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APRIL 2012 HydrocarbonProcessing.comciency degradation is summarized in Fig. 1B, as a function of the vapor-volume fraction in the liquid. In Fig. 2, an eight-stage cen-trifugal pump was operated in reverse and a hydrocarbon mixture was flashed through the machine. The turbine outlet fluid had 35% vapor volume. The measured efficiency is five points lower than with a single-phase nonflashing liquid.
Due to performance deteriorations, the radial-inflow centrifu-gal turbine was abandoned by the turbomachinery community for use with flashing liquids. It was correctly reasoned that the centrifugal field, which is the functioning basis for radial-inflow turbines, acts as a centrifugal separator between liquid and vapor.
Such action leads to poor efficiency as the vapor-volume fraction increases at the impeller inlet. An upper limit of near 0 is set on the amount of vapor that can be flashed before the flow enters the cen-trifugal impeller. From a design perspective, this can be reviewed in
the example P vs. h diagram of Fig. 3. For example, a 0.5 degree of reaction is assumed for the centrifugal turbine, although this could easily be lower for greater enthalpy drop in the nozzles. If vapor forms in the nozzle before entering the impeller, then efficiency deteriorates and vibration levels rise. This is due to the centrifugal separator effect, as the vapor and liquid have different densities.
The radial-pressure gradient acts on each phase with dP/dr = V2/r where P is the pressure, r is the radius, is the density and V is the tangential velocity. If the liquid begins to flash well inside the turbine impeller near the turbine outlet and not in the nozzle, then satisfactory performance for very low-vapor-content liquids can be achieved by the centrifugal turbine. The centrifugal field is not as strong near the impeller outlet. However, vibrations will still be problematic due to flashing liquid in the rotating impeller.
The poor performance and high vibrations caused by flashing liquids in radial-inflow centrifugal turbines were the motivation for NASA and the Jet Propulsion Laboratory (JPL) to embark on developing a new way to expand flashing liquids. The driving application was a magnetohydrodynamic power system project.5 The flashing liquid turbine methodology applied at JPL was a linear nozzle expansion of the flashing liquid flow, avoiding curvature and ensuring close coupling between the expanding vapor and liquid droplets. This method proved highly successful; it produced the maximum conversion of available enthalpy drop to the nozzle out-let kinetic energy. The successful nozzle design was applied to a pure axial-impulse turbine impeller. The new style of turbine, as shown in Fig. 4, was an axial-impulse turbine, similar to an axial cross-flow impulse turbine or even similar to a Pelton style impulse turbine.6 Simple physics. In a radial-inflow centrifugal turbine, any flashing liquid flow will be separated by a centrifugal field into liquid and vapor. This is the basic functioning principle of a centrifugal separator or a centrifuge. The heavier liquid is slung outward, while the lighter vapor passes inward and a sizable recir-culation pattern is formed within the liquid-vapor mixture. This causes substantial mixing losses and efficiency degradation. Fur-thermore, the liquid droplets in the liquid-vapor mixture are large and uncontrolled in size. This has the consequences to generate entropy by flow and contribute to total flow losses. The simple slip velocity of a liquid droplet in a vapor stream is given by:
Vs = Vv – Vl
where Vs is the slip velocity Vv is the vapor velocity Vl is the liquid droplet velocity.
A larger slip velocity logically leads to larger entropy losses due to friction, wakes and mixing.7 Entropy losses will always be gener-ated due to the interphase exchange process of mass, momentum and heat transfer due to the phase change occurring from liquid to vapor. A low slip velocity will reduce these losses and lead to the highest efficiency during the flashing process. The size of the liquid droplets during flashing can be determined by examining a force balance between the two forces acting on the liquid droplet. These forces include drag force, due to the slip velocity, and buoyancy, due to the pressure gradient in the flow. In the Lagrangian reference frame (the frame moving with the particle), the force balance is:8
(Dynamic pressure of relative gas flow) (Drag coefficient)
(Frontal area of droplet)
(Volume of droplet) (Pressure gradient) = (Mass of droplet) (Droplet acceleration)
Turbine efficiency,
0.04 0.06 0.08 0.10 0.12
Flow coefficient,
Turbine efficiency vs. flowrate coefficient as measured on an eight-stage radial-inflow centrifugal turbine.
FIG. 2
Efficiency,Efficiency, TP/SPL–––TP SPL
0.0 0.1 0.2 0.3 0.4
Void fraction, z 1.0 bar back pressure
3.45 bar back pressure 5.9 bar back pressure 7.85 bar back pressure
Efficiency and energy correction factors due to vapor in a radial inflow centrifugal turbine. For a vapor-volume fraction of 30%, the 20 points decrease in efficiency from 1 to 0.8 can be seen.4
FIG. 1B
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75(0.5vVs2) (Cd) (πD2/4) – (πD3/6) (dP/dx) = (lπD3/6) (Vl dVl/dx)
Vs2 = 4D[l(Vl dVl/dx) + (dP/dx)]/(3vCd) where v is the vapor density
Cd is the drag coefficient along a linear direction x
l is the liquid density P is the pressure
D is the liquid droplet diameter.
The final equation shows that larger droplet diameters lead to a larger slip velocity and larger efficiency losses. When expanding a liquid to vapor through a turbine, large droplet diameters should be avoided to achieve the highest efficiency. This is the motiva-tion for a controlled linear acceleramotiva-tion of the flashing liquid, to provide a fine small-diameter uniformly distributed mist that has a small slip velocity. Curvature of the flashing flow must be avoided to ensure that the vapor mist is uniformly formed and distributed.
During a controlled linear acceleration of the flashing liquid, the maximum droplet diameter can be found from the Weber number (We). We is proportional to the ratio of the pressure force breaking up the liquid droplets to the surface tension force holding the drops together:
We = vD(Vv – Vl)2/2
where is the surface tension. Based on several experimental data sets in the literature, setting We equal to 6 for liquid droplet breakup is appropriate in linear acceleration nozzles.6,8 This gives a maximum liquid droplet diameter of:
Dmax = 12/vVs2
Example. If we take the following values for a methane-rich hydrocarbon flashing liquid at a nozzle exit, the representative values of = 0.013 N/m, v = 3.5 kg/m3, Vs = 60 m/s give Dmax = 12.4 m as the largest liquid droplet size during a controlled linear acceleration of the flashing flow. This is a very small diameter-sized mist, which is dispersed in the vapor to make up the liquid-vapor mixture. Large liquid droplets, or larger liquid slugs and plugs, are avoided with the linear acceleration of the flow in linear nozzles.
It has been suggested that there is a delay during flashing of a liquid to a vapor in the turbine so that a 50% degree of reaction, radial inflow centrifugal turbine may not have quite the amount of vapor predicted by a P vs. h equilibrium diagram (Fig. 3).
However, measurements with flashing hydrocarbons in short two-phase nozzles have shown that an almost equilibrium expan-sion does occur.
Mathematical models in the literature also tend to confirm that the time taken for the liquid to flash is equal to or less than the time it takes for the fluid to pass through the turbine. An almost equilibrium behavior is found during the flashing.9–11 There is very little measureable time delay, and the flashing of the liquid occurs practically instantaneously per the P vs. h diagram.
Fig. 5 shows a flashing hydrocarbon liquid-vapor jet exiting from a 100 mm-length linear nozzle. In this example, the mea-sured expansion efficiency of 92% agreed with the computed equilibrium expansion of the flashing liquid, which is proof of the near instantaneous flashing. Furthermore, in most flashing liquid-expander applications, some vapor is present in the liquid upstream of the turbine. Thus, the entire turbine must function with both liquid and vapor present. Even if there were a sizable delay and no liquid flashing through the turbine, then the turbine would merely
be a liquid turbine without gaining the additional enthalpy drop and power from the expansion of the flashing liquid into vapor.
Axial-impulse turbine. An axial-impulse turbine design that uses linear nozzles to flash a liquid to vapor has several advantages:
• Avoiding a centrifugal field that separates the flashing liquid and vapor phases
• No curvature of the flashing flow in the nozzles, which avoids separating the phases.
Fig. 6 is an example of a linear nozzle. In an axial-impulse tur-bine, the inlet liquid undergoes a controlled linear expansion in the nozzle and forms a flashing liquid-vapor mixture. This controlled expansion forms a fine mist of droplets that has a low slip velocity
0.16 xv
Typical P vs. h diagram for a single-stage radial-inflow centrifugal turbine during a liquid to vapor, flashing expansion with a hydrocarbon liquid.
FIG. 3
Impeller blades
Vapor Liquid Nozzle Two-phase jet from nozzle
Sketch of a vapor-liquid axial jet flow exiting the nozzle and entering an axial-impulse impeller blade.
Above right: A titanium axial-impulse impeller produces 1 MW of power. Below: Visualization of a flashing liquid mixture as it passes through an axial impulse impeller.
FIG. 4
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APRIL 2012 HydrocarbonProcessing.comand high efficiency nozzle. These findings were verified by NASA, JPL and Caltech by experimental testing and development.6 In the axial-impulse turbine, the impeller is an impulse style so there is no pressure or enthalpy drop across the impeller, only across the nozzles. The impeller can be manufactured from hard, lightweight titanium, which, together with impact velocities, is well-below the erosion threshold. This design eliminates any erosion that droplet impact could cause. Titanium impellers are commonplace in the turboexpander industry, with a long history of success.
Existing axial-impulse turbine designs. Over 100 axial-impulse style flashing liquid turbines have been in service for 30 years. Examples include in refrigeration chillers.12 The power levels are only at 20 kW to 55 kW in these chillers. Larger axial-impulse flashing liquid turbines are found operating in geothermal applications including units at 800 kW and 1.6 MW power levels.13 Ten other axial-impulse turbines for flashing liquids are found in the oil and gas industry, with sizes ranging from 20 kW to 100 kW.13
From a new construction point of view, Fig. 7 is a new 1-MW axial-impulse turbine for a flashing hydrocarbon liquid application now under commission. The design features an axial-impulse impel-ler with 10 nozzles to flash a liquid hydrocarbon. The generator is an external air-cooled type. The single-stage design keeps the unit axially compact to ensure stable rotordynamics and low vibrations.
Options. The research and development work done in the 1980s by several large turbomachinery manufacturers revealed that radial-inflow centrifugal turbines are not suitable for handling flashing liquid flows when the vapor volume fraction at the
tur-bine outlet is greater than 10%. The work by NASA and JPL has shown that axial-impulse turbines, which don’t use a centrifugal field for power transfer can achieve reasonable efficiency when liquid is flashed through the turbine. Axial-impulse turbines are known to have reduced vibration levels compared to the radial-inflow centrifugal turbines when a liquid is flashed. This has consequences for bearings and seals, as the reduced vibrations promote reliability and a longer service life. HP
LITERATURE CITED
1 Dipippo, R., “Ideal Thermal Efficiency for Geothermal Binary Plants,”
Geothermics—International Journal of Geothermal Research and its Applications, Vol. 36, pp. 276–285, 2007.
2 Hahn, P., et al.,“Application of a Flashing Liquid Expander to Enhance LNG Production,” LNG-15 Conference Poster Presentation, Barcelona, April 2007.
3 Apfelbacher, R., C. Hamkins, H. Jeske and O. Schuster, “Kreiselpumpen in Turbinenbetrieb bei Zweiphasen-Strömungen,” KSB Technische Berichte, Vol.
26, pp. 20–28, 1989.
4 Gülich, J., “Energierückgewinnung mit Pumpen in Turbinenbetrieb bei Expansion von Zweiphasengemischen,” Sulzer Technical Review, Vol. 3, pp.
87–91, 1981.
5 Gülich, J., “Kreiselpumpen: Handbuch für Entwicklung, Anlagenplanung und Betrieb,” Springer Verlag, Heidelberg, 2010.
6 Elliott, D. G., D. J. Ceromo and E. Weinberg, “Liquid-Metal MHD Power Conversion,” Space Power Systems Engineering, Academic Press Inc., pp.
1275–1297, 1966.
7 Elliott, D. G., Theory and Tests of Two-Phase Turbines, JPL Publication 81-105, DOE/ER-10614-1, Jet Propulsion Laboratory, Pasadena, California, 1982.
8 Young, J. B., “The Fundamental Equations of Gas-Droplet Multiphase Flow,”
International Journal of Multiphase Flow, Vol. 21, No. 2, pp. 175–191, 1995.
9 Elliott, D. G., and E. Weinberg, Acceleration of Liquid in Two-Phase Nozzles, JPL Publication 32-987, Jet Propulsion Laboratory, Pasadena, California, 1968.
10 Gopalakrishnan, S., “Power Recovery Turbines for the Process Industry,”
Proceedings of the Third International Pump Symposium, Houston, 1986.
11 Grison, P. and J. F. Lauro, “Biland es études de Thermohydraulique des Pompes Primaries de Reacteurs PWR,” La Houille Blanche 7/8, 1982.
12 Payvar, P., “Mass transfer-controlled bubble growth during rapid decompres-sion of a liquid,” International Journal of Heat Mass Transfer, Vol. 3.0, No. 4, 1987, pp. 99–706, 1987.
13 Hays, L. G. and J. J. Brasz, “Two-phase flow turbines as stand-alone throttle replacment units in large 2000–5000 ton centrifugal chiller installations,”
Proceedings of the 1998 International Compressor Engineering Conference, Purdue, Vol. 2, pp. 797–802.
14 Hays, L. G., “History and Overview of Two-Phase Flow Turbines,”
C542/082/99, IMechE International Conference on Compressors and Their Systems, Sept. 13–15, 1999, City University, London, UK, pp. 159–168.
Hydrocarbon-liquid flashing expansion at the outlet of a linear nozzle with no curvature. There is a fine mist in the expansion due to the high nozzle efficiency.
FIG. 5
The linear 1D nozzle design linearly accelerates the flashing liquid before the flow enters the axial flow impeller. Curvature is avoided to ensure a fine well-dispersed mist flow, as seen in Fig. 5.
FIG. 6
New 1-MW flashing liquid expander being commissioned using, hydrocarbon flashing liquid.
FIG. 7
Dr. Kevin Kaupert is the director of technology at OC Tur-boexpanders. He holds a doctorate in turbomachinery engineering from the ETH Zurich Swiss Federal Institute of Technology. He has over 25 years of experience in turbomachinery for cryogenics, power generation and aerospace applications.
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