Temporal slow-growth formulation for direct numerical simulation of compressible wall-bounded flows

Temporal slow-growth formulation for direct numerical simulation of compressible wall-bounded flows A slow-growth formulation for DNS of wall-bounded turbulent flow is developed and demonstrated to enable extension of slow-growth modeling concepts to wall-bounded flows with complex physics. As in previous slow-growth approaches, the formulation assumes scale separation between the fast scales of turbulence and the slow evolution of statistics such as the mean flow. This separation enables the development of approaches where the fast scales of turbulence are directly simulated while the forcing provided by the slow evolution is modeled. The resulting model admits periodic boundary conditions in the streamwise direction, which avoids the need for extremely long domains and complex inflow conditions that typically accompany spatially developing simulations. Further, it enables the use of efficient Fourier numerics. Unlike previous approaches [Guarini, Moser, Shariff, and Wray, J. Fluid Mech. 414, 1 (2000)JFLSA70022-112010.1017/S0022112000008466; Maeder, Adams, and Kleiser, J. Fluid Mech. 429, 187 (2001)JFLSA70022-112010.1017/S0022112000002718; Spalart, J. Fluid Mech. 187, 61 (1988)JFLSA70022-112010.1017/S0022112088000345], the present approach is based on a temporally evolving boundary layer and is specifically tailored to give results for calibration and validation of Reynolds-averaged Navier–Stokes (RANS) turbulence models. The use of a temporal homogenization simplifies the modeling, enabling straightforward extension to flows with complicating features, including cold and blowing walls. To generate data useful for calibration and validation of RANS models, special care is taken to ensure that the mean slow-growth forcing is closed in terms of the mean and other quantities that appear in standard RANS models, ensuring that there is no confounding between typical RANS closures and additional closures required for the slow-growth problem. The performance of the method is demonstrated on two problems: an essentially incompressible, zero-pressure-gradient boundary layer and a transonic boundary layer over a cooled, transpiring wall. The results show that the approach produces flows that are qualitatively similar to other slow-growth methods as well as spatially developing simulations and that the method can be a useful tool in investigating wall-bounded flows with complex physics. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review Fluids American Physical Society (APS)

Temporal slow-growth formulation for direct numerical simulation of compressible wall-bounded flows

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Temporal slow-growth formulation for direct numerical simulation of compressible wall-bounded flows

Abstract

A slow-growth formulation for DNS of wall-bounded turbulent flow is developed and demonstrated to enable extension of slow-growth modeling concepts to wall-bounded flows with complex physics. As in previous slow-growth approaches, the formulation assumes scale separation between the fast scales of turbulence and the slow evolution of statistics such as the mean flow. This separation enables the development of approaches where the fast scales of turbulence are directly simulated while the forcing provided by the slow evolution is modeled. The resulting model admits periodic boundary conditions in the streamwise direction, which avoids the need for extremely long domains and complex inflow conditions that typically accompany spatially developing simulations. Further, it enables the use of efficient Fourier numerics. Unlike previous approaches [Guarini, Moser, Shariff, and Wray, J. Fluid Mech. 414, 1 (2000)JFLSA70022-112010.1017/S0022112000008466; Maeder, Adams, and Kleiser, J. Fluid Mech. 429, 187 (2001)JFLSA70022-112010.1017/S0022112000002718; Spalart, J. Fluid Mech. 187, 61 (1988)JFLSA70022-112010.1017/S0022112088000345], the present approach is based on a temporally evolving boundary layer and is specifically tailored to give results for calibration and validation of Reynolds-averaged Navier–Stokes (RANS) turbulence models. The use of a temporal homogenization simplifies the modeling, enabling straightforward extension to flows with complicating features, including cold and blowing walls. To generate data useful for calibration and validation of RANS models, special care is taken to ensure that the mean slow-growth forcing is closed in terms of the mean and other quantities that appear in standard RANS models, ensuring that there is no confounding between typical RANS closures and additional closures required for the slow-growth problem. The performance of the method is demonstrated on two problems: an essentially incompressible, zero-pressure-gradient boundary layer and a transonic boundary layer over a cooled, transpiring wall. The results show that the approach produces flows that are qualitatively similar to other slow-growth methods as well as spatially developing simulations and that the method can be a useful tool in investigating wall-bounded flows with complex physics.
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Publisher
The American Physical Society
Copyright
Copyright © ©2017 American Physical Society
eISSN
2469-990X
D.O.I.
10.1103/PhysRevFluids.2.084602
Publisher site
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Abstract

A slow-growth formulation for DNS of wall-bounded turbulent flow is developed and demonstrated to enable extension of slow-growth modeling concepts to wall-bounded flows with complex physics. As in previous slow-growth approaches, the formulation assumes scale separation between the fast scales of turbulence and the slow evolution of statistics such as the mean flow. This separation enables the development of approaches where the fast scales of turbulence are directly simulated while the forcing provided by the slow evolution is modeled. The resulting model admits periodic boundary conditions in the streamwise direction, which avoids the need for extremely long domains and complex inflow conditions that typically accompany spatially developing simulations. Further, it enables the use of efficient Fourier numerics. Unlike previous approaches [Guarini, Moser, Shariff, and Wray, J. Fluid Mech. 414, 1 (2000)JFLSA70022-112010.1017/S0022112000008466; Maeder, Adams, and Kleiser, J. Fluid Mech. 429, 187 (2001)JFLSA70022-112010.1017/S0022112000002718; Spalart, J. Fluid Mech. 187, 61 (1988)JFLSA70022-112010.1017/S0022112088000345], the present approach is based on a temporally evolving boundary layer and is specifically tailored to give results for calibration and validation of Reynolds-averaged Navier–Stokes (RANS) turbulence models. The use of a temporal homogenization simplifies the modeling, enabling straightforward extension to flows with complicating features, including cold and blowing walls. To generate data useful for calibration and validation of RANS models, special care is taken to ensure that the mean slow-growth forcing is closed in terms of the mean and other quantities that appear in standard RANS models, ensuring that there is no confounding between typical RANS closures and additional closures required for the slow-growth problem. The performance of the method is demonstrated on two problems: an essentially incompressible, zero-pressure-gradient boundary layer and a transonic boundary layer over a cooled, transpiring wall. The results show that the approach produces flows that are qualitatively similar to other slow-growth methods as well as spatially developing simulations and that the method can be a useful tool in investigating wall-bounded flows with complex physics.

Journal

Physical Review FluidsAmerican Physical Society (APS)

Published: Aug 7, 2017

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