A finite volume approach to the problem of heat transfer in axisymmetric annulus geometry with internal heating element using local analytical solution techniques
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A. Salama
Abstract
In this paper we implement the local analytical solution technique to the problem of heat transfer in axisymmetric annulus geometry with internal heating element. This method has shown to be very accurate in estimating the temperature field for axisymmetric problems even for coarse mesh. It is shown that this method reduces to the analytical solution for unidirectional heat transfer in the radial direction in homogeneous media. The technique is based on finding an analytical expression for the temperature field in the radial direction within each grid cell. This means that the temperature field in each cell is allowed to change in a nonlinear fashion along the radial direction. We compare this technique with the traditional finite volume technique and show that; with only few cells in the radial direction, this technique arrives at the mesh-independent solution quite accurately whereas it required denser mesh to arrive closer to this solution using traditional techniques. This method is proposed to the 1D codes that are currently being used to simulate thermalhydraulic characteristics of reactor systems. Furthermore, we also implement the experimental temperature field algorithm in which the governing equations are approximated for each cell as it would without extra manipulation to the governing equations. This technique is very simple and separates the physics from the solving part.
Kurzfassung
In diesem Beitrag werden lokale analytische Lösungsverfahren angewendet zur Berechnung des Wärmeaustauschs bei rotationssymmetrischer ringförmiger Geometrie mit inneren Wärmeelementen. Diese Methode hat sich als sehr genau erwiesen zur Bestimmung des Temperaturfeldes bei rotationssymmetrischen Problemen. Es wird gezeigt, dass sich diese Methode reduziert auf die analytische Lösung für einseitigen Wärmetransfer in radialer Richtung in homogenen Medien. Das Verfahren basiert auf der Ermittlung eines analytischen Ausdrucks für das Temperaturfeld in radialer Richtung innerhalb jeder Gitterzelle. Das heißt, das Temperaturfeld kann sich in jeder Zelle auf nicht-lineare Art in radialer Richtung ändern. Diese Technik wird verglichen mit den üblichen Finite Volumen Verfahren. Es wird gezeigt, dass diese Technik, mit nur wenigen Zellen in radialer Richtung, eine netzunabhängige genaue Lösung erreicht, während ein dichteres Netz erforderlich ist, um mit Hilfe üblicher Verfahren dieser Lösung näher zu kommen. Diese Methode wird zur Verwendung bei den zur Zeit benutzten 1D Codes zur Simulation thermohydraulischer Eigenschaften von Reaktorsystemen vorgeschlagen. Des Weiteren wird auch der Temperaturfeldalgorithmus angewendet, in dem die zugrundeliegenden Gleichungen für jede Zelle angenähert werden, wie das auch der Fall wäre ohne Manipulation dieser Gleichungen. Dieses Verfahren ist einfach und trennt Physik und Lösungsteil.
References
1 Hazi, G.: On turbulence models for rod bundle flow computations. Annals on Nuclear Energy32 (2005) 755–76110.1016/j.anucene.2004.12.012Suche in Google Scholar
2 Chang, D.; Tavoularis, S.: Numerical simulation of turbulent flow in a 37-rod bundle. Nuclear Engineering and Design237 (2007) 575–59010.1016/j.nucengdes.2006.08.001Suche in Google Scholar
3 Gajapathy, R.; Velusamy, K.; Selvaraj, P.; Chellapandi, P.; Chetal, S. C.: A comparative CFD investigation of helical wire-wrapped 7, 19, and 37 fuel pin bundle and its extendibility to 217 pin bundle. Nuclear Engineering and Design239 (2009) 2279–229210.1016/j.nucengdes.2009.06.014Suche in Google Scholar
4 Toth, S.; Aszodi, A.: CFD analysis of flow field in a triangular rod bundle, Nuclear Engineering and Design240 (2010) 352–36310.1016/j.nucengdes.2008.08.020Suche in Google Scholar
5 El-Morshedy, S.; Salama, A.: 3D Thermal Hydraulic Simulation of a Typical Material Testing Reactor Hot Channel under Normal Operation. KERNTECHNIK75 (2010) 248–25410.3139/124.110098Suche in Google Scholar
6 Salama, A.; El-Morshedy, S.: CFD Simulation of the IAEA 10 MW Generic MTR Reactor under Loss of Flow Transient. Annals of Nuclear Energy38 (2011) 564–57710.1016/j.anucene.2010.09.025Suche in Google Scholar
7 Salama, A.: CFD investigation of flow inversion in typical MTR research reactor undergoing thermal-hydraulic transient. Annals Nuclear Energy38 (2011) 1578–159210.1016/j.anucene.2011.03.005Suche in Google Scholar
8 Salama, A.; El-Morshedy, S.: CFD Simulation of Flow Blockage through a Coolant Channel of a Typical Material Testing Reactor Core. Annals of Nuc Energy41 (2012) 26–3910.1016/j.anucene.2011.09.005Suche in Google Scholar
9 Salama, A.; El-Morshedy, S.: CFD Analysis of Flow Blockage in MTR Coolant Channel under Loss of Flow Transient: Hot Channel Scenario. Progress in Nuclear Energy55 (2012) 78–9210.1016/j.pnucene.2011.11.005Suche in Google Scholar
10 Salama, A.: CFD analysis of fast loss of flow accident in typical MTR reactor undergoing partial and full blockage: the average channel scenario. Progress in Nuclear Energy60 (2012) 1–1310.1016/j.pnucene.2012.05.002Suche in Google Scholar
11 Salama, A.; El-Amin, M. F.; Sun, S.: Three-dimensional, numerical investigation of flow and heat transfer in rectangular channels subject to partial blockage. Heat Transfer Engineering36–2 (2011) 152–16510.1080/01457632.2014.909191Suche in Google Scholar
12 Housiadas, C.: Simulation of loss of flow transients in research reactors. Annals of Nuclear Energy27 (2000) 1683–169310.1016/S0306-4549(00)00053-0Suche in Google Scholar
13 Hamidouche, T.; Bousbia-Salah, A.; Adorni, M., D'Auria, F.: Dynamic calculations of the IAEA safety MTR research reactor benchmark problem using RELAP5/3.2 code. Annals of Nuclear Energy31 (2004) 1385–140210.1016/j.anucene.2004.03.008Suche in Google Scholar
14 Hamidouche, T.; Bousbia-Salah, A.; Si-Ahmed, El-K.; D'Auria, F.: Overview of accident analysis in nuclear research reactors. Progress in Nuclear Energy50 (2008) 7–1410.1016/j.pnucene.2007.11.089Suche in Google Scholar
15 Lu, Q.; Qiu, S.; Su, G.H.: Flow blockage analysis of a channel in a typical material test reactor core. Nuclear Engineering and Design239 (2009) 45–5010.1016/j.nucengdes.2008.06.016Suche in Google Scholar
16 Kazeminijad, H.: Thermal-hydraulic modeling of flow inversion in a research reactor. Annals of Nuclear Energy35 (2008) 1813–181910.1016/j.anucene.2008.05.006Suche in Google Scholar
17 Li, W.; Yu, B.; Wang, X.; Wang, Q.; Sun, S.: A Finite Volume Method for Heat Conduction Problem Based on Local Analytical Solution. The Asian Symposium on Computational Heat Transfer and Fluid Flow, 2011, Kyoto, JapanSuche in Google Scholar
18 Sun, S.; Salama, A.; El Amin, M. F.: An Equation-Type Approach for the Numerical Solution of the Partial Differential Equations Governing Transport Phenomena in Porous Media, International Conference on Computational Science, ICCS June 2012, Omaha, Nebraska, USA10.1016/j.procs.2012.04.071Suche in Google Scholar
19 Salama, A.; Sun, S.; Wheeler, M.: Solving global problem by considering multitude of local problems: application to flow in anisotropic porous media using the multipoint flux approximation. J. Computational and Applied Mathematics267 (2014) 117–13010.1016/j.cam.2014.01.016Suche in Google Scholar
20 Salama, A.; Sun, S.; El Amin, M. F.: A multi-point flux approximation of the steady state heat conduction equation in anisotropic media. ASME J. Heat Transfer135 (2013) 1–610.1115/1.4023228Suche in Google Scholar
© 2014, Carl Hanser Verlag, München
Artikel in diesem Heft
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Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Decomposition analysis of the sodium void reactivity of the Korean sodium-cooled fast reactor
- Flow accelerated corrosion study in feeder pipes
- Analysis of the flow instability among channels of the OTSG in the naval craft NPP
- Experimental investigation of the MSFR molten salt reactor concept
- Investigation of neutronic behavior in a CANDU reactor with different (Am, Th, 235U)O2 fuel matrixes
- Atomistic nano-scale 3D simulations about effects of Cr percentage on the molecular dynamics parameters of Fe-9–12% Cr alloys at fusion reactor temperature conditions
- On an analytical evaluation of the flux and dominant eigenvalue problem for the steady state multi-group multi-layer neutron diffusion equation
- A finite volume approach to the problem of heat transfer in axisymmetric annulus geometry with internal heating element using local analytical solution techniques
- CO2 doped γ-irradiated hydroxyapatite for EPR dosimetry
- An investigation of the effect of the upper beryllium reflector on the moderator temperature coefficient of reactivity of miniature neutron source reactors
