Relevant bibliographies by topics / RG-flow

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'RG-flow'

Author: Grafiati
Published: 4 June 2021
Last updated: 11 March 2023

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Journal articles on the topic "RG-flow"

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LEE, BUM-HOON, SHESANSU SEKHAR PAL, and SANG-JIN SIN. "RG FLOW OF TRANSPORT QUANTITIES." International Journal of Modern Physics A 27, no. 13 (May 16, 2012): 1250071. http://dx.doi.org/10.1142/s0217751x12500716.

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The RG flow equation of various transport quantities are studied in arbitrary space–time dimensions, in the fixed as well as fluctuating background geometry both for the Maxwellian and DBI type of actions. The regularity condition on the flow equation of the conductivity at the horizon for the DBI action reproduces naturally the leading order result of Hartnoll et al. [J. High Energy Phys. 04, 120 (2010)]. Motivated by the result of van der Marel et al. [Science 425, 271 (2003], we studied, analytically, the conductivity versus frequency plane by dividing it into three distinct parts: ω < T, ω > T and ω ≫ T. In order to compare, we choose (3+1)-dimensional bulk space–time for the computation of the conductivity. In the ω < T range, the conductivity does not show up the Drude like form in any space–time dimensions. In the ω > T range and staying away from the horizon, for the DBI action with unit dynamical exponent, nonzero magnetic field and charge density, the conductivity goes as ω-2/3, whereas the phase of the conductivity, goes as, arctan ( Im σxx/ Re σxx) = π/6 and arctan ( Im σxy/ Re σxy) = -π/3. There exists a universal quantity at the horizon that is the phase angle of conductivity, which either vanishes or an integral multiple of π. Furthermore, we calculate the temperature dependence to the thermoelectric and the thermal conductivity at the horizon. The charge diffusion constant for the DBI action is studied.
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Hesamifard, F., and M. M. Rezaii. "Evolution of the Robertson–Walker metric under 2-loop renormalization group flow." International Journal of Modern Physics D 26, no. 03 (February 3, 2017): 1750021. http://dx.doi.org/10.1142/s0218271817500213.

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Here, we study the evolution of a Robertson–Walker (RW) metric under the Ricci flow and 2-loop renormalization group flow (RG-2 flow). We show that a RW metric is a fixed point of the Ricci flow and it is not a solution of the RG-2 flow. RG-2 flow is considered on a doubly twisted product metric with further assumptions and also we introduce a necessary condition for existence of the solution of RG-2 flow.
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Hassler, Falk. "RG flow of integrable E-models." Physics Letters B 818 (July 2021): 136367. http://dx.doi.org/10.1016/j.physletb.2021.136367.

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Lasso Andino, Óscar. "RG-2 flow, mass and entropy." Classical and Quantum Gravity 36, no. 6 (February 26, 2019): 065011. http://dx.doi.org/10.1088/1361-6382/ab05f6.

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IGARASHI, Y., K. ITOH, and H. SO. "EXACT SYMMETRIES REALIZED ON THE RG FLOW." International Journal of Modern Physics A 16, no. 11 (April 30, 2001): 2047–51. http://dx.doi.org/10.1142/s0217751x01004682.

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Mukhopadhyay, Ayan. "Understanding the holographic principle via RG flow." International Journal of Modern Physics A 31, no. 34 (December 6, 2016): 1630059. http://dx.doi.org/10.1142/s0217751x16300593.

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This is a review of some recent works which demonstrate how the classical equations of gravity in AdS themselves hold the key to understand their holographic origin in the form of a strongly coupled large N QFT whose algebra of local operators can be generated by a few (single-trace) elements. I discuss how this can be realized by reformulating Einstein’s equations in AdS in the form of a nonperturbative RG flow that further leads to a new approach toward constructing strongly interacting QFTs. In particular, the RG flow can self-determine the UV data that are otherwise obtained by solving classical gravity equations and demanding that the solutions do not have naked singularities. For a concrete demonstration, I focus on the hydrodynamic limit in which case this RG flow connects the AdS/CFT correspondence with the membrane paradigm, and also reproduces the known values of the dual QFT transport coefficients.
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Bazeia, Dionisio, Francisco A. Brito, and Laercio Losano. "Scalar fields, bent branes, and RG flow." Journal of High Energy Physics 2006, no. 11 (November 23, 2006): 064. http://dx.doi.org/10.1088/1126-6708/2006/11/064.

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Verlinde, Erik, and Herman Verlinde. "RG-flow, gravity and the cosmological constant." Journal of High Energy Physics 2000, no. 05 (May 18, 2000): 034. http://dx.doi.org/10.1088/1126-6708/2000/05/034.

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Bianchi, Massimo, Daniel Z. Freedman, and Kostas Skenderis. "How to go with an RG flow." Journal of High Energy Physics 2001, no. 08 (August 17, 2001): 041. http://dx.doi.org/10.1088/1126-6708/2001/08/041.

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Morales, Jose F., and Mario Trigiante. "Walls from fluxes: an analytic RG-flow." Journal of High Energy Physics 2002, no. 02 (February 15, 2002): 018. http://dx.doi.org/10.1088/1126-6708/2002/02/018.

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Dissertations / Theses on the topic "RG-flow"

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Vaduret, Jean-François. "GPPZ and the Holographic Triforce against Scalars." Thesis, Uppsala universitet, Teoretisk fysik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-397107.

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We use gauge-invariant cosmological perturbation theory to compute one-point functions of active and inert scalar fields of the GPPZ RG-flow in AdS5. Linearized Einstein equations are computed and made gauge-invariant for D-dimensional Euclidean domain-wall geometry. We briefly review the procedure of holographic renormalization for the GPPZ RG-flow in AdS5 to get different one-point functions. The source-dependant vev of the operator dual to the ∆ = 3 active scalar field in the GPPZ solution is computed and agrees with literature. We also find the source-dependant one-point function of the operator dual to the ∆ = 3 inert scalar.
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DE, LUCA GIUSEPPE BRUNO. "Non-Supersymmetric Space-Times and Renormalization Group Flows in String Theory." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2020. http://hdl.handle.net/10281/257784.

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In questa tesi studiamo soluzioni di teoria di stringa da diversi punti di vista. Iniziamo dal Capitolo 1, con un'introduzione alle principali idee proprie delle varie teorie di stringa, concentrandoci in particolare sulle loro descrizioni a bassa energia, le teorie di supergravità. Discutiamo gli ingredienti principali delle teorie di supergravità derivate dalle stringhe e presentiamo le loro soluzioni classiche corrispondenti agli oggetti fisicii che useremo nel resto della tesi. Nel capitolo 2, iniziamo lo studio di soluzioni non supersimmetriche della teoria delle stringhe, costruendo esplicitamente spazi Anti de Sitter (AdS) otto dimensionali come soluzioni delle equazioni del moto della supergravità IIA massiva. Come di consueto per soluzioni non supersimmetriche, siamo in grado di risolvere l'intero sistema di equazioni del moto solo numericamente. Utilizzando questi metodi troviamo soluzioni AdS_8 con uno spazio interno compatto che ha la topologia di una due-sfera con un orientifold plane (O8) al suo equatore. Nel capitolo 3 estendiamo il nostro studio di soluzioni non spersimmetriche con la ricerca di vuoti con costante cosmologica positiva. In particolare troviamo soluzioni de Sitter (dS) quattro dimensionali delle equazioni del moto della supergravità IIA massiva. Alcune di queste soluzioni coinvolgono gli stessi orientifold plane presenti nei vuoti AdS_8, che appaiono nell'approssimazione di supergravità come una particolare singolarità. Analizziamo quindi questa singolarità nel dettaglio, prima di spostarci sullo studio di soluzioni dS_4 con un diverso orientifold plane (O6). L'apparizione di orientifold plane in soluzioni classiche de Sitter delle teorie di supergravità è necessario per evadere un famoso teorema di impossibilità, che si applica anche alle soluzioni AdS_8 descritte nel Capitolo 2. Per questo motivo, lo analizziamo in questo particolare scenario all'inizio di tale capitolo. Infine, nel Capitolo 4 cambiamo la nostra propspettiva e usiamo la supergravità come uno stumento per studiare la fisica dei flussi del Gruppo di Rinormalizzazione (RG). In particolare, usando alcuni ingredienti noti, assembliamo una teoria di supergravità sette dimensionasle e la usiamo per costruire i duali olografici dei flussi RG tra teorie di campo sei dimensionali superconformi. La nostra costruzione è capace di identificare correttamente la fisica di questi flussi RG confermando, dal punto di vista gravitazionale, una congettura presente nella letteratura riguardante i flussi RG ammessi tra queste teorie sei dimensionali.
In this thesis we study solutions of string theories from different perspectives. We start in Chapter 1 with an introduction to the main ideas of string theory, focusing in particular on its low-energy description in terms of supergravity theories. We discuss the main ingredients of the supergravity theories derived from strings and we present their classical solutions corresponding to the physical objects we will use in the rest of the thesis. In Chapter 2 we begin the study of non-supersymmetric backgrounds of string theory, by building explicit eight-dimensional Anti de Sitter (AdS) solutions of massive type IIA supergravity. As is common for non-supersymmetric solutions, we are only able to solve the full set of equations of motion numerically. With these methods, we find AdS_8 solutions with a compact internal space having the topology of a two-sphere, with an orientifold plane (O8) sitting at its equator. In Chapter 3, we extend our study of non-supersymmetric solutions by looking for backgrounds with a positive cosmological constant. In particular, we find numerical four-dimensional de Sitter (dS) solutions of massive type IIA supergravity. Some of these solutions involve the same orientifold plane featuring in the AdS_8 backgrounds, which appears a particular singularity in the supergravity approximation. We analyze this singularity in detail before moving on and studying dS_4 solutions with a different orientifold plane (O6). The appearance of orientifold planes in classical de Sitter solutions of supergravity theories is required in order to evade a famous no-go theorem, which also applies to the AdS_8 solutions we describe in Chapter 2. For this reason, we review it in our particular setting at the beginning of the same chapter. Finally, in Chapter 4 we change our perspective and we use supergravity as a tool to study the physics of the Renormalization Group (RG) flows. In particular, by using known building blocks, we assemble a seven-dimensional gravitational theory and we use it to construct the holographic duals of RG flows between six-dimensional superconformal field theories. Our construction is able to correctly characterize the physics of these RG flows by confirming, from the gravitational point of view, a conjecture on the literature regarding the allowed RG flows between these six-dimensional theories.
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Books on the topic "RG-flow"

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Institute for Computer Applications in Science and Engineering., ed. Renormalization Group (RG) in turbulence: Historical and comparative perspective. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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Book chapters on the topic "RG-flow"

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Mukhopadhyay, Ayan. "Emergence of Gravity and RG Flow." In Gravity and the Quantum, 283–302. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-51700-1_17.

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"RG Flow of Preactivations." In The Principles of Deep Learning Theory, 71–108. Cambridge University Press, 2022. http://dx.doi.org/10.1017/9781009023405.006.

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"Lecture 14. Renormalization Group; RG Flow." In Quantum Field Theory II, 141–54. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813234192_0014.

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Zinn-Justin, Jean. "Stability of renormalization group fixed points and decay of correlations." In From Random Walks to Random Matrices, 101–10. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198787754.003.0007.

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Chapter 7 is devoted to a discussion of the renormalization group (RG) flow when the effective field theory that describes universal properties of critical phenomena depends on several coupling constants. The universal properties of a large class of macroscopic phase transitions with short range interactions can be described by statistical field theories involving scalar fields with quartic interactions. The simplest critical systems have an O(N) orthogonal symmetry and, therefore, the corresponding field theory has only one quartic interaction. However, in more general physical systems, the flow of quartic interactions is more complicated. This chapter examines these systems from the RG viewpoint. RG beta functions are shown to generate a gradient flow. Some examples illustrate the notion of emergent symmetry. The local stability of fixed points is related to the value of the scaling field dimension.
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"RG Flow of the Neural Tangent Kernel." In The Principles of Deep Learning Theory, 199–226. Cambridge University Press, 2022. http://dx.doi.org/10.1017/9781009023405.010.

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ARMONI, ADI. "RG FLOW AND WILSON LOOPS FROM NON-TACHYONIC TYPE 0 MODELS." In The Ninth Marcel Grossmann Meeting, 1109–13. World Scientific Publishing Company, 2002. http://dx.doi.org/10.1142/9789812777386_0177.

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Zinn-Justin, Jean. "The renormalization group (RG) approach: The critical theory near four dimensions." In Quantum Field Theory and Critical Phenomena, 357–90. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198834625.003.0015.

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In Chapter 14, the singular behavior of ferromagnetic systems with O(N) symmetry and short-range interactions, near a second order phase transition has been determined in the mean-field approximation, which is also a quasi-Gaussian approximation. The mean-field approximation predicts a set of universal properties, properties independent of the detailed structure of the microscopic Hamiltonian, the dimension of space, and, to a large extent, of the symmetry of systems. However, the leading corrections to the mean-field approximation, in dimensions smaller than or equal to four, diverge at the critical temperature, and the universal predictions of the mean-field approximation cannot be correct. Such a problem originates from the non-decoupling of scales and leads to the question of possible universality. In Chapter 9, the question has been answered in four dimensions using renormalization theory, and related renormalization group (RG) equations. Moreover, below four dimensions, in an expansion around the mean-field, the most singular terms near criticality can be also formally recovered from a continuum, low-mass φ4 field theory. More generally, following Wilson, to understand universality beyond the mean-field approximation, it is necessary to build a general renormalization group in the form of flow equations for effective Hamiltonians and to find fixed points of the flow equations. Near four dimensions, the flow equations can be approximated by the renormalization group of quantum field theory (QFT), and the fixed points and critical behaviours derived within the framework of the Wilson-Fisher ϵ expansion.
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Conference papers on the topic "RG-flow"

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Vacca, Gian Paolo. "Pomeron-Odderon interactions: A functional RG flow analysis." In DIFFRACTION 2016: International Workshop on Diffraction in High-Energy Physics. Author(s), 2017. http://dx.doi.org/10.1063/1.4977160.

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Bonanno, Alfio. "Proper-time regulators and RG flow in QEG." In GENERAL RELATIVITY AND GRAVITATIONAL PHYSICS: 16th SIGRAV Conference on General Relativity and Gravitational Physics. AIP, 2005. http://dx.doi.org/10.1063/1.1891541.

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Zaffaroni, Alberto. "The Holographic RG flow to conformal andnon-conformal theories." In Quantum aspects of gauge theories, supersymmetry and unification. Trieste, Italy: Sissa Medialab, 2000. http://dx.doi.org/10.22323/1.004.0053.

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Braun, J. "RG flow of the Polyakov-loop potential — first status report." In HADRONIC PHYSICS: Joint Meeting Heidelberg-Liege-Paris-Rostock; HLPR 2004. AIP, 2005. http://dx.doi.org/10.1063/1.1961053.

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Nakasato, Reo, Yusuke Takahashi, and Nobuyuki Oshima. "Numerical Study of Plasma Flow Around a Reentry Vehicle During Atmospheric Reentry With an Unstructured Grid Solver." In ASME/JSME/KSME 2015 Joint Fluids Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/ajkfluids2015-13593.

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When a reentry vehicle enters the planetary atmosphere, a strong shock wave is generated and the strong aerodynamic heating appears. Gas temperature in front of the vehicle exceeds 10,000K and chemical reactions (ionizations and dissociations) occur behind the shock wave. Because the reentry vehicle is damaged by the aerodynamic heating, accurate evaluation of the aerodynamic heating in the high-enthalpy flow is necessary for the design and the development of the vehicle. The communication blackout phenomenon which prevents the propagation of the electromagnetic waves can occur by the characteristics of electrons in the shock layer to absorb and reflect the electromagnetic waves. To estimate the communicationable time and understand the behavior of the electromagnetic waves around the vehicle, the accurate evaluation of the plasma flow around the vehicle is also necessary. In this study, the three-dimensional numerical analysis was conducted to consider an angle of attack by using the analysis software for compressible fluid, RG-FaSTAR which has been developed by JAXA. Moreover, unstructured grids were used to make it easier to generate computational grid around the vehicle with complicated shape. Note that RG-FaSTAR is a version of FaSTAR (FaST Aerodynamic Routine) installing the real gas effect. We reproduced the actual flow field around the Atmospheric Reentry Demonstrator (ARD) which was launched by the European Space Agency (ESA) in 1998 and revealed the aerodynamic heating and plasma flow properties during atmospheric reentry. The computational result showed good agreement with measured pressure coefficient at the stagnation point. In addition, the features of the shock layer and the rear region around ARD were revealed.
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Abduev, M. A. "ANTHROPOGENIC TRANSFORMATION OF THE STOCK OF WEIGHED WEIGHTS OF THE MOUNTAIN RIVERS OF AZERBAIJAN." In Prirodopol'zovanie i ohrana prirody: Ohrana pamjatnikov prirody, biologicheskogo i landshaftnogo raznoobrazija Tomskogo Priob'ja i drugih regionov Rossii. Izdatel'stvo Tomskogo gosudarstvennogo universiteta, 2020. http://dx.doi.org/10.17223/978-5-94621-954-9-2020-60.

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Based on the data of network hydrometric observations over a multi-year period, the transformation of suspended sediments of mountain rivers of Azerbaijan into the stock has been estimated. To quantify the anthropogenic transformation of suspended sediment runoff, we analyzed the dependences of the average annual flow rates of suspended sediment and water, Rg = f (Qg); It was revealed that in connection with the construction of reservoirs, the natural regime of sediment runoff has radically changed.
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Pfeifer, Uwe, and Dieter Warnack. "Simulation of Non-Steady and Non-Linear Flow Phenomena in Complex Piping Systems of Gas Turbines." In ASME Turbo Expo 2003, collocated with the 2003 International Joint Power Generation Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/gt2003-38056.

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In order to get information on how pressure fluctuations in the combustion chamber of a gas turbine act on the gas piping system and adapters for measurement of pressure fluctuations, a one-dimensional, compressible, unsteady, anisentropic code is applied. This is done to obtain more detailed information about particular flow phenomena like wave propagation, superposition and the influence of heat transfer and damping. The model used was formed by using the one-dimensional equation laws of mass, momentum and energy to a hyperbolic differential equation system. This system was solved numerically by using the well proven PROMO code originating from the automotive industry as described in detail by Go¨rg [1]. The existing model was extended and adapted to be applicable to the problems described above.
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Chu, Christopher C. M., and Md Mizanur Rahman. "A Method to Achieve Robust Aerodynamics and Enhancement of Updraft in Natural Draft Dry Cooling Towers." In ASME 2009 Heat Transfer Summer Conference collocated with the InterPACK09 and 3rd Energy Sustainability Conferences. ASMEDC, 2009. http://dx.doi.org/10.1115/ht2009-88289.

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A method to stabilize the draft through natural cooling towers is introduced. Natural draught dry cooling towers are widely used in arid regions of the world for the power industry especially those employing nuclear reactors. Their presence has become iconic of the process industry for their dominance of the landscape. These towers control the overall efficiency of power plants, and with the ongoing energy crisis it is desirable to raise efficiency by stabilising the draught through the tower. Energy comsumption is a substantial part of the overall cost of plant operation, and therefore even with a conservative 5 per cent improvement is feasible. It has been noted by some researchers like Baer, Ernst and Wurz (1980) that cooling towers do experience unstable flow with breezes. This phenomenon can be explained by Jo¨rg and Scorer (1967) to occur even in a still ambience with cold air inflow down into the tower shell from exit. Jo¨rg and Scorer (1967) developed a correlation to predict cold inflow to a glass tube for various fluids in a laboratory. By using their formula, it is found that under typical exit bulk velocities, of 3–5 m/s or below, cold air is liable to ‘sink’ into the shell, even in a quiescent surrounding. Indeed this phenomenon was demonstrated in the laboratory using a duct of size 457 × 457 mm2 of a heat exchanger by employing a smoke generator to detect that cold air did flow into the duct rather than the hot air filling the entire cross sectional area of the duct exit. A device was applied by Chu (1986) to prevent this cold air from sinking into the duct and enhance the stability and quantity of the updraft. In this paper, for the first time data obtained from a 700 × 700 mm2 cross-sectional flow area model air-cooled heat exchanger are presented that proves the air flow rate enhancement due to this device. It is hoped that more tests can be conducted to optimize the design for application in boiler chimneys and natural draught dry cooling towers.
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Rioua, X., J. Fabrea, and C. Colin. "Closure Laws for the Transport Equation of Interfacial Area in Dispersed Flow." In ASME 2002 Joint U.S.-European Fluids Engineering Division Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/fedsm2002-31386.

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Derivation of a transport equation for the interfacial area concentration. In two-phase flows, the interfacial area is a key parameter since it mainly controls the momentum heat and mass transfers between the phases. An equation of transport of interfacial area may be very useful, especially for the two-fluid models. Such an equation should be able to predict the transition between the flow regimes. With this aim in view, we shall focus our attention on pipe flow. Besides in a first step, our study will be limited to dispersed flows. Different models are used to predict the evolution of bubble sizes. Some models use a population balance that provides a detailed description of the bubble size distributions, but they require as many equations as diameter ranges (Coulaloglou & Tavlarides1). Some others use only one equation for the transport of the mean interfacial area (Hibiki & Ishii2). In that case the bubble size distribution is treated as it would be monodispersed, its mean diameter being equal to the Sauter diameter. An intermediate approach was proposed by Kamp et al.3, in which polydispersed size distributions can be taken into account. It is the starting point of the present study in which: • The choice of an interfacial velocity is discussed. • The sink and source terms due to bubble coalescence, break-up or phase change are established. The model of Kamp et al. consists of transport equations of the various moments of the density probability function P(d) of the bubble diameter. In many experimental situations, P(d) is well predicted by a log-normal law (with two characteristic parameters d00 the central diameter of the distribution and a width parameter): The different moments of order ? of P(d) may be calculated: Sγ=n∫P(d)dγd(d)(1) where n is the bubble number density, S1/n, the mean diameter and S2/?, the interfacial area. A transport equation can be written for each moment: ∂Sγ∂t+∇·(uGSγ)=φγ(2) The lhs of (2) is an advection term by the gas velocity uG and the rhs is a source or sink term due to bubble coalescence, break-up or mass transfer. Since the bubble size distribution is characterised by the two parameters d00 and σˆ, only two transport equations (for S1 and S2) have to be solved to calculate the space-time evolution of the bubble size distribution. These two equations are still too cumbersome for a two-fluid model. Under some hypotheses (σˆ ∼ constant), they are lead to a single equation for the interfacial area. In its dimensionless form the interfacial area ai+ (ai+ = π S2 D, where D is the pipe diameter) reads: d/dt+(ai+)=f(RG,Re,We,ai+)(3) where RG is the gas fraction, Re is the Reynolds number of the mixture, We the Weber number of the mixture and t+ a dimensionless time.
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Reiber, Christoph, Virginie Anne Chenaux, and Joachim Belz. "Aerodynamic Damping Predictions During Compressor Surge: A Numerical Comparison Between a Half and Full Transient Approach." In ASME Turbo Expo 2022: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/gt2022-81929.

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Abstract The prediction of the aerodynamic damping during compressor surge is a challenging task, because the flow is continuously evolving along the four surge cycle phases: Pressurization (PR), Flow-Breakdown (FB), Reversed Flow (RF) and Regeneration (RG) and complex flow conditions like shocks and separations occur. Damping predictions with current existing methods typically consist of two steps. In the first step a modified numerical model is used to simulate transient surge cycles. In the second step, damping analyses are performed for multiple timesteps along the surge cycle phases, which are then assumed as quasi-steady. The damping simulation can be performed using nonlinear or linear approaches. If shocks or separations occur, the latter yields inaccuracies in the flow and thus in the damping predictions. A new approach was developed to take into account and improve these inaccuracies. This new method includes the damping prediction within the transient surge simulation. Thus, all surge cycle phases and the continuously evolving flow conditions are considered and nonlinear simulations are performed to account for shocks and separations. The results of this new method are presented and compared to the former method.
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