Using a external variable in tcl

You need to store the value to disk somehow. Hoodiecrow gives you one sensible way to do it: in the actual filename. Other options:

1. in a config file somewhere
2. in a database (sqlite is good for this)

Demo for (1)

    # read the value
    if {[file exists num.dat]} {
        set fh [open num.dat r]
        set no [read -nonewline $fh]
        close $fh
    } else {
        set no 0
    }

    set logfile log_file_${no}

    # ...

    # write the value
    set fh [open num.dat w]
    puts $fh [incr no]
    close $fh

Demo for (2)

    package require Tcl 8.6
    package require tdbc::sqlite3

    set config_file config.db
    tdbc::sqlite3::connection create db $config_file

    # read the value
    if {[file exists $config_file]} {
        set stmt [$db prepare "create table config (number integer)"]
        $stmt execute
        $stmt close
        set no 0
    } else {
        set stmt [$db prepare "select number from config limit 1"]
        $stmt foreach row {
            set no [dict get $row number]
        }
        $stmt close
    }

    # ...

    # write the value
    set stmt [$db prepare "update config set number=:new limit 1"]
    $stmt execute [dict create new [incr no]]
    $stmt close

    $db close

You don't need a variable, you have the number you need in the file list:

set no [scan [lindex [lsort -dictionary [glob log_file_*]] end] log_file_%2d]

incr no

set fn [open log_file_$no w]

Let's break that up a bit. Create a list of log files:

set filelist [glob log_file_*]

Sort the list in dictionary order (where 10 comes after 2) and pick the last element:

set highest_numbered [lindex [lsort -dictionary $filelist] end]]

Extract the number from the file name:

set no [scan $highest_numbered log_file_%2d]

Increase the number and open a new log file:

incr no
set fn [open log_file_$no w]

If there is a possibility that no log files exist, the glob command will fail. To take care of this case, either do this:

set filelist [glob -nocomplain log_file_*]
if {[llength $filelist]} {
    set highest_numbered [lindex [lsort -dictionary $filelist] end]]
    set no [scan $highest_numbered log_file_%2d]
} else {
    set no 0
}
incr no
set fn [open log_file_$no w]

or this slightly safer version (if you have Tcl 8.6):

try {
    glob log_file_*
} on ok filelist {
    set highest_numbered [lindex [lsort -dictionary $filelist] end]
    set no [scan $highest_numbered log_file_%2d]
} trap {TCL OPERATION GLOB NOMATCH} {} {
    set no 0
} on error message {
    puts stderr "error when listing log files: $message"
    set no -1
}
if {$no > -1} {
    incr no
    set fn [open log_file_$no w]
    # ...
    chan close $fn
}

Documentation: chan, glob, if, incr, lindex, lsort, open, scan, set, try

(Note: the 'Hoodiecrow' mentioned elsewhere is me, I used that nick earlier.)