Flow and heat transfer studies of multijet impingement cooling for different configurations: A review

Increasing the gas turbine engine's turbine intake temperature has long been a potential strategy for increasing the specific work output of the engine. However, the melting temperature of the turbine blades and vane material limits the maximum intake temperature. As a result, internal and external cooling techniques are commonly used to maintain the vane material in a safe condition. This study provided an overview of internal impingement cooling to highlight the significance of geometrical variations, such as flat plate, curve plate, and actual vanes. It was observed that flat and curved plate impingement heat transfer studies were reported extensively, whereas limited studies were found on the conjugate effects on airfoil surfaces. The importance of conjugate heat transfer studies and their impact has recently been described in the literature. In most of the literature, a wide range of instruments, such as Laser Doppler Velocimeter, Particle Image Velocimeter, liquid crystal sheets, and so forth, were used for experimental investigations. According to most studies, the local value of internal surface temperature and heat transfer coefficient are vital factors of local flow behavior. Jet-to-jet spacing, jet-to-plate spacing, jet hole diameter, and jet Reynolds numbers played a crucial role in both numerical and experimental analyses. Different geometric variations strongly influence flow behavior. Therefore, the usual method for determining interior temperature distributions and heat transfer coefficients by considering generalized geometries like the flat and curved plate may not produce accurate conjugate solutions. Most of the computational studies on the flat and curved plate indicate the usage of κ−ω shear stress transport and κ–ε realizable model to predict the heat transfer coefficient.     

Effect of surface radiation on conjugate mixed convection in a vertical channel with a discrete heat source in each wall

The results of a numerical analysis of the problem of two-dimensional, steady, incompressible, conjugate, laminar, mixed convection with surface radiation in a vertical parallel-plate channel, provided with a flush-mounted, heat generating, discrete heat source in each wall, are presented here. Air, a radiatively non-participating medium, is used as the cooling agent. A computer code based on the finite volume method is written exclusively for solving the above problem. The effect of surface emissivity, aspect ratio, discrete heat source position and modified Richardson number on the fluid flow and heat transfer characteristics is explored. Useful correlations are evolved for the maximum temperature of the left and the right channel walls, the mean friction coefficient and the forced convection component of the mean friction coefficient.     

Conjugate heat transfer characterization in cooling channels

Cooling technology of gas turbine blades,primarily ensured via internal forced convection,is aimed towards withdrawing thermal energy from the airfoil.To promote heat exchange,the walls of internal cooling passages are lined with repeated geometrical flow disturbance elements and surface non-uniformities.Raising the heat transfer at the expense of increased pressure loss;the goal is to obtain the highest possible cooling effectiveness at the lowest possible pressure drop penalty.The cooling channel heat transfer problem involves convection in the fluid domain and conduction in the solid.This coupled behavior is known as conjugate heat transfer.This experimental study models the effects of conduction coupling on convective heat transfer by applying iso-heat-flux boundary condition at the external side of a scaled serpentine passage.Investigations involve local temperature measurements performed by Infrared Thermography over flat and ribbed slab configurations.Nusselt number distributions along the wetted surface are obtained by means of heat flux distributions,computed from an energy balance within the metal domain.For the flat plate experiments,the effect of conjugate boundary condition on heat transfer is estimated to be in the order of 3%.In the ribbed channel case,the normalized Nusselt number distributions are compared with the basic flow features.Contrasting the findings with other conjugate and convective iso-heat-flux literature,a high degree of overall correlation is evident.     

Numerical investigation on conjugate heat transfer to supercritical CO2 in membrane helical coiled tube heat exchangers

ABSTRACT

Conjugate heat transfer to supercritical CO₂ in membrane helical coiled tube heat exchangers has been numerically investigated in the present study. The purpose is to provide detailed information on the conjugate heat transfer behavior for a better understanding of the abnormal heat transfer mechanism of supercritical fluid. It could be concluded that the supercritical fluid mass flux and vertical/horizontal placement would significantly affect the abnormal heat transfer phenomenon in the tube side. The flow field of supercritical fluid is affected by both the buoyancy and centrifugal force in the conjugate heat transfer process. The local wall temperature and heat transfer coefficient in the tube side would rise and fall periodically for the horizontal heat exchanger, but this phenomenon will gradually disappear with the increase of the mass flow rate or fluid temperature in the tube side. The dual effects of buoyancy force and centrifugal force lead to the deflection of the second flow direction for the vertical placement, which further results in the heat transfer deterioration region on the top-generatrix wall for the downward flow being larger than that for the upward flow.     

Numerical heat transfer study of turbulent square-duct flow through inline V-shaped discrete ribs

A numerical work has been conducted to examine turbulent periodic flow and heat transfer characteristics in a three dimensional square-duct with inline 60° V-shaped discrete thin ribs placed on two opposite heated walls. The isothermal-flux condition is applied only to the upper and lower duct walls while the two sidewalls are insulated, similar to internal passage cooling of gas turbine blades. The computations are based on the finite volume method with the SIMPLE algorithm for handling the pressure–velocity coupling. Air is the working fluid with the flow rate in terms of Reynolds numbers ranging from 10,000 to 25,000. The numerical result is validated with available square-rib measured data and found to agree well with measurement. The computation reveals that the ribbed duct flow is fully developed periodic flow and heat transfer profiles at about x/D = 7–11 downstream of the inlet. Effects of different rib height to duct diameter ratios, BR, on thermal characteristics for a periodic ribbed duct flow are investigated. It is found that a pair of counter-rotating vortices (P-vortex) caused by the rib can induce impingement/attachment flows on the walls leading to greater increase in heat transfer over the test duct. In addition, the rise of BR values leads to the increase in heat transfer and friction loss. The maximum thermal performance is around 1.8 for the rib with BR = 0.0725 where the heat transfer rate is about 4.0 times above the smooth duct at lower Reynolds number.     

Conjugate heat/mass transfer from a circular cylinder with an internal heat/mass source in laminar crossflow at low Reynolds numbers

This paper presents a theoretical study of conjugate heat/mass transfer from a circular cylinder with an internal heat/mass source and a surrounding fluid flow. The heat/mass source consists of a constant temperature/concentration wire imbedded in the cylinder center. A finite difference method discretizes the equations. The multigrid method solves the discrete system. Numerical investigations were carried out for cylinder Re numbers equal to 2 and 20. The values of the Pr number were selected such that the product Re × Pr is constant and equal to 100. The main aspect analysed is the influence of the conductivity ratio on the local and average Nu numbers at different values of the wire diameter.     

Film cooling effectiveness: Comparison of adiabatic and conjugate heat transfer CFD models

This paper documents a computational investigation of the film cooling effectiveness of a 3-D gas turbine endwall with one fan-shaped cooling hole. The simulations were performed for adiabatic and conjugate heat transfer models. Turbulence closure was investigated using three different turbulence models: the realizable k–ε model, the SST k–ω model, as well as the v²–f turbulence model. Results were obtained for a blowing ratio of one, and a coolant-to-mainflow temperature ratio of 0.54. The simulations used a dense, high quality, O-type, hexahedral grid with three different schemes of meshing for the cooling hole: hexahedral-, hybrid-, and tetrahedral-topology grid. The computed flow/temperature fields are presented, in addition to local, two-dimensional distribution of film cooling effectiveness for the adiabatic and conjugate cases. Results are compared to experimental data in terms of centerline film cooling effectiveness downstream cooling-hole, the predictions with realizable k–ε turbulence model exhibited the best agreement especially in the region for (2 ≤ x/D ≤ 6). Also, the results show the effect of the conjugate heat transfer on the temperature (effectiveness) field in the film cooling hole region and, thus, the additional heating up of the cooling jet itself.     

Temperature prediction of heat sources using machine learning techniques

This paper explores the use of machine learning algorithms, such as XGBoost, random forest regression, support vector machine regression, and artificial neural network (ANN), which are employed for predicting temperatures of rectangular silicon heaters with dummy elements. A combination of these machine learning algorithms can predict better results over individual algorithm. Silicon heaters are equipped on an FR4 substrate board for cooling under forced convection in a horizontal channel. COMSOL Multiphysics 5.4 software is used for all the three-dimensional numerical simulations. Heat transfer at the solid and fluid interface is studied using a module based on conjugate heat transfer and nonisothermal fluid flow. Dummy elements are coupled with heated sources to evaluate heat transfer and analyze the flow of fluid. The study is performed with 2.5 m/s velocity and a uniform heat flux of 5000 W/m². The study is aimed at predicting and comparing results of support vector regression (SVR), ensemble learning with ANN to explore optimal configuration. Results indicate an agreement of less than 10% between the simulated and predicted temperatures. It is also found that SVR has given the best results compared with XG Boot and ANN when analyzed individually. The programming for these algorithms is performed using the Python programming language.     

Conjugated heat transfer investigation with racetrack-shaped jet hole and double swirling chamber in rotating jet impingement

A numerical study is performed to investigate the effects of jet hole shape and channel geometry on impingement cooling for both stationary and rotating condition. Two hole shapes and two channel geometries are introduced to counteract the adverse effects of centrifugal force and Coriolis force which are induced by rotation. Both the fluid and solid part are considered for realizing the conjugate heat transfer simulation. The unsteady k-ω SST turbulence model was employed to obtain the time-averaged Nusselt number distributions, time-averaged temperature and temperature gradient fields and the turbulent flow structure. The results show that the cooling jet from the racetrack-shaped hole can effectively withstand the intensive streamwise crossflow to enhance the heat transfer. The double swirling chamber (DSC) channel significantly improves the heat transfer characteristics on the cambered surface and diminishes the adverse effects of the Coriolis force. The high Nu number region is expanded while the temperature uniformity is improved. The combination of the racetrack-shaped hole and DSC channel provides the highest heat transfer among the four cases. The averaged Nu numbers on both the leading and trailing sides for all tested cases show obvious downtrend as rotation number increases, especially at high Reynolds number.     

Effect of Thermal Conductivity on Cooling of Square Heat Source Array under Natural Convection in a Vertical Channel

Abstract

This article presents experimental and numerical investigation on natural convection air-cooling of discrete square heat source array in a vertical channel. Conjugate heat transfer for three-dimensional laminar developing flows over an array of square heat sources representing integrated circuit components for electronic cooling has been studied. Experiments are conducted using three-substrate board materials viz. FR4, Bakelite, and copper clad board having thermal conductivities of 0.3, 1.4, and 8.8?W/m K to study the effects of substrate thermal conductivity on fluid flow and heat transfer. A finite element-based software is used to solve the coupling between heat transfer in solids and fluid region. Incompressible flow over discrete square heat sources is modeled using Navier–Stokes equations under Boussinesq approximation. Air-cooling of circuit boards populated with heat sources is modeled and simulated to present heat transport in combination with the fluid flow resulting from the natural air circulation at constant heat fluxes of 1,000, 2,000, and 3,000?W/m². Multilayer copper clad board of thermal conductivity of 40.5?W/m K have been studied numerically. The results show that single sided copper clad board is the preferred candidate. Experiments indicate a deviation of under 5% with simulations.     

Improvement of a Turbulence Model for Conjugate Heat Transfer Simulation

For the conjugate heat transfer simulation, two-equation turbulence models will predict an anomalously large growth of turbulent kinetic energy in high strain rate flows, and then the flow and heat transfer will be unreasonable. The current study improved the low Reynolds number Chien k-? two-equation model using the “realizability” based C _μ limiter and the production term P _k limiter. This study was conducted based on a developed preconditioned density-based conjugate heat transfer algorithm. Calculations are presented for the flat plate turbulence flow and the conjugate heat transfer of the MarkII cooling turbine blade using the improved model. The results were analyzed and compared with semi-empirical formula and experimental data. Significant improvement in the turbulent kinetic energy anomaly was obtained using both limiters. The prediction accuracy of the Chien k-? model for the flow and heat transfer in the conjugate heat transfer simulation was significantly enhanced. The changes in the model are guaranteed to not have unfavorable influence on the simulation of low strain rate flows.     

A heuristic approach to optimal arrangement of multiple heat sources under conjugate natural convection

Steady state numerical computations and experiments were performed to study three-dimensional, conjugate laminar natural convection heat transfer from multiple identical heat generating modules (heat sources) in a vertical duct. The heat sources were mounted on a wall at different positions in a defined grid of 5 × 5 positions. Air is used as the cooling medium. The governing flow and energy equations were solved using FLUENT 6.3. The optimum geometric configuration of the five heat sources that maximizes the heat transfer was determined by the introduction of a dimensionless distance parameter and an exhaustive search. The heuristic procedure based on the geometric parameter was tested for varying number of heat sources and for different heat source strengths. Experiments were performed to study the effect of modified Grashof number and the duct spacing on maximum temperatures of different configurations in order to support the numerical findings. Additionally, the temperatures of the heat sources arranged in the optimum configuration obtained by the heuristic approach have been experimentally validated.     

Three-dimensional modelling of fluid flow and heat transfer in micro-channels with synthetic jet

A three-dimensional computational model was developed to investigate the effect of synthetic jet interaction with cross flow in micro-channel on the cooling of microchip. A range of parametric studies by varying heat fluxes at the surface of the top of the silicon wafer and membrane oscillating amplitudes was conducted. The resulting complex, conjugate heat transfer through the silicon substrate was analysed. When the actuator was switched on, noticeable temperature drop was observed at all points in the substrate. Quasi steady states have been reached for the presented results which indicated the available cooling potential of single synthetic jet actuator.     

Numerical investigation on the heat transfer and flow in the mini-fin heat sink for CPU

Fluid flow and heat transfer in the mini-rectangular fin heat sink for CPU of PC using de-ionized water as working fluid are numerically investigated. Based on the real PC operating conditions, the three-dimensional governing equations for fluid flow and heat transfer characteristics are solved using finite volume scheme. The standard k–ε turbulent model is employed to describe the flow structure and behavior. The predicted results obtained from the model are verified by the measured data. There is a reasonable agreement between the predicted results and experiments. The results of this study are expected to lead to guidelines that will allow the design of the cooling system with improved cooling performance of the electronic equipments increasing reliable operation of these devices.     

Thermal investigation of the conjugate heat transfer problem in multi-row circular minichannels

A numerical three-dimensional flow and conjugate heat transfer in circular minichannel-based multi-row heat sink is presented in this article. Effects of geometrical parameters including channel dimensions, channel arrangements (inline or staggered), and the number of channel rows with a single-pass flow on the thermal performance of the heat sink are presented. The determination of the bottom surface temperature, average heat transfer coefficient, thermal resistance as well as the pressure drop was reported. The number of rows and the diameter of the circular channel for a constant Reynolds number were found to have a remarkable cooling effect on the heat sink. It was found out that in the case of using four channel rows with the channel diameter of 1?mm, the cooling capacity is 88.5?W/cm² compared to 28?W/cm² for a single row 1?mm diameter.     

Conjugate heat transfer investigation on the cooling performance of air cooled turbine blade with thermal barrier coating

A hot wind tunnel of annular cascade test rig is established for measuring temperature distribution on a real gas turbine blade surface with infrared camera. Besides, conjugate heat transfer numerical simulation is performed to obtain cooling efficiency distribution on both blade substrate surface and coating surface for comparison. The effect of thermal barrier coating on the overall cooling performance for blades is compared under varied mass flow rate of coolant, and spatial difference is also discussed. Results indicate that the cooling efficiency in the leading edge and trailing edge areas of the blade is the lowest. The cooling performance is not only influenced by the internal cooling structures layout inside the blade but also by the flow condition of the mainstream in the external cascade path. Thermal barrier effects of the coating vary at different regions of the blade surface, where higher internal cooling performance exists, more effective the thermal barrier will be, which means the thermal protection effect of coatings is remarkable in these regions. At the designed mass flow ratio condition, the cooling efficiency on the pressure side varies by 0.13 for the coating surface and substrate surface, while this value is 0.09 on the suction side.     

Three dimensional numerical analyses and optimization of offset strip-fin microchannel heat sinks

This paper presents a numerical study on laminar forced convection of water in offset strip-fin microchannels network heat sinks for microelectronic cooling. A 3-dimensional mathematical model, consisting of N–S equations and energy conservation equation, with the conjugate heat transfer between the heat sink base and liquid coolant taken into consideration is solved numerically. The heat transfer and fluid flow characteristics in offset strip-fin microchannels heat sinks are analyzed and the heat transfer enhancement mechanism is discussed. Effects of geometric size of strip-fin on the heat sink performance are investigated. It is found that there is an optimal strip-fin size to minimize the pressure drop or pumping power on the constraint condition of maximum wall temperature, and this optimal size depends on the input heat flux and the maximum wall temperature. The results of this paper are helpful to the design and optimization of offset strip-fin microchannel heat sinks for microelectronic cooling.     

A fully implicit conjugate heat transfer method

Abstract

This article deals with the development of an implicit and conservative method for conjugate heat transfer at solid-fluid interfaces. The technique is applicable for both conformal and non-conformal meshes. The method, which is implemented within a fully coupled in-house code, is symmetric in its treatment of the solid and fluid regions and is shown to be very robust for highly complex configurations. To demonstrate the performance of the method, two compressible turbulent conjugate heat transfer test cases, the Mark II and C3X with film cooling, which are benchmarks for simulating the hydrodynamic and thermal fields around and inside turbine blades, are used. Numerical results generated are in good agreement with available experimental measurements.     

Numerical study of the radiation effect on the jet array impinging heat transfer in a feeding pipe

The present study deals with the turbine casing radiation effect on the impinging cooling encountered in the blade tip active clearance control (ACC) system of aero-engine turbine. To this end, numerical simulations are carried out for a simplified model, that is, a pipe with a single row of impinging jets. The effects of the nozzle-to-plate distance to the diameter of the impinging hole (H/d?=?2–8), the number of the holes (n?=?17–68), the impinging wall temperature (T_p?=?400–800?K), and the inlet Reynolds number (Re?=?5,000–20,000) on the flow and heat transfer are investigated. Analysis is performed on the radiation heat transfer effects on the corresponding flow fields and surface heat flux distributions. The results indicate that, with the radiation included in the simulations, the mass flow rate of the cooling jet near the end of the pipe decreases significantly under the conditions of high wall temperature and small nozzle-to-plate distance. Radiation heat transfer should be accounted for in the numerical study for the casing cooling as it affects the flow and heat transfer remarkably. When the nozzle-to-plate distance is relatively large, such as H/d is larger than 8, the radiative heating leads to uniform heat flux and the radiative heating can suppress the uneven distributions of the heat flux.     

Fluid flow characteristics and convective heat transfer improvement on a gas turbine blade

The flow field features and heat transfer enhancement are investigated on a gas turbine blade by applying the jet impingement cooling method. The distribution of the flow field and the Nusselt number (Nu) was determined on the targeted surface in the cooling channel. The injection holes of different shapes, such as circular, square, and rectangular were considered. The Reynolds numbers (Re) of the airflow in the range of 2000–5000 and aspect ratios of 0.5–2 were particularly focused. The flow vortices and recirculation in the cooling channel and their influence on the heat transfer enhancement were analyzed in detail under different airflow and geometric conditions. Decreasing the ratio of the distance between jet-to-target plate to the diameter of the jet orifice (H/d) increased the heat transfer rate and produced high-intensity vortices and recirculation zones. It was noticed that the formation and generation of vortices and recirculation have important effects on the convective heat transfer rate at the impingement surface. Local Nusselt number, formation of complex vortices, and airflow recirculation in the cooling channel decreased with the increase in the distance between the jet hole and the targeted surface. It was found that with the increase in the Reynolds number of the jet, heat transfer between cold airflow and the targeted surface increased. Moreover, it was observed that the cooling performance of the round and square jet holes was better than the rectangular holes.