![Sample our Engineering & Technology journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5933/TOC-Subject-Sample-2021-Engineering-Tech.jpg"})
ABSTRACT
The step size used in the computational fluid dynamics (CFD)-based adjoint method has a significant effect on computing time. The constant step size usually used is obtained through a time-consuming trial-and-error process. This study used an adaptive step size for adjusting the design parameters in the CFD-based adjoint method. To validate the performance of the CFD-based adjoint method with the adaptive step size, this investigation evaluated three different inverse design cases with mixed convection flow. Our results confirmed that the adaptive step size is computationally efficient and can be used for the inverse design of an indoor environment.
Nomenclature
| A | = | source item in the adjoint momentum equations |
| B | = | source item in the adjoint energy equation |
| D (V) | = | rate of strain tensor |
| g | = | gravity vector |
| J | = | objective function |
| Jk − 1, Jk, Jk + 1 | = | objective function at previous, current, and succeeding design cycles, respectively |
| K | = | Lipschitz constant |
| L | = | augmented objective function |
| N | = | incompressible Navier–Stokes equations in vector form |
| N1 | = | continuity equation |
| N2, N3, N4 | = | momentum equations |
| N5 | = | energy equation |
| p | = | air pressure |
| Pa | = | adjoint pressure |
| T | = | air temperature |
| T0 | = | desired air temperature on a design domain |
| Ta | = | adjoint temperature |
| Tf | = | floor temperature |
| Tinlet | = | inlet air temperature |
| Tmax, Tmin | = | maximum and minimum temperatures of the experimental boundary condition, respectively |
| Top | = | operating air temperature |
| Tr | = | roof temperature |
| Tw | = | wall temperature |
| V | = | air velocity |
| V0 | = | desired air velocity on a design domain |
| Va | = | adjoint velocity |
| Vinlet | = | inlet air velocity |
| Vx, inlet, Vy, inlet, Vz, inlet | = | inlet air velocities in the x, y, and z directions, respectively |
| α, β | = | weighting factors |
| γ | = | air thermal expansion coefficient |
| δ | = | small constant set by the designer |
| Θ | = | design domain |
| κ | = | effective thermal conductivity |
| λ | = | step size |
| λk | = | step size in the kth design cycle |
| Λ | = | local Lipschitz constant |
| Λk | = | local Lipschitz constant in the kth design cycle |
| ν | = | effective viscosity |
| ξ | = | design parameters |
| ξk−1, ξk, ξk+1 | = | design parameters at the previous, current, and succeeding design cycles, respectively |
| Subscripts | = | |
| 0 | = | design domain |
| 1 | = | continuity equation |
| 2, 3, 4 | = | momentum equations |
| 5 | = | energy equation |
| a | = | adjoint method |
| fl | = | floor |
| inlet | = | inlet boundary condition |
| k − 1, k, k + 1 | = | previous, current, and succeeding design cycles, respectively |
| max | = | maximum |
| min | = | minimum |
| op | = | operate |
| r | = | roof |
| w | = | wall |
| x, inlet | = | x direction of the inlet boundary condition |
| y, inlet | = | y direction of the inlet boundary condition |
| z, inlet | = | z direction of the inlet boundary condition |
Nomenclature
| A | = | source item in the adjoint momentum equations |
| B | = | source item in the adjoint energy equation |
| D (V) | = | rate of strain tensor |
| g | = | gravity vector |
| J | = | objective function |
| Jk − 1, Jk, Jk + 1 | = | objective function at previous, current, and succeeding design cycles, respectively |
| K | = | Lipschitz constant |
| L | = | augmented objective function |
| N | = | incompressible Navier–Stokes equations in vector form |
| N1 | = | continuity equation |
| N2, N3, N4 | = | momentum equations |
| N5 | = | energy equation |
| p | = | air pressure |
| Pa | = | adjoint pressure |
| T | = | air temperature |
| T0 | = | desired air temperature on a design domain |
| Ta | = | adjoint temperature |
| Tf | = | floor temperature |
| Tinlet | = | inlet air temperature |
| Tmax, Tmin | = | maximum and minimum temperatures of the experimental boundary condition, respectively |
| Top | = | operating air temperature |
| Tr | = | roof temperature |
| Tw | = | wall temperature |
| V | = | air velocity |
| V0 | = | desired air velocity on a design domain |
| Va | = | adjoint velocity |
| Vinlet | = | inlet air velocity |
| Vx, inlet, Vy, inlet, Vz, inlet | = | inlet air velocities in the x, y, and z directions, respectively |
| α, β | = | weighting factors |
| γ | = | air thermal expansion coefficient |
| δ | = | small constant set by the designer |
| Θ | = | design domain |
| κ | = | effective thermal conductivity |
| λ | = | step size |
| λk | = | step size in the kth design cycle |
| Λ | = | local Lipschitz constant |
| Λk | = | local Lipschitz constant in the kth design cycle |
| ν | = | effective viscosity |
| ξ | = | design parameters |
| ξk−1, ξk, ξk+1 | = | design parameters at the previous, current, and succeeding design cycles, respectively |
| Subscripts | = | |
| 0 | = | design domain |
| 1 | = | continuity equation |
| 2, 3, 4 | = | momentum equations |
| 5 | = | energy equation |
| a | = | adjoint method |
| fl | = | floor |
| inlet | = | inlet boundary condition |
| k − 1, k, k + 1 | = | previous, current, and succeeding design cycles, respectively |
| max | = | maximum |
| min | = | minimum |
| op | = | operate |
| r | = | roof |
| w | = | wall |
| x, inlet | = | x direction of the inlet boundary condition |
| y, inlet | = | y direction of the inlet boundary condition |
| z, inlet | = | z direction of the inlet boundary condition |