Numerical Solutions for Prediction of Nozzle Loss Factor and Flow Coefficient of 1.5 Stage Axial Gas Turbine Utilizing Waste Heat from Marine Diesel Engine

Abstract

Main engine exhaust gas energy is by far the most appealing among the waste heat sources of marine diesel engines in ships in light of the heat flow and temperature. It is feasible to produce electrical power output using this exhaust gas energy in a waste heat recovery system containing power turbines and steam turbines (some portion of exhaust gas heat is used for creating steam). The essential wellspring of waste heat of the primary motor is the exhaust gas heat dissipation, which represents about portion of the complete waste hotness, for example around 25% of the total fuel energy. In the present study, a 1.5 stage axial turbine (with the turbine rotor interspaced between two stators) utilizing waste heat from the marine diesel engine is considered for investigating performance using ANSYS CFX. Simulations are carried out with rotor speed varying from 1000 RPM to 8000 RPM with turbine inlet pressure kept constant at 4 bar. The performance of axial gas turbine is analyzed with inlet temperatures varying from 523 K to 673 K for different mass flow rates and rotor speeds The Flow coefficient of the rotor is also found to be within the acceptable range between 0.5 to 1.1 and is observed to cut the efficiency line between 2800 RPM and 4000 RPM, corresponding to 70% to 78% efficiency. Nozzle Loss Coefficient (NLC) represents the deviation of the actual process with the isentropic process in a stator blade of the turbine.

Introduction

Waste Heat Recovery (WHR) from Marine Diesel Engines:
Waste heat recovery from marine diesel engine exhaust is a highly effective method to utilize energy that would otherwise be lost. Marine ships offer steady engine operation and large heat output, unlike vehicles. Diesel engines produce significant waste heat due to continuous thermodynamic cycles. This heat can be recovered for:

• Preheating heavy fuel oil (maintaining low viscosity)

• Steam generation using exhaust gas boilers (EGBO)

• Absorption or adsorption refrigeration

• Combined cycles such as the Organic Rankine Cycle (ORC) for large ships

Literature Survey:

• Z. Mat Nawi et al.: Studied ORC power plants using organic fluids derived from microalgae; exhaust temperature varied with engine load (548–573 K, 1.15–2 kg/s).

• Fotis Kyriakidis et al.: Investigated dual Rankine cycle designs with WHR and EGR to reduce NOx emissions in two-stroke engines.

• Mojtaba Tahani et al.: Tested ORC configurations with R-134a, R-123, R-245fa; R-123 showed best performance.

• A. Giovannelli et al.: Analyzed radial turbine performance for ORC; efficiency is low at low temperatures, requiring turbine optimization.

• Simone Lion et al.: Highlighted ORC as the most effective method for marine diesel exhaust heat recovery, improving efficiency and system reliability.

Turbine Parameter Analysis:

• A 1.5-stage axial turbine was simulated using ANSYS CFX with rotor speeds of 1000–8000 RPM, inlet pressure 4 bar, and varying temperatures (618–673 K) and mass flow rates (26–44 kg/s).

• Container ship and marine diesel engine specs:

  • Bulk carrier, 55,000 tons, 185 m length, 32 m breadth, 14.5 knots speed

  • Two-stroke & four-stroke engines, ~8800 kW power, 122–500 RPM

Flow Coefficient (?):

• Defined as the ratio of meridional velocity at rotor inlet to blade speed.

• At 1000 RPM, 44 kg/s, 673 K: ? = 2.17 (V_f1 = 95.3 m/s, U = 43.9 m/s)

• Flow coefficient decreases rapidly at low speeds, stabilizes beyond 4000 RPM.

• Useful range corresponds to 70–78% isentropic efficiency.

Nozzle Loss Factor (ζ_N):

• Represents deviation from isentropic behavior in stator blades.

• Calculated using adiabatic enthalpy loss and rotor exit velocity.

• Example at 1000 RPM, 44 kg/s, 673 K: ζ_N = 0.0699, nozzle efficiency 93.16%.

• Variation across speeds, temperatures, and mass flow rates is minimal (~0.003), indicating stator performance is largely independent of rotor speed and exhaust temperature.

Results and Observations:

• Flow Coefficient vs Rotor Speed: Decreases at low speeds, stabilizes above 4000 RPM; optimal efficiency between 2800–4000 RPM.

• Nozzle Loss Coefficient vs Rotor Speed: Nearly constant across all conditions, confirming minor deviation from isentropic behavior.

Conclusion

1) The Flow coefficient is observed with an acceptable range between 0.5 to 1.1 which cuts the efficiency line between 2800 RPM and 4000 RPM, corresponding to 70% to 78% efficiency. Hence it is concluded that at this particular point, the flow coefficient is maximum. 2) The NLC tends to be zero as the deviation becomes smaller and smaller. It is also observed that the variation of Nozzle Loss Coefficient is very small and the difference between the maximum and minimum value is only 0.003. 3) The numerical solutions demonstrate that the actual process in the stator blade isn\'t impacted by rotor speed thus it is free of the gulf temperature of the exhaust gases from the marine diesel engine.

References

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Copyright

Copyright © 2026 Dr. Srinivasa Prasad Katrenipadu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.