F rom production to transportation and into consumption, reliable pumps are needed to transfer cryogenic liquid along the LNG supply and demand journey. In the production phase,

gas is captured and liquefied near the production site. The LNG is then transferred to and from carrying vessels as it is transported near the consumption site. Upon arrival, the LNG is transferred, stored, regasified and distributed to the end-user.

Depending on the applicable pumping needs, different models are utilised to satisfy varying operating requirements. However, regardless of the application, the basic function of the pump is to capture a desired quantity of liquid (Q) and increase its static pressure or produce a required head (H). In centrifugal pumps, a rise in pressure is produced via a

rotating assembly, driven a by submerged electric motor. Motor action causes the assembly to rotate at a particular frequency (f1), thus enabling the rotating blades to pull flow from an inlet port and deliver it into a discharge port. Cryogenic pumps are vertically-oriented, but are presented horizontally in this article for clarity of explanation.

In the field, however, pumps may operate at flows below the supplier’s recommended minimum; an event that causes the formation of secondary vortex structure called ‘rotating stall’. Rotating stall consists of stalled flow cells, which form due to flow separation off the suction-sides of the rotating blades. Once formed, they rotate, but at a slower frequency (f2). This article reveals the fluid dynamics of rotating stall, with an emphasis on what happens at shut-off; the zero-flow point where normal through-flow ceases, and the mechanism for producing pressure is switched to be entirely due to a rotating vortex structure.

Vital frequenciesA device can produce lift if a frequency is present while carrying out the required motion.

Yousef Jarrah and Motoyasu Ogawa, Nikkiso Cryo Inc., USA and Japan, reveal the fluid dynamics of rotating stall in LNG pumps.

FLUID FLOWS

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This requirement is essential regardless of the motion type (rotary or linear), moving surface elasticity (rigid or flexible) and fluid type. Examples include centrifugal compressors and reciprocating pumps, where producing lift can only be maintained if a frequency is present. Furthermore, the device’s ability to produce pressure improves when additional frequencies are introduced – provided that all present frequencies act in a coordinated manner.

When two discrete frequencies (f1 and f2), one due to normal fluid motion (f1) and one due to secondary vortex structure (f2), are present and carried out in a simultaneous and coordinated manner, free lift or additional pressure rise can be produced. The hovering agility of hummingbirds and the V-shaped formation of

flying pelicans are two examples. When flying at high angle of attack, instead of stalling (because airflow over the wing tends to separate from the surface), the hummingbird’s wing flapping generates a leading edge vortex (LEV) structure, which enhances the production of lift. In fact, a hummingbird develops approximately 25% of lift during upstroke (wings move backward) and 75% during downstroke (wings move forward), the additional lift during downstroke is due to LEV.

During migration, pelicans fly in V-shaped formation so that each trailing bird can benefit from a rotating vortex generated at the wingtips of the bird in front of it. While the flow directly behind the leading bird is pushing down, the flow behind its wingtips is pushing upwards, thus adding free-lift to the trailing bird. The trailing bird flapping frequency (f1) is lower than that of the front bird because additional lift is produced by the incoming tip vortex (with frequency f2).

But sometimes the birth of additional frequencies can lead to undesired product behaviour. When flow is reduced in centrifugal gas compressors, for example, the compressor surges and loses its ability to produce unique pressure-rise. Instead of having organised stall (weak instability), surge (severe and random instability) occurs, causing strong pressure fluctuations.

The instability in centrifugal pumps, which consists of rotating stalled cells with unique frequency, is

Figure 1: Normal-Flow thru 15-stage cryogenic pump

Motor

Shaft (Rotational Frequency f1)

ImpellerInducer

Figure 2: Stalled-Flow-Zones within rotating components of 2-stage pump

Stalled-Flow-ZonesShaft Frequency = f1 Rotating-Stall Frequency = f2

Figure 5: Model 60731 measurements within stationary diffuser vanes

Pressure Fluctuations

Decreasing Flow

ShaftDisplacement

Stall zone formed at reduced flow (due to large incidence)

Figure 1. Normal flow through a 15-stage cryogenic pump.

Figure 2. Stalled flow zones within the rotating components of a two-stage pump.

Figure 3. Model 60731 measurements within stationary diffuser vanes.

coordinated with normal flow operation. When flow is reduced; the pump continues to produce useful pressure rise, even when both flow and efficiency are zero. Two pressure fields with two unique frequencies, one due to primary flow activity (f1) and one due to secondary flow activity (f2), coexist, and the transition from one to the other is highly organised.

Coherent instabilityIn centrifugal pumps, the mechanism of creating and maintaining the stalled cell structure is not only coherent and predictable, but also has advantages and disadvantages. The onset of the process depends on the magnitude of the flow factor (FF), which is defined as the ratio of delivered flow to best efficiency point (BEP) flow: FF = Q / Q-BEP.

Rotating stall forms whenever FF is less than one-third and has the following properties:

n Rotates in the same direction as the wheels. n Rotates at a reduced f2 frequency. n Occupies up to 50% of flow passages. n Migrates.

The first and second of the properties listed above give rise to additional pressure patterns that can cause increased lateral displacements of the rotating assembly. Instead of having a single fundamental frequency (f1), dual frequencies coexist, with f2 equal to approximately f1/2. This structurally destabilising effect can cause excessive pressure

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pulsations and is responsible for nearly one-third of all pump failures.

The third and fourth properties cause spatial and temporal pressure fluctuations as different blade-sections are blocked and rendered ineffective during operation. The cells are not localised. Instead, besides rotating circumferentially, they also move radially and axially. Because the stalled zones change location within the rotating blades, the total effective percentage of blade surfaces is continuously varying. This is why the pump head obtained when reducing flow is not the same as the head obtained when increasing flow. As time passes, the cells move to occupy different locations.

The pump’s ability to produce pressure is not hindered by a stall occurring as the flow is reduced. In fact, the pressure rise increases as the flow is reduced towards shutoff, even while the efficiency is also decreasing towards zero. The reason why stalled flow yields increased pressure rise is rooted in fundamental physics. The birth of an additional coherent frequency (f2) due to rotating stall enables the production of additional pressure. This is why pressure rise is higher

with stall than without it. When two frequencies are present, the pump produces more pressure rise than when only one fundamental frequency (f1) is present.

Initiating mechanismThe rotating blades of a centrifugal pump pull the liquid from an inlet port, increase its static pressure along internal travel pathways, and deliver it into a discharge port. At large FF values (when FF is greater than one-third), pump function is normal and flow separation is not possible anywhere along the liquid pathways (Figure 1).

But when the flow is reduced (when FF is less than one-third), stall cells begin to form. Figures 2 and 3 show where stall cells may reside. When formed inside a rotating component, the cells rotate in the direction of rotation (relative to a stationary part or against the direction of rotation relative to the moving blade) at approximately half the motor speed.

Stall occurs when the incidence angle is relatively large. As shown in Figures 4 and 5, the incidence angle is near zero at BEP flow, becoming larger towards shutoff and smaller towards maximum flow. Along the entire flow range, a redistribution of the three kinetic energies occurs due to changes in blade velocity (U), absolute flow velocity (C), and relative-flow velocity (W); such that each combination produces unique pressure rise.

Vectorially, in Figure 4, the absolute velocity is the sum of relative and blade velocities (C = W + U). Under normal operation, the flow enters the

impeller and leaves in an orderly fashion. But as the flow is reduced (C becoming smaller), it cannot turn around the leading edge. Instead, the flow separates off the suction side as shown and a stall zone is formed.

Case studyWhile flow stalling does not hinder the pump’s ability to produce pressure rise, it can create increased vibrations, even when stall occurs within a stationary diffuser (Figure 3). Measurements made within diffuser vanes for pump model 60731 show that as the flow is reduced, the onset of stall begins and creates increased pressure pulsations which, in turn, cause increased shaft displacements.

The same response (pressure fluctuations and shaft vibrations causing shaft bearings wear in a relatively short time) was observed when different diffuser vane shapes were tested. The sequence of events starts with operating at low flow, rendering the incidence angle large. Large incidence causes flow separation downstream of the blade leading edge. Flow separation creates secondary vortex structure which acts on blade

Figure 4: Model 60882 performance with impeller leading edge incidence profile

0

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0 100 200 300 400 500 600 700 800 900 1000 1100

I = + 13

I = - 7

I = 0

Flow (Q, m3/h)

Head(H, m) I = - 5

I = - 12

I = + 5

Shutoff, I = + 25 degreesRotating stall concentrated at LE

1-Stage @ 60 HzI = Difference between flow and blade anglesBlade angle measured at mean radii+ I means flow strikes the blade pressure-side

Figure 5. Model 60882 performance with impeller leading edge incidence profile.

Figure 3: Impeller rotating CCW with inlet and outlet velocities

U2

W2C2

U1 U1

C1

W1

W1C1

I

Normal operationIncidence angle (I) near 0 degrees

Low-Flow operationIncidence angle >> 0

Stall Zone

Figure 4. Impeller rotating counter clockwise with inlet and outlet velocities.

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surfaces to create an alternating force field via a varying pressure profile. Pressure forces are then transmitted into the rotating assembly, potentially causing bearings damage and/or thrust imbalances.

The absolute flow velocity component (C) is due to mass flow approaching the impeller leading edge (Figures 4 and 5). It should be large at large flows, small at low flows, and zero at shutoff. But complete elimination of C is not technically correct, even when through-flow across the pump is exactly zero. C may not be zero even at shutoff due to the coexistence of two flow structures; primary where C is zero and secondary where C is not zero.

Primary action pressurises and delivers liquid throughout and into the discharge port. Exactly at shutoff, the primary flow ceases and its associated absolute velocity (C) is zero. However, secondary action, which produces pressure via circulation near the leading edge of rotating wheels, needs a finite absolute velocity to be maintained. Therefore, at shutoff, the primary flow is off but the secondary flow is on.

Consider the normal primary flow in Figure 4, where the flow enters at the impeller leading edge (station 1) and leaves at the impeller trailing edge (station 2). At shutoff, C1 = C2 = 0, U1 and W1 become equal (but opposite in direction), and U2 and W2 become equal (but opposite in direction). Thus, the net head becomes zero (head due to increased wheel-speed kinetic energy exactly cancels the head due to reduction in relative-flow kinetic energy). At shutoff, the normal process for producing pressure is completely off and the associated absolute flow velocity is zero.

But the absolute flow velocity associated with the secondary flow may not be near zero. Secondary flow circulation is localised – it occurs near the leading edges of all rotating components. The stall penetration depth (or stall zone extent) from the impeller leading edge towards the trailing edge depends on the value of FF.

At shutoff, the secondary circulation becomes concentrated near the leading edge where a fully circular flow pattern is established. The absolute flow velocity (C) enters the leading edge at small radii near the hub, makes a 180° turn just downstream of the leading edge, leaves at large radii (near the inlet shroud), and makes another 180° turn to re-enter at the same small radii. The 360° circulation process goes on, with the vortex pattern rotating (at f2), creating its unique pressure rise.

ConclusionsDue to the additional frequency associated with highly organised rotating stall, additional pressure rise is produced as the flow of centrifugal pumps is reduced. Rotating stall offers a hydrodynamic benefit because it enables the orderly production of pressure, all the way to shutoff, without discontinuity in the performance curve (Figure 5). But, rotating stall can also be structurally destabilising because interactions between the fundamental and secondary frequencies may increase the rotating assembly’s lateral displacements.

At shutoff, primary through-flow activity ceases and is replaced by rotary vortex structure that is concentrated near the leading edges of the rotating wheels. With two active and coordinated frequencies (f1 and f2), additional pressure rise is produced.