Research on Duct Flow Field Optimisation of a Robot Vacuum Cleaner

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1 Interntionl ournl of Advnced Robotic Systems ARTICLE Reserch on Duct Flow Field Optimistion of Robot Vcuum Clener Regulr Pper Xio-bo Li 1 Hi-shun Wng 1* nd Hu-shn Liu 2 1 College of Informtion Technology Zhejing Chinese Medicl University Chin 2 College of Informtion Science nd Technology Donghu University Chin *Corresponding uthor e-mil: shopo@zjtcm.net Received 21 Sep 2011; Accepted 17 Nov Li et l.; licensee InTech. This is n open ccess rticle distributed under the terms of the Cretive Commons Attribution License ( which permits unrestricted use distribution nd reproduction in ny medium provided the originl work is properly cited. Abstrct The duct of robot vcuum clener is the length of the flow chnnel between the inlet of the rolling brush blower nd the outlet of the vcuum blower. To cope with the pressure drop problem of the duct flow field in robot vcuum clener method bsed on Pressure Implicit with Splitting of Opertors (PRISO) lgorithm is introduced nd the optimistion design of the duct flow field is implemented. Firstly the duct structure in robot vcuum clener is tken s reserch object with the computtionl fluid dynmics (CFD) theories dopted; three dimensionl fluid model of the duct is estblished by mens of the FLUENT solver of the CFD softwre. Secondly with the k ε turbulence model of threedimensionl incompressible fluid considered nd the PRISO pressure modifiction lgorithm employed the flow field numericl simultions inside the duct of the robot vcuum clener re crried out. Then the velocity vector plots on the rbitrry plne of the duct flow field re obtined. Finlly n investigtion of the dynmic chrcteristics of the duct flow field is done nd defects of the originl duct flow field re nlysed the optimistion of the originl flow field hs then been conducted. Experimentl results show tht the duct flow field fter optimistion cn effectively reduce pressure drop the fesibility s well s the correctness of the theoreticl modelling nd optimistion pproches re vlidted. Keywords robot vcuum clener duct flow field optimistion CFD pressure loss modeling 1. Introduction It is known tht household clening is series of repeted nd tedious mnul tsks crried out by thousnds of people every dy. Hence in the ge of rpid developments in science nd technologies how to pply these high tech chievements to reduce the intensity of lbour nd improve qulity of life is n importnt issue tht should be solved by reserchers. In recent yers utonomous mobile robots hve come under the spotlight of mny reserchers [ ]. In the twenty first century the successful development of the robot vcuum clener hs mde possible clening the floor utomticlly. However the pressure drop of the duct inside the robot vcuum clener hs significnt influence on clening efficiency. Therefore how to optimise the duct flow field inside the robot vcuum clener hs become prticulrly importnt. The duct of the robot vcuum clener is the length of the flow chnnel between the inlet of the rolling brush blower nd the outlet of the vcuum blower which lso includes the dust continer nd other intermediries. It hs Int Xio-bo Adv Robotic Li Hi-shun Sy 2011 Wng Vol. nd 8 No. Hu-shn Liu: Reserch on Duct Flow Field Optimistion of Robot Vcuum Clener 104

2 significnt impct on the fluid dynmics performnce of the entire duct system. Trditionl duct design methods minly rely on the results of comprehensive survey to test the duct properties. One disdvntge of these pproches is tht their design cycles re very long. Moreover the testing costs of three dimensionl flow field re very high becuse the duct shpe is usully complex. Fortuntely the development of computtionl fluid dynmics provides good wy to understnd the flow field distribution nd the unstedy trnsformtion of the duct for the mjority of reserchers. Ishtique et l. [5] modified the design of the trnsport duct nd nlysed the ir flow inside the trnsport duct with the computtionl fluid dynmics (CFD) softwre FLUENT fter creting the trnsport duct geometry in the geometricl model softwre GAMBIT. Then the physicl properties of finer nd corser count yrns mde from modified s well s conventionl trnsport ducts were compred to ssess the enhncement of properties with trnsport duct modifiction. Gs solid two phse flow in 180 degrees curved duct ws simulted with stndrd k epsilon model RNG (Renormlistion Group) bsed k epsilon model Low Re k epsilon model nd n extended version of the stndrd k epsilon model ws dopted. It showed tht the RNG bsed k epsilon model predicted the flow behviour better thn other models [6]. Computtionl fluid dynmics (CFD) simultions re performed for convective het nd mss trnsfer between wter surfce nd humid ir flowing in horizontl three dimensionl rectngulr duct [7]. Moujes nd Aekul [8] present new results for numericl predictions of ir flow nd pressure distribution in two commonly used elbows. A k epsilon turbulence model for high Reynolds number nd k epsilon Chen model re used for comprtive purposes. To vlidte the CFD results the results of two experimentl ppers using guided vnes re compred with simulted vne run under the sme condition. The simultions greed resonbly well with published experimentl results. The present pper focuses on the duct flow field optimistion of the robot vcuum clener. The flow field nlysis of originl duct structure inside the robot vcuum clener is crried out using the computtionl fluid dynmics softwre FLUENT fter creting the duct geometry in the geometricl model softwre Pro/Engineer. The simultions re done using the k ε turbulence model of three dimensionl incompressible fluid. With the velocity vector plots on rbitrry plne of the duct flow field obtined the defects of the originl duct structure flow field re nlysed. After tht the duct structure is modified nd optimised nd the irflow behviour is simulted. The totl flow rtes of the originl duct s well s the optimised duct re compred nd comprisons between the experimentl vlues nd the simultion vlues re lso chieved. All the results vlidte the effectiveness nd correctness of the modelling in the pper. 2. Mthemticl model of the duct flow field 2.1 Governing equtions The mss conservtion eqution sttes the rte of increse of mss in the fluid element is equted to the net rte of flow of mss into the element cross its fces. This yields u v w 0 t x y z or in more compct vector nottion (1) divu 0 (2) t where ρ is the density t is the time u is the velocity vector. u v w re the components of the velocity vector u in the x y z direction. Eq. (2) is the unstedy three dimensionl mss conservtion t point in compressible fluid. The first term on the left hnd side is the rte of chnge in time of the density. The second term describes the net flow of mss out of the element cross the boundries. For n incompressible fluid the density ρ is constnt nd Eq. (2) becomes or in longhnd nottion div 0 u (3) u v w 0. x y z Newton s second lw sttes tht the rte of chnge of momentum of fluid prticle equls the sum of the forces on the prticle. Then the x component of the momentum eqution is found by setting the rte of chnge of x momentum of the fluid prticle equl to the totl force in the x direction on the element due to surfce stresses plus the rte of increse of x momentum due to sources. This yields p yx Du Dt x y z xx zx S. mx (4) (5) 105 Int Adv Robotic Sy 2011 Vol. 8 No

3 It is not too difficult to verify tht the y component of the momentum eqution is given by Dv p xy yy zy S Dt x y z nd the z component of the momentum eqution by Dw p Dt x y z xz yz zz Du Dv Dw Where re the rtes of increse of x Dt Dt Dt y nd z momentum per unit volume of fluid prticle. The pressure norml stress is denoted by p. Viscous stresses re denoted by τ. The suffix nottion τij is pplied to indicte the direction of the viscous stresses. The suffices i nd j in τij indicte tht the stress component cts in the j direction on surfce norml to the i direction. The momentum conservtion lw is usully expressed s the prtil differencing equtions of the Nvier Stokes eqution in fluid dynmics. Currently the simultion pproches of the Nvier Stokes (N S) equtions bsed on the Reynolds time verge re used to solve the problem of the incompressible flow in projects. It cn be written s follows: 2 u uiu j u uiu j i i si (8) t x x x x x j i i j j where u iu j is the turbulent Reynolds stress si is the source term. i j = When the ρ nd si re known the solutions of the simultneous equtions combined Eq. (4) nd Eq. (8) re not unique u iu j is still unknown. At the moment dditionl turbulence models of these unknowns re required to mke the solutions of the simultneous equtions closed. Since the softwre FLUENT provides vriety of turbulence models the k ε turbulence model is chosen in this pper. 2.2 Pressure correction equtions According to the mss conservtion eqution nd momentum conservtion eqution the continuity eqution cn be written s follows: u v x y 0. S my mz (6) (7) (9) Eq. (9) cn be rewritten in the discretistion form s follows: [( ua) ( ua) ] [( va) ( va) ] 0 (10) i1 i I j1 I j following the correction vlues in Eq. (11) where u u d p p v v d p p u u d p p u u d p p * i i i I 1 I * I j I j I j I 1 I * i 1 i 1 i 1 I I 1 * i 1 i 1 i 1 I I 1 d d i1 I j1 A A i1 i1 I j1 I j1. (11) Substitute the discretistion Eq. (11) into Eq. (10) we obtin da da da da p i1 I j1 i I j I da da p da p da p p i1 I 1 i I 1 I j1 I 1 I I 1 * * * * u A u A v A v A i i1 I j I j1 Eq. (12) cn be simplified to (12) I p I I 1 p I 1 I 1 p I 1 I 1 p I 1 I 1 p I 1 b I (13) where I I 1 i1 I 1 i I 1 I j1 da da da da I 1 I j I I 1 I 1 I 1 I 1 b u A u A v A v A * * * * i i1 I j I j1 The PRISO lgorithm which stnds for Pressure Implicit with Splitting of Opertors [ ] is pressure velocity clcultion procedure developed originlly for nonitertive computtion of unstedy compressible flows. PRISO involves one predictor step nd two corrector steps nd my be seen s n extension of SIMPLE with further corrector step to enhnce it. The PRISO lgorithm solves the pressure correction eqution twice so the method requires dditionl storge for clculting the. Xio-bo Li Hi-shun Wng nd Hu-shn Liu: Reserch on Duct Flow Field Optimistion of Robot Vcuum Clener 106

4 source term of the second pressure correction eqution. Although this method implies considerble increse in computtionl effort it hs been found to be efficient nd fst [12]. Therefore the PRISO lgorithm is dopted to simulte the fluid dynmicl chrcteristics of the duct flow field in the robot vcuum clener. 3. Geometric models nd boundry conditions 3.1 Geometric models The grid models of the duct structure in the robot vcuum clener re shown in Fig.1 minly including the inlet the outlet rolling brush blower vcuum blower nd dust continer. To reduce the grid number nd execution time we mke some simplifiction without ffecting the computtionl ccurcy. However the key components (such s the rolling brush blower vcuum blower wll etc.) re modelled without mking ny simplifiction. The specific plces simplified re shown below: (1) The duct system hs good seling properties nd there is no ir lekge except vi the inlet nd the outlet. (2) The vcuum blower is viewed s prt of the duct system nd not discussed seprtely First of ll the stp formt cse is imported from the softwre Pro/Engineer to the GAMBIT for pre processing nd closed spce computtionl domin is obtined. Then the grid model fter pre processing is imported into the STAR CCM+ to be checked. If there re no geometric errors or gps the required volume mesh cn be generted directly. The block method is dopted to meshing nd the whole geometric model is divided into multi blocks. Among them prt of the rolling blower nd the vcuum blower re meshed with the unstructured grid to meet the complicted surfce structures of the rotting bldes. The internl wlls of the blowers re divided into two regions including the internl regions nd externl regions. The former contin the bldes rotting shft nd surrounded fluid regions. The rotting coordinte frme is pplied to the clcultion process in these regions nd the speed equls the ctul speed of the bldes. Other res re lso divided into severl blocks nd meshed with the structured grids to improve the computtionl efficiency. The ltter comprises the outer wll of the blowers nd res round them using the fixed coordinte frme in the clcultion process. The totl grid number of the duct model in the robot vcuum clener generted is bout 105 million in the pper Boundry conditions The physicl prmeters of the fluid regions nd the solid regions (such s fluid density etc.) re constnts nd the fluid flow in the duct is stedy stte flow nmely the pressure together with the temperture does not chnge with time. The fluid flow medium is ir nd the tmospheric pressure of the experimentl environment is one stndrd tmospheric pressure nmely P = P temperture T = 295K ir density ρ = 1.25kg/m 3 ir viscosity μ = N s/m 2. The duct inlet is defined to the flow inlet so tht the dt cn be obtined from experiments the duct outlet is defined to the pressure outlet. Suppose tht the speed of the fluid in the duct inlet is uniform in which the direction is perpendiculr to the border nd the bck pressure of the duct outlet is zero. The number of the bldes on the rolling brush blower is 6 nd the rottion direction is counter clockwise with the speed of 700rpm. The number of the bldes on the vcuum blower is 5 nd the rottion speed is 15000rpm. Since the ir flow in the duct is not very lrge the compressibility of the ir hs little influence on the flow behviour of the fluid nd the pressure distribution. Hence it cn be ssumed tht the ir is incompressible nd the density is constnt. In this pper the solution lgorithm to the pressure velocity coupling is the PRISO method the convection diffusion problems re nlysed with the stndrd second order upwind differencing scheme. Considering the design requirements of the duct in the robot vcuum clener the convergence condition to be determined is tht the errors of ll the physicl quntities should be less thn Figure 1. Grid models 107 Int Adv Robotic Sy 2011 Vol. 8 No

5 Figure 2. 3D model of originl duct structure 4. Simultion nd experimentl results nlysis 4.1 CFD simultion of the originl duct structure The fluid model shown in Fig.2 is bsed totlly on the design dimensions of the originl duct structure in the robot vcuum clener which ws generted without mking ny chnges except the simplifictions. The working principle of the robot vcuum clener cn be seen from Fig.2. Firstly the dust prticles on the ground re stirred nd rised by the rotting bldes of the rolling brush; then they enter the negtive pressure cvity formed by the bldes nd the cvity wll of the rolling brush. At the sme time driven by the rolling brush bldes the dust prticles cn conveniently rush into the junction between the rolling brush cvity nd the dust continer. Secondly the vcuum blower with high speed rottion forms high negtive pressure chmber in the dust continer. Finlly the dust prticles with high speed enter the dust continer nd gther under the ction of the filters. This prevents the dust prticles going into the interior of the vcuum blower from the inlet nd voids dmge to the vcuum blower. Figure 3. Velocity vector plot of the originl duct structure Fig.3 shows the overll velocity vector plot on n rbitrry plne of the originl duct structure in the robot vcuum clener which is obtined by CFD simultion. It cn be seen from the figure tht there is n obvious lrge eddy in the top right of the ir intke of the dust continer. The eddy is generted due to the mbiguity of the flow trend fter the ir comes into the dust continer. At the sme time the ir speed is specilly high in the ir intke of the dust continer resulting in prt of the ir seprting in the sequent prt The eddy formed in this position not only results in higher locl flow loss but would lso produce reltively lrge noise. In this wy it reduces the clening efficiency of the duct in the robot vcuum clener. Figure 4. Rolling brush blower velocity vector plot of the originl duct structure In Fig.4 the seling property between the top of the rolling brush bldes nd the rolling brush cvity is not idel resulting in some ir long the rottion direction of the rolling brush bldes leking into the rolling brush Xio-bo Li Hi-shun Wng nd Hu-shn Liu: Reserch on Duct Flow Field Optimistion of Robot Vcuum Clener 108

6 cvity from the left of the ir intke of the dust continer insted of entering the dust continer directly from the ir intke of the duct continer. This leds to sitution in which the ir circultion is not idel nd does not esily form the tip vortex flow nd the bckflow. Therefore the originl structure should be optimised nd improved. 4.2 CFD simultion of the optimised duct structure Through the bove nlysis the lrge eddy tip flow bckflow nd other defects exist in the flow field of the originl duct structure inside the robot vcuum clener which hve gret influence on clening efficiency. In the view of the computtionl fluid dynmics the fluid pressure drop is lrgely cused by the eddy. Therefore lrge scle or even smll eddy should be voided when we design the duct structure of the robot vcuum clener. This mens tht the duct structure inside the robot vcuum clener should be optimised ccording to the theories of the computtionl fluid dynmics mximlly reducing the energy loss cused by the eddy. As is shown in Fig.5 the optimistion scheme of the originl duct structure in the pper is s follows: Step 1: Minimize the spce t the top right of the ir intke in the dust continer nd dd spoiler t the ir intke of the dust continer so tht the ir cn enter the dust continer just inside the left voiding lrge eddy production nd the pressure drop. Step 2: The internl wll of the ir intke in the dust continer should be tngent to the top of the rolling brush bldes which plys similr role s the jw. Accordingly the dust prticles re stroked down nd then enter the dust continer from the ir intke. Step 3: To mximlly eliminte the lrge eddy inside the duct the ir intke long the xil direction ought to be mde in n eight shpe trumpet for smooth trnsition. Step 4: The rolling brush bldes re mde into bent shpe so tht they hve the rel blower effect As is shown in Fig.6 the fluid model of the optimised duct structure is simulted through CFD softwre the boundry conditions remin the sme; the overll velocity vector plot on rbitrry plne of the duct structure cn be obtined. We cn see from Fig.6 tht the lrge eddy in the top right of the dust continer hs been significntly reduced nd effectively controlled fter the duct structure is optimised. Menwhile the smoothness of the rolling brush cvity trnsition to the ir intke hs been improved gretly nd the field flow of the duct structure in the robot vcuum clener hs been perfected. Fig.7 shows tht the seling property between the top of the rolling brush bldes nd the rolling brush cvity wll is better thn in the originl duct structure lmost no ir long the rottion direction of the rolling brush bldes is leking into the rolling brush cvity from the left of the ir intke in the dust continer. The smoothness of the ir flow is good which effectively controls the production of the tip flow nd the bckflow. Figure 5. 3D model of the optimised duct structure 109 Int Adv Robotic Sy 2011 Vol. 8 No

7 Figure 6. Velocity vector plot of the optimised duct structure Figure 7. Rolling brush blower velocity vector plot of the optimised duct structure 4.3 Vlidtion of clcultion results Both the originl duct structure nd the optimised duct structure re mde into physicl models nd then the totl ir flow rte from the outlet of the vcuum blower is mesured with the ir flow meter. The physicl model of the optimised rolling brush bldes the dust continer nd the ir intke of the dust continer re shown in Fig.8 Fig.9 nd Fig.10 respectively. Tble 1 shows the totl ir flow rte from the outlet of the originl physicl model nd the optimised physicl model under different speed conditions respectively. The rottion speed of the rolling brush blower mintins 700rpm. It cn be seen from Tble 1 tht the totl ir flow rte of the optimised physicl model is lrger thn tht of the originl physicl model of the duct structure with the sme speed which verifies the correctness of the duct structure optimistion in this pper. Fig.11 () shows the comprison between the experimentl results nd the CFD simultion results of the totl ir flux rte from the vcuum blower outlet of the originl duct structure. Likewise Fig.11 (b) shows the comprison between the experimentl results nd the CFD simultion results of the totl ir flux rte from the vcuum blower outlet of the optimised duct structure. All the results in Fig.11 () nd Fig.11 (b) re tested with different rottion speeds of the vcuum blower. The dt comprisons of Fig.11 () nd Fig.11 (b) verify the correctness nd the fesibility of theoreticl modelling presented in the pper. Xio-bo Li Hi-shun Wng nd Hu-shn Liu: Reserch on Duct Flow Field Optimistion of Robot Vcuum Clener 110

8 Figure 8. Physicl model of the optimised rolling brush Figure 9. Physicl model of the optimised dust continer Figure 10. Physicl model of the optimised ir intke Rotte speed 10000/rpm 12000/rpm 14000/rpm 16000/rpm Originl structure 49.3/(m 3.h 1 ) 54.1/(m 3.h 1 ) 60.9/(m 3.h 1 ) 66/(m 3.h 1 ) Optimised structure 52/(m 3.h 1 ) 56.5/(m 3.h 1 ) 61/(m 3.h 1 ) 69.3/(m 3.h 1 ) Tble 1. Comprison of totl ir flow rte from the vcuum blower outlet t different speeds Figure 11. Totl ir flow rte comprison between experimentl vlues nd simultion vlues 111 Int Adv Robotic Sy 2011 Vol. 8 No

9 5. Conclusions Aiming t the pressure loss problem of the duct flow field in the robot vcuum clener by mens of computtionl fluid dynmics nd erodynmics with the mss conservtion eqution nd momentum conservtion eqution considered the duct structure inside the robot vcuum clener is tken s reserch object in this pper. The convection diffusion problems re nlysed with the stndrd second order upwind differencing scheme nd the k ε turbulence model of 3D incompressible fluid nd the PRISO lgorithm re used to crry out the flow field numericl simultions of the duct structure in the robot vcuum clener. To obtin good dynmic performnce optimistion design bsed on the nlysed results is chieved. The experimentl nd simultion results show tht the method of optimising the duct structure inside the robot vcuum clener cn effectively reduce the impct on the duct flow field introduced by the lrge eddy tip eddy nd bckflow. The pressure drop is decresed nd the clening efficiency of the robot vcuum clener is improved. Wht is more the correctness nd the fesibility of theoreticl modelling presented in the pper re verified which cn overcome the shortcomings of the duct trditionl design method. The conclusions obtined from this pper provide useful reference nd prcticl significnce to the reserch on the erodynmics chrcteristics of the duct flow field in other robots. 6. References [1] Hong. Prk K..A new mobile robot nvigtion using turning point serching lgorithm with the considertion of obstcle voidnce. Interntionl ournl of Advnced Mnufcturing Technology (5 8): [doi: /s ] [2] Klncr G. Mtko D. Blzic S..A control strtegy for pltoons of differentil drive wheeled mobile robot. Robotics nd Autonomous Systems (2): [doi: /j.robot ] [3] Smsudin K. Ahmd F. A. Mshohor S..A highly interpretble fuzzy rule bse using ordinl structure for obstcle voidnce of mobile robot. Applied Soft Computing (1): [doi: /j.soc ] [4] Mtveev A. S. Teimoori H. Svkin A. V..Nvigtion of unicycle like mobile robot for environmentl extremum seeking. Automtic (1): [doi: /j.utomtic ] [5] Ishtique S. M. Singh S. N. Ds A. et l.optimistion of fluid flow phenomen inside the trnsport duct of DREF friction spinning mchine. ournl of the Textile Institute (10): [doi: / ] [6] EI Behery S. M. Hmed M. H. EI Kdi M. A. et l.cfd prediction of ir solid flow in 180 degrees curved duct. Powder Technology (1 2): [doi: /j.powtec ] [7] Tlukdr P. Iskr C. R. Simonson C...Combined het nd mss trnsfer for lminr flow of moist ir in 3D rectngulr duct: CFD simultion nd vlidtion with experimentl dt. Interntionl ournl of Het nd Mss Trnsfer (11 12): [doi: /j.ijhetmsstrnsfer ] [8] Moujes S. F. Aekul S..CFD predictions nd experimentl comprisons of pressure drop effects of turning vnes in 90 degrees duct Elbows. ournl of Energy Engineering ASCE (4): [doi: /(ASCE) (2009)135:4(119)] [9] Iss R. I..Solution of the implicitly discretised fluid flow equtions by opertor splitting. ournl of Computtionl Physics (1): [doi: / (86) ] [10] Prk TS. Effects of time integrtion method in lrge eddy simultion using the PISO lgorithm: Prt I Flow field. Numericl Het Trnsfer Prt A Applictions (3): [doi: / ] [11] Kng KG Ryou HS. Computtion of solidifiction nd melting using the PISO lgorithm. Numericl Het Trnsfer Prt B Applictions (2): [doi: / ] [12] Iss R. I. Gosmn A. D. Wtkins A. P..The computtion of compressible nd incompressible recirculting flows. ournl of Computtionl Physics (1): [doi: / (86) ] Xio-bo Li Hi-shun Wng nd Hu-shn Liu: Reserch on Duct Flow Field Optimistion of Robot Vcuum Clener 112