Adiabatic Flat Plate Research Articles

A revised WENO‐THINC scheme for the general structured mesh and applications in the direct numerical simulation of compressible turbulent flows

AbstractThe Tangent of Hyperbola for INterface Capturing (THINC) scheme allows a jump‐like reconstruction and brings about a significant improvement in resolving the discontinuous part of the numerical solutions. However, it is found that the original THINC scheme loses accuracy when working on the stretched, curvilinear or highly‐skewed grid. In this study, we propose a simple strategy to determine the jump thickness parameter in the THINC function, so as to effectively suppress the unphysical oscillation. A Boundary Variation Diminishing (BVD) guideline is introduced to make options between the Weighted Essentially Non‐Oscillatory (WENO) scheme and the modified THINC scheme, thus both the smooth and discontinuous solutions can be reconstructed properly avoiding distortion of grids. Numerical validations indicate that the improved WENO‐THINC‐BVD approach maintains high resolution and is more robust on various types of non‐uniform meshes. The present method is further extended to validate the low‐dissipation property in resolving higher wave numbers portions by simulating an isotropic turbulence decay problem. Finally, we perform the direct numerical simulation (DNS) of a spatially evolving adiabatic flat plate boundary‐layer flow problem at a supersonic Mach number (). Numerical results show the predicted mean flow variables and the normalized shear stress agree well with the experimental data, significant improvements are found in the resolution of the small‐scale vortices, especially in the transition process.

Theoretical profiles of two-phase transcritical laminar boundary layer near the Widom line

Boundary layers can be defined as sub-, trans-, and supercritical regime according to whether their temperature profiles cross the Widom line. The transcritical boundary layers which contain liquid and supercritical phases are hard to solve. In this paper, adiabatic flat plate laminar boundary layers of supercritical carbon dioxide (SCO2) are preliminarily explored by the self-similar solution. We analyze the difference of boundary layer profiles at 8 MPa - inflow pressure by varying inflow temperature Te and Mach number Ma. The influence of Te and Ma on the velocity profiles exhibits complex diversity at three boundary layer regimes. Compared with subcritical and supercritical boundary layers, transcritical boundary layers with smaller skin friction coefficients are the most special, and they include the “sub-layer”. Notably, there is no transcritical boundary layer when Te increases to pseudo-critical temperature Tpc at small Ma. The wall temperature Tw of transcritical boundary layers may be greater than inflow total temperature T0 at larger Ma.

Effect of multi-hole trench cooling on an adiabatic flat plate for gas turbine application

Abstract A 3D numerical analysis on an adiabatic flat plate for multi-hole trench cooling with forward, backward and mixed injection holes is performed in the current investigation. The numerical setup is validated before the performances of different cooling configurations are compared. The effect of three different multi-hole trench arrangements, square-diamond, long-diamond, and super-long-diamond with constant perforated percentage (3.27%), on film cooling performance is studied at blowing ratio 1.0. The row-to-row interaction between coolant jets and mainstream is analysed, and lateral film cooling effectiveness is calculated downstream. The dimensionless temperature contour overlaid with streamlines concluded that the SLD trench hole arrangement with forward injection forms a developed effusion layer due to counter-rotating vortex pairs, which helps in proper mixing of coolant jets into the mainstream and improves film cooling effectiveness in lateral as well as in longitudinal direction. It is observed that super-long-diamond arrangement with forward injection provides the highest film cooling effectiveness than square-diamond and long-diamond arrangements and favours early development of the coolant film layer.

Effect of multi-zone effusion cooling on an adiabatic flat plate for gas turbine application

Abstract The present study performed a three-dimensional numerical analysis on an adiabatic flat plate with forward injection holes for multi-zone film cooling. The cooling holes were divided into three-zone, and the cold air was supplied from cylindrical holes at a velocity ratio of 0.5 and 1.5 with 30° inclination to the primary flow. The effect of multi-zone arrangement in film cooling effectiveness is studied, and a comparison between two-zone and three-zone arrangement has been made. Results show that the three-zone arrangement helps achieve better film cooling effectiveness than the two-zone arrangement due to the uniform flow of coolant at a higher velocity ratio. It also reduces the mass flow rate of secondary flow by decreasing the number of cylindrical holes in the perforated plate.

The Effect of Inclination on Natural Convective Heat Transfer from a Slender Cuboid

A numerical study was undertaken of the naturally occurring laminar convective heat transfer from a slender cuboid with a relatively narrow cross-section (square) and an exposed top surface. The cuboid was perpendicularly placed on an adiabatic flat base plate and two types of surface boundary conditions were considered. The slender cuboid was inclined relative to the vertical axis at angles ranging from 0 to 180 degrees. The flow was considered symmetrical along the vertical axis of the slender cuboid. The equations governing the system were numerically solved in terms of dimensionless variables using FLUENT software. From the results obtained, mean Nusselt numbers over the slender cuboid were calculated using parameters such as: the Rayleigh number for heat flux, Ra*; the Rayleigh number, Ra; the slender cuboid dimensionless width, i.e., the ratio of the width to the height of the heated slender cuboid, W = w/h; and the position of the slender cuboid relative to the vertical, φ. Simulation results were produced for the boundary conditions of constant temperature, constant heat flux, and for Pr = 0.7. The effects of these parameters on the mean Nusselt number for the combined and for the individual surfaces of the slender cuboid are presented and the mean Nusselt numbers are correlated.

Effect of multi-hole arrangement on the effusion cooling with backward injection

Abstract In the present work, a three-dimensional numerical analysis of multi-hole film cooling on an adiabatic flat plate with combined backward and forward injection holes is carried out at varying velocity ratios from 0.5 to 2.5. The effect of three different multi-hole arrangements, square-diamond, long-diamond, and super-long-diamond with constant perforated percentage (3.27%), on film cooling performance is studied. Combining backward and forward injection holes help in achieving higher velocity boundary layer thickness in the multi-hole arrangement. It is observed that super-long-diamond arrangement provides the highest film cooling effectiveness than square-diamond and long-diamond arrangements and favours early development of coolant film layer.

Effect of multi-hole arrangement on the effusion cooling with backward injection

Abstract In the present work, a three-dimensional numerical analysis of multi-hole film cooling on an adiabatic flat plate with combined backward and forward injection holes is carried out at varying velocity ratios from 0.5 to 2.5. The effect of three different multi-hole arrangements, square-diamond, long-diamond, and super-long-diamond with constant perforated percentage (3.27%), on film cooling performance is studied. Combining backward and forward injection holes help in achieving higher velocity boundary layer thickness in the multi-hole arrangement. It is observed that super-long-diamond arrangement provides the highest film cooling effectiveness than square-diamond and long-diamond arrangements and favours early development of coolant film layer.

Film cooling behind two rows of trenches on a flat surface

The paper presents the results of computer simulation of film cooling behind two rows of trenches on an adiabatic flat plate with coolant supply through inclined round holes in the trench. The calculations were carried out in the wide range of injection parameter from 0.4 to 2.2 using the commercial computer package ANSYS CFX 14 and the SST turbulence model. It was found that for the injection parameter m > 0.6, the asymmetry in the film cooling effectiveness is observed behind the second trench increasing with the injection parameter growth. This is explained by the unsteady nature of interaction of the cooling jets discharged from holes of the first and second rows. In the area between the first and second rows of trenches near the end “strips”, the film cooling effectiveness is 5–10% higher than near the middle ones, however, behind the second trench it is 8–20 % lower, due to the staggered arrangement of the injection holes in trenches. For all injection parameters, the globally-averaged film cooling effectiveness near the end “strips” of the adiabatic surface is lower than that near the middle ones.

Hybrid RANS-LES of Shaped Hole Film Cooling on an Adiabatic Flat Plate at Low Reynolds Number

Hybrid RANS-LES methods offer a means of reducing computational cost and setup time to simulate transitional flows. Several methods are evaluated in ANSYS CFX, including Scale-Adaptive Simulation (SAS), Shielded Detached Eddy Simulation (SDES), Stress-Blended Eddy Simulation (SBES), and Zonal Large Eddy Simulation (ZLES), along with a no-model laminar simulation. Each is used to simulate an adiabatic flat plate film cooling experiment of a shaped hole at low Reynolds number. Adiabatic effectiveness is calculated for Blowing Ratio (BR) = 1.5 and Density Ratio (DR) = 1.5. The ZLES method and laminar simulation most accurately match experimental lateral-average adiabatic effectiveness along the streamwise direction from the trailing edge of the hole to 35 hole diameters downstream of the hole (X/D = 0 to X/D = 35), with RMS deviations of 5.1% and 4.2%, and maximum deviations of 8% and 11%, respectively. The accuracy of these models is attributed to the resolution of turbulent structures in not only the mixing region but in the upstream boundary layer as well, where the other methods utilize RANS and do not switch to LES.

Effect of Injection Angle on Performance of Full Coverage Film Cooling with Opposite Injection Holes

Abstract Characteristics of full coverage film cooling of an adiabatic flat plate are studied for opposite injection of coolant at different angles. Two in-line adjacent rows of cooling holes injecting in opposite directions are considered in this study. The cooling performance is compared with the configurations having forward and reverse injecting holes at similar injection angles. The holes are arranged in an array of 20 rows with equal spacing both span-wise and stream-wise. Computational analyses are carried out over a wide range of velocity ratios (VR) of practical importance ranging from 0.5 to 2.0 at density ratio of about 1.0. Injection angle and velocity ratio are found to have strong influence on film cooling effectiveness of opposite injection. At low velocity ratio of VR=0.5, film cooling performance of opposite injection at 45° is found better than at other angles, i. e. 30° and 60°. At higher velocity ratios, injection at 30° is found superior. Film cooling effectiveness becomes insensitive to velocity ratios at higher range for 45° and 60° injections. Evolution of effusion film layer and interaction between coolant and primary flow is also studied in this paper.

Enhancement of Full Coverage Film Cooling Effectiveness with Mixed Injection Holes

Abstract In the present work numerical study of full coverage film cooling on an adiabatic flat plate is carried out. Cooling performance of three configurations of cylindrical holes is studied with downstream injection, upstream injection and mixed injection. In mixed injection configuration one column of holes inject in downstream direction and the holes in the adjacent column inject in the upstream direction. Numerical simulations are carried out at different velocity ratios and circumferentially averaged value of adiabatic film cooling effectiveness is estimated. Simulation results indicate that the mixed injection configuration has better and more uniform cooling, throughout the perforated plate, than with downstream injection. The difference is greater with increase in the velocity ratio. Configuration with upstream injection gives better cooling than mixed injection at front few rows of cooling holes but it shows poorer performance with downstream injection in the downstream rows of cooling holes. The obtained results from this study can be an invaluable input for highly loaded combustion chambers.

Enhancement of full coverage film cooling performance with opposite injection holes

In the present work numerical study of effusion cooling on an adiabatic flat plate is carried out for three different configurations of cylindrical holes namely forward injection, reverse injection and opposite injection. Opposite injection configuration comprises of holes with both forward and reverse injections where holes just in front of the other inject in opposite directions. The holes are arranged in an array of 20 rows with spanwise hole-to-hole pitch (p) of 4.9d and streamwise hole-to-hole pitch (s) of 4.9d.Diameter (d) of the cylindrical holes is 1.0 mm. The injection angles are 30° for forward injection and 150° for reverse injection holes. Numerical simulations are carried out for a wide range of velocity ratios (VR) ranging from 0.25 to 5.0 and at density ratio (DR) of about 1.0. Laterally averaged adiabatic film cooling effectiveness is calculated to study the film cooling performance of the three configurations. Opposite injection demonstrates higher and more uniform cooling than forward and reverse injections especially at high velocity ratio. At higher velocity ratio, area weighted average of film cooling effectiveness for opposite injection is found around 30% higher than that for forward injection and around 10% higher than that for reverse injection configurations. Opposite injection also supports early growth of developed effusion film layer from developing stage

Computational study of drag increase due to wall roughness for hypersonic flight

ABSTRACTIn this study, a series of numerical experiments are performed on supersonic/hypersonic flows over an adiabatic flat plate with transitionally and fully rough surfaces. The Mach numbers simulated are 4, 5, 6, and 7; the flight heights considered are 20, 24, 28, 32, and 36 km. First, a modified roughness correction is proposed and validated with the measured data for low-speed flat-plate cases. It is verified that for the equivalent sand grain heights in the intermediate and fully rough regimes, there is a good agreement with the semi-empirical formula available in the open literature. Then, this roughness correction is applied to high-speed flow regime to investigate the effects of flight heights and Mach numbers on drag for rough-wall flat-plate cases. It is found that within the roughness measured in real flight, the roughness height change has little effect on drag compared to the variations of both flight heights and Mach numbers. The drag coefficient derivation between rough-wall and smooth-wall conditions, achieves the maximum value of 0.79% for the 60 cases selected.

Numerical study of effusion cooling on an adiabatic flat plate

The present study aims to investigate the effectiveness of effusion film cooling on an adiabatic flat plate. Cylindrical holes of 30° inclination are used for supplying cold air to the hot primary flow. A non-dimensional parameter called the film cooling effectiveness is calculated for studying the influence of the velocity ratio for a continuous array of cooling holes. A new approach by splitting the full coverage of film holes into two zones of cooling rows is presented in this paper. The computational results from the investigation show that there exists strong relationship between velocity ratio and adiabatic film cooling effectiveness. The simulations of two zones indicate that a careful analysis of the distribution of cooling holes can significantly reduce the demand for the supply of cold air.

Improving Low-Frequency Characteristics of Recycling/Rescaling Inflow Turbulence Generation

For the study of turbulent flows with low-frequency dynamics (e.g. shock-wave/boundary-layer interactions), it is desirable that the inflow turbulence does not contaminate the solution with spurious spatiotemporal correlations introduced by the mechanism of inflow turbulence generation. To investigate the creation and mitigation of these adverse low-frequency effects, large-eddy simulation of a Mach 2.28 boundary layer over an adiabatic flat plate is carried out using a typical recycling/rescating procedure. Spurious temporal autocorrelations and energy spectral peaks are observed associated with the recycling frequency and its harmonics. Comparisons are made with common synthetic turbulence-generation techniques, and improvements to the standard recycling/rescaling procedure are suggested to substantially reduce or eliminate the inherent low-frequency contamination. It is found that by applying a nonconstant reflection or translation operation to the recycled turbulence plane at randomly-distributed time intervals, one is able to maintain realistic turbulence without low-frequency contamination.

Numerical Simulation and Theoretical Analysis of Perturbations in Hypersonic Boundary Layers

Direct numerical simulations of receptivity in a boundary layer over a flat plate and a sharp wedge were carried out with two-dimensional perturbations introduced into the flow by periodic-in-time blowing-suction through a slot. The free stream Mach numbers are equal to 5.92 and 8 in the cases of adiabatic flat plate and sharp wedge, respectively. The perturbation flow field was decomposed into normal modes with the help of the multimode decomposition technique based on the spatial biorthogonal eigenfunction system. The decomposition allows filtering out the stable and unstable modes hidden behind perturbations having another physical nature.

Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at M=2.25

A spatially developing supersonic adiabatic flat plate boundary layer flow (at M∞=2.25 and Reθ≈4000) is analyzed by means of direct numerical simulation. The numerical algorithm is based on a mixed weighted essentially nonoscillatory compact-difference method for the three-dimensional Navier–Stokes equations. The main objectives are to assess the validity of Morkovin’s hypothesis and Reynolds analogies, and to analyze the controlling mechanisms for turbulence production, dissipation, and transport. The results show that the essential dynamics of the investigated turbulent supersonic boundary layer flow closely resembles the incompressible pattern. The Van Driest transformed mean velocity obeys the incompressible law-of-the-wall, and the mean static temperature field exhibits a quadratic dependency upon the mean velocity, as predicted by the Crocco–Busemann relation. The total temperature has been found not to be precisely uniform, and total temperature fluctuations are found to be non-negligible. Consistently, the turbulent Prandtl number is not unity, and it varies between 0.7 and 0.8 in the outer part of the boundary layer. Nonetheless, a modified strong Reynolds analogy is still verified. In agreement with the low Mach number results, the streamwise velocity component and the temperature are only weakly anti-correlated. The turbulent kinetic energy budget also shows similarities with the incompressible case provided all terms of the equation are properly scaled; indeed, the leading compressibility contributions are negligible throughout the boundary layer.

Heat transfer characteristics of a boundary-layer flow driven by a power-law shear over a semi-infinite flat plate

The hydrodynamic and thermal boundary layer similarity flows driven past a semi-infinite impermeable flat plate by a power-law shear with asymptotic velocity profile U ∞( y)= βy −1/2 ( y→∞, β>0) is considered ( y denotes the coordinate normal to the plate). Assuming that the buoyancy and viscous dissipation effects may be neglected, the special cases of an isothermal and of an adiabatic flat plate are examined both analytically and numerically.

Large-Eddy Simulation of a Supersonic Boundary Layer Using an Unstructured Grid

A Mach 3 adiabatic flat plate turbulent boundary layer is studied using large-eddy simulation (LES). The filtered compressible Navier-Stokes equations are solved on a three-dimensional unstructured grid of tetrahedral cells. A compressible extension of the rescaling-reintroducing process of Lund et al. is developed to generate the inflow conditions. The effect of the subgrid-scale motion is incorporated using two approaches, namely, monotone integrated LES (MILES) and the Smagorinsky subgrid-scale model. A detailed grid refinement study is performed

Variations on a [formula omitted]– [formula omitted] turbulence model for supersonic boundary layer computations

Several modifications of the baseline k– ε model are considered for the computation of supersonic boundary layers on an adiabatic flat plate, up to Mach number 5. The numerical computations are performed with particular reference to well documented experiments. Three versions of a two-equation low-Reynolds number model and a two-layer model are used. They were originally defined for incompressible flows and have to be extended to compressible cases. Slight alterations of the original formulation are necessary to obtain good numerical performances. The use of compressibility models is also investigated, as well as a possible simple modification of the dissipation rate equation to take into account the turbulence balance in the logarithmic region. The numerical results are in good agreement with the experimental data. Some numerical issues are addressed and the importance of suitable boundary conditions is pointed out.