Coherent structures in trailing-edge cooling and the challenge for turbulent heat transfer modelling

The present paper tests the capability of a standard Reynolds-Averaged Navier–Stokes (RANS) turbulence model for predicting the turbulent heat transfer in a generic trailing-edge situation with a cutback on the pressure side of the blade. The model investigated uses a gradient-diffusion assumption with a scalar turbulent-diffusivity and constant turbulent Prandtl number. High-fidelity Large-Eddy Simulations (LES) were performed for three blowing ratios to provide reliable target data and the mean velocity and eddy viscosity as input for the heat transfer model testing. Reasonably good agreement between the LES and recent experiments was achieved for mean flow and turbulence statistics. The LES yielded coherent structures which were analysed, in particular with respect to their effect on the turbulent heat transfer. For increasing blowing ratio, the LES replicated an also experimentally observed counter-intuitive decrease of the cooling effectiveness caused by the coherent structures becoming stronger. In contrast, the RANS turbulent heat transfer model failed in predicting this behaviour and yielded significantly too high cooling effectiveness. It is shown that the model cannot predict the strong upstream and wall-directed turbulent heat fluxes caused by large coherent structures, which were found to be responsible for the counter-intuitive decrease of the cooling effectiveness.     

Effects of injection angle orientation on concave and convex surfaces film cooling

The present study employs a transient liquid crystal thermography to measure film cooling performance over constant curvature of concave and convex surfaces. This work investigates detailed distributions of both film cooling effectiveness and heat transfer coefficient on concave and convex surfaces with one row of injection holes inclined stream-wise at 35° at four blowing ratios (0.5, 1.0, 1.5 and 2.0) on four test pieces with different hole configurations. All test models have a row of discrete holes with a stream-wise injection angle (γ of 35° and a pitch-to-diameter ratio (P/d) of 3. The current work examines four different injection configurations, one with simple and three with 8° forward-expanded holes. Three compound angles of 0, 45 and 90° with air (ρ_c/ρ_m = 0.98) as coolants are tested under the mainstream Reynolds number (Re_d) of 2300 on concave surface, and 1700 on convex surface. Measured results of the concave surface show that both the span-wise averaged heat transfer coefficient and film cooling effectiveness increase with blowing ratios for all tested models. Higher heat transfer levels induced by large flow disturbance of compound-angle injection also lead to poorer overall film cooling performance, especially at high blowing ratio and large span-wise injection angle. Present results show that the best surface protection on the concave surface over the widest range of M can be provided by the forward-expanded holes with β = 0° (Model-B), followed by the forward-expanded holes with β = 45° (Model-C). Convex surface results show that the compound-angle injection indicates increases in both film cooling effectiveness and heat transfer at moderate and high blowing ratios. The forward-expanded hole with simple-angle injection provides the best film performance because of high film cooling effectiveness and low heat transfer coefficient at blowing ratio of 0.5.     

Numerical investigation of the influence of incidence angle on asymmetrical turbine blade model showerhead film cooling effectiveness

The influence of various incidence angles on film cooling effectiveness of an axial turbine blade cascade with leading edge ejection from two rows of cooling holes is numerically investigated. The rows are located in the vicinity of the stagnation line. One row is located on the suction side and the other one is on the pressure side. The predicted pressure field for various blowing ratios (M = 0.7, 1.1 and 1.5) is compared with available experimental results at the design condition. Moreover, the effect of various incidence angles (?10°, ?5°, 0°, 5° and 10°) at three blowing rates is investigated by analyzing the results of both laterally averaged and area averaged values of adiabatic film cooling effectiveness. Numerical results indicate that the incidence angle can strongly affect the thermal protection of the blade at low blowing ratio but becomes less dominant at high blowing ratio. In fact, for the low blowing ratio, a small change in the incidence angle that relates to the design condition can deeply affect the thermal protection of the blade, which is evident from the laterally and area averaged film cooling effectiveness distributions.     

Film cooling on a convex surface: influence of external pressure gradient and Mach number on film cooling performance

 The film cooling performance on a convex surface subjected to zero and favourable pressure gradient free-stream flow was investigated. Adiabatic film cooling effectiveness values were obtained for five different injection geometries, three with cylindrical holes and two with shaped holes. Heat transfer coefficients were derived for selected injection configurations. CO₂ was used as coolant to simulate density ratios between coolant and free-stream close to gas turbine engine conditions. The film cooling effectiveness results indicate a strong dependency on the free-stream Mach number level. Results obtained at the higher free-stream Mach number show for cylindrical holes generally and for shaped holes at moderate blowing rates significant higher film cooling effectiveness values compared to the lower free-stream Mach number data. Free-stream acceleration generally reduced adiabatic film cooling effectiveness relative to constant free-stream flow conditions. The different free-stream conditions investigated indicate no significant effects on the corresponding heat transfer increase due to film injection. The determined heat flux ratios or film cooling performance indicated that coolant injection with shaped film cooling holes is much more efficient than with cylindrical holes especially at higher blowing rates. Heat flux penalties can occur at high blowing rates when using cylindrical holes. Received on 29 May 2000     

Flow structures and heat transfer on dimples in a staggered arrangement

Vortex structures and heat transfer enhancement mechanism of turbulent flow over a staggered array of dimples in a narrow channel have been investigated using Large Eddy Simulation (LES), Laser Doppler Velocimetry (LDV) and pressure measurements for Reynolds numbers Re_H = 6521 and Re_H = 13,042.The flow and temperature fields are calculated by LES using dynamic mixed model applied both for the velocity and temperature. Simulations have been validated with experimental data obtained for smooth and dimpled channels and empiric correlations. The flow structures determined by LES inside the dimple are chaotic and consist of small eddies with a broad range of scales where coherent structures are hardly to detect. Proper Orthogonal Decomposition (POD) method is applied on resolved LES fields of pressure and velocity to identify spatial–temporal structures hidden in the random fluctuations. For both Reynolds numbers it was found that the dimple package with a depth h to diameter D ratio of h/D = 0.26 provides the maximum thermo-hydraulic performance. The heat transfer rate could be enhanced up to 201% compared to a smooth channel.     

Experimental research on the thermal performance of converging slot holes with different divergence angles

Thermal performances of two kinds of converging slot-hole (console) with different divergence angles have been measured using transient liquid crystal measurement technique which can process the nonuniform initial wall temperature. Four momentum ratios are tested. Consoles with different divergence angles produce different cooling effectiveness distributions in the upstream region. However, the cooling effectiveness distributions of the two consoles are similar in the downstream. The laterally averaged cooling effectiveness results show that the differences between the two consoles are very small and the best momentum ratio for both consoles’ cooling effectiveness distribution is around two. With the momentum ratio increasing, the normalized heat transfer coefficient h/h₀ of both consoles increases, but the h/h₀ value of small divergence case is higher and becomes progressively higher than that of large divergence case. Moreover, the effect of the couple vortices on the heat transfer coefficient distributions is more significant for the large divergence case. Both consoles provide the surface a certain degree of thermal protection, especially in the upstream region. The distributions of heat flux ratio q/q₀ are similar with those of η because the influence of η on q/q₀ is much larger than that of h/h₀ on q/q₀.     

Influence of blowing on the anisotropy of the Reynolds stress tensor in a turbulent channel flow

The effects of localized wall blowing through a porous strip are investigated using hot-wire anemometry in a turbulent channel flow. Three blowing magnitudes are studied: σ=0.22, 0.36 and 0.58, where σ is the momentum flux gain ratio and that of the incoming channel flow at three different positions from the spanwise porous strip. The main emphasis of this work was the departure from isotropy of the turbulent flow with localized blowing. The anisotropic invariant map (AIM) for the Reynolds stress tensor revealed that blowing decreased the anisotropy of the turbulent structure in the near-wall region, and a decrease in the longitudinal integral length scale was observed when the blowing rate increased.     

Investigation of transitional and turbulent heat and momentum transport in a rotating cavity

The paper gives the results of the DNS/LES which was performed to investigate the transitional and turbulent non-isothermal flows within a rotor/stator cavity. Computations were performed for the cavity of aspect ratio L = 2–35, Rm = 1.8 and for rotational Reynolds numbers up to 290000. The main purpose of the investigations was to analyze the influence of aspect ratio and Reynolds number on the flow structure and heat transfer. The numerical solution is based on a pseudo-spectral Chebyshev–Fourier–Galerkin collocation approximation. The time scheme is semi-implicit second-order accurate, which combines an implicit treatment of the diffusive terms and an explicit Adams–Bashforth extrapolation for the non-linear convective terms. In the paper we analyze distributions of the Reynolds stress tensor components, the turbulent heat flux tensor components, Nusselt number distributions and the turbulent Prandtl number and other structural parameters, which can be useful for modeling purposes. Selected results are compared with the experimental data obtained for single heated rotating disk by Elkins and Eaton (2000).     

Heat transfer in film-cooled turbulent boundary layers at different blowing ratios as affected by longitudinal vortices

Effects of embedded longitudinal vortices on heat transfer in film-cooled turbulent boundary layers at different blowing ratios are discussed. These results were obtained in boundary layers at free-stream velocities of 10 and 15 m/s. Film coolant was injected from a single row of holes at blowing ratios of 0.47–1.26. A single longitudinal vortex was induced upstream of the film-cooling holes using a half-delta wing attached to the wind tunnel floor. Heat transfer measurements were made downstream of injection using a constant heat flux surface with 126 thermocouples for surface temperature measurements. For all blowing ratios examined, the embedded vortices cause significant alterations to wall heat transfer and to film cooling distributions. Measurrments of mean temperatures and mean velocities in spanwise planes show that high wall heat transfer regions are associated with regions of high near-wall longitudinal velocity where very little film coolant is present. In addition to high heat transfer regions associated with the vortex downwash, there are also secondary heat transfer peaks. These secondary peaks develop due to shear layer mixing and interaction between the vortex and cooling jets and become higher in magnitude and more persistent with downstream distance as the blowing ratio increases from 0.47 to 1.26.     

Wall temperature effects on shock unsteadiness in a reattaching compressible turbulent shear layer

In this study, the effect of heat transfer on the compressible turbulent shear layer and shockwave interaction in a scramjet has been investigated. To this end, highly resolved Large Eddy Simulations (LES) are performed to explore the effect of wall thermal conditions on the behavior of a reattaching free shear layer interacting with an oblique shock in compressible turbulent flows. Various wall-to-recovery temperature ratios are considered, and results are compared to the adiabatic wall. It is found that the wall temperature affects the reattachment location and the shock behavior in the interaction region. Furthermore, fluctuating heat flux exhibits a strong intermittent behavior with severe heat transfer compared to the mean, characterized by scattered spots. The distribution of the Stanton number shows a strong heat transfer and complex pattern within the interaction, with the maximum thermal (heat transfer rates) and dynamic loads (root-mean-square wall pressure) found for the case of the cold wall. The analysis of LES data reveals that the thermal boundary condition can significantly impact the wall pressure fluctuations level. The primary mechanism for changes in the flow unsteadiness due to the wall thermal condition is linked to the reattaching shear layer, which agrees with the compressible turbulent boundary layer theory.     

Turbulent heat transfer characteristics of water flow in a rotating pipe

Large-Eddy-Simulation of turbulent heat transfer for water flow in rotating pipe is performed, for various rotation ratios (0 ≤ N ≤ 14). The value of the Reynolds number, based on the bulk velocity and pipe diameter, is Re = 5,500. The aim of this study is to examine the effect of the rotating pipe on the turbulent heat transfer for water flow, as well as the reliability of the LES approach for predicting turbulent heat transfer in water flow. Some predictions for the case of non-rotating pipe are compared to the available results of literature for validation. To depict the influence of the rotation ratio on turbulent heat transfer, many statistical quantities are analyzed (distributions of mean temperature, rms of fluctuating temperature, turbulent heat fluxes, higher-order statistics). Some contours of instantaneous temperature fluctuations are examined.     

A computational fluid dynamics study by conjugate heat transfer in OpenFOAM: A liquid cooling concept for high power electronics

A conjugate heat transfer (CHT) study of a liquid cooling heat exchanger is carried out using the open source computational fluid dynamics (CFD) library OpenFOAM. The heat exchanger was 3D printed using aluminium and experimentally verified by temperature probing and thermal imaging. The functionality of the heat exchanger in cooling localized heat sources is demonstrated. Three different turbulence models were utilized including k-$\omega$ shear stress transport (SST) model, the standard k-$\epsilon$ model and large-eddy simulation (LES). The numerical results indicate that the k-$\omega$ SST and LES models produced similar results in terms of flow structures and temperature levels while the k-$\epsilon$ model deviated from the two other models. The scalability of the heat exchanger was numerically demonstrated by comparing the flow uniformity by varying the inlet Reynolds number between 4960 and 14880. The conclusions of the paper consists of the following main results. (1) The numerical results indicate that the flow uniformity in the channels is noted to be affected by the flow structures before and after the fin system. (2) The simulated hot-spot temperatures were noted to be relatively sensitive to the predicted flow laminarization inside the channels. (3) The heat exchanger was shown to be functional and to maintain cool surface temperatures in the simulations and the experiments. Additionally, the used CHT solver in OpenFOAM is tested and verified in different ways.     

Direct numerical simulation of turbulent heat transfer in annuli: Effect of heat flux ratio

Fully developed turbulent flow and heat transfer in a concentric annular duct is investigated for the first time by using a direct numerical simulation (DNS) with isoflux conditions imposed at both walls. The Reynolds number based on the half-width between inner and outer walls, δ=(r₂-r₁)/2, and the laminar maximum velocity is Re_δ=3500. A Prandtl number Pr=0.71 and a radius ratio r^*=0.1 were retained. The main objective of this work is to examine the effect of the heat flux density ratio, q^*=q₁/q₂, on different thermal statistics (mean temperature profiles, root mean square (rms) of temperature fluctuations, turbulent heat fluxes, heat transfer, etc.). To validate the present DNS calculations, predictions of the flow and thermal fields with q^*=1 are compared to results recently reported in the archival literature. A good agreement with available DNS data is shown. The effect of heat flux ratio q^* on turbulent thermal statistics in annular duct with arbitrarily prescribed heat flux is discussed then. This investigation highlights that heat flux ratio has a marked influence on the thermal field. When q^* varies from 0 to 0.01, the rms of temperature fluctuations and the turbulent heat fluxes are more intense near the outer wall while changes in q^* from 1 to 100, lead to opposite trends.     

Numerical Simulations of the Sandia Flame D Using the Eddy Dissipation Concept

A turbulent piloted methane/air diffusion flame (Sandia Flame D) is calculated using both compressible Reynolds-averaged and large-eddy simulations (RAS and LES, respectively). The Eddy Dissipation Concept (EDC) is used for the turbulence-chemistry interaction, which assumes that molecular mixing and the subsequent combustion occur in the fine structures (smaller dissipative eddies, which are close to the Kolmogorov length scales). Assuming the full turbulence energy cascade, the characteristic length and velocity scales of the fine structures are evaluated using a standard k- ?? turbulence model for RAS and a one-equation eddy-viscosity sub-grid scale model for LES. Finite-rate chemical kinetics are taken into account by treating the fine structures as constant pressure and adiabatic homogeneous reactors (calculated as a system of ordinary-differential equations (ODEs)) described by a Perfectly Stirred Reactor (PSR) concept. A robust implicit Runge-Kutta method (RADAU5) is used for integrating stiff ODEs to evaluate reaction rates. The radiation heat transfer is treated by the P1-approximation. The assumed β-PDF approach is applied to assess the influence of modeling of the turbulence-chemistry interaction. Numerical results are compared with available experimental data. In general, there is good agreement between present simulations and measurements both for RAS and LES, which gives a good indication on the adequacy and accuracy of the method and its further application for turbulent combustion simulations.     

Large-eddy simulation of buoyancy-driven natural ventilation in an enclosure with a point heat source

Rising buoyant plumes from a point heat source in a naturally ventilated enclosure have been investigated using large-eddy simulation (LES). The aim of the work is to assess the performance and the accuracy of LES for modelling buoyancy-driven displacement ventilation of an enclosure and to shed more light on the transitional behaviour of the plume and the coherent structures involved. The Smagorinsky sub-grid scale model is used for the unresolved small-scale turbulence. The Rayleigh number, Ra is chosen to be in the range where spatial transition from laminar to turbulent flow takes place (Ra = 1.5 × 10⁹). The plume properties (source strength and rate of spread) as well as the ventilation properties (stratification height and temperature of stratified layer) estimated using the theory of Linden et al. are found to agree reasonably well with the LES results. The variation of the plume width with height indicates a linear variation of the entrainment coefficient rather than a constant value used by Linden et al. for a fully turbulent thermal plume. Flow visualisation revealed the nature of the large-scale coherent structures involved in the transition to turbulence in the plume. The most excited modes observed in the velocity, pressure and temperature fields spectra correspond to Strouhal number in the range 0.3 ≤ St ≤ 0.55 which is in agreement with those observed by Zhou et al. for a turbulent forced plume. Excited modes less than thisvalue (St = 0.2) were observed and may be due to low-frequency motions felt throughout the flow.     

Hysteresis phenomenon in turbulent convection

Coherent large-scale circulations of turbulent thermal convection in air have been studied experimentally in a rectangular box heated from below and cooled from above using Particle Image Velocimetry. The hysteresis phenomenon in turbulent convection was found by varying the temperature difference between the bottom and the top walls of the chamber (the Rayleigh number was changed within the range of 10⁷–10⁸). The hysteresis loop comprises the one-cell and two-cells flow patterns while the aspect ratio is kept constant (A=2–2.23). We found that the change of the sign of the degree of the anisotropy of turbulence was accompanied by the change of the flow pattern. The developed theory of coherent structures in turbulent convection (Phys Rev E 66:1–15, 2002, Boundary-Layer Meteorol, 2005) is in agreement with the experimental observations. The observed coherent structures are superimposed on a small-scale turbulent convection. The redistribution of the turbulent heat flux plays a crucial role in the formation of coherent large-scale circulations in turbulent convection.     

Large-eddy simulation in a mixing tee junction: High-order turbulent statistics analysis

This study analyses the mixing and thermal fluctuations induced in a mixing tee junction with circular cross-sections when cold water flowing in a pipe is joined by hot water from a branch pipe. This configuration is representative of industrial piping systems in which temperature fluctuations in the fluid may cause thermal fatigue damage on the walls. Implicit large-eddy simulations (LES) are performed for equal inflow rates corresponding to a bulk Reynolds number Re = 39,080. Two different thermal boundary conditions are studied for the pipe walls; an insulating adiabatic boundary and a conducting steel wall boundary. The predicted flow structures show a satisfactory agreement with the literature. The velocity and thermal fields (including high-order statistics) are not affected by the heat transfer with the steel walls. However, predicted thermal fluctuations at the boundary are not the same between the flow and the solid, showing that solid thermal fluctuations cannot be predicted by the knowledge of the fluid thermal fluctuations alone. The analysis of high-order turbulent statistics provides a better understanding of the turbulence features. In particular, the budgets of the turbulent kinetic energy and temperature variance allows a comparative analysis of dissipation, production and transport terms. It is found that the turbulent transport term is an important term that acts to balance the production. We therefore use a priori tests to evaluate three different models for the triple correlation.     

Wall Heat Flux and Thermal Stratification Investigations during the Compression Stroke of an engine-like Geometry: A comparison between LES and DNS

The near wall regions in internal combustion engines contain a significant amount of the gaseous mass in the cylinder and thus have a high relevance for the amount of unburned hydrocarbons, the wall heat transfer and the thermal stratification in the cylinder. In this context in the following study the predictive capability of Large Eddy Simulation (LES) with respect to wall heat flux and thermal stratification during the compression stroke i.e. under non-reactive conditions in an Internal Combustion Engine (ICE) are investigated based on a comparison with Direct Numerical Simulations (DNS). Two different modeling approaches for the near wall region, the low Reynolds damping approach and the LES adapted model from Plengsaard and Rutland, have been tested. During the first half of the compression stroke the low Reynolds damping approach agreed well with the DNS data, but increasing deviations were observed after 270° CA (piston halfway up). The underprediction of the wall heat flux at later stages was found to stem from the underestimation of the y ₊ values of the first cell centroid, compared to values obtained by evaluating the DNS data at the same location, and originates from the model used to determine the friction velocity. As a consequence of the underpredicted y ₊ value, the cell is not located in the viscous sublayer as expected, and the temperature gradient which is needed for the heat flux calculation is underpredicted. The results of the LES wall heat transfer model from Plengsaard and Rutland on the other hand showed overall reasonable agreement with the DNS data, but the model strongly depended on the modeling constants. With respect to the increasing thermal stratification during the compression both methods were found to significantly under predict the DNS results. These findings are especially relevant for LES of auto ignition phenomena in engines, since ignition timing and location are known to strongly depend on the temperature distribution.     

Influences of peripherally-cut twisted tape insert on heat transfer and thermal performance characteristics in laminar and turbulent tube flows

Effects of peripherally-cut twisted tape insert on heat transfer, friction loss and thermal performance factor characteristics in a round tube were investigated. Nine different peripherally-cut twisted tapes with constant twist ratio (y/W = 3.0) and different three tape depth ratios (DR = d/W = 0.11, 0.22 and 0.33), each with three different tape width ratios (WR = w/W = 0.11, 0.22 and 0.33) were tested. Besides, one typical twisted tape was also tested for comparison. The measurement of heat transfer rate was conducted under uniform heat flux condition while that of friction factor was performed under isothermal condition. Tests were performed with Reynolds number in a range from 1000 to 20,000, using water as a working fluid. The experimental results revealed that both heat transfer rate and friction factor in the tube equipped with the peripherally-cut twisted tapes were significantly higher than those in the tube fitted with the typical twisted tape and plain tube, especially in the laminar flow regime. The higher turbulence intensity of fluid in the vicinity of the tube wall generated by the peripherally-cut twisted tape compared to that induced by the typical twisted tape is referred as the main reason for achieved results. The obtained results also demonstrated that as the depth ratio increased and width ratio decreased, the heat transfer enhancement increased. Over the range investigated, the peripherally-cut twisted tape enhanced heat transfer rates in term of Nusselt numbers up to 2.6 times (turbulent regime) and 12.8 times (laminar regime) of that in the plain tube. These corresponded to the maximum performance factors of 1.29 (turbulent regime) and 4.88 (laminar regime).     

Reynolds-Averaged,Scale-Adaptive and Large-Eddy Simulations of Premixed Bluff-Body Combustion Using the Eddy Dissipation Concept

A lean premixed propane/air bluff-body stabilized flame (Volvo test rig) is calculated using the Scale-Adaptive Simulation turbulence model (SAS) and Large-Eddy simulations (LES) as well as the conventional Reynolds-averaged approach (RAS). RAS and SAS are closed by the standard k-?? and the k-ω Shear Stress Transport (SST) turbulence models, respectively. The conventional Smagorinsky and the k-equation sub-grid scales models are used for the LES closure. Effects of the sub-grid scalar flux modeling using the classical gradient hypothesis and Clark’s tensor diffusivity closures both for the inert and reactive LES flows are discussed. The Eddy Dissipation Concept (EDC) is used for the turbulence-chemistry interaction. It assumes that molecular mixing and the subsequent combustion occur in the ’fine structures’ (smaller dissipative eddies, which are close to the Kolmogorov scales). Assuming the full turbulence energy cascade, the characteristic length and velocity scales of the ’fine structures’ are evaluated using different turbulence models (RAS, SAS and LES). The finite-rate chemical kinetics is taken into account by treating the ’fine structures’ as constant pressure and adiabatic homogeneous reactors, calculated as a system of ordinary-differential equations (ODEs) described by a Perfectly Stirred Reactor (PSR) concept. Several further enhancements to model the PSRs are proposed, including a new Livermore Solver (LSODA) for integrating stiff ODEs and a new correction to calculate the PSR time scales. All models have been implemented as a stand-alone application \(\text {edcPisoFoam}\) based on the OpenFOAM technology. Additionally, several RAS calculations were performed using the Turbulence Flame Speed Closure model in Ansys Fluent to assess effects of the heat losses by modeling the conjugate heat transfer between the bluff-body and the reactive flow. Effects of the turbulence Schmidt number on RAS results are discussed as well. Numerical results are compared with available experimental data. Reasonable consistency between experimental data and numerical results provided by RAS, SAS and LES is observed. In general, there is satisfactory agreement between present LES-EDC simulations, numerical results by other authors and measurements without any major modification to the EDC closure constants, which gives a quite reasonable indication on the adequacy and accuracy of the method and its further application for turbulent premixed combustion simulations.