ALBERT

Description:    Different flow regimes have been observed, both experimentally and in CFD simulations, in narrow channels with gas evolution. In this manuscript, we examine, using the Euler–Euler model, the flow in a narrow channel, where gas is evolved from a vertical wall. We find some pseudo-turbulent features at conditions described in this manuscript. The transition to this pseudo-turbulent regime is associated with the value of a specific dimensionless group. Content Type Journal Article Category Original Article Pages 1-14 DOI 10.1007/s00162-011-0248-4 Authors A. Alexiadis, Department of Energy, Environmental and Chemical Engineering, Washington University in St. Louis, One Brookings Drive, Campus Box 1180, St. Louis, MO 63130, USA M. P. Dudukovic, Department of Energy, Environmental and Chemical Engineering, Washington University in St. Louis, One Brookings Drive, Campus Box 1180, St. Louis, MO 63130, USA P. Ramachandran, Department of Energy, Environmental and Chemical Engineering, Washington University in St. Louis, One Brookings Drive, Campus Box 1180, St. Louis, MO 63130, USA A. Cornell, Department of Chemical Engineering and Technology, Applied Electrochemistry, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden J. Wanngård, Eka Chemicals AB, 445 80 Bohus, Sweden A. Bokkers, AKZO Nobel Central Research BV, Velperweg 76, P. O. Box 9300, 6800 SB Arnhem, The Netherlands Journal Theoretical and Computational Fluid Dynamics Online ISSN 1432-2250 Print ISSN 0935-4964

Description:    Vorticity stretching in wall-bounded turbulent and transitional flows has been investigated by means of a new diagnostic measure, denoted by Γ, designed to pick up regions with large amounts of vorticity stretching. It is based on the maximum vorticity stretching component in every spatial point, thus yielding a three-dimensional scalar field. The measure was applied in four different flows with increasing complexity: (a) the near-wall cycle in an asymptotic suction boundary layer (ASBL), (b) K-type transition in a plane channel flow, (c) fully turbulent channel flow at Re τ = 180 and (d) a complex turbulent three-dimensional separated flow. Instantaneous data show that the coherent structures associated with intense vorticity stretching in all four cases have the shape of flat ‘pancake’ structures in the vicinity of high-speed streaks, here denoted ‘h-type’ events. The other event found is of ‘l-type’, present on top of an unstable low-speed streak. These events (l-type) are further thought to be associated with the exponential growth of streamwise vorticity in the turbulent near-wall cycle. It was found that the largest occurrence of vorticity stretching in the fully turbulent wall-bounded flows is present at a wall-normal distance of y +  = 6.5, i.e. in the transition between the viscous sublayer and buffer layer. The associated structures have a streamwise length of ~200–300 wall units. In K-type transition, the Γ-measure accurately locates the regions of interest, in particular the formation of high-speed streaks near the wall (h-type) and the appearance of the hairpin vortex (l-type). In the turbulent separated flow, the structures containing large amounts of vorticity stretching increase in size and magnitude in the shear layer upstream of the separation bubble but vanish in the backflow region itself. Overall, the measure proved to be useful in showing growing instabilities before they develop into structures, highlighting the mechanisms creating high shear region on a wall and showing turbulence creation associated with instantaneous separations. Content Type Journal Article Category Original Article Pages 1-15 DOI 10.1007/s00162-011-0245-7 Authors Johan Malm, Linné FLOW Centre, Swedish e-Science Research Centre (SeRC), KTH Mechanics, Osquars Backe 18, SE-100 44 Stockholm, Sweden Philipp Schlatter, Linné FLOW Centre, Swedish e-Science Research Centre (SeRC), KTH Mechanics, Osquars Backe 18, SE-100 44 Stockholm, Sweden Neil D. Sandham, School of Engineering Sciences, University of Southampton, University Road, Southampton, SO17 1BJ UK Journal Theoretical and Computational Fluid Dynamics Online ISSN 1432-2250 Print ISSN 0935-4964

Description:    The knowledge of the channel bed topography is paramount in modeling the hydrodynamics of open channel flows. Indeed, flow models based on the Shallow Water Approximation require prior information on the channel bed topography to accurately capture the flow features in natural rivers, estuaries, and flood plains. We present here a numerical technique for reconstructing the channel bed topography from given free surface elevation data for steep open channel flows for which the zero-inertia shallow water approximation holds. In this context, the shallow water equations are modified by neglecting inertia terms while retaining the effects of the bed slope and friction terms. We show in this work that by algebraic manipulation, we can recast the governing equations into a single first-order partial differential equation which describes the inverse problem which consists in finding the bed topography from known free surface elevation data. Interestingly, the analysis shows that the inverse problem does not require the knowledge of the bed roughness. The forward problem is solved using MacCormack’s explicit numerical scheme by considering unsteady modified shallow water equations. However, the inverse problem is solved using the method of characteristics. The results of the inverse and the forward problem are successfully tested against each other on two different test cases. Content Type Journal Article Category Original Article Pages 1-12 DOI 10.1007/s00162-012-0287-5 Authors Alelign Gessese, Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch, New Zealand Kabila Mawanzi Wa, Département de Mécanique des fluides, Université Pierre et Marie Curie, Bâtment Esclangon, 4 place Jussieu, 75005 Paris, France Mathieu Sellier, Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch, New Zealand Journal Theoretical and Computational Fluid Dynamics Online ISSN 1432-2250 Print ISSN 0935-4964

Description:    Operational state of many miniaturized devices deals with flow field in microchannels. Pressure-driven flow (PDF) and electroosmotic flow (EOF) can be recognized as the two most important types of the flow field in such channels. EOF has many advantages in comparison with PDF, such as being vibration free and not requiring any external mechanical pumps or moving parts. However, the disadvantages of this type of flow such as Joule heating, electrophoresis demixing, and not being suitable for mobile devices must be taken into consideration carefully. By using mixed electroosmotic/pressure-driven flow, the role of EOF in producing desired velocity profile will be reduced. In this way, the advantages of EOF can be exploited, and its disadvantages can be prevented. Induced pressure gradient can be utilized in order to control the separation in the system. Furthermore, in many complicated geometries such as T-shape microchannels, turns may induce pressure gradient to the electroosmotic velocity. While analytical formulas are completely essential for analysis and control of any industrial and laboratory microdevices, lack of such formulas in the literature for solving Poisson–Boltzmann equation and predicting electroosmotic velocity field in rectangular domains is evident. In the present study, first a novel method is proposed to solve Poisson–Boltzmann equation (PBE). Subsequently, this solution is utilized to find the electroosmotic and the mixed electroosmotic/pressure-driven velocity profile in a rectangular domain of the microchannels. To demonstrate the accuracy of the presented analytical method in solving PBE and finding electroosmotic velocity, a general nondimensional example is analyzed, and the results are compared with the solution of boundary element method. Additionally, the effects of different nondimensional parameters and also aspect ratio of channels on the electroosmotic part of the flow field will be investigated. Content Type Journal Article Category Original Article Pages 1-18 DOI 10.1007/s00162-012-0283-9 Authors Saeid Movahed, Department of Mechanical Engineering, Shiraz University, Shiraz, Fars, Iran Reza Kamali, Department of Mechanical Engineering, Shiraz University, Shiraz, Fars, Iran Mohammad Eghtesad, Department of Mechanical Engineering, Shiraz University, Shiraz, Fars, Iran Amir Khosravifard, Department of Mechanical Engineering, Shiraz University, Shiraz, Fars, Iran Journal Theoretical and Computational Fluid Dynamics Online ISSN 1432-2250 Print ISSN 0935-4964

Description:    We present a range of numerical tests comparing the dynamical cores of the operationally used numerical weather prediction (NWP) model COSMO and the university code Dune , focusing on their efficiency and accuracy for solving benchmark test cases for NWP. The dynamical core of COSMO is based on a finite difference method whereas the Dune core is based on a Discontinuous Galerkin method. Both dynamical cores are briefly introduced stating possible advantages and pitfalls of the different approaches. Their efficiency and effectiveness is investigated, based on three numerical test cases, which require solving the compressible viscous and non-viscous Euler equations. The test cases include the density current (Straka et al. in Int J Numer Methods Fluids 17:1–22, 1993 ), the inertia gravity (Skamarock and Klemp in Mon Weather Rev 122:2623–2630, 1994 ), and the linear hydrostatic mountain waves of (Bonaventura in J Comput Phys 158:186–213, 2000 ). Content Type Journal Article Category Original Article Pages 1-20 DOI 10.1007/s00162-012-0264-z Authors Slavko Brdar, Section of Applied Mathematics, University of Freiburg, Freiburg in Breisgau, Germany Michael Baldauf, Deutscher Wetterdienst (DWD), Offenbach am Main, Germany Andreas Dedner, Warwick Mathematical Institute, Coventry, UK Robert Klöfkorn, Institut für Angewandte Analysis und Numerische Simulation (IANS), University of Stuttgart, Stuttgart, Germany Journal Theoretical and Computational Fluid Dynamics Online ISSN 1432-2250 Print ISSN 0935-4964

Description:    This article deals with the linear dynamics of a transitional boundary layer subject to two-dimensional Tollmien–Schlichting instabilities. We consider a flat plate including the leading edge, characterized by a Reynolds number based on the length of the plate equal to Re  = 6 × 10 5 , inducing a displacement thickness-based Reynolds number of 1,332 at the end of the plate. The global linearized Navier–Stokes equations only display stable eigenvalues, and the associated eigen-vectors are known to poorly represent the dynamics of such open flows. Therefore, we resort to an input–output approach by considering the singular value decomposition of the global resolvent. We then obtain a series of singular values, an associated orthonormal basis representing the forcing (the so-called optimal forcings) as well as an orthonormal basis representing the response (the so-called optimal responses). The objective of this paper is to analyze these spatial structures and to closely relate their spatial downstream evolution to the Orr and Tollmien–Schlichting mechanisms. Analysis of the spatio-frequential diagrams shows that the optimal forcings and responses are respectively localized, for all frequencies, near the upstream neutral point (branch I) and the downstream neutral point (branch II). It is also shown that the spatial growth of the dominant optimal response favorably compares with the e N method in regions where the dominant optimal forcing is small. Moreover, thanks to an energetic input–output approach, it is shown that this spatial growth is solely due to intrinsic amplifying mechanisms related to the Orr and Tollmien–Schlichting mechanisms, while the spatial growth due to the externally supplied power by the dominant optimal forcing is negligible even in regions where the dominant optimal forcing is strong. The energetic input–output approach also yields a general method to assess the strength of the instability in amplifier flows. It is based on a ratio comparing two quantities of same physical dimension, the mean-fluctuating kinetic energy flux of the dominant optimal response across some boundary and the supplied mean external power by the dominant optimal forcing. For the present boundary-layer flow, we have computed this amplification parameter for each frequency and discussed the results with respect to the Orr and Tollmien–Schlichting mechanisms. Content Type Journal Article Category Original Article Pages 1-19 DOI 10.1007/s00162-012-0265-y Authors Denis Sipp, ONERA-The French Aerospace Lab, 8 rue des vertugadins, 92190 Meudon, France Olivier Marquet, ONERA-The French Aerospace Lab, 8 rue des vertugadins, 92190 Meudon, France Journal Theoretical and Computational Fluid Dynamics Online ISSN 1432-2250 Print ISSN 0935-4964

Description:    Large-eddy simulation (LES) has been extensively used as a tool to understand how various processes contribute to the dynamics of the stratocumulus layer. These studies are complicated by the fact that many processes are tied to the dynamics of the stably stratified interface that caps the stratocumulus layer, and which is inadequately resolved by LES. Recent direct numerical simulations (DNS) of isobaric mixing due to buoyancy reversal in a cloud-top mixing layer show that molecular effects are in some instances important in setting the cloud-top entrainment rate, which in turn influences the global development of the layer. This suggests that traditional LES are fundamentally incapable of representing cloud-top processes that depend on buoyancy reversal and that numerical artefacts can affect significantly the results. In this study, we investigate a central aspect of this issue by developing a test case that embodies important features of the buoyancy-reversing cloud-top layer. So doing facilitates a one-to-one comparison of the numerical algorithms typical of LES and DNS codes in a well-established case. We focus on the numerical effects only by switching off the subgrid-scale model in the LES code and using instead a molecular viscosity. We systematically refine the numerical grid and quantify numerical errors, validate convergence and assess computational efficiency of the low-order LES code compared to the high-order DNS. We show that the high-order scheme solves the cloud-top problem computationally more efficiently. On that basis, we suggest that the use of higher-order schemes might be more attractive than further increasing resolution to improve the representation of stratocumulus in LES. Content Type Journal Article Category Original Article Pages 1-13 DOI 10.1007/s00162-012-0263-0 Authors Eckhard Dietze, Faculty of Mechanical, Electrical and Industrial Engineering, Cottbus University of Technology, Siemens-Halske-Ring 14, 03046 Cottbus, Germany Juan Pedro Mellado, Max Planck Institute for Meteorology, Hamburg, Germany Bjorn Stevens, Max Planck Institute for Meteorology, Hamburg, Germany Heiko Schmidt, Faculty of Mechanical, Electrical and Industrial Engineering, Cottbus University of Technology, Siemens-Halske-Ring 14, 03046 Cottbus, Germany Journal Theoretical and Computational Fluid Dynamics Online ISSN 1432-2250 Print ISSN 0935-4964

Description:    A low-order point vortex model for the two-dimensional unsteady aerodynamics of a flat plate wing section is developed. A vortex is released from both the trailing and leading edges of the flat plate, and the strength of each is determined by enforcing the Kutta condition at the edges. The strength of a vortex is frozen when it reaches an extremum, and a new vortex is released from the corresponding edge. The motion of variable-strength vortices is computed in one of two ways. In the first approach, the Brown–Michael equation is used in order to ensure that no spurious force is generated by the branch cut associated with each vortex. In the second approach, we propose a new evolution equation for a vortex by equating the rate of change of its impulse with that of an equivalent surrogate vortex with identical properties but constant strength. This impulse matching approach leads to a model that admits more general criteria for shedding, since the variable-strength vortex can be exchanged for its constant-strength surrogate at any instant. We show that the results of the new model, when applied to a pitching or perching plate, agree better with experiments and high-fidelity simulations than the Brown–Michael model, using fewer than ten degrees of freedom. We also assess the model performance on the impulsive start of a flat plate at various angles of attack. Current limitations of the model and extensions to more general unsteady aerodynamic problems are discussed. Content Type Journal Article Category Original Article Pages 1-22 DOI 10.1007/s00162-012-0279-5 Authors Chengjie Wang, Mechanical and Aerospace Engineering Department, University of California Los Angeles, 420 Westwood Plaza, Los Angeles, CA 90095-1597, USA Jeff D. Eldredge, Mechanical and Aerospace Engineering Department, University of California Los Angeles, 420 Westwood Plaza, Los Angeles, CA 90095-1597, USA Journal Theoretical and Computational Fluid Dynamics Online ISSN 1432-2250 Print ISSN 0935-4964

Description:    In this paper, we report on the development of a methodology for stochastic parameterization of convective transport by shallow cumulus convection in weather and climate models. We construct a parameterization based on Large-Eddy Simulation (LES) data. These simulations resolve the turbulent fluxes of heat and moisture and are based on a typical case of non-precipitating shallow cumulus convection above sea in the trade-wind region. Using clustering, we determine a finite number of turbulent flux pairs for heat and moisture that are representative for the pairs of flux profiles observed in these simulations. In the stochastic parameterization scheme proposed here, the convection scheme jumps randomly between these pre-computed pairs of turbulent flux profiles. The transition probabilities are estimated from the LES data, and they are conditioned on the resolved-scale state in the model column. Hence, the stochastic parameterization is formulated as a data-inferred conditional Markov chain (CMC), where each state of the Markov chain corresponds to a pair of turbulent heat and moisture fluxes. The CMC parameterization is designed to emulate, in a statistical sense, the convective behaviour observed in the LES data. The CMC is tested in single-column model (SCM) experiments. The SCM is able to reproduce the ensemble spread of the temperature and humidity that was observed in the LES data. Furthermore, there is a good similarity between time series of the fractions of the discretized fluxes produced by SCM and observed in LES. Content Type Journal Article Category Original Article Pages 1-16 DOI 10.1007/s00162-012-0281-y Authors Jesse Dorrestijn, CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands Daan T. Crommelin, CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands A. Pier. Siebesma, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands Harm J. J. Jonker, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands Journal Theoretical and Computational Fluid Dynamics Online ISSN 1432-2250 Print ISSN 0935-4964

Description:    In the process of EDM, due to the electrical current, very small bubbles are created within the gap. These bubbles are connected to each other and generate a single bubble. The vapor bubble continues to grow until it finally collapses to small bubbles. The bubble behavior can be ascertained on the distribution of the pressure in the dielectric fluid around the bubble. In this paper, velocity fields and pressure distribution in the dielectric fluid around the bubble that is generated in the process of EDM are investigated numerically. The tool and the workpiece are assumed as two parallel rigid boundaries with dielectric liquid between them. The boundary integral equation method is applied for the numerical solution of the problem. This study can lead to better understanding of the bubble importance in the performance of the electrical discharge machining process. Content Type Journal Article Category Original Article Pages 1-19 DOI 10.1007/s00162-012-0274-x Authors Mohammad T. Shervani-Tabar, Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran Nima Mobadersany, Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran Journal Theoretical and Computational Fluid Dynamics Online ISSN 1432-2250 Print ISSN 0935-4964