The rate of heat transfer in helical pipes is much more than straight pipes. In the present study, heat transfer and fluid flow in a double‐coil heat exchanger with an innovative swirl generator with a curved structure in the inner channel (hot side) are studied, numerically. The proposed turbulator has a curved structure and 12 blades to produce swirl flows. Also, two holes are considered at the semi‐conical part of the turbulator. The effects of geometrical parameters of the proposed turbulator including the inner radius of the turbulator and the radius of the turbulator's holes are evaluated. Results indicate that the maximum effectiveness belongs to the case with inner diameter of the turbulator and radius of turbulator' holes equal to 19 and 3.6 mm, respectively, at ṁ=0.008 normalknormalgnormal/normals. Also, the generated swirl flows by the turbulator has a significant influence on heat transfer augmentation. Furthermore, a high inner radius of the turbulator leads to an increase in heat transfer rate and effectiveness, consequently. As a result, by increasing the inner radius of turbulator by 26.7%, the effectiveness rises by 80% (maximum at trueṁ = 0.008 kg/s). Increasing the radius of turbulator's hole by 133.34% leads to an growth in effectiveness of about 50% (maximum at trueṁ = 0.058 kg/s).