Dr. R. Nagarajan Professor Dept of Chemical Engineering IIT Madras

1. Advanced Transport Phenomena Module 1 Lecture 2 Overview & “Hot Corrosion” Example Dr. R. Nagarajan Professor Dept of Chemical Engineering IIT Madras

2. HOT CORROSION • In marine environments, turbines ingest NaCl in air intake • Fuel contains sulfur as impurity • They react to form molten Na2SO4 • The molten salt deposits on turbine blades (rotors and stator vanes)… • and dissolve the protective oxide coating on the blades, leading to… • direct corrosive attack of the exposed nickel-base super alloy surface, resulting in… • catastrophic failure of the blade.

3. HOT CORROSION

4. THERMODYNAMIC CONSTRAINTS • Vapor phase equilibrium (local thermochemical equilibrium) at the mainstream of gas flow • Vapor/condensate equilibrium at the blade surface • “Chemically-frozen” boundary layer in between

5. TRANSPORT PROCESSES INVOLVED • Flow of combustion product gases past surfaces of rotor blades and stator vanes • Momentum transfer • Extraction of heat from the combustion gases • Heat transfer • Multi-component Chemical Vapor Deposition of molten sodium sulphate on blade surfaces • Mass transfer All occurring in the chemically reactive environment of a gas turbine combustor….

6. BOUNDARY LAYER CONFIGURATION

7. DIFFUSION FLUX TO THE BLADE SURFACE where Fi(Soret), F(ncp) and F(turb) are, resp., augmentation factors to the mass-transfer Nusselt number, Num,i due to: • thermal diffusion, • variable boundary-layer gas properties, and • free-stream turbulence

8. DIFFUSION FLUX TO THE BLADE SURFACECONTD… Chemical element fluxes are related to species fluxes via: where is the mass fraction of the element in species i. Total deposition rate is then calculated as:

9. FLUX RATIO CONSTRAINT The elemental molar fluxes must be in the same ratio as condensate stoichiometry for steady-state deposition of a non-flowing condensate • i.e., for Na2SO4 (l) to form, must be equal to two. • For Na2CO3 (s) to form, (when one or more element is in excess, only the trace element needs to satisfy non-zero flux constraint)

10. DEW POINT • Temperature at which the condensate first forms as surface is cooled, or • Temperature at which a pre-existing condensate begins to evaporate as surface is heated • The two may not be the same (hysteresis, or dew-point shift effect associated with multi-component diffusion) • Definitions reversed for commercial CVD application, where higher temperatures favor film formation

11. DEW POINT CONTD… • Operational definition of dew-point: • When T (surface) is between Tdp and T solidification, “hot corrosion” can occur as salt is molten in nature

12. MOLTEN SALT LAYERS IN FLOW • Arrival by vapor diffusion • Film set in motion by aerodynamic and centrifugal shear • Local thickness, as a function of time, depends on balance between deposition and flow phenomena

13. MOLTEN SALT LAYERS IN FLOW CONTD… • Local oxide dissolution rate depends on: • local thickness of salt film • its viscosity • oxide diffusivity • oxide solubility • Local “hot corrosion” rate, hence useful lifetime, depends on local oxide dissolution rate

14. THIN CONDENSATE LAYER DYNAMICS ON ROTOR BLADES Objectives: Primary flow, and its metal oxides Dissolution Rate Consequences Relation to observed hot corrosion patterns?

15. OXIDE DISSOLUTION RATE where kd is a rate constant, is liquid layer density, is local undersaturation of oxide in liquid, and nd the order of the rate process

16. OXIDE DISSOLUTION RATE CONTD… Diffusion in the liquid is calculated via: where subscripts w and b represent blade surface and bulk liquid, resp., and km is a mass-transfer coefficient. Under steady-state conditions:

17. HOT CORROSION RATE • Hot corrosion rates will track oxide dissolution rates • Local oxide thickness, will depend inversely on local oxide dissolution rate • When falls below a threshold value, , catastrophic failure at the local site will occur • ‘Corrosion maps” can be generated in this manner, and compared against field or burner-rig data • Model can be refined, re-run, results compared again, etc… • Let us now consider another example….

18. EXAMPLE 3: FOULING OF HEAT EXCHANGER SURFACES • In power plants burning fossil fuels, such as coal, the combustion gases contain unburnt particulate matter– “ash” • Ash particles deposit on heat exchanger tubes, and reduce heat transfer efficiency • Ultimately, ash deposits get so thick, they interfere with the flow of gases

19. EXAMPLE 3: FOULING OF HEAT EXCHANGER SURFACES CONTD… • Periodically, plant operation must be stopped and ash removed or tube replaced • Loss of productivity, cost of replacement • Need to estimate rate of ash deposition so that proper planning can be done

20. PC FURNACE + HEAT EXCHANGER

21. HEAT EXCHANGER TUBE IN CROSS-FLOW OF COMBUSTION GAS

22. DESIGN PARAMETERS • Diameter of h.e. tube of circular cross-section = 5 cm • Te = 1200 K • p = 1 atm • Ue = 10 m/s • Ash composition: SiO2 • Size distribution: • dp = 0.1 mm at wp = 2 X 10-4 • dp = 20 mm at wp = 1 X 10-2

23. DESIGN REQUIREMENTS • Rate of energy gain (kW) per meter of tube length if outer tube surface temperature is to be maintained at Tw = 800K • Rate at which submicron and super-micron ash will accumulate per unit length of cylinder

24. ASSUMPTIONS • Gas flow in continuum regime • Forced convection dominates over natural • Negligible viscous dissipation • Mainstream turbulence level not very high • For submicron particle transport, analogy between mass- and energy-transfer holds All assumptions must later be validated…

25. ENERGY TRANSFER RATE Average heat-transfer coefficient for transverse flow past a circular cylinder is given by: where Reynolds number And Prandtl number

26. ENERGY TRANSFER RATE CONTD… Approximation: Rate of energy flow, -qw is calculated by:

27. ESTIMATED VALUES For Tw = 800K and Te = 1200K, and P = 1 atm: Re ≈ 4000, ≈ 36 and Thermal conductivity k ≈ 1.62 X 10-4 cal cm-1 s -1 K-1 Heat transfer rate (from combustion gases), -qw, given by: may be estimated (per meter of heat-exchanger tube) as 733 cal s-1, or 3 kW.

28. TUBE-FOULING RATE DUE TO ASH ACCUMULATION Mass transfer Nusselt number, , is given by: where jp,w is the rate of ash mass transfer to a circular cylinder in cross-flow, and Sc = Schmidt number =

29. TUBE-FOULING RATE DUE TO ASH ACCUMULATION CONTD… For dp = 0.1 mm, Sc ≈ 3,000, ≈ 1,260, -jp,w ≈ 0.035 kg/year For dp = 20 mm, Sc ≈ 108 , ≈ 15,600, -jp,w ≈ 0.011 kg/year Are these estimates realistic? NO!

30. RE-EXAMINING ASSUMPTIONS • A1: Convection & Brownian diffusion are primary mechanisms of ash particle transport • A2: Particle flow is coupled closely enough to fluid flow that “single-phase” flow may be assumed. Neither assumption is valid in a high-temperature flow system involving ash particles of sizes ranging from sub-micron to mm’s. • appropriate correction factors must be developed and applied.

31. EFFECT OF “ANALOGY-BREAKING” PHENOMENA • Thermophoresis: • Particle mass flux induced by a temperature gradient • Increases ash capture rate to 7.2 kg/year for 0.1 mm-sized particles • Inertial Capture: • Significant for Stokes number values near 0.1 and higher • Increases ash capture rate to 9 metric tonnes/year for 20 mm sized particles

32. SUMMARY SO FAR • Many practical process applications involve simultaneous transport phenomena, high temperatures and chemical reactions. • In order to analyze such processes, and develop control/ optimization strategies, a fundamental understanding of the interplay between these phenomena is required. • In the remainder of the course, we will attempt to develop this understanding.