This paper describes SCADOPT, a highly-scalable open-source HPC framework written in C++ for solving PDE constrained optimization problems. The framework is designed to handle explicit time-stepping methods over structured grids for the approximation of time-dependent PDEs. It provides an interface to gradient-based optimization algorithms like L-BFGS-B. Derivatives needed for the optimization are computed via algorithmic differentiation (AD) since this approach provides exact derivatives values with a reasonable computational overhead. Hence, the integration of the AD-tool ADOL-C has been a major design principle for the data management of SCADOPT. We describe the core components of SCADOPT, the employed parallelization methods, and the integration of ADOL-C. Furthermore, we illustrate the solution of an optimization problem based on the heat equation with SCADOPT in about 90 lines. To demonstrate the excellent performance of SCADOPT, we show the weak and strong scaling with respect to MPI on a modern HPC cluster.