In this study, we propose a novel unsupervised Change Detection (CD) model to detect flood extent using Synthetic Aperture Radar (SAR) time series data. The proposed model is based on a spatiotemporal variational autoencoder, trained with reconstruction and contrastive learning techniques. The change maps are generated with a proposed novel algorithm that utilizes differences in latent feature distributions between pre-flood and post-flood data. The model is evaluated on nine different flood events by comparing the results with reference flood maps collected from the Copernicus Emergency Management Services (CEMS) and Sen1Floods11 dataset. We conducted a range of experiments and ablation studies to investigate the performance of our model. We compared the results with existing unsupervised models. The model achieved an average of 70% Intersection over Union (IoU) score which is at least 7% better than the IoU from existing unsupervised CD models. In the generalizability test, the proposed model outperformed supervised models ADS-Net (by 10% IoU) and DAUSAR (by 8% IoU), both trained on Sen1Floods11 and tested on CEMS sites. Our implementation will be available here https://github.com/RituYadav92/CLVAE-Unsupervised_Change_Detection_TimeSeriesSAR.