	Applies To
	Product(s):	HAMMER
	Version(s):	All
	Area:	Calculations
	Original Author:	Jesse Dringoli, Bentley Technical Support Group

Problem

How does HAMMER calculate vapor pocket formation and collapse? (column separation / cavitation)

Background

HAMMER uses the Discrete Vapor Cavity Model (DVCM) as the standard methodology to simulate vapor pockets. The basic principle behind this is that a discrete vapor pocket can form at any calculation point in the model. The ‘single cavity’ model on the other hand is a more simplified approach.

At a higher level, the Method of Characteristics (MOC) is used in the HAMMER calculation engine to find the transient impact on a system. With this method, the hydraulic grade and flow at a calculation point in a pipe is affected by hydraulic grade and flow results at adjacent calculation points. Note: a calculation point can include node elements as well as points within a pipe.

When the pressure at a calculation point drops to the vapor pressure limit (-14.2 psi or -10 m by default, but can be changed in the transient Calculation Options), a vapor pocket will form at the calculation point. When this occurs, the calculation point is treated as a constant pressure water source, similar to a reservoir. The Method of Characteristics equation is used to calculate the flow rate at both sides of vapor pocket. Using flow rate at both sides of the vapor pocket, the vapor pocket volume is calculated. When the calculated vapor pocket volume is zero, the vapor pocket collapses. The hydraulic grade and flow at the calculation point is calculated by using the hydraulic grade and flow results at adjacent calculation points at last time step.

Momentum change in the flow is the cause of high pressure in pipes. The MOC equation is derived from the momentum equations and continuity equations. The hydraulic grade and flow at a calculation point are found by satisfying the MOC equations at two adjacent calculation points.

Details: When pressure is larger than vapor pressure (normal conditions, no vapor pocket)

This section describes what happens in normal conditions when the pressure is above the vapor pressure limit (-14.2 psi or -10 m by default)

When the pressure is above the vapor pressure limit, the MOC equations are used to calculate HGL and flow at calculation point:

Points 1, 2 and 3 in the screenshot above are three adjacent calculation points in a pipe. (the MOC calculates at intermediate points along a pipe based on the wave speed and timestep).

For calculation point 2, the hydraulic grade and flow can be calculated using the hydraulic grade and flow results at adjacent nodes 1 and 3 at last time step. HAMMER applies the MOC equations to the adjacent calculation points.

H₂ + a₁Q₂ = h₁+ a₁q₁ (1)

H₂ + a₂Q₂ = h₃ + a₂q₃(2)

Where:	H	=	head at the end of current time step
	Q	=	flow at the end of current time step
	h	=	head computed during previous time step
	q	=	flow computed during previous time step
		(where a is the wave speed, S is the pipe cross-sectional area and g is gravity acceleration)

By solving the two equations, you will get the hydraulic grade and flow at calculation point 2.

Details: When pressure is smaller than vapor pressure (vapor pocket)

When the calculated pressure at a calculation point is smaller than vapor pressure limit (-14.2 psi or -10 m by default), that calculation point (see 2 below) is treated as a constant pressure water source with pressure equal to vapor pressure.

The hydraulic grade at the calculation point 2 is: H2 = z + vp, where z is elevation at point 2 and vp is vapor pressure (gauge pressure, negative value)

Flow values at the vapor pocket in both pipe sections (point 1 to point 2 and point 2 to point 3) are calculated using the MOC equations:

H2 + a1Qa = h1+ a1q1 (3)

H2 + a2Qb = h3 + a2q3 (4)

where H2 = z + vp, z is elevation and vp is vapor pressure (gauge pressure, negative value).

Vapor volume calculation

To calculate the vapor pocket volume, the following equation is used:

V = V0 – (Qa + Qb) * ∆t (5)

where V0 is vapor pocket volume at last time step and ∆t is calculation time step.

Qa and Qb are positive when flow directions are to the pocket. If flow directions are out from vapor pocket, Qa and Qb are negative.

When the vapor pocket collapses

When the calculated vapor pocket volume from (5) is equal to or smaller than zero, the vapor pocket collapses.

The MOC equations (1) and (2) above are used to solve HGL H2 and flow Q2.

This will typically cause an upsurge (positive pressure wave) due to the sudden momentum change from the adjacent water columns suddenly colliding.