Stirred Tank Mixing: Reynolds Number & Power Draw

simulator intermediate ~10 min
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Re = 4,000 โ€” Transitional turbulent mixing

At 150 RPM with a 0.4m impeller in fluid with viscosity 0.1 Pa.s, the impeller Reynolds number is 4,000 (transitional regime). Power draw is approximately 18W with a blend time of 13 seconds.

Formula

Re = rho * N * D^2 / mu
P = Np * rho * N^3 * D^5

Mixing: The Hidden Unit Operation

Mixing is arguably the most ubiquitous operation in chemical processing, yet it remains one of the least understood. Nearly every chemical process requires blending of raw materials, suspension of solids, dispersion of gases, or homogenization of products. Poor mixing causes hot spots in reactors, inconsistent product quality, and wasted energy. The stirred tank, with its rotating impeller and optional baffles, is the most common mixing vessel in industry.

Flow Regimes and the Reynolds Number

The impeller Reynolds number Re = rho*N*D^2/mu determines whether mixing occurs by orderly laminar flow or chaotic turbulent eddies. In laminar flow (Re < 10, typical of viscous polymers), mixing relies on stretching and folding fluid elements. In turbulent flow (Re > 10,000), energy cascades from large eddies to small ones, achieving rapid micromixing. The transition regime requires careful impeller selection.

Power and Scale-Up

The power number Np relates the power drawn by the impeller to the fluid properties and operating conditions. In turbulent flow, Np is constant for a given impeller geometry, meaning power scales as N^3*D^5. This has profound scale-up implications: maintaining the same tip speed when scaling up from lab to plant requires dramatically different RPM, and the power per unit volume changes non-linearly.

Visualizing the Flow

This simulation shows tracer particles moving through the flow field generated by a radial-flow impeller with baffles. Watch how particles near the impeller experience high shear and rapid mixing, while regions far from the impeller mix more slowly. The color gradient from red (unmixed) to cyan (fully mixed) reveals the spatial non-uniformity that is the central challenge of mixing design.

FAQ

What is the impeller Reynolds number?

The impeller Reynolds number Re = rho*N*D^2/mu characterizes the flow regime in a stirred tank. Re < 10 is laminar, 10 < Re < 10000 is transitional, and Re > 10000 is fully turbulent. It determines the mixing mechanism and power number.

How is mixing power calculated?

Power draw P = Np * rho * N^3 * D^5, where Np is the power number (a dimensionless constant depending on impeller type and Re). In turbulent flow, Np is approximately constant (5.0 for a Rushton turbine), so power increases with the cube of speed.

What is blend time?

Blend time is the duration required to achieve a specified degree of homogeneity (typically 95% uniformity) after adding a tracer. It depends on impeller speed, tank geometry, and fluid properties. Shorter blend times require more power.

Why are baffles important in stirred tanks?

Baffles prevent solid-body rotation (where the fluid just spins with the impeller without actual mixing). They convert tangential flow into axial and radial flow, dramatically improving mixing efficiency. Standard design uses 4 baffles at T/12 width.

Sources

Embed

<iframe src="https://homo-deus.com/lab/chemical-engineering/fluid-mixing/embed" width="100%" height="400" frameborder="0"></iframe>
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