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An gudanar da gwaje-gwaje a cikin tashar murabba'i mai kusurwa huɗu da aka toshe ta hanyar layuka masu ratsawa na sandunan silinda guda huɗu masu karkata. An auna matsin lamba akan saman sandar tsakiya da raguwar matsin lamba a fadin tashar ta hanyar canza kusurwar karkata sandar. An gwada haɗa sandunan diamita uku daban-daban. Ana nazarin sakamakon aunawa ta amfani da ƙa'idar kiyaye ƙarfin motsi da la'akari da rabin-empirical. Ana samar da saitin sigogi marasa canzawa da yawa waɗanda ba sa canzawa waɗanda ke danganta matsin lamba a wurare masu mahimmanci na tsarin da girman halayen sandar. An gano cewa ƙa'idar 'yancin kai tana riƙe da yawancin lambobin Euler waɗanda ke nuna matsin lamba a wurare daban-daban, watau idan matsin lamba ba shi da girma ta amfani da hasashen saurin shigarwa na yau da kullun zuwa sandar, saitin ba shi da alaƙa da kusurwar tsomawa. Ana iya amfani da haɗin kai na rabin-empirical da ya haifar don ƙirar irin wannan hydraulics.
Na'urori da yawa na canja wurin zafi da taro sun ƙunshi saitin kayayyaki, tashoshi ko ƙwayoyin halitta waɗanda ruwa ke ratsawa a cikin tsarin ciki mai rikitarwa kamar sanduna, buffers, inserts, da sauransu. Kwanan nan, an sake samun sha'awa wajen samun fahimtar hanyoyin da ke haɗa rarrabawar matsin lamba na ciki da ƙarfi akan abubuwan ciki masu rikitarwa zuwa ga raguwar matsin lamba gaba ɗaya na na'urar. Daga cikin wasu abubuwa, wannan sha'awar ta samo asali ne daga sabbin abubuwa a kimiyyar kayan aiki, faɗaɗa ƙarfin lissafi don kwaikwayon lambobi, da ƙara rage yawan na'urori. Nazarin gwaji na baya-bayan nan game da rarrabawar ciki da asarar matsin lamba sun haɗa da tashoshi masu ƙarfi da haƙarƙari daban-daban masu siffar 1, ƙwayoyin reactor na lantarki 2, matsewar capillary 3 da kayan firam ɗin lattice 4.
Tsarin ciki da aka fi sani shine sandunan silinda ta hanyar na'urori na naúrar, ko dai an haɗa su ko kuma an ware su. A cikin masu musayar zafi, wannan tsari ya zama ruwan dare a gefen harsashi. Faɗuwar matsin lamba a gefen harsashi yana da alaƙa da ƙirar masu musayar zafi kamar masu samar da tururi, masu sanyaya iska da masu fitar da iska. A cikin wani bincike na baya-bayan nan, Wang et al. 5 sun gano yanayin sake haɗawa da yanayin kwararar haɗin gwiwa a cikin tsarin sandunan guda ɗaya. Liu et al.6 sun auna raguwar matsin lamba a cikin tashoshi masu kusurwa huɗu tare da fakitin bututu masu siffar U guda biyu tare da kusurwoyi daban-daban na karkacewa kuma sun daidaita samfurin lambobi wanda ke kwaikwayon fakitin sanda tare da kafofin watsa labarai masu ramuka.
Kamar yadda aka zata, akwai wasu abubuwan daidaitawa da dama da ke shafar aikin hydraulic na bankin silinda: nau'in tsari (misali, mai tsayi ko a layi), girman dangi (misali, tsayi, diamita, tsayi), da kusurwar karkacewa, da sauransu. Marubuta da yawa sun mayar da hankali kan nemo ma'auni marasa girma don jagorantar ƙira don kama tasirin haɗin gwiwar sigogin lissafi. A cikin wani bincike na gwaji na baya-bayan nan, Kim et al. 7 sun gabatar da ingantaccen samfurin porosity ta amfani da tsawon tantanin halitta a matsayin sigar sarrafawa, ta amfani da jerin tandem da staggered da lambobin Reynolds tsakanin 103 da 104. Snarski8 ya yi nazarin yadda ƙarfin bakan, daga accelerometers da hydrophones da aka haɗa zuwa silinda a cikin ramin ruwa, ya bambanta da karkacewar alkiblar kwarara. Marino et al. 9 sun yi nazarin rarraba matsin lamba na bango a kusa da sandar silinda a cikin iskar yaw. Mityakov et al. 10 sun zana filin saurin bayan silinda mai yaw ta amfani da sitiriyo PIV.Alam et al. 11 sun gudanar da cikakken bincike kan silinda masu tandem, suna mai da hankali kan tasirin lambar Reynolds da rabon geometric akan zubar da vortex. Sun sami damar gano yanayi biyar, wato kullewa, kullewa ta lokaci-lokaci, rashin kullewa, kullewa ta subharmonic da yanayin sake haɗa layer. Nazarin lambobi na baya-bayan nan sun nuna samuwar tsarin vortex a cikin kwarara ta cikin silinda masu ƙuntatawa.
Gabaɗaya, ana sa ran aikin hydraulic na tantanin halitta ya dogara ne akan tsari da yanayin tsarin ciki, wanda yawanci ana ƙididdige shi ta hanyar alaƙar gwaji na takamaiman ma'aunin gwaji. A cikin na'urori da yawa waɗanda suka ƙunshi sassan lokaci-lokaci, ana maimaita tsarin kwarara a cikin kowace tantanin halitta, don haka, ana iya amfani da bayanai da suka shafi ƙwayoyin wakilci don bayyana halayen hydraulic na tsarin gabaɗaya ta hanyar samfuran sikelin da yawa. A cikin waɗannan shari'o'in daidaitawa, matakin takamaiman da ake amfani da ƙa'idodin kiyayewa gabaɗaya sau da yawa ana iya rage shi. Misali na yau da kullun shine lissafin fitarwa don farantin orifice 15. A cikin yanayin musamman na sandunan da aka karkata, ko a cikin kwararar da aka iyakance ko a buɗe, wani ma'auni mai ban sha'awa wanda galibi ake ambata a cikin wallafe-wallafen kuma masu ƙira ke amfani da shi shine girman hydraulic mafi rinjaye (misali, raguwar matsin lamba, ƙarfi, mitar zubar da vortex, da sauransu)) don tuntuɓar.) zuwa ga ɓangaren kwararar da ke tsaye zuwa ga axis na silinda. Wannan sau da yawa ana kiransa da ƙa'idar 'yancin kai kuma yana ɗauka cewa yanayin kwararar yana motsawa ne ta hanyar ɓangaren kwararar al'ada kuma tasirin ɓangaren axial da aka daidaita tare da axis na silinda ba shi da yawa. Kodayake babu wata yarjejeniya a cikin wallafe-wallafen kan kewayon ingancin wannan ma'auni, a lokuta da yawa yana ba da ƙiyasin amfani a cikin rashin tabbas na gwaji wanda aka saba da alaƙar gwaji. Nazarin da aka yi kwanan nan kan ingancin ƙa'idar mai zaman kanta sun haɗa da girgizar da vortex ke haifarwa16 da matsakaicin drag417 na mataki ɗaya da mataki biyu.
A cikin wannan aikin, an gabatar da sakamakon nazarin matsin lamba na ciki da raguwar matsin lamba a cikin tashar da ke da layin juye-juye na sandunan silinda guda huɗu masu karkata. A auna haɗakar sanduna uku tare da diamita daban-daban, canza kusurwar karkata. Babban burin shine a binciki hanyar da rarraba matsin lamba akan saman sandar ke da alaƙa da raguwar matsin lamba gaba ɗaya a cikin tashar. Ana nazarin bayanan gwaji ta amfani da lissafin Bernoulli da ƙa'idar kiyaye ƙarfin motsi don tantance ingancin ƙa'idar 'yancin kai. A ƙarshe, ana samar da alaƙa mara girma mara girma waɗanda za a iya amfani da su don tsara na'urorin hydraulic iri ɗaya.
Saitin gwaji ya ƙunshi sashin gwaji mai kusurwa huɗu wanda ya karɓi kwararar iska daga fanka mai siffar axial. Sashen gwajin ya ƙunshi naúrar da ta ƙunshi sandunan tsakiya guda biyu masu layi ɗaya da kuma rabin sanduna guda biyu da aka saka a bangon tashar, kamar yadda aka nuna a Hoto na 1e, duk diamita ɗaya ne. Hotuna 1a–e suna nuna cikakken yanayin da girman kowane ɓangare na saitin gwaji. Hoto na 3 yana nuna saitin tsari.
Sashen Shiga (tsawon a mm). Ƙirƙiri b ta amfani da Openscad 2021.01, openscad.org. Babban sashen gwaji (tsawon a mm). An ƙirƙira shi da Openscad 2021.01, openscad.org c Ra'ayin sashe na babban sashen gwaji (tsawon a mm). An ƙirƙira shi ta amfani da Openscad 2021.01, openscad.org d sashen fitarwa (tsawon a mm). An ƙirƙira shi da Openscad 2021.01, ra'ayin ɓangaren gwaje-gwaje na openscad.org e. An ƙirƙira shi da Openscad 2021.01, openscad.org.
An gwada saitin sanduna uku masu diamita daban-daban. Tebur na 1 ya lissafa halayen siffofi na kowane akwati. An ɗora sandunan a kan na'urar haskawa ta yadda kusurwarsu dangane da alkiblar kwararar ruwa za ta iya bambanta tsakanin 90° da 30° (Hotuna na 1b da 3). Duk sandunan an yi su ne da bakin ƙarfe kuma an sanya su a tsakiya don kiyaye tazara iri ɗaya tsakanin su. An saita matsayin sandunan ta hanyar masu sarari guda biyu da ke wajen sashin gwaji.
An auna yawan kwararar ruwa da ke shiga sashen gwaji ta hanyar amfani da na'urar venturi mai daidaitawa, kamar yadda aka nuna a Hoto na 2, kuma an sa ido a kai ta amfani da na'urar DP Cell Honeywell SCX. An auna zafin ruwan da ke fitowa daga sashen gwaji da ma'aunin zafi na PT100 kuma an sarrafa shi a 45±1°C. Don tabbatar da rarraba saurin gudu da kuma rage matakin rudani a ƙofar tashar, ana tilasta kwararar ruwa da ke shigowa ta cikin allon ƙarfe uku. An yi amfani da nisan da ke tsakanin allon ƙarshe da sandar, kuma tsawon fitowar shine diamita 11 na hydraulic.
Zane-zanen tsarin bututun Venturi da aka yi amfani da shi don auna saurin kwararar shiga (tsawon a cikin milimita). An ƙirƙira shi da Openscad 2021.01, openscad.org.
Kula da matsin lamba a kan ɗaya daga cikin fuskokin sandar tsakiya ta hanyar amfani da famfon matsi na 0.5 mm a tsakiyar ɓangaren gwajin. Diamita na famfon ya yi daidai da tsawon kusurwar 5°; saboda haka daidaiton kusurwar yana kusan 2°. Ana iya juya sandar da aka sa ido a kanta a kusa da axis ɗinta, kamar yadda aka nuna a Hoto na 3. An auna bambanci tsakanin matsin lamba a saman sandar da matsin lamba a ƙofar sashin gwajin da jerin DP Cell Honeywell SCX daban-daban. Ana auna wannan bambancin matsin lamba ga kowane tsari na sanduna, saurin kwararar da ya bambanta, kusurwar karkata \(\alpha \) da kusurwar azimuth \(\theta \).
Saitunan kwarara. Bangon tashar suna da launin toka. Gudun yana gudana daga hagu zuwa dama kuma sandar ta toshe shi. Lura cewa ra'ayi "A" yana tsaye a kan sandar. Sandunan waje suna da rabin-haɗe a cikin bangon tashar gefe. Ana amfani da protractor don auna kusurwar karkacewa \(\alpha \).An ƙirƙira shi da Openscad 2021.01, openscad.org.
Manufar gwajin ita ce a auna da kuma fassara raguwar matsin lamba tsakanin hanyoyin shiga tashar da matsin lamba a saman sandar tsakiya, \(\theta\) da \(\alpha\) don azimuths da dips daban-daban. Don taƙaita sakamakon, za a bayyana matsin lamba mai bambanci a cikin siffa mara girma kamar lambar Euler:
inda \(\rho \) shine yawan ruwa, \({u}_{i}\) shine matsakaicin saurin shiga, \({p}_{i}\) shine matsin lamba na shiga, kuma \({p }_{w}\) shine matsin lamba a wani wuri da aka bayar akan bangon sandar. Saurin shiga yana dawwama a cikin jeri uku daban-daban da aka ƙayyade ta hanyar buɗewar bawul ɗin shiga. Saurin da ya haifar yana tsakanin 6 zuwa 10 m/s, daidai da lambar tashar Reynolds, \(Re\equiv {u}_{i}H/\nu \) (inda \(H\) shine tsayin tashar, kuma \(\nu \) shine danko na kinematic) tsakanin 40,000 da 67,000. Lambar sandar Reynolds (\(Re\equiv {u}_{i}d/\nu \)) tana tsakanin 2500 zuwa 6500. Ƙarfin girgizar da aka kiyasta ta hanyar daidaitaccen karkacewar siginar da aka rubuta a cikin venturi shine 5% a matsakaici.
Siffa ta 4 ta nuna alaƙar \({Eu}_{w}\) da kusurwar azimuth \(\theta \), wanda aka daidaita ta kusurwoyi uku masu nutsewa, \(\alpha \) = 30°, 50° da 70°. An raba ma'aunin zuwa jadawali uku bisa ga diamita na sandar. Ana iya ganin cewa a cikin rashin tabbas na gwaji, lambobin Euler da aka samu ba su da alaƙa da ƙimar kwarara. Dogaro gabaɗaya akan θ yana bin yanayin matsin lamba na bango da aka saba a kusa da kewayen wani cikas na zagaye. A kusurwoyin da ke fuskantar kwarara, watau, θ daga 0 zuwa 90°, matsin lambar bangon sandar yana raguwa, yana kaiwa mafi ƙarancin 90°, wanda ya yi daidai da rata tsakanin sandunan inda saurin ya fi girma saboda iyakokin yankin kwarara. Bayan haka, akwai dawo da matsin lamba na θ daga 90° zuwa 100°, bayan haka matsin lamba ya kasance iri ɗaya saboda rabuwar layin iyaka na baya na bangon sandar. Lura cewa babu canji a kusurwar mafi ƙarancin matsin lamba, wanda ke nuna cewa akwai yiwuwar rikice-rikice daga yankewa kusa da shi yadudduka, kamar tasirin Coanda, sune na biyu.
Bambancin adadin Euler na bangon da ke kewaye da sandar don kusurwoyi daban-daban na karkacewa da diamita na sandar. An ƙirƙira shi da Gnuplot 5.4, www.gnuplot.info.
A cikin waɗannan, muna nazarin sakamakon bisa ga zato cewa za a iya kimanta lambobin Euler ne kawai ta hanyar sigogin lissafi, watau rabon tsawon fasali \(d/g\) da \(d/H\) (inda \(H\) shine tsayin tashar) da karkacewa \(\alpha \). Wata doka mai amfani da aka saba amfani da ita ta bayyana cewa ƙarfin tsarin ruwa akan sandar yaw ana ƙaddara shi ta hanyar hasashen saurin shiga da ke tsaye zuwa ga axis ɗin sanda, \({u}_{n}={u}_{i}\mathrm {sin} \alpha \). Wannan wani lokacin ana kiransa ƙa'idar 'yancin kai. Ɗaya daga cikin manufofin binciken mai zuwa shine bincika ko wannan ƙa'idar ta shafi lamarinmu, inda kwarara da cikas ke cikin tashoshi masu rufewa.
Bari mu yi la'akari da matsin lambar da aka auna a gaban saman sandar tsakiya, watau θ = 0. Bisa ga lissafin Bernoulli, matsin lambar da ke wannan matsayi\({p}_{o}\) ya gamsar:
inda \({u}_{o}\) shine saurin ruwa kusa da bangon sandar a θ = 0, kuma muna ɗaukar ƙananan asarar da ba za a iya jurewa ba. Lura cewa matsin lamba mai ƙarfi yana da 'yanci a cikin kalmar kuzarin motsi. Idan \({u}_{o}\) babu komai (watau yanayin da ba ya tsayawa), ya kamata a haɗa lambobin Euler. Duk da haka, ana iya lura a cikin Hoto na 4 cewa a \(\theta =0\) sakamakon \({Eu}_{w}\) yana kusa da amma ba daidai yake da wannan ƙimar ba, musamman ga manyan kusurwoyin nutsewa. Wannan yana nuna cewa saurin da ke saman sandar ba ya ɓacewa a \(\theta =0\), wanda za a iya danne shi ta hanyar karkatar da layukan yanzu da aka ƙirƙira ta hanyar karkatar sandar. Tunda kwararar ta ta'allaka ne a saman da ƙasan sashin gwaji, wannan karkatarwar ya kamata ta haifar da sake zagayowar ta biyu, tana ƙara saurin axial a ƙasa da rage saurin a saman. Idan aka ɗauka cewa girman karkatarwar da ke sama shine hasashen saurin shiga akan shaft (watau \({u}_{i}\mathrm{cos}\alpha \)), sakamakon lambar Euler mai dacewa shine:
Siffa ta 5 ta kwatanta daidaiton.(3) Yana nuna kyakkyawar jituwa da bayanan gwaji masu dacewa. Matsakaicin karkacewar shine 25%, kuma matakin amincewa shine 95%. Lura cewa daidaiton.(3) Daidai da ƙa'idar 'yancin kai. Haka kuma, Siffa ta 6 ta nuna cewa lambar Euler ta yi daidai da matsin lamba a saman baya na sandar, \({p}_{180}\), da kuma a fita daga sashin gwaji, \({p}_{e}\), Hakanan yana bin yanayin da ya dace da \({\mathrm{sin}}^{2}\alpha \). Duk da haka, a cikin duka halayen biyu, ma'aunin ya dogara da diamita na sandar, wanda ya dace tunda na ƙarshe yana ƙayyade yankin da aka hana. Wannan fasalin yayi kama da raguwar matsin lamba na farantin orifice, inda tashar kwararar ta ragu a wasu wurare. A cikin wannan ɓangaren gwaji, rawar da ramin ke takawa tana gudana ta hanyar rata tsakanin sandunan. A wannan yanayin, matsin lamba yana raguwa sosai a matsewa kuma yana murmurewa kaɗan yayin da yake faɗaɗa baya. Idan aka yi la'akari da ƙuntatawa a matsayin toshewa A tsaye a kan sandar, za a iya rubuta raguwar matsin lamba tsakanin gaba da bayan sandar kamar haka:
inda \({c}_{d}\) wani ma'aunin jan bayanai ne wanda ke bayanin dawo da matsin lamba na ɓangare tsakanin θ = 90° da θ = 180°, kuma \({A}_{m}\) da \({A}_{f}\) shine mafi ƙarancin giciye-sashe kyauta a kowane tsawon raka'a a tsaye zuwa ga axis ɗin sandar, kuma alaƙarsa da diamita na sandar shine \({A}_{f}/{A}_{m}=\ ​​Hagu (g+d\right)/g\). Lambobin Euler masu dacewa sune:
Lambar bango ta Euler a \(\theta =0\) a matsayin aikin dip. Wannan lanƙwasa ya yi daidai da lissafin.(3). An ƙirƙira shi da Gnuplot 5.4, www.gnuplot.info.
Lambar bango ta Euler tana canzawa, a cikin \(\theta =18{0}^{o}\) (cikakken alama) da kuma fita (alamar babu komai) tare da dip. Waɗannan lanƙwasa sun yi daidai da ƙa'idar 'yancin kai, watau \(Eu\propto {\mathrm{sin}}^{2}\alpha \).An ƙirƙira shi da Gnuplot 5.4, www.gnuplot.info.
Siffa ta 7 ta nuna dogaro da \({Eu}_{0-180}/{\mathrm{sin}}^{2}\alpha \) akan \(d/g\), yana nuna daidaito mai kyau sosai.(5). Ma'aunin ja da aka samu shine \({c}_{d}=1.28\pm 0.02\) tare da matakin amincewa na 67%. Haka kuma, jadawalin iri ɗaya kuma yana nuna cewa jimillar raguwar matsin lamba tsakanin shigarwa da fitarwa na sashin gwaji yana bin irin wannan yanayin, amma tare da ma'auni daban-daban waɗanda ke la'akari da dawo da matsin lamba a cikin sararin baya tsakanin sandar da fitowar tashar. Ma'aunin ja da ya dace shine \({c}_{d}=1.00\pm 0.05\) tare da matakin amincewa na 67%.
Ma'aunin jan yana da alaƙa da faɗuwar matsin lamba ta \(d/g\) gaba da bayan sandar \(\left({Eu}_{0-180}\right)\) da kuma jimillar faɗuwar matsin lamba tsakanin shigarwar tashar da fitarwa. Yankin launin toka shine band na amincewa na 67% don haɗin gwiwa. An ƙirƙira shi da Gnuplot 5.4, www.gnuplot.info.
Mafi ƙarancin matsin lamba \({p}_{90}\) akan saman sandar a θ = 90° yana buƙatar kulawa ta musamman. Dangane da lissafin Bernoulli, tare da layin yanzu ta cikin rata tsakanin sandunan, matsin lamba a tsakiya \({p}_{g}\) da saurin \({u}_{g}\) a cikin rata tsakanin sandunan (ya yi daidai da tsakiyar tashar) yana da alaƙa da waɗannan abubuwan:
Matsin \({p}_{g}\) na iya dangantawa da matsin saman sandar a θ = 90° ta hanyar haɗa rarrabawar matsin lamba a kan rata da ke raba sandar tsakiya tsakanin tsakiyar wurin da bango (duba Hoto na 8). Daidaiton ƙarfi yana ba da 19:
inda \(y\) shine daidaitawar da ta dace zuwa saman sandar daga tsakiyar wurin rata tsakanin sandunan tsakiya, kuma \(K\) shine lanƙwasa layin yanzu a matsayi \(y\). Don kimantawa na nazari na matsin lamba akan saman sandar, mun ɗauka cewa \({u}_{g}\) iri ɗaya ne kuma \(K\left(y\right)\) layi ne. An tabbatar da waɗannan zato ta hanyar lissafin lambobi. A bangon sandar, lanƙwasa ana ƙayyade shi ta hanyar sashin ellipse na sandar a kusurwar \(\alpha \), watau \(K\left(g/2\right)=\left(2/d\right){\ mathrm{sin} }^{2}\alpha \) (duba Hoto na 8). Sannan, game da lanƙwasa na layin da ke ɓacewa a \(y=0\) saboda daidaito, lanƙwasa a daidaitaccen duniya \(y\) an bayar da shi ta:
Siffar hangen nesa ta giciye, gaba (hagu) da sama (ƙasa). An ƙirƙira shi da Microsoft Word 2019,
A gefe guda kuma, ta hanyar kiyaye nauyi, matsakaicin gudu a cikin jirgin sama yana da alaƙa da kwararar da ke wurin aunawa \(\langle {u}_{g}\rangle \) yana da alaƙa da saurin shiga:
inda \({A}_{i}\) shine yankin kwararar da ke tsakanin sassan biyu a wurin shiga tashar kuma \({A}_{g}\) shine yankin kwararar da ke tsakanin sassan biyu a wurin aunawa (duba Hoto na 8) bi da bi ta hanyar:
Lura cewa \({u}_{g}\) ba daidai yake da \(\langle {u}_{g}\rangle \) ba. A gaskiya ma, Hoto na 9 yana nuna rabon gudu \({u}_{g}/\langle {u}_{g}\rangle \), wanda aka ƙididdige ta hanyar lissafi.(10)–(14), wanda aka zana bisa ga rabon \(d/g\). Duk da wasu bambance-bambance, ana iya gano wani yanayi, wanda aka kimanta ta hanyar polynomial na tsari na biyu:
Rabon matsakaicin gudun \({u}_{g}\) da matsakaicin \(\langle {u}_{g}\rangle \) na tsakiyar tashar\(.\) Lanƙwasa masu ƙarfi da masu lanƙwasa sun yi daidai da daidaito.(5) da kewayon bambancin ma'aunin ma'auni masu dacewa \(\pm 25 \% \). An ƙirƙira shi da Gnuplot 5.4, www.gnuplot.info.
Siffa ta 10 ta kwatanta \({Eu}_{90}\) da sakamakon gwaji na lissafin.(16). Matsakaicin karkacewar dangi shine 25%, kuma matakin amincewa shine 95%.
Lambar Bango ta Euler a \(\theta ={90}^{o}\). Wannan lanƙwasa ya yi daidai da lissafin.(16). An ƙirƙira shi da Gnuplot 5.4, www.gnuplot.info.
Ana iya ƙididdige ƙarfin da ke aiki a kan sandar tsakiya mai lanƙwasa zuwa ga axis ɗinta ta hanyar haɗa matsin lamba a saman sandar kamar haka:
inda ma'aunin farko shine tsawon sandar da ke cikin tashar, kuma haɗin yana gudana tsakanin 0 da 2π.
Haskawar \({f}_{n}\) a alkiblar kwararar ruwa ya kamata ta yi daidai da matsin lamba tsakanin shiga da fita na tashar, sai dai idan gogayya tana daidai da sandar kuma ƙarami saboda rashin cikakkiyar ci gaban ɓangaren na gaba. Guduwar motsi ba ta daidaita ba. Saboda haka,
Siffa ta 11 ta nuna jadawalin daidaito.(20) ta nuna kyakkyawar yarjejeniya ga duk yanayin gwaji. Duk da haka, akwai ɗan karkacewa 8% a hannun dama, wanda za a iya danganta shi da kuma amfani da shi azaman kimanta rashin daidaiton motsi tsakanin shigarwar tashar da fitarwa.
Daidaiton wutar lantarki ta tashar. Layin ya yi daidai da lissafin.(20). Ma'aunin haɗin Pearson shine 0.97. An ƙirƙira shi da Gnuplot 5.4, www.gnuplot.info.
An auna canjin kusurwar karkata sandar, matsin lamba a bangon saman sandar da kuma raguwar matsin lamba a cikin tashar tare da layukan da suka karkata na sandunan silinda guda huɗu masu karkata. An gwada haɗa sandunan silinda guda uku daban-daban. A cikin kewayon lambobin Reynolds da aka gwada, tsakanin 2500 da 6500, lambar Euler ba ta dogara da yawan kwararar ba. Matsi a saman sandar tsakiya yana bin yanayin da aka saba gani a cikin silinda, yana da matsakaicin matsayi a gaba kuma mafi ƙaranci a tazara tsakanin sandunan, yana murmurewa a ɓangaren baya saboda rabuwar layin iyaka.
Ana nazarin bayanan gwaji ta amfani da la'akari da kiyaye yanayin motsi da kimantawa na rabin-empirical don nemo lambobi marasa canzawa waɗanda ke danganta lambobin Euler da girman halayen tashoshi da sanduna. Duk fasalulluka na geometric na toshewa ana wakilta su gaba ɗaya ta hanyar rabo tsakanin diamita na sandar da rata tsakanin sandunan (a gefe) da tsayin tashar (a tsaye).
An gano cewa ƙa'idar 'yancin kai ta dogara ne ga yawancin lambobin Euler waɗanda ke nuna matsin lamba a wurare daban-daban, watau idan matsin ba shi da girma ta amfani da hasashen saurin shigarwa na yau da kullun zuwa sandar, saitin ba ya dogara da kusurwar nutsewa. Bugu da ƙari, fasalin yana da alaƙa da taro da motsin kwararar. Lissafin kiyayewa suna da daidaito kuma suna tallafawa ƙa'idar gwaji da ke sama. Matsin saman sandar ne kawai a rata tsakanin sandunan ya ɗan karkata kaɗan daga wannan ƙa'idar. Ana samar da alaƙa mara girma mara girma waɗanda za a iya amfani da su don tsara na'urorin hydraulic iri ɗaya. Wannan hanyar gargajiya ta yi daidai da aikace-aikacen makamancin haka da aka ruwaito kwanan nan na lissafin Bernoulli zuwa hydraulics da hemodynamics20,21,22,23,24.
Wani sakamako mai ban sha'awa musamman ya samo asali ne daga nazarin raguwar matsin lamba tsakanin shigarwa da fita na sashin gwaji. A cikin rashin tabbas na gwaji, sakamakon ma'aunin ja daidai yake da haɗin kai, wanda ke nuna wanzuwar waɗannan sigogi marasa canzawa:
Lura da girman \(\left(d/g+2\right)d/g\) a cikin ma'aunin lissafi.(23) shine girman a cikin baka a cikin lissafi.(4), in ba haka ba ana iya ƙididdige shi da mafi ƙarancin kuma ɓangaren giciye kyauta wanda ke tsaye a kan sandar, \({A}_{m}\) da \({A}_{f}\). Wannan yana nuna cewa ana ɗaukar lambobin Reynolds su kasance cikin kewayon binciken da ake yi a yanzu (40,000-67,000 don tashoshi da 2500-6500 don sanduna). Yana da mahimmanci a lura cewa idan akwai bambancin zafin jiki a cikin tashar, yana iya shafar yawan ruwa. A wannan yanayin, ana iya kimanta canjin dangi a cikin lambar Euler ta hanyar ninka ma'aunin faɗaɗa zafi ta matsakaicin bambancin zafin jiki da ake tsammani.
Ruck, S., Köhler, S., Schlindwein, G., da Arbeiter, F. Ma'aunin canja wurin zafi da raguwar matsin lamba a cikin tashar da haƙarƙari masu siffofi daban-daban suka yi kauri a bango. expert. Canja wurin Zafi 31, 334–354 (2017).
Wu, L., Arenas, L., Graves, J., da Walsh, F. Halayyar ƙwayoyin kwarara: hangen nesa na kwarara, raguwar matsin lamba, da jigilar taro a cikin electrodes masu girma biyu a cikin tashoshi masu kusurwa huɗu. J. Electrochemistry. Jam'iyyar Socialist.167, 043505 (2020).
Liu, S., Dou, X., Zeng, Q. & Liu, J. Mahimman sigogi na tasirin Jamin a cikin ƙwayoyin jini masu ƙunci. J. Gasoline.science.Britain.196, 107635 (2021).