Vertical temperature slice through the tank: two cold jets rising from the floor and spreading along the thermocline

Design studyPotable water storage

What decides whether a storage tank actually mixes.

Transient, buoyancy-driven jet mixing in a stratified 246,727-gallon potable water tank, five inlet configurations run concurrently on one workstation. Destratification is set by the momentum flux the inlet delivers, not by flow rate and not by Froude number.

2.7×

MORE DESTRATIFICATION · SAME FLOW

1.6%

APART ON A CONTROLLED MESH

CASES CONCURRENT ON ONE BOX

2.8 H

WALL CLOCK, ALL FIVE

THE FINDING

Mixing tracks jet momentum flux. The matrix was built to let that answer lose.

The case matrix was organized on the densimetric Froude number, Fr = U/√(g′d), on purpose, because it gives a velocity-holding port a chance to fail. It didn't. The destratification rate tracks jet momentum flux, Q·U.

This is not a new result. Rossman and Grayman established from scale-model experiments in 1999 that tank mixing time during fill scales as V²ᐟ³/M¹ᐟ², with M = Q·U, and it is the basis variable-orifice inlets are designed on. This study reproduces that structure independently, from first principles.

Tank	40 ft × 26 ft SWD	246,727 gallons, potable water
Stratification	5 K	thermocline at 55% of depth
Solver	OpenFOAM v2412	buoyantBoussinesqPimpleFoam, transient
Model	URANS k-ω SST	deliberately not labeled LES
Mesh	block-structured O-grid	locally refined on the four jet columns
Cases	5 concurrent	one 64-core workstation

TWO CASES SETTLE IT

Froude numbers 2.8× apart, momentum flux identical. The results overlap.

A2 is a fixed nozzle at 500 gpm. A5 is a variable orifice at 250 gpm with the port throttled to a quarter of its area. Their momentum flux is identical by construction, and they land within 1.1% of each other on mixing index, on residual stratification, and on tracer uniformity. A3, meanwhile, has a lower Froude number than A5 and almost three times the mixing. Froude ordering is wrong by about 200%, far outside any numerical doubt here.

Thermal mixing index against jet momentum flux, fixed nozzle series with the variable orifice case landing on the same curve — Mixing index against jet momentum flux at the common comparison time. The variable-orifice case sits on the fixed-nozzle curve, not above it, which is the point: it is not doing anything exotic, it is buying momentum that a fixed nozzle only gets from more flow.

Froude number still does a job: it predicts whether the jet penetrates the thermocline at all. A1 at Fr 17 stalls at 0.57× tank depth, A5 at Fr 98 reaches 1.61×. What it does not set is how fast the tank then turns over. That is two parameters, not one.

THE CONTROLLED COMPARISON

Same mesh, same timestep, only the port differs.

C2 (fixed 4×100 mm port, 500 gpm) against A5 (variable orifice 4×50 mm, 250 gpm) on an identical mesh at an identical 0.3727 s timestep. They finish 1.6% apart on mixing index, 0.2542 against 0.2501, while A5 carries half the flow.

Mixing index against time into fill for C2 and A5, the two curves almost coincident — Mesh and timestep are controlled; only the port area differs. Half the flow, the same mixing.

Case	Inlet	gpm	U · m/s	Fr	Re	z max /H	M @ 18 min
A1	Fixed nozzle	250	0.50	17	50k	0.57	0.091
A2	Fixed nozzle	500	1.00	35	100k	1.14	0.247
A3	Fixed nozzle	1000	2.00	69	199k	2.28	0.734
A4	Fixed nozzle	2000	3.99	138	399k	4.56	0.984
A5	Variable orifice	250	2.00	98	100k	1.61	0.250
C2	Fixed nozzle	500	1.00	35	100k	1.14	0.254

Every case was generated from one parameter table, and all values are as simulated, computed from the discrete inlet area of the mesh, not from the nominal circle. A3 is both design points: at 1000 gpm the variable orifice is fully open, so fixed and variable are the same simulation. It is run once and reported once.

WHAT THE TANK LOOKS LIKE

One jet stalls under the thermocline. The other works on it.

Vertical section through two opposed nozzles, colored by temperature. Cold inflow enters at the floor; the warm stored layer sits above the thermocline at 55% of depth. Both frames are the same 250 gpm.

Temperature slice for A1, the fixed nozzle at 250 gpm, with cold water spreading along the floor — A1, fixed nozzle at 250 gpm. The jet cannot reach the thermocline. Cold water spreads along the floor toward the drain.

Temperature slice for A5, the variable orifice at the same 250 gpm, with jets reaching the thermocline — A5, variable orifice at the same 250 gpm. The jet reaches the thermocline and works on it: residual stratification is 3.96 K after 18 minutes, against A1's 4.82 K.

Three-dimensional view of A1 showing the jets stalling below the thermocline surface — A1. The four jets rise but stall below the thermocline (orange surface). The stratified layer above is barely touched.

Three-dimensional view of A5 showing the jets reaching and spreading along the thermocline — A5. Same flow as A1, four times the jet velocity. The jets reach the thermocline and spread along it, eroding it from below.

Small multiples, one panel per case, showing mixing index developing over time — One panel per case, single series each, the whole matrix on one row.

THE COMMERCIAL ARGUMENT

Q² becomes Q. That is the case for a variable orifice.

For a fixed nozzle, U = Q/A, so momentum flux Q·U scales as Q². Mixing performance therefore falls with the square of turndown. Halve the flow and you lose three quarters of your mixing energy. A variable orifice that throttles area to hold jet velocity makes momentum scale as Q instead: linear, not quadratic. At 8:1 turndown that is an 8× advantage in momentum.

Scaling beyond what was simulated is arithmetic, not simulation, and is flagged as such. The fitted exponent on the unsaturated fixed-nozzle cases is M ∝ (Q·U)⁰·⁷⁵², so an 8× momentum advantage extrapolates to roughly 4.8× the mixing, not 8×. The largest turndown actually simulated is 2:1 in flow at 4:1 in area.

MEASURED HERE, UNDER CONTROL

Throttling to 25% port area at 250 gpm produced mixing indistinguishable from a fixed nozzle at 500 gpm: 0.2501 against 0.2542, a 1.6% difference against a measured numerical uncertainty of 2.7%. Half the flow, the same mixing.

BRING US THE DECISION

Before the inlet manifold is specified.

If a tank has to hold water quality across an 8:1 turndown, the question is what the inlet delivers at the bottom of that range, not at the top. Send us the tank and the duty curve.

TALK TO AN ENGINEER

OpenFOAM v2412 (ESI), buoyantBoussinesqPimpleFoam, transient, Boussinesq buoyancy, k-ω SST run URANS. Block-structured O-grid, locally refined on the four jet columns; max non-orthogonality 39.9°, max skewness 0.635, volume error −0.03%. Transported scalars: temperature, inlet tracer, water age and chlorine with first-order decay. Full prototype scale, no model scaling. Comparison time 1080 s of tank fill. Basis: a representative tank, not a named client.