrust requirement in the shallow water.

[0004] The water jet propelling is a special propelling technology developed rapidly in the past three decades. The impeller blades of the axial flow propelling pump in the vehicle rotate at high speed to drive the fluid to work, and the high-speed water flow is formed by the contraction of the guide vane and the flow passage, and is sprayed from the outlet of the flow passage to generate the reaction force to push the vehicle forward. In the high-speed working condition in the shallow water, the water jet propelling has high efficiency and good anti-cavitation performance, and has the characteristics of strong adaptability to variable working conditions, small shallow water effect, simple transmission mechanism and low noise.

[0005] The water jet propelling pump used in the underwater vehicle has the characteristics of high rotating speed, high lift, small flow, large hub ratio and compact structure compared with the water jet propelling pump of the ship. The commonly used axial flow pump design method has many deficiencies when applied in the field of underwater vehicles. In addition, when the underwater vehicle is sailing at high speed near the water surface, the suction surface of the single-stage axial flow pump blade will be cavitated in a large area, resulting in a decrease in the lift and the propelling pump cannot provide sufficient thrust. SUMMARY

[0006] The purpose of the application is to provide a design method of a two-stage high-speed axial flow propelling pump suitable for a shallow water working condition, which can quickly and efficiently design the two-stage axial flow pump used by the underwater vehicle in the high-speed working condition in the shallow water, and improve the sailing power of the underwater vehicle in the shallow water working condition.

[0007] The technical scheme adopted by the application is a design method of a two-stage high-speed axial flow propelling pump suitable for a shallow water working condition, which comprises a primary stage impeller and a secondary stage impeller, and is implemented according to the following steps.

[0008] Step 1, according to the actual head of the primary impeller, the actual head of the secondary impeller, the water jet propulsion pump thrust and the vehicle resistance balance equation, the actual design head of the underwater vehicle at the design condition is determined;

[0009] Step 2, the cascade of the primary impeller and the secondary impeller is designed by using the "lift method", the section shape of the primary impeller and the secondary impeller is taken as an airfoil, the best airfoil shape in anti-cavitation is selected, the parameters in the actual design head of the underwater vehicle at the design condition are corrected according to the fluid dynamic characteristics of the airfoil, and the double-stage axial flow pump impeller design is completed.

[0010] The application also has the characteristics that:

[0011] The specific process of step 1 is:

[0012] Step 1.1, when the underwater vehicle sails at the design speed v t and the design depth y, the thrust and resistance balance equation is met:

[0013]

[0014] In the formula, Q is the mass flow of fluid flowing through the internal flow passage, v e is the flow velocity at the outlet of the axial flow pump, A e is the area at the outlet of the axial flow pump, v t is the sailing speed of the vehicle when sailing at a constant speed, k iv is the flow passage inlet velocity coefficient, X is the sailing resistance of the vehicle, and p is the liquid density;

[0015] In the formula, v e is the flow velocity at the outlet of the flow passage:

[0016]

[0017] In the formula, k ip is the flow passage inlet static pressure recovery coefficient, k wp is the flow passage outlet static pressure recovery coefficient, and k H is the head loss coefficient;

[0018] The sailing resistance X is expressed as:

[0019]

[0020] In the formula, C f is the sailing resistance coefficient characterized by the maximum wetted area, and A1 is the maximum cross-sectional area of the vehicle;

[0021] The flow passage design flow Q v is expressed as:

[0022] Qv = A e v e (4)

[0023] Design head H of two-stage high-speed axial flow propeller pump z is expressed as:

[0024]

[0025] NPSH of two-stage axial flow pump a is expressed as:

[0026]

[0027] Step 1.2, the auxiliary impeller of the two-stage high-speed axial flow propeller pump is opposite in rotation direction to the main impeller, the total head is borne by the auxiliary impeller head and the main impeller head, the pre-cavitation head of the main impeller is improved to meet the demand of the auxiliary impeller head, and the auxiliary impeller head distribution and the NPSH of the device are distributed in the head distribution process a are the same,

[0028] The auxiliary impeller head distribution H is expressed as:

[0029] H = NPSH a (7)

[0030] The main impeller head distribution H' is expressed as:

[0031] H' = H z -H (8);

[0032] Step 1.3, the basic calculation equation for designing the impeller by using the lift method is:

[0033]

[0034] In the formula: C L is the lift coefficient of the airfoil in the cascade, l / t is the cascade density, g is the local gravity acceleration, H t is the theoretical head of the main impeller or the auxiliary impeller, ω ∞ is the geometric average speed of the liquid flow relative speed, v m is the axial surface speed in the impeller, u is the circumferential speed, λ is the lift-drag ratio angle of the airfoil, β ∞ is the angle between the direction of the geometric average speed ω ∞ of the liquid flow relative speed and the horizontal direction;

[0035] Step 1.4, when designing the main impeller, the guide vane head loss H xz is expressed as:

[0036]

[0037] where k is a correction factor, v u2 is the tangential component of the absolute velocity at the outlet of the main impeller;

[0038] H sj is the actual design head of the main impeller;

[0039] H sj = H xz + H

[0040] where H xz is the theoretical head of the main impeller, and H L is the guide vane head loss.

[0041] The specific process of using the "lift method" to design the cascade of the main impeller and the auxiliary impeller in step 2 is as follows: a plurality of calculation sections are selected according to the linear change between the hub and the rim of the impeller, the cascade density l / t is determined by selecting the blade overlap coefficient m, the lift coefficient C L of the airfoil in the cascade is solved by substituting the cascade density l / t into formula (9), the given airfoil lift-drag ratio angle λ, and finally the attack angle and camber of the airfoil section are determined.

[0042] The specific process of correcting the parameters in the actual design head of the underwater vehicle in the design condition according to the fluid dynamic characteristics of the airfoil is as follows: the motion of the liquid in the impeller is regarded as a compound motion, the compound motion is decomposed into the relative motion of the relative motion to the impeller and the entrainment motion with the rotation of the impeller, the motion characteristics of the liquid in the impeller are determined by solving the velocity triangle, the subscript "1" represents the inlet of the impeller, the subscript "2" represents the outlet of the impeller, and the parameters in the actual design head are represented as:

[0043] The axial velocity v m is represented as:

[0044]

[0045] where Q v is the volume flow, A is the flow area, and η v is the volumetric efficiency;

[0046] The peripheral velocity u is represented as:

[0047]

[0048] where r is the radius of the calculation section;

[0049] The tangential component v u2 of the absolute velocity at the outlet of the auxiliary impeller is represented as:

[0050] v u2 = v u1 + Ht • g / u (14)

[0051] where v u1 is the tangential component of the absolute velocity at the inlet of the secondary impeller;

[0052] Assuming that the incoming flow at the inlet of the secondary impeller has no pre-whirl, the tangential component of the absolute velocity at the inlet of the secondary impeller v u1 = 0;

[0053] Neglecting the hydraulic loss between the two impellers, the tangential component of the absolute velocity at the inlet of the primary impeller v u1 is equal in magnitude but opposite in direction to the tangential component of the absolute velocity at the outlet of the secondary impeller v u2 , so we have:

[0054] v u1 ′ = -v u2 (15)

[0055] The absolute velocity at the outlet of the impeller v2is:

[0056]

[0057] The geometric mean of the relative velocities at the inlet and outlet of the impeller ω ∞ :

[0058]

[0059] The radial angle β of the geometric mean of the relative velocities at the inlet and outlet of the impeller: ∞ :

[0060]

[0061] The hydraulic efficiency of the cascade η h :

[0062]

[0063] The theoretical head H of the primary impeller and the secondary impeller designed: t :

[0064] H t = H sj / η h (20)

[0065] Based on the numerical simulation method to determine the influence of the cascade on the hydrodynamic characteristics of the airfoil and make corrections, determine the value of λ:

[0066] The cascade pitch is represented as t, and the expression is:

[0067] t = 2πr / z (21)

[0068] where r is the radius at the calculation section, and z is the number of impeller blades.

[0069] The l / t of the cascade is expressed as:

[0070] l / t = m / cosβ' (22)

[0071] where m is the blade overlap coefficient, and β' is the blade installation angle,

[0072] The blade installation angle β' is:

[0073] β' = β + α (23) ∞

[0074] where α is the airfoil angle of attack;

[0075] The lift coefficient C of the airfoil is equal to the sum of the lift coefficient C L generated by the camber and the lift coefficient C Lh generated by the angle of attack α; Lα

[0076] The lift coefficient C Lh generated by the camber is:

[0077]

[0078] where h max / l is the maximum relative camber of the airfoil, y max / l is the maximum relative thickness of the airfoil, and k' is the camber lift loss coefficient;

[0079] The angle of attack α is calculated by:

[0080]

[0081] The camber correction formula is:

[0082]

[0083] The pump NPSH is: r

[0084]

[0085] where x is the cavitation allowance coefficient.

[0086] According to the airfoil chord length l, thickness y max , camber h max l and the airfoil coordinate and camber line coordinate determined by the section calculation results, the two-dimensional value point coordinate of each section airfoil is determined according to the above parameters, the two-dimensional value point coordinate of each section airfoil is projected on the three-dimensional cylindrical surface to obtain the three-dimensional space coordinate of the airfoil;

[0087] ​​​The modified parameters are returned to step 1 until the number of iterations reaches 100, and the parameters of the two-stage axial flow pump impeller are output.

[0088] The two-dimensional value point coordinates obtained are projected on a three-dimensional cylindrical surface projection formula as follows:

[0089]

[0090] In the formula, θ is the inclination angle; φ is the installation angle; R is the radius of the cylindrical surface where the blade section is located; x1 and y1 are the horizontal and vertical coordinates corresponding to the two-dimensional airfoil; L is the length from the two-dimensional airfoil coordinate origin to the rotation center; and x, y and z are three-dimensional space coordinates of different sections of the impeller. i

[0091] The present application has the following beneficial effects:

[0092] The present application is suitable for a two-stage high-speed axial flow propeller pump design method under shallow water conditions, the required head and flow of the two-stage axial flow propeller pump are determined by balancing the thrust and drag and determining various loss coefficients in the flow passage, the head distribution of the double-stage pump is realized according to the non-cavitation of the system and the total pressure before the pump, the lift method water pump design criterion is adopted, the anti-cavitation airfoil is selected according to the water pump basic equation, and the wireless wing span correction method suitable for small axial flow pumps is proposed and used, so that the two-stage axial flow pump used by the underwater vehicle under the shallow water high-speed working condition can be quickly and efficiently designed, and the anti-cavitation performance requirement is met. BRIEF DESCRIPTION OF DRAWINGS

[0093] Figure 1 is a flow chart of the two-stage high-speed axial flow propeller pump design method suitable for shallow water conditions according to the present application;

[0094] Figure 2 is a schematic diagram of the inlet and outlet velocity triangle of the secondary impeller in the present application;

[0095] Figure 3 is a schematic diagram of the blade row section in the present application;

[0096] Figure 4 is an airfoil line type diagram in the present application;

[0097] Figure 5 is a schematic diagram of the inlet and outlet velocity triangle of the primary impeller in the present application;

[0098] Figure 6 is a schematic diagram of the two-stage high-speed axial flow pump structure in the present application. DETAILED DESCRIPTION

[0099] The present application will be described in detail below in combination with the drawings and specific embodiments.

[0100] The present application is suitable for a two-stage high-speed axial flow propeller pump design method under shallow water conditions, the required head and flow of the two-stage axial flow propeller pump are determined by balancing the thrust and drag and determining various loss coefficients in the flow passage, the head distribution of the double-stage pump is realized according to the non-cavitation of the system and the total pressure before the pump, the lift method water pump design criterion is adopted, the anti-cavitation airfoil is selected according to the water pump basic equation, and the wireless wing span correction method suitable for small axial flow pumps is proposed and used, so that the two-stage axial flow pump used by the underwater vehicle under the shallow water high-speed working condition can be quickly and efficiently designed, and the anti-cavitation performance requirement is met.​Figure 1 As shown in the figure, the two-stage high-speed axial flow propeller pump comprises a main-stage impeller and an auxiliary-stage impeller, and is implemented according to the following steps:

[0101] Step 1, according to the actual head of the main-stage impeller and the actual head of the auxiliary-stage impeller, the actual design head of the underwater vehicle at the design condition is determined through the water jet propeller thrust and the vehicle resistance balance equation, and the specific process is as follows:

[0102] Step 1.1, when the underwater vehicle is sailing at the design speed v t and the design depth y, the thrust and resistance balance equation is satisfied:

[0103]

[0104] In the formula, is the mass flow rate of the fluid flowing through the internal flow passage, v e is the flow rate at the outlet of the axial flow pump, A e is the area at the outlet of the axial flow pump, v t is the sailing speed of the vehicle when sailing at a constant speed, k iv is the flow passage inlet velocity coefficient, X is the sailing resistance of the vehicle, and p is the liquid density;

[0105] In the formula, v e is the flow rate at the outlet of the flow passage:

[0106]

[0107] In the formula, k ip is the flow passage inlet static pressure recovery coefficient, k wp is the flow passage outlet static pressure recovery coefficient, k H is the head loss coefficient;

[0108] The sailing resistance X is expressed as:

[0109]

[0110] In the formula, C f is the sailing resistance coefficient characterized by the maximum wetted area, and A1 is the maximum cross-sectional area of the vehicle;

[0111] The flow passage design flow rate Q v is expressed as:

[0112] Q v =A e v e (4)

[0113] The design head H z of the two-stage high-speed axial flow propeller pump is expressed as:

[0114]

[0115] Device NPSH of double-stage axial flow pump a is expressed as:

[0116]

[0117] Step 1.2, the auxiliary impeller of the double-stage high-speed axial flow propelling pump is opposite in rotation direction to the main impeller, the total head is borne by the head of the auxiliary impeller and the head of the main impeller, the pump pre-cavitation allowance of the main impeller is improved to meet the demand of the head of the auxiliary impeller (without cavitation), and in the head distribution process, the auxiliary impeller distribution head and the device NPSH a are the same,

[0118] The auxiliary impeller distribution head H is expressed as:

[0119] H = NPSH a (7)

[0120] The main impeller distribution head H' is expressed as:

[0121] H' = H z -H (8);

[0122] Step 1.3, the basic calculation equation for designing the impeller by using the lift method is:

[0123]

[0124] In the formula, C L is the lift coefficient of the airfoil in the cascade, l / t is the cascade density, g is the local gravity acceleration, H t is the theoretical head of the main impeller or the auxiliary impeller, ω ∞ is the geometric average speed of the liquid flow relative speed, v m is the axial surface speed in the impeller, u is the circumferential speed, λ is the lift-drag ratio angle of the airfoil, β ∞ is the angle between the direction of the geometric average speed ω ∞ of the liquid flow relative speed and the horizontal direction;

[0125] Step 1.4, the main impeller is directly driven by the high-speed first-stage turbine, the impeller speed is high, and the total pressure loss of the liquid in the rear guide vane cannot be ignored. When designing the main impeller, the guide vane head loss H xz needs to be added, which is expressed as:

[0126]

[0127] In the formula, k is a correction coefficient, v u2 ' is the circumferential component of the absolute speed at the outlet of the main impeller;

[0128] actual design head H of the main stage impeller sj :

[0129] H sj = H' + H xz (11)

[0130] wherein H' is the theoretical head of the main stage impeller, H xz is the guide vane head loss.

[0131] Step 2, the "lift method" is used to design the cascade of the main stage impeller and the auxiliary stage impeller respectively, specifically: according to the linear change of the hub to the rim of the impeller, a plurality of calculation sections are selected, the cascade density l / t is determined by selecting the blade overlap coefficient m, substituted into formula (9), the given wing profile lift-drag ratio angle λ is given, the lift coefficient C L of the wing profile in the cascade is solved, and finally the attack angle and camber of the wing profile section are determined.

[0132] The section shape of the main stage impeller and the auxiliary stage impeller is taken as a wing profile, the wing profile shape with the best anti-cavitation property is selected, the parameters in the actual design head of the underwater vehicle at the design condition are corrected according to the fluid dynamic characteristics of the wing profile, and the design of the double-stage axial flow pump impeller is completed.

[0133] The parameters in the actual design head of the underwater vehicle at the design condition are corrected according to the fluid dynamic characteristics of the wing profile, specifically: the motion of the liquid in the impeller is taken as a kind of compound motion, the compound motion is decomposed into the relative motion of the relative motion and the relative motion of the relative motion, the motion characteristics of the liquid in the impeller are determined by solving the velocity triangle, the subscript "1" represents the inlet of the impeller, the subscript "2" represents the outlet of the impeller, and the parameters in the actual design head are represented as:

[0134] the axial velocity v m is represented as:

[0135]

[0136] In the formula, Q v is the volume flow, A is the flow area, η v is the volumetric efficiency;

[0137] The peripheral velocity u is represented as:

[0138]

[0139] In the formula, r is the radius of the calculation section;

[0140] The peripheral component v u2 of the absolute velocity at the outlet of the auxiliary stage impeller is represented as:

[0141] v u2 = v u1 + H t · g / u (14)

[0142] where v u1 is the circumferential component of the absolute velocity at the inlet of the secondary impeller;

[0143] Assuming that the incoming flow at the inlet of the secondary impeller is not pre-rotated, the circumferential component v u1 of the absolute velocity at the inlet of the secondary impeller is:

[0144] Neglecting the hydraulic losses between the two impellers, the circumferential component v u1 of the absolute velocity at the inlet of the primary impeller is equal in magnitude and opposite in direction to the circumferential component v u2 of the absolute velocity at the outlet of the secondary impeller, so that:

[0145] v u1 ′ = - v u2 (15)

[0146] The absolute velocity v2at the outlet of the impeller is:

[0147]

[0148] The geometric mean ω ∞ of the relative velocities at the inlet and outlet of the impeller is:

[0149]

[0150] The radial angle β ∞ of the geometric mean of the relative velocities at the inlet and outlet of the impeller is:

[0151]

[0152] The hydraulic efficiency η h of the cascade is:

[0153]

[0154] The theoretical head H t designed for the primary and secondary impellers is:

[0155] H t = H sj / η h (20)

[0156] The cascade airfoil is NACA66 a＝0.8The airfoil has maximum thickness in the middle, has good cavitation resistance, and can meet the requirements of low resistance and high lift. The airfoil uses a camber line of α=0.8, and has uniform pressure distribution in the range of 80% of the chord length. The influence of the cascade on the hydrodynamic characteristics of the airfoil is determined based on a numerical simulation method and is corrected, and the value of λ is determined:

[0157] The cascade pitch is expressed as t, and the expression is:

[0158] t=2πr / z (21)

[0159] In the formula, r is the radius at the calculation section, and z is the number of impeller blades;

[0160] The cascade density l / t is expressed as:

[0161] l / t=m / cosβ' (22)

[0162] In the formula, m is the blade overlap coefficient, and β' is the blade installation angle,

[0163] The blade installation angle β' is:

[0164] β'=β ∞ +α (23)

[0165] In the formula, α is the airfoil attack angle;

[0166] The lift coefficient C L of the airfoil is equal to the sum of the lift coefficient C Lh generated by the camber and the lift coefficient C Lα generated by the attack angle α;

[0167] The lift coefficient C Lh generated by the camber is:

[0168]

[0169] In the formula, h max / l is the maximum relative camber of the airfoil, y max / l is the maximum relative thickness of the airfoil, and k' is the camber lift loss coefficient;

[0170] For NACA66 a＝0.8 Such cambered airfoils make the fluid flowing through the cascade curved, causing the liftless angle of the airfoil to decrease and weakening the ability of the airfoil camber to generate lift. The attack angle α is calculated as follows:

[0171]

[0172] The camber correction formula is:

[0173]

[0174] Design h max / l can be given a set of initial values, generally y max / l of 1 / 2, and can be calculated by iteration.

[0175] Pump NPSH r :

[0176]

[0177] In the formula, x is the cavitation allowance coefficient.

[0178] By comparing the pump cavitation allowance and the device cavitation allowance, it is determined whether the impeller will cavitate.

[0179] According to the chord length l of the airfoil obtained from the section calculation result, the thickness y max , the camber h max l and the airfoil coordinate and camber line coordinate of the determined shape, the two-dimensional value point coordinates of each section airfoil are determined according to the above parameters, the two-dimensional value point coordinates of each section airfoil are projected on the three-dimensional cylindrical surface, and the three-dimensional space coordinates of the airfoil are obtained.

[0180] The obtained two-dimensional value point coordinates are projected on the three-dimensional cylindrical surface projection formula:

[0181]

[0182] In the formula, θ is the pitch angle; φ is the installation angle; R i is the radius of the cylindrical surface where the blade section is located; x1, y1 are the corresponding horizontal and vertical coordinates of the two-dimensional airfoil, L is the length from the two-dimensional airfoil coordinate origin to the rotation center, and x, y, z are the three-dimensional space coordinates of different sections of the impeller.

[0183] The corrected parameters are returned to step 1 until the iteration number reaches 100, and the double-stage axial flow pump impeller parameters are output.

[0184] Embodiment

[0185] The present application provides a double-stage high-speed axial flow propeller pump under shallow water conditions, which meets the power indicators of a 324 caliber underwater vehicle with a navigation depth of 10 m and a navigation speed of 70 Kn.

[0186] When the underwater vehicle operates at a water depth of 10 m and a navigation speed of 70 knots, the liquid density ρ = 998.2 kg / m 3 , the given flow passage coefficient k iv = 0.72, k ip = 0.18, k wp = 0.1, k H = 1.06, the resistance coefficient C f= 0.094, cross-sectional area A1 = 0.0824 m2 2 .

[0187] Flow rate v at the outlet of the flow passage e :

[0188]

[0189] Design head H of the two-stage high-speed axial propeller pump z :

[0190]

[0191] Navigation resistance X:

[0192]

[0193] Design flow rate Q:

[0194]

[0195] Net positive suction head NPSH of the device a :

[0196]

[0197] According to the thrust resistance balance equation, the calculation of the navigation resistance and the flow rate at the outlet of the flow passage, the head H of the multi-stage high-speed axial propeller pump is obtained z = 129.3 m, flow rate Q = 0.21 m3 / s, hub diameter is 80 mm, and rim diameter is 134 mm. 3

[0198] Net positive suction head NPSH of the secondary impeller a = 31.9 m, the secondary impeller is allocated a head H = 32 m, and the number of blades z = 6; the head H' of the primary impeller is H z = 97.3 m, the rotational speed n' of the primary impeller is 10,000 rpm, the number of blades z' is 7, and the gap S1 between the secondary impeller and the primary impeller is 10% of the outer diameter D of the impeller, which is 13.4 mm.

[0199] Now according to Figure 1 the impeller design flowchart, the design of the secondary impeller and the primary impeller is continuously iterated.

[0200] The inlet and outlet velocity triangles of the secondary impeller are as shown in Figure 2 , seven calculation sections are selected as shown in Figure 3 , the blade overlap coefficient m of each section is 1.2, the lift-drag ratio angle λ is 0.036, the maximum relative thickness y max / l at the blade root is 0.08, and the maximum relative thickness y max ​ / l=0.03, the intermediate section changes linearly. Solve the inlet and outlet velocity triangles by section:

[0201] axial velocity v m :

[0202]

[0203] In the formula Q v Let A be the volumetric flow rate, A be the channel area, and η be the flow rate. v Let η be the volumetric efficiency. v =0.99;

[0204] Circular velocity u:

[0205]

[0206] Auxiliary stage impeller inlet absolute velocity v u1 Circumferential component v u1 =0,

[0207] Circumferential component v of the absolute velocity at the outlet of the auxiliary stage impeller u2 for:

[0208] v u2 =v u1 +H t ·g / u

[0209] The absolute velocity v2 at the outlet of the auxiliary stage impeller is:

[0210]

[0211] Geometric mean ω of the relative velocities at the inlet and outlet of the auxiliary stage impeller ∞ :

[0212]

[0213] The radial angle β of the geometric mean of the relative velocities at the inlet and outlet of the auxiliary stage impeller ∞ :

[0214]

[0215] Hydraulic efficiency η of auxiliary stage impeller blades h :

[0216]

[0217] Theoretical head H of auxiliary stage impeller t :

[0218] H t =H / η h

[0219] NACA66a＝0.8 airfoil Figure 4 As shown, this airfoil employs a camber line of α = 0.8, resulting in a uniform pressure distribution within 80% of the chord length. Its maximum thickness is located in the middle of the airfoil, exhibiting characteristics of a high-cavitation-resistance airfoil. In lift-based design, each airfoil has a minimum λ angle; the region with the minimum λ angle corresponds to the region of highest lift-to-drag ratio. When the airfoil's angle of attack is located in the region of highest lift-to-drag ratio, the cascade efficiency reaches its maximum. NACA66 a＝0.8 The airfoil has a maximum lift-to-drag ratio of 27.5, which translates to a design parameter λ = 0.036.

[0220] Blade pitch t:

[0221] t = 2πr / z

[0222] In the formula, r is the radius at the calculated section, and the number of impeller blades z = 6;

[0223] Leaf lattice density l / t:

[0224] l / t=m / cosβ′

[0225] In the formula, m is the blade overlap coefficient, and β′ is the blade installation angle.

[0226] Required lift coefficient C for the blade cascade L :

[0227]

[0228] For NACA66 a＝0.8 This type of cambered airfoil causes the fluid flowing through the blade cascade to bend, resulting in a decrease in the airfoil's zero-lift angle and weakening its ability to generate lift. The camber correction formula is:

[0229]

[0230] The lift coefficient C generated by the camber Lh

[0231]

[0232] In the formula, h max / l represents the maximum relative camber of the airfoil, y max / l is the maximum relative thickness of the airfoil, and k′ is the camber lift loss coefficient, which is taken as 0.73;

[0233] The angle of attack α is calculated by the following formula:

[0234]

[0235] Blade installation angle β′:

[0236] β′=β ∞+ α

[0237] Net positive suction head NPSH r :

[0238]

[0239] Where x is the cavitation factor, x = 0.63C L ;

[0240] The difference between the pump NPSH and the device NPSH can be used as a basis for judging whether the impeller is cavitated. When the pump NPSH is too large, the design needs to be re-designed by adjusting the blade overlap coefficient m.

[0241] According to the above steps and Figure 1 The calculation results of each section of the secondary impeller are obtained through continuous iteration of the impeller design flowchart as shown in Table 1:

[0242] Table 1

[0243] Serial number Parameter Unit [r1] [r2] [r3] [r4] [r5] [r6] [r7] 1 r m 0.04 0.0444 0.0490 0.0535 0.0580 0.0625 0.0670 2 H m 32 32 32 32 32 32 32 3 u m / s 33.50 37.27 41.04 44.81 48.58 52.35 56.12 4 v u2 ]]> m / s 12.53 11.32 10.33 9.51 8.82 8.23 7.72 5 v m ]]> m / s 23.61 23.61 23.61 23.61 23.61 23.61 23.61 6 ∞ ]]> ​ ° 36.04 39.45 42.94 46.49 50.08 53.70 57.34 7 β ∞ ]]> ° 40.93 36.76 33.35 30.52 28.13 26.08 24.31 8 [C L ]]> 0.3990 0.3504 0.3065 0.2684 0.2359 0.2082 0.1847 9 α ° 2.88 2.53 2.25 2.02 1.85 1.72 1.63 10 β′ ° 43.81 39.29 35.60 32.54 29.98 27.81 25.95 11 [[ y max ]]> m 0.0056 0.0052 0.0048 0.0044 0.00392 0.0034 0.0028 12 h maxl ]]> m 0.0028 0.0026 0.0024 0.0022 0.0020 0.0017 0.0014 13 l m 0.0696 0.0722 0.0757 0.0797 0.0841 0.0888 0.0936

[0244] The inlet and outlet velocity triangles of the primary impeller are as shown in Figure 5 The root blade overlap coefficient m is selected as 1, the blade overlap coefficient m at the tip is selected as 0.9, the linear profile of each section decreases in the middle, the lift-drag ratio angle λ is selected as 0.036, the maximum relative thickness y max / l at the root is selected as 0.08, the maximum relative thickness y max / l at the tip is selected as 0.03, and the linear profile of the middle section changes.

[0245] The design of the secondary impeller is basically the same, and it needs to be noted that the circumferential component v u1 ′ of the absolute velocity at the inlet of the primary impeller is the same in size and opposite in direction as the circumferential component v u2 of the absolute velocity at the outlet of the secondary impeller;

[0246] v u1 ′ = -v u2

[0247] The actual design head H sj of the primary impeller needs to include the head loss in the guide vane:

[0248] H sj = H′ + H xz

[0249] The theoretical head H t of the primary impeller:

[0250] H t = H sj / η h

[0251] The design process of the auxiliary stage impeller was repeated, and the calculation results of each section of the main stage impeller were obtained as shown in Table 2:

[0252] Table 2

[0253] Serial number Parameter Unit [r1] [r2] [r3] [r4] [r5] [r6] [r7] 1 r m 0.04 0.0444 0.0490 0.0535 0.0580 0.0625 0.0670 2 H m 97.3 97.3 97.3 97.3 97.3 97.3 97.3 3 H sj ]]> m 108.48 105.51 103.67 102.43 101.54 100.88 100.36 3 u m / s 41.87 46.58 51.29 56.01 60.72 65.44 70.15 4 v u2 ]]> m / s 15.00 12.91 11.43 10.32 9.43 8.71 8.11 5 v m ]]> m / s 23.61 23.61 23.61 23.61 23.61 23.61 23.61 6 ∞ ]]> ​ ° 46.99 51.51 55.96 60.40 64.86 69.33 73.82 7 β ∞ ]]> ° 30.16 27.28 24.95 23.01 21.34 19.90 18.65 8 [C L ]]> 0.8549 0.7373 0.6449 0.5706 0.5101 0.4602 0.4186 9 α ° 7.96 6.71 5.79 5.10 4.60 4.25 4.02 10 β′ ° 38.12 33.99 30.74 28.11 25.95 24.16 22.67 11 [[ y max ]]> m 0.0036 0.0034 0.0031 0.0027 0.0024 0.0020 0.0016 12 h maxl ]]> m 0.0018 0.0017 0.0015 0.0014 0.0012 0.0010 0.0008 13 l m 0.0456 0.0468 0.0483 0.0499 0.0515 0.0529 0.0543

[0254] Based on the airfoil chord length l and thickness y obtained from the section calculation results max curvature h maxl and NACA66 α＝0.8 First, determine the airfoil coordinates and camber line coordinates, then determine the two-dimensional profile coordinates of each airfoil section. Project these two-dimensional profile coordinates onto the surface of a three-dimensional cylinder to obtain the airfoil's three-dimensional spatial coordinates. The coordinate transformation formula is shown below:

[0255]

[0256] In the formula, θ is the pitch angle, taken as 0°; φ is the installation angle; R i y1 is the radius of the cylindrical surface on which the blade section is located; x1 and y1 are the abscissa and ordinate of the two-dimensional airfoil, respectively; L is the length from the origin of the two-dimensional airfoil coordinate system to the center of rotation. When the axis of rotation is the coordinate axis, L is 0.

[0257] By importing the three-dimensional coordinates of each section into modeling software for modeling, the geometric structure diagram of the two-stage axial flow pump can be obtained, such as... Figure 6 As shown, 1 is the auxiliary stage impeller, 2 is the main stage impeller, and 3 is the rear guide vane. The auxiliary stage impeller rotates counterclockwise at 8000 rpm, providing a head of 32 m without cavitation, thus increasing the net positive suction head (NPSH) of the main stage impeller. The main stage impeller, rotating at a high speed of 10000 rpm, provides a head of 97.3 m. The rear guide vane recovers the rotational kinetic energy of the preceding impeller, allowing the liquid at the main stage impeller outlet to flow axially.

[0258] Through the above methods, this invention provides a design method for a two-stage high-speed axial-flow propulsion pump suitable for shallow water conditions, enabling rapid and efficient design of a two-stage axial-flow propulsion pump applicable to underwater vehicles at a water depth of 10m and a speed of 70Kn. This two-stage axial-flow propulsion pump has a large hub ratio and a compact structure, meeting the space assembly requirements of underwater vehicles. In this invention, the head previously borne by a single-stage axial-flow pump is split into two stages. The main function of the auxiliary stage impeller is to increase the available net positive suction head (NPSH) before the main stage impeller. Thus, the main stage impeller receives less head than a single stage, and its NPSH is also higher, enhancing its anti-cavitation performance and ensuring the power requirements of the underwater vehicle.

Claims

1. A design method for a two-stage high-speed axial flow propulsion pump applicable to shallow water conditions, wherein the two-stage high-speed axial flow propulsion pump includes a main stage impeller and an auxiliary stage impeller, characterized in that, The specific steps are as follows: Step 1: Based on the actual head of the main stage impeller and the actual head of the auxiliary stage impeller, determine the actual design head of the underwater vehicle under the design conditions through the balance equation of thrust of the water jet propulsion pump and resistance of the vehicle. Step 2: Using the "lift method", the blade cascades of the main stage impeller and the auxiliary stage impeller are designed separately. The cross-sectional shapes of the main stage impeller and the auxiliary stage impeller are used as airfoils. The airfoil shape with the best anti-cavitation performance is selected. Based on the hydrodynamic characteristics of the airfoil, the parameters of the actual design head of the underwater vehicle under the design conditions are corrected to complete the design of the two-stage axial flow pump impeller. The specific process for correcting the parameters of the actual design head of the underwater vehicle under design conditions based on the hydrodynamic characteristics of the airfoil is as follows: The motion of the liquid in the impeller is treated as a composite motion, which is decomposed into the entrainment motion due to the impeller rotation and the relative motion relative to the impeller motion. The motion characteristics of the liquid within the impeller are determined by solving the velocity triangle. Subscript "1" represents the impeller inlet, and subscript "2" represents the impeller outlet. The parameters of the actual design head are expressed as follows: axial velocity Represented as: （12） In the formula Where A is the volumetric flow rate and A is the channel area. For volumetric efficiency; Circular speed u Represented as: （13） In the formula, r To calculate the cross-sectional radius; Circumferential component of the absolute velocity at the outlet of the auxiliary stage impeller Represented as: （14） In the formula, The circumferential component of the absolute velocity at the inlet of the auxiliary stage impeller; Assuming no pre-swirl in the incoming flow, the circumferential component of the absolute velocity at the auxiliary stage impeller inlet... =0; Neglecting hydraulic losses between the two impeller stages, the circumferential component of the absolute velocity at the inlet of the main stage impeller... Circumferential component of the absolute velocity at the outlet of the auxiliary stage impeller If they are the same size but have opposite directions of rotation, then: （15） Impeller outlet absolute velocity for: （16） Geometric mean of the relative velocities at the impeller inlet and outlet : （17） Radial angle of the geometric mean of the relative velocities at the impeller inlet and outlet : （18） Hydraulic efficiency of the cascade : （19） The theoretical head of the main stage impeller and auxiliary stage impeller. : （20） The influence of the blade cascade on the hydrodynamic characteristics of the airfoil was determined and corrected based on numerical simulation methods. Values: The cascade pitch is denoted as t, and its expression is: （21） In the formula, r is the radius at the calculated section, and z is the number of impeller blades; Leaf lattice density l / t Represented as: （22） In the formula, m is the blade overlap coefficient. Install the blade angle. Blade installation angle : （23） In the formula, It is an airfoil angle of attack; Lift coefficient of airfoil Equal to the lift coefficient generated by the curvature With the angle of attack The resulting lift coefficient sum; Lift coefficient generated by camber : （24） In the formula, This represents the maximum relative camber of the airfoil. This represents the maximum relative thickness of the airfoil. This is the camber lift loss coefficient; Angle of Attack Then it is calculated by the following formula: （25） The curvature correction formula is: （26） Pump Net Positive Suction Head (NPSH) r : （27） In the formula, x is the net positive suction head (NPSH) coefficient; The airfoil chord length obtained from the section calculation results l Thickness y max curvature h max l and the coordinates of the airfoil and the camber line of the defined shape are determined. Based on the above parameters, the coordinates of the two-dimensional profile points of each airfoil section are determined. The coordinates of the two-dimensional profile points of each airfoil section are projected onto the surface of a three-dimensional cylinder to obtain the three-dimensional spatial coordinates of the airfoil. Return the corrected parameters to step 1 until the iteration count reaches 100, and output the impeller parameters of the two-stage axial flow pump.

2. The design method for a two-stage high-speed axial flow propulsion pump suitable for shallow water conditions according to claim 1, characterized in that, Step 1 is as follows: Step 1.1: The underwater vehicle navigates at its designed speed v. t When designing the navigation depth y, the thrust-resistance balance equation must be satisfied: （1） In the formula, v is the mass flow rate of the fluid flowing through the inner channel. e Let A be the flow velocity at the outlet of the axial flow pump. e v is the area at the outlet of the axial flow pump. t k is the speed of the vehicle when it is traveling at a constant speed. iv X is the inlet velocity coefficient of the flow channel, and X is the drag experienced by the vehicle. The density of the liquid; Among them, the flow velocity v at the outlet of the flow channel e : （2） In the formula, It is the static pressure recovery coefficient at the inlet of the flow channel. The static pressure recovery coefficient at the flow channel outlet. This is the head loss coefficient; The resistance to navigation, X, is expressed as: （3） In the formula, The drag coefficient is characterized by the maximum wetted area. This represents the maximum cross-sectional area of ​​the aircraft. The design flow rate Q of the flow channel is obtained from equations (1) to (3). v Represented as: （4） Design head H of a two-stage high-speed axial flow propulsion pump z Represented as: （5） Net Positive Suction Head (NPSH) of Two-Stage Axial Flow Pump Represented as: （6）； Step 1.2: In this two-stage high-speed axial flow propulsion pump, the auxiliary stage impeller rotates in the opposite direction to the main stage impeller. The total head is shared by the auxiliary stage impeller head and the main stage impeller head. While meeting the head requirements of the auxiliary stage impeller, the pump inlet net positive suction head (NPSH) of the main stage impeller is increased. During the head distribution process, the head of the upstream auxiliary stage impeller is distributed along with the NPSH of the system. same, The auxiliary stage impeller head H is expressed as: （7） Main stage impeller head distribution Represented as: （8）； Step 1.3: The basic calculation equation for designing the impeller using the lift method is as follows: （9） In the formula: C L is the lift coefficient of the airfoil in the cascade, and l / t is the cascade density. It is the local gravitational acceleration. It is the theoretical head of the main stage impeller or the auxiliary stage impeller. It is the geometric mean velocity of the relative velocity of the liquid flow. It is the velocity of the impeller's central axial surface. It is the circumferential velocity. It is the lift-to-drag ratio of the airfoil. It is the geometric mean velocity ω of the relative velocity of the liquid flow. ∞ The angle between the direction and the horizontal direction; Step 1.4: When designing the main stage impeller, it is necessary to add guide vane head loss. Expressed as: （10） In the formula, k is the correction coefficient. The circumferential component of the absolute velocity at the outlet of the main stage impeller; Actual design head of the main stage impeller : （11） in, The theoretical head of the main stage impeller, This is due to the loss of head for the guide vanes.

3. The design method for a two-stage high-speed axial flow propulsion pump suitable for shallow water conditions according to claim 2, characterized in that, Step 2 describes the specific process of designing the blade cascades of the main stage impeller and auxiliary stage impeller using the "lift method": Multiple calculation sections are selected based on the linear variation between the impeller hub and rim, and the blade overlap coefficient is chosen. m Determine the cascade density l / t, substitute it into formula (9), and give the airfoil lift-to-drag ratio angle. Calculate the lift coefficient C of the airfoil in the cascade. L Finally, the angle of attack and camber of the airfoil section were determined.

4. The design method for a two-stage high-speed axial flow propulsion pump suitable for shallow water conditions according to claim 3, characterized in that, The formula for projecting the obtained two-dimensional point coordinates onto the three-dimensional cylindrical surface is as follows: （28） In the formula, θ is the pitch angle; For installation angle; R i y1 is the radius of the cylindrical surface on which the blade section is located; x1 and y1 are the horizontal and vertical coordinates corresponding to the two-dimensional airfoil; L is the length from the origin of the two-dimensional airfoil coordinate system to the center of rotation; and x, y, and z are the three-dimensional spatial coordinates of different sections of the impeller.

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