A mathematical analysis for constructal design of tree flow networks under unsteady flow

2020 ◽  
Vol 476 (2240) ◽  
pp. 20200377
Author(s):  
Bharat Soni ◽  
Antonio F. Miguel ◽  
Ameeya Kumar Nayak
Keyword(s):  
Optimal Design ◽  
Unsteady Flow ◽  
Mathematical Analysis ◽  
Analytical Approach ◽  
Unsteady Flows ◽  
Flow Networks ◽  
Constructal Design ◽  
Flow Impedance ◽  
Minimization Procedure ◽  
Steady And Unsteady Flows

Tree flow networks play an important role in both natural and man-made systems. In an effort to develop a deeper understanding of the optimal design of these networks, we have developed a simple analytical approach to deal with steady and unsteady flows. As a result, optimal relations for the homothetic ratio of tube sizes and optimal angles between daughter tubes are obtained. The obtained optimum homothetic ratios satisfy the criterion of the minimization procedure of flow impedance based on geometry and the svelteness ratio. The robustness, accuracy and convergence of model are also proved mathematically in order to validate the results.

On nonlocal fractal laminar steady and unsteady flows

2021 ◽  
Vol 232 (4) ◽  
pp. 1413-1424
Author(s):  
Rami Ahmad El-Nabulsi
Keyword(s):  
Unsteady Flows ◽  
Steady And Unsteady Flows

Grid adaptation for unsteady flow computations

1997 ◽  
Vol 211 (4) ◽  
pp. 237-250 ◽  
Author(s):  
C B Allen
Keyword(s):  
Unsteady Flow ◽  
Unsteady Flows ◽  
Processing Unit ◽  
Flow Solver ◽  
Transfinite Interpolation ◽  
Central Processing ◽  
Grid Adaptation ◽  
Euler Flows ◽  
Adaptation Procedure ◽  
Grid Points

A grid adaptation procedure suitable for use during unsteady flow computations is described. Transfinite interpolation is used to generate structured grids for the computation of steady and unsteady Euler flows past aerofoils. This technique is well suited to unsteady flows, since instantaneous grid positions and speeds required by the flow solver are available directly from the algebraic mapping. A different approach to grid adaptation is described, wherein adaptation is performed by redistributing the interpolation parameters, instead of the physical grid positions. This results in the adapted grid positions, and hence speeds, still being available algebraically. Grid adaptation during an unsteady computation is performed continuously by imposing an ‘adaptation velocity’ on grid points, thereby applying the adaptation over several time steps and avoiding the interpolation of the solution from one grid to another, which is associated with instantaneous adaptation. For both steady and unsteady flows the adapted grid technique is shown to produce sharper shock resolution for a very small increase in CPU (central processing unit) requirements.

scholarly journals Optimal design of diamond-air microcavities for quantum networks using an analytical approach

2018 ◽  
Vol 20 (11) ◽  
pp. 115004 ◽  
Author(s):  
Suzanne B van Dam ◽  
Maximilian Ruf ◽  
Ronald Hanson
Keyword(s):  
Optimal Design ◽  
Analytical Approach ◽  
Quantum Networks

Predicting Bladerow Interactions Using a Multistage Time-Linearized Navier-Stokes Solver

2003 ◽  
Vol 125 (1) ◽  
pp. 25-32 ◽  
Author(s):  
W. Ning ◽  
Y. S. Li ◽  
R. G. Wells
Keyword(s):  
Unsteady Flow ◽  
Frequency Domain ◽  
Test Data ◽  
Computational Efficiency ◽  
Unsteady Flows ◽  
Navier Stokes ◽  
Test Cases ◽  
Numerical Accuracy ◽  
Flow Solver ◽  
Time Marching

A multistage frequency domain (time-linearized/nonlinear harmonic) Navier-Stokes unsteady flow solver has been developed for predicting unsteady flows induced by bladerow interactions. In this paper, the time-linearized option of the solver has been used to analyze unsteady flows in a subsonic turbine test stage and the DLR transonic counter-rotating shrouded propfan. The numerical accuracy and computational efficiency of the time-linearized viscous methods have been demonstrated by comparing predictions with test data and nonlinear time-marching solutions for these two test cases. It is concluded that the development of efficient frequency domain approaches enables unsteady flow predictions to be used in the design cycles to tackle aeromechanics problems.

Numerical Investigation of Sub-Iteration Criterions for Unsteady Flow Computations with Dual-Time Method

2013 ◽  
Vol 432 ◽  
pp. 189-195
Author(s):  
Guang Ning Li ◽  
Min Xu
Keyword(s):  
Unsteady Flow ◽  
Unsteady Flows ◽  
Numerical Results ◽  
Iteration Step ◽  
Convergence Criterion ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Physical Time ◽  
New Criterion

The convergence of sub-iteration with the dual-time method is very important for the prediction of unsteady flow field. The influence of sub-iteration step number, criterion of sub-iteration convergence and the choice of physical time step size on the calculation results are discussed by solving of the two-dimensional unsteady Euler equations. A new convergence criterion (named residual criterion) of sub-iteration for unsteady flows is proposed, and the unsteady flow test case AGARD-CT5 is calculated to verify the new criterion. The results show that, with the same criterion of sub-iteration, the results from different physical time step sizes are in agreement with each other. The difference between the experiment data and the numerical results are small, and if the sub-iteration criterion used is reasonable and small enough, the dependence of numerical results of unsteady flows on the physical time step will be decreased as possible. The new criterion of sub-iteration for dual-time step unsteady calculations can be used for engineering problem.

Predicting Bladerow Interactions Using a Multistage Time-Linearized Navier-Stokes Solver

2002 ◽  
Author(s):  
W. Ning ◽  
Y. S. Li ◽  
R. G. Wells
Keyword(s):  
Unsteady Flow ◽  
Frequency Domain ◽  
Test Data ◽  
Computational Efficiency ◽  
Unsteady Flows ◽  
Navier Stokes ◽  
Test Cases ◽  
Numerical Accuracy ◽  
Flow Solver ◽  
Time Marching

A multistage frequency domain (time-linearized/nonlinear harmonic) Navier-Stokes unsteady flow solver has been developed for predicting unsteady flows induced by bladerow interactions. In this paper, the time-linearized option of the solver has been used to analyze unsteady flows in a subsonic turbine test stage and the DLR transonic counter-rotating shrouded propfan. The numerical accuracy and computational efficiency of the time-linearized viscous methods have been demonstrated by comparing predictions with test data and nonlinear time-marching solutions for these two test cases. It is concluded that the development of efficient frequency domain approaches enables unsteady flow predictions to be used in the design cycles to tackle aeromechanics problems.

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