A three-component laser Doppler anemometer was used to measure the fully developed, turbulent flow in a closed, symmetric, smooth-wall compound channel. Measurements were made across one quadrant of the cross-section since the flow was assumed symmetric. Measurements were made for a single channel Reynolds number. All mean velocity components were calculated and are reported. The mean velocity field results are in good agreement with results reported for similar geometries. The vector plots and the axial vorticity distribution reveal the existence of secondary flow cells in both the main channel and the flood plain. The maximum values of the secondary velocities are at the comer region, on the interface between the main channel and the flood plain. In this region the mean velocity gradients are large, indicating that this might be an area of high turbulence production. The distributions of all Reynolds stresses across the cross-section are reported. The Reynolds stress distributions show peak values near the interface corner region and small values near the center-line and on the axes of symn1etry of the channel. The turbulence kinetic energy distribution verifies the existence of high turbulence energy fluid in the comer region. / Master of Science

No description available.

Renormalization group analysis is a useful tool for studying critical behaviour of stochastic systems. In this thesis, field-theoretic renormalization group will be applied to the scalar model representing directed percolation, known as Gribov model, in presence of the random velocity field. Turbulent mixing will be modelled by the compressible form of stochastic Navier-Stokes equation where the compressibility is described by an additional field related to the density. The task will be to find corresponding scaling properties.

Simulacó numérica directa de la dispersió turbulenta de plomalls amb flotació en un flux en un canal Alexandre Fabregat Tomás, Tarragona, octubre del 2006 1 IntroduccióL'objectiu d'aquest treball és estudiar la dispersió turbulenta de calor en diferents configuracions basades en el canal desenvolupat mitjançant DNS (Direct Numerical Simulations). Aquesta eina ha demostrat ser de gran utilitat a l'hora d'estudiar fluxos turbulents ja que permet, donada una malla computacional capaç de capturar totes les estructures del flux i un esquema que minimitzi els errors i la dissipació numérica, descriure acuradament l'evolució temporal del flux. Permet a més, donada la descripció tridimensional i temporal del flux, determinar amb precisió qualsevol quantitat que seria impossible d'obtenir experimentalment.En el flux en un canal, el fluid esmou entre dues parets planes, llises i paral·leles separades una distància 2d impulsat per un gradient constant mitjà de pressió. El flux s'anomena desenvolupat quan ja no hi ha efectes de regió d'entrada i la única inhomogeneïtat es troba en la direcció normal a la paret. Sota aquestes condicions, les quantitats promitjades esdevenen estacionàries en el temps.En aquest treball s'ha validat el codi computacional mitjançant la reproducció d'algunes configuracions de flux prèviament estudiades per altres autors. Els nous coneixements en l'estudi de la dispersió turbulenta de calor s'han obtingut a l'incloure, en un flux totalment desenvolupat en un canal, una font lineal centrada verticalment que provoca l'aparició d'un plomall amb una temperatura més alta que la del flux del fons i que per tant, al tenir una menor densitat, experimenta flotació i es deflecteix. L'amitjanament temporal del flux permet estudiar les diferents contribucions dels diferents termes rellevants en les equacions de transport.És d'especial interés la comparativa d'aquests resultats amb els corresponents a la formació d'un plomall a partir d'una font lineal d'un escalar passiu.Per altra banda també s'ha estudiat l'eficiència en paral·lel dels mètodes multigrid en la resolució d'equacions de Poisson. Aquestes equacions són d'especial interés ja que apareixen en el càlcul de la pressió i representen un coll d'ampolla en termes de costos computacionals. Aquest mètode numèric ha estat comparat amb els mètodes de gradient conjugat (anteriorment emprats en el codi 3DINAMICS) en la resolució de diferents problemes comparant els costos en termes de temps de CPU i la seua escalabilitat en la màquina multiprocessador de memòria distribuïda del grup de recerca de Mecànica de Fluids de Tarragona.2 Descripció matemàticaUn cop adimensionalitzades mitjançant les escales adequades, les equacions de transport de quantitat de moviment i energia han estat discretitzades sobre una malla desplaçada mitjançant el mètode de volums finits emprant un esquema centrat de segon ordre. La discretització dels termes advectius en els casos amb fonts lineals ha requerit, però, d'un cura especial ja que la no-linealitat d'aquests termes pot provocar oscil·lacions artificials en el camp dels escalars. La difusió numèrica dels mètodes upwind, com el QUICK, ha estat quantificada i comparada amb resultats obtinguts per a esquemes centrats de segon ordre. Les equacions han estat integrades en el temps mitjançant un esquema implícit de segon ordre tipus Crank-Nicholson. També ha estat necessari implementar condicions de sortida per a la temperatura en els casos A i C del tipus no reflectant per tal de garantir la conservació i evitar l'aparició d'estructures artificials en el flux.3 Descripció físicaLa figura 1 presenta un esquema del domini computacional corresponent al canal desenvolupat. De l'esquema es desprén que x, y i z corresponen a les direccions principal del flux, la perpendicular i la normal a les parets respectivament. Les configuracions del flux estudiades es troben resumides a la taula 1 on s'indica la resolució de la xarxa computacional, el nombre de Reynolds (basat en la velocitat de fricció ut) i en el casos amb flotació, el nombre de Grashof, la temperatura de referència i la direcció de flotació (la direcció del vector gravetat).Les dimensions del canal s´on 8pd×2pd×2d en les direccions x, y i z respectivament.En el cas A la temperatura representa un escalar de manera que el plomall format és passiu, és a dir, no hi ha acoblament entre les equacions de quantitat de moviment i energia. A diferència d'aquest, en els casos B i C totes dues equacions queden acoblades pel terme de flotació. Aquest terme apareix quan les diferències de temperatura en el si del fluid generen diferències de densitat. En el cas B, el canal vertical amb convecció mixta, cada paret del canal es troba a una temperatura constant però diferent. El vector gravetat i la direcció del corrent estan alineades de manera que aquesta direcció continua sent homogènia. En la zona propera a la paret calenta la flotació actua en la direcció del corrent imposada pel gradient mitjà de pressió. En canvi, en la zona propera a la paret freda, la flotació s'oposa al moviment del flux.El cas C és similar al cas A però en aquesta ocasió la temperatura no es considera un escalar passiu i per tant la flotació acobla el camp dinàmic amb el de temperatures. El vector gravetat actua en aquest cas en la direcció normal. La inhomogeneïtat en la direcció del flux no permet continuar emprant condicions de contorn periòdiques i per tant, al domini presentat en la figura 1, se li ha acoblat una regió auxiliar a l'entrada on es resolen únicament les equacions de quantitat de moviment. Els camps de velocitat i pressió per a un canal totalment desenvolupat obtinguts en aquest domini auxiliar s'empraran com a condició de contorn a l'entrada del domini de computació. No és necessari cap tipus d'interpolació ja que la resolució del a xarxa d'aquest domini auxiliar és la mateixa que l'emprada en el domini de computació.4 ResultatsEls resultats per a les simulacions presentades en la taula 1 contenen, principalment, els perfils de velocitat i temperatura mitjans així com la intensitat de les fluctuacions. A més, es presenten els perfils de les diferents contribucions dels termes relevants de les equacions de transport amitjanades. Per al cas C, els camps dinàmics i de temperatura no estan desenvolupats. Els perfils mitjans a diferents posicions aigües avall permeten estudiar l'evolució del plomall ascendent a més d'analitzar com la flotació afecta al balanç de les diferents contribucions. La figure 2 presenta el camp mitjà de temperatures per al cas C amb les tres posicions en la direcció principal del flux per a les quals s'han inclòs els perfils.Finalment, es presenten els resultats corresponents a la comparativa entre els diferents solvers per a una equació de Poisson. Tots els mètodes numèrics han es-3Figura 2: Camp mitjà de temperatures per al cas C tat paral·lelitzats mitjançant les llibreries Message Passing Interface. En la figura 3 es presenten com a exemple els resultats (en termes de temps de CPU i speedup) per a la resolució de l'equació de Poisson per al desacoblament de pressió i velocitat en el cas del flux desenvolupat en un canal.Els resultats de speed-up per als diferents mètodes mostren la baixa escalabilitat del solver multigrid comparat amb els altres mètodes del tipus gradient conjugat. La raó radica en les grans necessitats de comunicació d'un algoritme construït sobre un esquema de relaxació tipus SOR. Tanmateix, multigrid és el mètode numèric que requereix menys temps de CPU per concloure la tasca. El factor respecte als mètodes de gradient conjugat pot arribar a ser de 30 i per tant és el millor candidat per a la resolució d'aquests tipus de problemes. / The main goal of this work is to study the turbulent heat transfer in a developed channel flow using Direct Numerical Simulations (DNS). These simulations solve explicitly all the scales present in the turbulent flow so, even for moderate Reynolds numbers, the discretization grids need to be fine enough to capture the smallest structures of the flow and, consequently, DNS demands large computational resources. The flow, driven by a mean constant pressure gradient in the streamwise direction, is confined between two smooth, parallel and infinite walls separated a distance 2d.The turbulent heat transport is studied for three different flow configurations.Some of them are used as benchmark results for this work. The three cases reported can be summarized as:· case A: Scalar plume from a line source in a horizontal channel.· case B:Mixed convection with the gravity vector aligned with the streamwise direction (vertical channel).· case C: Buoyant plume from a line source in a horizontal channel.In addition, preliminary results for a turbulent reacting flow in a fully developed channel are also presented.In the case B heat flux results from a temperature difference between the channel walls. The gravity vector is aligned with the streamwise direction and the Grashof, Reynolds and Prandtl numbers are Gr = 9.6 · 106, Ret = 150 and Pr = 0.71 respectively. Close to the hot wall, buoyancy acts aligned to the flow direction imposed by the mean pressure gradient so velocities are generally increased in comparison with a purely forced convection flow. Oppositely, near the cold wall, buoyancy is opposed to the flow and consequently velocities are decreased.Cases A and C are similar because in both cases a hot fluid is released within a cold background flow through a line source vertically centered in the wall-normal direction located at the inlet. The height of the source is 0.054d. The injected hot fluid disperses forming a hot plume that is convected downstream between the two adiabatic walls of the channel.The difference between cases A and C lies in the fact that for case A heat and momentum are decoupled and temperature acts as an scalar. Advection and diffusion are the only phenomena responsible for the evolution of the plume. On the other hand, in case C, buoyancy couples heat and momentum and, consequently, the plume floats drifting upward as it advances in the channel due to its lower density. In case C, the streamwise direction is not homogenous because of the coupling between heat and momentum. To guarantee developed conditions at the inlet of the channel it has been necessary to attach a buffer domain just before the computational domain. In this buffer domain, the momentum transport equations for a fully developed channel are solved with the same resolution used in the main domain.The results of cases A and B have been used to validate the 3DINAMICS CFD code by comparison with data reported in the literature. This code is written in FORTRAN 90 and parallelized using the Message Passing Interface (MPI-CHlibrary). It uses the second order in time Crank-Nicholson scheme to integrate numerically the transport equations which are discretized spatially using the centered second-order finite volume approach.The analysis of averaged turbulent quantities and the contributions of the different terms of the time-averaged transport equations is used to show how buoyancy affects the turbulent transport of momentum and heat along the channel.Finally, following a similar configuration than that of case A, a chemical reactantA released through line source reacts with a background reactant B following a second order chemical reaction with Damkh¨oler number of 1. Preliminary results for turbulent species transport are also included in this work.Special attention have been devoted to the discretization of the advective terms to avoid non-realistic values of the variables because of the non-linearities of the transport equations. The conservative non-reflecting boundary conditions have been implemented at the outlet to simulate the convected outflow when the streamwise direction can not be considered homogeneous, as in case C. For homogeneous directions, periodic boundary conditions have been used.Large grid resolutions (up to 8 million grid nodes for case C including the buffer region) demand important computational resources. A parallel Multigrid solver has substituted the previous conjugate gradient method to solve the Poisson equation in the pressure calculation. This step was the most expensive in terms of CPU costs. The Multigrid method efficiency has been compared with two different versions of the conjugate gradient approach and it has been demonstrated that this method is the most efficient in terms of CPU time although the current algorithmcan be improved to enhance the scalability inmultiprocessor computers.

No description available.

No description available.

A computer program based on the discrete-element method has been developed to compute friction factors and Nusselt Numbers for fully-developed turbulent flows with randomly-rough surfaces. Formulations of the discrete-element model for fully-developed turbulent flows inside circular pipes and between infinite parallel plates with the necessary adaptations for randomly-rough surfaces are provided. Utilizing the output of a three-dimensional profilometer, proper description of the randomly-rough surface is necessary for use within the discrete-element model. Proper description of the randomly-rough surface is achieved by the McClain (2002) method of characterization. Predictions from the discrete-element model computer program are compared with the classical, laminar and turbulent, smooth-wall results. In addition to the smooth-wall evaluations, predictions are compared with experimental results for turbulent internal flows with deterministic surface roughness. Predictions from the model demonstrated excellent agreement in all cases. Friction factor and Nusselt Number predictions for fully-developed flows over randomly-rough surfaces are also presented. With the friction factor and Nusselt Number data, velocity profiles for flows over randomly-rough, deterministically-rough and smooth surfaces are provided for comparison.

The present thesis focuses on evaluating a conjugate heat transfer (CHT) simulation in a ribbed cooling passage with a fully developed flow assumption using LES with the immersed boundary method (IBM-LES-CHT). The IBM with the LES model (IBM-LES) and the IBM with CHT boundary condition (IBM-CHT) frameworks are validated prior to the main simulations by simulating purely convective heat transfer (iso-flux) in the ribbed duct, and a developing laminar boundary layer flow over a two-dimensional flat plate with heat conduction, respectively. For the main conjugate simulations, a ribbed duct geometry with a blockage ratio of 0.3 is simulated at a bulk Reynolds number of 10,000 with a conjugate boundary condition applied to the rib surface. The nominal Biot number is kept at 1, which is similar to the comparative experiment. As a means to overcome a large time scale disparity between the fluid and the solid regions, the use of a high artificial solid thermal diffusivity is compared to the physical diffusivity. It is shown that while the diffusivity impacts the instantaneous fluctuations in temperature, heat transfer and Nusselt numbers, it has an insignificantly small effect on the mean Nusselt number. The comparison between the IBM-LES-CHT and iso-flux simulations shows that the iso-flux case predicts higher local Nusselt numbers at the back face of the rib. Furthermore, the local Nusselt number augmentation ratio (EF) predicted by IBM-LES-CHT is compared to the body fitted grid (BFG) simulation, experiment and another LES conjugate simulation. Even though there is a mismatch between IBM-LES-CHT prediction and other studies at the front face of the rib, the area-averaged EF compares reasonably well in other regions between IBM-LES-CHT prediction and the comparative studies. / Master of Science / The present thesis focuses on the computational study of the conjugate heat transfer (CHT) investigation on the turbine internal ribbed cooling channel. Plenty of prior research on turbine internal cooling channel have been conducted by considering only the convective heat transfer at the wall, which assumes an iso-flux (constant heat flux) boundary condition at the surface. However, applying an iso-flux condition on the surface is far from the realistic heat transfer mechanism occurring in internal cooling systems. In this work, a conjugate heat transfer analysis of the cooling channel, which considers both the conduction within the solid wall and the convection at the ribbed inner wall surface, is conducted for more realistic heat transfer coefficient prediction at the inner ribbed wall. For the simulation, the computational mesh is generated by the immersed boundary method (IBM), which can ease the mesh generation by simply immersing the CAD geometry into the background volume grid. The IBM is combined with the conjugate boundary condition to simulate the internal ribbed cooling channel. The conjugate simulation is compared with the experimental data and another computational study for the validation. Even though there are some discrepancy between the IBM simulation and other comparative studies, overall results are in good agreement. From the thermal prediction comparison between the iso-flux case and the conjugate case v using the IBM, it is found that the heat transfer predicted by the conjugate case is different from the iso-flux case by more than 40 percent at the rib back face. The present study shows the potential of the IBM framework with the conjugate boundary condition for more complicated geometry, such as full turbine blade model with external and internal cooling system.

Scalar (heat or mass) transfer plays an important role in many industrial and engineering applications. Difficulties in experimental measurements means that there is limited detailed information available, especially in the near-wall region. Prediction in simple flows is well documented and the basis for development of many Computational Fluid Dynamics (CFD) models. This is, however, not the case for scalar transfer, especially when the Prandtl (Pr) or Schmidt number (Sc) is much greater than unity. In complex flows that involve separation and reattachment, the scalar transfer coefficient is significantly different to that of fully developed turbulent flow. The purpose of this Thesis is to investigate high Prandtl number (Pr ≥ 10) scalar transfer in fully developed (pipe) and disturbed (sudden pipe expansion) turbulent flow using CFD. Direct Numerical Simulation (DNS) is the most straight-forward approach to the solution of turbulent flows with scalar transfer. However, this technique is computationally intensive because all turbulent scales need to be resolved by the simulation. Large eddy simulation (LES) is a compromise compared to DNS. Instead of resolving all spatial scales, LES resolves only the large-scales with the small-scales being accounted for by a subgrid-scale model. Chapter 2 details the mathematical, numerical and computational details of LES with scalar transfer. From this, an optimized and highly scalable parallel LES solver was developed based on state-of-the-art LES subgrid-scale models and numerical techniques. Chapter 3 provides a verification of the LES solver for fully developed turbulent pipe flow. Reynolds numbers between Re = 180 and 1050 were simulated with a single Prandtl number of Pr = 0.71. Detailed turbulent statistics are provided for Re = 180, 395 and 590 with varying grid resolution for each Reynolds number. The results from these simulations were compared to established experimental and numerical databases of fully developed turbulent pipe and channel flows. The LES solver was shown to be in good agreement with the prior work with most discrepancies being accounted for by only reporting the resolved (large-scale) component directly reported from the LES results. For a Prandtl number close to unity, the mechanisms of turbulent transport and scalar transfer are similar. The near-wall region was shown to be dominated by large-scale sweeping structures that bring high momentum and scalar concentrations to the near-wall region. These are convected parallel to the wall as diffusion mechanisms act to transfer this to the wall where dissipation takes effect. An ejection structure then acts to transport the resultant low momentum, scalar depleted fluid back to the bulk to be replenished and continue the cycle. As the Prandtl number increases, molecular diffusivity decreases relative to viscosity, and the mechanisms of scalar transfer differ to those at Pr = 0.71. This is investigated in Chapter 4 using simulations at Re = 180, 395 and 590, with detailed statistics at Re = 395 for Pr = 0.71, 5, 10, 100 and 200. Where possible the results are compared to other numerical work and the LES solver was shown to accurately resolve the higher Prandtl number flows. There are marked variations in the scalar transfer with increasing Prandtl number as the turbulent scalar transfer becomes concentrated closer to the wall and dominated by large-scale turbulent structures. Sweeping structures are still responsible for bringing the high scalar concentrations towards the wall, however, high Prandtl number scalars are unable to completely diffuse to the wall in the time that the structure is convected parallel to the wall adjacent to the diffusive sublayer. Therefore, most of the high Prandtl number scalar is returned to the bulk via the ejection structure rather than being dissipated at the wall. Chapter 5 uses the sudden pipe expansion (SPE) to investigate disturbed turbulent flow for an inlet Reynolds numbers of Reb = 15600 and a diameter ratio of E = 1.6. These simulation parameters were chosen to match the experimental LDA measurements of Stieglmeier et al. (1989). The LES results for a range of grid resolutions were shown to be in very good agreement with the experimental work. From the LES results it was determined that the fluctuations in the wall shear stress are important in the near-wall turbulent transport. These are the result of eddies originating from the free shear layer down-washing and impinging upon the wall. This is a more effective sweeping mechanism than that observed for the fully developed turbulent pipe flow. Despite the down-wash structures impinging upon the wall, a viscous sublayer still exists in the reattachment region, albeit much thinner than the fully developed turbulent pipe flow further downstream. Using the same Reynolds number and diameter ratio, scalar transfer simulations were also undertaken in the SPE with Prandtl numbers of Pr = 0.71, 5, 10, 100 and 200. An applied scalar flux was used to heat the expanded pipe wall. The LES results are in agreement with experimental Nusselt numbers from Baughn et al. (1984) for Pr = 0.71. The disturbed turbulent flow enhances the scalar transfer and this is the result of down wash events transporting low (cold) scalar from the inlet pipe to the near-wall of the expanded pipe. This cools the heated wall and enhances localized scalar transfer downstream of the expansion. A diffusive sublayer still exists in the reattachment region within the viscous sublayer for Prandtl numbers greater than unity. As the Prandtl number increases the diffusivity decreases relative to viscosity and near-wall scalar transfer enhancement decreases as the diffusion time-scales increase.

The heat transfer and friction augmentation in the fully developed portion of a 2:1 aspect ratio rectangular channel with orthogonal ribs at channel Reynolds numbers of 20,000, 30,000, and 40,000 is studied both experimentally and computationally. Ribs are applied to the two opposite wide walls. The rib aspect ratio is varied systematically at 1, 3, and 5, with a constant rib height and constant rib pitch (rib-pitch-to-rib-height ratio of 10). The purpose of the study is to extend the knowledge of the performance of rectangular channels with ribs to include high aspect ratio ribs. The experimental investigation is performed using transient Thermochromic Liquid Crystals technique to measure the distribution of the local Nusselt numbers on the ribbed walls. Overall channel pressure drop and friction factor augmentation is also obtained with the experimental setup. A numerical simulation is also performed by solving the 3-D Reynolds-averaged Navier-Stokes equations using the realizable-k-Greek lowercase letter episilon] turbulence model for closure. Flow visualization is obtained from the computational results as well as numerical predictions of local distributions of Nusselt numbers and overal channel pressure drop. Results indicate that with increasing rib width, the heat transfer augmentation of the ribbed walls decreases with a corresponding reduction in channel pressure drop.