An apparatus includes a slotted multi-nozzle grid with a plate having multiple elongated slotlettes through the plate. Each of at least some of the slotlettes has a convergent input, a divergent output, and a narrower throat portion separating the convergent input and the divergent output. At least some of the slotlettes are arranged in multiple rows. The plate further includes multiple cooling channels through the plate. At least some of the cooling channels are located between the rows of slotlettes. Each cooling channel is configured to transport coolant through the plate in order to cool the plate, such as to cool the plate as hot combustion gases pass through the plate. Each of at least some of the rows may include at least two slotlettes, and two adjacent slotlettes in one row may be separated by a structural ligament (which may have a tear-drop cross-sectional shape).