BEM/FDM conjugate heat transfer analysis of a two-dimensional air-cooled turbine blade boundary layer

A coupled boundary element method （BEM） and finite difference method （FDM） are applied to solve conjugate heat transfer problem of a two-dimensional air-cooled turbine blade boundary layer. A loosely coupled strategy is adopted, in which each set of field equations is solved to provide boundary conditions for the other. The Navier-Stokes equations are solved by HIT-NS code. In this code, the FDM is adopted and is used to resolve the convective heat transfer in the fluid region. The BEM code is used to resolve the conduction heat transfer in the solid region. An iterated convergence criterion is the continuity of temperature and heat flux at the fluid-solid interface. The numerical results from the BEM adopted in this paper are in good agreement with the results of analytical solution and the results of commercial code, such as Fluent 6.2. The BEM avoids the complicated mesh needed in other computation method and saves the computation time. The results prove that the BEM adopted in this paper can give the same precision in numerical results with less boundary points. Comparing the conjugate results with the numerical results of an adiabatic wall flow solution, it reveals a significant difference in the distribution of metal temperatures. The results from conjugate heat transfer analysis are more accurate and they are closer to realistic thermal environment of turbines.     

An experimental investigation of the dissipation mechanisms in the suction side boundary layer of a turbine blade

The present work is part of an extensive experimental activity carried out by the authors in recent years aimed at investigating the boundary layer transition phenomenon in turbine blades. The large scale of the cascade and the use of advanced LDV instrumentation and precision probe traversing mechanism resulted in high degree of spatial resolution and high accuracy of measurements. The main dissipation mechanism determining the profile losses in turbomachinery blades is the work of deformation of the mean motion within the boundary layer operated by both viscous and turbulent shear stresses. In the present paper, the local viscous and turbulent deformation works have been directly evaluated from the detailed measurements of boundary layer mean velocity and Reynolds shear stress. The results show the distributions and the relative importance of the viscous and turbulent contributions to the loss production, in relation with the boundary layer states occurring along the turbine profile.     

Study of transition from laminar to turbulent boundary layer on a tilted flat plate using heat transfer measurements

The boundary layer transition over a flat tilted plate has been studied by means of heat transfer measurements.Aheat flux sensor has been developed,in order to measure the efficiency of convective heat transfer for varioustypes of surfaces or flows.Its operation at constant temperature allows direct and fast measurements of heat flux.The present paper reports the development of the sensor and presents its application to the study of transition in aboundary layer depending on the angle of incidence of the external flow.An exponential relationship betweencritical Reynolds number and pressure gradient parameter has been found.     

Skin friction and heat transfer in power-law fluid laminar boundary layer along a moving surface

Analytical and numerical solutions are presented for momentum and energy laminar boundary layer along a moving plate in power-law fluids utilizing a similarity transformation and shooting technique. The results indicate that for a given power-law exponent n(0<n?1) or velocity ratio parameter ξ, the skin friction σ decreases with the increasing in ξ or n. The shear force decreases with the increasing in dimensionless tangential velocity t. When Prandtl number N_Pr=1, the dimensionless temperature w(t) is a linear function of t, and the viscous boundary layer is similar to that of thermal boundary layer. In particular, w(t)=t if ξ=0, i.e., the velocity distribution in viscous boundary layer has the same pattern as the temperature distribution in the thermal boundary and δ=δ_T. For N_Pr?1, the increase of viscous diffusion is larger than that of thermal diffusion with the increasing in N_Pr, and δ_T(t)<δ(t). The thermal diffusion ratio increases with the increasing in n(0<n?1) and ξ.     

Viscoelastic boundary layer flow and heat transfer over an exponential stretching sheet

Viscoelastic boundary layer flow and heat transfer over an exponential stretching continuous sheet have been examined in this paper. Approximate analytical similarity solution of the highly non-linear momentum equation and confluent hypergeometric similarity solution of the heat transfer equation are obtained. Accuracy of the analytical solution for stream function is verified by numerical solutions obtained by employing Runge-Kutta fourth order method with shooting. These solutions involve an exponential dependent of stretching velocity, prescribed boundary temperature and prescribed boundary heat flux on the flow directional coordinate. The effects of various physical parameters like viscoelastic parameter, Prandtl number, Reynolds number, Nusselt number and Eckert number on various momentum and heat transfer characteristics are discussed in detail in this work.     

Calculation of the VKI turbine blade with LES and DES

The prediction of the laminar to turbulent transition is essential in the calculation of turbine blades,compressorblades or airfoils of airplanes since a non negligible part of the flow field is laminar or transitional.In this paperwe compare the prediction capability of the Detached Eddy Simulation(DES)with the Large Eddy Simulation(LES)using the high-pass filtered(HPF)Smagorinsky model(Stolz et at.[1])when applied to the calculation oftransitional flows on turbine blades.Detailed measurements from Canepa et al.[2]of the well known VKI-turbineblade served to compare our results with the experiments.The calculations have been made on a fraction of theblade(10%)using non-reflective boundary conditions of Freund at the inlet and outer plane extended to internalflows by Magagnato et al.[3]in combination with the Synthetic Eddy Method(SEM)proposed by Jarrin et at.[4].The SEM has also been extended by Pritz et al.[5] for compressible flows.It has been repeatedly shown that hy-brid approaches can satisfactorily predict flows of engineering relevance.In this work we wanted to investigate ifthey can also be used successfully in this difficult test case.     

Numerical simulation of clocking effect on blade unsteady aerodynamic force in axial turbine

To give an insight into the clocking effect and its influence on the wake transportation and its interaction, the unsteady three-dimensional flow through a 1.5-stage axial low pressure turbine is simulated numerically by using a density-correction based, Reynolds-Averaged Navier-Stokes equations commercial CFD code. The 2nd stator clocking is applied over ten equal tangential positions. The results show that the harmonic blade number ratio is an important factor affecting the clocking effect. The clocking effect has very small influence on the turbine efficiency in this investigation. The difference between the maximum and minimum efficiency is about 0.1%. The maximum efficiency can be achieved when the 1st stator wake enters the 2nd stator passage near blade suction surface and its adjacent wake passes through the 2nd stator passage close to blade pressure surface. The minimum efficiency appears if the 1st stator wake impinges upon the leading edge of the 2nd stator and its adjacent wake of the 1st stator passes through the mid-channel in the 2nd stator. The wake convective transportation and the blade circulation variation due to its impingement on the subsequent blade are the main mechanism affecting the pressure variation in blade surface.     

Effects of freestream turbulence on bypass transition of separated boundary layer on low-pressure turbine airfoils

This paper presents experimental studies on bypass transition of separated boundary layer on low-pressure turbine airfoils,focusing on the effects of freestream turbulence on the transition process.Hot-wire probe measurements are performed on the suction side of an airfoil in the low-pressure linear turbine cascade at several Reynolds number conditions.Freestream turbulence is enhanced by use of turbulence grid located upstream of the cascade.The results of this experimental study show that the location of boundary layer separation does not strongly de-pend on the freestream turbulence level.However,as the freestream turbulence level increases,the size of separa-tion bubble becomes small and the location of turbulent transition moves upstream.The size of separation bubble becomes small as the Reynolds number increases.At low freestream turbulence intensity,the velocity fluctuation due to Kelvin-Helmholtz instability is observed clearly in the shear layer of the separation bubble.At high frees-tream turbulence intensity,the streak structures appear upstream of the separation location,indicating bypass transition of attached boundary layer occurs at high Reynolds number.     

Flowfield and heat transfer past an unshrouded gas turbine blade tip with different shapes

This paper describes the numerical investigations of flow and heat transfer in an unshrouded turbine rotor blade of a heavy duty gas turbine with four tip configurations. By comparing the calculated contours of heat transfer coefficients on the flat tip of the HP turbine rotor blade in the GE-E³ aircraft engine with the corresponding experimental data, the κ-ω turbulence model was chosen for the present numerical simulations. The inlet and outlet boundary conditions for the turbine rotor blade are specified as the real gas turbine, which were obtained from the 3D full stage simulations. The rotor blade and the hub endwall are rotary and the casing is stationary. The influences of tip configurations on the tip leakage flow and blade tip heat transfer were discussed. It’s showed that the different tip configurations changed the leakage flow patterns and the pressure distributions on the suction surface near the blade tip. Compared with the flat tip, the total pressure loss caused by the leakage flow was decreased for the full squealer tip and pressure side squealer tip, while increased for the suction side squealer tip. The suction side squealer tip results in the lowest averaged heat transfer coefficient on the blade tip compared to the other tip configurations.     

导叶约化中心位置对涡轮非定常气动计算的影响

针对工程上常用的基于叶片数约化的涡轮非定常计算方法,为了掌握导叶约化中心位置对于涡轮内部流动非定常计算结果的影响规律,对导叶前缘约化、导叶尾缘约化、不约化三个算例进行了非定常计算与对比分析.研究结果表明:导叶前缘约化方式对于涡轮气动性能时均值影响量级在1％以上,而导叶尾缘约化方式的影响不到前者的1/2;两种约化方式均能...     

The heat/mass transfer analogy for a simulated turbine endwall

Heat transfer measurements in gas turbine cascades are often difficult because of thin boundary layers, complex secondary flows, and large variation in local heat transfer rates. Thus mass transfer techniques have often been used as an alternative method, the heat transfer coefficients being then calculated from the heat/mass transfer analogy.To ensure confidence in the quantitative conversion to the heat transfer coefficients from the mass transfer results, evaluation of the analogy factors is crucial. The present paper examines the validity of the heat/mass transfer analogy, evaluating the analogy factors on a simulated turbine endwall, with separate heat and mass transfer experiments with equivalent flow and geometric conditions. The Nusselt numbers, determined from the heat transfer experiments with a constant wall temperature boundary condition are compared to Sherwood numbers from the mass transfer experiments employing a constant wall concentration boundary condition to evaluate the heat/mass transfer analogy.     

Numerical investigations on the steady and unsteady leakage flow and heat transfer characteristics of rotor blade squealer tip

The steady and unsteady leakage flow and heat transfer characteristics of the rotor blade squealer tip were conducted by solving Reynolds-Averaged Navier-Stokes(RANS) equations with k-ω turbulence model.The first stage of GE-E3 engine with squealer tip in the rotor was adopted to perform this work.The tip clearance was set to be 1% of the rotor blade height and the groove depth was specified as 2% of the span.The results showed that there were two vortexes in the tip gap which determined the local heat transfer characteristics.In the steady flow field,the high heat transfer coefficient existed at several positions.In the unsteady case,the flow field in the squealer tip was mainly influenced by the upstream wake and the interaction of the blades potential fields.These unsteady effects induced the periodic variation of the leakage flow and the vortexes,which resulted in the fluctuation of the heat transfer coefficient.The largest fluctuation of the heat transfer coefficient on the surface of the groove bottom exceeded 16% of the averaged value on the surface of the squealer tip.     

Modeling electrification of suspended particulate matter (SPM) in a two phase laminar boundary layer flow and heat transfer over a semi-infinite flat plate

The present paper envisages the effects of electrification of particles, volume fraction and diffusion of SPM on the boundary layer flow and heat transfer over a semi-infinite flat plate. Irrespective of the particle material density, it has been observed that the range of validity of the solution remains fixed and at x = 2.12 the nature of the profiles of the flow variables changes. Electrification of particles causes the particles to move faster for x < 1.0 and slows down for x > 1.0 but particle temperature increases with increase of M. It has been observed that heat transfer always occurs from the fluid to plate.     

Suitable Heat Transfer Model for Self-Similar Laminar Boundary Layer in Power Law Fluids

The classical power law non-Newtonian fluids energy boundary layer equation is proved improper to describe the self-similar heat transfer. A theoretical analysis for momentum and energy boundary layer transfer behavior is made and the full similarity heat boundary layer equation is developed, which may be characterized by a power law relationship between shear stress and velocity gradient with the Falkner-Skan equation as a special case. Both analytical and numerical solutions are presented for momentum and energy boundary layer equations by using the similarity transformation and shooting technique and the associated transfer characteristics are discussed.     

Experimental investigation of separation and transition processes on a high-lift low-pressure turbine profile under steady and unsteady inflow at low Reynolds number

The effects induced by the presence of incoming wakes on the boundary layer developing over a high-lift low-pressure turbine profile have been investigated in a linear cascade at mid-span. The tested Reynolds number is 70000, typical of the cruise operating condition. The results of the investigations performed under steady and unsteady inflow conditions are analyzed. The unsteady investigations have been performed at the reduced fre- quency off=0.62, representative of the real engine operating condition. Profile aerodynamic loadings as well as boundary layer velocity profiles have been measured to survey the separation and transition processes. Spectral analysis has been also performed to better understand the phenomena associated with the transition process under steady inflow. For the unsteady case, a phase-locked ensemble averaging technique has been employed to reconstruct the time-resolved boundary layer velocity distributions from the hot-wire instantaneous signal output. The ensemble-averaging technique allowed a detailed analysis of the effects induced by incoming wakesboundary layer interaction in separation suppression. Time-resolved results are presented in terms of mean velocity and unresolved unsteadiness time-space plots.     

Analysis of combustion MHD generator using a coupled core-boundary layer model

A coupled core-boundary layer model, is used to analyze a combustion MHD generator. Turbulent compressible steady state boundary layer equations near the electrode and insulator wall, along with the core region, are explicitly solved for a seeded combusion plasma. Effects of current density on core parameters, velocity and temperature profiles in the electrode boundary layer are analyzed. Effect of MHD terms on heat flux, friction coefficient and boundary layer growth are discussed. Current and voltage distributions across the boundary layer are also discussed. Some of the predicted data is compared with experimental values.     

The research of laminar-turbulent transition in hypersonic three-dimensional boundary layer

The results of experimental investigation of laminar-turbulent transition in three-dimensional flow under the high continuous pressure gradient including the flow with local boundary layer separation are presented. The experimental studies were performed within the Mach number range from 4 to 6 and Reynolds number 10-60×106 1/m, the angles of attack were 0°and 5°. The experiments were carried out on the three-dimensional convergent inlet model with and without sidewalls. The influence of artificial tubulator of boundary layer on transition and flow structure was studied. The conducted researches have shown that adverse pressure gradient increase hastens transition and leads to decrease of transition area length. If pressure gradient rises velocity profile fullness increases and profile transformation from laminar to turbulent occurs. As a result of it the decrease of separation area length occurs. The same effect was reached with Reynolds number increase. These results are compared with the data on two-dimensional model with longitudinal curvature.     

Experimental detection of laminar‐turbulent transition on a rotating wind turbine blade in the free atmosphere

This paper discusses the findings from a measurement campaign on a rotating wind turbine blade operating in the free atmosphere under realistic conditions. A total of 40 pressure sensors together with an array of 23 usable hot‐film sensors (based on constant temperature anemometry) were used to study the behavior of the boundary layer within a specific zone on the suction side of a 30 m diameter wind turbine at different operational states. A set of several hundreds of data sequences were recorded. Some of them show that under certain circumstances, the flow may be regarded as not fully turbulent. Accompanying Computational Fluid Mechanics (CFD) simulations suggest the view that a classical transition scenario according to the growth of so‐called Tollmien–Schlichting did not apply. Copyright © 2016 John Wiley & Sons, Ltd.     

Predictions of unsteady HAWT aerodynamics in yawing and pitching using the free vortex method

To predict the unsteady aerodynamic loads of horizontal-axis wind turbines (HAWTs) during operations under yawing and pitching conditions, an unsteady numerical simulation method is proposed. This method includes a nonlinear lifting line method to compute the aerodynamic loads on the blades and a time-accurate free-vortex method to simulate the wake. To improve the convergence property in the nonlinear lifting line method, an iterative algorithm based on the Newton–Raphson method is developed. To increase the computational efficiency and the accuracy of the calculation, a new wake vortex model consisting of the vortex core model, the vortex sheet model and the tip vortex model is used. Wind turbines with different diameters, such as NREL Phase VI, the TU Delft model turbine and the Tjæreborg wind turbine, are used to validate the method for rotors operating at given yaw and/or pitch angles and during yawing and/or pitching processes at different wind speeds. The results, including the blade loads, the rotor torque and the locations of the tip vortex cores in the wake, agree well with the measured data and the computed data. It is shown that the proposed method can be used for predictions of unsteady aerodynamic loads and rotor wakes in the operational processes of blade pitching and/or rotor yawing.     

Combined effect of grid turbulence and unsteady wake on convective heat transfer around a heated cylinder

Experiments are conducted to investigate the effects of free stream turbulence and unsteady wake on convective heat transfer of a heated cylinder. To serve as a heater, a stainless steel needs to be pasted on exterior surface of the bakelite test cylinder. In order to determine the heat transfer coefficient, 17 T-type thermocouples are placed in unequal distance around the circumference at the mid-span of the test cylinder. The range of Reynolds number is 30,000 to 120,000. The results and contributions of this study display that the higher wake passing frequency produces more frequent velocity fluctuations, more broad velocity profiles, and stronger degree of turbulence intensity which are caused by the upstream wake generator and turbulence grid to enhance the heat transfer.