Comp1

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Fundamentals of compressed air 1.2 Units and formula symbols The SI-units ( Système International d'Unités ) were agreed at the 14th General Conference for Weights and Measures. They have been generally prescribed since 16.10.1971. The basic units are defined independent units of measure and form the basis of the SI-system. 1.2.1 Basic units Basic unit Length Mass Time Strength of current Temperature Strength of light Qty of substance Formula symbol l m t I T I n Symbol [m] [ kg ] [s] [A] [K] [ cd ] [ mol ] Name Metre Kilogramme Second Ampere Kelvin Candela Mol 1.2.2 Compressed air units Engineering uses measures derived from the basic units. The following table shows the most frequently used units of measure for compressed air. Unit Force Pressure Area Volume Speed Mass Density Temperature Work Energy Tension Frequency Formula symbol F p A V v m ρ T W P U f Symbol [N] [ Pa ] [ bar ] [ m2 ] [ m3 ] [l] [m/s] [ kg ] [t] [ kg / m3 ] [ °C ] [J] [W] [V] [ Hz ] Name Newton Pascal Bar 1 bar = 100 000 Pa Square metre Cubic metre Litre 1 m3 = 1 000 l Metre per Second Kilogramme Tonne 1 t = 1 000 kg Kilogramme per cubic metre Degree Celsius Joule Watt Volt Hertz 6 Fundamentals of compressed air 1.3 1.3.1 What is compressed air ? The composition of air The air in our environment, the atmosphere, consists of: Nitrogen 78 % 78 % Nitrogen 21 % Oxygen 1 % other gases ( e.g.. carbon-dioxide and argon ) Oxygen 21 % other gases 1% Fig. 1.11: The composition of air 1.3.2 The properties of compressed air Compressed air is compressed atmospheric air. Compressed air is a carrier of heat energy. Compressed air Pressure energy Heat Compressed air can bridge certain distances ( in pipelines ), be stored ( in compressed air receivers ) and perform work ( decompress ). Fig. 1.12: Air compression 1.3.3 How does compressed air behave? As with all gases, the air consists of molecules. The molecules are held together by molecular force. If the air is enclosed in a tank ( constant volume ), then these molecules bounce off the walls of the tank and generate pressure p. The higher the temperature, the greater the movement of air molecules, and the higher the pressure generated. Volume ( V ) = constant p p p p p p p p p p V p p Temperature ( T ) = is increased Pressure ( p ) = rises T Fig. 1.13: Air in a closed container Boyle and Mariotte carried out experiments with enclosed volumes of gas independently of each other and found the following interrelationship: The volume of gas is inversely proportional to pressure. ( Boyle-Mariotte’s Law ) 7 Fundamentals of compressed air 1.4 Physical fundamentals The condition of compressed air is determined by the 3 measures of thermal state: T V p = Temperature = Volume = Pressure p × V ———— T = constant This means: Heat Volume constant ( isochore ) Pressure and temperature variable When the temperature is increased and the volume remains constant, the pressure rises. p0 , T0 p1 , T1 constant volume isochore compression p0 —— p1 = T0 —— T1 Temperature constant ( isotherm ) Pressure and volume variable p0 , V0 p1 , V1 When the volume is reduced and the temperature remains constant, the pressure rises. constant temperature isotherm compression p0 × V 0 = p1 × V1 = constant Heat Pressure constant ( isobar ) Volume and temperature variable V0 , T 0 V1 , T 1 When the temperature is increased and the pressure remains constant, the volume increases. constant pressure isobar compression V0 —— V1 = T0 —— T1 8 Fundamentals of compressed air 1.4.1 Temperature The temperature indicates the heat of a body and is read in °C on thermometers or converted to Kelvin ( K ). T 0°C Fig.1.14: Showing temperature [K] = t [ °C ] + 273,15 1.4.2 Volume Volume V [ l, m3 ] Compressed air in expanded state, open air The volume is determined, for example, by the size of a cylinder. It is measured in l or m 3 and relative to 20 ° C and 1 bar. The numbers in our documentation always refers to compressed air in its expanded state. d2 × π ———— × h 4 VCyl = Volume d = Diameter h = Height [m3] [m] [m] VCyl = Volume (V) Normal volume VNorm [ Nl, Nm3 ] Compressed air in expanded state under normal conditions The normal volume refers to the physical normal state as specified in DIN 1343. It is 8 % less than the volume at 20 ° C. 760 Torr = 1,01325 barabs = 101 325 Pa 273,15 K = 0 °C Norm volume 0°C + 8% = Volume 20 ° C Operating volume Voperat [ Bl, Bm3 ] Compressed air in compressed state The volume in operating state refers to the actual condition. The temperature, air pressure and air humidity must be taken into account as reference points. When specifying the operating volume the pressure must always be given, e.g., 1 m 3 at 7 bar means that 1 m 3 expanded (relaxed) air at 7 bar = 8 bar abs. compressed and only occupies 1/8 of the original volume. 0 barabs 8 barabs 9 Fundamentals of compressed air 1.4.3 Pressure Atmospheric pressure pamb [ bar ] Atmospheric pressure is caused by the weight of the air that surrounds us. It is independent of the density and height of the atmosphere. At sea level, 1 013 mbar = 1,01325 bar = 760 mm/Hg [ Torr ] = 101 325 Pa Under constant conditions atmospheric pressure decreases the higher the measuring location is. Fig.1.15: Atmospheric pressure Over-pressure pop [ barop ] Over-pressure is the pressure above atmospheric pressure. In compressed air technology, pressure is usually specified as over-pressure, and in bar without the index „ op“. Overpressure pop Absolute pressure pabs [ bar ] The absolute pressure pabs is the sum of the atmospheric pressure pamb and the over-pressure pop. barometric air pressure pabs pabs pvac = pamb + pop Partial vacuum According to the SI-System pressure is given in Pascal [ Pa ]. In practice, however, it is still mostly given in „ bar “. The old measure atm ( 1 atm = 0,981 bar-op ) is no longer used. pamb Force 100 % Vacuum Pressure = ———— Area F p = —— A pamb pop pvac pabs = = = = Atmospheric pressure Over-pressure Partial vacuum Absolute pressure 1 Pascal = 1 Newton ———— 1 m2 1N 1 Pa = —— 1 m2 [ mm water head ] Fig.1.16: Illlustration of different pressures 1 bar = 10195 mmWH 10 Fundamentals of compressed air • Volume flow V [ l/min, m³/min., m³/h ] The volume flow describes the volume ( l or m³ ) per unit of time ( minute or hour ). Working volume flow Induction rate 1.4.3 Volume flow Þ A distinction is made between the working volume flow ( induction rate ) and the volume flow ( output rate ) of a compressor. • Working volume flow VWor [ l/min, m³/min., m³/h ] Induction rate Volume flow Output rate The working volume flow is a calculable quantity on piston compressors. It is the product of the cylinder size ( piston capacity ), compressor speed ( number of strokes ) and the number of cylinders working. The working volume flow is given in l/min, m³/min or m³/h. • VWor Fig. 1.17: Working volume flow and volume flow TDC BDC TDC = Top dead centre BDC = Bottom dead centre Fig. 1.18: Cylinder movement Û = A × s × n × c • VWor A s n c = = = = Working volume flow [ l / min ] Cylinder area [ dm2] Stroke [ dm] Number of strokes [ 1/ min ] (compressor speed) = Number of working cylinders • Volume flow V [ l/min, m³/min, m³/h ] Output rate The output rate of a compressor is normally declared as the volume flow. In contrast to the working volume flow, the volume flow is not a calculated value, but one measured at the pressure joint of a compressor and calculated back to the induction state. The volume flow is dependent on the final pressure relative to the induction conditions of pressure and temperature. This is why when calculating the induction state the measured volume flow to induction pressure must be „ relaxed“ and to induction temperature it must be „ re-cooled“. The volume flow is measured according to VDMA 4362, DIN 1945, ISO 1217 or PN2 CPTC2 and given in l/min, m3/min or m3/h. The effective volume flow, i.e., the output that can actually be used, is an important consideration for the design of a compressor. Volume flows can only usefully be compared when measured under the same conditions. This means that the induction temperature, pressure, relative air humidity and measured pressure must match. 11 Fundamentals of compressed air • Norm volume flow VNorm [ Nl/min, Nm3/min, Nm3/h ] As with the volume flow, the norm volume flow is also measured. However, it does not refer to the induction state, but to a theoretical comparative value. With the physical norm state the theoretical values are: Volume flow 20°C Fig. 1.19: Norm volume flow + 8% = Norm volume flow 0°C Temperature= 273,15 K Pressure = 1,01325 bar Air density = 1,294 kg/m3 ( 0 °C ) ( 760 mm HG ) ( dry air ) • Operating volume flow VOperat [ Ol/min, Om3/min, Om3/h ] The operating volume flow gives the effective volume flow of compressed air. To be able to compare the operating volume flow with the other volume flows, the pressure of he compressed air must always be given in addition to the dimension Ol/min, Om3/min or Om3/h. 0 barabs Fig. 1.20: Operating volume flow 8 barabs 12 Fundamentals of compressed air 1.5 Compressed air in motion Different laws apply to compressed air in motion than to stationary compressed air. 1.5.1 Flow behaviour The volume flow is calculated from area and speed. A1 A2 • V = A1 × v 1 = A2 × v2 A1 v2 —— = —— A2 v1 v1 v2 • V = A 1, A 2 = v 1, v 2 = The result of the formula is that: The speed of flow is inversely proportional to the cross section. Volume flow Cross section Speed Fig. 1.21: Flow behaviour 1.5.2 Types of flow Flow can be laminar or even (Ideal), or turbulent ( with backflow and whirling ). Laminar flow ( even flow ) low drop in pressure slight heat transition Fig. 1.22: Laminar flow Turbulent flow ( whirl flow ) high drop in pressure great heat transition Fig. 1.23: Turbulent flow 13