TEST YOUR SKILLS
THE DIFFERENCE BETWEEN
ISOTHERMAL AND ADIABATIC CONDITIONS H
ydraulic accumulators use weights, springs, or gas pressure to generate the precharge force against the fluid that is stored for use in the system. Gas-charged accumulators use pistons, bladders, or diaphragms to separate the hydraulic fluid from the gas charge. Bladder type accumulators are available in sizes ranging from 115 cc (7 in3) to 300 liters (80 gallons), generally in pressure ranges of 21 MPa and 35 MPa (3,000 and 5,000 psi). Gas-charged accumulators operate by placing the compressible gas over the nearly incompressible hydraulic fluid in a constant volume pressure vessel. The hydraulic pressure and volume of fluid available to the system are dependent on the precharge pressure and the expansion characteristics of the gas. Dry nitrogen is typically used to precharge accumulators.
The ideal gas law:
p1 i V1 i t2 = p2 i V2 i t1
p1 = Initial pressure (psia)absolute V1 = Initial volume t1 = Initial temperature Rankine p2 = Final pressure (psia)absolute V2 = Final volume t2 = Final temperature Rankine
p1 = Initial pressure (MPa)absolute V1 = Initial volume t1 = Initial temperature Kelvin p2 = Final pressure (MPa)absolute V2 = Final volume t2 = Final temperature Kelvin
For isothermal conditions, the equation is:
Gas laws with temperature and pressure.
p1 i V1 = p2 i V2 = p3 i V3
p1 = Absolute precharge pressure V1 = Accumulator gas volume at precharge p2 = Absolute minimum pressure V2 = Accumulator gas volume at minimum pressure p3 = Absolute maximum pressure V3 = Accumulator gas volume at maximum pressure
Gas laws with pressure.
Note: Accumulators should be mounted vertically.
SAFETY TIP: Because of the risk of combustion, never use oxygen or air to precharge an accumulator. The terms "isothermal" and "adiabatic" are used to describe the expansion characteristics of the gas. Compressing and decomBladder-type accumulator pressing gas causes it to heat and cool respectively. If the volume of the gas is changed slowly, the changes in temperature are dissipated through the solid materials of the accumulator and so the temperature of the gas is kept constant. This is called isothermal (same temperature) contraction and expansion. When a gas is compressed and expanded quickly, heating and cooling cause pressure changes in addition to those occurring strictly as the result of volume changes. If the gas is insulated so that very little heat can escape, the pressure of the gas will increase and decrease more than inversely to the change in volume. Under compression, heat added to the gas as it is compressed will raise the pressure above the pressure increase caused by reducing the volume. Under expansion, the pressure will decrease more than would be expected just by decreasing the volume. This is called adiabatic (cannot pass) contraction and expansion. To accommodate changes in both pressure and temperature of the precharge gas, the general gas law can be used to compute the volume available from an accumulator. Absolute values are used for temperature and pressure when making computations. Rankine is the absolute scale for Fahrenheit and Kelvin is the absolute scale for Celsius. Formulas for converting from Fahrenheit to Rankine and Celsius to Kelvin are as follows: °F to °R: °R = °F + 459.7 °C to K: K = °C + 273.15
22
MARCH 2021
Temperature has an effect in the application of accumulators. The ideal gas laws tell us that for a given change in temperature, there will be a corresponding change in the pressure within an accumulator. This makes temperature a necessary consideration when sizing an accumulator. If the ambient temperature changes, the gas temperature in the accumulator will also change and will affect the pressure. For example, an accumulator on a piece of equipment that is outdoors may have a much different ambient condition in the early morning than it will have in the heat of the day. The designer must be sure that the accumulator will be adequately sized to address these conditions. In general, charging the accumulator can be considered an isothermal process and the normal operation of the accumulator considered an adiabatic operation. The following equations are for adiabatic conditions when solving for accumulator sizing or available volume:
VI =
VU ⎛p ⎜ 1 ⎜p ⎝ 2
1 n
−
p1 ⎞ ⎟ p3 ⎟⎠
1 n
1⎞ 1 ⎛ ⎜⎛ p ⎞ n ⎛ p ⎞ n ⎟ VU = VI i ⎜⎜⎜ 1 ⎟⎟ − ⎜⎜ 1 ⎟⎟ ⎟ ⎜⎝ p2 ⎠ ⎝ p3 ⎠ ⎟ ⎠ ⎝
VI = Initial accumulator volume VU = Available liquid volume P1 = Absolute precharge pressure P2 = Minimum system pressure P3 = Absolute maximum pressure 1 = Polytropic exponent (n=1.4 for nitrogen gas,1/n=0.714) n VI = Initial accumulator volume VU = Available liquid volume P1 = Absolute precharge pressure P2 = Absolute minimum pressure P3 = Absolute maximum pressure 1 = Polytropic exponent n (n=1.4 for nitrogen gas,1/n=0.714)
Sizing an accumulator with adiabatic conditions. Finding the available volume from an accumulator with adiabatic conditions.
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