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.

A Numerical Study of Laminar and Intermittently Turbulent Boundary Layer on an Oscillating Flat Plate Using Pseudo-Compressible RANS Model

2020 ◽  
Author(s):  
Shivank Srivastava ◽  
Brandon M. Taravella ◽  
Kazim M. Akyuzlu
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Flat Plate ◽  
Turbulent Flows ◽  
Numerical Study ◽  
Navier Stokes ◽  
Flow Conditions ◽  
Rans Model ◽  
Explicit Finite Difference ◽  
Turbulent Flow Conditions

Abstract A numerical study was conducted to study the unsteady characteristics of incompressible boundary layer flows over an oscillating flat plate under laminar and intermittently turbulent flow conditions using pseudo-compressible Reynolds Averaged Navier-Stokes (RANS) model. The numerical study is carried out using an in-house code and a commercial CFD package (Fluent). Two equation (k-ε) turbulence closure model, modified near the wall, is used along with RANS equations to simulate intermittently turbulent flows. Fully Explicit-Finite Difference technique (FEFD) is employed to solve the governing differential equations. For validation purposes, the velocity fields predicted by the in-house code and commercial CFD package are compared to the one given by analytical solution to Stokes’ second problem for an oscillating flat plate. Numerical experiments were conducted for unsteady cases for Stokes’ Reynolds number corresponding to laminar and intermittently turbulent flows, respectively. Time dependent velocity profiles, shear stress distribution, turbulence properties during the accelerating and decelerating stages of oscillations are predicted. The above predictions are then compared to ones predicted by commercial CFD code. The velocity magnitudes predicted by the in-house code and commercial CFD code are within acceptable range for laminar and intermittently turbulent flow conditions.

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 * →∞.

A Numerical Study of Unsteady Natural Convection in a Rectangular Enclosure: Transition From Laminar to Turbulent Flow

2010 ◽  
Author(s):  
K. M. Akyuzlu ◽  
M. Chidurala
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Turbulent Flow ◽  
Numerical Study ◽  
Second Order ◽  
Working Fluid ◽  
Two Dimensional ◽  
Rectangular Enclosure ◽  
Circulation Patterns ◽  
Vertical Walls

A two-dimensional, mathematical model is adopted to investigate the development of buoyancy driven circulation patterns and temperature stratification inside a rectangular enclosure. One of the vertical walls of the enclosure is kept at a higher temperature then the opposing vertical wall. The top and the bottom of the enclosure are assumed insulated. The physics based mathematical model for this problem consists of conservation of mass, momentum (two-dimensional, unsteady Navier-Stokes equations for turbulent compressible flows), and energy equations for the enclosed fluid subjected to appropriate boundary conditions. A standard two equation turbulence model is used to model the turbulent flow in the enclosure. The compressibility of the working fluid is represented by an ideal gas relation. The conservation equations are discretized using an implicit finite difference technique which employs second order accurate central differencing for spatial derivatives and second order (based on Taylor expansion) finite differencing for time derivatives. The linearized finite difference equations are solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns of the problem. Numerical experiments were then carried out to simulate the development of the buoyancy driven circulation patterns inside rectangular enclosures (with aspects ratios 0.5, 1 and 1.5) filled with a compressible fluid (Pr = 0.72). Experiments were repeated for various wall temperature differences which corresponded to Rayleigh numbers between 104 and 106. Changes in unsteady circulation patterns, temperature contours, and vertical and horizontal velocity profiles were predicted while the flow inside the enclosure transferred from laminar to turbulent flow due to the sudden temperature change imposed on the vertical walls of the enclosure. Only the results of the enclosure with aspect ratio one is presented in this paper. These results indicate that this transition is characterized by unicellular circulation patterns breaking up in to multicellular formations and increase in the values of the predicted wall heat fluxes and Nusselt number as flow becomes turbulent.

A numerical study of hybrid nanofluids near an irregular 3D surface having slips and exothermic effects

2021 ◽  
pp. 095440892110647
Author(s):  
Mumtaz Khan ◽  
Amer Rasheed
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Skin Friction ◽  
Numerical Study ◽  
Three Dimensional ◽  
Physical Parameters ◽  
Boundary Layer Problem ◽  
Boundary Layer Equations ◽  
Slip Effects ◽  
Hybrid Nanofluids

The current article presents a comprehensive investigation of MHD viscous flow of hybrid-nanofluids (Al2O3 − Ag/ water and (Al2O3 − Cu/) over a horizontally irregular 3D plane with non-uniform thickness combined with slip effects. The foremost aim of conducting this study is to enhance thermal transportation. Based on the following novelties, the subject study holds tremendous significance: i. A comparative analysis of two hybrid nanofluids with hybrid-base fluid together with slip effects ii. An exclusive study where the Tiwari and Das nanofluid model is employed combined with Fourier's heat flux model iii. Development of finite-difference code which implements the three-stage Lobatto IIIa approach for the designed problem. We have used suitable scaling transformations to convert the three-dimensional conservation equations of mass, momentum, and energy into a dimensionless system of boundary layer equations. The numerical solution of the coupled non-linear boundary layer problem is determined using the built-in finite-difference code designed to employ the three-stage Lobatto IIIa formula. A comprehensive assessment is carried out in how the velocity components, temperature, skin friction, and heat transfer rate are affected by the physical parameters of interest. The same is presented through graphs and in tabular form to offer a pictorial overview. The fluctuating trends of skin friction coefficients (x, y-directions) and Nusselt number are investigated to explore the physical landscape of the current study. The findings of this study offer a noticeable contrast to their existing counterparts.

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