在自定义分类模板中获取自定义字段

I've managed to list out all direct children of the custom parent taxonomy..

 Chocolates
 Marshmallows  
 Popcorn
 ..and so on...

with this code below.

<?php 
$term = get_term_by( 'slug', get_query_var( 'term' ), get_query_var( 'taxonomy' ) );
if ($term->parent == 0) { 
$terms = get_terms( 'product-type', 'parent='.$term->term_id ); } 
else { $terms = get_terms( 'product-type', 'parent='.$term->parent ); } 
foreach($terms as $term) { 
echo '
<div class="snack_type">
<a href="' . get_term_link( $term ) . '">' . $term->name . '</a>
</div>

'; }
?>

Each of the taxonomies showing above has an image uploaded to it with custom fields (advanced custom fields). How do i show a custom field (product_type_image) in each of the div that gets generated? like this

 Chocolates [product_type_image]
 Marshmallows [product_type_image] 
 Popcorn [product_type_image]
 ..and so on...

i was trying out with

 $productimage = get_field('product_type_image', $term->taxonomy.'_'.$term->term_id);

but it was unsuccessful to try to show anything

add this line

echo '<img src="' . get_field('product_type_image', $term->taxonomy . '_' . $term->term_id) . '"/>';

so it should look like this

<?php 
$term = get_term_by( 'slug', get_query_var( 'term' ), get_query_var( 'taxonomy' ) );
if ($term->parent == 0) { 
$terms = get_terms( 'product-type', 'parent='.$term->term_id ); } 
else { $terms = get_terms( 'product-type', 'parent='.$term->parent ); } 
foreach($terms as $term) { 
echo '<div class="snack_type"><a href="' . get_term_link( $term ) . '">' . $term->name . '</a></div>'; 
echo '<img src="' . get_field('product_type_img', $term->taxonomy . '_' . $term->term_id) . '"/>';
}
?>