The journey of LNG through the supply chain, from the production site to the end-user, requires reliable pumping devices in order to transfer the cryogenic liquid. The products utilised to perform this function, which fulfill an essential

requirement of the international LNG production and transportation system, are motor-driven centrifugal pumps.

The central structure of the vertically-oriented centrifugal pumps consists of rotating assembly driven by a submerged motor. Electric motor action causes the wheels, inducer and impellers, to rotate. The rotating wheels have two fundamental functions, to pull-and-push flow throughout and to increase the static pressure along the liquid travel path. The quantity of delivered flow (Q) and the magnitude of produced-head (H) depend on the machine size, rotational frequency, and number of stages.

WHEN TWO HEADSBECOME ONE

Yousef Jarrah and Zohaib Rehmat, Nikkiso Cryo Inc., USA, reveal why-and-how the two heads of a centrifugal pump are combined to produce the overall measured head.

OWT

Reprinted from January 2018

The total head, however, is the sum of two distinct head profiles, H1 and H2; the strength of each is a function of flowrate. H1 is due to primary-flow being pumped through the stages, as the rotating wheels are able to pull-and-push the flow in an orderly fashion. H2 is due to stalled-flow concentrated near the inlet of all stages, it begins to be active as the flow is reduced and it becomes dominant at shutoff; unable to push the flow, the

action of the wheels manifest in maintaining stalled-flow-circulation. In-between zero and normal flow levels, some flow passages are occupied by primary-flow while other passages are occupied by stalled-flow.

As the flow is reduced towards shutoff, the fundamental function of the rotating wheels transitions from pull-and-push, to pull-some and circulate-some, and finally to only circulating stalled-flow-cells at shutoff. The purposes of this article are to reveal why-and-how the two heads are combined to produce the overall measured head and to offer flow-based-criteria for maintaining reliable pump operation. Nearly one third of all pump failures occur while operating at flows much less than rated, or when the strength of the secondary stalled-flow is sufficient to be destabilising.

Differentiated flow activitiesWhile the pump as a machine is complex, its function is simple; mainly to pull a liquid, increase its static pressure, and deliver it into a discharge port. But the manner by which this happens depends on the flow magnitude because the structure of streamlines changes as the flow is reduced and, therefore, input power is consumed in establishing and maintaining any combination of three distinct flow patterns: Thru-flow, thru-flow with some stalled-flow, or only stalled-flow exactly at shutoff. To offer precise clarification; the concept of Flow-Factor [FF = (Q) / (Q-BEP)] is introduced as measure of the ratio of flow relative to that at the BEP (Best Efficiency Point), FF = 1.0 at BEP and FF = 0.0 at shutoff.

At one end of the flow spectrum, when FF >> 0.0, Figure 1 shows what happens. The flow is pulled-and-pushed through all the stages and is then delivered at a discharge port. No stall-zones persist anywhere along the flow pathways because flow separation zones may not form. The pump is most efficient when FF = 1.0; however, the efficiency drops for FF > 1.0 due to hydrodynamic reasons not associated with stall. Input power is effectively utilised to increase fluid enthalpy (or pressure and temperature) as the pump performs its intended function.

At the other end of the flow spectrum, when FF = 0.0, Figure 2 shows what happens. The flow is fully-stalled near the inlets of all rotating wheels, inducer and impellers. Flow is neither pulled nor delivered; instead, it circulates locally by entering near the wheel hub (small radii) and leaving near the wheel tip (large radii). Input power is used to sustain the highly organised U-shaped flow-circulation. In the electronics cooling fans industry, where the fluid is air and the power is low (thus it is safe to feel air motion via one’s finger); at shutoff, one can feel a jet-type flow entering the impeller near the hub and leaving the impeller near the tip.

For 0.0 < FF << 1.0, some flow is pulled-and-delivered and some flow is circulated, with the percentage of each depending on the FF value. But as the FF is increased above zero, the stalled-flow becomes concentrated more and more near the wheel tip until it completely disappears.

Whether alone or coexisting, the two distinct flow patterns generate two distinct heads, H1 due to flow being delivered and H2 due to flow being internally circulated; and the integrated sum, H = H1 + H2, is what is

Figure 1. Normal-flow delivery pathways.

Figure 2. Stalled-flow at shutoff (net thru flow = 0).

Reprinted from January 2018

actually measured during testing. In fact; the dismissal of H2 is a thermodynamic impossibility because one cannot then: (a) explain why a finite input power is required at shutoff, and (b) identify the fluid dynamics process of producing pressure at shutoff.

Thermodynamic fundamentalsThermodynamics offers an elegant explanation of how the liquid properties (enthalpy, entropy, pressure, and temperature) of the incompressible flow behave at all values of the FF and how input power at low-flows is utilised in producing H2. By splitting the total head into two distinct components, one associated with primary-thru-flow and one associated with secondary-circulatory-flow, a unique story of what happens is forged. The precise governing equations are Nikkiso Cryo Inc. (NCI) proprietary and are not listed in this article.

The head associated with normal-flow (H1) is simple and its profile is similar to the efficiency profile. Like the efficiency, H1 is zero when FF = 0.0 and at the maximum pumping capacity as shown in Figures 3 and 4 for two NCI models. H1 has its highest value exactly at the flow-point where the efficiency is also highest, or at BEP. H1 is function of the hydraulic efficiency, liquid specific heat, and the temperature-rise of the delivered liquid.

The head associated with stalled-flow (H2), also shown in Figures 3 and 4, is complex because the process of creating it must comply with thermodynamic constraints being carried out as the flow is reduced towards shutoff;

for example; exactly at shutoff, input power must become finite, not zero. H2 is function of the hydraulic efficiency, flow, liquid density, and heat-outflow-rate (into the housing). The energy equation must contain the heat-outflow-rate term so that, when Q = 0; it becomes possible for the pump to (a) consume finite power equaling exactly the heat-outflow-rate, and (b) have finite rate of entropy production.

At shutoff; H1 = 0.0 because Q = 0, however, H2 is finite and may not be zero. This is the technical reason why the head is finite even when the delivered flow is zero, the quantitative energy terms are constrained by boundary conditions imposed as the flow is reduced towards shutoff. Hydrodynamic-wise, a finite input power must be supplied in order to maintain-and-sustain the stalled-flow-structure shown in Figure 2 and, with nowhere to go, this power is conducted as heat into the surroundings.

Technical consequencesWhile the hydrodynamic and thermodynamic processes are elegant, the mechanisms are also challenging to engineers performing computational fluid dynamics (CFD) or lateral critical speeds (LCS) structural analyses. When the rotating stalled-cells instability is strong, at FF < 1/3; those performing CFD simulations are finding the codes do not numerically converge, and those performing LCS analysis are finding the codes yield very small displacements when in fact the pump may have structurally failed.

At the onset of instability, the formed stall-cells rotate in the same direction as the wheels but at reduced speeds, usually they rotate at about half the wheel RPM; they may also migrate along the radial direction while travelling circumferentially. This means; at different times, different portions of the blade surfaces are rendered ineffective, and that causes significant variations in pressure-production on any given location inside the wheel. The pressure fluctuations are space-and-time dependent, and they become stronger as the flow is reduced, becoming strongest at shutoff. This is also why the measured QH-curve obtained when reducing the flow (towards shutoff) is not identical to that obtained when increasing the flow (towards BEP); the stalled-cells have moved to block different blade surfaces.

Large pressure fluctuations, not only cause numerical convergence problems but also interact with the rotating assembly and may cause larger-than-expected lateral displacements. Like flutter in axial-flow compressors, the fluid dynamic instability can cause a structural instability due to varying time-dependent loading on the blade surfaces. Available commercial LCS codes do not take into account the additional frequency associated with the circulatory-flow.

In another hydro/thermo-dynamic limitation, the stalled-cell-zones may not occupy the entire space within the flow channel, 360º degrees circumferentially and hub-to-tip radially. Only partial blockage, limited to about 50% of volume, is possible. The stalled-cells are, however, continuously travelling; for example, a stalled-cell may be at the 12 O’clock position near the hub at time ‘t’, and at the 9 O’clock position near the tip at time ‘t + 5 seconds’. The root cause of both, numerical non-convergence and

Figure 3. Pump model 60788 performance (9 stages, 60 Hz).

Figure 4. Pump model 60882 performance (1 stage, 60 Hz).

Reprinted from January 2018

increased displacements of the rotating assembly; is the spatial-and-temporal variations associated with rotating stalled-flow-cells.

Operating the pump at low-flows, especially at FF < 1/3 when the stalled-cells are fully developed, can cause larger lateral displacements than clearances between rotating and stationary surfaces are designed to accommodate, resulting in structural failure. Under normal operation; the fundamental frequency (RPM or f1) generates vibrational disturbances with discrete frequencies and mode shapes, and the bearing system is designed to limit the growth in amplitude of the disturbances. But operating at low-flows generates additional instability modes because the stalled-cells themselves also rotate with unique frequency (usually about f1/2). The rotating stalled-cells can cause structural problems because they (a) travel at unique frequency that is different from the primary rotational frequency, and (b) continuously load-and-unload different locations on the surfaces of the rotating blades.

Another problem associated with operating at FF < 1/3 is conductive heating of the structures cloaking the rotating assembly. In fact, at shutoff (FF = 0); the entire finite input power is conducted as heat into the housing, and that can modify running clearances and negatively influence both performance and reliability.

Due to the above destabilising mechanisms; NCI recommends that pumps not operate at FF < 1/3. Like DND (Do-Not-Dwell) speed-zones which are used to avoid running for a long time near critical speeds, DNO (Do-Not-Operate) flow-zones are used to warn customers to avoid operating at low-flows.

ConclusionTechnical reasons for the production of head at shutoff, even though the net mass flow across the pump is zero, are provided by Nikkiso Cryo Inc. Depending on the magnitude of the Flow-Factor, FF = Q/Q-BEP; the structure of the flow-streamlines changes and manifest in the establishment of different flow-patterns:

z Pull-and-push when FF is sufficiently large.

z Push-some circulate-some when FF << 1.

z Stalled-zones-only when FF = 0.

Along the entire pump flow-range, one or more of two distinct flow-patterns persist, causing the creation of two distinct head producing processes which, when summed together, produce the overall measured head (H = H1 + H2):

z H1 associated with thru-flow.

z H2 associated with stalled-flow.

The continuously emerging stalled-cells can cause numerical-simulation-convergence and structural instabilities due to large temporal-and-spatial pressure fluctuations within all rotating wheels, mostly concentrated near the inlet portions of the inducer and impellers. Pressure fluctuations persist because the stalled-cells themselves migrate and rotate at about half the pump rotational frequency, thus rendering different portions of blade surfaces ineffective during operation.

Nikkiso Cryo recommends that, for FF < 1/3, pumps do not undergo CFD analysis or continuous operation because rotating stall introduces an additional de-stabilising frequency:

z Primary-flow frequency = RPM.

z Secondary-flow frequency is about RPM/2.

Finally, the complex sequence of events may be constructed as follows:

z Hydrodynamics creates 2 distinct flow patterns.

z Thermodynamics constrains and quantifies the 2 heads.

z Measured head during testing is the sum.

z Additional vibratory frequencies/modes are born when FF < 1/3.

z Conductive heating of the housing becomes active when FF < 1/3.

z DNO when FF < 1/3.