Transferência de calor em fluidos Não-Newtonianos

Foi realizado um estudo sobre o efeito do tipo de fluidos na transferência de calor. Pretende-se determinar a influência da concentração da solução de Goma de Xantano, do número de Reynolds, do número de Weissenberg, da temperatura e do tempo de escoamento no coeficiente de transferência de calor, jH. O estudo da transferência de calor foi feito num permutador de tubos duplos concêntricos. Já o estudo da reologia foi realizado num reómetro. Na caracterização reológica das soluções de XG, a viscosidade aumenta com a concentração das soluções, diminui para taxas de deformação crescentes e com o aumento da temperatura para ambas as soluções. Os dados mostram um aumento da intensidade da pseudoplasticidade com a concentração do polímero, sendo os valores representados pelo modelo de Sisco. A degradação da solução de 0,20% de goma de xantano a 25 ºC, com o escoamento, é muito acelerada. Os resultados dos ensaios apresentam uma diminuição da viscosidade de 9,4% a 22,9%, para tempos de escoamento de 12 a 47 horas, respectivamente. Num escoamento turbulento em conduta de secção circular constante os resultados mostram uma redução de arrasto total de 18 para 33%. Para a solução de 0,10 % de XG, verifica-se um aumento do calor transferido de 115% e de 130%, quando a temperatura aumenta de 25 ºC para 36 ºC, respectivamente. A água apresenta valores de calor transferido superiores, cerca de 170%, aos da solução de 0,1 %XG. O factor de correlação empírico de Colbourn (jH), utilizado neste trabalho apresenta valores de acordo com a relação de Cho and Hartnett (1985): jH<2/f. Quando o caudal do fluido quente aumenta verifica-se uma diminuição do factor jH. Em relação ao tempo de escoamento verifica-se uma diminuição de cerca de 70% do coeficiente de transferência de calor ao fim de 47 horas. Finalmente verificamos uma diminuição do factor de transferência de calor com o aumento da temperatura do fluido quente, para ambas as concentrações de goma de xantano. Para as soluções de 0,10 e 0,20% de XG essa diminuição variou entre 38 e 15% e entre 34 e 3%, respectivamente.

Friction losses of Newtonian and non-Newtonian fluids flowing in laminar regime in a helical coil

This study aimed to carry out experimental work to determine, for Newtonian and non-Newtonian fluids, the friction factor (fc) with simultaneous heat transfer, at constant wall temperature as boundary condition, in fully developed laminar flow inside a vertical helical coil. The Newtonian fluids studied were aqueous solutions of glycerol, 25%, 36%, 43%, 59% and 78% (w/w). The non-Newtonian fluids were aqueous solutions of carboxymethylcellulose (CMC), a polymer, with concentrations of 0.2%, 0.3%, 0.4% and 0.6% (w/w) and aqueous solutions of xanthan gum (XG), another polymer, with concentrations of 0.1% and 0.2% (w/w). According to the rheological study done, the polymer solutions had shear-thinning behavior and different values of viscoelasticity. The helical coil used has an internal diameter, curvature ratio, length and pitch, respectively: 0.00483 m, 0.0263, 5.0 m and 11.34 mm. It was concluded that the friction factors, with simultaneous heat transfer, for Newtonian fluids can be calculated using expressions from literature for isothermal flows. The friction factors for CMC and XG solutions are similar to those for Newtonian fluids when the Dean number, based in a generalized Reynolds number, is less than 80. For Dean numbers higher than 80, the friction factors of the CMC solutions are lower those of the XG solutions and of the Newtonian fluids. In this range the friction factors decrease with the increase of the viscometric component of the solution and increase for increasing elastic component. The change of behavior at Dean number 80, for Newtonian and non-Newtonian fluids, is in accordance with the study of Ali [4]. There is a change of behavior at Dean number 80, for Newtonian and non-Newtonian fluids, which is in according to previous studies. The data also showed that the use of the bulk temperature or of the film temperature to calculate the physical properties of the fluid has a residual effect in the friction factor values.

Uncertainty assessment approach for composite structures based on global sensitivity indices

The problem of uncertainty propagation in composite laminate structures is studied. An approach based on the optimal design of composite structures to achieve a target reliability level is proposed. Using the Uniform Design Method (UDM), a set of design points is generated over a design domain centred at mean values of random variables, aimed at studying the space variability. The most critical Tsai number, the structural reliability index and the sensitivities are obtained for each UDM design point, using the maximum load obtained from optimal design search. Using the UDM design points as input/output patterns, an Artificial Neural Network (ANN) is developed based on supervised evolutionary learning. Finally, using the developed ANN a Monte Carlo simulation procedure is implemented and the variability of the structural response based on global sensitivity analysis (GSA) is studied. The GSA is based on the first order Sobol indices and relative sensitivities. An appropriate GSA algorithm aiming to obtain Sobol indices is proposed. The most important sources of uncertainty are identified.

Uncertainty propagation in inverse reliability-based design of composite structures

An approach for the analysis of uncertainty propagation in reliability-based design optimization of composite laminate structures is presented. Using the Uniform Design Method (UDM), a set of design points is generated over a domain centered on the mean reference values of the random variables. A methodology based on inverse optimal design of composite structures to achieve a specified reliability level is proposed, and the corresponding maximum load is outlined as a function of ply angle. Using the generated UDM design points as input/output patterns, an Artificial Neural Network (ANN) is developed based on an evolutionary learning process. Then, a Monte Carlo simulation using ANN development is performed to simulate the behavior of the critical Tsai number, structural reliability index, and their relative sensitivities as a function of the ply angle of laminates. The results are generated for uniformly distributed random variables on a domain centered on mean values. The statistical analysis of the results enables the study of the variability of the reliability index and its sensitivity relative to the ply angle. Numerical examples showing the utility of the approach for robust design of angle-ply laminates are presented.

Slip flows of Newtonian and viscoelastic fluids in a 4:1 contraction

This work presents a numerical study of the 4:1 planar contraction flow of a viscoelastic fluid described by the simplified Phan-Thien–Tanner model under the influence of slip boundary conditions at the channel walls. The linear Navier slip law was considered with the dimensionless slip coefficient varying in the range ½0; 4500. The simulations were carried out for a small constant Reynolds number of 0.04 and Deborah numbers (De) varying between 0 and 5. Convergence could not be achieved for higher values of the Deborah number, especially for large values of the slip coefficient, due to the large stress gradients near the singularity of the reentrant corner. Increasing the slip coefficient leads to the formation of two vortices, a corner and a lip vortex. The lip vortex grows with increasing slip until it absorbs the corner vortex, creating a single large vortex that continues to increase in size and intensity. In the range De = 3–5 no lip vortex was formed. The flow is characterized in detail for De ¼ 1 as function of the slip coefficient, while for the remaining De only the main features are shown for specific values of the slip coefficient.

Particle transport in fouling caused by kaolin-water suspensions on copper tubes

Particulate fouling tests were carried out using kaolin-water suspensions flowing through an annular heat exchanger with a copper inner tube. The flow rate was changed from test to test, but the fluid temperature and pH, as well as the particle concentration, were maintained constant. In the lower range of fluid velocities (<0.5 m/s), the deposition process seemed to be controlled by mass transfer. The corresponding experimental transport fluxes were compared to the predictions obtained with several models, showing that diffusion governed particle transport. The absolute values of the mass transfer fluxes and their dependences on the Reynolds number were satisfactorily predicted by some of the models.

Runoff and sediment transport in a degraded area

Gully erosion occurs by the combined action of splash, sheetwash and rill-wash (interrill and rill erosion). These erosion processes have a great capacity for both sediment production and sediment transport. The objectives of this experiment were to evaluate hydrological and sediment transport in a degraded area, severely dissected by gullies; to assess the hydraulic flow characteristics and their aggregate transport capacity; and to measure the initial splash erosion rate. In the study area in Guarapuava, State of Paraná, Brazil (lat 25º 24' S; long 51º24' W; 1034 m asl), the soil was classified as Cambissolo Húmico alumínico, with the following particle-size composition: sand 0.116 kg kg-1; silt 0.180 kg kg-1; and clay 0.704 kg kg-1. The approach of this research was based on microcatchments formed in the ground, to study the hydrological response and sediment transport. A total of eight rill systems were simulated with dry and wet soil. An average rainfall of 33.7 ± 4.0 mm was produced for 35 to 54 min by a rainfall simulator. The equipment was installed, and a trough was placed at the end of the rill to collect sediments and water. During the simulation, the following variables were measured: time to runoff, time to ponding, time of recession, flow velocity, depth, ratio of the initial splash and grain size. The rainsplash of dry topsoil was more than twice as high as under moist conditions (5 g m-2 min-1 and 2 g m-2 min-1, respectively). The characteristics of the flow hydraulics indicate transition from laminar to turbulent flow [Re (Reynolds number) 1000-2000]. In addition, it was observed that a flow velocity of 0.12 m s-1 was the threshold for turbulent flow (Re > 2000), especially at the end of the rainfall simulation. The rill flow tended to be subcritical [Fr (Froude Number) < 1.0]. The variation in hydrological attributes (infiltration and runoff) was lower, while the sediment yield was variable. The erosion in the rill systems was characterized as limited transport, although the degraded area generated an average of 394 g m-2 of sediment in each simulation.

Rill erosion on an oxisol influenced by a thin compacted layer

The presence of compacted layers in soils can induce subprocesses (e.g., discontinuity of water flow) and induces soil erosion and rill development. This study assesses how rill erosion in Oxisols is affected by a plow pan. The study shows that changes in hydraulic properties occur when the topsoil is eroded because the compacted layer lies close below the surface. The hydraulic properties that induce sediment transport and rill formation (i.e., hydraulic thresholds at which these processes occur) are not the same. Because of the resistance of the compacted layer, the hydraulic conditions leading to rill incision on the soil surface differed from the conditions inducing rill deepening. The Reynolds number was the best hydraulic predictor for both processes. The formed rills were shallow and could easily be removed by tillage between crops. However, during rill development, large amounts of soil and contaminants could also be transferred.

Scale Effects in Hydraulic Model Tests of Rock Protected Structures, HR-119, 1970

A laboratory investigation was undertaken to determine the limiting model Reynolds number above which the scour behavior of rock protected structures can be reproduced in hydraulic models scaled according to the Froude criterion. A submerged jet was passed over an initially full scour pocket containing uniform glass spheres and the rate of scour was measured as a function of time. The dimensions of the scour pocket and jet and the particle diameters were varied as needed to maintain strict geometric similarity. For each of two different Froude numbers the Reynolds number was varied over a wide range. The normalized scour rate was found to be practically independent of the Reynolds number, R, (based on the jet velocity and particle diameter) at values of R above about 2.5 x 10^3, and to decrease with Rat smaller values. A grid placed in the jet was found to have a very strong effect on the scour rate. In an attempt to explain the effect of R on the scour behavior, turbulent pressure and velocity fluctuations were measured in air flows and water flows, respectively, over rigid scour pockets having the same geometry as those formed in the scour experiments. The normalized spectra of the fluctuations were found to be nearly independent of R, but the flow pattern was found to be very sensitive to the inlet condition, the jet deflecting upward or downward in a not wholly explainable manner. This indicates that scour behavior can be modeled only if the approach flow is also accurately modeled.

Aerodynamical instability of web

Diplomityön tavoitteena oli tutkia miten ilman turbulenttisuus vaikuttaa tasaisesti liikkuvan rainan tilaan. Yhtenä sovelluskohteena teollisuudessa voidaan mainita esimerkiksi leiju-kuivain. Tiedetään, että konenopeuksien kasvu ja siitä johtuva ilmavirran nopeuden kasvu aiheuttaa voimavaikutuksia rainaan ja voi aiheuttaa lepatusta. Lepatus johtaa dynaamiseen epästabiilisuuteen, joka voidaan havaita, kun lineaarinen systeemi tulee epävakaaksi ja joh-taa epälineaariseen, rajoitettuun värähtelyyn. Lepatus huonontaa tuotteiden laatua ja voi johtaa ratakatkoihin. Työssä on esitetty tietoa ilman ja rainan vuorovaikutuksesta, jota hyödyntämällä voidaan kehittää yksinkertaistettu malli, jonka avulla liikkuvaa rainaa voidaan simuloida kuivaimes-sa. Kaasufaasin virtausyhtälöt on ratkaistu eri turbulenttimalleja käyttäen. Myös viskoelas-tisen rainan muodonmuutosta on tarkasteltu. Koska rainalle ei ole kirjallisuudesta saatavilla tarkkoja fysikaalisia ja mekaanisia arvoja, näitä ominaisuuksia testattiin eri arvoilla, jotta rainan käyttäytymistä jännityksen alaisena voidaan tarkastella. Näiden ominaisuuksien tun-teminen on ensiarvoisen tärkeää määritettäessä rainan aeroviskoelastista käyttäytymistä. Virtaussimulointi on kallista ja aikaa vievää. Tämä tarkoittaa uusien tutkimusmenetelmien omaksumista. Tässä työssä vaihtoehtoisena lähestymistapana on esitetty yksinkertaistettu malli, joka sisältää ilman ja rainan vuorovaikutusta kuvaavat ominaisuudet. Mallin avulla saadaan tietoa epälineaarisuuden ja turbulenssin vaikutuksesta sekä monimutkaisesta yh-teydestä stabiilisuuden ja ulkoisesti aikaansaadun värähtelyn sekä itse aiheutetun värähtelyn välillä. Työn lopussa on esitetty havainnollinen esimerkki, jolla voidaan kuvata olosuhteita, jossa rainan tasainen liike muuttuu epävakaaksi. Kun turbulenttisuudesta johtuva painevaih-telu ylittää tietyn rajan, rainan värähtely kasvaa muuttuen satunnaisesta järjestäytyneeksi. Saaduttulokset osoittavat, että turbulenttisuudella on suuri vaikutus eikä sitä voi jättää huomioimatta. Myös rainan viskoelastiset ominaisuudet tulee huomioida, jotta rainan käyt-täytymistä voidaan kuvata tarkasti.

Sälerakenteiset sulku- ja säätölaitteet kaasuvirtauksessa

Sulku- jasäätölaitteita käytetään kaasuvirtausten estämiseen ja ohjaukseen. Yleinen rakennetyyppi on sälerakenne, jossa kanavaan asennettuja akseloituja säleitä kääntämällä saadaan virtauksen vapaata pinta-alaa säädettyä. Sulkulaitteiden virtauksenestokyky riippuu tiiveydestä kiinni-asennossa. Säätölaitteiden virtauksen rajoittamiskyky muuttuu asetuskulman mukaan eri konstruktioilla eri lailla. Työn tavoitteena on ollut tuottaa tehtyjen tutkimusten tuloksista pohjatiedot työn yhteydessä luotavaan raportointi- ja laskentasovellukseen, jolla on mahdollista riittävän tarkasti arvioida Sammet Dampers Oy:n tuotannossa olevien sälerakenteisten sulku- ja säälaitteiden ominaisuuksia ilman tapauskohtaista mittaamista tai mallintamista sekä tuottaa samalla asiakkaille valmiit raportit näistä ominaisuuksista. Tehtyjen tutkimusten pääpaino on ollut säätölaitteissa. Tutkimuksissa on selvitetty mm. säleiden lukumäärän, korkeussuhteen, sivusuhteen ja Reynoldsin luvun vaikutusta laitteen vastuskertoimeen ennalta määritellyillä asetuskulmilla. Tutkimukset koostuvat mallikokeista ja CFD-laskennasta. Lisäksi työn pohjana on ollut huomattava määrä aikaisempia selvityksiä. Työn tavoitteiden täyttämisessä on onnistuttu tyydyttävästi. Tutkittujen tekijöiden vaikutuksille vastuskertoimiin on luotu sovitteet mittausten ja CFD:n perusteella. CFDon osoittautunut käyttökelpoiseksi vain hyvin rajatulle joukolle tapauksia.

Numerical and ExperimentalModelling of Gas Flow and Heat Transfer in the Air Gap of An Electric Machine

This work deals with the cooling of high-speed electric machines, such as motors and generators, through an air gap. It consists of numerical and experimental modelling of gas flow and heat transfer in an annular channel. Velocity and temperature profiles are modelled in the air gap of a high-speed testmachine. Local and mean heat transfer coefficients and total friction coefficients are attained for a smooth rotor-stator combination at a large velocity range. The aim is to solve the heat transfer numerically and experimentally. The FINFLO software, developed at Helsinki University of Technology, has been used in the flow solution, and the commercial IGG and Field view programs for the grid generation and post processing. The annular channel is discretized as a sector mesh. Calculation is performed with constant mass flow rate on six rotational speeds. The effect of turbulence is calculated using three turbulence models. The friction coefficient and velocity factor are attained via total friction power. The first part of experimental section consists of finding the proper sensors and calibrating them in a straight pipe. After preliminary tests, a RdF-sensor is glued on the walls of stator and rotor surfaces. Telemetry is needed to be able to measure the heat transfer coefficients at the rotor. The mean heat transfer coefficients are measured in a test machine on four cooling air mass flow rates at a wide Couette Reynolds number range. The calculated values concerning the friction and heat transfer coefficients are compared with measured and semi-empirical data. Heat is transferred from the hotter stator and rotor surfaces to the coolerair flow in the air gap, not from the rotor to the stator via the air gap, althought the stator temperature is lower than the rotor temperature. The calculatedfriction coefficients fits well with the semi-empirical equations and precedingmeasurements. On constant mass flow rate the rotor heat transfer coefficient attains a saturation point at a higher rotational speed, while the heat transfer coefficient of the stator grows uniformly. The magnitudes of the heat transfer coefficients are almost constant with different turbulence models. The calibrationof sensors in a straight pipe is only an advisory step in the selection process. Telemetry is tested in the pipe conditions and compared to the same measurements with a plain sensor. The magnitudes of the measured data and the data from the semi-empirical equation are higher for the heat transfer coefficients than thenumerical data considered on the velocity range. Friction and heat transfer coefficients are presented in a large velocity range in the report. The goals are reached acceptably using numerical and experimental research. The next challenge is to achieve results for grooved stator-rotor combinations. The work contains also results for an air gap with a grooved stator with 36 slots. The velocity field by the numerical method does not match in every respect the estimated flow mode. The absence of secondary Taylor vortices is evident when using time averagednumerical simulation.

Lämmönsiirron numeerinen laskenta profiloidulle kanavalle.

Työn tavoitteena oli tutkia aaltomaisen profiloinnin vaikutusta suorien jäähdytyskanavien lämmönsiirtoon ja painehäviöön. Erilaisia profiileja oli kymmenen kappaletta ja ne olivat 5mm leveitä ja 30cm pitkiä kukin. Ne laskettiin kolmeulotteisina tapauksina FINFLO-virtausratkaisijalla kolmella eri Reynoldsin luvulla, jotka vastasivat laminaarista, osittain turbulenttista ja lähes kokonaan turbulenttista virtausta. Lämmönsiirtoaine oli kuiva +30°C ilma ja profiloinnin toteutustapa oli toisiaan sivuavat ympyräkaaret kolmella erilaisella säteen arvolla ja kolmella erilaisella aallonpituuden arvolla. Lisäksi laskettiin saman levyisen tasokanavan arvot jokaisella Reynoldsin luvulla kaksiulotteisina tapauksina. Näitä profiloimattomia kanavia pidettiin referenssitapauksina. Tuloksena havaittiin että profiloimalla saadaan yksiselitteisesti suurempi lämpöteho ulos samasta tilavuudesta. Lämmönsiirtokerroin kasvaa profiloinnin avulla parhaimmillaan n. 20% käytetystä turbulenssimallista tai lämmönsiirtokertoimen määritelmästä riippumatta. Painehäviö kasvaa myös aina, mutta kitkakerroin voi hieman pienentyä. Profiilin varsinaisena hyvyyskriteerinä pidettiin lämmönsiirtokertoimen ja kitkakertoimen suhdetta h/f. Se osoittautui riippuvaksi Reynoldsin luvusta ja turbulenssimallista; ASM ja Chien k-έ -mallit ennustavat transitioetäisyyden eri tavalla. Laminaarisilla virtauksilla h/f :n vaihtelu oli vähäistä; suhde vaihteli vain ±5% eri profiilien kesken. ASM-mallilla havaittiin sekundääripyörteilyä, ehkä siksi että se mallintaa anisotrooppisen turbulenssin. Chien k-έ malli ennusti suuremman ja aikaisemmin alkavan turbulenttisuuden kuin ASM. Lisäksi havaittiin mm. että tietyillä profiileilla muodostuu kanavan kapeimpaan kohtaan selvä virtausnopeuden paikallinen minimi seinämän läheisyyden takia.

Wavelet Analysis in Turbulence

The objective of this thesis is to study wavelets and their role in turbulence applications. Under scrutiny in the thesis is the intermittency in turbulence models. Wavelets are used as a mathematical tool to study the intermittent activities that turbulence models produce. The first section generally introduces wavelets and wavelet transforms as a mathematical tool. Moreover, the basic properties of turbulence are discussed and classical methods for modeling turbulent flows are explained. Wavelets are implemented to model the turbulence as well as to analyze turbulent signals. The model studied here is the GOY (Gledzer 1973, Ohkitani & Yamada 1989) shell model of turbulence, which is a popular model for explaining intermittency based on the cascade of kinetic energy. The goal is to introduce better quantification method for intermittency obtained in a shell model. Wavelets are localized in both space (time) and scale, therefore, they are suitable candidates for the study of singular bursts, that interrupt the calm periods of an energy flow through various scales. The study concerns two questions, namely the frequency of the occurrence as well as the intensity of the singular bursts at various Reynolds numbers. The results gave an insight that singularities become more local as Reynolds number increases. The singularities become more local also when the shell number is increased at certain Reynolds number. The study revealed that the singular bursts are more frequent at Re ~ 107 than other cases with lower Re. The intermittency of bursts for the cases with Re ~ 106 and Re ~ 105 was similar, but for the case with Re ~ 104 bursts occured after long waiting time in a different fashion so that it could not be scaled with higher Re.

Virtausjakauman kokeellinen määritys levylämmönsiirtimissä

Diplomityön tavoitteena oli kokeellisen tutkimuksen keinoin selvittää juotettujen levylämmönsiirtimien levypakkarakenteessa virtausten käyttäytyminen ja jakautuminen sekä löytää ideoita ja kehitysehdotuksia levylämmönsiirtimen levypakan ja levyprofiilin kehittämiseksi. Kokeellinen tutkimus suoritettiin Oy Danfoss Ab LPM:n levylämmönsiirtimien tutkimuslaboratoriossa. Virtausjakauman tutkimusta varten suunniteltiin ja valittiin tutkimuslaitteisto, joka koostui termoelementtiantureista, tiedonkeruulaitteistosta sekä ohjelmistosta. Lämmönsiirtimistä mitattiin ensiö- ja toisiopuolen tilavuusvirrat ja painehäviöt sekä lämpötilat ennen ja jälkeen lämmönsiirtimen. Tutkimuslaitteiston avulla mitattiin lämpötiloja lämmönsiirtimen sisältä levyväleistä. Mittaukset suoritettiin neljällä levypakkarakenteella useilla massavirran arvoilla. Mittaustuloksista määritettiin levylämmönsiirtimien lämpö- ja virtaustekniset ominaisuudet nesteen Reynoldsin luvun funktiona sekä selvitettiin nesteen virtausjakaumat. Mittaustuloksien perusteella laskettuja virtausjakauman arvoja verrattiin teorian mukaan laskettuihin jakaumiin. Mitatuista siirtimistä lasketut massavirrat viittaavat siihen, että suurin osa nesteestä virtaa siirtimien keskeltä tai lähempää loppupäätä kuin alkupäästä. Teorian mukaan suurin nestemäärä virtaisi siirtimen alkupäästä vähentyen tasaisesti kohti levypakan loppupäätä. Teorian mukaiselle virtausjakaumalle ja lasketuille jakaumille ei löydetty yhteyttä. Tutkimuksessa havaittiin suuria, jopa yli 20 asteen, lämpötilaeroja levyväleistä ulostulevissa virtauksissa. Levyvälien virtauksen käyttäytymisen ja jakautumisen tutkiminen nähdäänkin levypakan pitkittäistä kehittämistä suurempana mielenkiinnon ja kehittämisen kohteena.