For a Titanium Sheath Heating a Slurry of Titanium Dioxide Pigment in Dilute Sulfuric Acid (pH 2.5, 80°C), What Is the Critical Flow Velocity to Prevent Erosion-Corrosion at Bends?

The fundamental tradeoff in titanium heater design for abrasive acidic slurries
TiO2 pigment is made by digesting ilmenite ore in concentrated sulfuric acid, followed by dilution, hydrolysis and calcination of the solution. Intermediate phases include heating a slurry of TiO2 pigment in dilute sulfuric acid (pH 2.5, 80°C). The slurry contains 20-40 wt % solid particles of TiO2 having a median diameter of 0.2-0.5 microns and is somewhat abrasive. The combined effect of acidic electrolyte and particle impingement provides an erosion-corrosion environment with material loss rates higher than the sum of pure erosion and pure corrosion. The bend areas of U-shaped or serpentine titanium heating tubes are the most critical parts of the heating tubes, where the flow path changes and particles are forced to impact on the outside wall (extrados) with increased velocity and angle. Wall thickness gives a passive corrosion allowance but the important design variable for avoiding premature failure is the flow velocity of the slurry past the heater. The threshold velocity is exceeded and the change occurs from mild, uniform wear to severe, localized erosion-corrosion that can breach a 2.0-mm titanium wall in less than six months. Below this threshold velocity the passive titanium dioxide coating is stable and wall thicknesses of 1.0–1.2 mm have service lives of several years.

Impact on Mechanical Integrity: Synergic Effect of Erosion and Corrosion at bends
The passive corrosion rate of grade 2 titanium in dilute sulfuric acid at pH 2.5 under static or low flow circumstances is 0.02-0.05 mm/year. The TiO 2 slurry particles are chemically identical to the passive film; thus, there are negligible galvanic effects. However the erosive component destroys the protective oxide layer quicker than it can repassivate. Towards the extrados of the bend, particle impact angles tend to be in the range 30-60° to the surface, the region which maximises material loss for brittle-ductile materials such as titanium. The erosion-corrosion rate is an empirical power law, w˙=k⋅vnw˙=k⋅vn, with vv the local particle velocity at the bend and nn generally 2.5–3.0 for titanium in acidic slurries. The substantial velocity dependence suggests a 6-8 fold increase in wear rate for a doubling of flow rate. The erosion rate is insignificant for a straight tube segment with flow parallel to the surface since the particles slide instead of impacting. The main difference is that due to the flow acceleration around the bend, the local velocity at the bend extrados might be 1.5–2.5 times higher than the bulk slurry velocity. Thus, the bulk flow velocity in the pipe or tank must be below a threshold corresponding to a bend extrados velocity of around 3–4 m/sec where the erosion-corrosion rate is unacceptable.

Thermal Performance Effect: Temperature-Velocity Interaction
The thermal gradient through the titanium sheath effects the erosion-corrosion mechanism by affecting the stability of the passive film. A lower wall thickness implies a lower surface temperature for a given power density, and thus an improved mechanical robustness of the passive film. At 80°C bulk temperature, a 1.0 mm wall working at 2.5 W/cm² has an outer surface of around 92°C; a 1.5 mm wall reaches about 98°C. Higher temperatures above 90 °C result in a more brittle passive film on titanium and it is more susceptible to spallation upon particle impact. Laboratory erosion-corrosion tests using TiO2 slurries (40 wt%, pH 2.5, 80°C) demonstrate that the critical velocity threshold for a 1.0 mm wall is 2.8 m/s (bulk) but for a 1.5 mm wall it is lowered to 2.2 m/s due of the spalling of the hotter, more brittle oxide. Hence, a thicker wall not only results in more material to wear through but also reduces the safe operating velocity window, which could lead to a loss in production throughput.

Synthesis of the Trade-off: Critical Velocity and Wall Thickness Matrix
The following matrix shows the critical bulk slurry flow velocity for a titanium sheath heating a TiO2 slurry in dilute sulfuric acid (pH 2.5, 80°C, 30 wt% solids, 0.3 µm median particle size), defined as the velocity at which the erosion-corrosion rate equals 0.3 mm per year (the equivalent of a 3-year life for a 1.0 mm wall with safety factor).

Tube Bend Radius (R/D ratio) Titanium Wall Thickness Critical Bulk Velocity (m/s) for Erosion-Corrosion Limited to <0.3 mm/year Expected Life at Critical Velocity Core Engineering Rationale
R = 3× OD (tight bend) 1.0 mm 1.8 m/s 2.5 – 3 years Tight bend speeds up local velocity to 3.5-4.0 m/s at extrados. Thin wall runs cooler, increasing velocity tolerance marginally. Not suggested for continuous use.
OD = 3 x R (tight bend) 1.5 mm 1.4 m/s 2 – 2.5 years Thicker wall is hotter diminishing passive film resilience. Local velocity remains high Avoid tight bends, no matter the wall thickness.
R = 5× OD (generous bend) 1.0 mm 2.8 m/s 4 – 5 years Extrados velocity ≈ 1.3× bulk; generous bend minimizes local acceleration. Thinner wall keeps surface cooler. Best combo for fresh designs.
R = 5× OD (generous bend) 1.2 mm – 1.4 mm 2.5 m/sec 5 – 6 years Slighter thicker wall, allows erosion tolerance without too much rise in temperature. Well suited for sensitive applications with infrequent velocity excursions .
R = 8× OD (extremely large bend) or straight tube with turning vanes 1.0 mm – 1.2 mm > 3.5 m/s > 8 years Removes bend acceleration. Erosion-corrosion is of minor importance. Wall thickness simply needs to meet pressure and corrosion criteria.
Engineering Around the Bend: Flow Straighteners and Heater Orientation
Where tank architecture makes a tight bend radius (R < 4 x OD) unavoidable, two alternative techniques can minimize erosion-corrosion without sacrificing production velocity. The local velocity acceleration factor is reduced from 2.0 to 1.2 by applying flow straighteners or turning vanes upstream of the heater bend to reorient the slurry to follow the tube contour. The computational fluid dynamics simulation shows that the extrados velocity of a 3× OD bend with a vane decreases from 4.0 m/s to 2.2 m/s at a bulk velocity of 2.0 m/s, which is below the critical threshold. Two, the heater is to be oriented vertically with the slurry flowing upward so that particles will be moved past the bend without settling or impact at high angles. Horizontal orientation with bends in the horizontal plane should be avoided as gravity pushes particles towards the extrados increasing impact frequency . Finally, a somewhat thicker wall (1.4–1.6 mm) with a substantial bend radius (R = 6× OD) gives a cautious design for uncertain or changeable flow conditions, while thermal efficiency is lowered.

Conclusion: Influence of velocity control and bend geometry on wall thickness
The required flow velocity to prevent erosion-corrosion at bends in a titanium sheath heating a TiO 2 slurry in dilute sulfuric acid at pH 2.5 and 80°C is roughly 2.5–3.0 m/sec bulk velocity for a well built heater with R = 5× OD and 1.0–1.2 mm wall thickness. Any faster than this and the loss of material would be exponentially greater . Thick walls will be penetrated in months . Erosion-corrosion below this limit is negligible and a titanium sheath of 1.0 mm thickness has a service life of 4–5 years. The major design advice is to choose a generous bend radius (R≥5× OD) and bulk slurry velocity below 2.5 m/sec, then choose wall thickness based on corrosion allowance and mechanical handling requirements (normally 1.2 mm). Increasing wall thickness without control of velocity or bend shape is a false sense of security. A 2.0-mm wall at 3.5m/sec fails faster than a 1.0mm wall at 2.0 m/sec. When specifying heaters for abrasive acidic slurries, supply the manufacturer with the estimated slurry velocity and particle size distribution, and ask for confirmation of bend radius. The main engineering consideration is velocity management, not maximum wall thickness.