Indian Security Forces: Joint Exercises

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So shouldn't Kolkata class be more smokeless compared to Shivalik class other boats? Or am I wrong in that understanding? Smoke isn't good for stealth I understand.
Most of the white fumes isn't smoke. Its water vapor. Water is sprayed in regular intervals to the exhaust stack to reduce their temperature. This causes an occasional plume of water vapor to come out of the exhaust ports. This happens occasionally, not always. You can easily find photos of Kolkata class ships at sea without the visible white plume.

Water vapor is a good absorber of IR radiation, so the IR signature of the plume reduces significantly. The downside of this system is that the water vapor mixes & spreads soot in a much larger area of the ship. You will notice soot build up on the rear facing MF-STAR radar mast when the ship is deployed for 6+ months.

The Shivaliks don't have this system. That's you don't see the white plume. However, the exhaust stack of the Shivaliks run at a significantly higher temperature than that of the Kolkata. Basically, less visual signature but higher IR signature. Also, for low-speed maneuvers like the ones shown in the tweet, the Shivalik class frigates will prefer to use their diesel engines & not gas turbines.