Having spent 41 years dealing with multi-pump centrifugal pumping systems for a critical heating/cooling application (nuclear powerplants)and assiduously surveying the literature on the subject, I am not aware of the existence of any single textbook that fully addresses the complicated effects of systems interactions in multibranch, multipump fluid systems. Even the biblical Pump Handbook which addresses single-pump branch flows, abnormal centrifugal pump performance, piping system resistances and other related topics separately does not put it all together to provide guidance on multipump, multibranch system design , operations and critical interactions. I'd be the first to buy such a book if it ever appears in the open literature. Even engineering journal articles on the total subject are rare. Some engineering magazine articles on the subject can be found in publications like Pumps and Systems but they are usually elementary and cover only parts of the total fluid system interation problem.
Following are a few tips on multipump/multibranch fluid system design based on my experience
1. Use centrifugal pumps of the same design (same rated head and flow) in all branches to equalize pressure rises in all operating branches and to enable abnormal pump characteristics to be determined from single-pump tests.
2. Select pump designs to have a specific speed that will minimize adverse effects of abnormal operations, particularly under reverse flow conditions. Pump specific speeds in the range of 2000-4000 (US units)are preferred.
3. If calculated idle branch reverse flows will breakaway an idled pump and/or cause reverse rotor rotation at speeds higher than the forward rotation maximum speed, employ quick closing check valves in the branch lines that may be idled. Swing check valves should have disks that are fully backseated at normal system flowrates to avoid flow fluctuations in the system due to oscillating disks. At lower flowrates (with idled branches or reduced pump speeds) determine check valve disk angular positions and evaluate disk flutter tendencies and fluid system repetitive check valve slamming prospects (easier said than done). Use seat bypasses around closed check valve disks if temperature near-equalizations between idle and active branches is a concern with respect to pressurized thermal shock damage to piping or system components. Seat bypasses should be sized to reduce pressure surges in idled branches without causing excessive backlow that might compromise system heating/cooling requirements.
4. Selected pump design point flow should be based on the normal number of running pumps to meet 100% system rated heating/cooling capacity. That is, operation of more or less pumps are non-normal operating conditions and account needs to be taken of degraded pump performance particularly for below rated pump flows where high impeller inlet flow incidence angles can cause flow separation, stationary or rotating stall ands other undesirable flow conditions that might induce system flow instabilities.
5. Use pressurized flow systems with operating pressures sufficiently high at all pump running speeds and flow fractions to avoid two-phase (liquid-fluid vapor) flows that can damage system components by cavitation or cause system 2-phase flow instabilities. Establish and rigorously maintain minimum pump suction pressure requirements for all pump speeds and operating branch conditions (ie. 1,2,3,4, etc. branches operating).