Large Scale Topology Optimization of 3D Static Mixers

2020 ◽  
Author(s):  
Sicheng Sun ◽  
Jaal Ghandhi ◽  
Xiaoping Qian
Keyword(s):  
Topology Optimization ◽  
Pressure Drop ◽  
Cross Section ◽  
Large Scale ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Straight Channel ◽  
Navier Stokes Equation ◽  
Static Mixers ◽  
Static Fluid

Abstract Topology optimization (TO) was conducted for three dimensional static fluid mixers. The problem is optimized using the weakly coupled Navier-Stokes equation at low Reynolds number (Re ≤ 1) and a convection-diffusion equation. The domain was discretized with up to 10 million cells. The optimizations were run with 1024 to 2048 CPUs on a national supercomputer. For a mixer in a square cross-section channel, the mixing was improved by 83% for a modest 2.5 times higher pressure drop compared with the open straight channel. For a cylindrical cross-section tee arrangement, the mixing improved by 91% with a 2.5 times higher pressure drop compared to the straight channel.

scholarly journals Flux correlations in supersonic isothermal turbulence

2012 ◽  
Vol 713 ◽  
pp. 482-490 ◽  
Author(s):  
R. Wagner ◽  
G. Falkovich ◽  
A. G. Kritsuk ◽  
M. L. Norman
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Compressible Turbulence ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Barotropic Fluids ◽  
Gravity Driven ◽  
Dimensional Simulation ◽  
Using Data ◽  
Astrophysical Flows

AbstractUsing data from a large-scale three-dimensional simulation of supersonic isothermal turbulence, we have tested the validity of an exact flux relation derived analytically from the Navier–Stokes equation by Falkovich, Fouxon & Oz (J. Fluid Mech., vol. 644, 2010, p. 465). That relation, for compressible barotropic fluids, was derived assuming turbulence generated by a large-scale force. However, compressible turbulence in simulations is usually initialized and maintained by a large-scale acceleration, as in gravity-driven astrophysical flows. We present a new approximate flux relation for isothermal turbulence driven by a large-scale acceleration, and find it in reasonable agreement with the simulation results.

Approximate Calculation of Pressure Drop in Laminar Flow of Generalized Newtonian Liquid Through Channel of Noncircular Cross Section

1994 ◽  
Vol 59 (3) ◽  
pp. 603-615 ◽  
Author(s):  
Václav Dolejš ◽  
Ivan Machač ◽  
Petr Doleček
Keyword(s):  
Pressure Drop ◽  
Laminar Flow ◽  
Numerical Solution ◽  
Cross Section ◽  
Approximate Calculation ◽  
Newtonian Liquid ◽  
Straight Channel ◽  
Suggested Procedure ◽  
Noncircular Cross Section ◽  
Calculation Results

The paper presents a modification of the equations of Rabinowitsch-Mooney type for an approximate calculation of pressure drop in laminar flow of generalized Newtonian liquid through a straight channel whose cross section forms a simple continuous area. The suitability of the suggested procedure of calculation of pressure drop is demonstrated by the comparison of calculation results with both the published and original results of numerical solution and experiments.

Unsteady Three-Dimensional Analysis of Inlet Distortion in a Transonic Fan

2006 ◽  
Author(s):  
Peng Sun ◽  
Guotal Feng
Keyword(s):  
Shock Wave ◽  
Total Pressure ◽  
Large Scale ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Inlet Distortion ◽  
Flow Loss ◽  
Large Scale Vortex ◽  
Total Temperature ◽  
Transonic Fan

A time-accurate three-dimensional Navier-Stokes solver of the unsteady flow field in a transonic fan was carried out using "Fluent-parallel" in a parallel supercomputer. The numerical simulation focused on a transonic fan with inlet square wave total pressure distortion and the analysis of result consisted of three aspects. The first was about inlet parameters redistribution and outlet total temperature distortion induced by inlet total pressure distortion. The pattern and causation of flow loss caused by pressure distortion in rotor were analyzed secondly. It was found that the influence of distortion was different at different radial positions. In hub area, transportation-loss and mixing-loss were the main loss patterns. Distortion not only complicated them but enhanced them. Especially in stator, inlet total pressure distortion induced large-scale vortex, which produced backflow and increased the loss. While in casing area, distortion changed the format of shock wave and increased the shock loss. Finally, the format of shock wave and the hysteresis of rotor to distortion were analyzed in detail.

A 3D Unsteady Flow Analysis in a Doubly Constricted Tube

2000 ◽  
Author(s):  
B. V. Rathish Kumar ◽  
T. Yamaguchi ◽  
H. Liu ◽  
R. Himeno
Keyword(s):  
Pressure Drop ◽  
Unsteady Flow ◽  
Stokes Equations ◽  
Vortex Formation ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
In Series ◽  
3D Unsteady Flow

Abstract Unsteady flow dynamics in a doubly constricted vessel is analyzed by using a time accurate Finite Volume solution of three dimensional incompressible Navier-Stokes equations. Computational experiments are carried out for various values of Reynolds number in order to assess the criticality of multiple mild constrictions in series and also to bring out the subtle 3D features like vortex formation. Studies reveal that pressure drop across a series of mild constrictions can get physiologically critical. Further this pressure drop is found to be sensitive to the spacing between the constrictions and also to the oscillatory nature of the inflow profile.

Coriolis force influence on the AKA effect

2021 ◽  
Author(s):  
Peter Rutkevich ◽  
Georgy Golitsyn ◽  
Anatoly Tur
Keyword(s):  
Steady State ◽  
Stokes Equation ◽  
Nonlinear Equations ◽  
Coriolis Force ◽  
Large Scale ◽  
Fluid Velocity ◽  
Navier Stokes ◽  
Basic Solution ◽  
Navier Stokes Equation ◽  
Alpha Effect

<p>Large-scale instability in incompressible fluid driven by the so called Anisotropic Kinetic Alpha (AKA) effect satisfying the incompressible Navier-Stokes equation with Coriolis force is considered. The external force is periodic; this allows applying an unusual for turbulence calculations mathematical method developed by Frisch et al [1]. The method provides the orders for nonlinear equations and obtaining large scale equations from the corresponding secular relations that appear at different orders of expansions. This method allows obtaining not only corrections to the basic solutions of the linear problem but also provides the large-scale solution of the nonlinear equations with the amplitude exceeding that of the basic solution. The fluid velocity is obtained by numerical integration of the large-scale equations. The solution without the Coriolis force leads to constant velocities at the steady-state, which agrees with the full solution of the Navier-Stokes equation reported previously. The time-invariant solution contains three families of solutions, however, only one of these families contains stable solutions. The final values of the steady-state fluid velocity are determined by the initial conditions. After account of the Coriolis force the solutions become periodic in time and the family of solutions collapses to a unique solution. On the other hand, even with the Coriolis force the fluid motion remains two-dimensional in space and depends on a single spatial variable. The latter fact limits the scope of the AKA method to applications with pronounced 2D nature. In application to 3D models the method must be used with caution.</p><p>[1] U. Frisch, Z.S. She and P. L. Sulem, “Large-Scale Flow Driven by the Anisotropic Kinetic Alpha Effect,” Physica D, Vol. 28, No. 3, 1987, pp. 382-392.</p>

Cylinder rolling on a wall at low Reynolds numbers

2011 ◽  
Vol 685 ◽  
pp. 461-494 ◽  
Author(s):  
Alain Merlen ◽  
Christophe Frankiewicz
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Flow Around A Cylinder ◽  
Low Reynolds Numbers ◽  
Initial Location ◽  
Upstream Pressure ◽  
Small Reynolds Numbers ◽  
Onset Of Cavitation

AbstractThe flow around a cylinder rolling or sliding on a wall was investigated analytically and numerically for small Reynolds numbers, where the flow is known to be two-dimensional and steady. Both prograde and retrograde rotation were analytically solved, in the Stokes regime, giving the values of forces and torque and a complete description of the flow. However, solving Navier–Stokes equation, a rotation of the cylinder near the wall necessarily induces a cavitation bubble in the nip if the fluid is a liquid, or compressible effects, if it is a gas. Therefore, an infinite lift force is generated, disconnecting the cylinder from the wall. The flow inside this interstice was then solved under the lubrication assumptions and fully described for a completely flooded interstice. Numerical results extend the analysis to higher Reynolds number. Finally, the effect of the upstream pressure on the onset of cavitation is studied, giving the initial location of the phenomenon and the relation between the upstream pressure and the flow rate in the interstice. It is shown that the flow in the interstice must become three-dimensional when cavitation takes place.

Flow Characteristics in a Three-Dimensional Rectangular Channel With a Pair of Ribs Placed Symmetrically at the Channel Walls

2000 ◽  
Author(s):  
M. Singh ◽  
P. K. Panigrahi ◽  
G. Biswas
Keyword(s):  
Heat Transfer ◽  
Large Scale ◽  
Numerical Study ◽  
Rectangular Channel ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Navier Stokes ◽  
Complex Flow ◽  
Energy Equations

Abstract A numerical study of rib augmented cooling of turbine blades is reported in this paper. The time-dependent velocity field around a pair of symmetrically placed ribs on the walls of a three-dimensional rectangular channel was studied by use of a modified version of Marker-And-Cell algorithm to solve the unsteady incompressible Navier-Stokes and energy equations. The flow structures are presented with the help of instantaneous velocity vector and vorticity fields, FFT and time averaged and rms values of components of velocity. The spanwise averaged Nusselt number is found to increase at the locations of reattachment. The numerical results are compared with available numerical and experimental results. The presence of ribs leads to complex flow fields with regions of flow separation before and after the ribs. Each interruption in the flow field due to the surface mounted rib enables the velocity distribution to be more homogeneous and a new boundary layer starts developing downstream of the rib. The heat transfer is primarily enhanced due to the decrease in the thermal resistance owing to the thinner boundary layers on the interrupted surfaces. Another reason for heat transfer enhancement can be attributed to the mixing induced by large-scale structures present downstream of the separation point.

Large Scale Topology Optimization of 3D Static Mixers

2021 ◽  
Author(s):  
Sicheng Sun ◽  
Jaal Ghandhi ◽  
Xiaoping Qian
Keyword(s):  
Topology Optimization ◽  
Large Scale ◽  
Static Mixers

Large-scale three-dimensional anisotropic topology optimization of variable-axial lightweight composite structures

2021 ◽  
pp. 1-15
Author(s):  
Yuqing Zhou ◽  
Tsuyoshi Nomura ◽  
Enpei Zhao ◽  
Kazuhiro Saitou
Keyword(s):  
Topology Optimization ◽  
Composite Structures ◽  
Large Scale ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Optimization Method ◽  
Optimized Design ◽  
Adaptive Meshing ◽  
Design Synthesis ◽  
Fiber Placement

Abstract Variable-axial fiber-reinforced composites allow for local customization of fiber orientation and thicknesses. Despite their significant potential for performance improvement over the conventional multiaxial composites and metals, they pose challenges in design optimization due to the vastly increased design freedom in material orientations. This paper presents an anisotropic topology optimization method for designing large-scale, 3D variable-axial lightweight composite structures subject to multiple load cases. The computational challenges associated with large-scale 3D anisotropic topology optimization with extremely low volume fraction are addressed by a tensor-based representation of 3D orientation that would avoid the 2π periodicity of angular representations such as Euler angles, and an adaptive meshing scheme, which, in conjunction with PDE regularization of the density variables, refines the mesh where structural members appear and coarsens where there is void. The proposed method is applied to designing a heavy-duty drone frame subject to complex multi-loading conditions. Finally, the manufacturability gaps between the optimized design and the fabrication-ready design for Tailored Fiber Placement (TFP) is discussed, which motivates future work toward a fully-automated design synthesis.

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