Design method of header pipe for parallel connection of diaphragm pumps with multiple pump heads

Abstract

The invention discloses a main pipe design method for parallel connection of multi-pump-head diaphragm pumps. The dynamic pressure / static pressure in the trunk is redistributed through the diameter gradient of the header pipe, additional loss caused by near-end right-angle flow resistance and valve resistance is counteracted, meanwhile, far-end momentum accumulation caused by tail-end closing and an inertia effect is weakened, far-end water grabbing and near-end flow loss are remarkably inhibited, and the effect that delta is smaller than or equal to a preset threshold value is achieved. Compared with the scheme depending on throttling or active control, on the premise that the structure is simple and maintenance is convenient, the influence on the total pressure drop and energy consumption of a system is small, and good robustness is achieved on the valve opening degree deviation and manufacturing tolerance; the improvement of flow balance can also synchronously reduce pressure pulsation and noise, and the cavitation margin and the reliability of the whole machine are improved.

Description

Technical Field

[0001] This invention belongs to the field of fluid machinery and relates to a manifold design method for parallel multi-pump head diaphragm pumps. Background Technology

[0002] Parallel diaphragm pumps (including flexible hose pumps) are widely used in chemical liquid preparation, biopharmaceutical, and food processing. To meet redundancy and capacity expansion under varying operating conditions, multiple pump heads are often connected in parallel and merged through a main pipe and branch pipes. However, in traditional pipelines with constant diameter, right-angle tee connections, and significant local resistance from ball valves and check valves, the coupling of friction momentum and local losses can cause significant uneven flow: the first branch near the inlet experiences lower effective static pressure due to flow resistance caused by the right-angle turn and valve damping, easily resulting in flow deficit; while the closed main pipe at the end experiences local pressure rise due to transient pulsations and inertia, causing a flow surplus in the far-end branches (commonly known as "water grabbing"). This imbalance amplifies pressure pulsations and noise, increases the frequency of pump and valve opening and closing and mechanical fatigue, and induces cavitation or airlock on the low-pressure side, reducing system efficiency and reliability. Existing flow control measures, such as simple throttling, adding flow control plates, or lengthening branch lines, often lead to increased energy consumption, larger footprint, and the risk of unsanitary areas. Active control solutions, such as electrically controlled valves and variable frequency drives, significantly increase costs and maintenance complexity. Therefore, there is an urgent need for a passive flow equalization design method based on the geometry of the main pipe itself. This method, by rationally configuring the diameter gradient along the flow direction, can suppress water grabbing at distant points and improve the robustness and efficiency of parallel systems without significantly increasing energy consumption and structural complexity. Summary of the Invention

[0003] This invention addresses the problem of water grabbing at the far end and flow deficit at the near end in multi-head parallel diaphragm pumps under the combined effects of constant diameter main pipe, right-angle tee, and local resistance of valve components. It proposes a main pipe design method for multi-head parallel diaphragm pumps and a tapered main pipe structure based on this method, which achieves passive balance of flow in each branch without increasing complex control or significant energy consumption.

[0004] A method for designing a main pipe for parallel multi-head diaphragm pumps includes the following steps:

[0005] Step a) Acquire operating conditions and geometric parameters: Obtain the target total flow rate, back pressure, number of pump heads and position along the program, record the branch pipe size, tee structure and valve equivalent local resistance coefficient K, and determine the main pipe inlet pressure and far-end boundary conditions;

[0006] Step b) Set the imbalance criterion: Define the parallel current sharing index And use δ≤δ0 as the optimization convergence objective;

[0007] Step c) Construct the main pipe diameter distribution function D(x): Design the main pipe diameter along the flow direction as a continuous or piecewise function that gradually tapers from thick to thin, so that the diameter D1 near the first pump is larger than the diameter D at the far end. n* This forms a tapered main pipe; step d) establishes an equalization model for pressure drop distribution: the pressure drop Δp along the main pipe is calculated. header Local losses ΣΔp of each branch local,i And taking into account the additional momentum effect of the remote closure, with Q1≈Q2≈…≈Q n As a constraint, D(x) is iteratively adjusted to make δ approach δ0;

[0008] Step e) Output the final diameter distribution D(x) and corresponding geometric parameters, which are used to manufacture the tapered main pipe to achieve passive balance of flow in each branch.

[0009] A tapered manifold structure is obtained using the method described above.

[0010] The beneficial effects of this invention are:

[0011] First: By redistributing the dynamic / static pressure within the main trunk through the gradient of the main pipe diameter, the additional losses caused by the near-end right-angle flow resistance and valve resistance are offset. At the same time, the momentum accumulation at the far end caused by end closure and inertial effects is weakened, significantly suppressing water grabbing at the far end and flow deficit at the near end, so as to achieve δ less than or equal to the preset threshold.

[0012] Second: Compared with solutions that rely on throttling or active control, this invention has a small impact on the total pressure drop and energy consumption of the system under the premise of simple structure and convenient maintenance, and has good robustness to valve opening deviation and manufacturing tolerance; the improved flow balance can also reduce pressure pulsation and noise, and improve cavitation margin and overall reliability. Attached Figure Description

[0013] Figure 1 This is a schematic diagram of a parallel diaphragm pump system with three branch pipes and a closed end structure.

[0014] Figure 2a The mesh diagram used in the two-dimensional numerical simulation of the prototype main pipe section.

[0015] Figure 2b for Figure 2a The velocity distribution results are shown in the figure.

[0016] Figure 3 Add a location for damping in porous media.

[0017] Figure 4 To improve the comparison of instantaneous flow rates before and after, the left side shows the flow rate curve under the original main pipe section, and the right side shows the flow rate curve under the gradually changing main pipe diameter after applying this invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Unless otherwise stated, the present invention is not limited to the specific dimensions, materials, simulation platforms, or parameter values ​​described below. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] See Figure 1 The multi-head parallel diaphragm pump includes: a main inlet 1, an inlet manifold 2, several diaphragm pump units 3-1, 3-2, 3-3, and corresponding parallel branch pipes 4-1, 4-2, 4-3. Taking pump No. 1 as an example, a ball valve or check valve (inlet ball valve 7) is installed on this branch pipe. Between the inlet ball valve 7 and the outlet ball valve 8 are the pump diaphragm side 5 and the fixed side 6. The pump outlet is located after the outlet ball valve 8. A closed end 10 or a buffer chamber is provided at the far end of the manifold. In this application, the manifold adopts a diameter distribution D(x) that gradually tapers along the main flow direction. The diameter D1 near the first pump connection position is larger than the diameter D at the far end. n* By redistributing dynamic / static pressure within the main trunk through diameter gradient, the additional pressure drop caused by the near-end right-angle tee and valve damping is offset, and momentum accumulation caused by the far-end closure is weakened, thereby suppressing water grabbing at the far end and flow deficit at the near end.

[0020] In one embodiment, the specific design steps are as follows:

[0021] 1. Operating conditions and geometric data acquisition:

[0022] Determine the target total flow rate and back pressure, and record the number of pump heads and the number of bits along the program (x1). <x2<…<x n The branch pipe size, tee structure and ball valve / check valve equivalent local resistance coefficient K are obtained, and the pressure at the main pipe inlet and the end boundary conditions (the end is in a closed or buffered state) are measured or estimated.

[0023] Wherein: the K value can be obtained from sample, calibration or literature data; the buffer cavity can be represented by the equivalent compliance parameter to indicate its influence on transients.

[0024] 2. Imbalance Criterion Setting:

[0025] Define parallel current sharing index The design threshold δ0 (e.g., ≤3–5%) is given and used as the optimization convergence target.

[0026] Wherein: δ can be calculated by steady-state periodic average or transient moving average, and the evaluation criteria shall be based on δ ≤ δ0.

[0027] 3. Main pipe diameter distribution setting:

[0028] The main pipe is designed with a diameter function D(x) that gradually tapers along the flow direction, satisfying that the diameter D1 near the first pump is greater than the diameter D at the far end. n* .

[0029] Preferably, a segmented linear or double continuous taper is adopted, so that the local cross section of the first section is slightly larger to compensate for the additional pressure drop caused by the right-angle flow resistance and valve resistance of the No. 1 pump.

[0030] D(x) can be approximated by splicing several constant diameter segments or conical segments, or it can be described by a continuous function, and the two are equivalent.

[0031] In one embodiment, the diameter function D(x) of the main pipe is described by a continuous taper along the flow direction. The blind section diameter is D. n* The blind segment length is L n∗ The effective tapered length is the total length of the main pipe minus the blind section length, i.e., L. eff =L tot -L n* Then the corresponding diameter function D(x) is defined as:

[0032]

[0033] Among them, the length of the main pipe L tot The positions of each pump (x1, x2, x3) are determined by the overall assembly strategy, and the blind length L is usually... n* It is also locked by layout constraints, so the main parameters that need to be solved are the initial diameter D1 of the main pipe and the diameter D of the blind section. n* If necessary, a transition diameter D can be added between the two. i .

[0034] 4. Voltage drop equalization effect modeling:

[0035] Flow equations are established based on pipe friction and local resistance models, and the pressure drop Δp along the pipe is calculated. header Calculate the friction drop Δp as a function of the main pipe diameter D(x). header and the local losses ΣΔp of each branch. local,i The additional momentum / reflection effect caused by the superposition of end closure (in K) n Or end cavity compliance C n (represented by Q1≈Q2≈…≈Q) to form the total pressure differential distribution; n To constrain the process, solve D(x) to make δ approach δ0.

[0036] ① Pressure drop along the main pipeline section

[0037] The main pipe geometry is discretized into several conical segments k=1…m (each segment length L) based on the number of pump heads connected in parallel.k Diameter D k Traffic Q h,k Then the pressure drop along the friction path is:

[0038] ,

[0039] Where, f k K is the friction coefficient for this segment (it can be taken from conventional empirical formulas or handbooks such as Haaland, and the specific form is not limited). run,k V represents the local loss coefficient in the straight-through direction of this section (including tees, necessary bends, tapered sections, etc.). k This represents the flow velocity in that section. L k Q represents the length of the main pipe section preceding the k-th pump head. h,k This represents the flow rate of the main pipeline section. The main pressure from the inlet to the k-th pump connection node is:

[0040]

[0041] ② Pressure drop in each pump head branch i

[0042] Employing equivalent coupling along the path and locally:

[0043] ,

[0044] Where K local,i =K valve,i (Opening degree) + K branch,i (Dual flow operation) This is determined by the initial valve design. The effect of end-closing can be incorporated into the local loss Δp at the end in steady state. end =K n ρV m 2 / 2; If transient fluctuations are considered, C can be used. n Characterizing end-cavity compliance (Q end =C n (dp / dt), but does not change the steady-state balancing d of this method. b V represents the pipe diameter of each manifold branch. b,i Let be the flow velocity in the i-th manifold. Combine the branch energy and overall continuity:

[0045] ,

[0046] The flow rate Q of each branch can then be calculated. i Thus, the current sharing index of the parallel system is obtained. The average manifold flow rate .

[0047] ③ Since the inlet and outlet pressures are given, the main pipe pressure drop equation and the branch pressure drop equation can be solved simultaneously to obtain the functions of inlet and outlet pressures, main pipe diameter D(x), and flow rates Q of each manifold. i The overall equation:

[0048]

[0049] Adjust the main pipe diameter function D(x) according to this equation until the flow rate Q of each branch is reached. i This process can achieve the desired parallel current sharing index δ. Other iterative balancing or equivalent optimization methods can also be used to solve this problem; there are no limitations on the specific algorithm or optimization platform.

[0050] 5. Parameter solving and constraint verification:

[0051] Manufacturing and installation constraints (minimum wall thickness, maximum taper θ) max =D1 / D n* Under the standard dimensions of flange / tee interfaces, further iteratively solve D(x); if necessary, adjust the inner fillet radius of the tee, the length of the short straight section of the branch pipe, and the length of the blind section at the end L. n* Coordinated adjustments are made to reduce the pressure drop bias caused by secondary flow and separation.

[0052] Where: θ max The minimum wall thickness is determined based on process and strength verification to ensure manufacturability and reliability.

[0053] 6. Numerical simulation verification and optimization:

[0054] The current sharing effect and energy consumption change of this application are verified by a combination of two-dimensional mesh CFD rapid analysis and local three-dimensional CFD verification; through parameter scanning (D1 / D2, D... n-1 / D n Taper θ, L n* The D(x) is fine-tuned using parameters such as the radius of the tee corners to keep δ stable below the threshold and the total voltage drop of the system under control.

[0055] To illustrate the simulation method, a two-dimensional transient numerical simulation example of a three-head diaphragm pump in parallel is given:

[0056] ① Geometric and Comparative Schemes

[0057] Construct a two-dimensional geometry including the inlet main pipe, three parallel branch pipes, the equivalent region of valves, and the terminal closed section. The initial scheme is a constant diameter D. ref The improved solution is to adopt a tapered pipe with a gradually tapering diameter D(x) as described in this application, satisfying D1>D n* .

[0058] ② Grid and Time Step

[0059] A quadrilateral two-dimensional grid is used, with densification at the right-angle tee and before and after the valve; the time step Δt ≈ 1 / 100 to 1 / 200 of the pump drive fundamental frequency; the residual threshold ≤ 1×10 -5 The statistical interval is ≥5 pump cycles.

[0060] ③ Numerical Model

[0061] The simulation adopts an incompressible or weakly compressible transient form; the turbulence model can adopt k-ω SST; the end of the main pipe is a solid wall closed or connected to a small volume buffer cavity.

[0062] ④ Diaphragm and valve characterization

[0063] The diaphragm motion utilizes a Gaussian-like function displacement and flow pulsation provided by the UDF (to capture the asymmetric features of filling and discharging). The Gaussian function takes the following form:

[0064]

[0065] Parameter description: y is the transverse coordinate (diaphragm movement direction); t is the physical time; A is the displacement amplitude, directly controlling the peak displacement; σ is the Gaussian width, controlling the width and gradient of the deformation zone; y0 is the Gaussian center position, i.e., the position of maximum lateral node displacement, usually taken as the diaphragm center coordinate; T is the diaphragm movement period, determined by the target pump frequency f=1 / T. In one embodiment, this method effectively realizes the diaphragm movement and cavity volume change process, such as... Figure 2a and Figure 2b As shown, Figure 2a Divide the diaphragm cavity into grids. Figure 2b The cloud map shows the velocity distribution at a certain moment during the diaphragm movement under the control of the above equation, where pump 1 is in the suction state, pump 2 is about to enter the suction state, and pump 3 is in the discharge state.

[0066] The valve resistance is equivalent to a porous medium, and its resistance is mainly controlled by the Darcy coefficient in the porous medium model of the corresponding software platform, varying with the opening degree and mapped from the calibration curve during design or experimentation. The porous medium region is added upstream of the ball valve's lift limit position, and as close to this limit position as possible. In one embodiment, the porous medium region is added as follows: Figure 3 As shown, taking pump No. 1 as an example, porous medium 11-1 is added upstream of the inlet ball valve's lift limit position, and the other pumps are added at the same position.

[0067] The ball valve employs 6DOF rigid body dynamics coupled with a dynamic mesh when needed. Valve disc opening and closing hysteresis, limiting, and damping are set via UDF. In one embodiment, valve closure is achieved using fluid flow modeling rather than flow blocking to reduce distortion caused by abrupt mesh changes and achieve better flow resistance. The principle is that when the microchannel size between the ball valve and the valve seat falls below a certain value, the flow is stopped by artificially increasing the flow damping. The damping magnitude is controlled by the Reynolds number; a smaller Reynolds number indicates greater flow damping.

[0068] (6) Obtaining evaluation indicators

[0069] Monitor and calculate Q1, Q2, Q3 and δ, and record the total system pressure drop Δp_sys, branch pulsation amplitude, spectral characteristics, velocity and pressure distribution in each pump to determine the accuracy of the simulation.

[0070] (7) Result Comparison: In one embodiment, such as Figure 4 As shown, the original scheme A (constant diameter) has a flow surplus in the far-end branch and a flow deficit in the near-end branch, with δ being a typical value (e.g., ≈12%). After the improved scheme B adopts a reduced D(x) pipe diameter distribution, the static pressure at the inlet of the first branch increases and the peak dynamic pressure of the third branch decreases, with δ meeting the target threshold (e.g., ≤3~4%). After the improvement, the flow in the three manifolds is basically the same.

[0071] Note: The above values ​​are for illustrative purposes only; the actual values ​​should be based on specific models and operating conditions. Those skilled in the art can achieve the same technical effect using three-dimensional transient or two-way fluid-structure interaction (FSI) methods.

[0072] 7. Robustness and tolerance assessment:

[0073] Considering valve opening deviation, machining tolerance and installation error, the sensitivity of δ is evaluated; if necessary, a small-amplitude passive flow limiting insert (Δp0≤10-20% of system pressure drop) is added at the far end as a redundancy guarantee, without changing the "coarse-to-fine" design principle of this application.

[0074] Example extension: Sensitivity analysis was conducted on D deviation ±t, taper deviation ±Δθ, and valve opening deviation ±5%, and the robust range and suggested tolerance of δ were given.

[0075] 8. Finalization and Implementation:

[0076] The final diameter distribution D(x), segment length, and connection dimensions are determined, and manufacturing drawings and assembly datums are output. This geometry can be used for metal pipe fittings, sanitary piping, or molded manifolds. Different materials (such as stainless steel, polymers, and composite materials) and connection methods (welding, clamps, and flanges) can all be achieved using the same D(x), without affecting the applicability of the method in this application.

[0077] The tapered main pipe structure of this application is obtained according to the method of the above embodiment. The diameter of the main pipe along the main flow direction decreases gradually or continuously from the inlet to the closed end, and the cross-section of the main pipe near the first pump connection position is relatively increased. With the reasonable arrangement of the three-way transition and the end blind section / buffer cavity, it is used to achieve passive flow sharing of the parallel system under the target operating conditions.

[0078] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, but the protection scope of the present invention is not limited thereto. Any equivalent modifications or substitutions should be covered within the protection scope of the present invention.

Claims

1. A method for designing a main pipe for parallel connection of multi-pump-head diaphragm pumps, characterized in that: The method includes the following steps: Step a) Acquire operating conditions and geometric parameters: Obtain the target total flow rate, back pressure, number of pump heads and position along the program, record the branch pipe size, tee structure and valve equivalent local resistance coefficient K, and determine the main pipe inlet pressure and far-end boundary conditions; Step b) Set the imbalance criterion: Define the parallel current sharing index And use δ≤δ0 as the optimization convergence objective; Step c) Construct the main pipe diameter distribution function D(x): Design the main pipe diameter along the flow direction as a continuous or piecewise function that gradually tapers from thick to thin, so that the diameter D1 near the first pump is larger than the diameter D at the far end. n* This forms a gradually narrowing main pipe; Step d) Establish an equalization model for pressure drop distribution: Calculate the pressure drop Δp along the main pipe. header Local losses ΣΔp of each branch local,i And taking into account the additional momentum effect of the remote closure, with Q1≈Q2≈…≈Q n As a constraint, D(x) is iteratively adjusted to make δ approach δ0; Step e) Output the final diameter distribution D(x) and corresponding geometric parameters, which are used to manufacture the tapered main pipe to achieve passive balance of flow in each branch.

2. The method for designing a main pipe for parallel connection of multi-pump head diaphragm pumps according to claim 1, characterized in that: In step c), D(x) adopts a piecewise linear or quadratic continuous taper, and the local cross-sectional area of ​​the first segment is relatively increased to compensate for the additional pressure drop caused by the right-angle flow resistance and valve resistance of the first pump.

3. The method for designing a main pipe for parallel connection of multi-pump-head diaphragm pumps according to claim 1, characterized in that: Step d) describes the effect of additional momentum at the distal closure through the equivalent local drag coefficient K. n Or end cavity compliance C n This is taken into account in the total pressure differential distribution equation.

4. A method for designing a main pipe for parallel connection of multi-pump head diaphragm pumps according to any one of claims 1 to 3, characterized in that: During the iterative adjustment of D(x) in step d), the inner fillet radius of the tee, the length of the short straight section of the branch pipe, and the length of the blind section at the end are adjusted simultaneously. n* Collaborative corrections are implemented to reduce the pressure drop bias caused by secondary flow and separation.

5. A method for designing a main pipe for parallel connection of multi-pump-head diaphragm pumps according to claim 1, characterized in that: Step e) Before outputting the final D(x), further introduce manufacturing and installation constraints, including minimum wall thickness and maximum taper θ. max The standard dimensions of flange / tee interfaces are used to verify and optimize the diameter distribution parameters.

6. A method for designing a main pipe for parallel connection of multi-pump head diaphragm pumps according to claim 1 or 5, characterized in that: Following step e), numerical simulation verification is performed: a combination of two-dimensional mesh fast CFD and local three-dimensional CFD is used, by scanning D1 / D2, D n-1 / D n Taper θ, end blind length L n* The radius of the tee fillet is used to fine-tune D(x) so that δ is stably lower than δ0 and the change in the total system voltage drop is controllable.

7. A method for designing a main pipe for parallel connection of multi-pump-head diaphragm pumps according to claim 6, characterized in that: The CFD verification uses a diaphragm motion UDF to give a Gaussian function displacement to capture the filling and discharging asymmetry features, and uses a porous medium equivalent valve resistance.

8. A method for designing a main pipe for parallel connection of multi-pump head diaphragm pumps according to claim 6, characterized in that: After step e), robustness and tolerance assessment is performed: considering valve opening deviation, machining tolerance and installation error, the sensitivity of δ is quantified. If the δ margin is insufficient, a passive current limiting insert is added to the far branch, and its additional pressure drop Δp0 is controlled within 10-20% of the total system pressure drop.

9. A method for designing a main pipe for parallel connection of multi-pump-head diaphragm pumps according to claim 1, characterized in that: The method is applicable to metal pipe fittings, sanitary pipes or one-piece molded manifolds, and the selection of materials and connection methods does not change the distribution law of D(x).

10. The tapered manifold structure obtained by the method according to any one of claims 1 to 9.

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