There's always a reason for going to the expense of putting in an expansion joint. Generally, there are 2 reasons for installing such a joint, vibration and thermal contraction/expansion. I'm assuming your case is the latter since you're dealing with liquid nitrogen. It's not cheap to install these joints and it's not easy to determine exactly what type and length you need. In fact, if you can do away with them, you'll be much better off. But to get out of using them, the piping has to be flexible enough to prevent stresses in excess of what is allowed by the piping code for your country. Therefore, someone is going to have to do a piping stress analysis for your liquid nitrogen system and they'll need to accommodate thermal contraction of the piping, so an expansion joint is a common method. Today, most companies use a computer program to analyze stresses in piping, and that analysis is done in conformance with the applicable piping code for the country in question. For the US, that piping code will be ASME B31.3, but in other countries, other codes will apply.
You can't determine the type and location of the expansion joint yourself, you need someone that can provide the stress analysis per the applicable code for your country. Once you have requirements from that person, you can go off and determine what suppliers can provide that expansion joint.
Sorry if that sounds like I'm avoiding your question, but I have to assume this is an industrial application, not a college project.