scholarly journals SIMULASI NUMERIK PADA SILINDER DENGAN SUSUNAN SELANG-SELING (STAGGERED) DALAM SALURAN SEGI EMPAT MENGUNAKAN K Ԑ MODEL

2017 ◽  
Vol 17 (2) ◽  
pp. 89-100
Author(s):  
Nuzul Hidayat ◽  
Ahmad Arif ◽  
M Yasep Setiawan
Keyword(s):  
Boundary Layer ◽  
Nusselt Number ◽  
Turbulence Model ◽  
Second Order ◽  
Navier Stokes ◽  
Trailing Edge ◽  
Velocity Contour

Abstrak— Silinder digunakan pada alat penukar kalor untuk meningkatkan luasan perpindahan panas antara permukaan utama dengan fluida di sekitarnya. Idealnya, material untuk membuat silinder harus memiliki konduktivitas termal yang tinggi untuk meminimalkan perbedaan temperatur antara permukaan utama dengan permukaan yang diperluas. Aplikasi silinder sering dijumpai pada system pendinginan ruangan, peralatan elektronik, motor bakar, trailing edge sudu turbin gas, alat penukar kalor, dengan udara sebagai media perpindahan panasnya. Ada berbagai tipe silinder pada alat penukar kalor yang telah digunakan, mulai dari bentuk yang relatif sederhana seperti silinder segiempat, silindris, anular, tirus atau pin sampai dengan kombinasi dari berbagai geometri yang berbeda dengan jarak yang teratur dalam susunan segaris (in-line) ataupun selang-seling (staggered). Dalam penelitian ini bertujuan untuk mengetahui karakteristik boundary layer turbulen pada Cylinder tersusun staggered  untuk kasus dengan cara mendapatkan data secara kualitatif dan kuantitatif pada a) Coefficient of Pressure (Cp)   , Nusselt Number dan (c) Velocity contour  . Parameter tersebut diukur pada daerah mid span dengan, . Penelitian ini menggunakan software Fluent 6.3.26 dimana pada penelitian secara numerik digunakan turbulence model yaitu k  realisable dengan discretization Second Order Upwind mengunakan software Fluent . Analisa pada penelitian numerik dilakukan secara 2 dimensi (2D) Unsteady Reynolds Averages Navier Stokes. Didapat bahwa dengan meningkatkan Re maka hal yang terjadi Cd pada silinder mengalami penurunan apabila aliran tersebut diganggu oleh silinder yang lain pada susunan staggered karena akibat kenaikan turbulensi aliran,  turbuensi aliran meningkat juga mengakibatkan meningkatnya  perpindahan panas ditandai dengan kenaikan Nu.

On the flow near the trailing edge of a flat plate

1968 ◽  
Vol 306 (1486) ◽  
pp. 275-290 ◽  
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Governing Equations ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Multiplicative Constant ◽  
Boundary Layer Approximation ◽  
Uniform Shear

It is shown that the boundary layer approximation to the flow of a viscous fluid past a flat plate of length l , generally valid near the plate when the Reynolds number Re is large, fails within a distance O( lRe -3/4 ) of the trailing edge. The appropriate governing equations in this neighbourhood are the full Navier- Stokes equations. On the basis of Imai (1966) these equations are linearized with respect to a uniform shear and are then completely solved by means of a Wiener-Hopf integral equation. The solution so obtained joins smoothly on to that of the boundary layer for a flat plate upstream of the trailing edge and for a wake downstream of the trailing edge. The contribution to the drag coefficient is found to be O ( Re -3/4 ) and the multiplicative constant is explicitly worked out for the linearized equations.

The Impact of Viscous Effects on the Aerodynamic Damping of Vibrating Transonic Compressor Blades—A Numerical Study

2000 ◽  
Vol 123 (2) ◽  
pp. 409-417 ◽  
Author(s):  
Bjo¨rn Gru¨ber ◽  
Volker Carstens
Keyword(s):  
Boundary Layer ◽  
Turbulence Model ◽  
Navier Stokes ◽  
Implicit Time ◽  
Compressor Cascade ◽  
Viscous Effects ◽  
Aerodynamic Forces ◽  
Aerodynamic Damping ◽  
Transonic Compressor ◽  
The Impact

A parametric study which investigates the influence of viscous effects on the damping behavior of vibrating compressor cascades is presented here. To demonstrate the dependence of unsteady aerodynamic forces on the flow viscosity, a computational study was performed for a transonic compressor cascade of which the blades underwent tuned pitching oscillations while the flow conditions extended from fully subsonic to highly transonic flow. Additionally, the reduced frequency and Reynolds number were varied. In order to check the linear behavior of the aerodynamic forces, all calculations were carried out for three different oscillation amplitudes. Comparisons with inviscid Euler results helped identify the influence of viscous effects. The computations were performed with a Navier-Stokes code, the basic features of which are the use of an AUSM upwind scheme, an implicit time integration, and the implementation of the Baldwin-Lomax turbulence model. In order to demonstrate the possibility of this code to correctly predict the unsteady behavior of strong shock-boundary layer interactions, the experiment of Yamamoto and Tanida on a self-induced shock oscillation due to shock-boundary layer interaction was calculated. A significant improvement in the prediction of the shock amplitude was achieved by a slight modification of the Baldwin Lomax turbulence model. An important result of the presented compressor cascade investigations is that viscous effects may cause a significant change in the aerodynamic damping. This behavior is demonstrated by two cases in which an Euler calculation predicts a damped oscillation whereas a Navier-Stokes computation leads to an excited vibration. It was found that the reason for these contrary results are shock-boundary-layer interactions which dramatically change the aerodynamic damping.

scholarly journals The numerical solution of the asymptotic equations of trailing edge flow

1974 ◽  
Vol 340 (1620) ◽  
pp. 91-111 ◽  
Keyword(s):  
Boundary Layer ◽  
Outer Layer ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Boundary Layer Equations ◽  
Asymptotic Equations ◽  
Displacement Thickness

According to Stewartson (1969, 1974) and to Messiter (1970), the flow near the trailing edge of a flat plate has a limit structure for Reynolds number Re →∞ consisting of three layers over a distance O (Re -3/8 ) from the trailing edge: the inner layer of thickness O ( Re -5/8 ) in which the usual boundary layer equations apply; an intermediate layer of thickness O ( Re -1/2 ) in which simplified inviscid equations hold, and the outer layer of thickness O ( Re -3/8 ) in which the full inviscid equations hold. These asymptotic equations have been solved numerically by means of a Cauchy-integral algorithm for the outer layer and a modified Crank-Nicholson boundary layer program for the displacement-thickness interaction between the layers. Results of the computation compare well with experimental data of Janour and with numerical solutions of the Navier-Stokes equations by Dennis & Chang (1969) and Dennis & Dunwoody (1966).

Flow Analyses in a Single-Stage Propulsion Pump

1996 ◽  
Vol 118 (2) ◽  
pp. 240-248 ◽  
Author(s):  
Y. T. Lee ◽  
C. Hah ◽  
J. Loellbach
Keyword(s):  
Boundary Layer ◽  
Numerical Method ◽  
Turbulence Model ◽  
Eddy Viscosity ◽  
Single Stage ◽  
Acoustic Properties ◽  
Turbulent Eddy ◽  
Trailing Edge ◽  
Local Flow ◽  
Blade Row

Steady-state analyses of the incompressible flow past a single-stage stator/rotor propulsion pump are presented and compared to experimental data. The purpose of the current study is to validate a numerical method for the design application of a typical propulsion pump and for the acoustic analysis based on predicted flowfields. A steady multiple-blade-row approach is used to calculate the flowfields of the stator and the rotor. The numerical method is based on a fully conservative control-volume technique. The Reynolds-averaged Navier–Stokes equations are solved along with the standard two-equation k–ε turbulence model. Numerical results for both mean flow and acoustic properties compare well with measurements in the wake of each blade row. The rotor blade has a thick boundary layer in the last quarter of the chord and the flow separates near the trailing edge. These features invalidate many Euler prediction results. Due to the dramatic reduction of the turbulent eddy viscosity in the thick boundary layer, the standard k–ε model cannot predict the correct local flow characteristics near the rotor trailing edge and in its near wake. Thus, a modification of the turbulence length scale in the turbulence model is applied in the thick boundary layer in response to the reduction of the turbulent eddy viscosity.

scholarly journals Prediction of Airfoil Stall Based on a Modified k−v2¯−ω Turbulence Model

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 272
Author(s):  
Chenyu Wu ◽  
Haoran Li ◽  
Yufei Zhang ◽  
Haixin Chen
Keyword(s):  
Experimental Data ◽  
Shear Layer ◽  
Turbulence Model ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Trailing Edge ◽  
Naca0012 Airfoil ◽  
Separated Shear Layer ◽  
Non Equilibrium

The accuracy of an airfoil stall prediction heavily depends on the computation of the separated shear layer. Capturing the strong non-equilibrium turbulence in the shear layer is crucial for the accuracy of a stall prediction. In this paper, different Reynolds-averaged Navier–Stokes turbulence models are adopted and compared for airfoil stall prediction. The results show that the separated shear layer fixed k−v2¯−ω (abbreviated as SPF k−v2¯−ω) turbulence model captures the non-equilibrium turbulence in the separated shear layer well and gives satisfactory predictions of both thin-airfoil stall and trailing-edge stall. At small Reynolds numbers (Re~105), the relative error between the predicted CL,max of NACA64A010 by the SPF k−v2¯−ω model and the experimental data is less than 3.5%. At high Reynolds numbers (Re~106), the CL,max of NACA64A010 and NACA64A006 predicted by the SPF k−v2¯−ω model also has an error of less than 5.5% relative to the experimental data. The stall of the NACA0012 airfoil, which features trailing-edge stall, is also computed by the SPF k−v2¯−ω model. The SPF k−v2¯−ω model is also applied to a NACA0012 airfoil, which features trailing-edge stall and an error of CL relative to the experiment at CL>1.0 is smaller than 3.5%. The SPF k−v2¯−ω model shows higher accuracy than other turbulence models.

Investigation on the Effect of Different Lands on Trailing Edge Slot Film Cooling

2018 ◽  
Vol 0 (0) ◽  
Author(s):  
Yang Xu ◽  
Hui-ren Zhu ◽  
Wei-jiang Xu ◽  
Jian-sheng Wei
Keyword(s):  
Nusselt Number ◽  
Film Cooling ◽  
Turbine Blades ◽  
Experimental Studies ◽  
Navier Stokes ◽  
Trailing Edge ◽  
Cooling Effectiveness ◽  
Wall Functions ◽  
Film Cooling Effectiveness ◽  
Slot Film Cooling

Abstract Trailing edge slot film cooling is a widely used method for protecting the trailing edge of turbine blades from hot gas impingement. The structures that separate the slots, known as “lands,” come in a variety of configurations. This paper presents the effects of the trailing edge with different lands on the film cooling performance. Experimental studies are conducted on the film cooling effectiveness and Nusselt number with different lands. Four trailing edge configurations, including the straight lands, the beveling lands, the fillet lands and the tapered lands are considered under four blowing ratios (0.5, 0.7, 1.0 and 1.5). The Reynolds numbers of mainstream is fixed as 375,000. Film cooling effectiveness and Nusselt number performances are measured by transient liquid crystal measurement technique. Reynolds-averaged Navier-Stokes (RANS) simulation with realizable k-ε turbulence model and enhanced wall functions are performed using a commercial code Fluent. In each case, the slot height is kept constant. It is shown that the beveling lands, the fillet lands and the tapered lands have higher cooling effectiveness and lower Nusselt number compared with the straight lands. Under higher blowing ratios, the trailing edges of all four lands have higher cooling effectiveness and higher Nusselt number.

Shock–boundary layer interaction and energetics in transonic flutter

2017 ◽  
Vol 832 ◽  
pp. 212-240 ◽  
Author(s):  
Pradeepa T. Karnick ◽  
Kartik Venkatraman
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Turbulence Model ◽  
Viscous Effects ◽  
Trailing Edge ◽  
Aeroelastic System ◽  
Number Range ◽  
Shock Reversal ◽  
Transonic Flutter ◽  
Flutter Boundary

We study the influence of shock and boundary layer interactions in transonic flutter of an aeroelastic system using a Reynolds-averaged Navier–Stokes (RANS) solver together with the Spalart–Allmaras turbulence model. We show that the transonic flutter boundary computed using a viscous flow solver can be divided into three distinct regimes: a low transonic Mach number range wherein viscosity mimics increasing airfoil thickness thereby mildly influencing the flutter boundary; an intermediate region of drastic change in the flutter boundary due to shock-induced separation; and a high transonic Mach number zone of no viscous effects when the shock moves close to the trailing edge. Inviscid transonic flutter simulations are a very good approximation of the aeroelastic system in predicting flutter in the first and third regions: that is when the shock is not strong enough to cause separation, and in regions where the shock-induced separated region is confined to a small region near the trailing edge of the airfoil. However, in the second interval of intermediate transonic Mach numbers, the power distribution on the airfoil surface is significantly influenced by shock-induced flow separation on the upper and lower surfaces leading to oscillations about a new equilibrium position. Though power contribution by viscous forces are three orders of magnitude less than the power due to pressure forces, these viscous effects manipulate the flow by influencing the strength and location of the shock such that the power contribution by pressure forces change significantly. Multiple flutter points that were part of the inviscid solution in this regime are now eliminated by viscous effects. Shock motion on the airfoil, shock reversal due to separation, and separation and reattachment of flow on the airfoil upper surface, also lead to multiple aerodynamic forcing frequencies. These flow features make the flutter boundary quantitatively sensitive to the turbulence model and numerical method adopted, but qualitatively they capture the essence of the physical phenomena.

Asymptotic analysis of a linearized trailing edge flow

1972 ◽  
Vol 6 (3) ◽  
pp. 327-347 ◽  
Author(s):  
K. Capell
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Wake Region ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Uniform Shear ◽  
Uniform Shear Flow ◽  
Appl Math ◽  
Edge Flow

An Oseén type linearization of the Navier-Stokes equations is made with respect to a uniform shear flow at the trailing edge of a flat plate. Asymptotic expansions are obtained to describe a symmetrical merging flow for distances from the trailing edge that are, in a certain sense, large. Expansions for three regions are found:(i) a wake region,(ii) an inviscid region, and(iii) an upstream lower order boundary layer.The results are compared with those of Hakkinen and O'Neil (Douglas Aircraft Co. Report, 1967) and Stewartson (Proc. Roy. Soc. Ser. A 306 (1968)). They are further related to the results of Stewartson (Mathematika 16 (1969)) and Messiter (SIAM J. Appl. Math. 18 (1970)).

scholarly journals Flow Analyses in a Single-Stage Propulsion Pump

1994 ◽  
Author(s):  
Yu-Tai Lee ◽  
Chunill Hah ◽  
James Loellbach
Keyword(s):  
Boundary Layer ◽  
Numerical Method ◽  
Turbulence Model ◽  
Eddy Viscosity ◽  
Single Stage ◽  
Acoustic Properties ◽  
Turbulent Eddy ◽  
Trailing Edge ◽  
Local Flow ◽  
Blade Row

Steady-state analyses of the incompressible flow past a single-stage stator/rotor propulsion pump are presented and compared to experimental data. The purpose of the current study is to validate a numerical method for the design application of a typical propulsion pump and for the acoustic analysis based on predicted flowfields. A steady multiple-blade-row approach is used to calculate the flowfields of the stator and the rotor. The numerical method is based on a fully conservative control-volume technique. The Reynolds-averaged Navier-Stokes equations are solved along with the standard two-equation k-ε turbulence model. Numerical results for both mean flow and acoustic properties compare well with measurements in the wake of each blade row. The rotor blade has a thick boundary layer in the last quarter of the chord and the flow separates near the trailing edge. These features invalidate many Euler prediction results. Due to the dramatic reduction of the turbulent eddy viscosity in the thick boundary layer, the standard k-ε model cannot predict the correct local flow characteristics near the rotor trailing edge and in its near wake. Thus, a modification of the turbulence length scale in the turbulence model is applied in the thick boundary layer in response to the reduction of the turbulent eddy viscosity.

Torsional oscillations of a plane in a viscous fluid

1959 ◽  
Vol 6 (2) ◽  
pp. 206-220 ◽  
Author(s):  
S. Rosenblat
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Order Term ◽  
Transverse Velocity ◽  
Axial Flow ◽  
Second Order ◽  
Navier Stokes ◽  
Order Flow ◽  
Finite Radius ◽  
Navier Stokes Equations

On the assumption that the rotational oscillations of a rigid plane are small, boundary-layer type solutions of the Navier-Stokes equations are attempted by an expansion of the velocity components in power series of the amplitude. First-and third-order approximations to the transverse velocity are obtained, from which a correction to the moment on a disk of finite radius is found.The first non-vanishing approximation to the radial-axial flow (a second-order term) is seen to have a steady component and a component with frequency twice that of the plate. The former component appears to persist outside the boundary layer, and at large distances from the plate to have the character of an irrotational stagnation flow. A re-examination not involving the series approximation reveals that although steady radial flow does exist outside the boundary layer, it is a viscous flow and is confined within a secondary layer. The ratio of the thicknesses of the two layers is found to be inversely proportional to the amplitude of the oscillations. These results indicate that a second-order flow in a region where the first-order flow field vanishes should not be accepted without further discussion.

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