Flowmax · Transient

Validated against the textbooks

The transient solver of Flowmax is checked against the closed-form theory of hydraulic transients: results any engineer can verify in Wylie & Streeter, Chaudhry, Thorley, Parmakian and Jaeger.

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The ten cases

Theory against Flowmax.

Case	Theory	Values compared	Largest deviation	Result
A	Wave speed of a liquid in an elastic pipe	27	1.14 %	✓ within
B	Instantaneous closure: the Joukowsky rise and the timing of the wave	18	0.96 %	✓ within
C	Gradual closure: Allievi's interlocking equations	19	0.035 m	✓ within
D	Establishment of flow: the rigid water column	10	1.06 %	✓ within
E	Mass oscillation of a surge tank	5	2.68 %	✓ within
F	Air vessel: the column on a gas spring	10	1.32 %	✓ within
G	A tank whose level moves: draining through a valve	5	0.39 %	✓ within
H	Run-down of a tripped pump on a resistance	6	0.56 %	✓ within
I	Column separation at a closed valve: the discrete vapour cavity	12	2.48 %	✓ within
K	Surge relief valve: opening and flow	9	0.00 %	✓ within

How a case is judged

Nothing tuned to fit.

The smallest model

Each case builds the smallest Flowmax model the theory describes, runs it, and sets the two results side by side.

A tolerance on every value

1 to 3 % for a quantity the theory gives exactly, and one or two time steps for a time.

Nothing adjusted

A value outside its tolerance is never tuned to fit: it is explained, and what it says about the program is reported.

What the comparison looks like

Three of the ten cases.

Case B, instantaneous closure: the Joukowsky pressure rise at the valve and at mid-length, and the timing of the wave.

Case F, air vessel: gas pressure, gas volume and liquid level as the column swings on its gas spring.

Case I, column separation: the pressure at a closed valve holds at vapour pressure while the cavity is open, then rises when it closes.

References

Wylie, E. B. and Streeter, V. L., Fluid Transients in Systems, Prentice Hall, 1993.
Chaudhry, M. H., Applied Hydraulic Transients, 3rd edition, Springer, 2014.
Thorley, A. R. D., Fluid Transients in Pipeline Systems, 2nd edition, Professional Engineering Publishing, 2004.
Parmakian, J., Waterhammer Analysis, Dover, 1963.
Jaeger, C., Fluid Transients in Hydro-Electric Engineering Practice, Blackie, 1977.
Simpson, A. R. and Wylie, E. B., Large water-hammer pressures for column separation in pipelines, Journal of Hydraulic Engineering 117 (10), 1991.
Bergant, A., Simpson, A. R. and Tijsseling, A. S., Water hammer with column separation: a historical review, Journal of Fluids and Structures 22, 2006.