WPDB exporting custom query to csv - file not being created - database

Question

I'm using the following code to export a custom MYSQL query to CSV. The data and column headers are working fine (print $csv_output; is exactly as I expect) but the actual CSV file is not being created.
What am I getting wrong?
function generate_csv(){
global $wpdb;
$table_name = $wpdb->prefix."ck_shipment";// table name
$file = 'database_csv'; // csv file name
$results = $wpdb->get_results("SELECT * FROM $table_name",ARRAY_A );
// get column names
$query = "SELECT `COLUMN_NAME` FROM `INFORMATION_SCHEMA`.`COLUMNS` WHERE `TABLE_SCHEMA`='".$wpdb->dbname."' AND `TABLE_NAME`='".$table_name."'";
$columnNamesList = $wpdb->get_results($query);
foreach ( $columnNamesList as $column_name ) {
$csv_output.=$column_name->COLUMN_NAME.",";
}
// remove last additional comma
$csv_output = substr($csv_output,0,strlen($csv_output)-1);
// start dumping csv rows in new line
$csv_output.="\n";
if(count($results) > 0){
foreach($results as $result){
$result = array_values($result);
$result = implode(", ", $result);
$csv_output .= $result."\n";
}
}
$filename = $file."_".date("Y-m-d_H-i",time());
print $csv_output;
exit;
}
?>
<form method="post" action="<?php echo $_SERVER['REQUEST_URI']; ?>">
<br /><input type="submit" name="export" value="export" class="button-primary">
</form>
<?php
if (isset($_POST['export'])) {
generate_csv();
}
Thanks!