A Visualization Test Research Method for the Incipience of Cavitation in a Double-Suction Pump

Abstract

The present invention relates to a visualization test research method for the incipient cavitation of a double-suction pump, which includes the following steps: 1. Design a visualization test research device for the incipient cavitation of a double-suction pump, and respectively design observation windows on both sides of the water suction section of the double-suction pump to facilitate the observation of the incipient cavitation of the blades; 2. Uniformly set four pressure monitoring points at the inlet of the water suction section and four pressure monitoring points at the outlet section of the delivery chamber. Through the shooting of the high-speed camera, when the incipient cavitation of the impeller of the double-suction pump is transmitted through the observation window, record the average pressure at the inlet of the suction section and the outlet of the delivery chamber and calculate the corresponding incipient cavitation margin. The visualization test research device of the double-suction pump can intuitively and accurately capture the incipient cavitation bubbles at the inlet of the double-suction pump blades. Through experimental observation and recording and analysis of data such as the incipient cavitation margin, critical cavitation margin, incipient cavitation head, and critical cavitation head in the test pump, as well as the change in the bubble volume and flow pattern generated at the inlet of the blade during the operation of the pump.

Description

Technical Field

[0001] The present invention relates to a visualization test research method, and particularly to a visualization test research method for the incipient cavitation of a double-suction pump blade inlet, which can visually and accurately capture the incipient cavitation bubbles, and observe, record and analyze the data inside the test pump through experiments. Background Art

[0002] Double-suction pumps are widely used in industries such as building buildings, waterworks, power plants, steel plants, air-conditioning circulating water, water conservancy projects, and irrigation area water supply. When a double-suction pump is operating, the absolute pressure at the impeller inlet decreases. When the local pressure is lower than the local vaporization pressure, cavitation and cavitation erosion may occur. The occurrence of cavitation will not only cause the performance of the double-suction pump to decrease, but also cause vibration and noise, and even lead to a series of problems such as the pump stopping running, which is a difficult problem that has not been effectively solved at present. Compared with the research on efficiency, the research on cavitation performance is more difficult, and the research results far cannot meet the actual needs. At present, most double-suction pumps are operating in a micro-cavitation state during use, and their cavitation performance still fails to meet the actual requirements. Therefore, it is urgent to explore effective methods to improve the cavitation performance research of pumps.

[0003] Before leaving the factory, the double-suction pump will measure its cavitation margin value through a specified cavitation performance test. Logically, it is considered that cavitation should not occur when the double-suction pump is working normally, but in actual operation, it will still be severely damaged by cavitation and cavitation erosion. Due to the complexity of the cavitation phenomenon, the current understanding of the cavitation phenomenon is not deep enough, and the research on the mechanism of cavitation occurrence is relatively weak. The cavitation erosion of the double-suction pump directly affects the operation reliability and service life of the pump. Due to its double-helix inlet suction chamber, there is non-uniformity in the flow pattern. Therefore, to ensure the safe, stable and efficient operation of the double-suction pump, a visualization test research observation window for observing the incipient cavitation of the pump blade inlet is added in the inlet suction section. By observing the flow pattern distribution at the blade inlet during incipient cavitation and critical cavitation, analyzing the laws of incipient cavitation margin and critical cavitation margin, improving the cavitation performance of the double-suction pump, and providing a strong reference basis for realizing cavitation-free operation of the pump. Summary of the Invention

[0004] In view of the above problems, the main object of the present invention is to provide a visualization test research method for the incipient cavitation of a double-suction pump blade inlet, which can visually and accurately capture the incipient cavitation bubbles, and observe, record and analyze the data inside the test pump through experiments.

[0005] The present invention solves the above technical problems through the following technical solutions: A visualization test research method for the incipient cavitation of a double-suction pump proposed by the present invention, the visualization test research method for the incipient cavitation of the double-suction pump includes the following steps:

[0006] Step 1: Design a visualization test research device for the incipience of cavitation in a double-suction pump, and respectively design observation windows on both sides of the suction section of the double-suction pump to facilitate the observation of the incipience of blade cavitation;

[0007] Step 2: Uniformly set four pressure monitoring points at the inlet of the suction section and four pressure monitoring points at the outlet section of the delivery chamber. Through the shooting of the high-speed camera screen, when the incipience of cavitation in the impeller of the double-suction pump is transmitted through the observation window, record the average pressure at the inlet of the suction section and the outlet of the delivery chamber and calculate the corresponding incipient cavitation margin.

[0008] In a specific embodiment of the present invention, the specific steps of Step 1 are as follows:

[0009] Step 101: Design four visualization windows on both sides of the suction chamber of the double-suction pump that can observe the inlet edge of the impeller. Two observation windows are used for observing the incipience of cavitation at the blade inlet, and the other two observation windows on the same side are used for auxiliary observation of the light source input when cavitation occurs at the blade.

[0010] Step 102: Outside the observation window for observing the incipience of cavitation at the blade inlet, arrange a high-speed camera through design that can observe the incipience of cavitation at the impeller inlet and the flow field state.

[0011] Step 103: The observation angle and layout position of the high-speed camera need to be carried out through the layout of the on-site test device to ensure that the incipience of blade cavitation can be observed.

[0012] In a specific embodiment of the present invention, the specific steps of Step 2 are as follows: (2-1) According to the definition of cavitation: the pressure at the lowest point in the pump is equal to the vaporization pressure the pump is in a state of cavitation; the lowest pressure point in the pump usually occurs slightly behind the inlet of the blade back. Since it is inconvenient to measure, the average pressure near the suction port section of the pump will be uniformly used instead, and use to represent the suction port pressure value when the pump starts to cavitate; According to the definition in GB / T 13006 "Cavitation Margin for Centrifugal Pumps, Mixed-Flow Pumps and Axial-Flow Pumps": the cavitation margin when the head of the first stage of the pump drops by 3%: NPSH3 is used as the standard for the critical cavitation margin, and use to represent the suction port pressure value that meets the GB / T 13006 standard;

[0013] (2-2) NPSH3 is the calculation formula for the critical cavitation margin. During the cavitation test, keep the flow rate unchanged. By evacuating the closed circulation system and gradually reducing the system pressure, cavitation occurs in the pump;

[0014]

[0015] In the formula: (1) NPSH 3-iQn is the critical cavitation margin, in units of m;

[0016] (2)P iQn is the absolute pressure at the pressure measuring point at the inlet of the test device, measured by an absolute pressure transmitter, with the unit of Pa;

[0017] (3)P v is the saturated vapor pressure at the test water temperature, with the unit of Pa;

[0018] (4)h is the height value of the absolute pressure transmitter above the intersection point of the pump blade rotation center line of the test device and the impeller housing, with the unit of m;

[0019] (5)ρ—the density of the medium, kg / m 3 ;

[0020] (6)g—the acceleration of gravity, m / s 2 ;

[0021] During the test process, the flow rate is kept constant, and a 3% drop in the head is determined as the critical net positive suction head NPSH re ;

[0022] H P is the head at the specified point of the pump of the test device.

[0023] In the specific embodiments of the present invention, it is defined that is the pressure pulsation value of the pressure pulsation measuring point set at the inlet at the incipience of cavitation under different working conditions, is the inlet pressure pulsation value when the critical net positive suction head value is NPSH3 under the corresponding working conditions; the dimensionless parameter (i = 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, x, where x is the ratio of the maximum flow rate that can be tested by the test device to the rated flow rate) is used to draw an intuitive histogram of the dimensionless parameter D i0 and the flow coefficient i, and the variation laws of the inlet pressure pulsation at the incipience of cavitation and critical cavitation of the double-suction pump and under different working conditions can be obtained through analysis;

[0024] Define the net positive suction head at the incipience of cavitation of the double-suction pump under the corresponding conditions and the critical net positive suction head reached by the standard GB / T13006. The test research device needs to test and obtain at least 7 critical net positive suction head values and the at the incipience of cavitation of the pump (i = 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, x,) where x is the ratio of the maximum flow rate that can be tested by the test device to the rated flow rate) is used to introduce the dimensionless parameter E i0Make an intuitive histogram with the flow coefficient i, and through analysis, the variation and distribution laws of the suction specific speed of the double-suction pump under different operating conditions and the suction specific speed of the pump under the initial cavitation and critical cavitation conditions can be obtained;

[0025] Define the head at the initial cavitation of the double-suction pump under corresponding conditions And the head at the critical cavitation reached by the standard GB / T13006 Introduce dimensionless parameters (i = 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, x, where x is the ratio of the maximum flow rate that can be tested by the test device to the rated flow rate) Make an intuitive histogram of the dimensionless parameter F i0 Make an intuitive histogram with the flow coefficient i, and through analysis, the variation and distribution laws of the head of the double-suction pump under different operating conditions and the head of the pump under the initial cavitation and critical cavitation conditions can be obtained.

[0026] In the specific embodiment of the present invention, under different flow coefficients, perform analysis of variance on D i0 、E i0 And F i0 To obtain the influence degrees on the pressure pulsation at the inlet during critical cavitation The pressure pulsation at the inlet during initial cavitation Critical suction specific speed Initial suction specific speed The head H at critical cavitation iQn 、The head value at initial cavitation ;

[0027] For regression analysis, let x = D i0 , y = E i0 , z = F i0 , Through data regression analysis and fitting calculation, obtain y = f(x, z), analyze the operating variation laws of different operating conditions of the double-suction pump under initial cavitation and critical cavitation, so as to obtain the operating conditions for the double-suction pump to be completely cavitation-free.

[0028] The positive and progressive effects of the present invention are as follows: The visualization experimental research method for the inception of cavitation in a double-suction pump provided by the present invention, and the visualization experimental research device of the double-suction pump can visually and accurately capture the inception cavitation bubbles at the impeller inlet of the double-suction pump. Through experimental observation and recording and analysis of data such as the inception cavitation margin, critical cavitation margin, inception cavitation head, and critical cavitation head in the test pump, as well as the change in the cavitation volume and flow pattern generated at the impeller inlet during the pump operation process. On the one hand, it provides accurate experimental data information for the subsequent completely cavitation-free operation of the double-suction pump to improve the accuracy of predicting the inception of cavitation. The experimental laws of this technical solution can be extended and applied to the cavitation theory research of other model products. On the other hand, it can deeply reveal the flow pattern evolution characteristics at the impeller inlet, the cavitation volume distribution, and the inception mechanism of cavitation from the inception of cavitation to critical cavitation in the double-suction pump, providing strong experimental data support for the high cavitation performance design or optimization of the vane pump. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a schematic diagram of the device for the application of the visualization experimental research method of the present invention.

[0030] Figure 2 It is a schematic diagram of the pump unit part of the present invention.

[0031] The following are the names corresponding to the reference numerals in the present invention:

[0032] Frequency conversion control cabinet 1, power analyzer 2, motor 3, torque meter 4, research model pump unit 5, check valve 6, electromagnetic flow valve 7, pressure stabilizing tank 8, vacuum pump 9;

[0033] Inlet section pressure measurement point 11, suction section pressure pulsation measurement point 12, observation windows 13 - 16, outlet section pressure measurement point 17. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0034] The following further elaborates on the technical solution of the present invention in conjunction with the accompanying drawings.

[0035] Figure 1 It is a schematic diagram of the device for the application of the visualization experimental research method of the present invention. By Figure 1 The experimental research on the inception of cavitation in the double-suction pump impeller is completed. Figure 2 It is a schematic diagram of the pump unit part of the present invention. The specific steps to implement the present invention are as follows: (1), (1 - 1) As Figure 2 shown in the figure, two observation windows are designed on both sides of the inlet of the double-suction pump suction chamber. Through the observation windows, the flow state at the impeller inlet can be seen. By changing the pressure in the cavitation tank to achieve cavitation in the pump, when cavitation bubbles are initially generated at the impeller inlet as observed through observation windows 14 and 15, the inlet pressure value, outlet pressure value, and inlet section pressure pulsation value are observed and recorded using a high-speed camera, and the head and inception cavitation margin under the corresponding working conditions are calculated.

[0036] (1-2) Continuously change the pressure of the cavitation tank, and at the same time observe and record the inlet pressure value until critical cavitation is reached. When the head satisfies a 3% drop ratio, it is considered that critical cavitation has been reached. Record the average inlet pressure and outlet pressure value under this condition, and calculate the head and critical cavitation margin corresponding to the working condition.

[0037] (2) As Figure 2 shown, 4 pressure monitoring points are evenly arranged at the inlet of the suction section, and 4 pressure monitoring points are evenly arranged at the outlet section of the delivery chamber. For the pressure pulsation measurement points in the suction section, through the high-speed camera screen shooting, when the double-suction pump impeller incipient cavitation is observed through the observation window, record the average pressure at the inlet of the suction section and the outlet of the delivery chamber and calculate the corresponding incipient cavitation margin.

[0038] For (2), the specific steps are as follows:

[0039] (2-1) According to the cavitation definition: the pressure at the lowest point in the pump is equal to the vaporization pressure the pump is in a cavitation state. The lowest pressure point in the pump usually occurs slightly after the inlet on the back of the blade. Since it is inconvenient to measure, the average pressure near the suction port section of the pump will be uniformly used instead. Use to represent the suction port pressure value when the pump incipient cavitation occurs. According to the definition in GB / T 13006 "Net Positive Suction Head for Centrifugal, Mixed Flow and Axial Flow Pumps": the net positive suction head when the head of the pump drops by 3% for the first time: NPSH3 is used as the standard for the critical cavitation margin, and use to represent the suction port pressure value that meets the GB / T 13006 standard.

[0040] (2-2) NPSH3 is the calculation formula for the critical cavitation margin. During the cavitation test, keep the flow rate unchanged, and make cavitation occur in the pump by gradually reducing the system pressure through the method of pumping vacuum in the closed circulation system.

[0041]

[0042] In the formula: (1) NPSH 3-iQn is the critical cavitation margin, unit m;

[0043] (2) P iQn is the absolute pressure of the pressure measurement point at the inlet of the test device, measured by the absolute pressure transmitter, unit Pa;

[0044] (3) P v is the saturated vapor pressure at the test water temperature, unit Pa;

[0045] (4) h is the height value of the absolute pressure transmitter above the intersection point of the pump blade rotation center line and the impeller housing of the test device, unit m;

[0046] (5) ρ—the density of the medium, kg / m 3 ;

[0047] (6) g—the acceleration of gravity, m / s 2 ;

[0048] During the test, the flow rate is kept constant, and a 3% drop in the head is defined as the critical net positive suction head NPSH re .

[0049] H P is the head at the specified point of the pump in the test device.

[0050] (3) Definition: is the pressure pulsation value of the pressure pulsation measurement point set at the inlet at the onset of cavitation under different operating conditions, is the inlet pressure pulsation value when the critical net positive suction head value is NPSH3 under the corresponding operating conditions. The dimensionless parameter (i = 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, x, etc., where x is the ratio of the maximum measurable flow rate to the rated flow rate of the test device.) The dimensionless parameter D i0 is plotted against the flow coefficient i in an intuitive column chart, and the variation law of the inlet pressure pulsation at the onset of cavitation and critical cavitation of the double-suction pump under different operating conditions can be obtained through analysis.

[0051] (4) Definition: The net positive suction head at the onset of cavitation of the double-suction pump under corresponding conditions and the critical net positive suction head reached by the standard GB / T13006 The test research device needs to measure at least 7 critical net positive suction head values and the at the onset of cavitation of the pump (i = 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, x, etc.,) where x is the ratio of the maximum measurable flow rate to the rated flow rate of the test device.) The dimensionless parameter E i0 is plotted against the flow coefficient i in an intuitive column chart, and the variation and distribution laws of the net positive suction head at the onset of cavitation and critical cavitation of the double-suction pump under different operating conditions can be obtained through analysis.

[0052] (5) Definition: The head at the onset of cavitation of the double-suction pump under corresponding conditions and the head at critical cavitation reached by the standard GB / T13006 The dimensionless parameter (i = 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, x, etc.,) where x is the ratio of the maximum flow rate that the test device can measure to the rated flow rate.) The dimensionless parameter F i0 and the flow coefficient i are plotted in an intuitive bar chart. By analysis, the variation and distribution law of the pump head under different operating conditions of the double-suction pump at the incipient cavitation and critical cavitation conditions can be obtained.

[0053] (6) At different flow coefficients, D i0 , E i0 and F i0 are subjected to variance analysis to obtain the influence degree on the inlet pressure pulsation at critical cavitation the inlet pressure pulsation at incipient cavitation critical cavitation margin incipient cavitation margin pump head H at critical cavitation iQn , the pump head value at incipient cavitation .

[0054] (7) Regression analysis. Let x = D i0 , y = E i0 , z = F i0 . Through data regression analysis and fitting calculation, y = f(x, z) is obtained. Analyze the operation change law of different operating conditions of the double-suction pump at incipient cavitation and critical cavitation to obtain the operating conditions for the double-suction pump to operate completely without cavitation.

[0055] Equation: y = f(x, z) is a dimensionless equation related to incipient cavitation and critical cavitation. That is, the discrete (x, y, z) points are fitted into a three-dimensional coordinate system. By analyzing the points and coordinates in the coordinate system, the law between incipient cavitation and critical cavitation can be obtained, providing theoretical data support for the non-cavitation operation of the double-suction pump.

[0056] The visualization test research device of the double-suction pump of the present invention can visually and accurately capture the incipient cavitation bubbles at the inlet of the double-suction pump blades. Through test observation and recording and analysis of data such as incipient cavitation margin, critical cavitation margin, incipient cavitation head, and critical cavitation head in the test pump, the bubble volume and flow pattern changes generated at the inlet of the blades during the operation of the pump. On the one hand, it provides accurate test data information for the subsequent non-cavitation operation of the double-suction pump to improve the accuracy of predicting incipient cavitation. The test law of the present invention can be extended and applied to the cavitation theory research of other model products. On the other hand, it can deeply reveal the flow pattern evolution characteristics and bubble volume distribution at the blade inlet from incipient cavitation to critical cavitation and the incipient mechanism of cavitation, providing strong test data support for the high cavitation performance design or optimization of the vane pump.

[0057] The foregoing has shown and described the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments, and what is described in the above embodiments and the specification is only to illustrate the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will also have various changes and improvements, and these changes and improvements fall within the scope of the present invention claimed. The scope of the present invention claimed is defined by the appended claims and their equivalents.

Claims

1. A visualization test research method for the inception of cavitation in a double-suction pump, characterized in that: The visualization test research method for the incipient cavitation of the double-suction pump includes the following steps: Step 1: Design a visualization test research device for the incipient cavitation of the double-suction pump, and respectively design observation windows on both sides of the suction section of the double-suction pump to facilitate the observation of the incipient cavitation of the impeller blades; Step 2: Uniformly set four pressure monitoring points at the inlet of the suction section and four pressure monitoring points at the outlet section of the volute chamber. Through the shooting of the high-speed camera images, when the incipient cavitation of the impeller of the double-suction pump is transmitted through the observation window, record the average pressure at the inlet of the suction section and the outlet of the volute chamber and calculate the corresponding incipient cavitation margin; The specific steps of Step 1 are as follows: Step 101: Design four visualization windows on both sides of the suction chamber of the double-suction pump that can observe the inlet edge of the impeller. Two observation windows are used to observe the incipient cavitation at the inlet of the blade, and the other two observation windows on the same side are used to assist in observing the light source input when the incipient cavitation of the blade occurs; Step 102: Outside the observation window for observing the incipient cavitation at the inlet of the blade, arrange a high-speed camera that can observe the incipient cavitation and the flow field state at the inlet of the impeller; Step 103: The observation angle and layout position of the high-speed camera need to be carried out through the layout of the on-site test device to ensure that the incipient cavitation phenomenon of the blade can be observed; The specific steps of Step 2 are as follows: (2-1) According to the definition of cavitation: the pressure at the lowest point in the pump is equal to the vaporization pressure The pump is in a state of cavitation; The lowest pressure point inside the pump usually occurs slightly after the inlet on the back of the blade. Since it is inconvenient to measure, the average pressure near the suction port section of the pump will be uniformly used instead. Using to represent the suction port pressure value when the pump cavitation starts; According to the definition in GB / T 13006 "Net Positive Suction Head for Centrifugal, Mixed Flow and Axial Flow Pumps": The net positive suction head when the first stage head of the pump drops by 3%: NPSH3 is used as the standard for the critical net positive suction head. Using to represent the suction port pressure value that meets the GB / T 13006 standard; (2-2) NPSH3 is the calculation formula for the critical cavitation margin. During the cavitation test, keep the flow rate unchanged. By evacuating the closed circulation system and gradually reducing the system pressure, cavitation occurs in the pump; Where: (1) is the critical net positive suction head, unit m; (2) is the absolute pressure at the pressure measurement point at the inlet of the test device, measured by an absolute pressure transmitter, with the unit of Pa; (3)P v is the saturated vapor pressure at the test water temperature, in Pa; (4) h is the height value of the absolute pressure transmitter above the intersection point of the pump blade rotation center line and the impeller housing of the test device, with the unit of m; (5) ρ —— density of the medium, kg / m 3 ; (6)g——Acceleration due to gravity, m / s 2 ; During the test, the flow rate is kept constant, and a 3% decrease in the head is determined as the critical net positive suction head (NPSH). re ; H P Is the specified point head of the test device pump; Definition is the pressure pulsation value of the pressure pulsation measurement point set at the inlet at the incipience of cavitation under different working conditions; is the inlet pressure pulsation value when the critical cavitation margin value is NPSH3 under the corresponding working condition; The dimensionless parameter (i = 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, x, where x is the ratio of the maximum flow rate that can be tested by the test device to the rated flow rate) is introduced to plot the dimensionless parameter D i0 against the flow coefficient i in an intuitive histogram, and the inlet pressure pulsation under the incipience of cavitation and critical cavitation of the double-suction pump and its variation law under different working conditions can be obtained through analysis; Define the net positive suction head at the incipient cavitation of a double-suction pump under corresponding conditions The critical cavitation margin achieved in accordance with Standard GB / T 13006 The test research device needs to measure at least 7 critical cavitation margin values At the incipient cavitation of the pump Introduce a dimensionless parameter (i = 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, x), where x is the ratio of the maximum flow rate that can be measured by the test device to the rated flow rate). Plot the dimensionless parameter E i0 against the flow coefficient i in an intuitive column chart. By analysis, the changes and distribution laws of the net positive suction head of the pump under the incipient cavitation and critical cavitation conditions of the double-suction pump under different operating conditions can be obtained; Define the head at the incipient cavitation of a double-suction pump under corresponding conditions The head at the critical cavitation reached in accordance with Standard GB / T 13006 Introduce dimensionless parameters (i = 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, x, where x is the ratio of the maximum flow rate measurable by the test device to the rated flow rate) Plot an intuitive histogram of the dimensionless parameter F i0 against the flow coefficient i. By analysis, the variation and distribution laws of the head of the pump under the incipient cavitation and critical cavitation conditions of the double-suction pump under different operating conditions can be obtained.

2. The visualization test research method for the incipience of cavitation in a double-suction pump according to claim 1, wherein: Under different flow coefficients, D i0 , E i0 and F i0 are subjected to analysis of variance to obtain the influence degrees on the inlet pressure pulsation at critical cavitation inlet pressure pulsation at incipient cavitation critical cavitation margin incipient cavitation margin head H at critical cavitation iQn , head value at incipient cavitation ; Regression analysis, let x = D i0 , y = E i0 , z = F i0 , through data regression analysis and fitting calculation, we get y = f(x, z), and analyze the operation change rules of different working conditions under the incipient cavitation and critical cavitation of the double-suction pump, so as to obtain the operating conditions for the double-suction pump to be completely free of cavitation.

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