The Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) developed by Cacuci has been... more The Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) developed by Cacuci has been applied to compute deterministically the exact values of the 1st-order and 2nd-order sensitivities of the leakage response of a polyethylene-reflected plutonium (PoRP) experimental benchmark to the nuclear data characterizing this benchmark. The imprecisely known parameters underlying the nuclear data used in the neutron transport computational model for this benchmark include 180 group-averaged total microscopic cross sections, 21600 group-averaged scattering microscopic cross sections, 120 parameters describing the fission process, 60 parameters describing the fission spectrum, 10 parameters describing the system's sources, and 6 isotopic number densities. Thus, this benchmark comprises 21976 first-order sensitivities of the leakage response with respect to the model parameters, and 482,944,576 second-order sensitivities. Computing these sensitivities exactly represents the larges...
The present work experimentally investigates the thermal effects of a synthetic jet actuator on t... more The present work experimentally investigates the thermal effects of a synthetic jet actuator on the heat transfer performance of single-phase flow confined in a microchannel heat sink. The heat sink consisted of a single rectangular microchannel 500 μm wide, 300 μm deep and 26 mm long. Deionized water was employed as the cooling fluid. A synthetic jet actuator with a 100 μm diameter orifice was placed right above the microchannel and 5 mm downstream from the channel inlet. A Unimorph piezoelectric disc bender was employed as the synthetic jet actuator. The effects of the bulk microchannel flow Reynolds number, the synthetic jet operating voltage and frequency on the microchannel heat transfer performance are being investigated. The Reynolds number ranges from 100 to 500. The actuator driving voltage and frequency ranges in 20-180Vp-p and 10-150 Hz respectively. The results from the case without synthetic jet are compared to those with synthetic jet. It shows that the thermal effects...
This work extends the investigation of higher-order sensitivity and uncertainty analysis from 3rd... more This work extends the investigation of higher-order sensitivity and uncertainty analysis from 3rd-order to 4th-order for a polyethylene-reflected plutonium (PERP) OECD/NEA reactor physics benchmark. Specifically, by applying the 4th-order comprehensive adjoint sensitivity analysis methodology (4th-CASAM) to the PERP benchmark, this work presents the numerical results of the most important 4th-order sensitivities of the benchmark’s total leakage response with respect to the benchmark’s 180 microscopic total cross sections, which includes 180 4th-order unmixed sensitivities and 360 4th-order mixed sensitivities corresponding to the largest 3rd-order ones. The numerical results obtained in this work reveal that the number of 4th-order relative sensitivities that have large values (e.g., greater than 1.0) is far greater than the number of important 1st-, 2nd- and 3rd-order sensitivities. The majority of those large sensitivities involve isotopes 1H and 239Pu contained in the PERP benchm...
The Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) is applied to compute the fi... more The Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) is applied to compute the first-order and second-order sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental system with respect to the following nuclear data: Group-averaged isotopic microscopic fission cross sections, mixed fission/total, fission/scattering cross sections, average number of neutrons per fission (), mixed /total cross sections, /scattering cross sections, and /fission cross sections. The numerical results obtained indicate that the 1st-order relative sensitivities for these nuclear data are smaller than the 1st-order sensitivities of the PERP leakage response with respect to the total cross sections but are larger than those with respect to the scattering cross sections. The vast majority of the 2nd-order unmixed sensitivities are smaller than the corresponding 1st-order ones, but several 2nd-order mixed relative sensitivities are larger than the 1st-order...
Abstract Based on the adjoint sensitivity models for the saturated case of the counter-flow cooli... more Abstract Based on the adjoint sensitivity models for the saturated case of the counter-flow cooling tower developed in the accompanying Part I, this work computed and analyzed the sensitivities, with respect to all of the 52 model parameters, of the following responses (i.e., model outputs of interest): the outlet air temperature, outlet water temperature, outlet water mass flow rate, and outlet air relative humidity. The sensitivity results indicate that, in general, all these response of interest are mostly sensitive to the boundary-related parameters (e.g., , , , , , and ) and also somewhat sensitive to those parameters (e.g., , , , , , , and ) that directly relate to the heat and mass transfer terms in the cooling tower model. The rankings of these parameters depend on the respective model responses. With the sensitivities known, the propagation of the uncertainties in the model parameters to the uncertainties in the model outputs are readily obtained. The uncertainties associated with the model outputs were reduced by applying the “predictive modeling for coupled multiphysics systems” (PM_CMPS) methodology. For a typical case studied in this work, the uncertainties associated with the model outputs of the outlet air temperature, outlet water temperature, and outlet air relative humidity, are reduced by 22%, 38%, and 68%, respectively. Moreover, the PM_CMPS methodology also generated optimal best-estimate nominal values for the model parameters and model responses. It also improved (i.e., reduced) the uncertainties associated with model parameters through the process of model calibration, as shown in the paper. The results presented in this work demonstrate that the PM_CMPS methodology reduces the predicted standard deviations to values that are smaller than either the computed or the experimentally measured ones, even for responses (e.g., the outlet water flow rate) for which no measurements are available. These improvements stem from the global characteristics of the PM_CMPS methodology, which combines all of the available information simultaneously in phase-space, as opposed to combining it sequentially, as in current data assimilation procedures.
Abstract This work presents numerical results for the second-order sensitivities of the temperatu... more Abstract This work presents numerical results for the second-order sensitivities of the temperature distributions in a paradigm benchmark problem modeling heat transport in a reactor fuel rod and the surrounding coolant channel. The development of this benchmark problem was originally motivated by the need to verify the numerical results for the first-order sensitivities produced by the FLUENT Adjoint Solver for the G4M Reactor preconceptual design and for a test section designed to investigate thermal-hydraulic phenomena of importance to the safety considerations for this reactor. The relative sensitivities computed using the FLUENT Adjoint Solver had significantly large values, of order unity, thereby motivating the need to investigate the impact of nonlinearities, the bulk of which are quantified by the responses’ second-order sensitivities. However, the current FLUENT Adjoint Solver cannot compute second-order sensitivities, which in turn motivated the derivation of these sensitivities for the heat transport benchmark problem by using the recently developed second-order adjoint sensitivity analysis methodology. The numerical results obtained in this work used thermal-hydraulic parameters having mean values and standard deviations typical of the conditions found in the preliminary conceptual design of the G4M Reactor. These results show that the contributions of the second-order sensitivities to the expected values of the temperature distributions within the rod, on the rod’s surface, and in the coolant are <1% of the corresponding computed nominal values. Similarly, the contributions of the second-order sensitivities to the standard deviations of the temperature distributions within the rod, on the rod’s surface, and in the coolant are also 1%, or less, of the corresponding contributions stemming from the first-order sensitivities, to the respective total standard deviations (uncertainties). These results justify the use of first-order sensitivities for computing expected uncertainties in the temperature distributions within the benchmark problem and, hence, mutatis mutandis, for the test section and G4M Reactor design. On the other hand, the most important impact of the second-order sensitivities is the positive skewnesses they induce in the temperature distributions within the rod, on the rod’s surface, and in the coolant. This implies that all three temperature distributions, particularly in the heated rod, are non-Gaussian, asymmetric, and skewed toward temperatures higher than the respective mean temperatures.
ASME 2012 10th International Conference on Nanochannels, Microchannels, and Minichannels, 2012
ABSTRACT Two-phase flow instabilities in micro-channel exhibit pressure and temperature fluctuati... more ABSTRACT Two-phase flow instabilities in micro-channel exhibit pressure and temperature fluctuations with different frequencies and amplitudes. An active way to suppress the dynamic instabilities in the boiling micro-channels is to introduce synthetic jets into the channel fluid. Thus the bubbles can be condensed before they clog the channel and expand upstream causing flow reversal.The present work experimentally investigated the effect of synthetic jets on the suppression of flow boiling instabilities exhibited in a micro-channel heat sink. The heat sink is consisted of five parallel rectangular microchannels measured 500 μm wide, 500 μm deep each. An array of synthetic jets was placed right above the micro-channels with each channel corresponds to 8 jet orifices. The strength and frequency of the jets are controlled by changing the driving voltage and frequency of the piezoelectric driven synthetic jet actuator. Tests were performed with synthetic jets operating at 80 Hz and 150 Hz respectively. It is found that the bubbles were effectively condensed inside the jet cavity. The boiling flow reversals were notably delayed by the synthetic jets. Meanwhile, the pressure fluctuation amplitudes were substantially reduced. Test results were analyzed and discussed in detail.
ABSTRACT This study experimentally assesses single phase heat transfer characteristics of a shall... more ABSTRACT This study experimentally assesses single phase heat transfer characteristics of a shallow rectangular microchannel heat sink whose surface is enhanced with copper nanowires (CuNWs). The hydraulic diameter of the channel is 672 μm and the bottom wall is coated with Cu nanowires (CuNWs) of 200 nm in diameter and 50 μm in length. CuNWs are grown on the Cu heat sink by electrochemical synthesis technique which is inexpensive and readily scalable. The heat transfer and pressure drop results of CuNWs enhanced heat sink are compared with that of bare copper heat sink using deionized (DI) water as the working fluid at Reynolds Number (Re) ranging from 106–636. The experimental results indicate an enhancement in Nusselt Number (Nu) at all Re with a maximum enhancement of 24% at Re = 106. The enhanced thermal performance is attributed to two properties of Cu nanowire arrays — improvement in surface wettability characteristics and increased heat transfer surface area.
The Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) developed by Cacuci has been... more The Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) developed by Cacuci has been applied to compute deterministically the exact values of the 1st-order and 2nd-order sensitivities of the leakage response of a polyethylene-reflected plutonium (PoRP) experimental benchmark to the nuclear data characterizing this benchmark. The imprecisely known parameters underlying the nuclear data used in the neutron transport computational model for this benchmark include 180 group-averaged total microscopic cross sections, 21600 group-averaged scattering microscopic cross sections, 120 parameters describing the fission process, 60 parameters describing the fission spectrum, 10 parameters describing the system's sources, and 6 isotopic number densities. Thus, this benchmark comprises 21976 first-order sensitivities of the leakage response with respect to the model parameters, and 482,944,576 second-order sensitivities. Computing these sensitivities exactly represents the larges...
The present work experimentally investigates the thermal effects of a synthetic jet actuator on t... more The present work experimentally investigates the thermal effects of a synthetic jet actuator on the heat transfer performance of single-phase flow confined in a microchannel heat sink. The heat sink consisted of a single rectangular microchannel 500 μm wide, 300 μm deep and 26 mm long. Deionized water was employed as the cooling fluid. A synthetic jet actuator with a 100 μm diameter orifice was placed right above the microchannel and 5 mm downstream from the channel inlet. A Unimorph piezoelectric disc bender was employed as the synthetic jet actuator. The effects of the bulk microchannel flow Reynolds number, the synthetic jet operating voltage and frequency on the microchannel heat transfer performance are being investigated. The Reynolds number ranges from 100 to 500. The actuator driving voltage and frequency ranges in 20-180Vp-p and 10-150 Hz respectively. The results from the case without synthetic jet are compared to those with synthetic jet. It shows that the thermal effects...
This work extends the investigation of higher-order sensitivity and uncertainty analysis from 3rd... more This work extends the investigation of higher-order sensitivity and uncertainty analysis from 3rd-order to 4th-order for a polyethylene-reflected plutonium (PERP) OECD/NEA reactor physics benchmark. Specifically, by applying the 4th-order comprehensive adjoint sensitivity analysis methodology (4th-CASAM) to the PERP benchmark, this work presents the numerical results of the most important 4th-order sensitivities of the benchmark’s total leakage response with respect to the benchmark’s 180 microscopic total cross sections, which includes 180 4th-order unmixed sensitivities and 360 4th-order mixed sensitivities corresponding to the largest 3rd-order ones. The numerical results obtained in this work reveal that the number of 4th-order relative sensitivities that have large values (e.g., greater than 1.0) is far greater than the number of important 1st-, 2nd- and 3rd-order sensitivities. The majority of those large sensitivities involve isotopes 1H and 239Pu contained in the PERP benchm...
The Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) is applied to compute the fi... more The Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) is applied to compute the first-order and second-order sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental system with respect to the following nuclear data: Group-averaged isotopic microscopic fission cross sections, mixed fission/total, fission/scattering cross sections, average number of neutrons per fission (), mixed /total cross sections, /scattering cross sections, and /fission cross sections. The numerical results obtained indicate that the 1st-order relative sensitivities for these nuclear data are smaller than the 1st-order sensitivities of the PERP leakage response with respect to the total cross sections but are larger than those with respect to the scattering cross sections. The vast majority of the 2nd-order unmixed sensitivities are smaller than the corresponding 1st-order ones, but several 2nd-order mixed relative sensitivities are larger than the 1st-order...
Abstract Based on the adjoint sensitivity models for the saturated case of the counter-flow cooli... more Abstract Based on the adjoint sensitivity models for the saturated case of the counter-flow cooling tower developed in the accompanying Part I, this work computed and analyzed the sensitivities, with respect to all of the 52 model parameters, of the following responses (i.e., model outputs of interest): the outlet air temperature, outlet water temperature, outlet water mass flow rate, and outlet air relative humidity. The sensitivity results indicate that, in general, all these response of interest are mostly sensitive to the boundary-related parameters (e.g., , , , , , and ) and also somewhat sensitive to those parameters (e.g., , , , , , , and ) that directly relate to the heat and mass transfer terms in the cooling tower model. The rankings of these parameters depend on the respective model responses. With the sensitivities known, the propagation of the uncertainties in the model parameters to the uncertainties in the model outputs are readily obtained. The uncertainties associated with the model outputs were reduced by applying the “predictive modeling for coupled multiphysics systems” (PM_CMPS) methodology. For a typical case studied in this work, the uncertainties associated with the model outputs of the outlet air temperature, outlet water temperature, and outlet air relative humidity, are reduced by 22%, 38%, and 68%, respectively. Moreover, the PM_CMPS methodology also generated optimal best-estimate nominal values for the model parameters and model responses. It also improved (i.e., reduced) the uncertainties associated with model parameters through the process of model calibration, as shown in the paper. The results presented in this work demonstrate that the PM_CMPS methodology reduces the predicted standard deviations to values that are smaller than either the computed or the experimentally measured ones, even for responses (e.g., the outlet water flow rate) for which no measurements are available. These improvements stem from the global characteristics of the PM_CMPS methodology, which combines all of the available information simultaneously in phase-space, as opposed to combining it sequentially, as in current data assimilation procedures.
Abstract This work presents numerical results for the second-order sensitivities of the temperatu... more Abstract This work presents numerical results for the second-order sensitivities of the temperature distributions in a paradigm benchmark problem modeling heat transport in a reactor fuel rod and the surrounding coolant channel. The development of this benchmark problem was originally motivated by the need to verify the numerical results for the first-order sensitivities produced by the FLUENT Adjoint Solver for the G4M Reactor preconceptual design and for a test section designed to investigate thermal-hydraulic phenomena of importance to the safety considerations for this reactor. The relative sensitivities computed using the FLUENT Adjoint Solver had significantly large values, of order unity, thereby motivating the need to investigate the impact of nonlinearities, the bulk of which are quantified by the responses’ second-order sensitivities. However, the current FLUENT Adjoint Solver cannot compute second-order sensitivities, which in turn motivated the derivation of these sensitivities for the heat transport benchmark problem by using the recently developed second-order adjoint sensitivity analysis methodology. The numerical results obtained in this work used thermal-hydraulic parameters having mean values and standard deviations typical of the conditions found in the preliminary conceptual design of the G4M Reactor. These results show that the contributions of the second-order sensitivities to the expected values of the temperature distributions within the rod, on the rod’s surface, and in the coolant are <1% of the corresponding computed nominal values. Similarly, the contributions of the second-order sensitivities to the standard deviations of the temperature distributions within the rod, on the rod’s surface, and in the coolant are also 1%, or less, of the corresponding contributions stemming from the first-order sensitivities, to the respective total standard deviations (uncertainties). These results justify the use of first-order sensitivities for computing expected uncertainties in the temperature distributions within the benchmark problem and, hence, mutatis mutandis, for the test section and G4M Reactor design. On the other hand, the most important impact of the second-order sensitivities is the positive skewnesses they induce in the temperature distributions within the rod, on the rod’s surface, and in the coolant. This implies that all three temperature distributions, particularly in the heated rod, are non-Gaussian, asymmetric, and skewed toward temperatures higher than the respective mean temperatures.
ASME 2012 10th International Conference on Nanochannels, Microchannels, and Minichannels, 2012
ABSTRACT Two-phase flow instabilities in micro-channel exhibit pressure and temperature fluctuati... more ABSTRACT Two-phase flow instabilities in micro-channel exhibit pressure and temperature fluctuations with different frequencies and amplitudes. An active way to suppress the dynamic instabilities in the boiling micro-channels is to introduce synthetic jets into the channel fluid. Thus the bubbles can be condensed before they clog the channel and expand upstream causing flow reversal.The present work experimentally investigated the effect of synthetic jets on the suppression of flow boiling instabilities exhibited in a micro-channel heat sink. The heat sink is consisted of five parallel rectangular microchannels measured 500 μm wide, 500 μm deep each. An array of synthetic jets was placed right above the micro-channels with each channel corresponds to 8 jet orifices. The strength and frequency of the jets are controlled by changing the driving voltage and frequency of the piezoelectric driven synthetic jet actuator. Tests were performed with synthetic jets operating at 80 Hz and 150 Hz respectively. It is found that the bubbles were effectively condensed inside the jet cavity. The boiling flow reversals were notably delayed by the synthetic jets. Meanwhile, the pressure fluctuation amplitudes were substantially reduced. Test results were analyzed and discussed in detail.
ABSTRACT This study experimentally assesses single phase heat transfer characteristics of a shall... more ABSTRACT This study experimentally assesses single phase heat transfer characteristics of a shallow rectangular microchannel heat sink whose surface is enhanced with copper nanowires (CuNWs). The hydraulic diameter of the channel is 672 μm and the bottom wall is coated with Cu nanowires (CuNWs) of 200 nm in diameter and 50 μm in length. CuNWs are grown on the Cu heat sink by electrochemical synthesis technique which is inexpensive and readily scalable. The heat transfer and pressure drop results of CuNWs enhanced heat sink are compared with that of bare copper heat sink using deionized (DI) water as the working fluid at Reynolds Number (Re) ranging from 106–636. The experimental results indicate an enhancement in Nusselt Number (Nu) at all Re with a maximum enhancement of 24% at Re = 106. The enhanced thermal performance is attributed to two properties of Cu nanowire arrays — improvement in surface wettability characteristics and increased heat transfer surface area.
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