WooCommerce: display only products between two dates

Hi

I want to display only products according to a start date and an expiration date. When I only use one date in my function it works well, but when I also use the expiration date all the products are displayed even those out of date.

here is my code in functions.php

function custom_meta_query( $meta_query ){
$today = current_time('Ymd');
 $args = array (
    'meta_query' => array(
'relation' => 'AND',
    array(
        'key'=>'flash_sale_start',
        'value' => $today,
        'compare'=>'<=',
    'type' => 'DATE'
    ),
       array(
    'key'=>'flash_sale_end',
        'value' => $today,
        'compare'=>'=>',
    'type' => 'DATE'
    )),);
$date_query = new WP_Query( $args );
    //return $meta_query;
}

// The main shop and archives meta query
add_filter( 'woocommerce_product_query_meta_query', 'custom_product_query_meta_query', 10, 2 );
function custom_product_query_meta_query( $meta_query, $query ) {
    if( ! is_admin() )
        return custom_meta_query( $meta_query );
}

// The shortcode products query
add_filter( 'woocommerce_shortcode_products_query', 'custom__shortcode_products_query', 10, 3 );
function custom__shortcode_products_query( $query_args, $atts, $loop_name ) {
    if( ! is_admin() )
        $query_args['meta_query'] = custom_meta_query( $query_args['meta_query'] );
    return $query_args;
}

// The widget products query
add_filter( 'woocommerce_products_widget_query_args', 'custom_products_widget_query_arg', 10, 1 );
function custom_products_widget_query_arg( $query_args ) {
    if( ! is_admin() )
        $query_args['meta_query'] = custom_meta_query( $query_args['meta_query'] );
    return $query_args;
}

Can you help me please?

Thanks