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Ireneusz Szczygieł Institute of Thermal Technology Silesian University of Technology

Identification of Boundary Velocity Basing on Internal Temperature Measurements – sensitivity analysis. Ireneusz Szczygieł Institute of Thermal Technology Silesian University of Technology Gliwice, Poland. IPES 2003. Outline. Introduction Direct problem formulation

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Ireneusz Szczygieł Institute of Thermal Technology Silesian University of Technology

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  1. Identification of Boundary Velocity Basing on Internal Temperature Measurements – sensitivity analysis Ireneusz Szczygieł Institute of Thermal Technology Silesian University of Technology Gliwice, Poland IPES 2003

  2. Outline • Introduction • Direct problem formulation • Inverse problem formulation • Discussion on sensitivity coefficient field • Results of numerical tests • Final remarks IPES 2003

  3. Basic assumptions • 2D, Cartesian geometry • Steady state • Potential or laminar flow • Isoparametric fluid IPES 2003

  4. Direct problem formulation temperature field description IPES 2003

  5. Direct problem formulation velocity field description – potential flow IPES 2003

  6. Direct problem formulation velocity field description – incompressible flow IPES 2003

  7. Boundary conditions inflow profile symmetry walls flow direction heating pipes inflow surface outflow surface symmetry walls heating pipes surface outlet profile IPES 2003

  8. Inverse problem formulation Estimate inflow velocity knowing the value of internal temperature definition of sensitivity coefficients: IPES 2003

  9. Evaluation of sensitivity coefficients IPES 2003

  10. Evaluation of sensitivity coefficient boundary conditions inflow profile symmetry walls heating pipes surface IPES 2003

  11. Evaluation of sensitivity coefficient source term SA so IPES 2003

  12. Evaluation of sensitivity coefficients – potential flow boundary conditions IPES 2003

  13. Evaluation of sensitivity coefficients – NS flow IPES 2003

  14. Evaluation of sensitivity coefficients – NS flow source term Sux source term Suy IPES 2003

  15. Evaluation of sensitivity coefficients – NS flow boundary conditions inflow profile symmetry walls heating pipes surface outlet profile IPES 2003

  16. where Y stands for the measurementsresults Examplary iterative inverse procedure –potential flow • calculations of the Z field • assumption of the inflow velocity value • evaluation of the potential and the velocity field • evaluation of the temperature sensitivity coefficient distribution • calculation of the new boundary velocity • convergence test for the inflow velocity IPES 2003

  17. where Y stands for the measurementsresults Examplary iterative inverse procedure –NS flow • assumption of the inflow velocity value • evaluation of the velocity field • evaluation of the velocity sensitivity coefficient distribution Zux • evaluation of the velocity sensitivity coefficient distribution Zuy • evaluation of the temperature sensitivity coefficient distribution • calculation of the new boundary velocity • convergence test for the inflow velocity IPES 2003

  18. where Y stands for the measurementsresults Examplary iterative inverse procedure –NS flow • assumption of the inflow velocity value • evaluation of the velocity field • evaluation of the velocity sensitivity coefficient distribution Zux • evaluation of the velocity sensitivity coefficient distribution Zuy • evaluation of the temperature sensitivity coefficient distribution • calculation of the new boundary velocity • convergence test for the inflow velocity IPES 2003

  19. Results of numerical tests Simple channel, Re=500 Zux distribution Zuydistribution Velocity distribution IPES 2003

  20. Results of numerical tests Potential flow, Re=20 Temperature IPES 2003

  21. Results of numerical tests Potential flow, Re=20 Temperature sensitivity coefficients IPES 2003

  22. Results of numerical tests NS flow, Re=200 Temperature IPES 2003

  23. Results of numerical tests NS flow, Re=200 Velocity magnitude IPES 2003

  24. Results of numerical tests NS flow, Re=200 Sensitivity coefficients Zux IPES 2003

  25. Results of numerical tests NS flow, Re=200 Sensitivity coefficients Zuy IPES 2003

  26. Results of numerical tests NS flow, Re=200 Sensitivity coefficients ZT IPES 2003

  27. Results of numerical tests Estimation of nodal quantity, NS flow, Re=200 Temperature IPES 2003

  28. Results of numerical tests Estimation of nodal quantity, NS flow, Re=200 Velocity IPES 2003

  29. Results of numerical tests Estimation of nodal quantity, NS flow, Re=200 Sensitivity coefficient Zux IPES 2003

  30. Results of numerical tests Estimation of nodal quantity, NS flow, Re=200 Sensitivity coefficient Zux IPES 2003

  31. Results of numerical tests Estimation of nodal quantity, NS flow, Re=200 Sensitivity coefficient Zux IPES 2003

  32. Results of numerical tests Estimation of nodal quantity, NS flow, Re=200 Sensitivity coefficient Zux IPES 2003

  33. Results of numerical tests Estimation of nodal quantity, NS flow, Re=200 Sensitivity coefficient ZT IPES 2003

  34. Results of numerical tests Estimation of nodal quantity, NS flow, Re=200 Sensitivity coefficient ZT IPES 2003

  35. Results of numerical tests Estimation of nodal quantity, NS flow, Re=200 Sensitivity coefficient ZT IPES 2003

  36. Results of numerical tests Estimation of nodal quantity, NS flow, Re=200 Sensitivity coefficient ZT IPES 2003

  37. Results of numerical tests Estimation of mass velocity, NS flow, Re=50 Velocity IPES 2003

  38. Results of numerical tests Estimation of mass velocity, NS flow, Re=50 Sensitivity coefficient Zux IPES 2003

  39. Results of numerical tests Estimation of mass velocity, NS flow, Re=50 Sensitivity coefficient ZT IPES 2003

  40. Final remarks • the shape of the sensitivity coefficient distribution is a function of inlet velocity value. It means, the that the optimal location for the measurement sensors varies with the inlet velocity value; • the region of maximum values of the sensitivity coefficient is shifted from the inlet surface toward the flow direction: bringing the measurement sensors close to the inflow boundary can result in worse estimation of the inflow velocity; • the application of the inverse algorithm is possible on in the regions with nonuniform temperature distribution; • inverse procedure for the NS flow is much more time consuming than the procedure for the potential flow;

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