Sensitivity-based analysis of the k – ε model for the turbulent flow between two plates
Eddy viscosity models (EVM) constitute a powerful approach for turbulence modeling in engineering applications. However, the correct formulation of EVM models is still subject to discussion, in particular the impact of model parameters on the practical relevance of models in different classes of app...
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| Published in | Chemical engineering science Vol. 63; no. 19; pp. 4763 - 4775 |
|---|---|
| Main Authors | , , , , , , , , |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
01.10.2008
Elsevier |
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| Abstract | Eddy viscosity models (EVM) constitute a powerful approach for turbulence modeling in engineering applications. However, the correct formulation of EVM models is still subject to discussion, in particular the impact of model parameters on the practical relevance of models in different classes of application scenarios is not fully understood. A systematic approach for assessing parameter impact involves optimization methods for computational fluid dynamics that allow for quantitative model analysis by rigorous comparison with experimental data. In order to illustrate this systematic approach, the
k
–
ε
turbulence model is analyzed on the basis of laser Doppler velocimetry measurements for the flow between two plates. It is shown that ad hoc approaches for adapting parameter values for the
k
–
ε
model may easily fail due to over-parameterization of the underlying model or insufficient data. Therefore, an
a priori method for the identification of potential problems is important which is based on the sensitivity coefficients of the measurements with respect to the model parameters. The commercial software package FLUENT employed in our application is augmented using the automatic differentiation system ADIFOR for efficient sensitivity computation. Taken together, this results in reliable
a priori methods for model assessment and calibration. Noteworthy, the choice of turbulence parameters on the basis of the formal
a priori analysis agrees well with the physical understanding of the
k
–
ε
model. |
|---|---|
| AbstractList | Eddy viscosity models (EVM) constitute a powerful approach for turbulence modeling in engineering applications. However, the correct formulation of EVM models is still subject to discussion, in particular the impact of model parameters on the practical relevance of models in different classes of application scenarios is not fully understood. A systematic approach for assessing parameter impact involves optimization methods for computational fluid dynamics that allow for quantitative model analysis by rigorous comparison with experimental data. In order to illustrate this systematic approach, the
k
–
ε
turbulence model is analyzed on the basis of laser Doppler velocimetry measurements for the flow between two plates. It is shown that ad hoc approaches for adapting parameter values for the
k
–
ε
model may easily fail due to over-parameterization of the underlying model or insufficient data. Therefore, an
a priori method for the identification of potential problems is important which is based on the sensitivity coefficients of the measurements with respect to the model parameters. The commercial software package FLUENT employed in our application is augmented using the automatic differentiation system ADIFOR for efficient sensitivity computation. Taken together, this results in reliable
a priori methods for model assessment and calibration. Noteworthy, the choice of turbulence parameters on the basis of the formal
a priori analysis agrees well with the physical understanding of the
k
–
ε
model. Eddy viscosity models (EVM) constitute a powerful approach for turbulence modeling in engineering applications. However, the correct formulation of EVM models is still subject to discussion, in particular the impact of model parameters on the practical relevance of models in different classes of application scenarios is not fully understood. A systematic approach for assessing parameter impact involves optimization methods for computational fluid dynamics that allow for quantitative model analysis by rigorous comparison with experimental data. In order to illustrate this systematic approach, the k-epsilon turbulence model is analyzed on the basis of laser Doppler velocimetry measurements for the flow between two plates. It is shown that ad hoc approaches for adapting parameter values for the k-epsilon model may easily fail due to over-parameterization of the underlying model or insufficient data. Therefore, an a priori method for the identification of potential problems is important which is based on the sensitivity coefficients of the measurements with respect to the model parameters. The commercial software package FLUENT employed in our application is augmented using the automatic differentiation system ADIFOR for efficient sensitivity computation. Taken together, this results in reliable a priori methods for model assessment and calibration. Noteworthy, the choice of turbulence parameters on the basis of the formal a priori analysis agrees well with the physical understanding of the k-epsilon model. |
| Author | Marquardt, Wolfgang Martin Bücker, H. Dietze, Georg Bischof, Christian H. Kneer, Reinhold Bardow, André Slusanschi, Emil Renz, Ulrich Leefken, Ansgar |
| Author_xml | – sequence: 1 givenname: André surname: Bardow fullname: Bardow, André email: a.bardow@tudelft.nl organization: Process Systems Engineering, RWTH Aachen University, D-52056 Aachen, Germany – sequence: 2 givenname: Christian H. surname: Bischof fullname: Bischof, Christian H. organization: Institute for Scientific Computing, RWTH Aachen University, D-52056 Aachen, Germany – sequence: 3 givenname: H. surname: Martin Bücker fullname: Martin Bücker, H. organization: Institute for Scientific Computing, RWTH Aachen University, D-52056 Aachen, Germany – sequence: 4 givenname: Georg surname: Dietze fullname: Dietze, Georg organization: Institute of Heat and Mass Transfer, RWTH Aachen University, D-52056 Aachen, Germany – sequence: 5 givenname: Reinhold surname: Kneer fullname: Kneer, Reinhold organization: Institute of Heat and Mass Transfer, RWTH Aachen University, D-52056 Aachen, Germany – sequence: 6 givenname: Ansgar surname: Leefken fullname: Leefken, Ansgar organization: Institute of Heat and Mass Transfer, RWTH Aachen University, D-52056 Aachen, Germany – sequence: 7 givenname: Wolfgang surname: Marquardt fullname: Marquardt, Wolfgang organization: Process Systems Engineering, RWTH Aachen University, D-52056 Aachen, Germany – sequence: 8 givenname: Ulrich surname: Renz fullname: Renz, Ulrich organization: Institute of Heat and Mass Transfer, RWTH Aachen University, D-52056 Aachen, Germany – sequence: 9 givenname: Emil surname: Slusanschi fullname: Slusanschi, Emil organization: Institute for Scientific Computing, RWTH Aachen University, D-52056 Aachen, Germany |
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| Cites_doi | 10.1093/biomet/73.3.625 10.1115/1.1566048 10.1007/3-540-44843-8_9 10.1155/2003/854362 10.1021/ie0203025 10.1016/0094-4548(74)90150-7 10.1017/S0022112088002885 10.1007/978-3-642-55508-4 10.1007/978-1-4613-0075-5 10.1093/biomet/80.2.373 10.1002/fld.1168 10.1080/1061856032000101448 10.1115/1.2720475 10.1016/S0965-9978(03)00094-2 10.2514/6.1990-1481 10.2514/3.51043 10.1016/0045-7825(74)90029-2 10.1016/0017-9310(72)90076-2 10.1029/2000WR900350 10.1007/3-540-28438-9 10.1109/99.537089 10.1007/3-540-10861-0 10.1063/1.555859 10.1007/BF00384062 10.1016/0009-2509(95)00035-4 10.1205/cherd.05086 10.1115/1.3240815 10.1016/0005-1098(90)90116-Y 10.1088/0266-5611/17/5/309 10.1137/S1064827503426723 |
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| Keywords | Fluid mechanics Turbulence Computational fluid dynamics Experimental design Robustness Parameter identification Automatic differentiation Inverse problem |
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| References | Walter, E. (Ed.), 1987. Identifiability of Parametric Models. Pergamon Press, Oxford. Gay, D.M., 1990. Usage summary for selected optimization routines. Computing Science Technical Report 153, AT&T Bell Laboratories, Murray Hill. Sokolichin, Eigenberger (bib35) 1999; 54 Chien (bib15) 1982; 20 Turgeon, Pelletier, Borggaard (bib37) 2004; 18 Speziale, C.G., Abid, R., Anderson, E.C., 1990. A critical evaluation of two-equation models for near wall turbulence. In: AIAA. No. 90-1481. Seattle. Shiebener, Straub, Levelt Sengers, Gallagher (bib34) 1990; 19 Griewank (bib19) 2000 Launder, Sharma (bib27) 1974; 1 Gasser, Sroka, Jennen-Steinmetz (bib17) 1986; 73 Griewank, A., Corliss, G. (Eds.), 1991. Automatic Differentiation of Algorithms. SIAM, Philadelphia. Vaidyanathan, Senocak, Wu, Shyy (bib38) 2003; 125 Launder, Spalding (bib26) 1974; 3 Bücker, H.M., Corliss, G.F., Hovland, P.D., Naumann, U., Norris, B. (Eds.), 2005. Automatic Differentiation: Applications, Theory, and Implementations. In: Lecture Notes in Computational Science and Engineering, vol. 50. Springer, Berlin. Bischof, Bücker, Lang, Rasch (bib8) 2003; 34 Bischof, Bücker, Rasch (bib10) 2005; 26 Bischof, Bücker, Rasch, Slusanschi, Lang (bib11) 2007; 129 Corliss, G., Faure, C., Griewank, A., Hascoët, L., Naumann, U. (Eds.), 2002. Automatic Differentiation of Algorithms: From Simulation to Optimization. Springer, New York. Press, Teukolsky, Vetterling, Flannery (bib31) 1992 Albrecht, Borys, Damaschke, Tropea (bib1) 2003 Brun, Reichert, Kunsch (bib12) 2001; 37 Rall, L.B., 1981. Automatic differentiation: techniques and applications. Lecture Notes in Computer Science, vol. 120. Springer, Berlin. Grimstad, Kolltveit, Mannseth, Nordtvedt (bib21) 2001; 17 Lam, Bremhorst (bib25) 1981; 103 Bischof, Carle, Khademi, Mauer (bib6) 1996; 3 Walter, Pronzato (bib40) 1990; 26 Bischof, Bücker, Lang, Rasch (bib7) 2003; 11 Marquardt (bib29) 2005; 83 Seifert, Gasser, Wolf (bib33) 1993; 80 Atkinson, Donev (bib2) 1992 Chen, Asprey (bib14) 2003; 42 Pahlevani (bib30) 2006; 52 Jones, Launder (bib24) 1972; 15 Bischof, C.H., Bücker, H.M., Rasch, A., Slusanschi, E., 2003c. Evaluation of a computer model for wavy falling films using EFCOSS. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (Eds.), Computational Science and Its Applications–ICCSA 2003. In: Proceedings of the International Conference on Computational Science and its Applications, Montreal, Canada, May 18–21, 2003. Lecture Notes in Computer Science, vol. 2668, Part II. Springer, Berlin, pp. 78–84. Biegler, L.T., Ghattas, O., Heinkenschloss, M., Bloemen Waanders, B.v. (Eds.), 2003. Large-Scale PDE-Constrained Optimization. Springer, Berlin. Hrenya, Bolio, Chakrabarti, Sinclair (bib23) 1995; 50 Hjemfelt, Mockros (bib22) 1966; 16 Berz, M., Bischof, C., Corliss, G., Griewank, A. (Eds.), 1996. Computational Differentiation: Techniques, Applications, and Tools. SIAM, Philadelphia. Bard (bib3) 1974 Mansour, Kim, Moin (bib28) 1988; 194 Shiebener (10.1016/j.ces.2007.12.029_bib34) 1990; 19 Walter (10.1016/j.ces.2007.12.029_bib40) 1990; 26 Jones (10.1016/j.ces.2007.12.029_bib24) 1972; 15 Seifert (10.1016/j.ces.2007.12.029_bib33) 1993; 80 Hjemfelt (10.1016/j.ces.2007.12.029_bib22) 1966; 16 Chen (10.1016/j.ces.2007.12.029_bib14) 2003; 42 Bischof (10.1016/j.ces.2007.12.029_bib8) 2003; 34 Turgeon (10.1016/j.ces.2007.12.029_bib37) 2004; 18 Gasser (10.1016/j.ces.2007.12.029_bib17) 1986; 73 Atkinson (10.1016/j.ces.2007.12.029_bib2) 1992 10.1016/j.ces.2007.12.029_bib5 10.1016/j.ces.2007.12.029_bib4 10.1016/j.ces.2007.12.029_bib20 10.1016/j.ces.2007.12.029_bib9 Marquardt (10.1016/j.ces.2007.12.029_bib29) 2005; 83 Hrenya (10.1016/j.ces.2007.12.029_bib23) 1995; 50 Griewank (10.1016/j.ces.2007.12.029_bib19) 2000 Bischof (10.1016/j.ces.2007.12.029_bib10) 2005; 26 Bischof (10.1016/j.ces.2007.12.029_bib6) 1996; 3 Grimstad (10.1016/j.ces.2007.12.029_bib21) 2001; 17 Launder (10.1016/j.ces.2007.12.029_bib27) 1974; 1 Bischof (10.1016/j.ces.2007.12.029_bib7) 2003; 11 Mansour (10.1016/j.ces.2007.12.029_bib28) 1988; 194 Bard (10.1016/j.ces.2007.12.029_bib3) 1974 Brun (10.1016/j.ces.2007.12.029_bib12) 2001; 37 Launder (10.1016/j.ces.2007.12.029_bib26) 1974; 3 Lam (10.1016/j.ces.2007.12.029_bib25) 1981; 103 10.1016/j.ces.2007.12.029_bib32 Sokolichin (10.1016/j.ces.2007.12.029_bib35) 1999; 54 Chien (10.1016/j.ces.2007.12.029_bib15) 1982; 20 10.1016/j.ces.2007.12.029_bib16 Pahlevani (10.1016/j.ces.2007.12.029_bib30) 2006; 52 10.1016/j.ces.2007.12.029_bib36 10.1016/j.ces.2007.12.029_bib13 Bischof (10.1016/j.ces.2007.12.029_bib11) 2007; 129 10.1016/j.ces.2007.12.029_bib18 Vaidyanathan (10.1016/j.ces.2007.12.029_bib38) 2003; 125 10.1016/j.ces.2007.12.029_bib39 Press (10.1016/j.ces.2007.12.029_bib31) 1992 Albrecht (10.1016/j.ces.2007.12.029_bib1) 2003 |
| References_xml | – reference: Berz, M., Bischof, C., Corliss, G., Griewank, A. (Eds.), 1996. Computational Differentiation: Techniques, Applications, and Tools. SIAM, Philadelphia. – reference: Speziale, C.G., Abid, R., Anderson, E.C., 1990. A critical evaluation of two-equation models for near wall turbulence. In: AIAA. No. 90-1481. Seattle. – year: 2003 ident: bib1 article-title: Laser Doppler and Phase Doppler Measurement Techniques – reference: Griewank, A., Corliss, G. (Eds.), 1991. Automatic Differentiation of Algorithms. SIAM, Philadelphia. – volume: 194 start-page: 15 year: 1988 end-page: 44 ident: bib28 article-title: Reynolds-stress and dissipation-rate budgets in a turbulent channel flow publication-title: Journal of Fluid Mechanics – volume: 18 start-page: 29 year: 2004 end-page: 46 ident: bib37 article-title: A general continuous sensitivity equation formulation for the kappa-epsilon model of turbulence publication-title: International Journal of Computational Fluid Dynamics – reference: Gay, D.M., 1990. Usage summary for selected optimization routines. Computing Science Technical Report 153, AT&T Bell Laboratories, Murray Hill. – volume: 52 start-page: 381 year: 2006 end-page: 392 ident: bib30 article-title: Sensitivity computations of eddy viscosity models with an application in drag computation publication-title: International Journal for Numerical Methods in Fluids – year: 1974 ident: bib3 article-title: Nonlinear Parameter Estimation – reference: Bischof, C.H., Bücker, H.M., Rasch, A., Slusanschi, E., 2003c. Evaluation of a computer model for wavy falling films using EFCOSS. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (Eds.), Computational Science and Its Applications–ICCSA 2003. In: Proceedings of the International Conference on Computational Science and its Applications, Montreal, Canada, May 18–21, 2003. Lecture Notes in Computer Science, vol. 2668, Part II. Springer, Berlin, pp. 78–84. – volume: 26 start-page: 195 year: 1990 end-page: 213 ident: bib40 article-title: Qualitative and quantitative experiment design for phenomenological models—a survey publication-title: Automatica – volume: 17 start-page: 1373 year: 2001 end-page: 1390 ident: bib21 article-title: Assessing the validity of a linearized accuracy measure for a nonlinear parameter estimation problem publication-title: Inverse Problems – volume: 20 start-page: 33 year: 1982 end-page: 38 ident: bib15 article-title: Predictions of channel and boundary-layer flows with a low-Reynolds-number turbulence model publication-title: AIAA Journal – volume: 103 start-page: 456 year: 1981 end-page: 460 ident: bib25 article-title: Modified form of publication-title: Journal of Fluids Engineering – volume: 37 start-page: 1015 year: 2001 end-page: 1030 ident: bib12 article-title: Practical identifiability analysis of large environmental simulation models publication-title: Water Resource Research – reference: Corliss, G., Faure, C., Griewank, A., Hascoët, L., Naumann, U. (Eds.), 2002. Automatic Differentiation of Algorithms: From Simulation to Optimization. Springer, New York. – volume: 26 start-page: 510 year: 2005 end-page: 522 ident: bib10 article-title: Sensitivity analysis of turbulence models using automatic differentiation publication-title: SIAM Journal on Scientific Computing – year: 2000 ident: bib19 article-title: Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation – volume: 3 start-page: 269 year: 1974 end-page: 289 ident: bib26 article-title: The numerical computation of turbulent flows publication-title: Computer Methods in Applied Mechanics and Engineering – volume: 3 start-page: 18 year: 1996 end-page: 32 ident: bib6 article-title: ADIFOR 2.0: Automatic differentiation of Fortran 77 programs publication-title: IEEE Computational Science & Engineering – volume: 73 start-page: 625 year: 1986 end-page: 633 ident: bib17 article-title: Residual variance and residual pattern in nonlinear-regression publication-title: Biometrika – volume: 34 start-page: 633 year: 2003 end-page: 639 ident: bib8 article-title: Solving large-scale optimization problems with EFCOSS publication-title: Advances in Engineering Software – reference: Biegler, L.T., Ghattas, O., Heinkenschloss, M., Bloemen Waanders, B.v. (Eds.), 2003. Large-Scale PDE-Constrained Optimization. Springer, Berlin. – year: 1992 ident: bib31 article-title: Numerical Recipes in C: The Art of Scientific Computing – reference: Walter, E. (Ed.), 1987. Identifiability of Parametric Models. Pergamon Press, Oxford. – volume: 11 start-page: 263 year: 2003 end-page: 272 ident: bib7 article-title: An interactive environment for supporting the transition from simulation to optimization publication-title: Scientific Programming – volume: 16 start-page: 149 year: 1966 ident: bib22 article-title: Motion of discrete particles in a turbulent fluid publication-title: Applied Scientific Research – volume: 1 start-page: 131 year: 1974 end-page: 138 ident: bib27 article-title: Application of the energy dissipation model of turbulence to the calculation of flow near a spinning disc publication-title: Letters in Heat and Mass Transfer – volume: 50 start-page: 1923 year: 1995 end-page: 1941 ident: bib23 article-title: Comparison of low Reynolds number publication-title: Chemical Engineering Science – reference: Rall, L.B., 1981. Automatic differentiation: techniques and applications. Lecture Notes in Computer Science, vol. 120. Springer, Berlin. – volume: 83 start-page: 561 year: 2005 end-page: 573 ident: bib29 article-title: Model-based experimental analysis of kinetic phenomena in multi-phase reactive systems publication-title: Chemical Engineering Research & Design – volume: 19 start-page: 677 year: 1990 end-page: 717 ident: bib34 article-title: Refractive index of water and steam as function of wavelength, temperature and density publication-title: Journal of Physical and Chemical Reference Data – volume: 54 start-page: 1923 year: 1999 end-page: 1941 ident: bib35 article-title: Applicability of the standard publication-title: Detailed numerical simulations. Chemical Engineering Science – volume: 125 start-page: 447 year: 2003 end-page: 458 ident: bib38 article-title: Sensitivity evaluation of a transport-based turbulent cavitation model publication-title: Journal of Fluids Engineering—Transactions of the ASME – reference: Bücker, H.M., Corliss, G.F., Hovland, P.D., Naumann, U., Norris, B. (Eds.), 2005. Automatic Differentiation: Applications, Theory, and Implementations. In: Lecture Notes in Computational Science and Engineering, vol. 50. Springer, Berlin. – volume: 80 start-page: 373 year: 1993 end-page: 383 ident: bib33 article-title: Nonparametric estimation of residual variance revisited publication-title: Biometrika – volume: 129 start-page: 652 year: 2007 end-page: 658 ident: bib11 article-title: Automatic differentiation of the general-purpose computational fluid dynamics package FLUENT publication-title: Journal of Fluids Engineering – volume: 42 start-page: 1379 year: 2003 end-page: 1390 ident: bib14 article-title: On the design of optimally informative dynamic experiments for model discrimination in multiresponse nonlinear situations publication-title: Industrial & Engineering Chemistry Research – volume: 15 start-page: 301 year: 1972 end-page: 314 ident: bib24 article-title: The prediction of laminarization with a two-equation model of turbulence publication-title: International Journal of Heat and Mass Transfer – year: 1992 ident: bib2 article-title: Optimum Experimental Designs – year: 1974 ident: 10.1016/j.ces.2007.12.029_bib3 – volume: 73 start-page: 625 issue: 3 year: 1986 ident: 10.1016/j.ces.2007.12.029_bib17 article-title: Residual variance and residual pattern in nonlinear-regression publication-title: Biometrika doi: 10.1093/biomet/73.3.625 – volume: 125 start-page: 447 year: 2003 ident: 10.1016/j.ces.2007.12.029_bib38 article-title: Sensitivity evaluation of a transport-based turbulent cavitation model publication-title: Journal of Fluids Engineering—Transactions of the ASME doi: 10.1115/1.1566048 – ident: 10.1016/j.ces.2007.12.029_bib9 doi: 10.1007/3-540-44843-8_9 – volume: 11 start-page: 263 issue: 4 year: 2003 ident: 10.1016/j.ces.2007.12.029_bib7 article-title: An interactive environment for supporting the transition from simulation to optimization publication-title: Scientific Programming doi: 10.1155/2003/854362 – volume: 42 start-page: 1379 issue: 7 year: 2003 ident: 10.1016/j.ces.2007.12.029_bib14 article-title: On the design of optimally informative dynamic experiments for model discrimination in multiresponse nonlinear situations publication-title: Industrial & Engineering Chemistry Research doi: 10.1021/ie0203025 – volume: 1 start-page: 131 issue: 2 year: 1974 ident: 10.1016/j.ces.2007.12.029_bib27 article-title: Application of the energy dissipation model of turbulence to the calculation of flow near a spinning disc publication-title: Letters in Heat and Mass Transfer doi: 10.1016/0094-4548(74)90150-7 – year: 2000 ident: 10.1016/j.ces.2007.12.029_bib19 – ident: 10.1016/j.ces.2007.12.029_bib20 – volume: 194 start-page: 15 year: 1988 ident: 10.1016/j.ces.2007.12.029_bib28 article-title: Reynolds-stress and dissipation-rate budgets in a turbulent channel flow publication-title: Journal of Fluid Mechanics doi: 10.1017/S0022112088002885 – ident: 10.1016/j.ces.2007.12.029_bib5 doi: 10.1007/978-3-642-55508-4 – ident: 10.1016/j.ces.2007.12.029_bib16 doi: 10.1007/978-1-4613-0075-5 – volume: 80 start-page: 373 year: 1993 ident: 10.1016/j.ces.2007.12.029_bib33 article-title: Nonparametric estimation of residual variance revisited publication-title: Biometrika doi: 10.1093/biomet/80.2.373 – volume: 52 start-page: 381 issue: 4 year: 2006 ident: 10.1016/j.ces.2007.12.029_bib30 article-title: Sensitivity computations of eddy viscosity models with an application in drag computation publication-title: International Journal for Numerical Methods in Fluids doi: 10.1002/fld.1168 – year: 1992 ident: 10.1016/j.ces.2007.12.029_bib2 – volume: 18 start-page: 29 year: 2004 ident: 10.1016/j.ces.2007.12.029_bib37 article-title: A general continuous sensitivity equation formulation for the kappa-epsilon model of turbulence publication-title: International Journal of Computational Fluid Dynamics doi: 10.1080/1061856032000101448 – volume: 129 start-page: 652 issue: 5 year: 2007 ident: 10.1016/j.ces.2007.12.029_bib11 article-title: Automatic differentiation of the general-purpose computational fluid dynamics package FLUENT publication-title: Journal of Fluids Engineering doi: 10.1115/1.2720475 – year: 2003 ident: 10.1016/j.ces.2007.12.029_bib1 – ident: 10.1016/j.ces.2007.12.029_bib4 – volume: 34 start-page: 633 issue: 10 year: 2003 ident: 10.1016/j.ces.2007.12.029_bib8 article-title: Solving large-scale optimization problems with EFCOSS publication-title: Advances in Engineering Software doi: 10.1016/S0965-9978(03)00094-2 – ident: 10.1016/j.ces.2007.12.029_bib36 doi: 10.2514/6.1990-1481 – volume: 20 start-page: 33 issue: 1 year: 1982 ident: 10.1016/j.ces.2007.12.029_bib15 article-title: Predictions of channel and boundary-layer flows with a low-Reynolds-number turbulence model publication-title: AIAA Journal doi: 10.2514/3.51043 – volume: 3 start-page: 269 year: 1974 ident: 10.1016/j.ces.2007.12.029_bib26 article-title: The numerical computation of turbulent flows publication-title: Computer Methods in Applied Mechanics and Engineering doi: 10.1016/0045-7825(74)90029-2 – year: 1992 ident: 10.1016/j.ces.2007.12.029_bib31 – volume: 15 start-page: 301 year: 1972 ident: 10.1016/j.ces.2007.12.029_bib24 article-title: The prediction of laminarization with a two-equation model of turbulence publication-title: International Journal of Heat and Mass Transfer doi: 10.1016/0017-9310(72)90076-2 – volume: 37 start-page: 1015 issue: 4 year: 2001 ident: 10.1016/j.ces.2007.12.029_bib12 article-title: Practical identifiability analysis of large environmental simulation models publication-title: Water Resource Research doi: 10.1029/2000WR900350 – ident: 10.1016/j.ces.2007.12.029_bib13 doi: 10.1007/3-540-28438-9 – volume: 3 start-page: 18 issue: 3 year: 1996 ident: 10.1016/j.ces.2007.12.029_bib6 article-title: ADIFOR 2.0: Automatic differentiation of Fortran 77 programs publication-title: IEEE Computational Science & Engineering doi: 10.1109/99.537089 – ident: 10.1016/j.ces.2007.12.029_bib32 doi: 10.1007/3-540-10861-0 – volume: 19 start-page: 677 issue: 3 year: 1990 ident: 10.1016/j.ces.2007.12.029_bib34 article-title: Refractive index of water and steam as function of wavelength, temperature and density publication-title: Journal of Physical and Chemical Reference Data doi: 10.1063/1.555859 – volume: 16 start-page: 149 year: 1966 ident: 10.1016/j.ces.2007.12.029_bib22 article-title: Motion of discrete particles in a turbulent fluid publication-title: Applied Scientific Research doi: 10.1007/BF00384062 – volume: 50 start-page: 1923 issue: 12 year: 1995 ident: 10.1016/j.ces.2007.12.029_bib23 article-title: Comparison of low Reynolds number k–ε turbulence models in predicting fully developed pipe flow publication-title: Chemical Engineering Science doi: 10.1016/0009-2509(95)00035-4 – volume: 83 start-page: 561 issue: A6 year: 2005 ident: 10.1016/j.ces.2007.12.029_bib29 article-title: Model-based experimental analysis of kinetic phenomena in multi-phase reactive systems publication-title: Chemical Engineering Research & Design doi: 10.1205/cherd.05086 – volume: 103 start-page: 456 year: 1981 ident: 10.1016/j.ces.2007.12.029_bib25 article-title: Modified form of k–ɛ model for predicting wall turbulence publication-title: Journal of Fluids Engineering doi: 10.1115/1.3240815 – volume: 54 start-page: 1923 issue: 13–14 year: 1999 ident: 10.1016/j.ces.2007.12.029_bib35 article-title: Applicability of the standard k–ε turbulence model to the dynamic simulation of bubble columns. Part I publication-title: Detailed numerical simulations. Chemical Engineering Science – volume: 26 start-page: 195 issue: 2 year: 1990 ident: 10.1016/j.ces.2007.12.029_bib40 article-title: Qualitative and quantitative experiment design for phenomenological models—a survey publication-title: Automatica doi: 10.1016/0005-1098(90)90116-Y – ident: 10.1016/j.ces.2007.12.029_bib39 – volume: 17 start-page: 1373 year: 2001 ident: 10.1016/j.ces.2007.12.029_bib21 article-title: Assessing the validity of a linearized accuracy measure for a nonlinear parameter estimation problem publication-title: Inverse Problems doi: 10.1088/0266-5611/17/5/309 – volume: 26 start-page: 510 issue: 2 year: 2005 ident: 10.1016/j.ces.2007.12.029_bib10 article-title: Sensitivity analysis of turbulence models using automatic differentiation publication-title: SIAM Journal on Scientific Computing doi: 10.1137/S1064827503426723 – ident: 10.1016/j.ces.2007.12.029_bib18 |
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| Snippet | Eddy viscosity models (EVM) constitute a powerful approach for turbulence modeling in engineering applications. However, the correct formulation of EVM models... |
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| SubjectTerms | Automatic differentiation Computational fluid dynamics Engineering Sciences Experimental design Fluid mechanics Inverse problem Parameter identification Reactive fluid environment Robustness Turbulence |
| Title | Sensitivity-based analysis of the k – ε model for the turbulent flow between two plates |
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