Design studyStorage-tank mixing

Where sludge settles, and the aim that decides it.

A 12 m storage tank with two shell-mounted mixing nozzles. The pump, the nozzles and the flow rate are fixed; the only variable is which way the nozzles point. Aimed across the tank, they leave 90% of the floor below the shear stress that keeps sludge moving. Turned 53° to spin the tank instead, they leave 62%, and the tank-side pressure the loop has to overcome falls rather than rising.

Plan of the tank showing two discharge nozzles, the suction nozzle opposite, and both the radial and re-aimed jet directions — The tank and the loop. Red is the as-installed radial aim; green is the recommended 53°. Nozzle position, elevation, throat area, flow rate and jet velocity are identical in both.

90% → 62%

FLOOR BELOW SLUDGE THRESHOLD

4.0×

MORE SWEPT FLOOR AREA

NEW HARDWARE · SAME PUMP

CONFIGURATIONS

THE PROBLEM

Given a fixed pump, how much of the floor stays clear, and what decides it?

Sludge does not settle evenly. It settles where the liquid above it is not moving fast enough to carry it, and that is a property of the flow field, not of the tank. A cleaning contractor who knows where the deposit is can plan a non-entry clean against a drawing instead of an estimate; an operator who knows why it is there can often stop it forming.

The quantity that decides whether a deposit forms is the wall shear stress on the floor, so the deliverable is one number: the fraction of floor area where shear falls below the critical value. The answer turns out to be the nozzle aim, which costs nothing to change and is usually set by whatever the pipe routing made convenient.

Tank	12.0 m × 4.0 m	452 m³, 113 m² of floor
Fluid	870 kg/m³, 11.5 cSt	medium crude at storage temperature
Nozzles	2 × 168 mm bore	at 0.50 m above the floor
Jet velocity	7.0 m/s	jet Re 1.0 × 10⁵
Recirculation	1113 m³/h	one tank turnover every 24 min
Sludge threshold	τc = 1.5 Pa	swept over 0.5–3.0 Pa as a sensitivity

AS INSTALLED

The momentum is not too small. It is aimed at the outlet.

Two jets fired radially into a cylinder do not organise the tank. They cross, meet, and leave together for the suction. The result is a narrow high-shear lane joining the two nozzles to the outlet and stagnant liquid everywhere else: 90% of the floor below threshold, and a mean floor shear of 0.66 Pa against a peak of 8.7 Pa. The failure is not that there is too little momentum in the tank. It is that the momentum is spent in one direction and then removed through the suction, instead of being handed to the tank as circulation.

Speed on the nozzle plane for the radial aim beside the re-aimed case — Speed on the nozzle plane. Left: radial aim. The jets meet near the centre and the combined stream runs straight to the suction, leaving the rest of the tank still. Right: re-aimed, the same two jets set the whole tank rotating.

Floor wall shear stress on a polar grid, radial aim beside the re-aimed case — Floor wall shear stress, area-weighted onto a polar grid and averaged over the settled part of the run. Red is below the sludge threshold and will accumulate; green is swept. The dead region is not opposite the nozzles; it is everywhere the jets are not.

TURNING THE NOZZLES

The recommendation is a band, not an angle.

The sweep varies aim and nothing else: nozzle position, elevation, throat area, flow rate and delivered momentum are identical at every angle. The first 31° of turn takes 90% to 63%, which is 97% of the whole available gain for a change that costs a flange rotation.

Aim β	Dead area · % settled	Swept · %	Mean τw · Pa	Median τw · Pa	Tank head · Pa
0°	90.4 ±3.3	9.6	0.66	0.32	8769
31°	63.0 ±2.9	37.0	1.48	1.27	8536
41°	62.1 ±2.3	37.9	1.56	1.25	8279
48°	62.1 ±0.9	37.9	1.64	1.23	7952
53°	62.0 ±0.7	38.0	1.70	1.23	8018
60°	65.6 ±0.8	34.4	1.74	1.23	8261
65°	68.9 ±0.7	31.1	1.72	1.16	8515

Dead floor area against nozzle aim angle, with per-iteration scatter shown as vertical bars — Dead floor area against aim angle. Vertical bars are the scatter of the per-iteration answer across the averaging window: the flow does not settle to a fixed point, and that scatter is carried rather than hidden.

Between 41° and 53° the answer moves by 0.1 points, which is inside the run-to-run scatter, and past 53° it gets worse again. So the recommendation is 41–53°, being every angle whose answer falls inside the best case's own window scatter. That matters practically: an installer setting a nozzle against a shell has a few degrees of tolerance at best, and a recommendation that needed 53° exactly would not survive the field.

WHY IT WORKS, AND WHY IT STOPS

The two arrangements fail in opposite places.

A tangentially aimed jet does not spend its momentum on the far wall. It attaches to the shell and drives a rotating cell that fills the tank, so the near-wall floor sees moving liquid all the way round instead of only along one lane. Mean floor shear rises from 0.66 to 1.70 Pa, a factor of 2.6, on identical pump duty.

But rotation has a centre, and the centre does not move. Past the optimum the flow is increasingly a solid-body-like swirl with a stagnant core, and floor area lost at the middle starts to outweigh floor area gained at the rim. That trade is the minimum in the curve, and the reason the recommendation tops out around 53° rather than running as tangential as the shell will allow.

Floor shear against radius, averaged around the tank, for every aim angle. Red is the as-installed radial aim; blues run from 31° to 65°. The radial arrangement puts its highest shear at the centre and falls to 0.23 Pa at the shell; the swirling one does exactly the reverse. The two cross at about 3.3 m.

Swirl wins on total area only because area grows with radius: the floor outside 3.3 m is 70% of the tank. It is not a better flow everywhere; it is a better flow where most of the floor is.

WHAT RE-AIMING DOES NOT FIX

62% of the floor is still below threshold.

That is a 4.0× improvement and it is free, but it is not a clean tank, and a study that stopped at the good number would be misleading. The residual is concentrated in the central core, the same core the radial arrangement was scouring. Two things follow directly, and both were run.

Tilting the nozzles down

It does not help, and the way it fails is worth a moment. Tilting the jets down raises mean floor shear sharply, 1.64 to 3.12 Pa or 91% more, while making the dead area worse. The extra shear all lands in a small patch directly under each nozzle, where the floor was already being swept, and it is paid for out of the bulk rotation that was sweeping everywhere else. This is the case for not reporting a mean.

Downward tilt α	Dead area · % settled	Mean τw · Pa
0°	62.1 ±0.9	1.64
23°	66.1 ±1.2	2.64
31°	70.2 ±1.0	3.12

One nozzle of each

If the radial arrangement sweeps the core and the swirling one sweeps the rim, the obvious move is one of each. It is the first thing anyone suggests on seeing the radius plot, and it is the worst of the three. The radial jet fires straight through the middle of the rotation the other nozzle is trying to establish and breaks it up, while half the radial momentum is not enough to scour the core. Circulation in a tank is not additive across nozzles: it has to be driven coherently or it is not driven at all.

Aim · N1 / N2	Dead area · % settled	Mean τw · Pa	τw on axis · Pa	τw at wall · Pa
53° / 53°	62.0 ±0.7	1.70	0.05	2.70
0° / 53°	89.7 ±1.3	0.95	0.37	0.92
0° / 65°	89.3 ±1.1	1.01	0.26	1.77

Floor shear for both nozzles turned, against one radial and one tangential — Both nozzles turned, against one radial and one tangential. The mixed arrangement has flow everywhere and enough shear almost nowhere.

Dead area against the assumed sludge threshold. The direction of the recommendation holds across the whole plausible range; its size does not. At 0.5 Pa the re-aim is worth 52 points of floor area, at 1.5 Pa 28, and at 3.0 Pa 9.

Everything that would actually close the remaining 62% needs momentum delivered somewhere the shell cannot reach it from, or more of it: a third nozzle, a floor-mounted riser, or a higher jet velocity at the same pump flow through a smaller bore. None of those was run, and no number is claimed for them.

LIMITATIONS

Stated rather than buried.

Steady solver on an unsteady flow. The largest single source of uncertainty here.

Single phase. The sludge itself is not modelled; floor shear stands in for it.

The 1.5 Pa threshold is an assumption, not a measurement of this sludge.

Wall functions. The near-wall profile is modelled, not resolved.

Rigid flat lid. The free surface cannot deform.

One duty point: 1113 m³/h at 7 m/s.

BRING US THE DECISION

Before you book the tank clean.

If you are budgeting a non-entry clean, or wondering why one tank in a farm keeps filling with solids, send us the arrangement and the duty. Some of the answers cost a flange rotation.

TALK TO AN ENGINEER

OpenFOAM v2512, simpleFoam, steady, incompressible, SIMPLEC, k–ω SST with wall functions. Five-block O-grid from blockMesh with four nested hexRef8 levels on the floor band, jet paths and port mouths; max non-orthogonality 52.8, max skewness 0.61. Nozzle ports are a whole number of mesh faces at every admissible aim angle so flow rate and jet velocity are both held exactly. 3,000 SIMPLE iterations, fields averaged over the last 1,000. Basis: a representative geometry, not a named client.