Hydraulics and the meaning of turnovers

A recirculation turnover is a volume ratio, not a guarantee that every portion of water has undergone an identical pass. Using it for design requires the reference volume, actual flow, period and hydraulic regime to be stated. The distinction affects both concentration prediction and capacity calculation.

Four quantities that must remain distinct

Let Vb denote useful tank liquid volume, Qr the flow through the treatment circuit, Qf net feed flow and Vd volume treated over one day. If feed varies, Vd is its integral rather than a spot reading automatically multiplied by 24.

For a closed, constant-volume batch, mean hydraulic exposure is c = Qr*t/Vb. For variable flow use c = integral(Qr(t)/Vb) dt. Significant sampling, purges or evaporation require volume updates and a closed balance. Retaining a volume that no longer exists distorts exposure and load.

The configurator's daily index is c_d = sum(q_i*h_i)/Vd. Its denominator is daily production, not tank capacity. It describes the volume processed through units relative to production; alone, it does not determine residence-time distribution or the minimum exposure received by every fraction.

Synthetic example: a 5 m3 batch recirculated at 15 m3/h reaches c=4 after 4*5/15 = 1.3333 h, or 80 minutes. Another installation moves 15 m3/h for 20 hours while treating 75 m3/day, also giving c_d=4. Numerical agreement does not make the second system the first experiment.

Discrete passes and continuous mixing

If an entire portion passes through a unit, is collected separately and only then passes through again, a discrete sequence may be approximated. With constant removal fraction phi, the residual after n passes is (1-phi)^n. This excludes bypass and assumes comparable conditions for each pass.

A perfectly mixed tank with continuous withdrawal and return behaves differently. Water representative of the gradually changing tank concentration is withdrawn at every instant. If the side-stream reactor removes fraction phi of susceptible contaminant, the balance is:

Vb * dC/dt = -Qr * phi * C
C/C0 = exp(-phi*c)

The difference is not cosmetic. For phi=0.5 and c=4, the discrete sequence leaves 6.25% of the original fraction; the mixed tank leaves 13.53%. A more optimistic numerical curve does not establish superior equipment performance: it may describe another regime.

Under an idealisation of independent random visits to a negligible-volume side-stream reactor, visit count can be represented by a Poisson distribution with mean c. The unvisited fraction is then exp(-c): 1.83% at four mean turnovers. This explains mixing mathematically; it is not a measured T1 residence-time distribution. Short-circuiting or dead zones can cause major departures.

The engine curve alone does not identify the regime

The identity 0.5^c=exp(-ln(2)*c) allows the T1 curve to be read as an effective exponential response. It neither establishes nor excludes a mixed tank. With fixed treatable fraction theta=0.64, the current curve gives 60% total removal at four turnovers. A mixed balance separately assuming phi=0.5 would give 55.34%; an effective coefficient of ln(2) would also give 60%. These differences follow from assumptions, not new measurements.

The current curve is therefore not automatically replaced by the lower-yield curve. First identify what the coefficient represents and test it against flow, mixing and an exposure series. Until then, the T1 calculation is an engineering scenario with effective exposure, not experimental identification of the actual hydraulics.

Continuous feed

In a steady, mixed tank with feed Qf, equal outlet flow and side-stream circulation Qr, with no other reactions:

Qf*(Cin-C) = Qr*phi*C
beta = Qr/Qf
C/Cin = 1/(1+beta*phi)

For beta=4 and phi=0.5, removal is 66.67%. Load enters continuously and treated water leaves continuously. This must not be equated without explanation to a batch treated until a selected end time. Net hydraulic residence time tau=Vb/Qf and ratio beta complete the description.

These ideal balances help interpret per-pass literature without replacing measured hydraulics. A perspective on cavitation reactors discusses regimes and effective parameters. Cavitation reactor modelling.

Parallel and series modules

Two independent 15 m3/h parallel branches can provide 30 m3/h total circulation if the installation actually maintains those flows. Pump curves, head losses and branch distribution determine the real value; doubling units does not guarantee doubled flow.

With two modules hydraulically in series, the same 15 m3/h crosses both. There are two unit exposures per circuit, but the tank does not receive 30 m3/h return. Summing unit exposure is legitimate when explicitly described; using that sum to size pipework or claim hydraulic tank turnovers is not.

A third layout comprises successive tanks with separation between them. Each stage then has its own volume, time and composition. Mathematical module grouping does not establish that the physical arrangement exists. Draw feed, returns, purges, separators and sampling points before applying a numerical cascade.

Checking hydraulics efficiently

An initial check combines flow measurement, useful volume and operating-hour records. Measurements should represent operating conditions: loaded filters, usual valve positions, representative liquid level and gas where it affects the reading. Catalogue data are a starting point, not a replacement for actual flow.

If residence distribution is decisive, a compatible tracer test can reveal early arrival, tails and poorly used volume. Selecting tracer and detector depends on safety and matrix conditions. No particular reagent is proposed without compatibility assessment.

For a steady-operation test, observations during startup and stabilisation prevent transient samples being mistaken for sustained performance. When influent changes, inlet and outlet samples must be linked through the system's delay and mixing, not merely by date.

For example, inlet and outlet samples both taken at 10:00 may represent different loads if water remains in the system for hours. Computing a percentage is straightforward but the physical pairing may be wrong. Composite samples and a flow record can be more valuable than extra decimal places in the equation.

What an additional turnover adds

Extra exposure does not identify the limiting operation. Increasing Qr at fixed current increases circuits per hour without increasing electrical charge per hour. Increasing pressure at unchanged flow alters hydraulic energy without changing c. Removing sludge between circuits changes the matrix even when total recirculated volume is unchanged.

We therefore accompany c with specific energy, charge per volume, pressures, gas and separation. This does not weaken the indicator; it makes its meaning testable. Configurations can be compared while retaining the other variables rather than silently absorbing them into the word turnover.

The practical decision is simple. Use turnovers to plan exposure and time, balances to distinguish regimes, and measurement to confirm hydraulics. When two installations have identical c but different results, first investigate the conditions that the index does not represent before changing the equation arbitrarily.