Fluid circulation system for dishwasher appliances and related methods

A method of operating a dishwasher appliance, the method comprising:

• operating the dishwasher appliance in a wash mode for a first period of time, the wash mode comprising circulating fluid in the dishwasher appliance, circulating fluid comprising receiving fluid from a wash chamber of the dishwasher appliance, filtering the received fluid at a filtration rate with a filter medium, the filtration rate inversely proportional to a fouling status of the filter medium, and flowing the filtered fluid to a diverter such that the flow of filtered fluid urges the diverter to a first position and the diverter directing the filtered fluid to flow to a spray assembly when the diverter is in the first position;
• initiating a filter cleaning mode after operating the dishwasher appliance in the wash mode for the first period of time, initiating the filter cleaning mode comprising moving the diverter to a second position, the diverter directing the filtered fluid to flow to a filter cleaning assembly when the diverter is in the second position, wherein the diverter moves from the first position to the second position in response to a change in the filtration rate of the filter medium;
• detecting that the dishwasher appliance is in the filter cleaning mode;
• operating the dishwasher appliance in the filter cleaning mode for a second period of time;
• and
• performing a predetermined action after the second period of time.