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Author: Publisher: ISBN: Category : Languages : en Pages : 380
Book Description
This thesis is focused on direct numerical simulation (DNS) of compressible and incompressible fully developed and developing turbulent flows between isothermal walls using a discontinuous Galerkin method (DGM). Three cases (Ma = 0.2, 0.7 and 1.5) of DNS of turbulent channel flows between isothermal walls with Re ~ 2800, based on bulk velocity and half channel width, have been carried out. It is found that a power law seems to scale mean streamwise velocity with Ma slightly better than the more usual log-law. Inner and outer scaling of second-order and higher-order statistics have been analyzed. The linkage between the pressure gradient and vorticity flux on the wall has been theoretically derived and confirmed and they are highly correlated very close to the wall. The correlation coefficients are influenced by Ma, and viscosity when Ma is high. The near-wall spanwise streak spacing increases with Ma. Isosurfaces of the second invariant of the velocity gradient tensor are more sparsely distributed and elongated as Ma increases. DNS of turbulent isothermal-wall bounded flow subjected to favourable and adverse pressure gradient (FPG, APG) at Ma ~ 0.2 and Reref ~ 428000, based on the inlet bulk velocity and the streamwise length of the bottom wall, is also investigated. The FPG/APG is obtained by imposing a concave/convex curvature on the top wall of a plane channel. The flows on the bottom and top walls are tripped turbulent and laminar boundary layers, respectively. It is observed that the first and second order statistics are strongly influenced by the pressure gradients. The cross-correlation coefficients of the pressure gradients and vorticity flux remain constant across the FPG/APG regions of the flat wall. High correlations between the streamwise/wallnormal pressure gradient and the spanwise vorticity are found near the separation region close to the curved top wall. The angle of inclined hairpin structure to streamwise direction of the bottom wall is smaller (flatter) in the FPG region than the APG region.
Author: Publisher: ISBN: Category : Languages : en Pages : 380
Book Description
This thesis is focused on direct numerical simulation (DNS) of compressible and incompressible fully developed and developing turbulent flows between isothermal walls using a discontinuous Galerkin method (DGM). Three cases (Ma = 0.2, 0.7 and 1.5) of DNS of turbulent channel flows between isothermal walls with Re ~ 2800, based on bulk velocity and half channel width, have been carried out. It is found that a power law seems to scale mean streamwise velocity with Ma slightly better than the more usual log-law. Inner and outer scaling of second-order and higher-order statistics have been analyzed. The linkage between the pressure gradient and vorticity flux on the wall has been theoretically derived and confirmed and they are highly correlated very close to the wall. The correlation coefficients are influenced by Ma, and viscosity when Ma is high. The near-wall spanwise streak spacing increases with Ma. Isosurfaces of the second invariant of the velocity gradient tensor are more sparsely distributed and elongated as Ma increases. DNS of turbulent isothermal-wall bounded flow subjected to favourable and adverse pressure gradient (FPG, APG) at Ma ~ 0.2 and Reref ~ 428000, based on the inlet bulk velocity and the streamwise length of the bottom wall, is also investigated. The FPG/APG is obtained by imposing a concave/convex curvature on the top wall of a plane channel. The flows on the bottom and top walls are tripped turbulent and laminar boundary layers, respectively. It is observed that the first and second order statistics are strongly influenced by the pressure gradients. The cross-correlation coefficients of the pressure gradients and vorticity flux remain constant across the FPG/APG regions of the flat wall. High correlations between the streamwise/wallnormal pressure gradient and the spanwise vorticity are found near the separation region close to the curved top wall. The angle of inclined hairpin structure to streamwise direction of the bottom wall is smaller (flatter) in the FPG region than the APG region.
Author: Kevin Patrick Griffin Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
Turbulent wall-bounded flows are ubiquitous in engineering and understanding and predicting their dynamics is necessary to address pressing grand challenges in aerospace, energy, and environmental science. For example, control and prediction of wall-bounded turbulence can lead to improved aerodynamic performance of air, land, and sea vehicles, increased efficiency of gas turbines used for electricity generation or propulsion, and accurate predictions of changes in the weather or climate. However, for most real applications, directly simulating the governing physics is intractably expensive even when the world's largest supercomputers are employed. The immense computational complexity of simulating turbulence is due to its multiscale nature; quantities of engineering interest, such as aerodynamic forces on a vehicle, manifest on the macroscale but they depend strongly on accurately predicting microscale phenomena such as turbulent kinetic energy dissipation. To address the high cost of direct simulations of turbulence, it is common to use physical modeling, which is the process of simplifying the governing equations and boundary conditions in order to obtain approximate variants that are computationally efficient to simulate. If the models are accurate, then the resulting solutions can be useful to make engineering design decisions at affordable cost. Specifically, this work focuses on the modeling of turbulent flows near solid boundaries since this is often the rate-limiting region which dominates the computational cost of a simulation. The direct impact of the models developed herein will be that advanced models can deliver accurate engineering predictions at reduced computational costs. To quantify this impact, we present detailed estimates of the grid-point and time-step requirements for simulations of incompressible and compressible wall-bounded flows. When paired with estimates for the growth of computational power over time, these estimates are useful for planning the types of simulations that will be tractable in the future. For the wall models developed in this work, it is assumed that the boundary-layer thickness can be computed reliably. However in complex flows, this is not trivial to define because of the inherent complexity of the background inviscid flow. In this work, a robust method for computing the boundary layer thickness is developed. The proposed method is based on estimating the inviscid base flow that leads to the actual observed viscous solution. Then, the wall-normal location of the departure of the viscous solution from the reconstructed inviscid one is labeled as the boundary layer thickness. This method is used throughout this work. Two models for the near-wall flow are presented for incompressible flows. The first model is for flows over complex geometries with strong streamwise pressure gradients. Lagrangian history effects are incorporating by introducing additional dependence of the wall model on the outer partial differential equation solver. The second model is designed for cases where computational resources are extremely limited and even the boundary layer is difficult to resolve (e.g., very high Reynolds number flows). The boundary layer wake is incorporated into the wall model to expand its domain of applicability. Both of these models are found to improve the prediction of the wall shear stress in a priori analysis. In applications with significant wall heat transfer, such as high-speed aerospace applications, wall-normal variations in density and viscosity can alter the structure of wall-bounded turbulent flows. In this work, a compressible velocity transformation is developed, which enables the mapping of a wide range of compressible velocity profiles to a single universal incompressible law of the wall. The proposed transformation is unique in that it is successful in collapsing data from channel and pipe flows and boundary layers with and without heat transfer. In addition, the inverse of this transformation is derived and applied as a wall model for large-eddy simulation. It is found that the model is significantly more accurate than the classical model, especially in applications with strong wall heat transfer.
Author: Abhiram B. Aithal Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
Flow separation is encountered in many engineering devices, e.g., turbines, diffusers, wings and aftbodies of aircrafts. The physical mechanisms of separated turbulent boundary layers over curved walls are not yet well understood. The main objectives of the present study are to: (i) develop an efficient numerical methodology to perform direct numerical simulations (DNS) of spatially-developing turbulent boundary layers (SDTBLs) over curved walls, and (ii) enhance our knowledge on the dynamics of turbulence in SDTBLs separating over curved walls. To achieve these objectives, we have developed a new pressure-correction method, called FastRK3, for simulating incompressible flows over curved walls. FastRK3 solves the incompressible Navier-Stokes (NS) equations written in orthogonal curvilinear coordinates. The orthogonal formulation of the NS equations substantially reduces the computational cost of the flow solver and the numerical stencils of its second-order finite difference discretization mirror that of the Cartesian formulation. This property allows us to develop an FFT-based Poisson solver for pressure, called FastPoc, for those cases where the components of the metric tensor are independent of one spatial direction: surfaces of linear translation (e.g., curved ramps and bumps) and surfaces of revolution (e.g., axisymmetric shapes). Our results show that the new FFT-based Poisson solver, FastPoc, is thirty to sixty times faster than the multigrid-based linear solver, and the new flow solver, FastRK3, is overall four to seven times faster when using FastPoc rather than multigrid. FastRK3 is an explicit, three-stage, third-order Runge-Kutta based projection-method which requires solving the Poisson equation for pressure only once per time step. We show theoretically and numerically that (i) FastRK3 has the same temporal order of accuracy for pressure and velocity as the standard RK3 method for both free-shear and wall-bounded flows when the RK3 coefficients and the pressure extrapolation scheme satisfy specific conditions herein theoretically derived, (ii) FastRK3 is third-order accurate in time for velocity and second-order accurate in time for pressure for free-shear flows, and (iii) FastRK3 is second-order accurate in time for velocity and pressure for `stiff' wall-bounded flows. In summary, given that the computational mesh satisfies the property of orthogonality, FastRK3 simulates flows over curved walls with second-order accuracy in both space and time. Using FastRK3, we perform DNS of a SDTBL separating over a curved wall. We validate FastRK3 by comparing our numerical results with published experiments. For the first time, we derive the budget equations of the turbulence kinetic energy and of the Reynolds stresses in orthogonal coordinates, and report the results from our DNS. We study the dynamics of turbulence of the separated flow over the curved wall by analyzing these budget equations. Our analysis shows that, in the separated region over the curved ramp, the TKE production occurs through the production of (u2) as well as (v2) in contrast to a ZPG SDTBL where the TKE production is mostly through the production of (u2). In the curved ramp region, the viscous diffusion and dissipation of (v2) and (uv) are not zero at the wall, unlike that for both a ZPG SDTBL over a flat-plate as well as a pressure-gradient induced turbulent flow separation over a flat plate. And, the curved ramp region of the flow is characterized by enhanced transport of the Reynolds stresses compared to those of the upstream ZPG SDTBL due to the mixing layer created in the flow by the flow separation. Finally, our results have shown, for the first time, that the Reynolds stress profiles and budgets in the orthogonal curvilinear coordinates are very similar to those in the APG region of the 'pressure-gradient induced flow separation' in a flat-plate turbulent boundary layer. Such a comparison is only possible because (i) we employ a structured orthogonal grid over the curved ramp in our simulations, and (ii) FastRK3 solves the governing equations written in orthogonal curvilinear coordinates.
Author: O. Pironneau Publisher: Cambridge University Press ISBN: 9780521416184 Category : Mathematics Languages : en Pages : 536
Book Description
The workshop concentrated on the following turbulence test cases: T1 Boundary layer in an S-shaped duct; T2 Periodic array of cylinders in a channel; T3 Transition in a boundary layer under the influence of free-stream turbulence; T4 & T5: Axisymmetric confined jet flows.
Author: Thomas B. Gatski Publisher: Academic Press ISBN: 012397318X Category : Science Languages : en Pages : 343
Book Description
Compressibility, Turbulence and High Speed Flow introduces the reader to the field of compressible turbulence and compressible turbulent flows across a broad speed range, through a unique complimentary treatment of both the theoretical foundations and the measurement and analysis tools currently used. The book provides the reader with the necessary background and current trends in the theoretical and experimental aspects of compressible turbulent flows and compressible turbulence. Detailed derivations of the pertinent equations describing the motion of such turbulent flows is provided and an extensive discussion of the various approaches used in predicting both free shear and wall bounded flows is presented. Experimental measurement techniques common to the compressible flow regime are introduced with particular emphasis on the unique challenges presented by high speed flows. Both experimental and numerical simulation work is supplied throughout to provide the reader with an overall perspective of current trends. An introduction to current techniques in compressible turbulent flow analysis An approach that enables engineers to identify and solve complex compressible flow challenges Prediction methodologies, including the Reynolds-averaged Navier Stokes (RANS) method, scale filtered methods and direct numerical simulation (DNS) Current strategies focusing on compressible flow control
Author: Roger Peyret Publisher: Springer ISBN: 3709125901 Category : Science Languages : en Pages : 320
Book Description
This book collects the lecture notes concerning the IUTAM School on Advanced Turbulent Flow Computations held at CISM in Udine September 7–11, 1998. The course was intended for scientists, engineers and post-graduate students interested in the application of advanced numerical techniques for simulating turbulent flows. The topic comprises two closely connected main subjects: modelling and computation, mesh pionts necessary to simulate complex turbulent flow.
Author: J. H. Ferziger Publisher: ISBN: Category : Fluid dynamics Languages : en Pages : 172
Book Description
The five major categories of this paper are: Correlations, Integral methods, Reynolds-averaged equations, large eddy simulation, and full simulation.
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Author: Kevin Patrick Griffin
Author: Abhiram B. Aithal
Author: Debra J. Olejniczak
Author: O. Pironneau
Author: Thomas B. Gatski
Author: Stanford University. Thermosciences Division. Thermosciences Division
Author: Roger Peyret
Author: Raphael Gotthard Harald Arlitt
Author: J. H. Ferziger