Adopting inclined channel to decline the salinity mixing for rotary energy recovery device:Simulation and optimization

Wenjie Li,Yue Wang,Jie Zhou,Xiaoyu Qiao,Shichang Xu

Tianjin Key Laboratory of Membrane Science and Desalination Technology,State Key Laboratory of Chemical Engineering,School of Chemical Engineering and Technology,Tianjin University,Tianjin 300350,China

Keywords:CFD Inclined channel RERD Salinity mixing

ABSTRACT After years of research,the energy efficiency of energy recovery device has been raised to a high level,but the salinity mixing has not been effectively improved.Mixing will lead to a rise of high-pressure seawater salinity,which will increase the operating cost.In this paper,the computational fluid dynamics (CFD)simulation of the rotary energy recovery device (RERD) is carried out.It is found that the unstable flow caused by the non-parallel between the channel and the flow direction of fluid is an important reason for mixing.After the inclined channel structure is adopted,the non-parallel problem is improved.The formation of unstable flow is effectively controlled.Under the commercial product operating conditions,the volumetric mixing of the optimized device is reduced from 3.34% to 1.29%,showing the effectiveness of the structure.

1.Introduction

In recent years,with the increasingly serious shortage of fresh water,people pay much attention to seawater reverse osmosis(SWRO)[1].As the key equipment to reduce the energy consumption of SWRO system,the energy recovery device(ERD)pressurizes seawater by recovering the pressure of high-pressure brine rejected from the reverse osmosis membrane,and the operating cost of SWRO system is greatly reduced (up to 60%) [2–4].

There are mainly two kinds of energy recovery devices,pistontype and rotary-type in the SWRO system[5].For the rotary energy recovery device (RERD),after years of development,its efficiency and stability have been greatly improved [6–8].But the mixing problem has always troubled designers and users.Due to the existence of solid pistons in the hydraulic cylinder of the piston-type energy recovery device,brine and seawater hardly have any salinity mixing under normal conditions.However,it is not easy to add solid pistons in the RERD.How to reduce mixing based on the simple structure and stable flow of device has become a major direction in the field of RERD research [9,10].

The volumetric mixing Vmis one of the important index that evaluate the performance of RERD.It reflects the mixing degree of RERD,which is related to the structure of the device.Vmis defined as Eq.(1) based on the assumption that high-and lowpressure fluids are equal in flow rates [11].

where SHPsis the salinity of high-pressure seawater (mass fraction of dissolved matter in seawater,the same below),SLPsis the salinity of low-pressure seawater,and SHPbis the salinity of high-pressure brine.

As shown in Fig.1,the mixing causes the salinity increasing of the high-pressure seawater.Before going to the RO membranes,the seawater pressurized by the energy recovery device is mixed with the feed from the high-pressure pump,which increases the salinity of the seawater entering the RO membrane.Osmotic pressure is proportional to the salinity of seawater.In order to ensure constant water production,the high pressure pump must provide a higher pressure,so the energy consumption increases.

For example,the PX-220,a relatively successful RERD on the market,has a volumetric mixing of approximately 6% in the case of balanced flow [12].The salinity of the seawater entering the RO membrane increases about 2.5% with a membrane recovery of 40%.In order to ensure constant water production,additional costs need to be invested,such as providing an additional pressure of 0.13 MPa or increasing the membrane area by 6%[12].Therefore,reducing the mixing of brine and seawater in the energy recovery device is the key to improving the economics for the SWRO system.

Fig.1.Schematic of RO system with RERD.

In order to reduce mixing,the researchers put forward different opinions.The improved idea of Stover et al.is to increase the rotation speed,reduce the flow or extend the length of the rotor[13–15].These improvements have achieved certain results.However,the speed and flow of the self-driving RERD are related to each other,and it is difficult to adjust separately.At the same time,a rotor that is too long can cause the device to become unstable.All of the above limits the optimization of device performance.In addition,to limit non-ideal flow and reduce mixing,Z.Cao et al.proposed to extend the inlet on the endcover at an angle relative to the outlet,and verified it with the particle image velocimetry(PIV) technology,which also achieved certain results [16,17].Liu et al.research the formation and movement of liquid pistons by CFD.It is proved that the rotation speed and flow rate have opposite effects on the mixing process [18].

Fig.2.Structure of RERD.

The paper focuses on a kind of RERD which contains two rotary plates and a stator.The structure is shown in Fig.2.The seawater rotary plate includes two ports,one for inputting low-pressure seawater and one for outputting high-pressure seawater,which are symmetrically distributed.The brine rotary plates also contains two brine ports,a high-pressure input and a low-pressure output.The stator contains twelve axial channels,which are arranged evenly in a circle.The upper and lower rotary plates rotate synchronously,and the channels are connected with the high and low pressure areas respectively in the RERD.The pressurization process is carried out in the high pressure area,the brine transfers the pressure to the seawater and pushes the seawater out of the channel.At the same time,the depressurization process is carried out in the low pressure area,and the seawater pushes the brine out of the channel.A continuous pressure exchange is accomplished with this periodic process.

At any time,half of the channels in the stator are filled with high-pressure fluid and the other are filled with low-pressure fluid.Sealing areas are set between the channels to prevent pressure leakage.

For the traditional RERD,the mixing occurs in the rotating rotor channels,which brings great difficulties to the optimization work.In this paper,rotor is changed to a static structure,and the endcovers are rotated to complete the alternating flow of fluid,which makes it possible to reduce the mixing by optimizing the channel structure.In this paper,a kind of inclined channel structure is proposed to solve the mixing problem of the device,which can further reduce the operating cost of the SWRO system.

2.Theoretical and Numerical Methodologies

2.1.CFD model

Fig.3 shows the three-dimensional geometric model.The model consists of two high-pressure ports and two low-pressure ports,and 12 cylindrical channels with a diameter of 32 mm and a height of 200 mm.Since the gaps between the individual components are tiny,the leakage has no major effect on the mixing.Therefore,this simulation ignores the influence of fitting clearance.

Fig.3.Geometric model.

Solidworks 2016 was used as a geometry generator to construct the geometric model of the fluid computing domain.The computational grid was made in the preprocessor Pointwise 17.3.The quality of the grid was evaluated by orthogonality.The minimum orthogonal quality was 0.45,indicating that the grid quality is acceptable.At the same time,the grid independence test was performed by continuously increasing the number of grids.The specific results are shown in Table 1.It was found that after 3.2 × 105cells,the change in salinity of high-pressure seawater caused by further increase of cells was less than 1%.Therefore,a total cell count of 3.2 × 105was chosen for this simulation.

Table 1 Results of the grid independence

Finally,the mesh was imported into the commercial CFD software Star CCM+11.06 to solving.Stable operation of the iterative solution is guaranteed by adjusting the solution parameters such as the relaxation factor of the solution process.In the process of solving,when the residual value reaches the convergence standard and the physical field is stable,the program is stopped and the results of each monitoring site are recorded.

2.2.Governing equations

In the mathematical simulation of the flow process,the assumptions are as follows:(1) The fluid in simulation is an ideal incompressible fluid.(2) The viscous dissipation is negligible.(3)There is no heat exchange between seawater and brine.

The continuity equation and momentum equation can be described as:

where ν is the velocity vector,ρ is the density,p is the static pressure,τ is the stress tensor,and ρg is the gravitational body force.

The fluid in the channel is mostly turbulent,and the standard kε turbulence model is used.The specific equation is as follows:

In the above equations,μtis the viscosity of the fluid;the model constants σk,σε,c1,c2,and cμ are taken as 1.0,1.3,1.44,1.92,and 0.99 according to reference [19].To solve the mass transfer between the seawater and the brine,the species transport equation of non-reaction is utilized as [16]:

where Yiis the local mass fraction for species i and jiis the mass diffusion flux for species i,which is calculated by Eq.(8):

where Diis the mass diffusion coefficient for species in the mixture,Sctis the turbulent Schmidt number and its default value is 0.7.

2.3.Boundary conditions

Table 2 shows the boundary conditions of the simulation.The initial conditions of the model area are set as follows:the device is filled with low-pressure seawater with a pressure of 0.2 MPa(gauge pressure).The direction of gravity is down along the central axis,the operating temperature is set to 20 °C,and the rotation speed is 600 r﹒min-1.

2.4.Simulation scheme

The calculation of governing equations was performed by STARCCM+11.06.The implicit unsteady and standard k-ε turbulence model are adopted.And the gravitational acceleration is also considered in the simulation.The convection term adopts the secondorder upwind scheme,and the diffusion term adopts the secondorder central difference scheme (default).The time step is set to 0.00027 s,which is approximately equal to the time for the rotor to sweep an azimuth unit.When the residual value drops below 10-4and the salinity of the outlet fluid is stable,the iterative solution process is considered to converge.

3.Model Validation

In order to verify the accuracy of the established model,Xu Enle’s experiment was simulated [19].Xu studied the relationship between the inflow length and the mixing characteristics of the RERD by changing the rotor speed and flow rate.The experimental condition arrangements are listed in Table 3.

Table 2 Boundary conditions of the simulation

Table 3 Experimental conditions arrangement

Fig.4 is the comparison of simulation and experimental results under different rotor speed.From the figure,the curves of simulation and experimental data follow a similar trend,and the relative error range between simulation and experimental data is 5.06%-6.80%.The result makes an acceptable quantitative validation of the simulation model used in this work.

Fig.4.Comparison of simulation and experimental results under different rotor speed.

4.Results and Discussion

4.1.Analysis on mixing

There are two basic forms of mass transfer,molecular diffusion and convective diffusion.Ideally,the distribution of salinity in the RERD channel is linear along the axis from brine to seawater.There is almost no concentration difference in the same height plane.The molecular diffusion and convective diffusion only occur at the regular interface between seawater and brine,so the mixing in the device is not obvious.

However,the actual situation is far from ideal.Fig.5 shows the two-dimensional salinity profile of the cylindrical section of the RERD at the flow rate of 35,000 kg﹒h-1,the rotation speed of 600 r﹒min-1.In the figure,channels 2–6 are located in the depressurization area for depressurization process.Channels 8–12 are located in the pressurization area for pressurization process.Channel 1 and channel 7 are located in the sealed area.During the pressure exchange process,brine with salinity of 5.8% (mass) enters from the top whose color is red and seawater with salinity of 3.6%(mass) enters from the bottom whose color is blue.The rest color represents the mixing section of brine and seawater.It can be seen from the Fig.5,whether it is a pressurization process or a depressurization process,the inflow fluid flows along the right wall and is wedge-shaped flow instead of plug flow.

When the flow field is stabilized,the average value of the fluid salinity at the port does not change with time.It can be known from the simulation result that the salinity of high-pressure seawater is 3.6735%(mass).By integrating the salinity into Eq.(1),it can be known that the volume mixing of the device is 3.34%.

Fig.6 is a velocity vector corresponding to channel 10.Because the channel is in the middle of the pressurization process,its velocity field is typical.The high-pressure brine has a circumferential velocity due to the rotary plate rotation,which is related to the rotation speed and the radial position.As a result,the flow velocity of the fluid entering channel 10 is not parallel to the axis of the channel.Then,the flow direction is forced to change because the flowing fluid is blocked by the wall surface,and the flow velocity distribution is adjusted along the way.

In Fig.6,the fluid forms a wedge-shaped inflow and flows at a high speed on the right side.The mass transfer surface is elongated and the degree of molecular diffusion is enhanced.On the left side,the vortex formed because of the influence of high-speed fluid and intensified the convective diffusion between seawater and brine.

Fig.5.Two-dimensional salinity profile of the RERD.

Fig.6.Velocity vector of channel 10 in RERD.

Fig.7.Streamline and horizontal cross-section velocity field.

Fig.7 is the streamline in channel 10 and the horizontal crosssectional velocity vector at different heights.In this figure,the streamline is in a spiral shape,which is another reason for the intensified RERD mixing.It is similar to the flow in the elbow.When the fluid is flowing,the centrifugal force is proportional to the square of the flow velocity.Since the velocity of the fluid at the right side is large when it enters the channel,the centrifugal force is greater.And the fluid velocity near the left wall is smaller,the centrifugal force is smaller.As a result,the fluid in the highspeed area flows to the low-speed area under the effect of centrifugal force.The fluid in the low-speed area is forced to move along the circumference of the channel wall.A secondary flow is generated on the cross section of the channel and accelerates mass transfer between brine and seawater.

4.2.Inclined channel structure

In order to reduce the salinity mixing in the RERD,an inclined channel design scheme is proposed.The specific structure is shown in Fig.8.Part of the straight channel is changed to an inclined channel.The projection of the inclined channel in the horizontal direction is still the same circle as the straight channel.Its inclination angle is 31°,which is obtained by combining the velocity.

Fig.8.Structure of inclined channel RERD.

The axial velocity of the fluid u1can be obtained from the processing capacity,

where Q is the processing capacity of the device,S is the average connection area between the channel and one port.As the rotary plate rotates,the connection area between the channel and one port will change with time.The Fig.9 shows two possible states.For the convenience of calculation,an average connection area S is required.

The circumferential velocity u2can be obtained from the velocity of rotary plate,

where r is the radius at the center of the channel,and n is the rotation speed of the rotary plate.

The resultant velocity u at the center entrance of the channel is

The resultant velocity direction α is

Put u1,u2into Eq.(12)and get α≈31°.Where Q=35000 kg﹒h-1,S=3177 mm2,r=80 mm,n=600 r﹒min-1.In order to make the direction of the channel the same as the velocity direction,the angle between the channel and the horizontal plane should be designed to be 31°.

It can be calculated from reference [19] that the inflow length is:

When the length of the inclined channel is longer than the length of the inflow,the mixing will reach a minimum.However,a large value of the length of inclined channel may cause manufacturing difficulties.Therefore,the length of the inclined channel in this paper is 30 mm,which is about 1/4 of the inflow length.

It can be known from the simulation of the inclined channel RERD that when the flow field is stable,the salinity of highpressure seawater is 3.6311 wt%.It can be calculated from Eq.(1)that the volume mixing is 1.29%.Fig.10 is the two-dimensional salinity profile of the cylindrical section of the model at the flow rate of 35000 kg﹒h-1,the rotation speed of 600 r﹒min-1.Compared with Fig.5,the interface of brine and seawater in inclined channel is regular,and the flow is similar to the ideal piston flow.The flow gradually deforms until it enters the straight channel section.

Fig.9.The connection area between the channel and one port.

Fig.10.Two-dimensional salinity profile of the inclined channel RERD.

Fig.11 is a velocity vector corresponding to channel 10.The figure shows that the velocity in the inclined channel section is evenly distributed in the radial direction.Although there is still a radial velocity gradient after entering the straight channel section,the degree is greatly reduced.This also means that the mixing between seawater and brine is reduced.

In order to demonstrate the optimization effect,the salinity in channel 1 and channel 7 located in the sealed area is monitored.Channel 1 is located in the low-pressure seal area,and channel 7 is in the high-pressure seal area.When the channel moves to the seal area,the fluid in the channel reaches the maximum inflow length,so it can show the internal mixing more clearly.

Fig.12 is the salinity distributing of channel in the axial.In the figure,the abscissa represents the axial position of the channel.The negative number corresponds to the seawater port side,and the positive number corresponds to the brine port side.The ordinate represents the average salinity of the corresponding cross section.The curve 1#represents the channel 7 salinity of RERD.Due to the defects of the RERD,mixing has already occurred at the top of the channel,so the salinity of the incoming high-pressure brine is monitored below 5.8% (mass).The curve 1 represents the channel 7 salinity of the inclined channel RERD.It shows that the salinity of the high-pressure brine near the brine port is still 5.8%(mass),and the salinity of the high-pressure seawater at the outlet is also lower than the RERD.At the same time,it can also be found that compared with the RERD,the salinity at the inclined channel remains substantially constant.The 2 #,2 curves corresponding to channel 1 show the same results.This shows that the inclined channel RERD mixing situation is better than the RERD.The fluctuation on the curve is due to the calculated fluctuation at the junction of the inclined channel and the straight channel.

Fig.11.Velocity vector of channel 10 in inclined channel RERD.

Fig.12.Salinity distributing of channel (1:channel 7 salinity of the inclined channel RERD.2:channel 1 salinity of the inclined channel RERD.1:channel 7 salinity of RERD.2:channel 1 salinity of RERD.).

5.Conclusions

A three-dimensional unsteady sliding grid model of the rotary energy recovery device is established,and the mass transfer in the channel is simulated by the computational fluid dynamics.

Firstly,according to the simulation results,the wedge-shaped inflow,vortex and the secondary flow are generated due to the angle between the velocity direction of the fluid and the channel direction.Unstable flow patterns result in increased mixing.

Secondly,a unique inclined channel structure is proposed to make the direction of the channel consistent with the direction of inflow.And the mixing degree of the device is reduced from 3.34% to 1.29%,a drop of 61.4%.This research provides a new idea for the design of the rotary energy recovery device,which helps to further improve the performance of the device and reduce the energy consumption of the seawater reverse osmosis system.

The influence of the inclined channel length on the mixing degree is not discussed in this paper,which will be studied in the future.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work is supported by the National Key Research and Development Program of China (2017YFC0403800) and the State Key Laboratory of Chemical Engineering (SKL-ChE-17T02).

Nomenclature

cμ model constant

c1model constant

c2model constant

Dimass diffusion coefficient for species in the mixture

jimass diffusion caused by the concentration gradient

m number of channels communicating with a port

n rotation speed of the rotary plate,r﹒min-1

p static pressure,Pa

Q processing capacity of the device,m3

r radius at the center of the channel,m

S average connection area,m2

Sctturbulent Schmidt number

SHPbsalinity of high-pressure brine

SHPssalinity of high-pressure seawater

SLPssalinity of low-pressure seawater

u1axial velocity of the fluid,m﹒s-1

u2circumferential velocity,m﹒s-1

Vmvolumetric mixing

Yilocal mass fraction of species i

α velocity direction

β correction factor

?tviscosity of the fluid,Pa﹒s

ν velocity vector

ρ density,kg﹒m-3

σεmodel constant

σkmodel constant

τ stress tensor,Pa