Liquid Dynamics International Ltd. - Piping System Analysis / Piping System Simulation

LDi – P32

Predict valve, membrane, & liquid mass motion, responses to flow from reciprocating pump action, to generate the pressure pulsation. Ex: Initial choice, outline of equations, for compiling a fortran "dt" iterative LDi PulseView display for motions & resultant pressure pulsation.

Note, in this primitive skeletal outline example of LDi method, position numbers: D, G, L, P, & V, 00, 01, 02, 03, 04, etc. are as pg. 29.

Cfr – Viscous friction coefficient, N sec/m
Cspr – Spring rating, N/m
D – Diameter, m
E – Bulk modulus of liquid, Pa
F – Area meters squared m2
G – Mass flow, Kg/sec
l – L/F – Fluid column inertia, 1/m
L – Length, m
m – Mass, Kg
Nfr – Coulomb friction force, N
P – Pressure, Pa
R – Crankshaft radius, m
T – Time, sec
X – Piston position, m
Y & Z – Valve position, m
p – Density, kg/m3
w – Angular velocity, 1/radius
In these descriptions: N – Newtons, m – meters, Pa - Pascals

Assumption in this example are: That there is no vortex or other instability at system inlet, and that the system load, is not applied by a "spill back loop" or a "controller" that "modulates" open and closed.

1. Suction Source, Load
2. Suction Manifold Inlet Flow
3. Suction Manifold Outlet Flow
4. Suction Manifold Pressure Balance
5. Suction Check Inlet Mass Flow
6. Suction Check Pocket Flow Balance
7. Suction Check Motion
8. Piston Position
9. V11 Flow Balance
10. V11 Volume Change
11. Discharge Check Inlet Mass Flow
12. Discharge Check Motion
13. Discharge Check Pocket Flow Balance
14. Discharge Check Outlet Mass Flow
15. Discharge Manifold Pressure Balance
16. Discharge Manifold Outlet Mass Flow

References:
A. Pump Handbook, 2nd Ed. Karassik eq 38., p.3.8.
B. Mechanics of Fluids, 6th Ed. Massey eq 13.14 & 13.16
C. Handbook of Noise & Vibration, 6th Ed. Barber, M.I.T. 1960 Library of Congress Cat Card Nbr 59-6759 E&OE

Whilst LDi PulseView software also displays "acoustics", it is primarily a mass, motion, & pressure model - not an attempt to determine them from "acoustic" frequencies and amplitudes.