A unified hyperbolic formulation for viscous fluids and elastoplastic solids

We discuss a unified flow theory which in a single system of hyperbolic partial differential equations (PDEs) can describe the two main branches of continuum mechanics, fluid dynamics, and solid dynamics. The fundamental difference from the classical continuum models, such as the Navier-Stokes for example, is that the finite length scale of the continuum particles is not ignored but kept in the model in order to semi-explicitly describe the essence of any flows, that is the process of continuum particles rearrangements. To allow the continuum particle rearrangements, we admit the deformability of particle which is described by the distortion field. The ability of media to flow is characterized by the strain dissipation time which is a characteristic time necessary for a continuum particle to rearrange with one of its neighboring particles. It is shown that the continuum particle length scale is intimately connected with the dissipation time. The governing equations are represented by a system of first order hyperbolic PDEs with source terms modeling the dissipation due to particle rearrangements. Numerical examples justifying the reliability of the proposed approach are demonstrated.Comment: 6 figure

Entropy-satisfying scheme for a hierarchy of dispersive reduced models of free surface flow

International audienceThis work is devoted to the numerical resolution in multidimensional framework of a hierarchy of reduced models of the free surface Euler equations, also called water waves equations.The current paper, the first in a series of two, focuses on a hierarchy of monolayer dispersive models, such is the Serre-Green-Naghdi model.A particular attention is given to the dissipation of the mechanical energy at the discrete level, i.e. to design an entropy-satisfying scheme.To illustrate the accuracy and the robustness of the strategy, several numerical experiments are performed.In particular, the strategy is able to deal with dry areas without particular treatment

A rarefaction-tracking method for hyperbolic conservation laws

We present a numerical method for scalar conservation laws in one space dimension. The solution is approximated by local similarity solutions. While many commonly used approaches are based on shocks, the presented method uses rarefaction and compression waves. The solution is represented by particles that carry function values and move according to the method of characteristics. Between two neighboring particles, an interpolation is defined by an analytical similarity solution of the conservation law. An interaction of particles represents a collision of characteristics. The resulting shock is resolved by merging particles so that the total area under the function is conserved. The method is variation diminishing, nevertheless, it has no numerical dissipation away from shocks. Although shocks are not explicitly tracked, they can be located accurately. We present numerical examples, and outline specific applications and extensions of the approach.Comment: 21 pages, 7 figures. Similarity 2008 conference proceeding

Experimental validation of a one-dimensional twin-entry radial turbine model under non-linear pulse conditions

This is the author¿s version of a work that was accepted for publication in International Journal of Engine Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published as https://doi.org/10.1177/1468087419869157[EN] This article presents the experimental validation of a complete integrated one-dimensional twin-scroll turbine model able to be used in reciprocating internal combustion engine unsteady simulations. A passenger car with a twin-entry-type turbine has been tested under engine-like pulse conditions by means of a specifically built gas stand. To obtain high-resolution quality data, the turbine and turbine line pipes have been instrumented with mean and instantaneous pressure sensors as well as temperature and mass flow sensors, employing a uniquely designed rotating valve for the pulse generation. This experimental configuration enables to obtain the pressure decomposition in both inlets and outlets of the turbine. Using the experimental data obtained, the model is fully validated, with special focus on the reflected and transmitted components for analysing the performance of the model and its non-linear acoustics prediction capabilities. The model presents a very high degree of correlation with the experimental results, providing a range of errors similar to the uncertainty of the measurements, even in the medium- and high-frequency spectra.The author(s) disclosed receipt of the following financial support for the research, authorship and/or publication of this article: This work was supported by the 'Ayuda a Primeros Proyectos de Investigacion' (PAID-06-18), Vicerrectorado de Investigacion, Innovacion y Transferencia de la Universitat Politecnica de Valencia (UPV), Valencia, Spain. P.S. was partially supported through contract FPI-2017-S2-1428 of Programa de Apoyo para la Investigacion y Desarrollo (PAID) of Universitat Politecnica de Valencia.Serrano, J.; Arnau Martínez, FJ.; García-Cuevas González, LM.; Soler-Blanco, P.; Cheung, R. (2021). Experimental validation of a one-dimensional twin-entry radial turbine model under non-linear pulse conditions. 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A detailed one-dimensional model to predict the unsteady behavior of turbocharger turbines for internal combustion engine applications. International Journal of Engine Research, 20(3), 327-349. doi:10.1177/1468087417752525Galindo, J., Arnau, F. J., García-Cuevas, L. M., & Soler, P. (2018). Experimental validation of a quasi-two-dimensional radial turbine model. International Journal of Engine Research, 21(6), 915-926. doi:10.1177/1468087418788502Rajoo, S., Romagnoli, A., & Martinez-Botas, R. F. (2012). Unsteady performance analysis of a twin-entry variable geometry turbocharger turbine. Energy, 38(1), 176-189. doi:10.1016/j.energy.2011.12.017Rajoo, S., & Martinez-Botas, R. (2008). Variable Geometry Mixed Flow Turbine for Turbochargers: An Experimental Study. International Journal of Fluid Machinery and Systems, 1(1), 155-168. doi:10.5293/ijfms.2008.1.1.155Copeland, C. D., Martinez-Botas, R., & Seiler, M. (2010). Comparison Between Steady and Unsteady Double-Entry Turbine Performance Using the Quasi-Steady Assumption. Journal of Turbomachinery, 133(3). doi:10.1115/1.4000580Copeland, C. D., Martinez-Botas, R., & Seiler, M. (2011). Unsteady Performance of a Double Entry Turbocharger Turbine With a Comparison to Steady Flow Conditions. Journal of Turbomachinery, 134(2). doi:10.1115/1.4003171Costall, A. W., McDavid, R. M., Martinez-Botas, R. F., & Baines, N. C. (2010). Pulse Performance Modeling of a Twin Entry Turbocharger Turbine Under Full and Unequal Admission. Journal of Turbomachinery, 133(2). doi:10.1115/1.4000566Yang, M., Martinez-Botas, R., Rajoo, S., Yokoyama, T., & Ibaraki, S. (2015). An investigation of volute cross-sectional shape on turbocharger turbine under pulsating conditions in internal combustion engine. Energy Conversion and Management, 105, 167-177. doi:10.1016/j.enconman.2015.06.038Copeland, C. D., Newton, P. J., Martinez-Botas, R., & Seiler, M. (2011). The Effect of Unequal Admission on the Performance and Loss Generation in a Double-Entry Turbocharger Turbine. Journal of Turbomachinery, 134(2). doi:10.1115/1.4003226Cerdoun, M., & Ghenaiet, A. (2018). Unsteady behaviour of a twin entry radial turbine under engine like inlet flow conditions. Applied Thermal Engineering, 130, 93-111. doi:10.1016/j.applthermaleng.2017.11.001Payri, F., Benajes, J., & Reyes, M. (1996). Modelling of supercharger turbines in internal-combustion engines. International Journal of Mechanical Sciences, 38(8-9), 853-869. doi:10.1016/0020-7403(95)00105-0Chiong, M. S., Rajoo, S., Martinez-Botas, R. F., & Costall, A. W. (2012). Engine turbocharger performance prediction: One-dimensional modeling of a twin entry turbine. Energy Conversion and Management, 57, 68-78. doi:10.1016/j.enconman.2011.12.001Chiong, M. S., Rajoo, S., Romagnoli, A., Costall, A. W., & Martinez-Botas, R. F. (2016). One-dimensional pulse-flow modeling of a twin-scroll turbine. Energy, 115, 1291-1304. doi:10.1016/j.energy.2016.09.041Galindo, J., Navarro, R., García-Cuevas, L. M., Tarí, D., Tartoussi, H., & Guilain, S. (2018). A zonal approach for estimating pressure ratio at compressor extreme off-design conditions. International Journal of Engine Research, 20(4), 393-404. doi:10.1177/1468087418754899Payri, F., Olmeda, P., Arnau, F. J., Dombrovsky, A., & Smith, L. (2014). External heat losses in small turbochargers: Model and experiments. Energy, 71, 534-546. doi:10.1016/j.energy.2014.04.096Serrano, J. R., Olmeda, P., Arnau, F. J., Dombrovsky, A., & Smith, L. (2015). Turbocharger heat transfer and mechanical losses influence in predicting engines performance by using one-dimensional simulation codes. Energy, 86, 204-218. doi:10.1016/j.energy.2015.03.130Gil, A., Tiseira, A. O., García-Cuevas, L. M., Usaquén, T. R., & Mijotte, G. (2018). Fast three-dimensional heat transfer model for computing internal temperatures in the bearing housing of automotive turbochargers. International Journal of Engine Research, 21(8), 1286-1297. doi:10.1177/1468087418804949Serrano, J. R., Olmeda, P., Tiseira, A., García-Cuevas, L. M., & Lefebvre, A. (2013). Theoretical and experimental study of mechanical losses in automotive turbochargers. Energy, 55, 888-898. doi:10.1016/j.energy.2013.04.042Piñero, G., Vergara, L., Desantes, J. M., & Broatch, A. (2000). Estimation of velocity fluctuation in internal combustion engine exhaust systems through beamforming techniques. Measurement Science and Technology, 11(11), 1585-1595. doi:10.1088/0957-0233/11/11/307Zimmermann, R., Baar, R., & Biet, C. (2016). Determination of the isentropic turbine efficiency due to adiabatic measurements and the validation of the conditions via a new criterion. 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On the Nonlinearity of Modern Shock-Capturing Schemes

The development is reviewed of shock capturing methods, paying special attention to the increasing nonlinearity in the design of numerical schemes. The nature is studies of this nonlinearity and its relation to upwind differencing is examined. This nonlinearity of the modern shock capturing methods is essential, in the sense that linear analysis is not justified and may lead to wrong conclusions. Examples to demonstrate this point are given