Unfortunately, there is no way to record the simulation time in the legacy VTK file format. Thus, if you want to pass the time from the simulation to ParaView, you will need to use a different file format.
I think the easiest way to record the simulation time is to use a ParaView Data (PVD) file. A PVD file is a simple XML file that captures metadata about a group of data files, and time value information is one of the things that can be captured. A brief description of the PVD format is given at http://www.paraview.org/Wiki/ParaView/Data_formats#PVD_File_Format. The example on that page has "timestep" values that are integers starting at 0, but you can replace them with any sequence of floating point numbers.
The PVD file itself does not hold the data itself. Rather, it points to other files that have the actual data. The data files it points to have to be in the newer XML-based VTK file formats (vti
, vtr
, or vts
depending on the nature of your structured data). The XML-based VTK file format is also documented in http://www.vtk.org/VTK/img/file-formats.pdf (after the documentation for the legacy VTK format).