Axial and Displacement Pumps CIVE 401 – Hydraulic Engineering November 19th 2014

Gabrielle Davis, Jamie Deal, Mateus Cardoso Ramos

Table of Contents

Axial and Displacement Pumps, 2

Title Page ……………………………………………………………………………………………………… 1

Table of Contents…………………………………………………………………………………………… 2 List of Figures ……………………………………………………………………………………………….. 2

Introduction…………………………………………………………………………………………………… 3 Axial Pumps………………………………………………………………………………………… 3 Displacement Pumps…………………………………………………………………………… 4

Calculations ………………………………………………………………………………………………….. 5 Examples……………………………………………………………………………………………………… 7

Application……………………………………………………………………………………………………. 8 Axial Pumps………………………………………………………………………………………...9

Displacement Pumps………………………………………………………………….….…… 10

Conclusion…………………………………………………………………………………………………… 11

References …………………………………………………………………………………………………... 12

List of Figures Figure 1: Axial Flow Pump …………………………………………………………………………….… 3

Figure 2: Rotary positive displacement pump system ……………………………………..… 4

Figure 3: Reciprocating positive displacement pump system. ……………………….…. 5

Figure 4: Hydraulic Pump …………………………………………………………………………….…. 7 Figure 5: Axial Pump Expanded …………………………………………………………………........ 9 Figure 6: Axial Pump Flow ……………………………………………………………………………… 9

Figure 7: Piston Displacement Pump ……………………………………………………………... 10

Introduction

Axial and Displacement Pumps, 3

Pumps come is all different shapes and sizes. The many different types of pumps allow their use in a variety of different applications. Two types of pumps that are commonly used are axial and displacement pumps. Axial Pumps

Axial pumps utilize the momentum and velocity of a fluid moving through the pump, caused by an impeller applying a centrifugal force to the fluid, to create pressure in the pump. An axial pump is similar to a centrifugal pump in this way, except the fluid flow is parallel to the impeller shaft instead of radial to the shaft. This feature allows axial pumps to have a much greater capacity than most other pumps; however, it also causes the pump to have low pump head and discharge pressure. Axial pumps are sometimes termed propeller pumps owing to their similarity to the propeller of a boat. The difference, however, is that these pumps are usually shrouded in a casing to transmit fluids from one specific location to another.

For systems that require high flow rates and low pump head, axial pumps are the best type of pump to use (McGraw-Hill, 2003). A diagram of the operation of an axial pump can be seen in Figure 1.

Figure 1: Axial flow pump

Displacement Pumps

Axial and Displacement Pumps, 4

Another type of pump is a displacement pump. Inside a displacement pump, one part water is being replaced by another part using the inertia of the fluid flowing through the pipe. For example, in Figure 2 the water contained in cavity 2 is displaced by the water coming in from 1 as the lobes rotate inside the pump. This displacement of water is forced through the discharge of the pump, creating the increase in pressure necessary.

1

2

Figure 2: Rotary positive displacement pump system. There are two types of displacement pump exits: positive displacement and nonpositive displacement pumps. Non-positive pumps have slippage, which results in a continuous but variable flow through the pump. Slippage is when the fluid “slips” back as the external resistance is increased in the system; therefore, the discharge will decrease (Hydraulic Pump). These pumps rely heavily on pressure changes and cannot handle high-pressure outlets. They are best put to use in systems that require low-pressure and high-capacity flow (Hydraulic Pump) Positive displacement pumps have a constant volumetric output when the velocity of the fluid is kept constant regardless of the pressure of flow resistance (Engineering Principles, 2003). This characteristic is highly useful in applications that require a very high-pressure output, or is a certain measured output is necessary. It is necessary to remember to have the discharge valve shut on a positive displacement pump, or pressure could build up and cause damage.

Positive displacement pumps can be placed into two different classifications: rotary and reciprocating. Rotary positive displacement pumps involve a rotating piece of equipment inside the pump’s casing, such as gears or lobes (Figure 2), which rest very closely to the walls of the pump.

Axial and Displacement Pumps, 5

This traps the fluid in a cavity and forces the water through the discharge as the rotating pieces move. The closer the rotating pieces are to the casing of the pump, the less slippage occurs, and the more constant the flow of fluid becomes. Rotary pumps can be gear, lobe, or screw and can handle fluids with high viscosity better than most pumps (Seider, 2009).

Reciprocating pumps involve pistons fitting very closely inside cylinders. Usually this involves two cycles; a suction cycle and a discharge cycle. In a simple case, the suction cycle occurs when the piston is moved upward, causing the suction valve to open due to the creation of low pressure, and the discharge valve is closed. The cylinder then fills with the fluid. The discharge cycle happens when the discharge valve opens and the suction valve closes, releasing the fluid through the discharge of the pump. The volume of the fluid released is exactly to the volume of the cylinder in the case. This system can be seen in Figure 3.

Figure 3: Reciprocating positive displacement pump system.

Calculations The ultimate goal of a pump is to provide the necessary energy required to move a fluid from one place to another. This energy will allow the fluid to increase its elevation, velocity, or pressure. Since the net effect of an increase in elevation or velocity is ultimately an increase in pressure, the power required (𝑊𝑊̇ ) for a pump is: 𝑊𝑊̇ = 𝑛𝑛̇ ∙ 𝑉𝑉 ∙ ∆𝑃𝑃

(1)

In this general equation, 𝑛𝑛̇ is the molar flow rate of the fluid, V is the molar volume, and ∆𝑃𝑃 is the differential pressure between the inlet and the outlet of the pump. The ideal pump work is the total amount of energy added to the liquid from the suction

Axial and Displacement Pumps, 6

of the pump to the discharge. This can be described by equation (2) for pump head (𝐻𝐻𝑃𝑃 ), which is the addition of the velocity head, static head, and pressure head, derived from the Bernoulli’s equation. 𝑣𝑣 2

𝑃𝑃

𝑣𝑣 2

𝑃𝑃

2 1 𝐻𝐻𝑃𝑃 = � 2𝑔𝑔 + 𝑧𝑧2 + 𝛾𝛾2 � − � 2𝑔𝑔 + 𝑧𝑧1 + 𝛾𝛾1 �

(2)

The velocity head is half the change in the squared velocity of the liquid (𝑣𝑣 2 ) divided by gravity (𝑔𝑔). The static head is just the elevation increase (𝑧𝑧) while the pressure head is the change in pressure (𝑃𝑃) divided by the specific gravity of the liquid. The pump head and capacity of a pump, or flow rate of the fluid, are the two main characteristics that describe a pump.

A common way to calculate the horsepower required to drive a pump is to apply the following formula: Horsepower = Q x P x .0007 (3) The discharge (Q) is used in gallons per minute (gpm), and the pressure (P) has to have its units in bar. The value .0007 is used to give the horsepower in units of hp instead of watts (Engineering Toolbox, 2014).

If we need to calculate the Pump Output Flow (in gallons per minute), a practical equation is: GPM = RPM x Pump Displacement ÷ 231

(4)

The pump displacement is used in cubic inches, and the factor RPM refers to the frequency of rotation and is used in rpm (revolutions per minute). The number 231 must be used to give the flow in gallons per minute.

Similar to the equation defined above, the Pump Displacement Needed for GPM of Output Flow is: Displacement = 231 x GPM ÷ RPM

This time, the units of the pump displacement are cubic inches per revolution (in3/rev) because we need to consider the rotations when calculating the pump displacement.

(5)

When talking about hydraulic pump power, we can use other equations that will give us precise data about the pump being analyzed (Ly, 2014):

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Figure 4: Hydraulic Pump The ideal hydraulic power (𝑃𝑃ℎ,[𝑘𝑘𝑘𝑘] ) to drive a pump depends on the volumetric flow rate (𝑞𝑞), the liquid density (𝜌𝜌), the acceleration due to gravity (𝑔𝑔), and the differential head (ℎ) and can be calculated in kilowatts in equation (3) and in horse power per equation (4):

𝑞𝑞∙𝜌𝜌∙𝑔𝑔∙ℎ

𝑃𝑃ℎ,[𝑘𝑘𝑘𝑘] = 3.6×106

Examples

𝑃𝑃ℎ,[ℎ𝑝𝑝] =

𝑃𝑃ℎ,[𝑘𝑘𝑘𝑘] 0.746

(6) (7)

Example 1: A pump delivers 10 dm3/min with a pressure rise of 60 bar. The shaft speed is 1330 rev/min and the nominal displacement is 8 cm3 /rev. The Torque input is 11.4 Nm. Calculate: i. The volumetric efficiency. ii. The shaft power. iii. The overall efficiency. Solution: Ideal flow rate = Nominal Displacement x Speed = (8 cm3/min) x (1330 rev/min) = 10640 cm^3/min = 10.64 dm3/min i) Volumetric efficiency = Actual Flow/Ideal Flow = (10 dm3/min)/ (10.64 Q = (10 x 10−3 m3/min)/ (60 s/min) = 16.7 x 10−6 m3 /s ∆p = 60 x 〖10〗^5 N/m^2

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Fluid Power = Q∆p = 16.7 x 〖10〗^(-6)x 60 x 〖10〗^5= 1002 Watts ii) Shaft Power = 2πNT/60 = 2π x 1330 x 11.4 /60 = 1587.8 Nm iii) Overall Efficiency = F.P./S.P. = 1002/1695.2 = 0.631 or 63.1%.

Example 2: How many horsepower are needed to drive a 7 gpm pump at 1300 psi? Solution: Q = 7 gpm P = 1300 psi Q x P x .0007 = (7 gpm) x (1300 psi) x .0007 = 6.37 horsepower Example 3: How much oil will be produced by a 3 cubic inch pump operating at 1500 rpm? Solution: RPM = 1200 Pump Displacement = 2.5 cubic inches GPM = RPM x Pump Displacement ÷ 231 = 1500 rpm x 3 in3 ÷ 231 = 19.48 gpm Example 4: What displacement is needed to produce 8 gpm at 1000 rpm? Solution: GPM = 8 gpm RPM = 1000 rpm Displacement = 231 x GPM ÷ RPM = 231 x 8 gpm ÷ 1000 rpm = 1.85 in3/rev

Example 5: 2 m3/h of water is pumped at a head of 8 m. What is the hydraulic pump power? Solution: The theoretical pump power can be calculated as: Ph(kW) = (2 m3/h) (1000 kg/m3) (9.81 m/s2) (8 m) / (3.6 106) = 0.0436 kW.

Application When determining what type of pump to use for given conditions, there are factors that need to be taken into consideration. Some of these factors include, but are not limited to: flow discharge, flow velocity, head, and efficiency. It is necessary to determine what factors are ultimately the most important for a specific task.

Axial Pumps

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Axial pumps are used when you need to have a high discharge and a low head. They are also used when you have a small exit and entrance and in general, they have the smallest dimensions as far as pumps go (McGraw-Hill). Axial pumps differ depending on the direct use but they generally follow the same set up (Figure 5). Since a propeller powers axial pumps, a common application of them is in motorboats (Figure 6). With motorboats, they use the propeller to push water up though the pump to power the boat.

Figure 5. Axial Pump Expanded

Figure 6. Axial Pump Flow

Axial pumps are also used often in agriculture. They are very beneficial for lifting water for irrigation and drainage. If the liquid needs to go up less than 4 meters, an axial pump can pump up to 3 times more fluid. Since in irrigation having a large head is not an important factor but moving a lot of liquid is, axial pumps are a great option. They are also used for handling sewage from industrial, commercial and municipal sources. For sewage, axial pumps mainly are utilized for the internal mixed liquor recirculation. They are ideal for sewage for the same reasons that they are used in irrigation; they can move large amount of liquids fast but with a relatively small head. Axial pumps tend to not be as effective for sewage as they are for irrigation due to the fact that there tends to be a slightly larger head required for sewage.

In the chemical industry, they need to be able to circulate large masses of liquids. These liquids can include evaporators and crystallizers. Axial pumps work well for the chemical industry also because the main goal is to move large amount of liquids with a relatively small head required.

Power Plants also have a high demand for axial pumps. Power plants use axial pumps to pump water from a reservoir, river, lake or sea for the refrigeration line.

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For pumping water to the power plant, it is mainly important to get the liquids a long distance without a high head needed. They are also useful in flood dewatering applications where large quantities of water need to be moved a short distance, such as over a levee or dyke. These applications are not nearly as common as applications for radial flow pumps, so there are not nearly as many axial flow pumps as there are radial flow pumps. Displacement Pump

Displacement pumps are similar to axial pumps but instead of using a propeller, they have a piston or a plunger that moves back and forth to move the liquid (Figure 7). Displacement pumps are often used for hydraulic systems. In hydraulic systems, displacement pumps can withstand pressures of up to 5000 psi (Positive Displacement Pumps). They are ideal for applications where a constant flow is needed. Note that many types require pressure protection via a relief valve to safeguard the pump and system from over pressurization. They create medium to high pressure, and are often an excellent way to pump oils and other viscous fluids. PD pumps may also be needed for low flow and high-pressure combination, to move fluids containing fragile solids, or for other application niches. Some types are inherently selfpriming, and several types are seal less.

A type of displacement pump is a gear pump. Gear pumps are widely used for automotive engines for the oil pump. This is because gear pumps allow liquid to get in on the outermost part of the gear and not the central line. Therefore no liquid can go back because of the gears locking together in the center (Figure 2).

Figure 7. Piston Displacement Pump

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Roots-type pumps are also a subset of displacement pumps. These works by having two rotors that fit when they are 90° and provide equal volumes and do not allow a vortex to form. This type of pump is used often for high capacity industrial air compressors and also internal combustion engines.

Conclusion

In conclusion, axial and displacement pumps are used for a wide variety of reasons. Both of the different types of pumps have a high discharge and a low head that allows uses for systems that need to move high volumes of liquid. Axial pumps tend to relate more to agriculture, industrial waste, and power plants. Displacement pumps generally have wider uses since there are many different types. They can range from uses in hydraulic systems, to uses in car engines. Displacement pumps generally move smaller amounts of liquids than axial pumps but they still have the ability to move more than other types of pumps.

References

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Applied Engineering Principles Manual. Navy Department: 2003. Pg 30-38.

Dunn, DJ. "Hydraulic Pumps." FLUID POWER (n.d.): n. pag. Web. 2 Nov. 2014. "Engineering ToolBox." Engineering ToolBox. N.p., n.d. Web. 1 Nov. 2014.

Ly., and Perform. When to Use a Positive Displacement Pump (n.d.): n. pag.Pump

School. Web. 1 Nov. 2014.

McGraw-Hill. Dictionary of Scientific & Technical Terms. Ed 6. The McGraw-Hill Companies Inc: 2003. .

“Non-Positive Displacement Hydraulic Pumps”. Hydraulic Pump. December 22, 2010. < http://www.hydraulic-pump.info/hydraulic-engineering/hydraulic-pumpsand-pressure-regulation/non-positive-displacement-hydraulic-pumps.html>. "Positive-Displacement Pumps." Positive-Displacement Pumps. N.p., n.d. Web. 4 Nov. 2014.

Seider, Warren D. et al. Product and Process Design Principles. John Wiley and Sons Inc: 2009. Pg 510-513.