The half-cylindrical heat exchanger is formed by inserting a longitudinal plate in a cylindrical shell space of a U-tube heat exchanger to form dual shell passes for the countercurrent heat transfer purpose. The orifice baffle (OB) in the half-cylindrical shell-side space was proposed to overcome the problems of high-pressure drop in the segmental baffle scheme (SG) and complicated configuration in the unilateral ladder helical baffle scheme (UL). The thermal-hydraulic performances of the bottom part of the half-cylindrical U-tube heat exchanger of four configurations of OBs (fillet triangular, dual-foil square, trefoil, and quatrefoil square), the UL, and the SG were investigated numerically by Fluent in three baffle pitches (50, 40, and 30 mm). The accuracy of the simulated results was validated by experiment with satisfactory agreement. The orifice shape is not sensitive to the performances as long as with a similar flow area. The comprehensive indexes of the schemes OB are very close to that of the UL and much greater than that of the SG, while their overall and shell heat transfer coefficients and pressure drops are lower than those of the schemes UL and SG. Besides, the overall and shell heat transfer coefficients of all schemes increase as the baffle pitch decreases.