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Dean Flow

The phenomenon of Dean Flow was first brought up by W. R. Dean who studied the secondary flow created by the motion of fluid in a curved pipe.  His study shows that flow in a curved channel appears unstable for small disturbances, as compared with a sudden increase in the loss of head when flow passes through a straight pipe at the critical velocity (i.e. the transition between laminar and turbulent flow).  No such sudden increase in the loss of head has ever been observed in a curved pipe even though the flow velocity is much higher than the critical velocity.  This phenomenon suggests that the pressure drop is much smaller in a curved pipe than in a straight pipe at the critical velocity. This unstable flow in a curved channel has been characterized as double-vortex flow, as shown in the accompanied figure. The Dean Number, K, is the characteristic parameter used to describe the conditions of the


formation of vortices in this situation: where v is the tangential velocity of the fluid, d is the diameter of the pipe, R is the radius of the pipe curvature, and is the kinematic viscosity of the fluid. The higher the Dean Number is, the stronger the vortices are.

The incorporation of Dean Flow in filtration creates the following advantages,

  • Minimizes uneven fouling commonly seen in conventional cross-flow filtration -- Because the pressure drop from the feed inlet to the outlet, more fouling tends to occur at the inlet end, which has a higher trans-membrane pressure drop than is present at the outlet end.  Since the feed flow has the highest tangential velocity at the inlet, this means that the vortices are the strongest at the inlet end. This feature can compensate for the higher fouling at the inlet end of the cross-flow filtration.


  • Minimizes concentration polarization in membrane filtration -- Concentration  polarization is a phenomenon commonly found in a membrane separation process, in which the non-permeating or slowly permeating components in the solution (feed flow) accumulate adjacent to the membrane surface, elevating osmotic pressure above that which would exist in the absence of polarization. The effect of concentration polarization is to reduce the membrane flux rate and its selectivity.  The existing Dean Flow will remove and transport these non-permeating or slowly permeating components from the membrane surface (boundary layer) to the mainstream (bulk fluid) and thus minimize the effect of concentration polarization.

Test Filter of Dean Flow in Seawater.png
  • Lower energy consumption for fouling control -- A common practice to reduce contaminants from depositing onto the filter surface is to boost turbulent flow by roughening the feed channel; methods such as laying screens, building helical bumps, etc. have been deployed. Compared to eddy currents created from turbulence that vigorously dissipate energy, Dean Flow is a much more gentle and effective method for fouling control. The energy is reduced due to thinner boundary layer, and thus lower the trans-membrane pressure. 

FSI has been taking advantage of Dean Flow in their filter design through the years.  Their first-generation Dean Flow filter was developed for seawater RO pretreatment through an SBIR (OSD98-042; titled A Self-Cleaning Filtration System for Pretreatment of Reverse Osmosis Filtration).  A similar filter has also been developed for fuel purification through a different SBIR (N99-086; titled An Automatically Self-Cleaning 5 Micron Fuel Oil Filter). In the first-generation design, the Dean Flow was incorporated with other technologies to form a self-cleaning filtration system dubbed CCDB (Centrifugal, Cross-flow, Dean Flow and Back-wash). The CCDB system utilized commercial-off-the-shelf (COTS) cartridge filters. 

Test Filter of Dean Flow in Diesel Fuel-

The first photo shows that a test cartridge that has been used with a spiral guide for seawater filtration (see the figure below for the spiral guide). The top one third of the spiral guide was purposely machined out so there was no Dean Flow Effect. The result shows that a thin film of contaminants has adsorbed to the top one third of the filter surface.  The lower two thirds of the filter were kept clean due to the Dean Flow effect. A similar test was performed for marine diesel fuel loaded with solids contaminants. The test result is shown in the second photo.

The development of Dean Flow was successful in both projects and the test results proved its effectiveness in both applications. Compared to conventional cartridge filters deployed in dead-end filtration, the service life for the same cartridge filter can be typically extended 5 to 10 times (depending on contaminants loading and operating conditions) under the same application when utilizing cross-flow and Dean Flow technologies. Under the Navy SBIR, an advanced fuel filtration system was developed to replace the Navy shipboard centrifugal fuel purifier, which is a high maintenance and high operating cost item. Following a successful land-based testing performed in a shipyard, a full-size prototype was installed onboard a Navy destroyer for shipboard testing. The 20-month shipboard testing, including a 9-month major deployment, was completed in 2005. Based on a favorable return on investment (ROI) analysis, an SCD (Ship Change Document) was approved by Naval Sea Systems Command to replace centrifugal purifiers onboard DDGs.

Second-generation Dean Flow Filter

Due to performance advantages and the fallen costs, membrane filtration has made much progress in the past several decades. RO has been commoditized for desalination and brackish water treatment.  UF and MF have found more usage in various applications and the value of the processed fluid is no longer a dominant measurement of the adequacy of an application of UF /MF. As a matter of fact, they are now commonly used for wastewater treatment.  

The first-generation Dean Flow filter was developed for use with cartridge filters, which have pore size limited to roughly 0.5 to 1 µm (nominal pore rating).  To further improve filtrate quality and packing ratio (filter area in a given volume), a second-generation Dean Flow filter which takes advantage of modern tubular membrane filters (TMF) as well as hollow fiber membranes have been developed by FSI as
coiled membrane filters (CMF). See the figure with a coiled membrane. This second-generation filter not only covers all previous applications under the first-generation filter, but also expands its service to UF/MF as shown in the filtration spectrum. As an example, it is unlikely for the filtrate from cartridge filters to achieve an SDI 15  (Silt Density Index based on 15 minutes, ASTM D4189) less than 3 in most situations (either for surface water treatment or for industrial wastewater treatment). And, a feed with SDI 15 less than 3 is often required by RO filter suppliers to warrent a service life. The 0.02 to 0.05 µm CMF from FSI has proven that it can consistantly meet the requirement. Often, the SDI 15 can be less than 1 and the turbidity is less than 0.1 NTU. 

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Dean Flow in CMF.png
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