Parabolized stability equations （PSE） were used to study the evolution of disturbances in compressible boundary layers. The results were compared with those obtained by direct numerical simulations （DNS）, to check...Parabolized stability equations （PSE） were used to study the evolution of disturbances in compressible boundary layers. The results were compared with those obtained by direct numerical simulations （DNS）, to check if the results from PSE method were reliable or not. The results of comparison showed that no matter for subsonic or supersonic boundary layers, results from both the PSE and DNS method agreed with each other reasonably well, and the agreement between temperatures was better than those between velocities. In addition, linear PSE was used to calculate the neutral curve for small amplitude disturbances in a supersonic boundary layer. Compared with those obtained by linear stability theory （LST）, the situation was similar to those for incom- pressible boundary layer.展开更多
The previously developed single-sweep parabolized Navier-Stokes （SSPNS） space marching code for ideal gas flows has been extended to compute chemically nonequilibrium flows. In the code, the strongly coupled set of ...The previously developed single-sweep parabolized Navier-Stokes （SSPNS） space marching code for ideal gas flows has been extended to compute chemically nonequilibrium flows. In the code, the strongly coupled set of gas dynamics, species conservation, and turbulence equations is integrated with the implicit lower-upper symmetric GaussSeidel （LU-SGS） method in the streamwise direction in a space marching manner. The AUSMPW＋ scheme is used to calculate the inviscid fluxes in the crossflow direction, while the conventional central scheme for the viscous fluxes. The k-g two-equation turbulence model is used. The revised SSPNS code is validated by computing the Burrows-Kurkov non-premixed H2/air supersonic combustion flows, premixed H2/air hypersonic combustion flows in a three-dimensional duct with a 15° compression ramp, as well as the hypersonic laminar chemically nonequilibrium air flows around two 10° half-angle cones. The results of these calculations are in good agreement with those of experiments, NASA UPS or Prabhu＇s PNS codes. It can be concluded that the SSPNS code is highly efficient for steady supersonic/ hypersonic chemically reaction flows when there is no large streamwise separation.展开更多
An improved expansion of the parabolized stability equation(iEPSE) method is proposed for the accurate linear instability prediction in boundary layers. It is a local eigenvalue problem, and the streamwise wavenumber ...An improved expansion of the parabolized stability equation(iEPSE) method is proposed for the accurate linear instability prediction in boundary layers. It is a local eigenvalue problem, and the streamwise wavenumber α and its streamwise gradient dα/dx are unknown variables. This eigenvalue problem is solved for the eigenvalue dα/dx with an initial α, and the correction of α is performed with the conservation relation used in the PSE. The i EPSE is validated in several compressible and incompressible boundary layers. The computational results show that the prediction accuracy of the i EPSE is significantly higher than that of the ESPE, and it is in excellent agreement with the PSE which is regarded as the baseline for comparison. In addition, the unphysical multiple eigenmode problem in the EPSE is solved by using the i EPSE. As a local non-parallel stability analysis tool, the i EPSE has great potential application in the eNtransition prediction in general three-dimensional boundary layers.展开更多
The parabolized stability equation （PSE） method has been proven to be a useful and convenient tool for the investigation of the stability and transition problems of boundary layers. However, in its original formulat...The parabolized stability equation （PSE） method has been proven to be a useful and convenient tool for the investigation of the stability and transition problems of boundary layers. However, in its original formulation, for nonlinear problems, the complex wave number of each Fourier mode is determined by the so-called phase-locked rule, which results in non-self-consistency in the wave numbers. In this paper, a modification is proposed to make it self-consistent. The main idea is that, instead of allowing wave numbers to be complex, all wave numbers are kept real, and the growth or decay of each mode is simply manifested in the growth or decay of the modulus of its shape function. The validity of the new formulation is illustrated by comparing the results with those from the corresponding direct numerical simulation （DNS） as applied to a problem of compressible boundary layer with Mach number 6.展开更多
The phenomenon of laminar-turbulent transition exists universally in nature and various engineering practice. The prediction of transition position is one of crucial theories and practical problems in fluid mechanics ...The phenomenon of laminar-turbulent transition exists universally in nature and various engineering practice. The prediction of transition position is one of crucial theories and practical problems in fluid mechanics due to the different characteristics of laminar flow and turbulent flow. Two types of disturbances are imposed at the entrance, i.e., identical amplitude and wavepacket disturbances, along the spanwise direction in the incompressible boundary layers. The disturbances of identical amplitude are consisted of one two-dimensional （2D） wave and two three-dimensional （3D） waves. The parabolized stability equation （PSE） is used to research the evolution of disturbances and to predict the transition position. The results are compared with those obtained by the numerical simulation. The results show that the PSE method can investigate the evolution of disturbances and predict the transition position. At the same time, the calculation speed is much faster than that of the numerical simulation.展开更多
The nonlinear parabolized stability equations(NPSEs)approach is widely used to study the evolution of disturbances in hypersonic boundary layers owing to its high computational efficiency.However,divergence of the NPS...The nonlinear parabolized stability equations(NPSEs)approach is widely used to study the evolution of disturbances in hypersonic boundary layers owing to its high computational efficiency.However,divergence of the NPSEs will occur when disturbances imposed at the inlet no longer play a leading role or when the nonlinear effect becomes very strong.Two major improvements are proposed here to deal with the divergence of the NPSEs.First,all disturbances are divided into two types:dominant waves and non-dominant waves.Disturbances imposed at the inlet or playing a leading role are defined as dominant waves,with all others being defined as non-dominant waves.Second,the streamwise wavenumbers of the non-dominant waves are obtained using the phase-locked method,while those of the dominant waves are obtained using an iterative method.Two reference wavenumbers are introduced in the phase-locked method,and methods for calculating them for different numbers of dominant waves are discussed.Direct numerical simulation(DNS)is performed to verify and validate the predictions of the improved NPSEs in a hypersonic boundary layer on an isothermal swept blunt plate.The results from the improved NPSEs approach are in good agreement with those of DNS,whereas the traditional NPSEs approach is subject to divergence,indicating that the improved NPSEs approach exhibits greater robustness.展开更多
In this paper, a second-order implicit-explicit upwind algorithm has been developed for three-dimensional Parabolized Navier-Stokes(PNS) equations. The agreement between the results of the new upwind algorithm and tho...In this paper, a second-order implicit-explicit upwind algorithm has been developed for three-dimensional Parabolized Navier-Stokes(PNS) equations. The agreement between the results of the new upwind algorithm and those of the im- plicit upwind algorithm and its ability in marching a long distance along the stream- wise direction have been shown for the supersonic viscous flow past a sphere-cone body. The CPU time is greatly reduced.展开更多
A time semi-discrete Crank-Nicolson （CN） formulation with second-order time accuracy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed ...A time semi-discrete Crank-Nicolson （CN） formulation with second-order time accuracy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed finite volume element （SCNMFVE） formu- lation based on two local Gaussian integrals and parameter-free with the second-order time accuracy is established directly from the time semi-discrete CN formulation so that it could avoid the discussion for semi-discrete SCNMFVE formulation with respect to spatial wriables and its theoretical analysis becomes very simple. Finally, the error estimates of SCNMFVE solutions are provided.展开更多
In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence...In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0.展开更多
In this study, a time semi-discrete Crank-Nicolson （CN） formulation with second-order time accu- racy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete sta...In this study, a time semi-discrete Crank-Nicolson （CN） formulation with second-order time accu- racy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed finite element （SCNMFE） formulation based on two local Gauss integrals and parameter- free with the second-order time accuracy is established directly from the time semi-discrete CN formulation. Thus, it could avoid the discussion for semi-discrete SCNMFE formulation with respect to spatial variables and its theoretical analysis becomes very simple. Finaly, the error estimates of SCNMFE solutions are provided.展开更多
This study presents the design,construction,and thermal evaluation of a solar-powered cocoa roaster based on a Parabolic Cylinder Collector(PCC)with dual-axis solar tracking.The system integrates three functional subs...This study presents the design,construction,and thermal evaluation of a solar-powered cocoa roaster based on a Parabolic Cylinder Collector(PCC)with dual-axis solar tracking.The system integrates three functional subsystems:the cylindrical-parabolic reflecting surface,the stainless-steel absorber tube,and a microcontrollerbased tracking mechanism.The prototype enables continuous acquisition of key thermal variables(solar irradiance,ambient temperature,absorber surface temperature,and bean temperature),allowing a detailed characterization of heat transfer processes during roasting.Roasting experiments were conducted at controlled durations of 40,55,and 70 min between 10:00 and 14:00 h.Maximum roasting temperatures of 125℃–137℃ were reached under average irradiance levels of 685.7–930.5 W m−2.The lowest final moisture content was 2.19%,within the recommended range for high-quality cocoa.Longer roasting durations promoted thermal energy accumulation within the absorber tube,enhancing convective and radiative heat transfer to the bean mass even under fluctuating irradiance.The experimental trends reveal a strong coupling between irradiance variability,absorber temperature,and internal air-beam heat transfer.Comparison with reference parabolic trough collector studies indicate that,although the process-level roasting efficiency(3.83%–7.45%)is lower than conventional collector-level thermal efficiencies,the operating temperatures and moisture-reduction rates align with the thermal requirements of food-processing systems rather than high-enthalpy solar applications.These results also demonstrate the potential of coupling PCC-based solar concentration with lowtemperature convective–radiative roasting processes.Overall,the findings confirm the feasibility of implementing PCC-based roasting technologies in rural or off-grid regions,where solar-driven heat transfer offers a sustainable,low-cost alternative to fossil-fuel-based roasting systems,enabling a controlled thermophysical environment for cocoa transformation.展开更多
This study investigates the effects of ocean boundaries on modal shapes in very-low-frequency(VLF,1–10 Hz)sound propagation through the deep ocean.Utilizing a normal mode solution formulated in terms of parabolic cyl...This study investigates the effects of ocean boundaries on modal shapes in very-low-frequency(VLF,1–10 Hz)sound propagation through the deep ocean.Utilizing a normal mode solution formulated in terms of parabolic cylinder functions(PCF),we demonstrate that boundary interactions induce a phase change reduction below-πat frequencies of several hertz.This reduction,in turn,forces a key transition in the solution,shifting the order of the PCF from integer to non-integer values.Analysis of the characteristic shape of the PCF versus its order reveals that these boundary-influenced modes exhibit an energy shift toward deeper regions and a weakened axial convergence of the underwater sound field.展开更多
In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is de...In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is developed using the trigonometric scheme,which is based on zero,first,and second moments,and the direct discontinuous Galerkin(DDG)flux is used to discretize the diffusion term.Moreover,the DDG method directly applies the weak form of the parabolic equation to each computational cell,which can better capture the characteristics of the solution,especially the discontinuous solution.Meanwhile,the third-order TVD-Runge-Kutta method is applied for temporal discretization.Finally,the effectiveness and stability of the method constructed in this paper are evaluated through numerical tests.展开更多
Determining earth pressure on jacked pipes is essential for ensuring lining safety and calculating jacking force,especially for deep-buried pipes.To better reflect the soil arching effect resulting from the excavation...Determining earth pressure on jacked pipes is essential for ensuring lining safety and calculating jacking force,especially for deep-buried pipes.To better reflect the soil arching effect resulting from the excavation of rectangular jacked pipes and the distribution of the earth pressure on jacked pipes,we present an analytical solution for predicting the vertical earth pressure on deep-buried rectangular pipe jacking tunnels,incorporating the tunnelling-induced ground loss distribution.Our proposed analytical model consists of the upper multi-layer parabolic soil arch and the lower friction arch.The key parameters(i.e.,width and height of friction arch B and height of parabolic soil arch H 1)are determined according to the existing research,and an analytical solution for K l is derived based on the distribution characteristics of the principal stress rotation angle.With consideration for the transition effect of the mechanical characteristics of the parabolic arch zone,an analytical solution for soil load transfer is derived.The prediction results of our analytical solution are compared with tests and simulation results to validate the effectiveness of the proposed analytical solution.Finally,the effects of different parameters on the soil pressure are discussed.展开更多
This work aims at the mathematical modeling of a parabolic trough concentrator, the numerical resolution of the resulting equation, as well as the simulation of the heat transfer fluid heating process. To do this, a t...This work aims at the mathematical modeling of a parabolic trough concentrator, the numerical resolution of the resulting equation, as well as the simulation of the heat transfer fluid heating process. To do this, a thermal balance was established for the heat transfer fluid, the absorber and the glass. This allowed us to establish an equation system whose resolution was done by the finite difference method. Then, a computer program was developed to simulate the temperatures of the heat transfer fluid, the absorber tube and the glass as a function of time and space. The numerical resolution made it possible to obtain the temperatures of the heat transfer fluid, the absorber and the glass. The simulation of the fluid heating process was done in one-hour time steps, from six in the morning to six in the afternoon. The results obtained show that the temperature difference between the inlet and the outlet of the sensor is very significant. These results obtained, regarding the variation of the temperatures of the heat transfer fluid, the absorber and the glass, as well as the powers and efficiency of the parabolic trough concentrator and various factors, allow for the improvement of the performances of our prototype.展开更多
The effects of the Rashba spin–orbit interaction and external electric and magnetic fields on the thermodynamic properties of parabolic quantum dots are investigated.An explicit partition function is derived,and ther...The effects of the Rashba spin–orbit interaction and external electric and magnetic fields on the thermodynamic properties of parabolic quantum dots are investigated.An explicit partition function is derived,and thermodynamic quantities,including specific heat,entropy,and magnetic susceptibility,are analyzed.The behavior of Shannon entropy-related thermodynamic quantities is examined under varying magnetic fields and Hamiltonian parameters through numerical analysis.The results reveal a pronounced Schottky anomaly in the heat capacity at lower temperatures.The susceptibility exhibits a progressive enhancement and transitions to higher values with changes in the quantum dot parameters.In the presence of the Rashba spin–orbit interaction,the specific heat increases with temperature,reaches a peak,and then decreases to zero.Additionally,the susceptibility increases with theβparameter for varying Rashba spin–orbit interaction coefficients,and at a fixed temperature,it further increases with the Rashba coefficient.展开更多
In this paper,a class of semilinear parabolic equations with cross coupling of power and exponential functions and large initial values are studied.By constructing and solving ordinary differential equations,the upper...In this paper,a class of semilinear parabolic equations with cross coupling of power and exponential functions and large initial values are studied.By constructing and solving ordinary differential equations,the upper and lower bounds on the solution life span of the equations areobtained.展开更多
This paper deals with a semilinear parabolic problem involving variable coefficients and nonlinear memory boundary conditions.We give the blow-up criteria for all nonnegative nontrivial solutions,which rely on the beh...This paper deals with a semilinear parabolic problem involving variable coefficients and nonlinear memory boundary conditions.We give the blow-up criteria for all nonnegative nontrivial solutions,which rely on the behavior of the coefficients when time variable tends to positive infinity.Moreover,the global existence of solutions are discussed for non-positive exponents.展开更多
基金Project supported by the National Natural Science Foundation of China (Key Program)(No.10632050)the Science Foundation of Liuhui Center of Applied Mathematics,Nankai University and Tianjin University.
文摘Parabolized stability equations （PSE） were used to study the evolution of disturbances in compressible boundary layers. The results were compared with those obtained by direct numerical simulations （DNS）, to check if the results from PSE method were reliable or not. The results of comparison showed that no matter for subsonic or supersonic boundary layers, results from both the PSE and DNS method agreed with each other reasonably well, and the agreement between temperatures was better than those between velocities. In addition, linear PSE was used to calculate the neutral curve for small amplitude disturbances in a supersonic boundary layer. Compared with those obtained by linear stability theory （LST）, the situation was similar to those for incom- pressible boundary layer.
基金supported by the National Natural Science Foundation of China (51176003)
文摘The previously developed single-sweep parabolized Navier-Stokes （SSPNS） space marching code for ideal gas flows has been extended to compute chemically nonequilibrium flows. In the code, the strongly coupled set of gas dynamics, species conservation, and turbulence equations is integrated with the implicit lower-upper symmetric GaussSeidel （LU-SGS） method in the streamwise direction in a space marching manner. The AUSMPW＋ scheme is used to calculate the inviscid fluxes in the crossflow direction, while the conventional central scheme for the viscous fluxes. The k-g two-equation turbulence model is used. The revised SSPNS code is validated by computing the Burrows-Kurkov non-premixed H2/air supersonic combustion flows, premixed H2/air hypersonic combustion flows in a three-dimensional duct with a 15° compression ramp, as well as the hypersonic laminar chemically nonequilibrium air flows around two 10° half-angle cones. The results of these calculations are in good agreement with those of experiments, NASA UPS or Prabhu＇s PNS codes. It can be concluded that the SSPNS code is highly efficient for steady supersonic/ hypersonic chemically reaction flows when there is no large streamwise separation.
基金Project supported by the National Natural Science Foundation of China(Nos.11332007,11402167,11672205,and 11732011)the National Key Research and Development Program of China(No.2016YFA0401200)
文摘An improved expansion of the parabolized stability equation(iEPSE) method is proposed for the accurate linear instability prediction in boundary layers. It is a local eigenvalue problem, and the streamwise wavenumber α and its streamwise gradient dα/dx are unknown variables. This eigenvalue problem is solved for the eigenvalue dα/dx with an initial α, and the correction of α is performed with the conservation relation used in the PSE. The i EPSE is validated in several compressible and incompressible boundary layers. The computational results show that the prediction accuracy of the i EPSE is significantly higher than that of the ESPE, and it is in excellent agreement with the PSE which is regarded as the baseline for comparison. In addition, the unphysical multiple eigenmode problem in the EPSE is solved by using the i EPSE. As a local non-parallel stability analysis tool, the i EPSE has great potential application in the eNtransition prediction in general three-dimensional boundary layers.
基金supported by the National Natural Science Foundation of China(Nos.11202147,11472188,11332007,11172203,and 91216111)the Specialized Research Fund(New Teacher Class)for the Doctoral Program of Higher Education(No.20120032120007)
文摘The parabolized stability equation （PSE） method has been proven to be a useful and convenient tool for the investigation of the stability and transition problems of boundary layers. However, in its original formulation, for nonlinear problems, the complex wave number of each Fourier mode is determined by the so-called phase-locked rule, which results in non-self-consistency in the wave numbers. In this paper, a modification is proposed to make it self-consistent. The main idea is that, instead of allowing wave numbers to be complex, all wave numbers are kept real, and the growth or decay of each mode is simply manifested in the growth or decay of the modulus of its shape function. The validity of the new formulation is illustrated by comparing the results with those from the corresponding direct numerical simulation （DNS） as applied to a problem of compressible boundary layer with Mach number 6.
基金Project supported by the National Basic Research Program of China (No.2009CB724103)
文摘The phenomenon of laminar-turbulent transition exists universally in nature and various engineering practice. The prediction of transition position is one of crucial theories and practical problems in fluid mechanics due to the different characteristics of laminar flow and turbulent flow. Two types of disturbances are imposed at the entrance, i.e., identical amplitude and wavepacket disturbances, along the spanwise direction in the incompressible boundary layers. The disturbances of identical amplitude are consisted of one two-dimensional （2D） wave and two three-dimensional （3D） waves. The parabolized stability equation （PSE） is used to research the evolution of disturbances and to predict the transition position. The results are compared with those obtained by the numerical simulation. The results show that the PSE method can investigate the evolution of disturbances and predict the transition position. At the same time, the calculation speed is much faster than that of the numerical simulation.
基金the National Natural Science Foundation of China(Grant Nos.12072232 and 11672351)the National Key Project of China(Grant No.GJXM92579).
文摘The nonlinear parabolized stability equations(NPSEs)approach is widely used to study the evolution of disturbances in hypersonic boundary layers owing to its high computational efficiency.However,divergence of the NPSEs will occur when disturbances imposed at the inlet no longer play a leading role or when the nonlinear effect becomes very strong.Two major improvements are proposed here to deal with the divergence of the NPSEs.First,all disturbances are divided into two types:dominant waves and non-dominant waves.Disturbances imposed at the inlet or playing a leading role are defined as dominant waves,with all others being defined as non-dominant waves.Second,the streamwise wavenumbers of the non-dominant waves are obtained using the phase-locked method,while those of the dominant waves are obtained using an iterative method.Two reference wavenumbers are introduced in the phase-locked method,and methods for calculating them for different numbers of dominant waves are discussed.Direct numerical simulation(DNS)is performed to verify and validate the predictions of the improved NPSEs in a hypersonic boundary layer on an isothermal swept blunt plate.The results from the improved NPSEs approach are in good agreement with those of DNS,whereas the traditional NPSEs approach is subject to divergence,indicating that the improved NPSEs approach exhibits greater robustness.
基金The project supported by the National Natural Science Foundation of China
文摘In this paper, a second-order implicit-explicit upwind algorithm has been developed for three-dimensional Parabolized Navier-Stokes(PNS) equations. The agreement between the results of the new upwind algorithm and those of the im- plicit upwind algorithm and its ability in marching a long distance along the stream- wise direction have been shown for the supersonic viscous flow past a sphere-cone body. The CPU time is greatly reduced.
基金supported by National Science Foundation of China(11271127)Science Research Project of Guizhou Province Education Department(QJHKYZ[2013]207)
文摘A time semi-discrete Crank-Nicolson （CN） formulation with second-order time accuracy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed finite volume element （SCNMFVE） formu- lation based on two local Gaussian integrals and parameter-free with the second-order time accuracy is established directly from the time semi-discrete CN formulation so that it could avoid the discussion for semi-discrete SCNMFVE formulation with respect to spatial wriables and its theoretical analysis becomes very simple. Finally, the error estimates of SCNMFVE solutions are provided.
基金Supported by NSFC(No.12101482)the Natural Science Foundation of Shaanxi Province,China(No.2018JQ1052)。
文摘In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0.
基金Supported in part by the National Natural Science Foundation of China under Grant No.11671106the cultivation fund of the National Natural and Social Science Foundations in BTBU under Grant No.LKJJ2016-22
文摘In this study, a time semi-discrete Crank-Nicolson （CN） formulation with second-order time accu- racy for the non-stationary parabolized Navier-Stokes equations is firstly established. And then, a fully discrete stabilized CN mixed finite element （SCNMFE） formulation based on two local Gauss integrals and parameter- free with the second-order time accuracy is established directly from the time semi-discrete CN formulation. Thus, it could avoid the discussion for semi-discrete SCNMFE formulation with respect to spatial variables and its theoretical analysis becomes very simple. Finaly, the error estimates of SCNMFE solutions are provided.
基金the Program for Teaching Development(PRODEP)for funding the project UJAT-PTC-251(Development and Evaluation of a Cocoa Roaster in the Tabasco Region).
文摘This study presents the design,construction,and thermal evaluation of a solar-powered cocoa roaster based on a Parabolic Cylinder Collector(PCC)with dual-axis solar tracking.The system integrates three functional subsystems:the cylindrical-parabolic reflecting surface,the stainless-steel absorber tube,and a microcontrollerbased tracking mechanism.The prototype enables continuous acquisition of key thermal variables(solar irradiance,ambient temperature,absorber surface temperature,and bean temperature),allowing a detailed characterization of heat transfer processes during roasting.Roasting experiments were conducted at controlled durations of 40,55,and 70 min between 10:00 and 14:00 h.Maximum roasting temperatures of 125℃–137℃ were reached under average irradiance levels of 685.7–930.5 W m−2.The lowest final moisture content was 2.19%,within the recommended range for high-quality cocoa.Longer roasting durations promoted thermal energy accumulation within the absorber tube,enhancing convective and radiative heat transfer to the bean mass even under fluctuating irradiance.The experimental trends reveal a strong coupling between irradiance variability,absorber temperature,and internal air-beam heat transfer.Comparison with reference parabolic trough collector studies indicate that,although the process-level roasting efficiency(3.83%–7.45%)is lower than conventional collector-level thermal efficiencies,the operating temperatures and moisture-reduction rates align with the thermal requirements of food-processing systems rather than high-enthalpy solar applications.These results also demonstrate the potential of coupling PCC-based solar concentration with lowtemperature convective–radiative roasting processes.Overall,the findings confirm the feasibility of implementing PCC-based roasting technologies in rural or off-grid regions,where solar-driven heat transfer offers a sustainable,low-cost alternative to fossil-fuel-based roasting systems,enabling a controlled thermophysical environment for cocoa transformation.
基金Project supported by the National Natural Science Foundation of China(Grant No.12204128)。
文摘This study investigates the effects of ocean boundaries on modal shapes in very-low-frequency(VLF,1–10 Hz)sound propagation through the deep ocean.Utilizing a normal mode solution formulated in terms of parabolic cylinder functions(PCF),we demonstrate that boundary interactions induce a phase change reduction below-πat frequencies of several hertz.This reduction,in turn,forces a key transition in the solution,shifting the order of the PCF from integer to non-integer values.Analysis of the characteristic shape of the PCF versus its order reveals that these boundary-influenced modes exhibit an energy shift toward deeper regions and a weakened axial convergence of the underwater sound field.
基金The Natural Science Foundation of Xinjiang Uygur Autonomous Region of China“RBF-Hermite difference scheme for the time-fractional kdv-Burgers equation”(2024D01C43)。
文摘In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is developed using the trigonometric scheme,which is based on zero,first,and second moments,and the direct discontinuous Galerkin(DDG)flux is used to discretize the diffusion term.Moreover,the DDG method directly applies the weak form of the parabolic equation to each computational cell,which can better capture the characteristics of the solution,especially the discontinuous solution.Meanwhile,the third-order TVD-Runge-Kutta method is applied for temporal discretization.Finally,the effectiveness and stability of the method constructed in this paper are evaluated through numerical tests.
基金Project(2022YJS073)supported by the Fundamental Research Funds for the Central Universities,ChinaProject(2024YFE0198500)supported by the National Key Research and Development Program of China:Intergovernmental International Science and Technology Innovation CooperationProject(U2469207)supported by the National Natural Science Foundation Railway Innovation and Development Joint Fund Project,China。
文摘Determining earth pressure on jacked pipes is essential for ensuring lining safety and calculating jacking force,especially for deep-buried pipes.To better reflect the soil arching effect resulting from the excavation of rectangular jacked pipes and the distribution of the earth pressure on jacked pipes,we present an analytical solution for predicting the vertical earth pressure on deep-buried rectangular pipe jacking tunnels,incorporating the tunnelling-induced ground loss distribution.Our proposed analytical model consists of the upper multi-layer parabolic soil arch and the lower friction arch.The key parameters(i.e.,width and height of friction arch B and height of parabolic soil arch H 1)are determined according to the existing research,and an analytical solution for K l is derived based on the distribution characteristics of the principal stress rotation angle.With consideration for the transition effect of the mechanical characteristics of the parabolic arch zone,an analytical solution for soil load transfer is derived.The prediction results of our analytical solution are compared with tests and simulation results to validate the effectiveness of the proposed analytical solution.Finally,the effects of different parameters on the soil pressure are discussed.
文摘This work aims at the mathematical modeling of a parabolic trough concentrator, the numerical resolution of the resulting equation, as well as the simulation of the heat transfer fluid heating process. To do this, a thermal balance was established for the heat transfer fluid, the absorber and the glass. This allowed us to establish an equation system whose resolution was done by the finite difference method. Then, a computer program was developed to simulate the temperatures of the heat transfer fluid, the absorber tube and the glass as a function of time and space. The numerical resolution made it possible to obtain the temperatures of the heat transfer fluid, the absorber and the glass. The simulation of the fluid heating process was done in one-hour time steps, from six in the morning to six in the afternoon. The results obtained show that the temperature difference between the inlet and the outlet of the sensor is very significant. These results obtained, regarding the variation of the temperatures of the heat transfer fluid, the absorber and the glass, as well as the powers and efficiency of the parabolic trough concentrator and various factors, allow for the improvement of the performances of our prototype.
文摘The effects of the Rashba spin–orbit interaction and external electric and magnetic fields on the thermodynamic properties of parabolic quantum dots are investigated.An explicit partition function is derived,and thermodynamic quantities,including specific heat,entropy,and magnetic susceptibility,are analyzed.The behavior of Shannon entropy-related thermodynamic quantities is examined under varying magnetic fields and Hamiltonian parameters through numerical analysis.The results reveal a pronounced Schottky anomaly in the heat capacity at lower temperatures.The susceptibility exhibits a progressive enhancement and transitions to higher values with changes in the quantum dot parameters.In the presence of the Rashba spin–orbit interaction,the specific heat increases with temperature,reaches a peak,and then decreases to zero.Additionally,the susceptibility increases with theβparameter for varying Rashba spin–orbit interaction coefficients,and at a fixed temperature,it further increases with the Rashba coefficient.
基金Supported by Key Project Funding for Shaanxi Higher Education Teaching Reform Research (23BZ078)Shaanxi Provincial Education Science Planning Project (SGH24Y2782)+4 种基金Shaanxi Provincial Social Science Foundation Program(2024D008)Key Projects of the Second Huang Yanpei Vocational Education Thought Research Planning Project (ZJS2024ZN026)Shaanxi Higher Education Society Key Projects(XGHZ2301)2024 Annual Planning Project of the China Association for Non-Government Education (School Development Category)(CANFZG24095)the Youth Innovation Team of Shaanxi Universities。
文摘In this paper,a class of semilinear parabolic equations with cross coupling of power and exponential functions and large initial values are studied.By constructing and solving ordinary differential equations,the upper and lower bounds on the solution life span of the equations areobtained.
基金Supported by Shandong Provincial Natural Science Foundation(Grant Nos.ZR2021MA003 and ZR2020MA020).
文摘This paper deals with a semilinear parabolic problem involving variable coefficients and nonlinear memory boundary conditions.We give the blow-up criteria for all nonnegative nontrivial solutions,which rely on the behavior of the coefficients when time variable tends to positive infinity.Moreover,the global existence of solutions are discussed for non-positive exponents.
