Flow controller design for Joule-Thomson type crycooler

Joule-Thomson coolers are recuperative coolers in which the same fluid is used on the inlet and outlet sides. Fluid entering to JT cooler is precooled by lower temperature fluid flows on the outlet side. The actual temperature drop occurs as a result of Joule-Thomson effect in the rapid expansion of compressible real gases after precooling. A flow control unit is required to reduce gas consumption when the desired temperature is achieved.Various flow control units used in Joule-Thomson coolers were researched at the beginning of this study. However, only Joule Thomson coolers having bellow type flow control units have been studied. Pressurized bellows are common devices in order to perform flow control. The temperature of the gas inside the bellow is at room conditions in the beginning. However, it decreases as the temperature of the refrigerant flowing in the cooler reaches to the cryogenic temperatures. Therefore, the pressure of the gas in a bellow will decrease and consequently it begins to contract. There is a needle structure assembling to the bellow to adjust the flow rate. The needle moves with the bellows, thereby depending on the displacement caused by the contraction of the bellow. As the temperature drops, the needle will reduce the flow area in the orifice where the Joule-Thomson effect occurs. Essentially, the working principle of bellow type flow control units can be expressed in this way. This study was carried out to investigate the parameters that affect the design of bellows. At the end of the study, a unique approach has been developed to determine the dimensions of the bellow provide with required displacement. The bellows of different sizes were placed in a J-T cooler in literature which is known dimensions and they are examined. The first analysis in this thesis is calculation of temperature distribution on the J-T cooler in steady-state condition by using the methods in literature. For this aim, governing equations (for continuity, momentum and energy balance) derived in literature for inlet side (high-pressure) fluid and outlet side (low-pressure) fluid are solved by finite difference method in MATLAB software. Argon gas are used as a refrigerant. In addition, the thermophysical properties of this refrigerant are calculated by MBWR state equation solved with another inhouse code. The temperature distribution on the cooler is used as a new boundary condition to calculate the temperature distribution on the bellow and pressure inside the bellows in the steady-state condition. ANSYS commercial software (finite element model) is used in the calculations of whole JT cooler model. The heat transfer coefficients of the gases are calculated according to the temperature and the final pressures. Final pressure inside a bellow is found and contraction rate of the bellow is calculated according to the initial condition. This calculation was also accomplished by using ANSYS commercial software. The problem was modeled as 2-D axisymmetric. The rate of contraction was found by solving non-linear equations using the "log-strain" approach. Dimensions of bellow (Inner and outer diameter of bellow, Wall thickness, gap diameter) are defined parametrically in order to determine the effect of the basic dimensions of a bellow on the pressure. For this reason, the contraction rate for 108 different bellows and the maximum stress that caused by the high-pressure gas in the initial stage are calculated. The maximum amount of stress is important in the determination of the strength of the bellow at high pressures. Safe configurations were found among 108 different bellows that maximum contraction are obtained. It has been determined that as the bellows outer diameter increases and as the inner diameter, wall thickness and gap diameter decreases, the amount of bellow contraction increases. However, it has been observed that the inlet pressure in cryocooler are not effective so much on the contraction of bellow.