Heat-transfer coefficients(HTC)on surfaces exposed to convection environments are often measured by transient techniques such as thermochromic liquid crystal(TLC)or infrared thermography.In these techniques,the surfac...Heat-transfer coefficients(HTC)on surfaces exposed to convection environments are often measured by transient techniques such as thermochromic liquid crystal(TLC)or infrared thermography.In these techniques,the surface temperature is measured as a function of time,and that measurement is used with the exact solution for unsteady,zero-dimensional(0-D)or one-dimensional(1-D)heat conduction into a solid to calculate the local HTC.When using the 0-D or 1-D exact solutions,the transient techniques assume the HTC and the free-stream or bulk temperature characterizing the convection environment to be constants in addition to assuming the conduction into the solid to be 0-D or 1-D.In this study,computational fluid dynamics(CFD)conjugate analyses were performed to examine the errors that might be invoked by these assumptions for a problem,where the free-stream/bulk temperature and the heat-transfer coefficient vary appreciably along the surface and where conduction into the solid may not be 0-D or 1-D.The problem selected to assess these errors is flow and heat transfer in a channel lined with a staggered array of pin fins.This conjugate study uses three-dimensional(3-D)unsteady Reynolds-averaged Navier-Stokes(RANS)closed by the shear-stress transport(SST)turbulence model for the gas phase(wall functions not used)and the Fourier law for the solid phase.The errors in the transient techniques are assessed by comparing the HTC predicted by the time-accurate conjugate CFD with those predicted by the 0-D and 1-D exact solutions,where the surface temperatures needed by the exact solutions are taken from the time-accurate conjugate CFD solution.Results obtained show that the use of the 1-D exact solution for the semi-infinite wall to give reasonably accurate“transient”HTC(less than 5%〇relative error).Transient techniques that use the 0-D exact solution for the pin fins were found to produce large errors(up to 160%relative error)because the HTC varies appreciably about each pin fin.This study also showed that HTC measured by transient techniques could differ considerably from the HTC obtained under steady-state conditions with isothermal walls.展开更多
In this paper,a new sharp-interface approach to simulate compressible multiphase flows is proposed.The new scheme consists of a high order WENO finite volume scheme for solving the Euler equations coupled with a high ...In this paper,a new sharp-interface approach to simulate compressible multiphase flows is proposed.The new scheme consists of a high order WENO finite volume scheme for solving the Euler equations coupled with a high order pathconservative discontinuous Galerkin finite element scheme to evolve an indicator function that tracks the material interface.At the interface our method applies ghost cells to compute the numerical flux,as the ghost fluid method.However,unlike the original ghost fluid scheme of Fedkiw et al.[15],the state of the ghost fluid is derived from an approximate-state Riemann solver,similar to the approach proposed in[25],but based on a much simpler formulation.Our formulation leads only to one single scalar nonlinear algebraic equation that has to be solved at the interface,instead of the system used in[25].Away from the interface,we use the new general Osher-type flux recently proposed by Dumbser and Toro[13],which is a simple but complete Riemann solver,applicable to general hyperbolic conservation laws.The time integration is performed using a fully-discrete one-step scheme,based on the approaches recently proposed in[5,7].This allows us to evolve the system also with time-accurate local time stepping.Due to the sub-cell resolution and the subsequent more restrictive time-step constraint of the DG scheme,a local evolution for the indicator function is applied,which is matched with the finite volume scheme for the solution of the Euler equations that runs with a larger time step.The use of a locally optimal time step avoids the introduction of excessive numerical diffusion in the finite volume scheme.Two different fluids have been used,namely an ideal gas and a weakly compressible fluid modeled by the Tait equation.Several tests have been computed to assess the accuracy and the performance of the new high order scheme.A verification of our algorithm has been carefully carried out using exact solutions as well as a comparison with other numerical reference solutions.The material interface is resolved sharply and accurately without spurious oscillations in the pressure field.展开更多
基金This research was supported by the National Energy Technology Laboratory of the US Department of Energy with Robin Ames and Richard Dennis as the technical monitors.The authors are grateful for this support.
文摘Heat-transfer coefficients(HTC)on surfaces exposed to convection environments are often measured by transient techniques such as thermochromic liquid crystal(TLC)or infrared thermography.In these techniques,the surface temperature is measured as a function of time,and that measurement is used with the exact solution for unsteady,zero-dimensional(0-D)or one-dimensional(1-D)heat conduction into a solid to calculate the local HTC.When using the 0-D or 1-D exact solutions,the transient techniques assume the HTC and the free-stream or bulk temperature characterizing the convection environment to be constants in addition to assuming the conduction into the solid to be 0-D or 1-D.In this study,computational fluid dynamics(CFD)conjugate analyses were performed to examine the errors that might be invoked by these assumptions for a problem,where the free-stream/bulk temperature and the heat-transfer coefficient vary appreciably along the surface and where conduction into the solid may not be 0-D or 1-D.The problem selected to assess these errors is flow and heat transfer in a channel lined with a staggered array of pin fins.This conjugate study uses three-dimensional(3-D)unsteady Reynolds-averaged Navier-Stokes(RANS)closed by the shear-stress transport(SST)turbulence model for the gas phase(wall functions not used)and the Fourier law for the solid phase.The errors in the transient techniques are assessed by comparing the HTC predicted by the time-accurate conjugate CFD with those predicted by the 0-D and 1-D exact solutions,where the surface temperatures needed by the exact solutions are taken from the time-accurate conjugate CFD solution.Results obtained show that the use of the 1-D exact solution for the semi-infinite wall to give reasonably accurate“transient”HTC(less than 5%〇relative error).Transient techniques that use the 0-D exact solution for the pin fins were found to produce large errors(up to 160%relative error)because the HTC varies appreciably about each pin fin.This study also showed that HTC measured by transient techniques could differ considerably from the HTC obtained under steady-state conditions with isothermal walls.
文摘In this paper,a new sharp-interface approach to simulate compressible multiphase flows is proposed.The new scheme consists of a high order WENO finite volume scheme for solving the Euler equations coupled with a high order pathconservative discontinuous Galerkin finite element scheme to evolve an indicator function that tracks the material interface.At the interface our method applies ghost cells to compute the numerical flux,as the ghost fluid method.However,unlike the original ghost fluid scheme of Fedkiw et al.[15],the state of the ghost fluid is derived from an approximate-state Riemann solver,similar to the approach proposed in[25],but based on a much simpler formulation.Our formulation leads only to one single scalar nonlinear algebraic equation that has to be solved at the interface,instead of the system used in[25].Away from the interface,we use the new general Osher-type flux recently proposed by Dumbser and Toro[13],which is a simple but complete Riemann solver,applicable to general hyperbolic conservation laws.The time integration is performed using a fully-discrete one-step scheme,based on the approaches recently proposed in[5,7].This allows us to evolve the system also with time-accurate local time stepping.Due to the sub-cell resolution and the subsequent more restrictive time-step constraint of the DG scheme,a local evolution for the indicator function is applied,which is matched with the finite volume scheme for the solution of the Euler equations that runs with a larger time step.The use of a locally optimal time step avoids the introduction of excessive numerical diffusion in the finite volume scheme.Two different fluids have been used,namely an ideal gas and a weakly compressible fluid modeled by the Tait equation.Several tests have been computed to assess the accuracy and the performance of the new high order scheme.A verification of our algorithm has been carefully carried out using exact solutions as well as a comparison with other numerical reference solutions.The material interface is resolved sharply and accurately without spurious oscillations in the pressure field.
