local *FILE;
open FILE, "<", "./$nbdc_dir/$file" or die ...
...

##</code><code>##

open my $fh, "<", "./$nbdc_dir/$file" or die ...
$nbdc_filehandles[$index] = $fh;

##</code><code>##

open $nbdc_filehandles[$index], "<", "./$nbdc_dir/$file" or die ...

##</code><code>##

$_ = <$fh>;    # OK
$_ = < $fh >;  # not OK

##</code><code>##

my $fh = $nbdc_filehandles[$index];
$_ = <$fh>;
# instead of
# $_ = <$nbdc_filehandles[$index]>;

##</code><code>##

my @nbdc_filehandles;
my @nbdc_data;
my $index=0;

foreach my $file (@nbdc_files) {
    open my $fh, "<", "./$nbdc_dir/$file" or die "Can't open ./$nbdc_dir/$file";
    $nbdc_filehandles[$index] = $fh;
   
    #get the first set of data values
    
    $_ = <$fh>;
    $_ = <$fh>;
    chomp; #get rid of trailing \n
    $nbdc_data[$index] = [ split(/\t/, $_) ];
    # ...
    
    $index++;
}

# then sometime later, to reuse the stored filehandles

my $fh = $nbdc_filehandles[$idx];
my $line = <$fh>;
# ...