3Input guide (sidebar)

The sidebar is organised as six numbered steps. Ranges below are the exact limits enforced in the app.

Step 1 · Platform

Choose stirred, shaken or rocked. This decides which container families, impellers and result tabs are available.

Step 2 · Container family + geometry

Container family fixes the footprint shape: round cylinder · square PETG box · pillow wave bag. The vessel drawing changes with it.
Preset size seeds dimensions (you can override anything).
Fill fraction: 0.05 – 1.0 of the straight section.
Geometry (round): inner diameter T 0.02–3.0 m, straight height Ht 0.03–4.0 m, optional lock of H/T ratio 0.5–3.0.
Geometry (square): side S 0.02–2.0 m, height Ht 0.03–4.0 m.
Geometry (bag): width W 0.05–3.0 m, length L 0.05–4.0 m, height H 0.03–2.0 m.
Bottom (round stirred only): flat / dished / conical. Dished depth ≈ 0.15·T, cone height ≈ 0.30·T by default.
Baffles (round stirred only): toggle on/off; 2–8 baffles, width 0.04–0.15·T. Square bottles & bags are always flat-bottom and unbaffled.

Step 3 · Size — ONE method

Pick either "Type dimensions" or "Type target liquid litres" (e.g. 655 L). You never enter the same quantity twice.

Dimensions mode: directly edit T/H (or S/H, or W×L×H).
Litres mode: keep the footprint, solve Ht and fill so working volume == target. Range 0–5000 L.
Working liquid volume also editable directly 0–5000 L (fills derived from a fixed Ht).

Step 4 · Liquid property

Pick a fluid preset (water, PBS, CHO broth, glycerol, silicone oil, CMC, xanthan, kaolin slurry, blood, …) or toggle Custom liquid to type density 500–3000 kg/m³ and viscosity 0.01–1 000 000 mPa·s (≈ cP).
Temperature 2–90 °C. Non-Newtonian presets (CMC, xanthan, blood) use shear-thinning / yield models.

Step 5 · Impeller

Impeller count 1–4 on one shaft (round STR / mobile vessels). Bottles (square / DS) lock to a single stir bar.
For each impeller: Type (see atlas below), diameter D 0.005 – 0.95·T, off-bottom clearance 0.002 – (h_liq − 0.005) m.
Stir-plate coupling limit 0–300 mN·m (0 = auto by bar size): micro ≤20 mm → 8; lab 25–50 mm → 35; large 60–80 mm → 60; heavy-duty ≥80 mm → 120. Above the limit the bar slips / stalls.

Step 6 · Speed & process context

Speed 5–3000 rpm (stirred & shaken).
Shaken: orbit / shaking diameter 3–100 mm. Rocked: rock angle 1–12°, rate 5–45 rocks/min.
Process context (guideline bands): mammalian CHO/HEK, insect Sf9, plant cell, microbial E. coli/yeast, filamentous fungi. Drives P/V and tip-speed warnings.
Optional expanders (stirred): Gas sparge & mass transfer (vvm 0.005–3.0, O₂ 5–100 %), Heat transfer (ΔT 1–80 K, utility h 100–8000 W/m²K), Solids suspension (ρ 900–5000 kg/m³, d 1–5000 µm, x 0.01–40 %), Sampling probe (shear exposure at r, z).

Tip: The Overview tab runs "engineering checks" — flooding, Njs (just-suspended speed), tip-speed cell damage, torque vs stir-plate limit, unfavourable swirl. Fix what it flags before trusting the numbers.

4Blade-type atlas (23 impellers)

Every impeller is characterised by its turbulent power number Np∞, laminar asymptote Kp (Np·Re limit), primary flow number Fl, and Metzner–Otto shear constant ks. The family cards below use clean 3D product-style renders for realism; the close-clearance family uses a schematic because anchor/ribbon geometry is clearer drawn than rendered.

Radial Mixed flow Axial Close-clearance Disperser

RADIAL

Radial-flow turbines — discharge straight out, then split up & down

Rushton 6-blade disc turbine: a horizontal disc with six flat vertical rectangular blades mounted around the rim, viewed from above

Blades sit on a disc and throw liquid radially outward, creating two circulation loops (up the wall, down the centre, or vice-versa). Highest shear at the blade tips — great for gas dispersion, harsher on shear-sensitive cells.

Rushton DT-6 — the classic 6-blade disc turbine, Np≈5.0 (Bates et al. 1963).
CD-6 / BT-6 / Scaba 6SRGT — concave / hollow blades; better gas handling and kLa efficiency at lower Np.
Flat paddle (2-blade) — large-D/T, common in glass vessels & DS bottles.

MIXED

Mixed-flow — pitched blades, mostly downward axial with radial component

Pitched-blade turbines (PBT) blend axial and radial flow. 4×45° and 6×45° are axial-dominant workhorses for blending and moderate gas handling. Magnetic stir bars (egg, cylindrical, octagonal, cross, floating, pivot-ring) are up-pumping mixed-flow devices for bottles and shake-style vessels.

PBT 4×45°: Np∞ 1.60; PBT 6×45°: Np∞ 1.85.
Stir bars: Np∞ 0.70–1.15; cross strongest, floating weakest. Effective hydraulic D ≈ 0.7× bar length.

AXIAL

Axial-flow hydrofoils & propellers — strong top-to-bottom pumping, low shear

High-efficiency, low-power-number blades that push liquid axially (top-to-bottom), giving excellent bulk blending and gentle shear — ideal for cell cultures. Propellers and low-pitch PBTs also fall here.

A310 / HE-3 hydrofoils: Np∞ ≈ 0.30 — the efficiency champions.
Maxflo WSE: up-pumping, Np∞ 0.48.
Marine propellers (pitch 1.0 / 1.5): Np∞ 0.32 / 0.55.
PBT 4×30°: Np∞ 0.95, more axial than the 45° version.

CLOSE-CLEARANCE

Anchor & helical ribbon — hug the wall, dominate in laminar / high-viscosity duties

Close-clearance agitators sit near the wall to scrape and circulate highly viscous fluids. High Kp (laminar power asymptote) and high ks (shear). Used for heat-transfer and laminar blending.

Anchor (D/T≈0.9): Np∞ 0.55, Kp 280, ks 22.
Helical ribbon (D/T≈0.95, pitch 1): Np∞ 0.38, Kp 340, ks 30 — laminar blending workhorse.

DISPERSER

Sawtooth (Cowles) disperser — extreme local shear for emulsification & deagglomeration

A toothed disc that generates intense localized dissipation for dispersing solids into liquids and making fine emulsions. Very low flow number, very high local shear — not for bulk blending.

Cowles sawtooth: Np∞ 0.17, Kp 145, Fl 0.22, ks 14.

Full impeller data table

Impeller	Family	Pumping	Np∞	Kp	Fl	ks	Notes
Rushton DT-6 (6-blade disc)	radial	radial	5.00	110	0.75	11.5	Classic radial turbine; flat blades on disc.
Concave CD-6 (Smith)	radial	radial	3.05	90	0.76	11.0	Semi-circular blades; high gas-handling kLa.
Concave BT-6 (backward curved)	radial	radial	2.55	80	0.72	10.5	Backward-curved concave blade.
Scaba 6SRGT (hollow blade)	radial	radial	3.20	95	0.73	11.0	Hollow-blade radial gas disperser.
Flat paddle 2-blade (w/D=0.25)	radial	radial	1.75	58	0.65	11.0	Large-D/T; glass vessels & DS bottles.
Pitched blade 4×45°	mixed	down	1.60	62	0.79	11.0	Axial-dominant mixed flow.
Pitched blade 6×45°	mixed	down	1.85	70	0.83	11.5	Axial flow number ≈0.75.
Stir bar — egg / elliptical	mixed	up	0.85	55	0.55	11.0	Self-centring in round bottles; lab default.
Stir bar — cylindrical	mixed	up	0.80	52	0.52	10.5	Plain cylinder; spins out first at high N.
Stir bar — octagonal	mixed	up	0.95	58	0.58	11.5	Facets add shear/pumping vs cylinder.
Stir bar — cross / plus	mixed	up	1.15	64	0.62	12.0	Highest pumping of the bars; DS pooling bottles.
Stir bar — floating / bobbing	mixed	up	0.70	50	0.48	10.0	Rides near surface; weak bottom turnover.
Stir bar — pivot-ring	mixed	up	0.90	56	0.56	11.0	High-grip; higher coupling limit.
Pitched blade 4×30°	axial	down	0.95	52	0.68	10.5	More axial than the 45° version.
Lightnin A310 hydrofoil (3-blade)	axial	down	0.30	42	0.56	10.0	High-efficiency solid-set; low Po/Fl.
Chemineer HE-3 hydrofoil	axial	down	0.30	44	0.53	10.0	High-efficiency hydrofoil.
Maxflo WSE hydrofoil (4-blade)	axial	up	0.48	48	0.63	10.5	Up-pumping axial hydrofoil.
Marine propeller pitch 1.0	axial	down	0.32	41	0.50	10.0	Classic 3-blade marine propeller.
Marine propeller pitch 1.5 (SC-3)	axial	down	0.55	46	0.82	10.5	Higher pitch → more pumping.
Anchor (D/T≈0.9)	close	tangential	0.55	280	0.30	22.0	Heat-transfer duty; Np T/D-dependent.
Helical ribbon (D/T≈0.95, p=1)	close	tangential	0.38	340	0.25	30.0	Laminar blending workhorse.
Sawtooth disperser (Cowles)	disperser	radial	0.17	145	0.22	14.0	Ultra-high shear; extreme local dissipation.

Np∞ = turbulent power number at standard D/T=1/3, w/D=1/5. Kp = laminar Np·Re asymptote. Fl = primary flow number. ks = Metzner–Otto average shear-rate constant. All are editable in the app's Advanced panel.

9Theory, formulas & assumptions

Every number in CFD Surrogate Studio comes from closed-form correlations and a reduced-order (surrogate) flow field — not a mesh-resolved CFD solve. This section lists the exact equations so you can audit, reproduce, or override them. All coefficients (k≈5.9, k_s, Po, Fl, van't Riet a…) are editable in the app's Advanced panel.

1Reynolds number & flow regime

Shaft speed is converted to revolutions per second N = rpm / 60. The impeller Reynolds number sets the regime:

Re = ρ · N · D² / μ

For non-Newtonian broths the apparent viscosity is evaluated at the Metzner–Otto mean shear rate γ̇ = k_s · N (k_s ≈ 11.5 for a Rushton), so μ = μ_app(γ̇, T) feeds back into Re. Regime bands: Re < 10 laminar, 10–1000 transitional, > 1000 turbulent.

2Power, tip speed & Froude

Power number per impeller follows a generalised laminar→turbulent curve (Bates-style blending) into the turbulent plateau Np_∞:

Np(Re) = ( (K_p / Re)^c + Np_∞^c )^1/c

Power draw, intensity and the two dimensionless speeds then follow directly:

P = Np · ρ · N³ · D⁵ · P/V · ε̄ = P / (ρ·V) · u_tip = π·N·D · Fr = N²·D / g

Multiple impellers are de-rated when stacked closer than ≈1 D (interaction factor 0.55–1.0). Froude is used for the vortex-depth correction and the unbaffled-vessel warning (Fr > 0.2 → central vortex).

3Circulation & blend time (homogeneity)

Each impeller pumps a volumetric flow and the bulk turns over in a circulation time:

Q = Fl · N · D³ · τ_circ = V / (Q · 2.2) (2.2 = entrained-flow factor)

Blending time uses the Grenville & Nienow correlation. Turbulent:

N · θ95 = k · Po^−1/3 · (T/D)² with k ≈ 5.9

Laminar extension (Grenville & Tilton) and a smooth log(Re) blend in the transitional range:

N · θ95,lam = 183 · Po^−1/3 · (T/D)² → θ95 ∝ 1/N

Two physical corrections: (a) a floor θ95 ≥ τ_circ (you cannot blend faster than one turnover), and (b) a multi-impeller de-rating θ95 /= n_imp^0.25. Target windows default to 60 s (mammalian) / 30 s (microbial).

4Virtual tracer t95 (the time-to-mix model)

The "Agitation duration" input and the t95 verdict come from a reduced-order compartment model run on the developed flow. Each virtual probe relaxes toward the fully-mixed concentration as a first-order process:

C/C_∞(t) = 1 − A · exp(−k_i · t)

where the local rate k_i is set by the local |U|/shear field (dead corners mix ≈20× slower than the impeller jet) and the whole set is calibrated so the median probe t95 equals the Grenville θ95. A probe is "mixed" once its curve stays inside the ±5% band:

t95 = first t with 0.95 ≤ C/C_∞ ≤ 1.05 (and stays)

The reported "Homogeneity at chosen t" is the percentage of virtual probes whose C/C_∞ lies inside that same ±5% band at the instant you specify — i.e. the fraction of the tank homogeneous after your actual agitation time. The PDE-beta variant transports mass between cells on a coarse r–z grid (max-t95 ≈ 2× θ95, unpinned) for an audit-style cross-check; the OpenFOAM export gives fully mesh-resolved t95.

5Turbulence micro-scales (shear / cell damage)

The surrogate reconstructs turbulence from the velocity gradients of the reduced field. Fluctuating velocity uses a Prandtl mixing length:

u′ = ℓ_m · γ̇, ℓ_m = 0.41·d_wall (clipped to 0.002–0.09·T)

Turbulent kinetic energy, dissipation and the Kolmogorov microscale:

k = 1.5·u′² · ε = 0.164·k^1.5 / ℓ_m · η = (ν³ / ε)^1/4

Impeller-swept zones are floored at 6·ε̄ to reflect localised dissipation. The mammalian shear check uses η ≥ 25 µm pass, 15–25 marginal, < 15 fail (eddy ≈ cell size). Mean strain rate γ̇ = √(2·S:S).

6Gas mass transfer

Gassed power uses Michel–Miller (1962); kLa uses van't Riet (1979), steady-state, valid to ≈2600 W/m³:

kLa = a · (P_g/V)^e1 · v_s^e2 · exp(0.024·(T − 20))

Coalescing broth: a = 0.026, e1 = 0.4, e2 = 0.5; non-coalescing: a = 0.002, e1 = 0.7, e2 = 0.2. OTR (at the DO set-point) is compared against OUR to flag under-aeration; Nienow flooding correlation reports FLOODED / Loading / Dispersed (flooded = critical fail).

7Solids suspension

Just-suspended speed uses the Zwietering correlation Njs (critical fail if N < Njs); a homogeneous distribution needs roughly 1.3·Njs. A quiescent single-particle settling velocity Vt flags fast settlers (Vt > Q/A) but does not replace the Njs criterion.

8The 8-check verdict rule

The traffic-light in Overview answers "will this batch mix at this speed?": any critical fail (flooded / N < Njs / OTR < 0.5·OUR) or ≥2 fails → red; 1 fail or ≥3 marginals → amber; 1–2 marginals → amber "mostly mixed"; else green. The rough speed to hit a target blend time is rpm_hint ≈ N · θ / θ_target.

These are engineering screening correlations — excellent for ranking geometries, speeds and fluids and for catching unsafe regimes before you build or run the real vessel. They are not a substitute for mesh-resolved CFD or experimental confirmation on regulated final designs.

Preset	Mode	Footprint	H [m]	Fill	Baffled	Notes
Ambr-type mini bioreactor 250 mL	stirred	Ø68 mm	0.12	0.65	yes (4)	Glass, full jacket.
Glass STR 2 L	stirred	Ø130 mm	0.21	0.72	yes	Dished bottom.
Glass STR 10 L	stirred	Ø210 mm	0.31	0.75	yes	Dished bottom.
Pilot STR 50 L (316L)	stirred	Ø350 mm	0.52	0.75	yes	Stainless, dished.
Production STR 2000 L (316L)	stirred	Ø1.15 m	2.00	0.75	yes	Bottom-jacketed, dished.
Single-use stirred 200 L	stirred	Ø550 mm	0.85	0.70	no	Film wall; unbaffled swirl expected.
DS bottle 2 L (stir bar)	stirred	Ø135 mm	0.24	0.65	no	Circular, flat, stir bar.
DS bottle 10 L (stir bar)	stirred	Ø230 mm	0.36	0.70	no	Circular, flat, stir bar.
PETG bottle 500 mL (square)	stirred	70×70 mm	0.17	0.60	no	Deq≈79 mm (screening).
Shake flask 250 mL	shaken	Ø83 mm	0.13	0.18	no	Orbital shaker.
OSB 3 L / 50 L tube	shaken	Ø120 / 340 mm	0.32 / 0.62	0.28 / 0.25	no	Orbital shaken bioreactor.
Wave / rocking bag 20 L	rocked	300×500 mm	0.22	0.45	no	Pillow bag on rocking platform.
Mobile vessel 50–1000 L	stirred	Ø394–1070 mm	0.51–1.39	0.80	no	316L; bottom (flat/dished/conical) selectable.
Custom geometry	stirred	—	0.30	0.70	optional	Type any dimensions you like.

Context	P/V band [W/m³]	Tip-speed limit [m/s]
Mammalian (CHO / HEK)	20 – 80	2.0
Insect (Sf9)	25 – 120	2.2
Plant cell	10 – 40	1.2
Microbial (E. coli / yeast)	2000 – 12000	8.0
Filamentous fungi	1500 – 8000	6.0

1What is CFD Surrogate Studio?

When to use it

What you get

What it is NOT

23-step quick start

3Input guide (sidebar)

Step 1 · Platform

Step 2 · Container family + geometry

Step 3 · Size — ONE method

Step 4 · Liquid property

Step 5 · Impeller

Step 6 · Speed & process context

4Blade-type atlas (23 impellers)

Radial-flow turbines — discharge straight out, then split up & down

Mixed-flow — pitched blades, mostly downward axial with radial component

Axial-flow hydrofoils & propellers — strong top-to-bottom pumping, low shear

Anchor & helical ribbon — hug the wall, dominate in laminar / high-viscosity duties

Sawtooth (Cowles) disperser — extreme local shear for emulsification & deagglomeration

Full impeller data table

5Vessel preset library

6Liquid / fluid presets

Aqueous buffers & media

Sugar & glycerol solutions

Fermentation & microbial

Non-Newtonian & complex

Oils

Other

Process-context guideline bands

7Reading the results

Overview

Flow field

Turbulence & shear

Power & regime

Gas & mass transfer

Heat transfer

Solids

Scale-up

Report

8Worked example — 1000 L CHO fed-batch fermenter

9Theory, formulas & assumptions

1Reynolds number & flow regime

2Power, tip speed & Froude

3Circulation & blend time (homogeneity)

4Virtual tracer t95 (the time-to-mix model)

5Turbulence micro-scales (shear / cell damage)

6Gas mass transfer

7Solids suspension

8The 8-check verdict rule

10Model limitations & best practice

Surrogate, not CFD

Screening for non-round shapes

Stir-bar slip

Single-phase assumptions