Unfortunately glycerol is UV-silent so you will not be able to detect free glycerol with a UV detector without some sort of chemical modification.  We has a similar issue several years ago and developed a HPLC/UV-based method to detect benzoylated derivatives of glycerol and other polyols from biological samples.  The method is pretty simple, works well and provides excellent resolution and reproducibility (Journal of Chromatography B (2009) 877: 3667-3672).    At the end of this manuscript we also compare results using this method to other available methods, which may be of help if you decide not to use HPLC.