Conjugate Heat Transfer Methodology Research Articles

Conjugate Modeling of a Closed Co-Rotating Compressor Cavity

Abstract Robust methods to predict heat transfer are vital to accurately control the blade-tip clearance in compressors and the radial growth of the disks to which these blades are attached. Fundamentally, the flow in the cavity between the co-rotating disks is a conjugate problem: the temperature gradient across this cavity drives large-scale buoyant structures in the core that rotate asynchronously to the disks, which in turn governs the heat transfer and temperature distributions in the disks. The practical engine designer requires expedient computational methods and low-order modeling. A conjugate heat transfer (CHT) methodology that can be used as a predictive tool is introduced here. Most simulations for rotating cavities only consider the fluid domain in isolation and typically require known disk temperature distributions as the boundary condition for the solution. This paper presents a novel coupling strategy for the conjugate problem, where unsteady Reynolds averaged Navier–Stokes (URANS) simulations for the fluid are combined with a series of steady simulations for the solid domain in an iterative approach. This strategy overcomes the limitations due to the difference in thermal inertia between fluid and solid; the method retains the unsteady flow features but allows a prediction of the disk temperature distributions, rather than using them as a boundary condition. This approach has been validated on the fundamental flow configuration of a closed co-rotating cavity. Metal temperatures and heat transfer correlations predicted by the simulation are compared to those measured experimentally for a range of engine-relevant conditions.

Experimental and numerical study of the additive layer manufactured inter-layer channel heat exchanger

In this paper the performance of a recently patented additive layer manufactured (ALM) concept inter-layer heat exchanger (HE) is evaluated experimentally and numerically. Two numerical HE models are developed using the conjugate heat transfer (CHT) methodology. The first is an idealised HE core model, consisting of a single period width HE corrugation section (termed superchannel). The second approach uses a fully detailed HE unit model which resolves the flow and heat transfer inside the complete HE unit. A close agreement was found between the HE unit simulations and the experimentally obtained results, such that the fully detailed HE model could be validated. It was also shown that, a full CHT approach is necessary to accurately evaluate complex inter-layer ALM HE core flow and heat transfer behaviour and can serve as an approach for optimising HE designs. The results also reinforce the occurrence of the inter-layer flow mixing inside the HE core of the same flow streams and allows the mass flow to redistribute inside the HE core which is impossible with the current HE generation geometries. The superchannel model results in a slight over-estimation in heat transfer (ΔT≈4 K on average) making the simplified model acceptable as a conservative estimate. Using validated simulations a parametric study was conducted by changing the solid properties of the full CHT HE model to aluminium to investigate the effects of a significantly more conductive material. This resulted in ≈3% higher heat transfer effectiveness (ϵ) of the HE unit. All the simulations were carried out using CFD package OpenFOAM.

Robust optimization of the NASA C3X gas turbine vane under uncertain operational conditions

The aim of the current paper is the robust optimization of an internally cooled gas turbine vane by increasing the cooling performance and decreasing the sensitivity of the performance against operational uncertainties. The basic geometry of the C3X vane cooling system consists of ten circular channels for reducing the heat load. The numerical analysis is performed using the conjugate heat transfer methodology and the v2−f turbulence model to minimize the simulation error. The operational conditions are considered to be uncertain with Beta probability distribution functions. For quantification of the uncertainties, the polynomial chaos method is used. The main objective of the present study is to increase the blade life span through the minimization of the vane maximum temperature and maximum temperature gradient. To this end, both deterministic and robust optimizations are carried out via a hybrid evolutionary algorithm. The deterministic optimum blade yields lower maximum temperature and temperature gradients. The optimization results clearly show that the robust optimum design is less sensitive to the operational uncertainties, and the maximum blade temperature and temperature gradient are still remarkably lower than the corresponding values of the baseline C3X vane configuration.

A multi-scale conjugate heat transfer modelling approach for corrugated heat exchangers

The paper compares two serrated plate-fin Heat Exchanger (HE) corrugation modelling methods using Computational Fluid Dynamics (CFD). The first method follows closely recent literature studies and models a finite length single channel of a corrugation layer inside the HE core. The second method utilises the conjugate heat transfer methodology and models a section of the HE core with both cold and hot fluid streams separated by a solid conducting wall (HE corrugation). The results of latter model are then extrapolated for the full dimensions of a HE core layer to obtain flow and heat transfer characteristics. The conjugate heat transfer analysis methodology presented is novel and eliminates the need for analytical/empirical modelling currently widely used within industry. Furthermore, it provides more detailed information about the flow and heat transfer inside the HE core enabling potential for more efficient HE designs. Predictions at the corrugation level were carried out at 88⩽Recorrug⩽2957 with mesh independence studies completed for all the computational domains. The results obtained in the HE corrugation predictions were then implemented to the multi-scale HE unit model where the flow inside the HE core was modelled using two porous media simplifications whilst the heat transfer was simplified using the effectiveness source term. The HE unit predictions were validated against industrial experimental data with good agreement found between the numerical and experimental results. All the simulations were completed using the open-source CFD package OpenFOAM.

Development of a model for unsteady conjugate heat transfer simulations

Recent developments in CFD simulations go towards higher accuracy by using time-resolved simulations instead of steady RANS simulations and adding solid structures to the simulation instead of assuming constant wall temperatures or heat fluxes at wall boundaries. This means a very large number of time steps are necessary to both accurately resolve the turbulent fluctuations in the fluid parts and have a converged temperature field in the solid parts of the computational domain. Another problem in near-wall heat transfer is the often used assumption of a constant turbulent Prandtl number, which is not correct for many flow configurations. The present work therefore focuses on the development of a methodology for accelerated unsteady conjugated heat transfer simulations. Furthermore, the implementation of a near-wall heat transfer model that does not rely on a constant turbulent Prandtl number was evaluated. The models are implemented in the CFD solver ANSYS CFX. The validation of the turbulent heat transfer model shows improved agreement with the experimental results compared to a constant turbulent Prandtl number approach. The improved unsteady conjugate heat transfer methodology gives the same accuracy of the results as the implicit unsteady conjugate heat transfer model but with considerable reduction of the computational time.

Probabilistic CFD computations of gas turbine vane under uncertain operational conditions

The stochastic computations of a NASA gas turbine vane are conducted to investigate the effects of the operational uncertainties on the flow and heat transfer characteristics of the NASA C3X blade. The blade contains ten internal cooling channels to remove heat load. In order to minimize the analysis error the full conjugate heat transfer methodology has been employed to simulate the behavior of external hot gas flows, internal cooling air passages and the solid blade simultaneously. The v2-f turbulence model is used and it is shown the predicted results are in acceptable agreement with the available experimental data. Total pressure, total temperature, turbulence intensity, turbulent length-scale of the inlet and the outlet static pressure are assumed to be stochastic with Beta probability distribution functions. The effects of these uncertainties on flow and thermal fields as well as the blade temperature distribution are studied. The polynomial chaos method with polynomials order p=3 is used to quantify the effects of operational uncertainties. The non-deterministic CFD results are found to be in close agreement with the experimental data. Uncertainties specially in inlet total temperature and turbulent length-scale play key roles on the hydrodynamic and thermal fields around the airfoil also the turbine vane temperature distribution.

Conjugate Heat Transfer Methodology for Thermal Design and Verification of Gas Turbine Cooled Components

Gas turbine design has been characterized over the years by a continuous increase of the maximum cycle temperature, justified by a corresponding increase of cycle efficiency and power output. In such way, turbine components heat load management has become a compulsory activity, and then, a reliable procedure to evaluate the blades and vanes metal temperatures is, nowadays, a crucial aspect for a safe components design. In the framework of the design and validation process of high pressure turbine cooled components of the BHGE NovaLTTM 16 gas turbine, a decoupled methodology for conjugate heat transfer prediction has been applied and validated against measurement data. The procedure consists of a conjugate heat transfer analysis in which the internal cooling system (for both airfoils and platforms) is modeled by an in-house one-dimensional thermo-fluid network solver, the external heat loads and pressure distribution are evaluated through 3D computational fluid dynamics (CFD) analysis and the heat conduction in the solid is carried out through a 3D finite element method (FEM) solution. Film cooling effect has been treated by means of a dedicated CFD analysis, implementing a source term approach. Predicted metal temperatures are finally compared with measurements from an extensive test campaign of the engine in order to validate the presented procedure.

Fast Conjugate Heat Transfer Simulation of Long Transient Flexible Operations Using Adaptive Time Stepping

The emerging renewable energy market calls for more advanced prediction tools for turbine transient operations in fast startup/shutdown cycles. Reliable numerical analysis of such transient cycles is complicated by the disparity in time scales of the thermal responses in fluid and solid domains. Obtaining fully coupled time-accurate unsteady conjugate heat transfer (CHT) results under these conditions would require to march in both domains using the time-step dictated by the fluid domain: typically, several orders of magnitude smaller than the one required by the solid. This requirement has strong impact on the computational cost of the simulation as well as being potentially detrimental to the accuracy of the solution due to accumulation of round-off errors in the solid. A novel loosely coupled CHT methodology has been recently proposed, and successfully applied to both natural and forced convection cases that remove these requirements through a source-term based modeling (STM) approach of the physical time derivative terms in the relevant equations. The method has been shown to be numerically stable for very large time steps with adequate accuracy. The present effort is aimed at further exploiting the potential of the methodology through a new adaptive time stepping approach. The proposed method allows for automatic time-step adjustment based on estimating the magnitude of the truncation error of the time discretization. The developed automatic time stepping strategy is applied to natural convection cases under long (2000 s) transients: relevant to the prediction of turbine thermal loads during fast startups/shutdowns. The results of the method are compared with fully coupled unsteady simulations showing comparable accuracy with a significant reduction of the computational costs.

Turbine blade cooling passages optimization using reduced conjugate heat transfer methodology

Here we have optimized shape and location of cooling passages of a C3X turbine blade using a multi-objective strategy. The objective functions is selected to be the maximum temperature gradient and the maximum temperature through the three dimensional blade. Shape of cooling channels is modeled using a new method based on the Bezier curves and using forty design variables. The optimized channel shapes are found to be smooth and without corners. To reduce the computational time, parallel processing and the reduced conjugate heat transfer methodology RCHT is used. Using RCHT, the heat transfer between channels and blade are coupled, while the experimental data is used for heat transfer coefficient between the blade and the hot gases. The multi-objective optimization uses differential evolution algorithm to generate new generations, and using parallel processing for different members of each generation, the computational time is substantially reduced. The Pareto front is found, and different solutions on the Pareto front are analyzed and compared.

Improving a conjugate-heat-transfer immersed-boundary method

Purpose– The purpose of this paper is to provide the current state of the art in the development of a computer code combining an immersed boundary method with a conjugate heat transfer (CHT) approach, including some new findings. In particular, various treatments of the fluid-solid-interface conditions are compared in order to determine the most accurate one. Most importantly, the method is capable of computing a challenging three dimensional compressible turbulent flow past an air cooled turbine vane.Design/methodology/approach– The unsteady Reynolds-averaged Navier–Stokes (URANS) equations are solved within the fluid domain, whereas the heat conduction equation is solved within the solid one, using the same spatial discretization and time-marching scheme. At the interface boundary, the temperatures and heat fluxes within the fluid and the solid are set to be equal using three different approximations.Findings– This work provides an accurate and efficient code for solving three dimensional CHT problems, such as the flow through an air cooled gas turbine cascade, using a coupled immersed boundary (IB) CHT methodology. A one-to-one comparison of three different interface-condition approximations has shown that the two multidimensional ones are slightly superior to the early treatment based on a single direction and that the one based on a least square reconstruction of the solution near the IB minimizes the oscillations caused by the Cartesian grid. This last reconstruction is then used to compute a compressible turbulent flow of industrial interest, namely, that through an air cooled gas turbine cascade. Another interesting finding is that the very promising approach based on wall functions does not combine favourably with the interface conditions for the temperature and the heat flux. Therefore, current and future work aims at developing and testing appropriate temperature wall functions, in order to further improve the accuracy – for a given grid – or the efficiency – for a given accuracy – of the proposed methodology.Originality/value– An accurate and efficient IB CHT method, using a state of the art URANS parallel solver, has been developed and tested. In particular, a detailed study has elucidated the influence of different interface treatments of the fluid-solid boundary upon the accuracy of the computations. Last but not least, the method has been applied with success to solve the well-known CHT problem of compressible turbulent flow past the C3X turbine guide vane.

Conjugate heat transfer analysis of leading edge and downstream mist–air film cooling on turbine vane

Numerical simulations are performed to explore leading edge and downstream film cooling enhancement by application of injecting water mist into the air. The accuracy of numerical simulation program for conjugate heat transfer methodology is verified with the C3X gas turbine vane cooled with leading edge and downstream film holes. The Eulerian–Lagrangian particle tracking method is adopted to investigate the two phase film cooling. The effects of various parameters including mist concentration, mist diameter and mist injection location on the improvement of cooling performance are investigated in this paper. The results show that the average wall temperature reduction at mid span increases from 20K to 48K from 1% to 3% mist ratio, the corresponding average heat transfer coefficient reduction increases from 77Wm−2K−1 to 103Wm−2K−1. Mist cooling can decrease the boundary layer temperature without impact on the mainstream temperature and boundary layer thickness. The degree and the location of cooling performance can be controlled by manipulating the sizes of injected water mist. The superimposition of different mist injection locations can be used to further strengthen the two phase cooling performance.

Research on heavy-duty gas turbine vane high efficiency cooling performance considering coolant phase transfer

Conjugate simulation for heavy-duty gas turbine vane of mist/air phase transfer cooling is carried out to evaluate the cooling enhancement. The Eulerian–Lagrangian particle tracking method is adopted to investigate the two-phase cooling for a gas turbine vane. The accuracy of numerical simulation program for conjugate heat transfer methodology is verified with the C3X gas turbine vane cooled with leading film holes. The effect of various parameters including mist concentration and mist diameter on the cooling performance improvement is investigated in this paper. Results show that the average blade surface temperature reduction about 90 K, 119 K and 94 K are achieved at hub section, midspan section and tip section with 8% mist injection. This translates into a significant blade surface cooling effectiveness enhancement of 11%, 15% and 11%, respectively. The disparate trends are shown for the influence of mist diameter on the blade cooling performance at different spanwise and chordwise location, the results indicate that the degree and the location of cooling performance can be controlled by manipulating different sizes of injected water mist.

Numerical Simulation on Turbine Blade Leading-Edge High-Efficiency Film Cooling by the Application of Water Mist

Numerical simulation is performed to explore leading film cooling enhancement by the application of injecting water mist into the air. The accuracy of numerical simulation program for conjugate heat transfer methodology is verified with the C3X gas turbine vanes cooled with leading edge films. The effect of various parameters including mist concentration, mist diameter, different particle wall interactions conditions, and different forces on the improvement of cooling performance is investigated in this paper. It indicates that mist film cooling can decrease the temperature of boundary layer without impact on the temperature of the mainstream and the thickness of boundary layer.

Conjugate heat transfer simulation of turbine blade high efficiency cooling method with mist injection

The idea of utilizing a finely dispersed water-in-air mixture has been proven to be a feasible technique to produce very high cooling rates. The accuracy of numerical simulation program for conjugate heat transfer methodology is verified with the Mark II transonic high pressure turbine stator which is cooled by internal convection through radial round pipes, and different turbulence models and transition models are employed to analyze the influence on results. On the basis of it, the mist cooling is simulated under typical gas turbine operating conditions for internal convective cooling to discuss the improvement of cooling performance. Though the results indicate that mist cooling can decrease the temperature of boundary layer without impact on the temperature of the mainstream and the thickness of boundary layer, the cooling capacity is limited by inadequate evaporation of mist. Considering the distribution of thermal stress and mist evaporation, a compound cooling blade of film cooling with trailing edge ejection is acquired which is modified from the blade of Mark II internal convective cooling; the effects of various parameters including mist concentration and mist diameter on the improvement of cooling performance are investigated, meanwhile the impact of curvature on cooling efficiency and mist trajectory is analyzed finally.

Influence of turbulence model parameter settings on conjugate heat transfer simulation

Rationality of the parameter settings in turbulence model is an important factor affecting the accuracy of conjugate heat transfer (CHT) prediction. On the basis of a developed CHT methodology and the experimental data of Mark// cooling turbine blade, influences of the turbulence model parameter settings and the selection of turbulence models on CHT simulation are investigated. Results and comparisons with experimental data indicate that the inlet setting of the $$\tilde{v}$$ in Spalart–Allmaras model has nearly no influence on flow and heat transfer in blade surface. The inlet turbulence length scale l T in the low-Reynolds number Chien k-e turbulence model and the blade surface roughness in shear stress transport (SST) k-ω SST model have relatively obvious effects on the blade surface temperature which increases with the increase of them. Both of the laminar Prandtl number and turbulent Prandtl number have slight influences on the prediction, and they only need to be constant in CHT simulation. The k-ω SST model has the best accuracy in the turbine blade CHT simulation compared with the other two models.

Aerodynamic Characteristics of Low Pressure Turbine under the Condition of Altitude Low Reynolds Number

Low pressure turbine(LPT) is an important component of aeroengine.The performance of LPT greatly influences the thrust-weight ratio and specific fuel consumption of aeroengine.It is imperative to investigate the flow and heat transfer characteristics in LPT for improving the aeroengine performance research.Flow characteristics of an aeroengine LPT under altitude low Reynolds number are investigated by conjugate heat transfer methodology,meanwhile the effects of Reynolds number on the LPT efficiency and characteristics of flow are discussed in detail.The results indicate that,with the increasing of Reynolds number( 2×105),the efficiency of the LPT is increasing monotonically because of the decrease of boundary layer separation loss.

Analysis of a Cylindrical Specimen Heated by an Impinging Hot Hydrogen Jet

A computational conjugate heat transfer methodology was developed, as a first step towards an efficient and accurate multiphysics, thermo-fluid computational methodology to predict environments for hypothetical solid-core, nuclear thermal engine thrust chamber and components. A solid conduction heat transfer procedure was implemented onto a pressure-based, multidimensional, finite-volume, turbulent, chemically reacting, thermally radiating, and unstructured grid computational fluid dynamics formulation. The conjugate heat transfer of a cylindrical material specimen heated by an impinging hot hydrogen jet inside an enclosed test fixture was simulated and analyzed. The solid conduction heat transfer procedure was anchored with a standard solid heat transfer code. Transient analyses were then performed with ,variable thermal conductivities representing three composites of a material utilized as flow element in a legacy engine test. It was found that material thermal conductivity strongly influences the transient heat conduction characteristics. In addition, it was observed that high thermal gradient occur inside the cylindrical specimen during an impulsive or a 10 s ramp start sequence, but not during steady-state operations.

Conjugate Heat Transfer Analysis of a Cooled Turbine Vane Using the V2F Turbulence Model

The conjugate heat transfer methodology has been employed to predict the flow and thermal properties including the metal temperature of a NASA turbine vane at three operating conditions. The turbine vane was cooled internally by air flowing through ten round pipes. The conjugate heat transfer methodology allows a simultaneous solution of aerodynamics and heat transfer in the external hot gas and the internal cooling passages and conduction within the solid metal, eliminating the need for multiple/decoupled solutions in a typical industry design process. The model of about 3 million computational meshes includes the gas path and the internal cooling channels, comprising hexa cells, and the solid metal comprising hexa and prism cells. The predicted aerodynamic loadings were found to be in close agreement with the data for all the cases. The predicted metal temperature, external, and internal heat transfer distributions at the midspan compared well with the measurement. The differences in the heat transfer rates and metal temperature under different running conditions were also captured well. The V2F turbulence model has been compared with a low-Reynolds-number k-ε model and a nonlinear quadratic k-ε model. The V2F model is found to provide the closest agreement with the data, though it still has room for improvement in predicting the boundary layer transition and turbulent heat transfer, especially on the suction side. The overall results are quite encouraging and indicate that conjugate heat transfer simulation with proper turbulence closure has the potential to become a viable tool in turbine heat transfer analysis and cooling design.

A zTurbulent Conjugate Heat‐transfer Model for Freezing of Food Products

ABSTRACT: A 3‐dimensional conjugate heat‐transfer model for the analysis of freezing food products has been developed. The food‐freezing process is a multi‐medium, multi‐phase, and transient heat‐exchange phenomenon in connection with the cooling flow around the food items. The developed numerical model couples the energy equation with the Navier‐Stokes equations outside the food items to simulate the velocity distribution around the food items and the heat flux across the food surfaces. The conjugate heat‐transfer methodology and enthalpy method was used to solve the energy equation across the fluid‐solid interface into the food item. The heat convection in the fluid and conduction in the foods are implicitly coupled to predict the heat‐transfer rate and the enthalpy change during its freezing process. The conjugate heat‐transfer model presented here is applicable to perform various heat‐transfer calculations involved in the design of storage and refrigeration equipment and to estimate the process time required for freezing of foods. The article presents the mathematical model used, the outline of the numerical scheme, and the results of computations. The model‐predicted results are compared with the experimental data available in the literature. Overall good agreement was obtained.