Unsteady Heat Transfer Research Articles

Investigation of a High-Pressure Turbine Stage in a High-Speed Rotating Transient Test Facility for Rotor Tip Study and a Parametric Study for Improved Heat Transfer Calculation

Abstract The first part of the paper presents commissioning of a single-stage high-pressure (HP) turbine employed in a series of extensive experiments to study the aerodynamics and heat transfer on the rotor surface and casing liner. The Oxford Turbine Research Facility (OTRF), a high-speed rotating transient test facility has the capability to take unsteady aerodynamic and heat transfer measurements at engine representative conditions with a variety of inlet temperature profiles including radial distortion and swirl. A temperature profile survey was conducted at the inlet of the HP nozzle guide vane (NGV). Static and total pressure and temperature measurements have been taken at various locations on the rig including NGV surface, inlet and exit, and rotor exit to establish rig operating conditions. Detailed description of mass flow rate measurements along with calculation of heat loss factor in the rig is presented. The second part of the paper presents a parametric study performed to improve heat transfer measurement calculations from high-frequency response thin-film gauges. The effect of parameters like material properties and thickness of substrate on heat flux has been studied. A detailed uncertainty analysis for heat flux is also presented. A thermal model calibrated with analytical solutions has been developed to optimize thin-film gauge configurations and to study side-conduction effects.

Unsteady conjugate heat transfer characteristics in hexagonal cavity equipped with a multi-blade dynamic modulator

PurposeThe transient analysis of the thermal response and frictional loss characteristics for flow-modulated conjugate heat transfer phenomena has been investigated in the present study. The flow domain is a partitioned cavity of a hexagonal structure equipped with a multi-blade flow modulator. The clockwise rotating blade is adiabatic and stirrers the internal flow along with the natural convection caused by the bottom heated floor of uniform heat flux. The conjugate behavior is introduced through the solid subdomains consisting of two brick-made partitions and one glass partition of uniform thickness. The material of the partition wall reflects the physical aspects of industrial applications. ApproachThe two-dimensional unsteady continuity, momentum, and energy equations are expressed in a non-dimensional form where the buoyant force is modeled through the Boussinesq approximation. The Arbitrary Lagrangian Euler (ALE) finite element is adopted to solve the moving mesh problem by formulating a free triangular discretization scheme. Parametric computational investigations are carried out for air as the working fluid (Pr = 0.71) and 3 different configurations of the rotating modulator while varying the other parameters, i.e., Reynolds number (Re) and Rayleigh number (Ra) for a fixed Biot number (Bi = 104). This dynamic mesh problem encompasses a wide range of parameters, i.e., (100 ≤Re≤ 103), and (104≤Ra≤ 106) for Bi = 104 to evaluate the thermodynamic response of the present thermo-fluid system. Various thermo-fluid system responses are visualized through the spatially average Nusselt number evaluated on the heated surface, system effectiveness, average thermal storage capacity, and frictional power loss of the flow domain. The thermal response is fragmented into individual responses in terms of component signal frequency by the Fast Fourier Transform (FFT) analysis. FindingsAccording to the current analysis, increasing the number of blades increases the rate of heat transfer by a negligible amount. On the other hand, among three different types of modulators, the three-blade modulator shows the lowest power loss coefficient and the lowest power instability. Thus, a three-blade modulator qualifies as the optimum design to impart external motion to the working fluid to introduce forced convection. LimitationsThis research has some scope for improvement. Future studies can be conducted on the improvement of blade designs, thickness, and size of the blades. Practical ImplicationsThe present study can shed light on the modeling of a better storage system where heat transfer and moisture control are integrated for the proper functioning of the storage, such as food storage, cold storage, garment inventory, etc. OriginalityThis study is original, and no previous research has been conducted considering the hexagonal domain and variation of the number of blades. ConclusionThe present study reveals that a modulator best serves its purpose at low Rayleigh and high Reynolds numbers. Moreover, the three-blade modulator has the lowest power loss coefficient and lowest power instability, making it the most suitable modulator to impart external excitation to the working fluid.

Software Development for Thickness Optimization of Tile-Type Thermal Protection System

During the flight mission of hypersonic aircraft, severe aerodynamic heating will occur on the surface, so thermal protection system (TPS) is required to protect the load-bearing structure of the aircraft. The present paper develops an engineering software for automatic optimization of the thickness of tile-type TPS for reusable aircraft. For requirements on TPS of reusable aircraft in the reentry stage, the method of heat flow-time curve enveloping, automatic material selection, and one-dimensional unsteady heat transfer calculation for multilayer plates under thermal load conditions had been researched, an interactive engineering software had been developed. The software improves the calculation accuracy and calculation efficiency of TPS thickness optimization, and it is suitable for rapid design in the conceptual design stage of the aircraft. Finally, by an example, the function of the software is verified.

Chemical reaction and Soret effect on an unsteady MHD heat and mass transfer fluid flow along an infinite vertical plate with radiation and heat absorption

In the current investigation, it is anticipated to examine the influence of heat absorption and radiation on an unsteady transient MHD heat and mass transfer natural convective flow of an optically thin non-Grey Newtonian fluid through an abruptly started infinite vertical porous plate with ramped wall temperature and plate velocity in the presence of Soret and chemical reaction of the first order is solved precisely. Using the similarity variables, the governed PDE's are converted into dimensionless governing equations and they are solved numerically by employing the finite element technique. Numerical calculations and graphs are used to illustrate the important features of the solution on fluid flow velocity, heat, and mass transfer characteristics under different quantities of parametric circumstances entering into the problem. Moreover, we computed the physical variables such as the coefficient of drag force, rate of heat, and mass transfer. The findings indicate that when the thermal radiation parameter increases, the thermal boundary layer becomes thinner. To establish the veracity of our present results, we compared them to previously published research and found substantial concordance.

Numerical and asymptotic solutions of the unsteady mixed convection boundary-layer flow over an expanding/contracting vertical cylinder

PurposeThe purpose of this study is to obtain both the numerical and asymptotic solutions of the unsteady mixed convection flow and heat transfer over an expanding or contracting cylinder which is placed vertically.Design/methodology/approachSolutions of the governing ordinary (similarity) differential equations for the fluid flow and temperature field are obtained using the function bvp4c from MATLAB. The problem involves the Prandtl number σ, the mixed convection parameter λ and unsteadiness parameter S that characterize an expanding or contracting cylinder. This solution approach is capable of producing multiple solutions once the necessary assumptions are provided.FindingsIt is found that solutions exist for all negative values of S, expanding cylinder, and only for small positive values of S, contracting cylinder. Further, more than one solution is observed; numerical computation shows that the critical point of S becomes singular as λ approaching zero. For the case of expanding cylinder, the mixed convection parameter has a significant effect on both the flow and heat transfer characteristics. Asymptotic analysis also shows that when σ is large, dual solutions exist for some values of S and λ.Originality/valueThe present results are new and original for the study of the unsteady mixed convection flow and heat transfer over an expanding/contracting cylinder where numerical solutions are obtained for representative values of the involved parameters. Asymptotic solutions for large λ and large σ are derived.

Unsteady oblique stagnation-point flow and heat transfer of fractional Maxwell fluid with convective derivative under modified pressure field

Unsteady oblique stagnation-point flow and heat transfer of fractional Maxwell fluid with convective derivative towards an oscillating tensile plate are discussed in this paper. The fractional operator is introduced to material derivative for the first time to obtain a newly defined constitutive equation of Maxwell fluid. The Fourier's law is modified accordingly. The pressure gradient is innovatively obtained by solving the differential equation, which bases on the momentum equation away from the plate. Furthermore, the numerical solutions are acquired by virtue of the finite difference method combined with L1-algorithm. It turns out to be convergent through constructing numerical example. The influence of related parameters on the velocity and temperature are performed graphically in detail. Results show that the fluid velocity and temperature distributions tend to periodic oscillation near the plate. Both the velocity and the temperature reduce with the augment of fractional derivative parameters, which indicates the velocity and the temperature boundary layer become thinner. The smaller velocity relaxation time parameter leads to enhanced velocity, meaning that the pressure promotes the fluid velocity. It is evident that all the temperature curves have a tendency to increase first and then decrease with the diverse parameters due to the thermal relaxation characteristic.

MHD FLOW PAST A VERTICAL PLATE OF CASSON FLUID WITH HEAT AND MASS TRANSFER EFFECTS

The mode of heat transfer will play an important role in the heat engineering applications. The present work is focused on analytical investigation of unsteady heat and mass transfer rate through porous medium in the presence of uniform transverse magnetic field along with radiation/absorption, heat generation/ absorption and homogeneous chemical reaction effects. The coupled nonlinear partial equations into ordinary differential equations by perturbation method. The effects of various parameters on flow characteristics are investigated .The results are presented through various graphs which are plotted for the effect of different parameters on fluid flow. Impact of Casson parameter leads to decrease the fluid velocity. The heavier species with low conductivity reduces the flow within the boundary layer.The Casson parameter is taken due to the significance of nonNewtonian fluids in real time applications in chemical industries and petroleum refineries.

Dynamic Heat Transfer Characteristic of Heat Exchanger for Sensible Heat Recovery of Raw Coke Oven Gas

Abstract A simplified hybrid-dimensional unsteady heat transfer model for the ascension-pipe heat exchanger with a helically coiled tube embedded in the jacket and supported by high conductivity particles is established based on the non-thermal equilibrium theory of porous medium. This idea can also be used in the design of other heat exchange devices involving the helically coiled tube. According to calculations, the wall temperature of the ascension-pipe heat exchanger periodically varies due to the periodic variations of flow rate and temperature of raw coke oven gas. A great thermal stress will be produced due to this reason. The coal tar precipitation mainly occurs in the late stage of the coking period due to the continuous cooling of molten salt. Based on the detailed analysis, thermal conductivity of packing layer, heat capacity per unit volume of packing layer, volume of packing layer, flow rate of molten salt and inlet temperature of molten salt are important factors that should be scientifically designed in the design of this type of heat exchanger to reduce thermal stress and coal tar precipitation. Cutting off molten salt in the late stage of the coking period is an effective measure to control the wall temperature of the ascension pipe above the dew point of coal tar vapor.

Numerical research on the heat transfer model and performance of deep borehole heat exchangers combined with geothermal wells

• A deep borehole heat exchanger combined with the geothermal wells is proposed. • A three-dimensional mathematical model considering the forced seepage is established. • The dimensionless analytical solutions are developed and verified. • The effect of the exploitation quantity of geothermal water on the DBHE is analysed. • The thermal diffusion radius under different exploitation quantities is studied. For the purpose of carbon neutrality, deep borehole heat exchanger (DBHE) is widely utilized in building heating by efficiently developing hydrothermal geothermal resources. In this study, a DBHE combined with the geothermal wells is proposed given that there are abundant hydrothermal geothermal resources in the BoHai Bay basin, China. A three-dimensional unsteady heat and mass transfer model coupled with DBHE and thermal reservoir is developed taking into account the forced seepage. Based on the moving finite line source model, the transient dimensionless analytical solutions are derived by applying Fourier and Laplace transform. The proposed model and solving method are validated against the experimental data determined from a field test and the previous numerical simulations, respectively. The calculation results indicate that the heat transfer power per unit buried depth increases by 39.60 W/m and its decline rate throughout the operating period decreases by 7.17% when the exploitation quantity of geothermal water increases from 0 m 3 /h to 120 m 3 /h. With the increase of exploitation quantity, the thermal diffusion radius ranges from 10.11 m to 20.34 m at the downstream, however, the thermal diffusion radius decreases from 10.11 m to 9.01 m at the upstream. When the exploitation quantity of geothermal water is 0 m 3 /h, 60 m 3 /h and 120 m 3 /h, the average heat transfer power increases by 139.37 kW, 174.20 kW and 200.80 kW respectively with the increase of circular quantity of DBHE from 10 m 3 /h to 60 m 3 /h. When the exploitation quantity of geothermal water increases, the forced seepage (Darcy flow rate) in the thermal reservoir is enhanced, and the influence of the circular quantity of the DBHE on the heat transfer performance is improved. The DBHE combined with the geothermal wells can be utilized in the case of existing geothermal well construction, which will enhance the heat transfer performance of DBHE substantially. The conclusions obtained from this research will be a reference to guide further research and application of the DBHE or DBHE array combined with the geothermal wells under different geological conditions and operation modes.

The Hall Effect on MHD 2-Fluid Unsteady Heat Transfer Flow of Plasma in a Rotating System Via a Straight Channel Between Conducting Plates

Hall currents are used to investigate MHD unsteady two fluid flows and heat transport of plasma along a straight channel of conducting plates. In the two liquid zones, the velocity and temperature fields for the case of conducting side plates are obtained by solving the governing equations using a two-term series under the specified conditions. The distribution profiles are graphically resolved and examined. The distributions are thought to be dependent on the electron-to-total pressure ratio. The flow and heat transfer factors are also influenced by other parameters such as the Hartmann number, Hall parameter, rotation parameter, thermal conductivity and viscosity ratio.

Visualization of flow boiling heat transfer using temperature sensitive paint with high spatial and temporal resolution

Boiling heat transfer plays an important role in a wide range of industrial applications. Recent advances in optical measurement technology have made possible the visualization of the heat transfer distribution on the heating surfaces. We designed a multilayer structure of temperature sensitive paint (TSP) and transparent heating layer on a heat transfer surface to measure boiling heat transfer with high-speed visualization. A TSP layer containing a fluorescent material, platinum porphyrin (PtTFPP), was formed on a heat transfer surface, and a forced flow boiling experiment was conducted using HFE-7000 as the test fluid. The temperature of the heat transfer surface was visualized with a spatial resolution of 64 µm and measurement speed of 2 kHz under a mass velocity of 104 kg/(m2·s) and average heat flux of 96 kW/m2. We observed a high temperature area underneath the nucleated vapor bubbles on the heat transfer surface possibly due to heat transfer degradation caused by expansion of dry patches and a low temperature area around the vapor bubbles due to convective heat transfer in the liquid layer. We found that the temperature distribution at the bottom of the bubbles followed the growth and movement of the bubbles. In addition, we demonstrated that it is possible to quantitatively evaluate the unsteady heat transfer coefficient distribution when a dry zone is created at the bottom of large slug bubbles.

Heat exchange structure design and overall performance analysis of double-concentrator solar thermal thruster

In this paper, the platelet heat exchanger in the thermal propulsion system of micro satellite with liquefied gas as propellant was designed, the complete gasification and stabilization scheme of propellant was proposed. The unsteady conjugate heat transfer (CHT) characteristics between the heat exchanger and gaseous propellant were analyzed, and the cumulative data of error estimation in the numerical simulation process was provided to ensure the credibility of the results. The CHT computational fluid dynamics (CFD) simulation of the platelet 3D model under steady-state conditions was carried out to find the empirical correlation between the average Nusselt number and the average Reynolds number. A simplified unsteady 1D model of heat exchanger was established by using the loose coupling method based on quasi steady flow field. The results show that the platelet structure could heat the working medium to more than 2379 K with the heat transfer efficiency of 86%, the outlet temperature and heat transfer efficiency of the heat exchanger were maintained at 1871 K and 69% in steady state when the mass flow rate was 1.14e-6 kg/s. The 1D model could accurately reflect the real heat transfer situation to a certain extent, the simulation error was less than 8.5% compared with the 3D model, and the calculation time was greatly shortened, making the adjustment of heat transfer strategy more convenient. Intermittent heat transfer method could keep the outlet gas temperature, thrust and specific impulse of the thruster at a high level to improve the performance of the system. Taking the nanosatellite with a total mass of 7.55 kg and a propellant mass of 0.25 kg as an example, when the duration of valve open time was 1.5s, the velocity increment of the satellite reached 72.21 m/s with the specific impulse of over 2400 m/s, which was twice than that of nanosatellites without heat exchange structure.

Numerical investigation of pulsating flow structures and heat transfer enhancement performance in spherical corrugated helical tube

• Pulsating flow benefits heat transfer of helical tube with spherical corrugation. • Flow field and local heat transfer characteristic of a pulsating cycle are analyzed. • Optimum dimensionless pulsating frequency for thermal performance is Wo = 35. • Overall thermal performance parameter TP is in the range of 1.06–1.13. In this study, the innovative technology of a square wave pulsating flow combining with a spherical corrugated wall structure was applied in a helical tube to enhance heat transfer. Subsequently, the unsteady flow structure and heat transfer characteristics were numerically investigated. The accuracy of the numerical results was verified using experimental data and results in the open literature. For constant values of the geometrical parameters of the spherical corrugated helical tube, the effects of pulsating parameters on the heat transfer enhancement performance were explored, including dimensionless frequency ( Wo ) and dimensionless amplitude ( A ¯ ). The results indicated that the disturbance induced by the pulsating flow improved the local flow field inside the spherical corrugation. In addition, the intensity of the secondary flow and the turbulent kinetic energy of mainstream were simultaneously enhanced. Further, during more than 60% of one pulsation period, the average Nusselt number ( Nu m ) was noticeably greater than that in steady flow with the same average velocity. The maximum value of Nu m occurred at the end of the first half cycle and was increased by 38.5%. The optimum dimensionless pulsation frequency was Wo = 35 within the studied range. The Nusselt number and the friction factor increased with increase in the dimensionless amplitude. However, the comprehensive heat transfer enhancement performance was better under smaller A ¯ value. Furthermore, within the scope of the Dean number ( De ) De = 2936–4894, the overall thermal performance ( TP ) parameter was in the range of 1.06–1.13.

Performance of capillary box heat exchangers buried in seabed for seawater-source heat pumps

An innovative seawater-source heat pump system (SWHPs) was developed by employing capillary box heat exchangers (CBHEs) buried in the seabed as the front-end heat exchanger. Field experiments were firstly presented to test the efficiency of the SWHPs in a practical project. The experimental results show that even under extreme cold/hot climate conditions, the 24-hour COP/EER of the heat pump unit can reach respectively 2.96 and 5.39, which is superior to an alternative air source heat pump (ASHP). Furthermore, an unsteady state three-dimensional seepage and heat transfer model was established to study the thermal performance of CBHEs buried in the seabed using ANSYS FLUENT software. Based on the model, the influences of seawater seepage velocity, thermophysical characteristics of backfilled sand, and flow velocity in the capillary tube on the thermal characteristics of CBHEs were investigated. Moreover, considering the per area heat transfer rate of CBHEs as the evaluation target, the sensitivities of five representative factors including the flow velocity in capillary tubes, seawater seepage velocity, specific heat capacity, density and thermal conductivity of the backfilled sand were discussed using the single factor sensitivity analysis to detect the significant influence parameters.

Influence of local grid refinement on prediction of impinging jet heat transfer using Scale-Resolving-Simulation methods

A fine near-wall resolution plays a crucial role in simulations of unsteady heat transfer from a wall. A generation of fine structured grids for a complex domain is cumbersome and requires an enormous number of grid points and a local grid refinement is a possible technique for a grid point reduction. The present study addresses numerical simulations of impinging jet heat transfer on locally refined computational grids using the Scale-Resolving-Simulation methods (DES, LES and PANS). The study is performed at a Reynolds number Re = 23000 and two nozzle-plate distances H/D = 2 and H/D = 6. DES and the PANS model with f k = 0.25 predicted results closest to experimental data. However, DES significantly over-predicted heat transfer at the location r / D = 1 − 2 in the small nozzle-plate distance case ( H / D = 2). The decrease of physical resolution in the PANS model resulted in the over-prediction of heat transfer close to the nozzle axis. In conclusion, the influence of the local refinement in the perpendicular direction was rather low compared to the longitudinal direction. Moreover, the local grid refinement improved results predicted by LES and DES in the small nozzle-plate distance case.

Effects of Slip and Thermophoresis on Unsteady Flow and Heat Transfer of (MHD) Bioconvection of Nanofluids over a Stretching Sheet

Effects of Slip and Thermophoresis on Unsteady Flow and Heat Transfer of (MHD) Bioconvection of Nanofluids over a Stretching Sheet

Hall, Soret, and rotational effects on unsteady MHD rotating flow of a second-grade fluid through a porous medium in the presence of chemical reaction and aligned magnetic field

The effects of Hall current, rotation and Soret effects on an unsteady MHD free convection heat and mass transfer flow of a viscous, incompressible and electrically conducting fluid past an inclined plate embedded in a porous medium in the presence of chemical reaction and an aligned magnetic field are investigated. An exact analytical solution of the governing equations for fluid velocity, fluid temperature, and species concentration subject to appropriate initial and boundary conditions is obtained using the perturbation technique. Expressions for shear stress, rate of heat transfer and rate of mass transfer at the plate are derived for both ramped temperature and isothermal plates. The numerical values of primary and secondary fluid velocities, fluid temperature and species concentration are displayed graphically, whereas those of shear stress and rate of mass transfer at the plate are presented in tabular form for various values of pertinent flow parameters. It is concluded that, the resultant velocity is increased with an increasing in Hall and Soret parameters throughout fluid region. The thermal and solutal buoyancy forces contribute to the resultant velocity ever-increasing to high. The temperature distribution is trim downs through an increasing in heat source parameter. The concentration is reduced with an increase in the chemical reaction parameter in the entire fluid region. Concentration buoyancy force, hall current, and Prandtl number have tendency to reduce in skin friction whereas permeability of the porous medium, Rotation, chemical reaction, Soret number, thermal buoyancy force and mass diffusion have reverse effect on it.

A global thermal node model for no-load indirect solar dryer

ABSTRACT This paper presents a global thermal node model for predicting heat transfer in no-load indirect solar dryer. The overall influence of the interaction of the indirect solar dryer with the uppermost soil layer is considered. The mathematical model describing the solar drying system with a double-pass air-circulation collector is derived. Based on the Moore and Fisch approach, the soil surface fluxes are calculated using the surface layer similarity theory. The drying air temperature distribution based on dynamic descriptions of the drying environment is studied. The unsteady convection heat transfer results low thermal efficiency of the dryer at low air speed. The linear increase of the inner air speed from to makes the maximum efficiency increases of . When the offsetting air speed undergoes a convex quadratic increase, the average value of the energy efficiency in this case increases of compared to the scenario of constant air speed.

Understanding the influence of unsteady and convection terms in heat transfer model on the predicted heat flux in engines operated under different combustion modes

The aim of current research is to develop an enhanced heat transfer model to accurately predict the heat flux through the cylinder walls during the working process of internal combustion engines operated under different loads and combustion modes. Two enhanced models, i.e., the unsteady model and the steady convective contribution (SCC) model were respectively constructed based on the thermal wall function. The effects of the transient ambient gas temperature and pressure variations, as well as the chemical reaction source term, were included in the unsteady model. Then the contributions of the unsteady terms, such as the temporal derivative of gas temperature, the pressure work, and the chemical heat source in the energy equation were analyzed in detail. The results indicate that the mechanism of the unsteady heat transfer process is different in the engine operated under motored conditions and different combustion modes, including conventional diesel combustion (CDC), homogeneous charge compression ignition (HCCI), and reactivity controlled compression ignition (RCCI). Afterward, the influence of the gas velocity and the pressure difference perpendicular to the walls were included in the SCC model to consider their contributions to the heat fluxes near the chamber walls. It is found that the heat fluxes predicted by the SCC model are in better agreement with the experimental data, especially in the CDC mode under different swirl ratios and loads. The peak of the heat flux predicted by the SCC model shows superiority to that of the previous steady heat transfer models and the unsteady heat transfer model.

Unsteady film cooling characteristics of the high-pressure turbine shroud with blade rotation in an aero-engine

Abstract Three-dimensional unsteady numerical simulations were conducted to investigate the detailed film cooling mechanism of the high-pressure turbine shroud with the first-stage turbine blade and guide vane for an aero-engine under the high-speed rotation of blades and rotor-stator interaction. The slip mesh was used to realize the relative motion between the rotating blade and the stationary turbine shroud. It is found that the coolant jet is alternately influenced by the hot mainstream, tip clearance leakage flow and leakage vortex due to the high rotational speed of blades. The film cooling characteristics of the turbine shroud significantly present an unsteady and periodic flow and heat transfer phenomenon. The insufficient cooling margin for film holes at the upstream of the blade leading edge can occur not only under high blowing ratios due to the coolant jet liftoff, but also at low blowing ratios due to the insufficient coolant flow rate as a result of the high exit pressure. A novel shroud cooling structure with coolant supply by the added throttle chamber is put forward, and expected to provide better thermal protection for the high-pressure turbine shroud near the leading edge of blades with no extra increase in the total mass flow rate of coolant.