How do I refresh a TMS layer in OpenLayers?

Question

I have a TMS layer that looks something like this:

var v = 1;
my_tms = new OpenLayers.Layer.TMS(
    "My TMS",
    "my_mapserver.php?v="+my_var+"&",
     { transparent: 'true', type:'png', getURL:get_my_url }
);

Where my_mapserver.php returns map tiles according to the value of v.

The app allows users to change v, and I simply want to refresh the my_tms layer, however, so far the only way I can get it to refresh is by destroying the map and recreating it.

I thought I could just do something like this:

v = 2;
my_tms = new OpenLayers.Layer.TMS(
    "My TMS",
    "my_mapserver.php?v="+my_var+"&",
     { transparent: 'true', type:'png', getURL:get_my_url }
);
my_tms.redraw();

However, these tiles are not getting requested when I redraw().

Any help is appreciated.