Second-Order Boundary-Layer Equations for Supersonic, Rotational Flow over a Flat Plate

2015 ◽  
pp. 619-620
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Second Order ◽  
Rotational Flow ◽  
Boundary Layer Equations

scholarly journals A Numerical Study of Laminar and Intermittently Turbulent Flow Over a Flat Plate Using Pseudo-Compressibility Model

2019 ◽  
Author(s):  
S. Srivastava ◽  
J. R. Eastridge ◽  
B. M. Taravella ◽  
K. M. Akyuzlu
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Turbulent Flow ◽  
Flat Plate ◽  
Turbulent Flows ◽  
Numerical Study ◽  
Computer Code ◽  
Second Order ◽  
Boundary Layer Equations ◽  
Grid Convergence Index

Abstract A study was conducted to investigate the characteristics of incompressible unsteady boundary layer flows (laminar and intermittently turbulent), numerically and experimentally. The main objective of the study is to validate and verify (V&V) the accuracy of the proposed pseudo-compressibility model in solving the incompressible Navier-Stokes (NS) equations. This approach will enable one to use a second order accurate (temporally and spatially) implicit finite-difference (FD) technique to solve NS equations (including RANS equations). Here, the proposed pseudo-compressibility model is used for laminar and intermittent turbulent flow simulations. Flow over a flat plate is chosen as the benchmark case for the validation of the proposed pseudo-compressibility model. An in-house code is developed to solve the boundary layer equations using an Alternating-Direction Explicit (ADE) FD technique. The boundary layer equations are discretized using explicit FD techniques which are second order accurate. The velocity field predicted by this code is compared to the one given by Blasius’ analytical solution. A second in-house code is also developed which adopts the proposed model of pseudo-compressibility to solve the incompressible NS equations. The two dimensional, unsteady conservation of mass and momentum equations are discretized using explicit finite-difference techniques. A standard K-ε closure model is used along with RANS equation to simulate turbulent flows. The primitive variables (velocity and pressure) predicted by this code are compared to the ones predicted by a commercial CFD package (Fluent). Once the method of pseudo-compressibility is validated, it is then implemented into another in-house computer code which employs implicit FD technique and Coupled Modified Strongly Implicit Procedure (CMSIP) to solve for the unknowns of the problem under study. The predictions based on the pseudo-compressibility model for laminar flow are validated using the results of the experiments in which Particle Image Velocimetry (PIV) technique was employed. The verification; that is, the numerical uncertainty estimation of the pseudo-compressible code was accomplished by using the Grid Convergence Index (GCI) method. The results of the present study indicate that the proposed pseudo-compressibility model is capable of predicting experimentally observed characteristics of the external flows successfully, and deviations between the predicted velocity magnitudes and experimentally measured velocities are within an acceptable range for laminar and intermittently turbulent flows conditions.

24.—Eigenvalue and Eigenvector Solutions of a Wave System in a Non-Linear Dissipative Medium

1972 ◽  
Vol 70 ◽  
pp. 251-261
Author(s):  
M. A. S. Ross ◽  
D. F. Corner
Keyword(s):  
Boundary Layer ◽  
Numerical Methods ◽  
Flat Plate ◽  
Stability Theory ◽  
Plate Boundary ◽  
Second Order ◽  
Wave System ◽  
Dissipative Medium ◽  
Eigenvalue And Eigenvector ◽  
Flat Plate Boundary Layer

SynopsisThis paper gives an account of some numerical methods which have been applied to solve the equations of second order stability theory in the flat plate boundary layer.

Viscous flow past a flat plate with uniform injection

1965 ◽  
Vol 284 (1398) ◽  
pp. 370-396 ◽  
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Numerical Study ◽  
Central Zone ◽  
Outer Zone ◽  
Analytic Study ◽  
Boundary Layer Equations ◽  
Numerical Studies ◽  
High Degree ◽  
Uniform Injection

The boundary-layer equations for an incompressible fluid in motion past a flat plate are examined, numerically and analytically, in the special case when the pressure gradient vanishes and there is a uniform injection of fluid from the plate. In the numerical study the principal properties of the boundary layer are computed as far as separation ( x ═ x δ ≑ 0.7456) with a high degree of accuracy. In the analytic study the structure of the singularity at separation is determined. It is of a new kind in boundary layer theory and its elucidation requires the division of the boundary layer into three zones—an outer zone in which the non-dimensional velocity u is much larger than x * (the non-dimensional distance from separation), a central zone in which u ~ x * and an inner zone in which u ≪ x *. A match is effected between solutions in the central and inner zones from which it is inferred that the skin friction τ 0 ~ ( x * / In (1/ x *) 2 as x * → 0. A completely satisfactory agreement between the numerical and analytic studies was not possible. The reason is that the analytic study is only valid when ln ( 1 / x *) ≫ 1 which means that for the analytic and numerical studies to have a common region of validity, the numerical integration must be extended to much smaller values of x * than is possible at present. It was also not possible to effect a match between the central and outer zones in the analytic solution due to the difficulty of finding the properties of the stress τ in the central zone as u / x * →∞.

Second-order effects in free convection

1974 ◽  
Vol 62 (4) ◽  
pp. 793-809 ◽  
Author(s):  
I. C. Walton
Keyword(s):  
Boundary Layer ◽  
Free Convection ◽  
Equations Of State ◽  
Asymptotic Series ◽  
Inviscid Flow ◽  
Second Order ◽  
The Body ◽  
Order Effects ◽  
Boundary Layer Equations ◽  
Second Order Effects

The equations of conservation of momentum, energy and mass together with the equations of state are examined for free convection from a vertical paraboloid. A transformation due to Saville & Churchill is applied to the first- and second-order boundary-layer equations, which are then solved using series about the stagnation point, using asymptotic series far up the body and in between by a method due to Merk. The second-order outer inviscid flow is given in terms of infinite integrals as a solution of Laplace's equation in paraboloidal co-ordinates.Eight second-order effects are distinguished, depending on longitudinal and transverse curvatures, the displacement flow, heat flux into the boundary layer and the variation of density, viscosity, thermometric conductivity and the coefficient of expansion with temperature. Expressions for the skin friction, heat-transfer coefficient and various flux thicknesses are obtained and a comparison of the second-order effects is made.

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