Rigid-column theory is suitable for simulating changes in hydraulic transient flow or head that are gradual in terms of the system's characteristic time, T = 2 L/a (Appendix B). This type of hydraulic transient is often referred to as a mass-oscillation phenomenon, where gradual changes in momentum occur without significant or sharp pressure wave fronts propagating through the system.

For example, mass oscillations can occur when a vacuum-breaker or combination air valve lets air into the system at a local high point (to limit subatmospheric pressures). The water columns separate and move away from the high point as air rushes in to fill the space between them. Eventually, flow reverses towards the high point, where the air may be compressed as it is expelled. This back-and-forth motion of the water columns may repeat many times until friction dissipates the transient energy.

From the HAMMER Tools > Options menu, click the Other Options tab and set Extended CAV (combination air valve) to True. HAMMER will track the extent of the air pocket and the resulting mass-oscillation and water column accelerations. HAMMER still calculates the system-wide solution using MOC and elastic theory; it uses rigid-column theory only for the pipes nearest the high point. This results in more accurate solutions, without increasing execution times.

Elastic Simulation

Elastic theory is suitable for simulating changes in hydraulic transient flow or head of all types, whether gradual, rapid, or sudden in terms of the system's characteristic time. A popular and proven way to implement an elastic theory solver is the Method of Characteristics (MOC).

The MOC is an algebraic technique to compute fluid pressures and flows in a pressurized pipe system. Two partial differential equations for the conservation of momentum and mass are transformed to ordinary differential equations that can be solved in space-time along straight lines, called characteristics. Frictional losses are assumed to be concentrated at the many solution points.

HAMMER's power derives from its advanced implementation of elastic theory using the MOC, which results in several advantages:

• Rigorous solution of the Navier-Stokes equation, including higher-order minor terms and complex boundary conditions, whose physics can be described with mathematical rigor.
• Robust and stable results minimizing numerical artifacts and achieving maximum accuracy. Convergence is virtually assured for most systems and tolerances.
• Research and field-proven method based on numerous laboratory and field experiments, where transient data were measured and used to validate numerical simulation results.

Numerical methods for solving hydraulic transient systems or describing their boundary conditions are continuously evolving. The ideal model should have the right balance of proven algorithms and leading-edge methodologies. HAMMER is such a model. It is the result of decades of experience and innovation by Environmental Hydraulics Group's senior staff combined with Bentley Systems' software expertise and track record in bringing leading-edge technologies into widespread use.