Katika diffuser centrifugal pumps, rotating impeller blades na fixed diffuser vanes hupita karibu sana na kila nyingine. Tukio hili, linaloitwa rotor-stator interaction, huvuruga pressure field kati ya impeller outlet na diffuser inlet kwa periodic manner; linaweza kusababisha pressure fluctuations, hydraulic vibration, vortex clustering, energy loss na long-term mechanical fatigue risk. Effects hizi ni muhimu hasa katika ship cooling, seawater lifting, ballast, firefighting, offshore platform na ocean-energy pumping systems ambapo variable back pressures na inlet disturbances vinaweza kutokea.

Katika utafiti, original impeller blade trailing edge M0 ilitumika kama reference model, na geometries mbili mpya zikalinganishwa nayo. M1 ni thinned trailing edge iliyoundwa kwa fourth-order Bézier curve. M2 ni model yenye rounding ya radius 30 millimeters kwenye blade pressure surface. Watafiti walitathmini geometries hizi kwa closed-loop clean-water experiments, time-dependent CFD, spatio-temporal pressure transformations, standard deviation ya pressure coefficient na \(\Omega\) vortex-identification method.

Nominal flow rate ya pump iliyochunguzwa ni 14 m³/saa, nominal head 14 meters na rotational speed 2.850 rpm. Impeller ina blades sita na fixed diffuser ina vanes saba. CFD model inawakilisha full flow passage yenye suction chamber, impeller, diffuser, pump cavity na outlet volute. Calculations zilitumia structured mesh yenye takribani cells milioni 4,61, SST \(k-\omega\) turbulence model na time step ya \(5,84795\times10^{-5}\) seconds inayolingana na kila degree moja ya impeller rotation.

Blade-geometry modification ilipunguza kwa kiasi kikubwa difference kati ya highest na lowest static pressure kwenye impeller outlet. Katika reference M0 model difference ilikuwa \(0,51\times10^5\) Pa, yaani takribani 51 kPa; ilishuka hadi 28 kPa katika M1 na 35 kPa katika M2. Kulingana na values zilizotolewa, hii ni reduction ya takribani asilimia 45,1 kwa M1 na asilimia 31,4 kwa M2. Pressure field kuwa uniform zaidi inaonyesha kwamba sudden pressure drops na pressure-wave gradients zinazotokea wakati blade passages zinapita zimepungua.

M1 ilikuwa model yenye mafanikio zaidi hasa katika kusuppress pressure fluctuation na large-scale vortex clustering kwenye diffuser inlet. Katika \(\Omega\) vortex images, dense na merged vortex structures za M0 zinaonekana kubadilika katika M1 kuwa smaller, fragmented na more regularly distributed structures. Ingawa effect ya M2 kwenye vortexes na pressure fluctuation ni limited zaidi kuliko M1, experiment na CFD results zinaonyesha kwamba M2 huongeza efficiency katika all investigated flow rates na huongeza head kidogo katika low flow rates.

Utafiti unaripoti kwamba M2 huongeza pump efficiency kwenye nominal point kwa takribani 0,9-1,2 percentage points relative na M0. Kulingana na authors' scaling calculation, kwa typical 15 kW marine pump inayofanya kazi saa 5.000 kwa mwaka, difference hii inaweza kuokoa 900-1.200 kWh electricity na 450-600 kg carbon dioxide kwa mwaka. Hata hivyo, baseline efficiency, hydraulic duty profile na electricity emission factor zilizotumika katika calculation hii hazijatolewa kwa kina. Carbon-dioxide result, kwa kadiri numbers zinavyoonyesha, inaonekana kutumia implicitly emission factor ya 0,5 kg CO₂/kWh.

Licha ya marine emphasis ya utafiti, experiments zilifanywa kwenye clean-water laboratory setup bila salinity, corrosion, marine biofouling, wave-induced inlet disturbance au ship motion. Best pressure na vortex results za M1 hazikupatikana directly kwa experiment bali predominantly kupitia CFD; experimental performance comparison imewasilishwa kati ya M0 na M2. Kwa hiyo, results zinatoa strong mechanistic indication kwa marine pump design, lakini bado hazithibitishi field success katika real seawater environment.

Kwa nini rotor-stator interaction ni muhimu kwa pump?

Impeller ya centrifugal pump hubadilisha mechanical energy kutoka motor kuwa velocity na pressure ya fluid. Diffuser vanes hujaribu kupunguza speed ya flow inayotoka kwa kasi kubwa kwenye impeller na kubadilisha sehemu kubwa zaidi ya velocity energy kuwa static pressure. Wakati impeller blades zinapozunguka, hupita periodically mbele ya leading edges za fixed diffuser vanes.

Flow kwenye impeller outlet si uniform kabisa. Nyuma ya kila blade kuna low-velocity wake region, pressure difference kati ya pressure na suction surfaces, secondary flow na vortex structures. Irregular flow hii inapofika kwenye fixed diffuser vane:

• Sudden pressure rises na drops zinaweza kutokea kwenye diffuser inlet.
• Pressure waves zinaweza kuenea pande zote mbili kati ya impeller outlet na diffuser inlet.
• Impeller shaft power, head na efficiency vinaweza kuonyesha small lakini regular oscillations.
• Large vortex clusters zinaweza kuongeza hydraulic losses na irregular forces.
• Vibration na fatigue risk katika pump casing, piping na connections vinaweza kuongezeka.

Utafiti unatambua kwamba pressure fluctuation haisababishwi tu na kuwepo kwa diffuser vane, bali pia na interaction ya wake na vortexes zinazoundwa kwenye impeller trailing edge na fixed vanes. Kwa hiyo, badala ya kubadilisha entire impeller, design intervention inalenga sehemu ya mwisho ya blade pekee, yaani trailing au exit edge.

Pengo la fasihi linalolengwa

Previous studies zimechunguza effects za V-shaped notch, circular au elliptical cuts, exit-edge inclination na different rounding radii kwenye pump head, efficiency na pressure fluctuation. Kulingana na literature review ya utafiti, suitable trailing-edge modification inaweza kupunguza jet-wake structure, secondary flow na velocity-pressure nonuniformity kwenye outlet.

Kwa upande mwingine, watafiti wanaeleza kwamba integrated explanation bado haijakamilika kati ya geometric modification na processes zifuatazo:

• Vortexes huundwa wapi katika impeller-diffuser gap,
• Vortexes hukua na kutawanyika vipi kwa muda,
• Vortex clustering hubadilika vipi kuwa pressure waves,
• Pressure waves huenea vipi kupitia impeller na diffuser passages,
• Mechanism hii inaunganishwaje na pressure fluctuation na energy efficiency.

Lengo la utafiti si kujibu tu “geometry ipi ina efficiency kubwa?”, bali kueleza trailing-edge geometry hubadilisha rotor-stator interaction kupitia flow mechanism gani.

Blade trailing edges tatu zilizolinganishwa

Kielelezo 3 kinaonyesha close-up mesh views za exit edges za models tatu. M1 exit tip imethinned wazi relative na M0, huku katika M2 transition kutoka pressure surface kwenda exit ikiwa more rounded.

Fourth-order Bézier geometry

M1 trailing edge inategemea fourth-order Bézier curve iliyofafanuliwa kwa control points tano:

\[ B(t)=(1-t)^4P_0+4(1-t)^3tP_1+6(1-t)^2t^2P_2+4(1-t)t^3P_3+t^4P_4,\qquad 0\leq t\leq1 \]

• \(B(t)\): Vector inayofafanua position kwenye curve.
• \(P_0-P_4\): Control points tano zinazobainisha curve shape.
• \(t\): Dimensionless parameter inayobadilika kati ya 0 na 1 along the curve.

Table 4 inatoa values za 20, 20, -30, 20 na 20 mm kwa control points. Hata hivyo, two- au three-dimensional coordinate components za values hizi hazijaelezwa kwa kina. Kwa hiyo, ingawa geometry inaweza kueleweka kupitia figure na existing table, additional coordinate information inahitajika ili M1 model irecreated independently katika exact CAD form.

Closed-loop experimental system

Closed-loop setup iliyoonyeshwa katika Kielelezo 1 ina variable-frequency motor, centrifugal pump, electromagnetic flowmeter, electrically controlled valve, constant-pressure water tank, pressure sensors na pump performance measurement system.

Motor speed ilidhibitiwa kwa frequency drive, flow rate ikabadilishwa kupitia electromagnetic valve na motor input power ikabainishwa kwa electrical measurement. Main measurement specifications zilizotolewa katika utafiti ni:

Experimental setup ilitumika kuthibitisha external performance curves. Experimental comparison iliyowasilishwa kwa head na efficiency inahusisha M0 na M2 models pekee. Equivalent experimental curve ya M1 haijatolewa.

Physical characteristics za pump

Kielelezo 2 kinaonyesha suction chamber, impeller, diffuser, pump cavity na outlet chamber katika assembled na exploded views. Model ilichaguliwa kuwakilisha small- na medium-sized seawater circulation au offshore water-supply pumps.

Computational mesh

Impeller na diffuser zilimesh kwa Turbogrid, na other flow volumes kwa ICEM kwa structured hexahedral cells. Near-wall regions zili-refine locally ili boundary layer iweze resolved. Average \(y^+\) katika whole flow field iliripotiwa kuwa 5,13.

Mesh densities tano tofauti zililinganishwa; head, shaft power, axial force na wear-ring leakage flow rate zilifuatiliwa. Results zili-stabilize kwa kiasi kikubwa baada ya takribani cells milioni 4,61, na mesh hii ikachaguliwa kwa subsequent transient analyses.

Kwa Grid Convergence Index analysis inayotegemea Richardson extrapolation, meshes tatu zenye takribani cells milioni 8,80, milioni 4,61 na milioni 2,32 zilitumika. Utafiti unaripoti GCI values chini ya asilimia 1 kwa selected principal outputs.

Ingawa title ya Kielelezo 3 katika document imetolewa kama “mesh independence validation”, image yenyewe inaonyesha hasa close-up mesh structures za M0, M1 na M2 trailing edges. Actual mesh-independence curves ziko katika Kielelezo 4 kinachofuata.

Flow equations na model assumptions

Utafiti unatatua single-phase, incompressible, constant-density water flow. Temperature variation imepuuzwa.

Mass conservation:

\[ \frac{\partial \rho}{\partial t}+\nabla\cdot(\rho\mathbf{u})=0 \]

Katika constant density, equation hii inapunguzwa kuwa:

\[ \nabla\cdot\mathbf{u}=0 \]

.

Momentum conservation:

\[ \frac{\partial\mathbf{u}}{\partial t}+(\mathbf{u}\cdot\nabla)\mathbf{u} =\mathbf{f}-\frac{1}{\rho}\nabla p+\nu\nabla^2\mathbf{u} \]

• \(\mathbf{u}\): Velocity vector katika m/s.
• \(p\): Static pressure katika Pa.
• \(\rho\): Fluid density katika kg/m³.
• \(\nu\): Kinematic viscosity katika m²/s.
• \(\mathbf{f}\): Body force acting per unit mass.

Reynolds-averaged SST \(k-\omega\) model ilitumika kwa turbulence. Ili kutabiri near-wall separation na adverse pressure gradients, model hutatua additional transport equations mbili kwa turbulent kinetic energy \(k\) na specific dissipation rate \(\omega\).

Transient CFD settings

• Initial solution: Steady CFD result.
• Inlet boundary: One standard-atmosphere total pressure.
• Outlet boundary: Mass-flow outlet.
• Rotor-stator interface: Transient Rotor Stator method.
• Convection term: High-order discretization.
• Time term: Second-order backward Euler.
• Iterations per time step: 20.
• RMS residual convergence criterion: \(10^{-5}\).
• Total calculation: 15 impeller revolutions.
• Frequency analysis: Last six stable impeller revolutions.

Impeller speed ya 2.850 rpm inalingana na 47,5 revolutions per second. One full revolution ni takribani 0,02105 seconds. Selected one-degree time step ilikokotolewa kama:

\[ \Delta t=\frac{60}{2850\times360}=5,84795\times10^{-5}\ \mathrm{s} \]

. Corresponding sampling frequency ni 17.100 Hz.

Courant number na time-step independence

Courant number, inayoonyesha fluid inasafiri cell lengths ngapi ndani ya one time step, imefafanuliwa kama:

\[ Co=\frac{v\Delta t}{\Delta x} \]

Hapa \(v\) ni local velocity, \(\Delta t\) time step na \(\Delta x\) cell size.

Kwa kuwa change katika average outputs ilikuwa ndogo wakati moving from two degrees to one degree, one-degree step ilichaguliwa ili pressure waves na vortex motion ziresolved kwa undani zaidi.

Experiment na CFD validation

Kielelezo 6 kinalinganisha experimental na CFD head-flow na efficiency-flow curves kwa M0 na M2. M2 head katika low flow ni slightly higher than M0, huku difference ikipungua karibu nominal na high flow rates.

Both experiment na CFD zinaonyesha M2 efficiency ni higher than M0 katika investigated flow range. Hata hivyo, high-efficiency region katika CFD imehamia kwa takribani 2 m³/saa higher flow kuliko experimental result.

Utafiti unatafsiri agreement hii kama validation ya numerical method. Hata hivyo:

• Validation inahusisha M0 na M2 pekee.
• Experimental performance curve ya M1 haijaonyeshwa.
• RMSE, confidence interval au uncertainty budget ya experiment-CFD differences hazijatolewa.
• Measurement repeats au error bars hazipo kwenye graphs.

Pressure monitoring points

Ili pressure field kwenye rotor-stator interface iweze kufuatiliwa kulingana na time na circumferential position, numerical sensor points nyingi ziliwekwa:

• 180 points kwenye impeller outlet katika radius \(r=58,7\) mm.
• 175 points kwenye diffuser inlet katika radius \(r=61,3\) mm.
• Angular spacing kati ya diffuser points takribani 2,0571°.
• Difference ya 19° kati ya starting lines za impeller na diffuser coordinates.

Kielelezo 7 kinaonyesha annular interface kati ya impeller blades na diffuser vanes pamoja na sensor points zilizowekwa circumferentially. Kielelezo 8 kinalinganisha locations za special monitoring points karibu na suction na pressure surfaces katika M0, M1 na M2 geometries.

Ingawa Table 2 inaeleza kwamba kuna impeller blades sita, sehemu moja ya monitoring-point description inaandika impeller blades kama “Bi1-Bi7”. Kwa kuwa images na rotor-frequency analyses zinaunga mkono impeller blades sita, expression hii inaonekana kuwa internal numbering error katika document.

Blade-passing frequencies

Impeller rotational frequency:

\[ f_n=\frac{2850}{60}=47,5\ \mathrm{Hz} \]

Kwa sababu ya impeller blades sita, basic impeller-blade passing frequency kwenye diffuser inlet ni:

\[ 6f_n=285\ \mathrm{Hz} \]

Kwa sababu ya diffuser vanes saba, fixed-vane interaction frequency kwenye impeller outlet ni:

\[ 7f_n=332,5\ \mathrm{Hz} \]

Kwa hiyo, \(7f_n,14f_n,21f_n,28f_n\) components zilichunguzwa katika impeller-outlet spectra, huku \(6f_n,12f_n,18f_n,24f_n\) components zikichunguzwa kwenye diffuser inlet. Frequencies hizi ni geometric signature ya interaction kati ya rotating blades sita na fixed vanes saba.

Pressure coefficient

Ili kulinganisha pressure fluctuations katika regions tofauti kwa common scale, dimensionless pressure coefficient ilitumika:

\[ C_p=\frac{p-\bar{p}}{0,5\rho u_2^2} \]

• \(p\): Instantaneous static pressure.
• \(\bar p\): Average static pressure during sampling period.
• \(\rho\): Fluid density.
• \(u_2\): Circumferential velocity kwenye impeller outlet.

Pressure-fluctuation intensity

Spread ya pressure coefficient kwa muda katika point moja ilipimwa kwa standard deviation:

\[ S_{C_p}=\sqrt{\frac{1}{N}\sum_{i=1}^{N}\left(C_{p,i}-\bar C_p\right)^2} \]

• \(N\): Number of pressure samples.
• \(C_{p,i}\): Pressure coefficient ya sample i.
• \(\bar C_p\): Average pressure coefficient.
• \(S_{C_p}\): Higher value inaonyesha stronger local pressure fluctuation.

\(\Omega\) vortex-identification method

Velocity-gradient tensor iligawanywa kuwa symmetric na antisymmetric components. Symmetric \(A\) tensor inawakilisha local deformation, na antisymmetric \(B\) tensor rotational motion.

\[ \Omega=\frac{\|B\|_F^2}{\|A\|_F^2+\|B\|_F^2+\varepsilon} \]

• \(\|A\|_F\): Frobenius norm ya deformation component.
• \(\|B\|_F\): Frobenius norm ya rotation component.
• \(\varepsilon\): Small regularization term inayozuia denominator kukaribia zero.
• \(\Omega>0,5\): Inatafsiriwa kama region ambapo rotational component ya local flow ni dominant.

Method hii inalenga kutofautisha regions zenye high shear lakini zisizo na real rotational core kutoka vortex centers.

External-performance oscillations katika one impeller revolution

Kielelezo 9 kinaonyesha head, shaft power, efficiency, pump outlet pressure, impeller-outlet average pressure na diffuser-inlet average pressure katika one impeller revolution.

Main cycles sita zinaonekana ndani ya revolution moja; number hii inaendana na impeller blades sita. Ndani ya kila main cycle kuna smaller oscillations saba; structure hii inaakisi fixed diffuser vanes saba.

Fluctuation form na phase ya circumferentially averaged impeller-outlet pressure na shaft power ziko karibu. Watafiti wanatafsiri result hii kwamba significant part ya instantaneous shaft power inaathiriwa na variable pressure field kwenye impeller outlet.

Spatio-temporal pressure field kwenye impeller outlet

Katika Kielelezo 10, horizontal axis ni time na vertical axis ni impeller circumferential angle. Color scale inaonyesha low na high static pressure.

Katika M0 model, broad low-pressure lines na high pressure gradients zinaonekana along blade positions. Katika M1 na M2, low-pressure regions nyuma ya blade zimekuwa narrow zaidi kwa wazi.

Inclined pressure bands kwenye maps zinawakilisha relative motion ya fixed diffuser vanes dhidi ya rotating impeller. Local maximum pressure hutokea katika region ambapo impeller suction surface na diffuser pressure surface zinakutana; minimum pressure hutokea katika intersection ya impeller pressure surface na diffuser suction surface.

M1 na M2 zimefanya pressure field kwenye impeller outlet kuwa homogeneous zaidi kwa kupunguza pressure drop inayotokea wakati blade passing.

Spatio-temporal pressure field kwenye diffuser inlet

Kielelezo 11 kinaonyesha pressure motion katika one impeller revolution kwa monitoring points kwenye fixed diffuser. Katika kila point kuna periodic structures sita katika time direction na saba katika circumferential direction.

Katika M0, inclined low-pressure bands huundwa wakati impeller blade inasweep diffuser passage. Katika M2, general structure ileile huhifadhiwa lakini pressure difference hupungua. Katika M1, pressure drop imesuppress zaidi na map inabadilika kwa kiasi kikubwa kuwa horizontal, smoother pressure bands.

Moja ya main conclusions za utafiti ni kwamba exit-edge geometry hubadilisha pressure fluctuation kwenye diffuser inlet zaidi kuliko kwenye impeller outlet. M1 imeonyesha strongest suppression effect na M2 second strongest.

Pressure difference katika single impeller passage

Vielelezo 12 na 13 vinaonyesha pressure distribution kutoka suction surface kwenda pressure surface katika single impeller-blade passage.

High-pressure peak na low-pressure trough katika M0 huenea kuelekea passage center na kuunda double-peak wave structure. Katika M1, typical double peak imepotea kwa kiasi kikubwa, na propagation ya high- na low-pressure waves imedhoofika. Katika M2, wave structure bado inafanana na M0, lakini amplitude na gradient ziko lower.

Special monitoring points kwenye impeller outlet

Kielelezo 14 kinalinganisha \(\theta_{i1}\) point karibu na suction surface, \(\theta_{i2}\) katika passage center na \(\theta_{i3}\) karibu na pressure surface.

Katika M0, pressure ya \(\theta_{i1}\) ni takribani \(0,34\times10^5\) Pa, yaani 34 kPa higher than pressure ya \(\theta_{i3}\). Pressure waves kutoka ends mbili huenea kwenda middle point na kuunda double-peak signal katika \(\theta_{i2}\).

Katika M1, difference kati ya points tatu imepungua kwa wazi, na low pressure inayosambaa kutoka pressure surface kwenda middle region huacha weak trough pekee.

Katika M2, main peak na smaller secondary trough zimehifadhiwa, lakini kwa sababu minimum-pressure amplitude imeongezeka, total pressure difference ndani ya passage imepungua. Rounding imesmooth sudden drop hasa katika last 45°-60° circumferential section ya blade.

Pressure propagation katika diffuser passage

Vielelezo 15-17 vinaonyesha pressure kwenye suction surface, middle region na pressure surface ya single diffuser passage.

Katika M0, low pressure kutoka impeller pressure surface huunda symmetric V-shaped trough katika diffuser passage. High pressure husambaa kutoka diffuser pressure surface kwenda suction surface, na low pressure katika opposite direction. Difference kati ya highest na lowest regions ni takribani \(0,43\times10^5\) Pa, yaani 43 kPa.

Katika M1, propagation ya high-pressure peak na low-pressure trough kupitia diffuser imepungua kwa kiasi kikubwa. Katika M2, structure inafanana na M0 lakini amplitudes ni lower.

Katika time signals, M1 peak na trough amplitudes ni lowest, na M2 values ziko kati ya M0 na M1.

Frequency spectra

Kielelezo 18 kinaonyesha amplitude ya pressure coefficient katika harmonics tofauti kwenye single impeller na diffuser passage kama three-dimensional surfaces.

Kwenye impeller outlet:

• M0 imezalisha regular peak-trough pairs katika \(7f_n\), \(14f_n\), \(21f_n\) na \(28f_n\) components.
• M2 distribution imefanana na M0, huku amplitudes zikipungua kidogo tu.
• Katika M1, fundamental \(7f_n\) component imebadilika kuwa more single-peaked structure kutoka suction surface kwenda pressure surface.

Kwenye diffuser inlet:

• Katika M0, \(6f_n\), \(12f_n\), \(18f_n\) na \(24f_n\) harmonics zinaonekana wazi.
• M2 imezalisha lower amplitudes than M0 katika all principal harmonics.
• M1 imetoa lowest amplitudes among all models.
• Katika M1, position ya \(6f_n\) peak imehamia kutoka passage center kuelekea diffuser pressure surface.

Utafiti unalinganisha frequency amplitudes kutoka graphs, lakini hautoi numerical reduction-percentage table kwa kila harmonic.

Pressure-fluctuation distribution katika whole pump

Kielelezo 19 kinaonyesha \(S_{C_p}\) value kwenye impeller mid-plane, meridional plane, streamlines, impeller-outlet annular surface na diffuser-inlet annular surface.

Main trends ni:

• Pressure fluctuation huongezeka kutoka impeller inlet kuelekea impeller outlet.
• Katika diffuser hupungua kutoka inlet kuelekea outlet.
• Strongest geometry effect inaonekana kwenye diffuser inlet.
• Effect kwenye impeller inlet na diffuser outlet ni limited zaidi.
• Katika M0, high-fluctuation regions huundwa karibu na diffuser suction surface na inlet edge.
• M2 hupunguza regions hizi, na M1 huzisuppress kwa nguvu zaidi.

M1 pia inaonekana kuunda \(S_{C_p}\) peak iliyo higher than M0 katika specific local point kwenye impeller outlet. Kwa hiyo, M1 haijapunguza fluctuation katika kila point ya whole pump field; overall advantage yake imejitokeza hasa katika critical rotor-stator region kwenye diffuser inlet.

\(\Omega\) vortex structures

Kielelezo 20 kinaonyesha vortex structures za models tatu katika \(1/3T\), \(2/3T\) na \(T\) moments za one impeller revolution. Structures zimecolor kwa turbulent vortex frequency.

Katika M0:

• Distinct vortex clusters zimeundwa karibu na trailing edge.
• Vortex intensity iliongezeka katika \(2/3T\) na kusambaa kwenye rotor-stator gap.
• Large-scale clustered structures zilihifadhiwa mwisho wa full revolution.

Katika M1 na M2:

• Vortexes zimekuwa smaller na more fragmented.
• Single large high-intensity vortex region inaonekana less pronounced.
• Vortexes zimesambazwa more regularly katika rotor-stator gap.
• Suppression effect ya M1 inaonekana stronger than M2.

Images hizi zinaunga mkono mechanistic interpretation kwamba thinning trailing edge hupunguza thick wake region na vortex merging. Hata hivyo, utafiti hautoi comparative numerical table ya total vortex volume, average \(\Omega\), vortex energy au vortex lifetime. Conclusion ya “best vortex control” inategemea predominantly qualitative evaluation ya three-dimensional images pamoja na pressure field.

Je, M1 na M2 zinatumika kwa lengo lilelile?

Designs mbili zina strengths tofauti:

M1 inaweza kutafsiriwa kama design inayoprioritize low fluctuation na stability; M2 kama more balanced design inayolenga efficiency increase pamoja na fluctuation reduction. Utafiti haujalinganisha manufacturing cost, durability au long-term erosion properties za geometries hizi mbili.

Energy na carbon-dioxide calculation

Waandishi wamescale nominal-point efficiency increase ya M2 ya 0,9-1,2 percentage points kwa typical 15 kW marine pump na kuripoti, kwa saa 5.000 za operation kwa mwaka:

• 900-1.200 kWh/year electricity saving,
• 450-600 kg/year CO₂ reduction

.

900-1.200 kWh/year ikigawanywa kwa saa 5.000 inalingana na average electrical demand iliyo lower kwa 0,18-0,24 kW. Hata hivyo, information ifuatayo inahitajika ili result hii iwe reproduced:

• Ikiwa 15 kW value ni motor input power au hydraulic output power,
• Actual baseline na optimized operating efficiencies,
• Flow rate na head ambazo pump inafanya kazi nazo throughout year,
• Motor na drive efficiencies,
• Electricity emission factor iliyotumika.

Kwa kuwa inputs hizi hazijatolewa kwa detail katika PDF, energy na CO₂ values zinapaswa kutathminiwa zaidi kama approximate example ya possible scaled impact ya design, si direct reproducible life-cycle calculation.

Transfer kwenda marine applications

Utafiti unapendekeza kwamba reduced pressure fluctuation inaweza kupunguza piping vibration na fatigue risk katika offshore platforms; smaller vortex-induced forces zinaweza kupunguza underwater radiated noise; na efficiency increase inaweza kupunguza fuel na electricity demand ya ship au hybrid marine power system.

Hata hivyo, marine conditions zifuatazo hazijatathminiwa katika experiment au CFD:

• Seawater salinity na density-viscosity difference,
• Corrosion na surface roughness increase over time,
• Marine biofouling,
• Sand, sediment au particulate flow,
• Wave-induced variable inlet pressure na flow rate,
• Effect ya ship roll na pitch motion kwenye inlet flow,
• Cavitation na net positive suction head,
• Actual piping vibration na acoustic-noise measurement,
• Long-term wear na fatigue.

Waandishi pia wanaeleza kwamba future studies zinahitaji seawater, wave-induced transient flow na long-term corrosion experiments.

Nguvu za utafiti

• Unaunganisha trailing-edge design si na efficiency pekee bali pia na pressure-wave na vortex mechanism.
• Unatumia closed-loop experiments pamoja na time-dependent CFD.
• Unamodel full flow passage na rotor-stator interface.
• Unatoa mesh-independence na time-step comparison.
• Unaweka hundreds of monitoring points kwenye impeller outlet na diffuser inlet.
• Unachambua pressure kwa pamoja katika time, circumferential-position na frequency domains.
• Unawasilisha single-passage na full-circumference analyses separately.
• Unahamisha pressure-coefficient standard deviation kwenye three-dimensional surfaces.
• Unaonyesha vortex clustering kwa \(\Omega\) method.
• Unatenganisha different design strengths za M1 na M2.

Main limitations za utafiti

• Utafiti ni preprint ambayo haijapitia peer review.
• Experiments zilifanywa kwa clean water katika laboratory closed loop.
• Seawater, wave, ship-motion na corrosion conditions hazijajaribiwa.
• Kwa M1, M0-M2-level experimental external-performance comparison haijawasilishwa.
• Best pressure na vortex results za M1 zinategemea mainly CFD.
• Quantitative error metric au uncertainty budget ya experiment-CFD agreement haijatolewa.
• Experimental repeats, standard deviations na error bars hazijaonyeshwa.
• Single pump geometry na nominal rotational speed pekee zimechunguzwa.
• Detailed pressure-mechanism analysis ni mainly katika nominal-flow condition.
• Cavitation haijamodeliwa.
• Fluid-structure interaction, actual vibration na piping fatigue hazijakokotolewa.
• Underwater noise haijapimwa directly.
• Aggregate numerical vortex-volume au energy metric haijatolewa kwa \(\Omega\) vortex comparison.
• Full coordinate definition ya M1 Bézier control points haijakamilika.
• Structural strength ya trailing-edge modification haijatathminiwa.
• Manufacturability, machining tolerance na cost analysis hazijafanywa.
• Long-term erosion na wear behavior hazijatathminiwa.
• All intermediate inputs za energy na CO₂ saving calculation hazijatolewa.
• Kuna inconsistencies katika baadhi ya figure captions na blade numbers.

Utafiti unaunga mkono nini?

• Unaunga mkono kwamba blade exit-edge geometry hubadilisha pressure field katika rotor-stator region.
• Unaonyesha kwamba M1 na M2 hupunguza low-pressure region kwenye impeller outlet.
• Unaonyesha kwamba M1 hupunguza high-low pressure difference katika impeller passage kwa takribani asilimia 45 relative na M0.
• Unaonyesha kwamba M2 hupunguza difference ileile kwa takribani asilimia 31.
• Unaonyesha kwamba trailing-edge optimization ina stronger effect kwenye diffuser-inlet pressure fluctuation kuliko impeller outlet.
• Unaunga mkono kwamba M1 hutoa lowest diffuser-inlet fluctuation katika investigated CFD conditions.
• Unaunga mkono kwamba M2 huongeza efficiency katika experiment na CFD na huongeza head kidogo katika low flow.
• Unatoa visual flow evidence kwamba optimized geometries hupunguza large vortex clustering.
• Unaunga mkono mechanistic relation kati ya pressure-wave propagation na vortex-induced disturbances.

Utafiti haujathibitisha nini?

• Haujaonyesha kwamba M1 au M2 zitatoa same efficiency increase katika all marine pumps.
• Hauonyeshi kwamba same pressure-fluctuation reduction itadumishwa katika seawater environment.
• Haukokotoi piping vibration au fatigue-life change.
• Hauthibitishi measurable reduction ya underwater noise.
• Hauonyeshi kwamba cavitation resistance imeboreshwa.
• Haithibitishi directly kwamba M1 itatoa better pressure suppression than M2 katika real experimental setup.
• Hauthibitishi kwamba 900-1.200 kWh saving itatokea katika specific ship au offshore facility.
• Hauonyeshi kwamba 450-600 kg CO₂ reduction itakuwa valid kwa different electricity au fuel mixes.
• Hauthibitishi kwamba structural life ya thinned trailing edge inatosha.

Mbinu na Matokeo ya Utafiti

Research design

Technical summary ya model comparison

Summary ya pressure-wave mechanism

1. Impeller blade inapokaribia diffuser vane, pressure field kati yao inacompress.
2. Local high pressure huundwa katika intersection ya impeller suction surface na diffuser pressure surface.
3. Low pressure huundwa katika intersection ya impeller pressure surface na diffuser suction surface.
4. High na low pressure regions huenea kuelekea kila nyingine across passage.
5. Katika M0, propagation hii huunda distinct peak-trough pairs.
6. M2 hupunguza pressure-change gradient kwa kuround transition.
7. M1 hudhoofisha pressure-wave na vortex source kwa nguvu zaidi kwa thinning wake region.

Frequency-domain findings

Limit ya experimental validation

Kwa M2, experiment na CFD curves zimeonyesha similar general trend. Hii inaunga mkono kwamba numerical method inaweza kuwakilisha M0-M2 performance difference. Hata hivyo, M1 best pressure-suppression result haijavalidate kwa same experimental scope. Kwa hiyo, evidence level ya M1 results inategemea numerical flow field zaidi kuliko M2 external-performance result.

Assessment ya publication na application readiness

Utafiti ni strong preliminary study kwa sababu unatatua rotor-stator pressure field kwa detail na kuonyesha different advantages za designs mbili. M2, kutokana na available experimental data, ni efficiency-improvement candidate iliyo karibu zaidi na application. M1 inaonekana promising zaidi kwa low pressure fluctuation lakini inahitaji prototype na experimental validation katika same scope.

Kabla ya real marine application, validations zifuatazo zinahitajika:

• Physical prototypes za M1 na M2 zenye same manufacturing tolerance,
• Performance katika seawater na different temperatures,
• Cavitation experiments,
• Transient inlet conditions zinazowakilisha wave au ship motion,
• Piping vibration na acoustic-noise measurements,
• Long-term corrosion, erosion na structural-fatigue tests,
• Energy na emission calculation based on real duty profile.

Maelezo ya Chanzo na Mbinu

Kichwa kamili cha asili cha utafiti: Blade trailing edge optimization for diffuser centrifugal pumps in marine applications: Enhancing energy efficiency and suppressing rotor-stator interaction toward low-carbon marine pumping systems

Waandishi kwa mpangilio wa PDF: Hui Li; Yuyang Guo; Yong Han; Jiaxing Lu; Junhui Zhang; Yang Yang; Weidong Shi; Ling Zhou.

Equal contribution: PDF haina equal-contribution au co-first authorship information.

Corresponding authors katika PDF: Jiaxing Lu na Ling Zhou.

Contact addresses zilizotolewa katika PDF: jiaxinglu@mail.xhu.edu.cn na lingzhou@ujs.edu.c, ambayo inaonekana imeandikwa incomplete. Official record ya Jiangsu University inaonyesha address ya Ling Zhou kama lingzhou@ujs.edu.cn.

SSRN contact author: Official SSRN record summary inamlist Yuyang Guo kama contact author. Information hii si sawa na two corresponding-author marks katika PDF.

Institution 1: School of Energy and Power Engineering, Xihua University, Chengdu 610039, China.

Institution 2: Key Laboratory of Fluid and Power Machinery, Ministry of Education, Xihua University, Chengdu 610039, China.

Institution 3: National Research Center of Pumps, Jiangsu University, Zhenjiang 212013, China.

Institution 4: School of Mechanical Engineering, Nantong University, Nantong 226019, China.

Institution 5: Hefei Huasheng Pumps & Valves Co. Ltd, Hefei 231131, China.

Institution 6: College of Hydraulic Science and Engineering, Yangzhou University, Yangzhou 225009, China.

Author-institution mapping: Hui Li: 1, 2 na 5; Yuyang Guo: 1 na 2; Yong Han: 1 na 2; Jiaxing Lu: 1 na 2; Junhui Zhang: 3 na 5; Yang Yang: 6; Weidong Shi: 4; Ling Zhou: 3.

DOI:10.2139/ssrn.6947172.

Publication platform: SSRN.

Official link:Official SSRN record page.

Publication year: 2026.

Journal: Peer-reviewed journal version haijathibitishwa.

Original journal publisher: Haiwezi kuthibitishwa kutoka preprint version hii.

Peer-review status: Utafiti haujapitia peer review. Kila page ya PDF ina warning “This preprint research paper has not been peer reviewed”.

Source type: Fluid-machinery na marine-engineering research preprint inayounganisha closed-loop clean-water experiment, transient CFD, spatio-temporal pressure analysis na \(\Omega\) vortex identification.

Funding: National Natural Science Foundation of China General Program, 52479089; Key Project of Joint Fund for Regional Innovation and Development of NSFC, U23A20669; Natural Science Foundation of Sichuan Province General Program, 2024NSFSC0214; National Natural Science Foundation of China, 52079058; Key Laboratory of Fluid and Power Machinery Open Research Subject, LTDL-2025020.

Conflict of interest: Waandishi walitangaza kwamba hakuna known financial interest au personal relationship inayoweza kuathiri utafiti.

Data access: Imeelezwa kwamba data zitatolewa kwa request. Hakuna open-data au open-code repository iliyotolewa.

CRediT contributions: Hui Li; resources, conceptualization, investigation, project administration, supervision na review. Yuyang Guo; first draft, review-editing, investigation, conceptualization, validation na data curation. Yong Han; review na investigation. Jiaxing Lu; funding na methodology. Junhui Zhang, Yang Yang na Weidong Shi; investigation, data curation na validation. Ling Zhou; editing na formal analysis.

CRediT presentation note: Katika PDF, project-administration role ya Hui Li na investigation na validation roles za Yuyang Guo zinaonekana zimeandikwa repeatedly.

Content-preparation method: Makala hii ya Kituruki imeandaliwa kwa kuchunguza entire uploaded 39-page PDF pamoja na experimental-setup photo, pump geometry, mesh images, M0-M1-M2 exit edges, mesh na time-step tables, experiment-CFD curves, pressure-monitoring layout, spatio-temporal contour maps, three-dimensional waterfall graphs, time na position signals, frequency spectra, \(S_{C_p}\) maps na \(\Omega\) vortex images. Hakuna scientific finding iliyoongezwa nje ya PDF. External verification ilitumika tu kwa DOI, SSRN contact author na bibliographic verification ya incomplete e-mail address.

Main scientific warning: Marine-application claims zimetolewa kutoka clean-water laboratory experiments na single-phase CFD. Real seawater, wave-induced inlet disturbance, corrosion, cavitation na long-term field conditions hazijavalidate.

Main experimental warning: Experimental external-performance comparison ni limited kwa M0 na M2. M1 best pressure-fluctuation na vortex-control result haijaonyeshwa directly katika same experimental scope.

Energy na emission warning: 900-1.200 kWh/year na 450-600 kg CO₂/year values ni approximate scaling za authors kwa assumptions za 15 kW na saa 5.000/year. Kwa kuwa baseline efficiency, duty profile na emission-factor details hazijatolewa, results haziwezi reproduced kikamilifu kwa information ya PDF pekee.

Document-consistency warning: Full coordinates za M1 control points hazijaelezwa. Title ya Kielelezo 3 haiendani kikamilifu na content. Ingawa impeller blade count katika table ni sita, expression Bi1-Bi7 imetumika katika text section moja. E-mail address ya Ling Zhou inaonekana incomplete katika PDF.