Compared to a steady state, fluid friction increases during hydraulic transient events because rapid changes in transient pressure and flow increase turbulent shear. Bentley HAMMER V8i can track the effect of fluid accelerations to estimate the attenuation of transient energy more closely than would be possible with quasi-steady or steady-state friction.

It is known that past velocity and/or temporal acceleration play a significant role in determining transient friction (Brunone et al., 1991; Bughazem and Anderson, 2000; Vardy and Hwang, 1991). Motivated by experimental data and published formulae in recent years for estimating the transient friction factor (Brunone et al., 2000; Vardy and Brown, 1995; Vitkovsky et al., 2000), we have proposed an unsteady friction model defined by an amplification of the quasi-steady friction factor by the following factor:

where V is velocity, t is time, g is gravitational acceleration, = 10,000 and = 4 (0) for acceleration (deceleration). The partial derivative of velocity with respect to time is the temporal acceleration at any point and is evaluated at the previous time step. On account of ongoing research in this area, an alternative transient friction method has also been provided (Bergant, Simpson and Vitkovsky, 2001). Selecting "Unsteady - Vitkovsky" as the transient friction method will employ the below formulation:

Where f is the Darcy-Weisbach friction factor, f_q is the quasi-unsteady component of the friction factor (based on updating Reynolds number for each new computation), D is pipe diameter, V is flow velocity, t is time, a is wave speed, sign(V) is equal to +1 when velocity is greater than zero and -1 when velocity is less than zero, x is distance, and k is Brunone's friction coefficient. The coefficient k can be computed using the following equation:

Where C^* is Vardy's shear decay coefficient.

For laminar flow C^* =0.00476

For turbulent flow

This unsteady friction method from Vitkovsky is now the recommended unsteady friction method for use in HAMMER.

Computational effort increases significantly if transient friction must be calculated for each time step. This can result in long model-calculation times for large systems with hundreds or pipes or more. Typically, transient friction has little or no effect on the initial low and high pressures, and these are usually the largest ever reached in the system. This is illustrated from the following Bentley HAMMER CONNECT simulation results comparing steady, quasi-steady and transient friction methods.

Figure 14-11: Bentley HAMMER CONNECT Results for Steady-State, Quasi-Steady, and Transient Friction Methods

The steady-state friction method yields conservative estimates of the extreme high and low pressures that usually govern the selection of pipe class and surge-protection equipment. However, if cyclic loading is an important design consideration, the unsteady friction method can yield less-conservative estimates of recurring and decaying extremes.

Discussion

For the initial pressure rise or decline, the various models yield results which are nearly identical to each other, as well as to empirical data. As time passes, however, the match progressively deteriorates for subsequent peaks and valleys especially when the flow changes are more abrupt as illustrated above. The usual convex velocity profile in steady state begins to break down when the flow is rapidly varied with regions of flow recirculation, flow reversal and increased intensity of turbulence (Brunone et al., 2000). Thus, the fundamental assumption of one-dimensional flow is severely strained. Although the unsteady model, in particular, matches the empirical decay in amplitude quite well, it fails to account for the attendant change in the shape of the wave with increasing time. The topic of unsteady friction remains in the forefront of hydraulics research.