Numerical modelling of film cooling from converging slot-hole

This paper presents a numerical prediction of a new 3D film cooling hole geometry, the converging slot-hole or console. The console geometry is designed in order to improve the heat transfer and aerodynamic loss performance of turbine vane and rotor blade cooling systems without loosing the mechanical strength of a row of discrete holes. The cross section of the console changes from a circular shape at the inlet to a slot at the exit. Previous successful application of a new anisotropic DNS based two-layer turbulence model to cylindrical and shaped hole injections is extended to predict film cooling for the new console geometry. The suitability of the proposed turbulence model for film cooling flow is validated by comparing the computed and the measured wall-temperature distributions of cylindrical hole injections. The result shows that the anisotropic eddy-viscosity/diffusivity model can correctly predict the spanwise spreading of the temperature field and reduce the strength of the secondary vortices. Comparative computations of the adiabatic film cooling effectiveness associated with the three geometries tested in the present study (cylindrical, shaped, and console) show that the new console film-cooling hole geometry is definitely superior to the other geometries as shown by the uniform lateral spreading of the effectiveness with a slight enhancement downstream of the intersection of the two consoles.     

Wind tunnel simulation of wind effect on a group of high Cooling towers

Aerodynamic interference between high cooling towers in the atmospheric boundary layer (ABL) and uniform flow has been discussed. For the 1/1000 ABL model set up in the 2.25m low speed wind tunnel at Peking University, the similarity condition of the cooling tower in the ABL, the simulation results of a single tower and some typical tower groups have been provided. Experiments showed that the Circumferential pressure distributions were consistent between the smooth model tower and the prototype tower, and between the rough model tower and the prototype tower with ribs; the two dimensional characteristics in the circumferential pressure distribution were also noticeable around the middle 1/3 part of the tower after nondimensionalization by local dynamic pressure. Results demonstrate that, in the flow with strong turbulence the lift coefficient of the downstream cylinder approaches 0.4. In the flow with weak turbulence, the pressure distribution reflects a strong nonsymmetry, and the lift coefficient or stagnation pressure of the downstream cylinder switches alternately between 1 and 0, where a concentrated vortex rolls up and then sheds toward the front of the downstream cylinder and exerts a decisive influence on the aerodynamic properties of the downstream cylinder.     

Effect of incidence angle with wake passing on a film cooled leading edge: A numerical study

This work presents the numerical study of a film‐cooled blade under the influence of wake passing at different incidence angles. The film cooling technology has been proven to be effective to increase the blade life of first turbine stages. However, the leading edge is affected by an high heat transfer rate and cooling this region is difficult. Moreover, separated regions downstream the coolant injection increases the local heat transfer coefficient and can have a detrimental effect in terms of airfoil life. This work analyses how the flow field is affected by the wake passing at different incidence angles (?5, 0, 5) and the impact on heat transfer coefficient. The test case is a linear cascade with two rows of cylindrical holes at the leading edge. Two different holes arrangements are compared in terms of film cooling structures, namely AGTB‐B1 and AGTB‐B2 with 0 and 45^° spanwise inclination. The numerical results show a good agreement with the experiments. A deeper investigation is carried out on AGTB‐B1. The results obtained show that the wake passing and the incidence angle have a strong effect on coolant jets. In particular, there is a significative impact on coolant redistribution near the leading edge. The wake passing has a stronger effect on pressure side, mainly at negative incidence. The predictive approach is based on an U‐RANS in‐house CFD solver using a conventional two‐equations closure. In order to avoid extra turbulence production, critical in the leading edge region, the turbulence model incorporates an extra algebraic equation that enforces a realizability constraint. The unsteady formulation is based on a dual time stepping approach with a sliding plane between the moving bars and the cascade. Copyright © 2009 John Wiley & Sons, Ltd.     

Aerodynamic performance of an annular cascade of film cooled nozzle guide vanes under engine representative conditions

This paper addresses two important issues relevant to efficiency measurements in film-cooled annular cascades: the definition of the ideal flow to be used in loss calculation, and the measurements that are necessary for such loss calculation. The paper also addresses the question of the correct parameterisation of coolant density effects, showing that the momentum flux ratio, rather than the blowing rate, is the most appropriate parameter. Experiments examining the effect of extensive aerofoil surface film cooling on the aerodynamic efficiency of an annular cascade of transonic nozzle guide vanes are reported. A dense foreign gas (SF₆/Ar mixture) is used to simulate engine representative coolant-to-mainstream density ratios, momentum ratios and blowing rates under ambient temperature conditions. Experiments are also conducted with air coolant to study the effect of density ratio on efficiency. The flowfield measurements have been obtained using a four-hole pyramid probe in a short duration blowdown facility which correctly models engine Reynolds and Mach numbers. This work compares the measured aerodynamic efficiencies of uncooled vanes with those which employ an extensive amount of cooling. The engine-representative cooling geometry investigated features 14 rows of cylindrical cooling holes, and a second geometry where 8 of these rows are replaced by holes having a fan-shaped exit. The effects of adding trailing edge slot ejection are also presented. By selectively blocking rows of holes, the cumulative effect on the mid-span efficiency of adding rows of cooling holes has also been determined. Experimental results are presented as area traverse maps (total pressure, isentropic Mach number and flow angles), from which the relative changes in efficiency due to film cooling have been calculated. These calculations reveal that the presence of foreign-gas coolant from the cylindrical-hole geometry increases the aerodynamic loss (relative to the uncooled baseline) by 6.7%; and coolant from the fan-shaped holes increases the loss by 15%. The effects of different assumptions for the coolant total pressure are shown to significantly change the measured loss; if the loss measurements are based on the mainstream total pressure, rather than the total pressure in the coolant cavity, the respective increase in loss (relative to the uncooled baseline) of cylindrical and fan-shaped holes is 4.5% and 12.5%. Experimental data is compared with loss predictions using a Hartsel model. Received: 4 December 1998/Accepted: 1 September 1999     

Two‐dimensional prediction of time dependent,turbulent flow around a square cylinder confined in a channel

This paper presents two‐dimensional and unsteady RANS computations of time dependent, periodic, turbulent flow around a square block. Two turbulence models are used: the Launder–Sharma low‐Reynolds number k–ε model and a non‐linear extension sensitive to the anisotropy of turbulence. The Reynolds number based on the free stream velocity and obstacle side is Re=2.2×10⁴. The present numerical results have been obtained using a finite volume code that solves the governing equations in a vertical plane, located at the lateral mid‐point of the channel. The pressure field is obtained with the SIMPLE algorithm. A bounded version of the third‐order QUICK scheme is used for the convective terms. Comparisons of the numerical results with the experimental data indicate that a preliminary steady solution of the governing equations using the linear k–ε does not lead to correct flow field predictions in the wake region downstream of the square cylinder. Consequently, the time derivatives of dependent variables are included in the transport equations and are discretized using the second‐order Crank–Nicolson scheme. The unsteady computations using the linear and non‐linear k–ε models significantly improve the velocity field predictions. However, the linear k–ε shows a number of predictive deficiencies, even in unsteady flow computations, especially in the prediction of the turbulence field. The introduction of a non‐linear k–ε model brings the two‐dimensional unsteady predictions of the time‐averaged velocity and turbulence fields and also the predicted values of the global parameters such as the Strouhal number and the drag coefficient to close agreement with the data. Copyright © 2009 John Wiley & Sons, Ltd.     

An application of the finite difference‐based lattice Boltzmann model to simulating flow‐induced noise

This paper presents a novel approach to simulate aerodynamically generated sounds by modifying the finite difference‐based lattice BGK compressible fluid model for the purpose of speeding up the calculation and also stabilizing the numerical scheme. With the model, aerodynamic sounds generated by a uniform flow around a two‐dimensional circular cylinder at Re = 150 are simulated. The third‐order‐accurate up‐wind scheme is used for the spatial derivatives, and the second‐order‐accurate Runge–Kutta method is applied for the time marching. The results show that we successively capture very small acoustic pressure fluctuations, with the same frequency of the Karman vortex street, much smaller than the whole pressure fluctuation around a circular cylinder. The propagation velocity of the acoustic waves shows that the points of peak pressure are biased upstream owing to the Doppler effect in the uniform flow. For the downstream, on the other hand, it is faster. It is also apparent that the amplitude of sound pressure is proportional to r^?1/2, r being the distance from the centre of the circular cylinder. Moreover, the edgetone generated by a two‐dimensional jet impinging on a wedge to predict the frequency characteristics of the discrete oscillations of a jet‐edge feedback cycle is investigated. The jet is chosen long enough to guarantee the parabolic velocity profile of the jet at the outlet, and the edge is of an angle of α = 23°. At a stand‐off distance w, the edge is inserted along the centreline of the jet, and a sinuous instability wave with real frequency is assumed to be created in the vicinity of the nozzle exit and to propagate towards the downstream. We have succeeded in capturing small pressure fluctuations resulting from periodic oscillation of jet around the edge. Copyright © 2006 John Wiley & Sons, Ltd.     

High order numerical simulation of the thermal load on a lobed strut injector for scramjet applications

In this paper, the thermal load on an actively cooled lobed strut injector for scramjet (supersonic combustion ramjet) applications is investigated numerically. This requires coupled simulations of the strut internal and external flow fields together with the heat conduction in the solid injector body. In order to achieve a fast mixing, the lobed strut is positioned at the channel axis to inject hydrogen into the core of a Mach 3 air stream. There it is exposed to the extremely high temperatures of the high speed flow. While the external air and hydrogen flows are supersonic, the strut internal hydrogen flow is mainly subsonic, in some regions at very low Mach numbers. To enable a simulation of the internal flow field which ranges from very low to very high Mach numbers (approximately Mach 2.25 at the nozzle exit), a preconditioning technique is employed. The compressible finite‐volume scheme uses a spatially fourth order multi‐dimensional limiting process discretization, which is used here for a first time to simulate a geometrically and fluid mechanically highly complex problem. It will be demonstrated that besides its high accuracy the multi‐dimensional limiting process scheme is numerically stable even in case of demanding practical applications. The coupled simulation of the lobed strut injector delivers unique insight into the flow phenomena inside and outside the strut, the heat fluxes, the temperature distribution in the solid material, the required hydrogen mass flux with respect to cooling requirements and details concerning the conditions at the exit of the injector. Copyright © 2016 John Wiley & Sons, Ltd.     

The effect of turbulence intensity on film cooling of gas turbine blade from trenched shaped holes

This paper reports a computational investigation on the effects of mainstream turbulence intensity on film cooling effectiveness from trenched holes over a symmetrical blade. Computational solutions of the steady, Reynolds-Averaged Navier–Stokes equations are obtained using a finite volume method with k − ε Turbulence model. Whenever possible, computational results are compared with experimental ones from data found in the open literature. Computational results are presented for a row of 25° forward-diffused film hole within transverse slot injected at 35° to AGTB symmetrical blade. Four blowing ratios, M = 0.3, 0.5, 0.9 and 1.3 are studied together with four mainstream turbulence intensities of Tu = 0.5, 2, 4 and 10%. Results indicate that the trenched shaped holes tend to give better film cooling effectiveness than that obtained from discrete shaped holes for all blowing ratios and all turbulence intensities. The trenching of shaped holes has changed the optimum blowing ratio and also the location of re-attachment of separated jet at high blowing ratios. Moreover, it has been found that the effect of mainstream turbulence intensity for trenched shaped holes is similar to that obtained for discrete shaped holes with the exception that the sensitivity of film cooling effectiveness to turbulence intensity has decreased for trenched shaped holes.     

Numerical simulation of transpiration cooling through porous material

Transpiration cooling using ceramic matrix composite materials is an innovative concept for cooling rocket thrust chambers. The coolant (air) is driven through the porous material by a pressure difference between the coolant reservoir and the turbulent hot gas flow. The effectiveness of such cooling strategies relies on a proper choice of the involved process parameters such as injection pressure, blowing ratios, and material structure parameters, to name only a few. In view of the limited experimental access to the subtle processes occurring at the interface between hot gas flow and porous medium, reliable and accurate simulations become an increasingly important design tool. In order to facilitate such numerical simulations for a carbon/carbon material mounted in the side wall of a hot gas channel that are able to capture a spatially varying interplay between the hot gas flow and the coolant at the interface, we formulate a model for the porous medium flow of Darcy–Forchheimer type. A finite‐element solver for the corresponding porous medium flow is presented and coupled with a finite‐volume solver for the compressible Reynolds‐averaged Navier–Stokes equations. The two‐dimensional and three‐dimensional results at Mach number Ma = 0.5 and hot gas temperature T_HG=540 K for different blowing ratios are compared with experimental data. Copyright © 2014 John Wiley & Sons, Ltd.     

On the performance of sudden‐expansion pipe without/with cross‐flow injection: experimental and numerical studies

The paper explores the possibilities that different turbulence closures offer, for in‐depth analysis of a complex flow. The case under investigation is steady, turbulent flow in a pipe with sudden expansion without/with normal‐to‐wall injection through jets. This is a typical geometry where generation of turbulence energy takes place, due to sudden change in boundary conditions. This study is aimed at investigating the capability of a developed computational program by the present authors with three different turbulence models to calculate the mean flow variables. Three two‐equation models are implemented, namely the standard linear k ? ε model, the low Reynolds number k ? ε model and the cubic nonlinear eddy viscosity (NLEV) k ? ε model. The performance of the chosen turbulence models is investigated with regard to the available data in the literature including velocity profiles, turbulent kinetic energy and reattachment position in a pipe expansion. In order to further assess the reliability of the turbulence models, an experimental program was conducted by the present authors also at the fluid mechanics laboratory of Menoufiya University. Preliminary measurements, including the surface pressure along the two walls of the expansion pipe and the pressure drop without and with the presence of different arrangements of wall jets produced by symmetrical or asymmetrical fluid cross‐flow injection, are introduced. The results of the present studies demonstrate the superiority of the cubic NLEV k ? ε model in predicting the flow characteristics over the entire domain. The simple low Reynolds number k ? ε model also gives good prediction, especially when the reattachment point is concerned. The evaluation of the reattachment point and the pressure‐loss coefficient is numerically addressed in the paper using the cubic NLEV k ? ε model. The results show that the injection location can control the performance of the pipe‐expansion system. It is concluded that the introduction of flow injection can increase the energy loss in the pipe expansion. The near‐field turbulence structure is also considered in the present study and it is noticed that the turbulence level is strongly affected by the cross‐flow injection and the jet location. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical and experimental investigation of transverse injection flows

The flow field resulting from a transverse injection through a slot into supersonic flow is numerically simulated by solving Favre-averaged Navier–Stokes equations with κ − ω SST turbulence model with corrections for compressibility and transition. Numerical results are compared to experimental data in terms of surface pressure profiles, boundary layer separation location, transition location, and flow structures at the upstream and downstream of the jet. Results show good agreement with experimental data for a wide range of pressure ratios and transition locations are captured with acceptable accuracy. κ − ω SST model provides quite accurate results for such a complex flow field. Moreover, few experiments involving a sonic round jet injected on a flat plate into high-speed crossflow at Mach 5 are carried out. These experiments are three-dimensional in nature. The effect of pressure ratio on three-dimensional jet interaction dynamics is sought. Jet penetration is found to be a non-linear function of jet to free stream momentum flux ratio.     

Pressure recovery in a radiused sudden expansion

Experiments on a steady flow through a nominally 2-D exit geometry with rounded edges are presented for the Reynolds number range 300<Re<25,000. The results indicate that the channel flow expands and decelerates upstream of the exit plane resulting in large pressure recovery, especially for turbulent channel flow. It is shown that pressure recovery is a function of the dimensionless edge radius and Re. Pressure recoveries of up to 20% are reported at large Re for dimensionless radii as small as r/h=0.625. It is also found that the rounded exit results in turbulence levels as much as 25% higher than sharp-edged exits.     

Prediction of developing turbulent flow in 90°‐curved ducts using linear and non‐linear low‐Re k–ε models

This paper reports the outcome of applying two different low‐Reynolds‐number eddy‐viscosity models to resolve the complex three‐dimensional motion that arises in turbulent flows in ducts with 90^° bends. For the modelling of turbulence, the Launder and Sharma low‐Re k–ε model and a recently produced variant of the cubic non‐linear low‐Re k–ε model have been employed. In this paper, developing turbulent flow through two different 90^° bends is examined: a square bend, and a rectangular bend with an aspect ratio of 6. The numerical results indicate that for the bend of square cross‐section the curvature induces a strong secondary flow, while for the rectangular cross‐section the secondary motion is confined to the corner regions. For both curved ducts, the secondary motion persists downstream of the bend and eventually slowly disappears. For the bend of square cross‐section, comparisons indicate that both turbulence models can produce reasonable predictions. For the bend of rectangular cross‐section, for which a wider range of data is available, while both turbulence models produce satisfactory predictions of the mean flow field, the non‐linear k–ε model returns superior predictions of the turbulence field and also of the pressure and friction coefficients. Copyright © 2006 John Wiley & Sons, Ltd.     

A numerical evaluation on the effect of sister holes on film cooling effectiveness and the surrounding flow field

A numerical study was performed to evaluate the effectiveness of the novel sister hole film cooling technique. Two secondary coolant holes bound the primary coolant hole slightly downstream of its midpoint, intended to minimize the primary vortex pair and improve cooling performance. An unstructured hexahedral mesh was generated and the realizable k–ε turbulence model with near-wall modeling was used in these simulations. Blowing ratios of 0.2, 0.5, 1.0, and 1.5 were simulated to evaluate the applicability of sister holes in practical applications. It was found that sister holes significantly improved cooling performance over the entire computational domain, particularly at high blowing ratios. These results arose by countering the primary vortex pair with a secondary pair from these sister holes, ultimately maintaining flow adhesion where the coolant stream would have otherwise separated.     

Numerical study of magnetohydrodynamic laminar flow separation in a channel with smooth expansion

The flow of an electrically conducting incompressible viscous fluid in a plane channel with smooth expansion in the presence of a uniform transverse magnetic field has been analysed. A solution technique for the governing magnetohydrodynamic equations in primitive variable formulation has been developed. A co‐ordinate transformation has been employed to map the infinite irregular domain into a finite regular computational domain. The governing equations are discretized using finite‐difference approximations in staggered grid. Pressure Poisson equation and pressure correction formulae are derived and solved numerically. It is found that with increase in the magnetic field, the size of the flow separation zone diminishes and for sufficiently large magnetic field, the separation zone disappears completely. The peak u‐velocity decreases with increase in the magnetic field. It is also found that the asymmetric flow in a symmetric geometry, which occurs at moderate Reynolds numbers, becomes symmetric with sufficient increase in the transverse magnetic field. Thus, a transverse magnetic field of suitable strength has a stabilizing effect in controlling flow separation, as also in delaying the transition to turbulence. Copyright © 2008 John Wiley & Sons, Ltd.     

Numerical simulation of two‐dimensional laminar slot‐jet impingement flows confined by a parallel wall

Two‐dimensional laminar incompressible impinging slot‐jet is simulated numerically to gain insight into flow characteristics.Computations are done for vertically downward‐directed slot‐jets impinging on a plate at the bottom and confined by a parallel surface on top. The behaviour of the jet with respect to aspect ratio (AR) and Reynolds number (Re) are described in detail. The computed flow patterns for various AR (2–5) and for a range of jet‐exit Reynolds numbers (100–500) are analysed to understand the flow characteristics. The transient development of the flow is also simulated for AR = 4 and Re = 300. It is found that the reattachment length is dependent on both AR and Reynolds number for the range considered. The correlation for reattachment length is suggested. The maximum resultant velocity V_rmax and its trajectory is reported. A detailed study of horizontal velocity profile at different downstream locations is reported. It is found that the effect of Reynolds number and AR is significant to the bottom wall vorticity in the impingement and wall jet regions. Copyright © 2007 John Wiley & Sons, Ltd.     

Simulations of high‐aspect‐ratio jets

There are many practical situations when jets are emanating from non‐axis‐symmetric apertures, yet numerical simulations of such three‐dimensional jets are scarce and most of them have failed to reproduce some of the unique flow features. Examples of this type of jets are gas leaks from flanges. These can be treated as jets issuing from high aspect ratio rectangular orifices. The present work consists of a series of large eddy simulations typifying such jets using different inflow boundary conditions. Good agreement with available experiments was observed provided appropriate boundary conditions were present. A discrete method for formulating turbulence data with a known energy spectrum for an inflow condition is outlined and evaluated with three other inflow conditions–a steady uniform profile, a steady parabolic profile and pseudo‐random noise. The implementation of the new inlet condition results in a more realistic centreline velocity decay where the division between the end of the potential core region and the start of the characteristic decay region is clearly visible. Large velocity oscillations are also observed in the final quarter of the domain (15–20 slot widths downstream). Similar oscillations have been observed in real jets. Off‐centre mean velocity peaks are present along the major axis 10 slot widths downstream of the exit in all the simulations. The peaks are approximately 3% of the centreline velocity. The presence of the off‐centre peaks are proved to be independent of jet inflow boundary conditions and an explanation for the mechanism causing the off‐centre peaks is given. Copyright © 2002 John Wiley & Sons, Ltd.     

A two‐scale low‐Reynolds number turbulence model

In this study, a two‐scale low‐Reynolds number turbulence model is proposed. The Kolmogorov turbulence time scale, based on fluid kinematic viscosity and the dissipation rate of turbulent kinetic energy (ν, ε), is adopted to address the viscous effects and the rapid increasing of dissipation rate in the near‐wall region. As a wall is approached, the turbulence time scale transits smoothly from a turbulent kinetic energy based (k, ε) scale to a (ν, ε) scale. The damping functions of the low‐Reynolds number models can thus be simplified and the near‐wall turbulence characteristics, such as the ε distribution, are correctly reproduced. The proposed two‐scale low‐Reynolds number turbulence model is first examined in detail by predicting a two‐dimensional channel flow, and then it is applied to predict a backward‐facing step flow. Numerical results are compared with the direct numerical simulation (DNS) budgets, experimental data and the model results of Chien, and Lam and Bremhorst respectively. It is proved that the proposed two‐scale model indeed improves the predictions of the turbulent flows considered. Copyright © 2000 John Wiley & Sons, Ltd.     

On the construction of manufactured solutions for one and two‐equation eddy‐viscosity models

This paper presents manufactured solutions (MSs) for some well‐known eddy‐viscosity turbulence models, viz. the Spalart & Allmaras one‐equation model and the TNT and BSL versions of the two‐equation k–ω model. The manufactured flow solutions apply to two‐dimensional, steady, wall‐bounded, incompressible, turbulent flows. The two velocity components and the pressure are identical for all MSs, but various alternatives are considered for specifying the eddy‐viscosity and other turbulence quantities in the turbulence models. The results obtained for the proposed MSs with a second‐order accurate numerical method show that the MSs for turbulence quantities must be constructed carefully to avoid instabilities in the numerical solutions. This behaviour is model dependent: the performance of the Spalart & Allmaras and k–ω models is significantly affected by the type of MS. In one of the MSs tested, even the two versions of the k–ω model exhibit significant differences in the convergence properties. Copyright © 2006 John Wiley & Sons, Ltd.