TY - JOUR
T1 - On stagnation pressure increases in calorically perfect, ideal gases
AU - Williams, D. M.
AU - Kamenetskiy, D. S.
AU - Spalart, P. R.
N1 - Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2016/4/1
Y1 - 2016/4/1
N2 - When stagnation pressure rises in a natural or numerically simulated flow it is frequently a cause for concern, as one usually expects viscosity and turbulence to cause stagnation pressure to decrease. In fact, if stagnation pressure increases, one may suspect measurement or numerical errors. However, this need not be the case, as the laws of nature do not require that stagnation pressure continually decreases. In order to help clarify matters, the objective of this work is to understand the conditions under which stagnation pressure will rise in the unsteady/steady flows of compressible, viscous, calorically perfect, ideal gases. Furthermore, at a more practical level, the goal is to understand the conditions under which stagnation pressure will increase in flows simulated with the Reynolds averaged Navier-Stokes equations and eddy-viscosity turbulence models. In order to provide an improved understanding of increases in stagnation pressure for both these scenarios, transport equations are derived that govern its behavior in the unaveraged and Reynolds averaged settings. These equations are utilized to precisely determine the relationship between changes in stagnation pressure and zeroth, first, and second derivatives of fundamental flow quantities. Furthermore, these equations are utilized to demonstrate the relationship between changes in stagnation pressure and fundamental non-dimensional quantities that govern the conductivity, viscosity, and compressibility of the flow. In addition, based on an analysis of the Reynolds averaged equation (for eddy-viscosity turbulence models), it is shown that stagnation pressure is particularly likely to experience a spurious rise at the outer edges of shear layers that are undergoing convex curvature. Thereafter, numerical experiments are performed which confirm the primary aspects of the theoretical analysis.
AB - When stagnation pressure rises in a natural or numerically simulated flow it is frequently a cause for concern, as one usually expects viscosity and turbulence to cause stagnation pressure to decrease. In fact, if stagnation pressure increases, one may suspect measurement or numerical errors. However, this need not be the case, as the laws of nature do not require that stagnation pressure continually decreases. In order to help clarify matters, the objective of this work is to understand the conditions under which stagnation pressure will rise in the unsteady/steady flows of compressible, viscous, calorically perfect, ideal gases. Furthermore, at a more practical level, the goal is to understand the conditions under which stagnation pressure will increase in flows simulated with the Reynolds averaged Navier-Stokes equations and eddy-viscosity turbulence models. In order to provide an improved understanding of increases in stagnation pressure for both these scenarios, transport equations are derived that govern its behavior in the unaveraged and Reynolds averaged settings. These equations are utilized to precisely determine the relationship between changes in stagnation pressure and zeroth, first, and second derivatives of fundamental flow quantities. Furthermore, these equations are utilized to demonstrate the relationship between changes in stagnation pressure and fundamental non-dimensional quantities that govern the conductivity, viscosity, and compressibility of the flow. In addition, based on an analysis of the Reynolds averaged equation (for eddy-viscosity turbulence models), it is shown that stagnation pressure is particularly likely to experience a spurious rise at the outer edges of shear layers that are undergoing convex curvature. Thereafter, numerical experiments are performed which confirm the primary aspects of the theoretical analysis.
UR - http://www.scopus.com/inward/record.url?scp=84955321791&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84955321791&partnerID=8YFLogxK
U2 - 10.1016/j.ijheatfluidflow.2015.12.005
DO - 10.1016/j.ijheatfluidflow.2015.12.005
M3 - Article
AN - SCOPUS:84955321791
SN - 0142-727X
VL - 58
SP - 40
EP - 53
JO - International Journal of Heat and Fluid Flow
JF - International Journal of Heat and Fluid Flow
ER -