Double-Pipe Scraped Surface Heat Exchanger (SSHE) Sizing Calculator
Perform industrial thermal and mechanical sizing of scraped surface heat exchangers. Model film heat transfer coefficients, scraper blade pass frequency, viscous shear dissipation power, required heat exchange area, and motor load using Trommelen penetration theory.
1. Process Fluid & Mechanical Inputs
2. Thermal Performance & Power Dissipation
First-Principles Mathematical Derivation of Scraped Surface Heat Transfer
Scraped surface heat exchangers operate under unsteady transient thermal conduction combined with periodic boundary layer scraping. The mathematical framework combines penetration theory with non-Newtonian viscous power dissipation.
1. Trommelen Penetration Heat Transfer Model
Between blade wipes, a fresh thin layer of product conducts heat directly with the cylinder wall. Integrating Fourier's conduction equation over the contact period $t_c = 1 / (N \cdot n_b)$ yields the theoretical scraped film coefficient:
Where $k_p$ is thermal conductivity (W/m·K), $\rho_p$ is density ($kg/m^3$), $c_p$ is specific heat (J/kg·K), and $f_b$ is blade pass frequency.
2. Overall Heat Transfer Coefficient ($U$)
The clean overall heat transfer coefficient accounts for inside scraped film ($h_i$), cylinder metal wall thickness $t_w$, and boiling refrigerant or liquid coolant jacket film ($h_j$):
3. Viscous Shear Dissipation Power ($P_{shear}$)
In the narrow annular gap between the rotating rotor shaft ($D_s$) and the stationary cylinder wall ($D_i$), mechanical shear generates substantial thermal power:
In product cooling operations ($T_{in} > T_{out}$), mechanical viscous dissipation acts as an internal heat source, requiring increased cooling capacity: $Q_{net} = Q_{proc} + P_{shear}$.
5 Fatal Traps & Engineering Pitfalls in SSHE Sizing
1. Viscous Dissipation Temperature Inversion Trap
For high-viscosity foods (e.g. margarine, fudge, or polymers $>10\,\text{Pa}\cdot\text{s}$), mechanical dissipation scales with shaft speed squared ($N^2$) and viscosity. Increasing RPM to improve $h_i$ can inject more heat into the product than the jacket can remove, causing product outlet temperature to rise instead of drop.
2. Scraper Blade Hydrodynamic Lift-Off (Hydroplaning)
Scraper blades rely on centrifugal acceleration and fluid drag to press against the tube wall. In highly viscous shear-thickening fluids, hydrodynamic wedge pressures build underneath the blade edge, forcing the blade inward. Hydroplaning leaves an insulating layer of frozen or burned product on the wall, cutting heat transfer by up to 75%.
3. Annular Axial Channelling in Low-Speed Laminar Regimes
When processing shear-thinning pastes at low RPM, fluid near the center shaft experiences zero scraping and flows straight through as an unmixed core plug. This produces wide residence time distributions and product quality variability, where part of the flow exits under-pasteurized or under-crystallized.
4. Shaft Whirling Deflection & Tube Galling
In cylinders longer than 2.0 meters, unsupported mutator shafts suffer high centrifugal and gravitational deflections. If shaft deflection exceeds blade clearance, metal-to-metal contact occurs between the rotor body and cylinder wall, generating metallic wear shavings that contaminate food/pharmaceutical batches.
5. Flash Freezing & Drive Pin Shear Overload
During refrigerant start-up in ice cream or freeze concentration, the cylinder wall temperature can plummet below product crystallization temperature before product flow is fully established. Product solidifies solidly against the wall, seizing the mutator and shearing torque-limiting safety pins or destroying the reduction gearbox.