Investigation of Transition Delay by Dynamic Surface Deformation

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Donald P. Rizzetta ◽  
Miguel R. Visbal
Keyword(s):  
Phase Shift ◽  
Surface Deformation ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Implicit Time ◽  
Local Dynamic ◽  
Two Dimensional ◽  
Dynamic Surface ◽  
Disturbance Growth

Numerical calculations were carried out to investigate control of transition on a flat plate by means of local dynamic surface deformation. The configuration and flow conditions are similar to a previous computation which simulated transition mitigation. Physically, the surface modification may be produced by piezoelectrically driven actuators located below a compliant aerodynamic surface, which have been employed experimentally. One actuator is located in the upstream plate region and oscillated at the most unstable frequency of 250 Hz to develop disturbances representing Tollmien–Schlichting instabilities. A controlling actuator is placed downstream and oscillated at the same frequency, but with an appropriate phase shift and modified amplitude to decrease disturbance growth and delay transition. While the downstream controlling actuator is two-dimensional (spanwise invariant), several forms of upstream disturbances were considered. These included disturbances which were strictly two-dimensional, those which were modulated in amplitude and those which had a spanwise variation of the temporal phase shift. Direct numerical simulations were obtained by solution of the three-dimensional compressible Navier–Stokes equations, utilizing a high-fidelity computational scheme and an implicit time-marching approach. A previously devised empirical process was applied for determining the optimal parameters of the controlling actuator. Results of the simulations are described, features of the flowfields elucidated, and comparisons made between solutions of the uncontrolled and controlled cases for the respective incoming disturbances. It is found that the disturbance growth is mitigated and the transition is delayed for all forms of the upstream perturbations, substantially reducing the skin friction.

Direct simulation of evolution and control of three-dimensional instabilities in attachment-line boundary layers

1995 ◽  
Vol 291 ◽  
pp. 369-392 ◽  
Author(s):  
Ronald D. Joslin
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Computationally Efficient ◽  
Simulation Results ◽  
Dimensional Simulation ◽  
Attachment Line

The spatial evolution of three-dimensional disturbances in an attachment-line boundary layer is computed by direct numerical simulation of the unsteady, incompressible Navier–Stokes equations. Disturbances are introduced into the boundary layer by harmonic sources that involve unsteady suction and blowing through the wall. Various harmonic-source generators are implemented on or near the attachment line, and the disturbance evolutions are compared. Previous two-dimensional simulation results and nonparallel theory are compared with the present results. The three-dimensional simulation results for disturbances with quasi-two-dimensional features indicate growth rates of only a few percent larger than pure two-dimensional results; however, the results are close enough to enable the use of the more computationally efficient, two-dimensional approach. However, true three-dimensional disturbances are more likely in practice and are more stable than two-dimensional disturbances. Disturbances generated off (but near) the attachment line spread both away from and toward the attachment line as they evolve. The evolution pattern is comparable to wave packets in flat-plate boundary-layer flows. Suction stabilizes the quasi-two-dimensional attachment-line instabilities, and blowing destabilizes these instabilities; these results qualitatively agree with the theory. Furthermore, suction stabilizes the disturbances that develop off the attachment line. Clearly, disturbances that are generated near the attachment line can supply energy to attachment-line instabilities, but suction can be used to stabilize these instabilities.

A Quasi-Generalized-Coordinate Approach for Numerical Simulation of Complex Flows

2006 ◽  
Vol 128 (6) ◽  
pp. 1394-1399 ◽  
Author(s):  
Donghyun You ◽  
Meng Wang ◽  
Rajat Mittal ◽  
Parviz Moin
Keyword(s):  
Coordinate System ◽  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Effective ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Curvilinear Coordinate ◽  
Generalized Coordinate

A novel structured grid approach which provides an efficient way of treating a class of complex geometries is proposed. The incompressible Navier-Stokes equations are formulated in a two-dimensional, generalized curvilinear coordinate system complemented by a third quasi-curvilinear coordinate. By keeping all two-dimensional planes defined by constant third coordinate values parallel to one another, the proposed approach significantly reduces the memory requirement in fully three-dimensional geometries, and makes the computation more cost effective. The formulation can be easily adapted to an existing flow solver based on a two-dimensional generalized coordinate system coupled with a Cartesian third direction, with only a small increase in computational cost. The feasibility and efficiency of the present method have been assessed in a simulation of flow over a tapered cylinder.

Three-dimensional impulsive vortex formation from slender orifices

2011 ◽  
Vol 666 ◽  
pp. 506-520 ◽  
Author(s):  
F. DOMENICHINI
Keyword(s):  
Stokes Equations ◽  
Intermediate Phase ◽  
Vortex Formation ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Vortex Ring Formation ◽  
Long Time ◽  
Definition Of

The vortex formation behind an orifice is a widely investigated phenomenon, which has been recently studied in several problems of biological relevance. In the case of a circular opening, several works in the literature have shown the existence of a limiting process for vortex ring formation that leads to the concept of critical formation time. In the different geometric arrangement of a planar flow, which corresponds to an opening with straight edges, it has been recently outlined that such a concept does not apply. This discrepancy opens the question about the presence of limiting conditions when apertures with irregular shape are considered. In this paper, the three-dimensional vortex formation due to the impulsively started flow through slender openings is studied with the numerical solution of the Navier–Stokes equations, at values of the Reynolds number that allow the comparison with previous two-dimensional findings. The analysis of the three-dimensional results reveals the two-dimensional nature of the early vortex formation phase. During an intermediate phase, the flow evolution appears to be driven by the local curvature of the orifice edge, and the time scale of the phenomena exhibits a surprisingly good agreement with those found in axisymmetric problems with the same curvature. The long-time evolution shows the complete development of the three-dimensional vorticity dynamics, which does not allow the definition of further unifying concepts.

Secondary instability of a temporally growing mixing layer

1987 ◽  
Vol 184 ◽  
pp. 207-243 ◽  
Author(s):  
Ralph W. Metcalfe ◽  
Steven A. Orszag ◽  
Marc E. Brachet ◽  
Suresh Menon ◽  
James J. Riley
Keyword(s):  
Growth Rates ◽  
Stokes Equations ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Mixing Layers ◽  
Navier Stokes ◽  
Small Scale ◽  
Two Dimensional ◽  
Mean Flow ◽  
Direct Numerical Integration

The three-dimensional stability of two-dimensional vortical states of planar mixing layers is studied by direct numerical integration of the Navier-Stokes equations. Small-scale instabilities are shown to exist for spanwise scales at which classical linear modes are stable. These modes grow on convective timescales, extract their energy from the mean flow and exist at moderately low Reynolds numbers. Their growth rates are comparable with the most rapidly growing inviscid instability and with the growth rates of two-dimensional subharmonic (pairing) modes. At high amplitudes, they can evolve into pairs of counter-rotating, streamwise vortices, connecting the primary spanwise vortices, which are very similar to the structures observed in laboratory experiments. The three-dimensional modes do not appear to saturate in quasi-steady states as do the purely two-dimensional fundamental and subharmonic modes in the absence of pairing. The subsequent evolution of the flow depends on the relative amplitudes of the pairing modes. Persistent pairings can inhibit three-dimensional instability and, hence, keep the flow predominantly two-dimensional. Conversely, suppression of the pairing process can drive the three-dimensional modes to more chaotic, turbulent-like states. An analysis of high-resolution simulations of fully turbulent mixing layers confirms the existence of rib-like structures and that their coherence depends strongly on the presence of the two-dimensional pairing modes.

Applying Ensemble Kalman Filter to Transonic Flows Through a Two-Dimensional Turbine Cascade

2021 ◽  
Vol 143 (12) ◽  
Author(s):  
Sasuga Ito ◽  
Masato Furukawa ◽  
Kazutoyo Yamada ◽  
Kaito Manabe
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Optimization Approach ◽  
Two Dimensional ◽  
Turbine Cascade ◽  
Eddy Simulation

Abstract Turbulence is one of the most important phenomena in fluid dynamics. Large eddy simulation (LES) generally allows us to analyze smaller eddies than when using simulations based on unsteady Reynolds-averaged Navier–Stokes equations (URANS). In addition, the numerical solutions of LES show good agreements with experiments and numerical solutions based on direct numerical simulation. URANS simulations are, however, frequently used in academia and industry because LES computations are much more expensive compared with URANS simulations. In this investigation, an optimization of unsolved coefficients of the k–ω two equations model is performed on the transonic flow around T106A low-pressure turbine cascade to improve the accuracy of turbulence prediction with URANS. For the optimization approach, two-dimensional URANS is combined with ensemble Kalman filter which is one of the data assimilation techniques. In the assimilation process, a time- and spanwise-averaged LES result is used as pseudo-experimental data. Three-dimensional URANS simulations are performed for the evaluation of the optimization effect. URANS simulations are also applied to a different turbine cascade flow for the evaluation of the robustness of the optimized coefficients. These URANS results confirmed that the optimized coefficients improve the accuracy of turbulence prediction.

Solution of three-dimensional incompressible flow problems

1977 ◽  
Vol 82 (2) ◽  
pp. 309-319 ◽  
Author(s):  
S. M. Richardson ◽  
A. R. H. Cornish
Keyword(s):  
Stream Function ◽  
Incompressible Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Flow Problems ◽  
Vector Potentials

A method for solving quite general three-dimensional incompressible flow problems, in particular those described by the Navier–Stokes equations, is presented. The essence of the method is the expression of the velocity in terms of scalar and vector potentials, which are the three-dimensional generalizations of the two-dimensional stream function, and which ensure that the equation of continuity is satisfied automatically. Although the method is not new, a correct but simple and unambiguous procedure for using it has not been presented before.

scholarly journals Turbulent 2.5-dimensional dynamos

2016 ◽  
Vol 799 ◽  
pp. 246-264 ◽  
Author(s):  
K. Seshasayanan ◽  
A. Alexakis
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Two Dimensional Flow

We study the linear stage of the dynamo instability of a turbulent two-dimensional flow with three components $(u(x,y,t),v(x,y,t),w(x,y,t))$ that is sometimes referred to as a 2.5-dimensional (2.5-D) flow. The flow evolves based on the two-dimensional Navier–Stokes equations in the presence of a large-scale drag force that leads to the steady state of a turbulent inverse cascade. These flows provide an approximation to very fast rotating flows often observed in nature. The low dimensionality of the system allows for the realization of a large number of numerical simulations and thus the investigation of a wide range of fluid Reynolds numbers $Re$, magnetic Reynolds numbers $Rm$ and forcing length scales. This allows for the examination of dynamo properties at different limits that cannot be achieved with three-dimensional simulations. We examine dynamos for both large and small magnetic Prandtl-number turbulent flows $Pm=Rm/Re$, close to and away from the dynamo onset, as well as dynamos in the presence of scale separation. In particular, we determine the properties of the dynamo onset as a function of $Re$ and the asymptotic behaviour in the large $Rm$ limit. We are thus able to give a complete description of the dynamo properties of these turbulent 2.5-D flows.

scholarly journals Three-Dimensional Separations in Axial Compressors

2004 ◽  
Author(s):  
Semiu A. Gbadebo ◽  
Nicholas A. Cumpsty ◽  
Tom P. Hynes
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Tip Clearance ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Compressor Blades ◽  
Navier Stokes Equations ◽  
Linear Cascade ◽  
Axial Compressors ◽  
Limiting Streamlines

Flow separations in the corner regions of blade passages are common. The separations are three dimensional and have quite different properties from the two-dimensional separations that are considered in elementary courses of fluid mechanics. In particular the consequences for the flow may be less severe than the two-dimensional separation. This paper describes the nature of three-dimensional separation and addresses the way in which topological rules, based on a linear treatment of the Navier-Stokes equations, can predict properties of the limiting streamlines, including the singularities which form. The paper shows measurements of the flow field in a linear cascade of compressor blades and compares these with the results of 3D CFD. For corners without tip clearance, the presence of three-dimensional separation appears to be universal and the challenge for the designer is to limit the loss and blockage produced. The CFD appears capable of predicting this.

High Fidelity Simulation of Safety Relief Valve Internal Flows

2015 ◽  
Author(s):  
Yunchao Yang ◽  
Alexis Lefebvre ◽  
Ge-Cheng Zha ◽  
Qing-Feng Liu ◽  
Jun Fan ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Complex Geometry ◽  
Three Dimensional ◽  
Weno Scheme ◽  
Inlet Pressure ◽  
Navier Stokes ◽  
Implicit Time ◽  
Complex Flow ◽  
Relief Valve ◽  
Expansion Waves

This paper presents a numerical methodology and simulation for three-dimensional transonic flow in Safety Relief Valves. Simulation of safety relief valve flows is very challenging due to complex flow paths, high pressure variation, supersonic flow with shock and expansion waves, boundary layers, etc. The 3D unsteady Reynolds averaged Navier-Stokes (URANS) equations with one-equation Spalart-Allmaras turbulence model is used. A fifth order WENO scheme for the inviscid flux and a second order central differencing for the viscous terms are employed to discretize the Navier-Stokes equations. The low diffusion E-CUSP scheme used as the approximate Riemann solver suggested by Zha et al. is utilized with the WENO scheme to evaluate the inviscid fluxes. Implicit time marching method with 2nd order temporal accuracy using Gauss-Seidel line relaxation is employed to achieve a fast convergence rate. Parallel computing is implemented to save wall clock simulation time. The valve flows with air under different inlet pressures and temperatures are successfully simulated for the full geometry with all the fine leakage channels. A 3D mesh topology is generated for the complex geometry. Detailed simulations of air flow are accomplished with inlet gauge pressure 0.5MPa and 2.1MPa. The simulated air mass flow rate agrees excellently with the experimental results with an error of 0.26% for the inlet pressure of 0.5Mpa, and an error of 2.5% for the inlet pressure of 2.1MPa. The shock waves and expansion waves downstream of the orifice are very well resolved.

Pseudo Compressible Mixed Interpolation Finite Element Method for Solving Three Dimensional Navier-Stokes Equations

2013 ◽  
Author(s):  
Shrinivas G. Apte ◽  
Brian H. Dennis
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Compressibility Factor ◽  
Navier Stokes ◽  
Implicit Time ◽  
Navier Stokes Equations ◽  
Linear Solver ◽  
Element Method

A pseudo compressible finite element method for solving three dimensional incompressible Navier-Stokes equations is presented. A physical problem discretized using tetrahedral elements with linear and quadratic interpolation functions for pressure and velocity variables respectively is then marched in time by using implicit time marching scheme based on finite differencing. The possible formation of indefinite matrix due to incompressibility constraint is avoided by inserting an artificial/pseudo time dependent term (Chorin, 1974) into the continuity equation that is eliminated when steady state is reached. This definite matrix system can then be solved using standard pre-conditioners and iterative solvers. Solutions for pressure driven flows obtained using this method are validated with the ones obtained from a standard problem of flow over a cylinder and also with numerical benchmark case of a 3-D laminar flow around an obstacle. An object oriented C++ program was developed which uses exact integrals of shape functions in its calculations rather than numerical integrations. This program was tested with different values of artificial compressibility factor (β), Reynolds numbers (Re) and grid sizes (number of Elements) and time steps (dt). The effect of these parameters on the the number of linear solver iterations required for convergence is studied efficiently using the non-dimensional numbers Pseudo Compressibility Number (PCN) and Elemental Reynolds Number (ERe). Although the relationship between the linear solver performance and these two non dimensional numbers remain complicated, it is found that there exists an optimum range of PCN as a function of ERe for which the solution convergence can be obtained with the minimum number of iterations.

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