Methods of forming and restricting fluid flow with a valve assembly

A method of forming a valve assembly, the method comprising:

• positioning a restriction element within a casing having a seat;
• defining quartic lima bean-shaped flow passages having a quartic lima-bean cross-sectional shape perpendicular to a longitudinal axis of the valve assembly in an internal flow path of the casing with ribs that extend through the internal flow path and converge with at least another of the ribs at an apex of the casing to define a cage in which the restriction element is configured to move axially through the internal flow path;
• in an open position, enabling the restriction element to be displaced toward the apex of the casing to enable fluid flow through the internal flow path and through the quartic lima bean-shaped flow passages defined between the ribs, the quartic lima bean-shaped flow passages exhibiting a non-circular and a non-oval cross section;
• and
• in a closed position, enabling the restriction element to engage with the seat to restrict fluid flow through the internal flow path.

A method of restricting fluid flow with a valve assembly, the method comprising:

• positioning a restriction element in an internal flow path of a casing having a seat;
• in an open position:
• displacing the restriction element toward an apex of the casing to enable fluid flow through the internal flow path in the casing;
• and
• flowing fluid through quartic lima bean-shaped flow passages having a quartic lima-bean cross-sectional shape perpendicular to a longitudinal axis of the valve assembly defined between protrusions in the casing, the protrusions converging at the apex of the casing to define a cage in which the restriction element moves axially through the internal flow path;
• and
• in a closed position, engaging the restriction element with the seat to restrict fluid flow through the internal flow path.