# Tensys Hydro

Tensys Hydro simulates dynamic fluid flows across a complex surface. The application solves depth-averaged free surface flow equations to obtain water depth, and flow rate across the analysis domain.

### Introduction

· Visualise flow patterns over a structure including direction and flow rate

· Estimate drainage requirements

· Study effect of local obstructions

· Identity ponding locations

· Iteratively examine structure behaviour in response to transient fluid flows

### Features

· Model import : Any surface can be used as import including an inTENS analysis model

· Shoal regions : Modelling of wet/dry transitions in a numerically stable way

· Mass conserving : Volume remains constant if inflow and outflow are zero

· Well balanced : Converges to a lake at rest when all inputs are removed

· Friction : Stable computation of frictional forces at low depths

· Rainfall and “Dam Break” simulation

· Multiple boundary conditions: Inflow, outflow, smooth wallor absorbent walls

· Problem specific code : Modular solver architecture allows simulation to be customised with features such as moving boundaries, complex initial conditions or bespoke results output

### Theory

The solver uses the 2D shallow water equations on a regular grid. The equations are solved iteratively by considering mass and momentum flux across the boundaries of each computational cell.

**Assumptions:**

· Viscous forces are assumed to be negligible

· Depth averaged flow

· Only horizontal components of velocity are propagated between cells.

**Limitations**

Shallow water theory assumes that the horizontal dimensions are significantly greater than the vertical. The accuracy of the model thus decreases for very steep surface gradients or rapidly changing flow conditions.

Shallow water models may also include Turbulence terms which have been omitted from the current version of Tensys Hydro. Turbulent flow calculations are difficult to implement and equally difficult to validate. The addition of Turbulence terms would thus not guarantee improved simulation accuracy, particularly when steady state results are required.

### Validation

The Hydro tool has been calibrated against a variety of published example cases and assessed against three distinct criteria.

1. Is the software implementation bug free?

2. Is the algorithm able to model the shallow water equations accurately?

3. Are the shallow water equations suitable for use for this kind of problem?

Items 1 and 2 have been addressed by comparison with analytical, numerical, experimental and real world results. Published data is used to verify the simulation output in conjunction with manual verification to check the results appear feasible. A selection of images from validation studies are shown below.

Item 3 on the validation checklist is by far the hardest to quantify without structure specific experimental data. Published literature is also non-specific about the maximum slopes permissible for shallow water theory. Water depth is also sensitive to the surface friction parameters which may not be known for the surface in question. Results on water depths for steep slopes (> 10°) must thus be used with care, particularly for simulations of transient waves.

# Application

In engineering design it is generally the fluid distribution in the steady state condition is of most interest, and for this latter case the Tensys Hydro solver can be used with a high degree of confidence. In the steady state, what comes in must come out again, and thus the software can be used to assess flow rates at outflow drainage points under constant rain loading.

The determination of local water velocity and depth is limited by the need to provide realistic assessments of turbulence and friction factors. Without careful calibration against experimental testing for a similar problem, industrial applications of Tensys Hydro should focus on flowrate assessment.