1. Adiabatic throttling process

 

Throttling is a process in which a high-pressure fluid gas, a liquid, or a gas-liquid mixture), in a steady flow, encounters a resistance element such as a shrinkage or a valve, due to local resistance, and the pressure drops significantly. Since the throttling expansion process has no external power output, and the throttling process in the process proceeds rapidly, the heat exchange between the fluid and the outside is negligible, and is treated as an adiabatic process. According to the steady flow energy equation:

 

δq=dh+δw(2.1)

 

It is concluded that the specific value of the fluid before and after the adiabatic throttling is constant. Because of the frictional resistance loss inside the fluid during throttling, it is a typical irreversible process, and the entropy after throttling must increase.

 

After adiabatic throttling, how the temperature of the fluid changes is different for fluids of different characteristics. For any single substance in the gas-liquid two-phase zone, the temperature is always reduced after throttling. This is because the saturation temperature and the saturation pressure in the two-phase region are one-to-one, and the saturation temperature decreases as the pressure decreases. For an ideal gas, helium is a single-valued function of temperature, so the ablation value does not change after adiabatic throttling, and the temperature does not change. For the actual gas, helium is a function of temperature and pressure. After adiabatic throttling, the temperature may decrease, rise and remain unchanged. This temperature change phenomenon is called the Joule-Thomson effect, referred to as the J-T effect.

 

2. Throttling effect of actual gas

In actual gas throttling, the change in temperature with a small pressure drop is defined as the differential throttling effect, also known as the Joule-Thomson coefficient:

 

αh=(ɑT/ɑp)2.2)

Hh>0 indicates a decrease in temperature after throttling, and αh<0 indicates an increase in temperature after throttling. When the pressure drop (P2-P1) is a finite value, the temperature change produced by the entire throttling process is called the integral throttling effect:

 

ΔTh=T2-T1= p2p1αhdp(2.3)

In theory, the expression of αh can be derived using the thermodynamic basic relational expression for analysis. The flawed features show that:

 

dh=cpdT-[T(αv/aT)p-v]dp(2.4)

Due to the constant value is unchanged, dh=0, the above formula can be adjusted to:

 

αh=(αT/αp)h=1/cp[T(αv/αT)p-v](2.5)

It can be known from equation (2.3) that the positive and negative of the differential throttling effect depends on the difference between T(αv/aT)p and v. If the difference is greater than 0, the temperature decreases when αh>0 is throttled; if it is equal to 0, αh=0, the temperature is constant during throttling; if less than 0, αh<0, the temperature increases when throttling.

 

Starting from the physical essence, the energy conversion relationship in the gas throttling process can be used to explain the occurrence of three kinds of conditions. Since the enthalpy of the gas before and after throttling is constant, the change of internal energy before and after throttling is equal to the difference between the push and the push work. value:

 

　u2-u1=p1v1-p2v2

The internal energy of a gas includes two parts: internal kinetic energy and internal energy. Whether the gas temperature is lowered, raised, or unchanged depends only on the gas internal motion.

 

Can it be reduced, increased, or unchanged. Since the pressure is always reduced after the gas is throttled, the specific volume is increased, and the internal energy is always increased. Since the actual gas deviates from the law of Boyle, after the throttling at a certain temperature, there may be three changes in the pv value:

　①p1v1

②When p1v1=p2v2, u2=u1 means that the internal energy can be unchanged after throttling. At this point, the increase in internal energy is equal to the decrease in internal kinetic energy, and the gas temperature after throttling is still reduced.

③When 3p1v1>p2v2, u2>u1 can increase after throttling. At this time, if the increase of internal energy is less than the increase of internal energy, the internal kinetic energy is reduced, and the temperature is still reduced; if the increase of internal energy is greater than the increase of internal energy, the internal kinetic energy must increase, and the temperature must be increased. rise.

It can be seen from the above analysis that under a certain pressure, when the gas has a certain temperature, p1v1>p2v2 is satisfied after throttling and the decrease of the pv value just complements the increase of the internal energy. At this time, the temperature before the throttling is constant, that is, the differential The throttling effect is equal to 0. This temperature is called the conversion temperature and is expressed in Tinv.

 

The calculation and variation relationship of the transformation temperature can be obtained according to the formula (2.5), and αh=0. The following is analyzed using the Van der Val equation. 2a/9Rb(2±)

 

The van der Waals equation p=RT/v-b-a/v2 is derived from Ti under equal pressure to obtain (αv/αT)p progeny into equation (2.5):

 

Αh=(αv/αT)h=(1/cp)(2a(1-b/v)2-RbT)/(RT-2a/v(1-b/v)2)(2.6)

 

When αh=0, the gas temperature is the conversion temperature. Solved by the van der Waals equation:

 

Tinv=2a/9Rb(2±√1-(3b2/a)p)2(2.7)

The conversion temperature and pressure as a function of the equation (2.7) is a continuous curve on the Kun map, called the conversion curve. As shown in Figure 2.11, the dashed line is calculated according to equation (2.7), and the solid line is obtained experimentally. The difference between the two is caused by the quantitative inaccuracy of the van der Waals equation.

 

The conversion curve has a **** conversion pressure pmax. When p>pmax, there is no conversion temperature; when p=pmax, there is only one transformation temperature; when p0, the cold effect is produced after throttling. The **** conversion temperature Tmax of the gas corresponding to p=0 can also be obtained from the formula (2.7) and Fig. 2.11. Table 2.5 lists the **** conversion temperatures for various gases. For most gases, such as 02, N2, CO, air, etc., the conversion temperature is higher than the ambient temperature, so the Joule-Thomson effect can be used to cool down at ambient temperature. The conversion temperature of Ne, H2, He is lower than room temperature, and cannot be cooled by the Joule-Thomson effect alone. Pre-cooling or other expanders must be used to reduce the temperature before throttling, and then cold after throttling. effect.

 

There are many ways to calculate the integral throttling effect. The empirical formula of ah can be directly substituted into the integral solution of equation (2.3). The more practical method in engineering is to use the gas T-s diagram h-T or the physical property database to calculate. As shown in Figure 2.12, the fuse line is drawn from the state point 1 (p1, T1) before the throttling, and the pressure line of the pressure p2 after the throttle is intersected at the point 2, the temperature difference between the two points (T1-T2) This is the required integral throttling effect. The graphical method is simple to use, but the accuracy is poor, especially in the low pressure zone, and the normal and isotherms are nearly parallel, and the error is larger.

 

Since the enthalpy value is constant before and after throttling, the throttling process 1 - 2 shown in Figure 2.12 is a process of cooling without cooling. If the gas is isothermally compressed from the initial state 0 (p2, T1) to state 1 (p1, T1), and then throttled to state 2 (P2, T2), the throttled gas returns to the original state 0 ( P2, T1), the amount of heat absorbed is the unit cooling capacity:

Therefore, the gas has a cooling capacity after isothermal compression and throttling expansion, which is called isothermal throttling effect - the refrigeration capacity of the Δht gas is obtained during isothermal compression and is also expressed by throttling.

3. Adiabatic throttling refrigeration cycle

A simple adiabatic throttling refrigeration cycle is also known as the Linde cycle (see Figure 2.13). Figure 2.14 shows the T-s diagram of the loop. Ideally, the gas is pumped in the compressor as an isothermal compression process 1-2. In fact, the gas is compressed from low pressure p1 (state 1) to p2 and is isostatically cooled to normal temperature by the cooler (state 2, which is approximately considered to be simultaneous with the compression and cooling process. The compressed gas is passed through the countercurrent heat exchanger, The heat exchange with the cold gas stream is cooled to a lower temperature (state 3), then expanded through the throttle valve to state 4 and into the evaporator. In the evaporator, the liquid working fluid formed after throttling absorbs heat from the outside, That is, the amount of refrigeration is generated. The saturated steam is reheated to the temperature B through the heat exchanger (actual state I, there is a small temperature difference from the state l), and then sucked into the compressor to complete the entire cycle.

The cooling temperature obtained by the Linde cycle can be adjusted by controlling the evaporation pressure by a throttle valve. The lower limit of the cooling temperature is limited by the triple point temperature and the difficulty of maintaining the high vacuum. To obtain a lower cooling temperature than the liquid N, the working fluids Ne, H2, He can be used. However, the throttling of these working fluids at normal temperature produces a thermal effect, and the gas temperature must first be pre-cooled below the conversion temperature.

The throttling refrigeration cycle has a low coefficient of performance and poor economics, but it is still valued because of its simple composition, no moving parts at low temperatures, and high reliability. The open-type throttling refrigeration cycle using a high-pressure gas cylinder instead of a compressor as a gas source is more convenient for miniaturization and light weight, and has been widely used in the field of infrared guidance and the like. At present, the new development of throttling refrigeration cycle research is to replace the pure working fluid with mixed working fluid in order to achieve the purpose of reducing pressure and improving efficiency.

 

4. Throttling liquefaction cycle

 

The gas adiabatic throttling can be expanded to a gas-liquid two-phase region containing a large amount of liquid, and an important application thereof is gas liquefaction. The gas liquefaction system differs from the conventional refrigeration system for the purpose of producing cold capacity: in the ordinary refrigeration cycle, the refrigerant performs a closed cycle process; and the gas liquefaction cycle is an open cycle, and the gas used is in the process of circulation. It acts as a refrigerant and is itself partially or completely liquefied as a liquid product.