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John L Lumley - One of the best experts on this subject based on the ideXlab platform.
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a new reynolds stress Algebraic Equation model
Computer Methods in Applied Mechanics and Engineering, 1995Co-Authors: Tsanhsing Shih, Jiang Zhu, John L LumleyAbstract:A New Reynolds Stress Algebraic Equation ModelTsan-Hsing Shih and Jiang ZhuCenter for Modeling of Turbulence and TransitionInstitute for Computational Mechanics in PropulsionNASA Lewis Research Center, Cleveland, OhioJohn L. LumleyCornell University, Ithaca, New YorkAbstractA general turbulent constitutive relation (Shih and Lumley, 1993) is directly appliedto propose a new Reynolds stress Algebraic Equation model. In the development of thismodel, the constraints based on rapid distortion theory and realizability (i.e. the positivityof the normal Reynolds stresses and the Schwarz' inequality between turbulent velocitycorrelations) are imposed. Model coefficients are calibrated using well-studied basic flowssuch as homogenous shear flow and the surface flow in the inertial sublayer. The performanceof this model is then tested in complex turbulent flows including the separated flow over abackward-facing step and the flow in a confined jet. The calculation results are encouragingand point to the success of the present model in modeling turbulent flows with complexgeometries.1. IntroductionThe present study concentrates on complex turbulent shear flows which are of greatinterest in propulsion systems. The particular flows presented in this paper are for thebackward-facing step and the confined jet, both of which have complex structures. Forexample, a confined jet combines several types of flow structure and flow phenomena suchas a shear layer, jet, recirculation, separation and reattachment. Accurate prediction ofthese flows is of great importance in all the key elements of engine design.The turbulence model developed in this study is a Reynolds stress Algebraic Equationmodel which is based on a turbulent constitutive relation (Shill and Lum]ey, 1993), a result ofrapid distortion theory (Reynolds, 1987) and the turbulent realizability principle (Schumann1977, Lumley, 1978). The constitutive relation is obtained using the invariance theory incontinuum mechanics. For flows including a passive scalar, this theory leads to a generalconstitutive relation for the Reynolds stress tensor uiuj in terms of the mean deformationrate tensor Ui,j and the turbulent velocity and length scales characterized by the turbulentkinetic energy k and its dissipation rate s. Pope (1975) applied a similar constitutiverelation to Rodi's Algebraic Reynolds stress formulation (Rodi, 1972) in conjunction withthe LRR second order closure model (Launder et ai., 1975) and obtained an explicit Algebraic
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a realizable reynolds stress Algebraic Equation model
rrsa, 1993Co-Authors: Tsanhsing Shih, Jiang Zhu, John L LumleyAbstract:The invariance theory in continuum mechanics is applied to analyze Reynolds stresses in high Reynolds number turbulent flows. The analysis leads to a turbulent constitutive relation that relates the Reynolds stresses to the mean velocity gradients in a more general form in which the classical isotropic eddy viscosity model is just the linear approximation of the general form. On the basis of realizability analysis, a set of model coefficients are obtained which are functions of the time scale ratios of the turbulence to the mean strain rate and the mean rotation rate. The coefficients will ensure the positivity of each component of the mean rotation rate. These coefficients will ensure the positivity of each component of the turbulent kinetic energy - realizability that most existing turbulence models fail to satisfy. Separated flows over backward-facing step configurations are taken as applications. The calculations are performed with a conservative finite-volume method. Grid-independent and numerical diffusion-free solutions are obtained by using differencing schemes of second-order accuracy on sufficiently fine grids. The calculated results are compared in detail with the experimental data for both mean and turbulent quantities. The comparison shows that the present proposal significantly improves the predictive capability of K-epsilon based two Equation models. In addition, the proposed model is able to simulate rotational homogeneous shear flows with large rotation rates which all conventional eddy viscosity models fail to simulate.
Tsanhsing Shih - One of the best experts on this subject based on the ideXlab platform.
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a new reynolds stress Algebraic Equation model
Computer Methods in Applied Mechanics and Engineering, 1995Co-Authors: Tsanhsing Shih, Jiang Zhu, John L LumleyAbstract:A New Reynolds Stress Algebraic Equation ModelTsan-Hsing Shih and Jiang ZhuCenter for Modeling of Turbulence and TransitionInstitute for Computational Mechanics in PropulsionNASA Lewis Research Center, Cleveland, OhioJohn L. LumleyCornell University, Ithaca, New YorkAbstractA general turbulent constitutive relation (Shih and Lumley, 1993) is directly appliedto propose a new Reynolds stress Algebraic Equation model. In the development of thismodel, the constraints based on rapid distortion theory and realizability (i.e. the positivityof the normal Reynolds stresses and the Schwarz' inequality between turbulent velocitycorrelations) are imposed. Model coefficients are calibrated using well-studied basic flowssuch as homogenous shear flow and the surface flow in the inertial sublayer. The performanceof this model is then tested in complex turbulent flows including the separated flow over abackward-facing step and the flow in a confined jet. The calculation results are encouragingand point to the success of the present model in modeling turbulent flows with complexgeometries.1. IntroductionThe present study concentrates on complex turbulent shear flows which are of greatinterest in propulsion systems. The particular flows presented in this paper are for thebackward-facing step and the confined jet, both of which have complex structures. Forexample, a confined jet combines several types of flow structure and flow phenomena suchas a shear layer, jet, recirculation, separation and reattachment. Accurate prediction ofthese flows is of great importance in all the key elements of engine design.The turbulence model developed in this study is a Reynolds stress Algebraic Equationmodel which is based on a turbulent constitutive relation (Shill and Lum]ey, 1993), a result ofrapid distortion theory (Reynolds, 1987) and the turbulent realizability principle (Schumann1977, Lumley, 1978). The constitutive relation is obtained using the invariance theory incontinuum mechanics. For flows including a passive scalar, this theory leads to a generalconstitutive relation for the Reynolds stress tensor uiuj in terms of the mean deformationrate tensor Ui,j and the turbulent velocity and length scales characterized by the turbulentkinetic energy k and its dissipation rate s. Pope (1975) applied a similar constitutiverelation to Rodi's Algebraic Reynolds stress formulation (Rodi, 1972) in conjunction withthe LRR second order closure model (Launder et ai., 1975) and obtained an explicit Algebraic
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a realizable reynolds stress Algebraic Equation model
rrsa, 1993Co-Authors: Tsanhsing Shih, Jiang Zhu, John L LumleyAbstract:The invariance theory in continuum mechanics is applied to analyze Reynolds stresses in high Reynolds number turbulent flows. The analysis leads to a turbulent constitutive relation that relates the Reynolds stresses to the mean velocity gradients in a more general form in which the classical isotropic eddy viscosity model is just the linear approximation of the general form. On the basis of realizability analysis, a set of model coefficients are obtained which are functions of the time scale ratios of the turbulence to the mean strain rate and the mean rotation rate. The coefficients will ensure the positivity of each component of the mean rotation rate. These coefficients will ensure the positivity of each component of the turbulent kinetic energy - realizability that most existing turbulence models fail to satisfy. Separated flows over backward-facing step configurations are taken as applications. The calculations are performed with a conservative finite-volume method. Grid-independent and numerical diffusion-free solutions are obtained by using differencing schemes of second-order accuracy on sufficiently fine grids. The calculated results are compared in detail with the experimental data for both mean and turbulent quantities. The comparison shows that the present proposal significantly improves the predictive capability of K-epsilon based two Equation models. In addition, the proposed model is able to simulate rotational homogeneous shear flows with large rotation rates which all conventional eddy viscosity models fail to simulate.
Prodromos Daoutidis - One of the best experts on this subject based on the ideXlab platform.
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control of nonlinear differential Algebraic Equation systems an overview
1998Co-Authors: Aditya Kumar, Prodromos DaoutidisAbstract:Chemical processes are inherently nonlinear and their dynamics are naturally described by systems of coupled differential and Algebraic Equations (DAEs); the differential Equations arise from the standard dynamic balances of mass, energy and momentum, while the Algebraic Equations typically include thermodynamic relations, empirical correlations, quasi-steady-state relations etc. In many cases, the Algebraic Equations in the DAE model can be readily eliminated to obtain an equivalent ordinary differential Equation (ODE) model, which can be used as the basis for controller design. On the other hand, there is a broad class of chemical processes for which the Algebraic Equations in the DAE models are “singular” in nature, and thus, inhibit a direct reduction of the DAE model into an ODE system. Such DAE systems with singular Algebraic Equations are said to have a high “index” and they are fundamentally different from ODE systems.
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feedback regularization and control of nonlinear differential Algebraic Equation systems
Aiche Journal, 1996Co-Authors: Aditya Kumar, Prodromos DaoutidisAbstract:The feedback control of nonlinear high-index differential-Algebraic-Equation systems for which the underlying Algebraic constraints among the system variables involve the manipulated inputs is addressed in this work. A state-space realization of such systems cannot be derived independently of the controller design. In view of this fact, a two-step methodology is proposed for the control of such systems. The first step involves the derivation of a dynamic state-feedback compensator such that in the resulting system, the underlying constraints are independent of the new inputs. In the second step, a state-space realization of the feedback modified system is derived and used as the basis for a state-feedback controller synthesis. Application of the developed control methodology is demonstrated on an interconnection of a two-phase exothermic reactor and a condenser.
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control of nonlinear differential Algebraic Equation systems with disturbances
Industrial & Engineering Chemistry Research, 1995Co-Authors: Aditya Kumar, Prodromos DaoutidisAbstract:We address the control of a class of nonlinear, multivariable, high-index differential-Algebraic-Equation systems with external disturbances. Initially, an algorithmic procedure is developed to derive an equivalent state-space realization of the constrained system, valid for arbitrary disturbances. Then, on the basis of the derived state-space realization, a feedforward/feedback controller is developed to completely eliminate the effects of the measurable disturbances and induce a well-characterized input/output behavior in the constrained system. The application of the proposed control methodology is illustrated on a high-purity absorption column.
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feedback control of nonlinear differential Algebraic Equation systems
Aiche Journal, 1995Co-Authors: Aditya Kumar, Prodromos DaoutidisAbstract:The output feedback control problem is addressed for a class of nonlinear multivariable high-index differential-Algebraic-Equation systems in semiexplicit form. Initially, an algorithmic procedure is developed and used to derive an equivalent state-space relization of the constrained system. An output feedback synthesis problem is then formulated on the basis of the derived state-space realization and solved through the combination of state feedback and appropriate state observers. The developed methodology is applied to a two-phase reactor, and its performance and robustness characteristics are evaluated through simulations.
Jiang Zhu - One of the best experts on this subject based on the ideXlab platform.
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a new reynolds stress Algebraic Equation model
Computer Methods in Applied Mechanics and Engineering, 1995Co-Authors: Tsanhsing Shih, Jiang Zhu, John L LumleyAbstract:A New Reynolds Stress Algebraic Equation ModelTsan-Hsing Shih and Jiang ZhuCenter for Modeling of Turbulence and TransitionInstitute for Computational Mechanics in PropulsionNASA Lewis Research Center, Cleveland, OhioJohn L. LumleyCornell University, Ithaca, New YorkAbstractA general turbulent constitutive relation (Shih and Lumley, 1993) is directly appliedto propose a new Reynolds stress Algebraic Equation model. In the development of thismodel, the constraints based on rapid distortion theory and realizability (i.e. the positivityof the normal Reynolds stresses and the Schwarz' inequality between turbulent velocitycorrelations) are imposed. Model coefficients are calibrated using well-studied basic flowssuch as homogenous shear flow and the surface flow in the inertial sublayer. The performanceof this model is then tested in complex turbulent flows including the separated flow over abackward-facing step and the flow in a confined jet. The calculation results are encouragingand point to the success of the present model in modeling turbulent flows with complexgeometries.1. IntroductionThe present study concentrates on complex turbulent shear flows which are of greatinterest in propulsion systems. The particular flows presented in this paper are for thebackward-facing step and the confined jet, both of which have complex structures. Forexample, a confined jet combines several types of flow structure and flow phenomena suchas a shear layer, jet, recirculation, separation and reattachment. Accurate prediction ofthese flows is of great importance in all the key elements of engine design.The turbulence model developed in this study is a Reynolds stress Algebraic Equationmodel which is based on a turbulent constitutive relation (Shill and Lum]ey, 1993), a result ofrapid distortion theory (Reynolds, 1987) and the turbulent realizability principle (Schumann1977, Lumley, 1978). The constitutive relation is obtained using the invariance theory incontinuum mechanics. For flows including a passive scalar, this theory leads to a generalconstitutive relation for the Reynolds stress tensor uiuj in terms of the mean deformationrate tensor Ui,j and the turbulent velocity and length scales characterized by the turbulentkinetic energy k and its dissipation rate s. Pope (1975) applied a similar constitutiverelation to Rodi's Algebraic Reynolds stress formulation (Rodi, 1972) in conjunction withthe LRR second order closure model (Launder et ai., 1975) and obtained an explicit Algebraic
-
a realizable reynolds stress Algebraic Equation model
rrsa, 1993Co-Authors: Tsanhsing Shih, Jiang Zhu, John L LumleyAbstract:The invariance theory in continuum mechanics is applied to analyze Reynolds stresses in high Reynolds number turbulent flows. The analysis leads to a turbulent constitutive relation that relates the Reynolds stresses to the mean velocity gradients in a more general form in which the classical isotropic eddy viscosity model is just the linear approximation of the general form. On the basis of realizability analysis, a set of model coefficients are obtained which are functions of the time scale ratios of the turbulence to the mean strain rate and the mean rotation rate. The coefficients will ensure the positivity of each component of the mean rotation rate. These coefficients will ensure the positivity of each component of the turbulent kinetic energy - realizability that most existing turbulence models fail to satisfy. Separated flows over backward-facing step configurations are taken as applications. The calculations are performed with a conservative finite-volume method. Grid-independent and numerical diffusion-free solutions are obtained by using differencing schemes of second-order accuracy on sufficiently fine grids. The calculated results are compared in detail with the experimental data for both mean and turbulent quantities. The comparison shows that the present proposal significantly improves the predictive capability of K-epsilon based two Equation models. In addition, the proposed model is able to simulate rotational homogeneous shear flows with large rotation rates which all conventional eddy viscosity models fail to simulate.
Aditya Kumar - One of the best experts on this subject based on the ideXlab platform.
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control of nonlinear differential Algebraic Equation systems an overview
1998Co-Authors: Aditya Kumar, Prodromos DaoutidisAbstract:Chemical processes are inherently nonlinear and their dynamics are naturally described by systems of coupled differential and Algebraic Equations (DAEs); the differential Equations arise from the standard dynamic balances of mass, energy and momentum, while the Algebraic Equations typically include thermodynamic relations, empirical correlations, quasi-steady-state relations etc. In many cases, the Algebraic Equations in the DAE model can be readily eliminated to obtain an equivalent ordinary differential Equation (ODE) model, which can be used as the basis for controller design. On the other hand, there is a broad class of chemical processes for which the Algebraic Equations in the DAE models are “singular” in nature, and thus, inhibit a direct reduction of the DAE model into an ODE system. Such DAE systems with singular Algebraic Equations are said to have a high “index” and they are fundamentally different from ODE systems.
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feedback regularization and control of nonlinear differential Algebraic Equation systems
Aiche Journal, 1996Co-Authors: Aditya Kumar, Prodromos DaoutidisAbstract:The feedback control of nonlinear high-index differential-Algebraic-Equation systems for which the underlying Algebraic constraints among the system variables involve the manipulated inputs is addressed in this work. A state-space realization of such systems cannot be derived independently of the controller design. In view of this fact, a two-step methodology is proposed for the control of such systems. The first step involves the derivation of a dynamic state-feedback compensator such that in the resulting system, the underlying constraints are independent of the new inputs. In the second step, a state-space realization of the feedback modified system is derived and used as the basis for a state-feedback controller synthesis. Application of the developed control methodology is demonstrated on an interconnection of a two-phase exothermic reactor and a condenser.
-
control of nonlinear differential Algebraic Equation systems with disturbances
Industrial & Engineering Chemistry Research, 1995Co-Authors: Aditya Kumar, Prodromos DaoutidisAbstract:We address the control of a class of nonlinear, multivariable, high-index differential-Algebraic-Equation systems with external disturbances. Initially, an algorithmic procedure is developed to derive an equivalent state-space realization of the constrained system, valid for arbitrary disturbances. Then, on the basis of the derived state-space realization, a feedforward/feedback controller is developed to completely eliminate the effects of the measurable disturbances and induce a well-characterized input/output behavior in the constrained system. The application of the proposed control methodology is illustrated on a high-purity absorption column.
-
feedback control of nonlinear differential Algebraic Equation systems
Aiche Journal, 1995Co-Authors: Aditya Kumar, Prodromos DaoutidisAbstract:The output feedback control problem is addressed for a class of nonlinear multivariable high-index differential-Algebraic-Equation systems in semiexplicit form. Initially, an algorithmic procedure is developed and used to derive an equivalent state-space relization of the constrained system. An output feedback synthesis problem is then formulated on the basis of the derived state-space realization and solved through the combination of state feedback and appropriate state observers. The developed methodology is applied to a two-phase reactor, and its performance and robustness characteristics are evaluated through simulations.