In recent papers, Surana et al. presented internal polar non-classical Continuum theory in which velocity gradient tensor in its entirety was incorporated in the conservation and balance laws. Thus, this theory incorp...In recent papers, Surana et al. presented internal polar non-classical Continuum theory in which velocity gradient tensor in its entirety was incorporated in the conservation and balance laws. Thus, this theory incorporated symmetric part of the velocity gradient tensor (as done in classical theories) as well as skew symmetric part representing varying internal rotation rates between material points which when resisted by deforming continua result in dissipation (and/or storage) of mechanical work. This physics referred as internal polar physics is neglected in classical continuum theories but can be quite significant for some materials. In another recent paper Surana et al. presented ordered rate constitutive theories for internal polar non-classical fluent continua without memory derived using deviatoric Cauchy stress tensor and conjugate strain rate tensors of up to orders n and Cauchy moment tensor and its conjugate symmetric part of the first convected derivative of the rotation gradient tensor. In this constitutive theory higher order convected derivatives of the symmetric part of the rotation gradient tensor are assumed not to contribute to dissipation. Secondly, the skew symmetric part of the velocity gradient tensor is used as rotation rates to determine rate of rotation gradient tensor. This is an approximation to true convected time derivatives of the rotation gradient tensor. The resulting constitutive theory: (1) is incomplete as it neglects the second and higher order convected time derivatives of the symmetric part of the rotation gradient tensor;(2) first convected derivative of the symmetric part of the rotation gradient tensor as used by Surana et al. is only approximate;(3) has inconsistent treatment of dissipation due to Cauchy moment tensor when compared with the dissipation mechanism due to deviatoric part of symmetric Cauchy stress tensor in which convected time derivatives of up to order n are considered in the theory. The purpose of this paper is to present ordered rate constitutive theories for deviatoric Cauchy strain tensor, moment tensor and heat vector for thermofluids without memory in which convected time derivatives of strain tensors up to order n are conjugate with the Cauchy stress tensor and the convected time derivatives of the symmetric part of the rotation gradient tensor up to orders 1n are conjugate with the moment tensor. Conservation and balance laws are used to determine the choice of dependent variables in the constitutive theories: Helmholtz free energy density Φ, entropy density η, Cauchy stress tensor, moment tensor and heat vector. Stress tensor is decomposed into symmetric and skew symmetric parts and the symmetric part of the stress tensor and the moment tensor are further decomposed into equilibrium and deviatoric tensors. It is established through conjugate pairs in entropy inequality that the constitutive theories only need to be derived for symmetric stress tensor, moment tensor and heat vector. Density in the current configuration, convected time derivatives of the strain tensor up to order n, convected time derivatives of the symmetric part of the rotation gradient tensor up to orders 1n, temperature gradient tensor and temperature are considered as argument tensors of all dependent variables in the constitutive theories based on entropy inequality and principle of equipresence. The constitutive theories are derived in contravariant and covariant bases as well as using Jaumann rates. The nth and 1nth order rate constitutive theories for internal polar non-classical thermofluids without memory are specialized for n = 1 and 1n = 1 to demonstrate fundamental differences in the constitutive theories presented here and those used presently for classical thermofluids without memory and those published by Surana et al. for internal polar non-classical incompressible thermofluids.展开更多
A thermofluidic-metallurgical integrated model is proposed to investigate the thermofluidic transport and solidification characteristics of 316 L stainless steel under conventional laser-directed energy deposition(CL-...A thermofluidic-metallurgical integrated model is proposed to investigate the thermofluidic transport and solidification characteristics of 316 L stainless steel under conventional laser-directed energy deposition(CL-DED)and high-speed laser-directed energy deposition(HL-DED).Compared to the CL-DED strategy,the weaker Marangoni convection effect produced by the HL-DED strategy results in a lower flow velocity within the pool.A higher scanning speed can shorten the laser-scanning distance when the melt pool reaches a steady-state temperature and reduce the temperature gradients in the solid-phase zone at the rear of the melt pool.Because of the higher scanning speed and lower heat input per unit length,the HL-DED strategy can significantly decrease the flatness ratio of the melt pool,average the growth direction,and average the morphology indicator of the solidification interface,but can remarkably increase the average solidification velocity and cooling rate.Under the HL-DED strategy,the grain morphologies from the top to the bottom of the pool change from fully equiaxed grains to columnar/equiaxed mixed grains and then to fully columnar grains.However,fully equiaxed grains are not observed using the CL-DED strategy because of the larger morphological indicator.Finer grains are induced by the higher cooling rate in the HL-DED strategy.展开更多
The paper presents constitutive theories for non-classical thermoviscoelastic fluids with dissipation and memory using a thermodynamic framework based on entirety of velocity gradient tensor. Thus, the conservation an...The paper presents constitutive theories for non-classical thermoviscoelastic fluids with dissipation and memory using a thermodynamic framework based on entirety of velocity gradient tensor. Thus, the conservation and the balance laws used in this work incorporate symmetric as well as antisymmetric part of the velocity gradient tensor. The constitutive theories derived here hold in coand contra-variant bases as well as in Jaumann rates and are derived using convected time derivatives of Green’s and Almansi strain tensors as well as the Cauchy stress tensor and its convected time derivatives in appropriate bases. The constitutive theories are presented in the absence as well as in the presence of the balance of moment of moments as balance law. It is shown that the dissipation mechanism and the fading memory in such fluids are due to stress rates as well as moment rates and their conjugates. The material coefficients are derived for the general forms of the constitutive theories based on integrity. Simplified linear (or quasi-linear) forms of the constitutive theories are also presented. Maxwell, Oldroyd-B and Giesekus constitutive models for non-classical thermoviscoelastic fluids are derived and are compared with those derived based on classical continuum mechanics. Both, compressible and incompressible thermoviscoelastic fluids are considered.展开更多
A data-driven surrogate model is proposed for a 64-cell air-cooled condenser system at a power plant.The surro-gate model was developed using thermofluid simulation data from an existing detailed 1-D thermofluid netwo...A data-driven surrogate model is proposed for a 64-cell air-cooled condenser system at a power plant.The surro-gate model was developed using thermofluid simulation data from an existing detailed 1-D thermofluid network simulation model.The thermofluid network model requires a minimum of 20 min to solve for a single set of in-puts.With operating conditions fluctuating constantly,performance predictions are required in shorter intervals,leading to the development of a surrogate model.Simulation data covered three operating scopes across a range of ambient air temperatures,inlet steam mass flow rates,number of operating cells,and wind speeds.The surrogate model uses multi-layer perceptron deep neural networks in the form of a binary classifier network to avoid ex-trapolation from the simulation dataset,and a regression network to provide performance predictions,including the steady-state backpressure,heat rejections,air mass flowrates,and fan motor powers on a system level.The integrated surrogate model had an average relative error of 0.3%on the test set,while the binary classifier had a 99.85%classification accuracy,indicating sufficient generalisation.The surrogate model was validated using site-data covering 10 days of operation for the case-study ACC system,providing backpressure predictions for all 1967 input samples within a few seconds of compute time.Approximately 93.5%of backpressure predictions were within±6%of the recorded backpressures,indicating sufficient accuracy of the surrogate model with a significant decrease in compute time.展开更多
文摘In recent papers, Surana et al. presented internal polar non-classical Continuum theory in which velocity gradient tensor in its entirety was incorporated in the conservation and balance laws. Thus, this theory incorporated symmetric part of the velocity gradient tensor (as done in classical theories) as well as skew symmetric part representing varying internal rotation rates between material points which when resisted by deforming continua result in dissipation (and/or storage) of mechanical work. This physics referred as internal polar physics is neglected in classical continuum theories but can be quite significant for some materials. In another recent paper Surana et al. presented ordered rate constitutive theories for internal polar non-classical fluent continua without memory derived using deviatoric Cauchy stress tensor and conjugate strain rate tensors of up to orders n and Cauchy moment tensor and its conjugate symmetric part of the first convected derivative of the rotation gradient tensor. In this constitutive theory higher order convected derivatives of the symmetric part of the rotation gradient tensor are assumed not to contribute to dissipation. Secondly, the skew symmetric part of the velocity gradient tensor is used as rotation rates to determine rate of rotation gradient tensor. This is an approximation to true convected time derivatives of the rotation gradient tensor. The resulting constitutive theory: (1) is incomplete as it neglects the second and higher order convected time derivatives of the symmetric part of the rotation gradient tensor;(2) first convected derivative of the symmetric part of the rotation gradient tensor as used by Surana et al. is only approximate;(3) has inconsistent treatment of dissipation due to Cauchy moment tensor when compared with the dissipation mechanism due to deviatoric part of symmetric Cauchy stress tensor in which convected time derivatives of up to order n are considered in the theory. The purpose of this paper is to present ordered rate constitutive theories for deviatoric Cauchy strain tensor, moment tensor and heat vector for thermofluids without memory in which convected time derivatives of strain tensors up to order n are conjugate with the Cauchy stress tensor and the convected time derivatives of the symmetric part of the rotation gradient tensor up to orders 1n are conjugate with the moment tensor. Conservation and balance laws are used to determine the choice of dependent variables in the constitutive theories: Helmholtz free energy density Φ, entropy density η, Cauchy stress tensor, moment tensor and heat vector. Stress tensor is decomposed into symmetric and skew symmetric parts and the symmetric part of the stress tensor and the moment tensor are further decomposed into equilibrium and deviatoric tensors. It is established through conjugate pairs in entropy inequality that the constitutive theories only need to be derived for symmetric stress tensor, moment tensor and heat vector. Density in the current configuration, convected time derivatives of the strain tensor up to order n, convected time derivatives of the symmetric part of the rotation gradient tensor up to orders 1n, temperature gradient tensor and temperature are considered as argument tensors of all dependent variables in the constitutive theories based on entropy inequality and principle of equipresence. The constitutive theories are derived in contravariant and covariant bases as well as using Jaumann rates. The nth and 1nth order rate constitutive theories for internal polar non-classical thermofluids without memory are specialized for n = 1 and 1n = 1 to demonstrate fundamental differences in the constitutive theories presented here and those used presently for classical thermofluids without memory and those published by Surana et al. for internal polar non-classical incompressible thermofluids.
基金supported by National Natural Science Foundation of China(Grant No.52365041)Guizhou Provincial Basic Research Program(Natural Science)(Grant No.QKHJC-ZK[2023]017)+2 种基金Guizhou Provincial Talent Project(Grant No.QKH-GCC[2022]007–1)Guizhou Province Science and Technology Foundation(Grant No.BQW[2024]011)Guizhou University Fund Project(Grant No.[2024]03).
文摘A thermofluidic-metallurgical integrated model is proposed to investigate the thermofluidic transport and solidification characteristics of 316 L stainless steel under conventional laser-directed energy deposition(CL-DED)and high-speed laser-directed energy deposition(HL-DED).Compared to the CL-DED strategy,the weaker Marangoni convection effect produced by the HL-DED strategy results in a lower flow velocity within the pool.A higher scanning speed can shorten the laser-scanning distance when the melt pool reaches a steady-state temperature and reduce the temperature gradients in the solid-phase zone at the rear of the melt pool.Because of the higher scanning speed and lower heat input per unit length,the HL-DED strategy can significantly decrease the flatness ratio of the melt pool,average the growth direction,and average the morphology indicator of the solidification interface,but can remarkably increase the average solidification velocity and cooling rate.Under the HL-DED strategy,the grain morphologies from the top to the bottom of the pool change from fully equiaxed grains to columnar/equiaxed mixed grains and then to fully columnar grains.However,fully equiaxed grains are not observed using the CL-DED strategy because of the larger morphological indicator.Finer grains are induced by the higher cooling rate in the HL-DED strategy.
文摘The paper presents constitutive theories for non-classical thermoviscoelastic fluids with dissipation and memory using a thermodynamic framework based on entirety of velocity gradient tensor. Thus, the conservation and the balance laws used in this work incorporate symmetric as well as antisymmetric part of the velocity gradient tensor. The constitutive theories derived here hold in coand contra-variant bases as well as in Jaumann rates and are derived using convected time derivatives of Green’s and Almansi strain tensors as well as the Cauchy stress tensor and its convected time derivatives in appropriate bases. The constitutive theories are presented in the absence as well as in the presence of the balance of moment of moments as balance law. It is shown that the dissipation mechanism and the fading memory in such fluids are due to stress rates as well as moment rates and their conjugates. The material coefficients are derived for the general forms of the constitutive theories based on integrity. Simplified linear (or quasi-linear) forms of the constitutive theories are also presented. Maxwell, Oldroyd-B and Giesekus constitutive models for non-classical thermoviscoelastic fluids are derived and are compared with those derived based on classical continuum mechanics. Both, compressible and incompressible thermoviscoelastic fluids are considered.
基金The authors would like to thank the National Research Foundation(NRF)[Grant Number 122957]the University of Cape Town,and the Eskom EPPEI program for funding this research.
文摘A data-driven surrogate model is proposed for a 64-cell air-cooled condenser system at a power plant.The surro-gate model was developed using thermofluid simulation data from an existing detailed 1-D thermofluid network simulation model.The thermofluid network model requires a minimum of 20 min to solve for a single set of in-puts.With operating conditions fluctuating constantly,performance predictions are required in shorter intervals,leading to the development of a surrogate model.Simulation data covered three operating scopes across a range of ambient air temperatures,inlet steam mass flow rates,number of operating cells,and wind speeds.The surrogate model uses multi-layer perceptron deep neural networks in the form of a binary classifier network to avoid ex-trapolation from the simulation dataset,and a regression network to provide performance predictions,including the steady-state backpressure,heat rejections,air mass flowrates,and fan motor powers on a system level.The integrated surrogate model had an average relative error of 0.3%on the test set,while the binary classifier had a 99.85%classification accuracy,indicating sufficient generalisation.The surrogate model was validated using site-data covering 10 days of operation for the case-study ACC system,providing backpressure predictions for all 1967 input samples within a few seconds of compute time.Approximately 93.5%of backpressure predictions were within±6%of the recorded backpressures,indicating sufficient accuracy of the surrogate model with a significant decrease in compute time.
