My initial response is that, if you have a wedge-shaped airfoil on a glider, what sort of spec are you designing to? Most of the time, gliders are low-subsonic aircraft with airfoils similar to Epplers, Wortmann FX, or 4-series NACAs, not wedges. I associate wedges with massive flow separation or supersonic flows. Can you provide a picture of what you're talking about, as well as a discussion of what you're designing to? Also, are you attempting to produce a 3D analysis of a wing that, at its wing box, has this wedge-shaped airfoil?
That said, my short answer is this: XFLR is a panel-method solver, which means that it cannot deal with flow separation save by approximation. As a result, shapes such as a wedge, which are quite prone to flow separation by virtue of their shape, are very hard, if not impossible, to analyze with these solvers. Unfortunately, lower-order solvers (i.e., something short of finite-element or finite-volume methods, such as Fluent, CFX, etc.) bank on using these panel methods or other lower-order fluid flow equations that cannot handle flow separation.
If you want to try to accurately model flow separation, you'll need a higher order CFD solver, which brings with it additional complexity, cost, and headache--and getting accurate drag information is a tricky prospect. There are some freeware solvers out there, but, by far, the most popular (and widely validated) is OpenFOAM. This is a command-line program at heart, but there are some GUIs developed for it that you may be able to obtain for free or at a reduced cost, such as SimScale. Some other packages are discussed here as well, if you'd like to have a look.
That said, what data do you need? If all you need is a sectional drag coefficient, I would highly recommend a look through Hoerner's Fluid Dynamic Drag (not to be confused with his other text, Fluid Dynamic Lift), a vital reference that contains data from a plethora of experiments done on a multitude of shapes. In it, he describes the drag force on objects from ellipsoids to cones to cylinders and more, all based on size, aspect, roughness, and Reynold's number. There is an updated copy available, but I haven't found it online as of yet.
my professor is insistent that it at least looks hypersonic.
Please tell me that this is a professor in the field of visual communication or marketing, not in the field of aerospace engineering. $\endgroup$