VACUUM PUMP CALCULATION, IPT E&C

 

IPT E&C VACUUM PUMP CALCULATION

 

   

Introduction to Vacuum The earth's atmosphere exerts a pressure upon us, known as the atmospheric pressure, which can be measured in a number of ways. At sea level the standard pressure is 14.7 psia or 29.92" Hg or 760 mm of Hg (Torr). Because the barometric pressure varies, the above sea level pressures are used as a reference point. The term "vacuum" is used to describe the zone of pressure below atmospheric pressure. The most common standard to measure rough vacuum is inches of mercury ("Hg), which can be measured in two different ways. one method is as "Hg gauge" ("HgV), where the scale starts at 0 "Hg (atmospheric pressure) and goes up to 29.92 "Hg, which is perfect vacuum. The other way is to measure in "Hg absolute ("HgA), which is a gauge with a reversed scale. In this case the scale on the gauge reads 29.92" Hg at atmospheric pressure and 0 "Hg would be perfect vacuum. Note that a perfect vacuum is not possible on earth, no matter which vacuum pump is used. To show the relationship between "Hg gauge and "Hg absolute we can use the following example: 26 "Hg gauge at sea level would be 29.92 - 26 = 3.92 "Hg absolute. Because of the two different ways of measurement, the customer should be asked if they mean "Gauge" or "absolute". It is important to know which scale is used because the wrong assumption can mean a large error. When we operate in the higher vacuum range (low absolute pressure) it is more common to measure in Torr. 1 Torr = 1 mm Hg and is always absolute pressure. 25.4 mm = 1 ", therefore calculating the barometric pressure gives 29.92 X 25.4 = 760 Torr. An absolute pressure gauge reading in Torr reads 760 Torr at atmospheric pressure, which is zero vacuum and would read 0 Torr at perfect vacuum. The conversion table below shows the relationship between the different pressure measurements.   Conversion Formulas Torr(mm Hg) = 760 - ("HgV x 25.4) = "HgA x 25.4 = psia x 51.7 = mbar x .75 = "wc x 1.868 " Hg Absolute = mm Hg / 25.4 = 29.92 - "HgV = psia x 2 = mbar x 0.0295 = "wc x 0.0734 "Hg (gauge) = 29.92 - (mm Hg / 25.4) = 29.92 - "HgA = 29.92 - (psia x 2.036) = 29.92 - (mbar x 0.0295) = "wc x 0.0735       Pump Capacity Ratings The capacity for vacuum pumps is specified in a couple of different ways, depending on the type of vacuum pump and manufacturer. It is important to know the ACFM ("Actual Cubic Feet per Minute) inlet capacity at a specific vacuum level. Liquid-ring vacuum pumps are all rated in ACFM, the actual capacity at the different vacuum levels as shown on the individual pump performance curves. Capacities expressed in CFM or SCFM (Standard Cubic Feet per Minute) can be very misleading because we have to take into consideration the volumetric efficiency of the pump at a specific vacuum level (refer to example below). Rotary vane pumps are generally rated in CFM of free air displacement, which is the theoretical displacement at 0 "Hg vacuum. Manufacturers of small rotary vane pumps, such as Gast, rate their pumps in SCFM at different vacuum levels. In order to convert these values to ACFM refer to the calculations on the following page. Piston vacuum pumps are rated by the theoretical displacement in CFM, known as piston displacement (PD). To be able to compare capacities of different pumps we need to calculate the actual capacity (ACFM) at different vacuum levels. To be able to do this we need to know the volumetric efficiency of the pump at a specific vacuum level (request this form from the manufacturer), which can vary anywhere between 90% and 40%, depending on the pump design. For example, if a specific pump has a displacement of 100 CFM and the volumetric efficiency at 28 "Hg gauge is 80%, the actual pump capacity at 28 "Hg would be 80 ACFM. These values can also be obtained from the individual performance curves, if available.   Inlet Volume Calculations There is a great deal of confusion about the terms SCFM and ACFM: SCFM is measured at standard conditions (68 oF, 20 oC, 29.92 "Hg or 14.7 psia). ACFM is measured at actual inlet conditions. Conversion from SCFM to ACFM and vice versa, is derived form the gas laws, specifically Boyle's law. BOYLE'S LAW states that the volume and pressure of a gas will change in inverse proportion to one another. i.e. if the pressure in a system decreases (higher vacuum) then the volume the gas occupies will increase proportionally according to the following formula: P1 V1 = P2 V2 The product of the initial pressure and volume equals the product of the final pressure and volume. When using the above formula in calculations the values must be in absolute terms ("Hg absolute or Torr). Example 1: Convert 20 SCFM of air to ACFM at a vacuum level of 25 "Hg at sea level. Solution: First convert 25 "Hg gauge to "Hg absolute: P2 = 29.92 - 25 = 4.92 "HgA or 125 Torr Use above formula to convert: 29.92 x 20 SCFM = 4.92 x V2 ACFM V2 = (29.92/4.92) x 20 = 121.6 ACFM Example 2: The customer has a 200 ACFM pump installed which holds a vacuum level of 22 "Hg and they want to increase the vacuum level to 26 "Hg. Solution: Convert the vacuum levels quoted to absolute terms: P1 = 29.92 - 22 = 7.92 "HgA P2 = 29.92 - 26 = 3.92 "HgA Use above formula to convert: 7.92 x 200 ACFM = 3.92 x V2 ACFM V2 = (7.92/3.92) x 200 = 400 ACFM Therefore, in order to increase the vacuum level to 26 "Hg the customer would have to double the pump capacity from 200 ACFM to 400 ACFM. Example 3: Show the effect of pressure loss in inlet piping and filters on pump capacity. The customer requires a total capacity of 100 SCFM at a vacuum level of 24 "Hg at sea level. Inlet line losses, including inlet filters are 2 "Hg. Solution: First convert to ACFM based on 24 "Hg: P2 = 29.92 - 24 = 5.92 "HgA 29.92 x 100 SCFM = 5.92 x V2 ACFM V2 = (29.92/5.92) x 100 = 505 ACFM Without any line losses we would require a vacuum pump sized for 505 ACFM at 24 "Hg. However, we must overcome these losses and it will increase the required capacity substantially: P2 = 29.92 - 24 - 2 = 3.92 "HgA 29.92 x 100 SCFM = 3.92 x V2 ACFM V2 = (29.92/3.92) x 100 = 763 ACFM This indicates that the pump capacity needs to be 33% higher to overcome the 2 " pressure drop at 24 "Hg. NOTE: The above calculations are based on constant temperatures. If the temperature varies substantially from one condition to another, a correction needs to be made. If this is the case, contact G.E.E. for more details.   The table below shows the effect of undersized inlet piping and dirty inlet filters on the capacity of a pump at four different inlet pressure drops at a vacuum range from 15 - 28 "Hg at sea level. Process Vacuum Level Capacity Loss At Inlet Pressure Drop The following example below as well as the graph on the next page showing the expansion factor (F), are computed assuming that the pump is evacuating a closed, dry vessel. No leaks or presence of moisture have been considered. Example 4: The volume of a tank including connecting piping is 750 ft3. Initial atmospheric pressure (760 mm HgA [Torr]). Vacuum level required is 24 "HgV (150 Torr). The amount of gas to be removed from the vessel can be calculated by using the following formula: Q = V x Ln(P1/P2) in which, Q = total amount of air to be removed (ft3) V = volume of reservoir plus connecting piping P1 = Initial pressure P2 = Required pressure Solution: Ln(P1/P2) = Ln(760/150) = Ln 5.067 = 1.62 When using the log graph, locate the required vacuum level on the chart (150 Torr) and read expansion factor (F) off the scale (1.62). The total amount of air to be removed to reduce the pressure inside the vessel from atmospheric pressure to a vacuum level of 24 "HgV: 750 x 1.62 = 1215 ft3 If evacuation is required in three minutes, the average pump capacity from 760 to 150 Torr should be: 1215/3 = 405 ACFM Therefore, select a pump with this capacity. Expansion Factor (F)   Altitude Effects on Liquidring Vacuum Pumps Performance curves for vacuum pumps are always derived relative to atmospheric pressure at sea level. When a vacuum pump operates at altitudes higher than sea level, the atmospheric pressure decreases. The important thing to remember when you encounter applications at altitude is to measure the vacuum level relative to barometric pressure. Refer to the example below to see how this affects the calculation of vacuum level. As a quick rule of thumb, you can assume that for each increase of 1,000 feet of elevation, the barometric pressure will decrease by 1 "Hg. Example: The installation site is located in Denver, CO (elevation 5280 ft). A capacity of 750 ACFM at 20 "Hg gauge is required for the application. What is the equivalent vacuum level at sea level? Solution: The following formula helps to calculate the equivalent vacuum level: Pref = P1 x (29.92/P2) which Pref = corrected vacuum level P2 = barometric pressure at altitude = 25.3 "HgA (chart) P1 = P2 - required vacuum level at altitude = 25.3 "HgA - 20 "Hg = 5.3 "HgA Pref = 5.3 "Hg x (29.92/25.3) = 6.3 "HgA or 23.4 "HgV Therefore, select the pump with a minimum capacity of 750 ACFM at 23.4 "HgV.   Effect of Saturated Air Service on the Capacity of Liquidring Vacuum Pumps The following graphs illustrated below show the average condensing factors for vacuum pumps in saturated air service. When handling air/water vapor mixtures, the pump capacity will increase depending on the saturated air temperature as well as the sealing liquid temperature as well as the sealing liquid temperature entering the pump. Example: Consider a liquidring vacuum pump operating at 27 "HgV (75 Torr) with a dry air capcity of 200 ACFM of dry air when using 59 0C seal water. If the same pump handles saturated air at 86 0F and seal-water of 59 0F, the actual pump capacity would be: CFM (dryair) x condensing factor = Actual CFM 200 x 1.37 = 274 ACFM               Effect of Service ater Temperature on the Capacity of Liquidring Vacuum Pumps The temperature of the sealing fluid (water) can have a dramatic effect on the capacity of liquidring vacuum pump. The performance data are based on using 59 0F water as the sealing liquid for the vacuum pump. The vapour pressure of the service liquid has a direct influence on the vacuum pump capacity. When the vapour pressure of the service liquid is less than that of water at 59 0F, the pump capacity will increase and when the vapour pressure of the service liquid is higher, the pump capacity will decrease. The diagrams below allow the user to select the correct pump for the application in question, while taking capacity correction factors into account. Example: A high seal-water temperature (approx. 860F) can have a significant effect on the capacity of the pump. For a single stage pump, the capacity correction factor when operating at 75 Torr (27 "HgV), is 0.76. This means that if the published capacity of the pump is 300 ACFM at 75 Torr, the pump will have a corrected capacity of 228 ACFM with the higher seal water temperature.   Liquidring Vacuum Pump Principle of Operation Figure 1: In a cylindrical housing, partially filled with sealing liquid, a multi-blade impeller on a shaft is positioned eccentrically. Port plates with inlet and discharge openings are positioned on either side of the impeller.     Figure 2: A liquid ring is created by the centrifugal force generated by the rotating impeller. This force holds the liquid ring against the inner wall of the pumping chamber. Since the impeller is located eccentric to the pumping chamber, the depth of entry of the blades into the liquid ring decreases and increases as the impeller rotates. This creates increasing impeller cell volume on the inlet port side, creating a vacuum. on the discharge port side, the impeller cell volume decreases, as the blades move further into the liquid ring, increasing the pressure, until discharge takes place through the discharge port. A continuous flow of fresh sealing liquid is supplied to the pump via the sealing liquid inlet.   Radial Blower Principle Radial blowers operate using a dynamic principle (the velocity of air is changed into pressure). This method has proved very successful for the generation of both low vacuum and pressure combined with relatively large capacities. Single stage and multi stage models, as well as those with direct or gear box drive, produce vacuum up to 92 "H2O or pressure up to 120 "H2O. Capacities range from 60 to 1770 cfm. Radial blowers are air-cooled and non-contact operation means there is no wear, making the design virtually maintenance free. As soon as the impeller starts rotating, the air in the blade chamber (1) of the impeller (2) is directed in a centrifugal outward movement and exits at the edge of the impeller (3). Therefore, in the center (4) of the impeller, suction is created causing air to flow in from the inlet port (5). At the hub (6) this entering air is deflected from an axial into a radial direction, and enters into the blade chambers (7). Due to the high speed on the impeller circumference, the air flows outward into the spiral housing (8). At this point the velocity is reduced with part of the energy transferred into compression energy. Inside the spiral housing an airstream is created. Its energy comes partly from its high speed and partly from the produced over pressure. The airstream flows through the outlet (9) of the spiral housing into the pressure line and is transported to the workplace. For vacuum operation, a pipeline is connected to the suction port (5) of the blower. When the suction opening is throttled, a vacuum is produced in the suction line. With this method of operation, the impeller again produces a pressure increase, but this time from vacuum to atmospheric pressure. At a higher motor speed, for example 60 Hz operation instead of 50 Hz, both capacity and pressure difference are increased. The performance of the blower and subsequently the required motor power are also increased considerably.   Side Channel Principle The side channel principle is also based on the method of dynamic compression (transforming flow energy into pressure energy). The side channel design is suited for applications requiring both, pressure and vacuum. Depending upon model size-single stage or two stage-vacuum up to 20 "H2O in suction operation and pressure mode can be obtained. The capacities range from 10 to 650 CFM. Non-contact operation means side channel blowers are practically free of wear and maintenance. The pumping medium is not contaminated from carbon dust or oil, as occurs with dry running or oil lubricated rotary vane pumps. The ring-shaped working chamber (1) has a circular cross section (2). one half of this cross section is formed by the impeller (3) with its radial blades (4) on one side, while the other fixed half is formed in the housing (5). The working chamber has an inlet port (6) and an outlet port (7) with the impeller shown in the diagram rotating in an anti-clockwise direction. Between the inlet and outlet ports is the rotor (8) filling up the side channel. Air is trapped between the impeller pockets of the rotating impeller and is then accelerated centrifugally. The air stream is ducted by the centrifugal force into the side channel blower. The impeller pockets then take it up and the air is then re-directed back into the following pocket, which repeats the process. The air is accelerated and compressed in the impeller several times. The more the blower is throttled, either at the inlet or discharge, the greater the number of impeller re-entries and hence increased compression. One can compare the movement of an air molecule within a side channel with a spring, the pitch of which tighter the more the air is throttled. When you measure the pressure at different points on the ring channel, you find that it rises constantly from inlet (6) to outlet (7). The side channel principle works as a vacuum pump when throttled on the suction side, and as a compressor when throttled on the pressure side. Rotary Vane Principle Pressure increase by volume reduction is the principle behind rotary vane operation. This static design offers excellent service in pressure, vacuum or a combination of both. Depending upon size and design (i.e. oil lubricated or dry running) vacuum up to 29.92 "Hg gauge with capacities ranging from 2 to 700 cfm and pressures up to 21.8 psig with capacities ranging from 2 to 350 cfm can be reached. When used as a combined unit, 23.6 "Hg gauge vacuum and 11.6 psig pressure can be achieved simultaneously. In a cylindrical housing (1) a rotor (2) is positioned eccentrically so that it is on the top (3) almost touching the cylinder. Rotor blades (5) are positioned into numerous rotor slots (4). When the rotor starts turning, due to centrifugal force the blades are thrown out and slide against the internal surface of the cylinder. In this way a cell (6) is formed between two blades with a volume which changes constantly during rotation. Air enters from the inlet port into a cell until the rear blade reaches the inlet port (8). At this point the cell (6) has achieved its maximum air volume. As the cell then moves away from the port its volume becomes smaller and smaller, the air is thus compressed and pressure rises. This continues until the pressure in the cell (9) exceeds that in the pressure chamber (10) and the air then exits through the outlet port (11). Some models are fitted with exhaust valves (12) which stop the back flow of this discharged air if the maximum pressure has been reached. In a vacuum pump the process is similar, but the cell (9) gives decreasing pressure, and the chamber (10) is atmospheric pressure. On pressure/vacuum pumps the lower end of the inlet port(s) (7) for the vacuum is moved forward. This provides the ability to fill the cell from a second inlet (14). To avoid impairing the vacuum, this second inlet port is located about one cell segment away from the main suction port (7). The ratio between vacuum and pressure capacities can be influenced by the arrangement of the inlet ports (7) and (14).   Roots Principle Similar to the rotary vane pumps, the Roots pumps are also static compression systems, although the compression does not result from an internal volume reduction. The single stage Roots vacuum pumps that G.E.E. use are designed for use in pump sets in combination with a rotary vane backing vacuum pump. The conveyed air is not discharged to atmosphere but piped into the inlet port of the connected high-pressure stage (rotary vane pump). The achievable capacities range from 300 to 2800 cfm at an ultimate vacuum of 29.92 "Hg gauge. Similar to the rotary vane pump, air enters the inlet opening (1) into a conveying cell formed by the two rolling pistons (2) in the housing. This is until the cell is separated from the inlet by the following piston head (5). The air in the cell is conveyed without reduction until it reaches the outlet (6), the air with a higher absolute pressure flows from the pressure chamber into the following cell, and must then be discharged. It is during this stage of the conveying that external compression takes place. Claw Principle Similar to rotary vane pumps and roots blowers, claw compressors and vacuum pumps utilize a static compression principle of design. In contrasts to roots blowers, compression works by internal volume contraction. Whether used for pressure, vacuum or both combined, the claw principle provides very favorable efficiency and operational characteristics. Depending on size, vacuum up to 25.5 "Hg (gauge) and capacities between 59 and 353 cfm, or pressure up to 32 psig at flow rates between 59 and 353 cfm can be achieved. In combined pressure/vacuum operation simultaneous vacuum up to 18.1 "Hg (gauge) and pressure up to 14.5 psig can be obtained. A claw pump consists of two rotors (1, 2). They turn in opposite directions in a compressor housing (9) without friction and with very tight clearances. They are synchronized via a precision gear. As the claw moves over the suction connection (3) and the axial suction channel inlet (4) the gas is sucked into the compressing chamber. Due to the revolution of the rotors the gas is conveyed from the suction side to the pressure side. There it is compressed by volume reduction between the rotors until the lower rotor uncovers the discharge port (5). This "internal compression" leads to high differential pressures at efficiencies of more than 60 %. Afterwards, the compressed gas is discharged via the pressure connection (8). To remove heat of compression, cooling air is sucked between the compressing housing (9) and a silencing cover (10) and then it is laterally exhausted.   Temperature Conversion Table Locate in the center column of the known temperature. If the known temperature is in Fahrenheit, the Centigrade equivalent is in the left-hand column, and vice versa Basic conversion formulas: 0C = 0F - 32 x 5/9 or 0C = (0F - 32)/1.8 0F = 0C x 9/5 + 32 or 0F = 0C x 1.8 + 32   Conversion Table