Estuarine tidal-range lagoon and barrage modelling, from first head to first turbine

The Severn has the second-largest tidal range on Earth. A spring tide at Avonmouth can lift the sea by 14 metres between low water and high water, twice a day, with the regularity of an orbit. That range is the whole case for tidal-range energy, and also its whole difficulty. Energy in an impounded basin scales with the square of the head, so a scheme that looks marginal at a 6 metre range becomes four times as rich at 12 metres. The same square law punishes any scheme that cannot hold its head long enough for the runners to use it.

Our work sits between that equation and a bankable energy yield. We build two-dimensional and three-dimensional hydrodynamic models of the estuary with and without the impoundment, run the turbine and sluice schedule through a full nodal tidal year, and check the proposed bulb runners against the cavitation envelope at every head the schedule asks of them. Then we look at the mud.

The diagram below is generated from a simple hold, generate and sluice logic over two M2 cycles. Sea level is the solid navy curve. The basin level is the dashed teal line. Shaded areas are the working head the runners see. Notice that the flood working head is a little smaller than the ebb head, and that the basin spends almost a quarter of each cycle doing nothing but waiting. That waiting is where head utilisation is lost, and where most of the engineering judgement lives.

Ebb-only schemes hold the basin at high water, let the sea fall away, and generate once. They are simpler, kinder to fish passage, and easier to defend at a planning inquiry. Dual-mode schemes generate on both legs and lift the annual yield by roughly 60 to 80 percent for the same civil works, but they need runners that run efficiently in reverse pitch and they shorten the holding periods, which trims the starting head. Our calculator applies an 80 percent head factor to the flood direction to reflect that, and you can set the operational utilisation yourself if your schedule is tighter or looser than ours.

A tide is a sum of cosines. Each constituent has a fixed angular speed set by astronomy and an amplitude and phase set by the shape of the basin it is squeezing into. The eight below are the ones that matter for a Severn yield model. Amber-edged cards are the constituents that build the spring tide when they fall into phase with M2. The amplitudes are from our own reductions of a bed-mounted pressure gauge off Portishead and will differ slightly from the published Admiralty values for Avonmouth.

Why the fuss over the small ones? Because the shallow-water overtides, M4 and MS4, are what make the Severn curve asymmetric. They shorten the flood and stretch the ebb, which changes the generating window in each direction and shifts the balance between ebb and flood yield. A model that uses only M2 and S2 will overstate flood generation by several percent in the inner estuary.

The table follows a single M2 cycle at mean spring range. Hours are counted from high water. Each phase has a job: hold the basin to build head, generate while the head is in the runner's efficient band, sluice to reset the basin level as far as possible before the sea turns. The figures are the same ones used to draw Figure 1.

The starting head of 2.6 metres and the cut-off of 0.8 metres are typical for a 7 metre diameter low-head bulb unit. Below the cut-off the runner is still turning, but the cavitation number falls and the draft tube begins to vent, which is where runner damage and the quiet drop in efficiency begins. The lower the cut-off you can push with a well-designed draft tube, the more of the ideal energy you can bank. That is the single most valuable number in a tidal-range feasibility study, and it is why we spend so much of our time on cavitation.

What we take on

• Tidal-range lagoon and barrage feasibility, from a basin outline to a 0-D and 2-D yield model with a full 18.6 year nodal cycle.
• Bi-directional low-head bulb turbine selection and cavitation analysis, including draft tube and submergence checks against the operating schedule.
• Intertidal sediment transport, morphological change and scour at caissons, sluices and turbine outfalls.
• Civil coastal engineering for embankments, caissons and closure works, with wave overtopping and armour sizing for the Bristol Channel climate.
• Expert evidence for development consent and marine licensing in England and Wales.

Write to [email protected] with a basin outline, a tide gauge you trust, and the question you are trying to answer. More about the practice and its principal.