Unsteady Heat Flux Research Articles

Numerical Inverse Heat Transfer Analysis for Temperature-Sensitive-Paint Measurements in Hypersonic Tunnels

This paper describes a numerical inverse method used in temperature-sensitive-paint measurements for quantitative global heat flux diagnostics in hypersonic tunnels. An iterative algorithm is developed to solve the one-dimensional inverse heat transfer problem for unsteady heat flux into a polymer layer (temperature-sensitive paint) on a semi-infinite base, where the temperature dependencies of the thermal properties of materials are taken intoaccount.Surfaceheat fluxdistributionsonconemodelsarecalculatedbyusingthisalgorithmfromtemperaturesensitive-paint images acquired in hypersonic wind tunnel testing. Nomenclature a = thermal diffusivity c = specific heat I = luminescent intensity k = thermal conductivity L = polymer thickness qs = surface heat flux qs� 1D� = surface heat flux obtained by using the onedimensional method T = temperature Tin = initial temperature t = time x, z = coordinates on surface y = coordinate in normal direction to surface

Unsteady aerothermodynamics: Proposal for the establishment of a new branch within the discipline of aerothermodynamics

Researchers from the College of Physical Sciences, GUCAS, have proposed to establish a new branch, unsteady aerothermodynamics, within the discipline of aerothermodynamics. The principal objectives of this new branch, to treat by theoretical means the study of physical phenomena relating to attached boundary layer flows, have been outlined in a preliminary investigation. A report based on a feasibility study has appeared in Vol. 54 No. 8 of Science China Physics, Mechanics & Astronomy. Aerothermodynamics, a cross-discipline based mainly on aerodynamics and thermodynamics, deals with hypersonic motion or high temperature gas flows and their interactions with objects, and in particular vehicles, travelling at hypersonic speeds. In itself, aerothermodynamics is of great importance in understanding aerodynamic and structural design of hypersonic vehicles, especially their thermal protection systems. However, traditionally in aerodynamics, according to simple oscillatory criterion characterized by the Strouhal number, engineers often ignore oscillatory flow mechanisms that give rise to the unsteadiness in vehicular aerothermodynamic environments. This stance has never been questioned and whether this criterion is appropriate within aerothermodynamics has never undergone critical assessment. The authors of this paper believe that this traditional thesis may not be strictly adequate and the application of aerothermodynamics to attached boundary layer flows should be studied from a more appropriate perspective that accounts for these unsteady flow mechanisms. In this work, unsteady aerothermodynamics has been studied using simple attached boundary layer flow models and its principles explored in preliminary accounts using the governing equations for the flow. Analytic solutions to unsteady temperature fields and the unsteady wall heat fluxes were obtained for simple flow models and interaction characteristics between these unsteady temperature velocity fields were investigated exploiting these solutions. The authors have shown that unsteadiness in wall heat fluxes is dominated by two contributions: unsteady heat transfer originating from the temperature field and unsteady viscous dissipation originating from the velocity field. Subsequently, characteristics of the influence of unsteady velocity field on unsteady heat flux were discussed, and within the framework of these simplified models the main parameters describing these effects identified. Furthermore, the authors derived similar criteria based on the compressible boundary layer equations that are valid within unsteady aerothermodynamics and discovered a new unsteadiness criterion for the temperature field. According to the dimensionless energy equation, the authors concluded that, rather than applying traditional methods developed for unsteady aerodynamics, the unsteadiness of flows in unsteady aerothermodynamics would be more comprehensively quantified by comparing the relative magnitudes of the unsteadiness criterion number newly encountered for the temperature field with coefficients of other terms in the dimensionless energy equation. To support their point of view, a numerical simulation of the unsteady boundary layer flow has been presented. In this paper, the authors have proposed and initiated studies on phenomena falling within the new discipline of unsteady aerothermodynamics such as high speed flows. They also have suggested that further research should be instigated to better understand this special subject and its specific engineering challenges. The authors all have backgrounds in aerothermodynamics developed within the research group lead by Professor TONG BingGang at GUCAS. This group focuses on fundamental theoretical studies on aerothermodynamic phenomena, including rarefied and real gas effects on hypersonic aerothermodynamics, physical criteria in computational aerothermodynamics, and unsteady aerothermodynamics.

A theoretical study on the unsteady aerothermodynamics for attached flow models

The principle of the unsteady aerothermodynamics was theoretically investigated for the attached flow. Firstly, two simplified models with analytic solutions to the N-S equations were selected for the research, namely the compressible unsteady flows on the infinite flat plate with both time-varying wall velocity and time-varying wall temperature boundary conditions. The unsteady temperature field and the unsteady wall heat flux (heat flow) were analytically solved for the second model. Then, the interaction characteristic of the unsteady temperature field and the unsteady velocity field in the simplified models and the effects of the interaction on the transient wall heat transfer were studied by these two analytic solutions. The unsteady heat flux, which is governed by the energy equation, is directly related to the unsteady compression work and viscous dissipation which originates from the velocity field governed by the momentum equation. The main parameters and their roles in how the unsteady velocity field affects the unsteady heat flux were discussed for the simplified models. Lastly, the similarity criteria of the unsteady aerothermodynamics were derived based on the compressible boundary layer equations. Along with the Strouhal number Stu, the unsteadiness criterion of the velocity field, StT number, the unsteadiness criterion of the temperature field was proposed for the first time. Different from the traditional method used in unsteady aerodynamics which measures the flow unsteadiness only by the Stu number, present results show that the flow unsteadiness in unsteady aerothermodynamics should be comprehensively estimated by comparing the relative magnitudes of the temperature field unsteadiness criterion StT number with the coefficients of other terms in the dimensionless energy equation.

A vaporization model for discrete multi-component fuel sprays

A vaporization model for multi-component fuel sprays is described. The discrete multi-component (DMC) fuel approach was used to model the properties and composition of gasoline and diesel model fuels. Unsteady vaporization of single and multi-component fuel droplets and sprays was considered for both normal and flash-boiling evaporation conditions. An unsteady internal heat flux model and a model for the determination of the droplet surface temperature were formulated. An approximate solution to the quasi-steady energy equation was used to derive an explicit expression for the heat flux from the surrounding gas to the droplet–gas interface, with inter-diffusion of fuel vapor and the surrounding gas taken into account. The density change of the drop as a function of temperature was also considered. In order to treat phase change under trans-critical conditions, a characteristic length was defined to determine the amount of vaporized fuel as a function of time. The present vaporization models were implemented into a multi-dimensional CFD code and applied to calculate evaporation processes of single and multi-component fuel droplets and sprays for various ambient temperatures and droplet temperatures. Differences between representing model fuels using the single and multi-component fuel descriptions are discussed.

Unsteady wall heat flux in spark-ignited, homogeneous charge engines fuelled with reformer gas/gasoline blends

On-board partial oxidation of gasoline to produce reformer gas seems to be an attractive strategy to abate pollutant emissions from internal combustion engines. The engine behaviour in terms of efficiency and combustion process can be better understood by means of in-cylinder heat flux measurements. The study of the unsteady wall heat transfer, supported by previous studies of flame propagation and flame speed through ion sensors and optical fibres, reveals a limited influence of the reformer gas upon the heat transfer coefficient and possibly upon the flame-quenching distance, which is estimated in three different and independent ways. A detailed statistical analysis of single-cycle heat flux shows that the cycle-to-cycle variation remains large when the fraction of reformer gas in the fuel blend increases, even if the global engine stability improves. The comparison of numerous data shows how the chemical energy is released partly within the flame and partly within the post-flame region. This last can account for as much as 30 per cent of the total energy release. The analysis of slow and fast-burning cycles with different fuel blends shows that this fraction of energy is released only when, during the expansion stroke, the cylinder temperature decreases below a certain threshold, allowing radicals to recombine and carbon monoxide (CO) completely to oxidize to CO 2.

A 3D model for simulating the spatial and temporal distribution of temperature within ellipsoidal fruit

A physical model simulating the spatio-temporal distribution of temperature in an ellipsoidal fruit has been developed. It is based on the numerical resolution of the three-dimensional (3D) unsteady heat conduction equation with unsteady and non-homogeneous heat fluxes as boundary conditions. The numerical scheme and the physical models have been tested by comparing with an analytical solution for simple configurations. The model quality has been assessed by comparing model outputs to temperature measured with thermocouples at several locations in isolated peach and apple fruits. The root mean square error (RMSE) for temperature simulated at a 1 min time step was about 0.8 °C. A sensitivity analysis showed that accurate estimations of the surface conductance to water vapor diffusion and of the thermal conductivity are necessary. The model has also been used for identifying the main microclimate variables governing temperature dynamics within fruits.

An investigation of the balance method of measuring unsteady heat flux

A method of measuring unsteady heat flow, based on the balance equation of heat flows at the entrance and inside the object, is described. The theoretical principles for obtaining formulas and results of investigations on a thermal model are presented. Diagrams of a heat meter and of a measuring system are given.

Unsteady state temperature fields in a slab induced by line sources

Solutions for the unsteady state temperature fields and heat fluxes from the surfaces due to single or multiple line sources in a slab and in a semi-infinite solid are derived by using integral transform techniques. The convective boundary condition (boundary condition of the third kind) is applied at the surfaces. Responses to a step change in the coil power are given. Also a cyclic case is studied, in which power in coils is alternately switched on and off as described by a cyclic square wave function. As an application the use of a floor or a wall as storage of heat from electric cables is discussed and equations applicable for dimensioning of the heat storage system and simulation of operation are given. The temperature isotherms generated by a line source are approximately circular in the vicinity of the line source. Based on this an approximate method to calculate heat losses in steady state from single or several pipes in a slab or ground with convective heat transfer at surface is illustrated.

Parametric identification of unsteady heat fluxes using thin-disc heat meters

A unified procedure for measuring unsteady heat fluxes based on one-dimensional receivers is proposed. A digital Kalman filter algorithm is used to obtain optimum estimates. The results of investigations of heat meters, the operating principle of which is based on the thin-disc method, are presented.

Improved fast-response heat transfer instrumentation for short-duration wind tunnels

This paper describes the recent innovations associated with the fabrication and application of fast-response heat flux gauges in short-duration wind-tunnel facilities in Oxford. This work has been driven by the need to measure the heat transfer in an environment with large spatial and temporal variations in surface heat flux, caused by a flow-field that has significant high-frequency periodic fluctuations in both recovery temperature and heat transfer coefficient (namely, an axial flow turbine). A new approach to the fabrication of miniature surface heat flux thin-film gauges is described; this involves the use of a pulse laser to ablate (etch) the gauge and connecting track patterns directly onto electrically insulated and platinized components. This automated technique is shown to produce gauges of high geometrical tolerance at precisely known locations, and to create arrays of gauges on the experimental components rapidly. Typically, the platinum resistance elements are 1 mm by 0.08 mm in plan form and have closely repeatable characteristics (for example, resistance and temperature coefficient). A novel technique for measuring the adiabatic wall temperature and heat transfer coefficient in short-duration facilities is also presented; this includes the capability to measure the deterministic component of these unsteady parameters in periodic (pulsating) flows. The combination of the new high spatial density gauge arrays and the capability to measure unsteady adiabatic wall temperature allows unprecedented insight into the flow physics that influences the unsteady heat flux. In particular, it has been possible to establish whether heat transfer rate fluctuations in a turbine experiment are caused by changes in flow recovery temperature or by changes in heat transfer coefficient. Some example measurements taken in a high-speed turbine test facility are described. Finally, some of the recently manufactured heat transfer gauge systems are presented.

A Model for Droplet Vaporization for Use in Gasoline and HCCI Engine Applications

A model for unsteady droplet vaporization is presented that considers the droplet temperature range from flash-boiling conditions to normal evaporation. The theory of continuous thermodynamics was used to model the properties and compositions of multicomponent fuels such as gasoline. In order to model the change of evaporation rate from normal to boiling conditions more realistically, an unsteady internal heat flux model and a new model for the determination of the droplet surface temperature is proposed. An explicit form of the equation to determine the heat flux from the surrounding gas mixture to the droplet-gas interface was obtained from an approximate solution of the quasi-steady energy equation for the surrounding gas mixture, with the inter-diffusion of fuel vapor and the surrounding gas taken into account. The model was applied to calculate evaporation processes of droplets for various ambient temperatures and droplet temperatures.

High Frequency Surface Heat Flux Imaging of Bypass Transition

Abstract A high-frequency surface heat flux imaging technique was used to investigate bypass transition induced by freestream turbulence. Fundamental experiments were carried out at the University of Oxford using high-density thin film arrays on a flat plate wind tunnel model. Bypass transition was induced by grid-generated turbulence with varying intensities of 2.3%, 4.2%, and 17% with a fixed integral length scale of approximately 12mm. Unique high resolution temporal heat flux images are shown which detail significant differences between unsteady surface heat flux events induced by freestream turbulence and the classical Emmons-type spots which many turbomachinery transition models are based on. The temporal imaging technique presented allows study of unsteady surface heat transfer in detail, and helps elucidate the complex nature of transition in the high-disturbance environment of turbomachinery.

A study of heat flux in a constant-volume combustion chamber

In the production of internal combustion engines, there has been a move towards the development of high-performance engines with fuel economy, lighter weights and smaller sizes. These trends help to answer problems related to thermal load and abnormal combustion, etc., in these engines. In order to clarify these problems, a thin film-type probe for instantaneous measurement of surface temperatures has been suggested. A method for manufacturing such a probe was established in this study. The instantaneous surface temperature of a constant-volume combustion chamber was measured by this probe, and heat flux was calculated and analysed with a Fourier series. For a thorough understanding of the characteristics of combustion, the authors measured the wall temperature of the combustion chamber and computed heat flux through a cylinder wall while varying the protrusion height of the probe. To achieve the above goals, an instantaneous temperature probe was developed, thereby making possible the analysis of the instantaneous temperature of the wall surface and unsteady heat flux in the constant-volume combustion chamber.

The application of a multicomponent droplet vaporization model to gasoline direct injection engines

A model for unsteady droplet vaporization is presented that considers the droplet temperature range from flash-boiling conditions to normal evaporation. The theory of continuous thermodynamics was used to model the properties and compositions of multicomponent fuels such as gasoline. In order to model the change of evaporation rate from normal to boiling conditions more realistically, an unsteady internal heat flux model and a new model for the determination of the droplet surface temperature are proposed. An explicit form of the equation to determine the heat flux from the surrounding gas mixture to the droplet/gas interface was obtained from an approximate solution of the quasi-steady energy equation for the surrounding gas mixture, with the interdiffusion of fuel vapour and the surrounding gas taken into account. The model was applied to calculate normal and boiling evaporation processes of droplets for various ambient temperatures and droplet temperatures. Single-droplet evaporation calculated using the present model was compared with the results calculated by using the standard evaporation routine of the KIVA-3V code. Also, simulations of the vaporization of a single-component fuel (iso-octane) were compared with multi-component fuel cases. The vaporization of a hollow cone spray of fuel injected into a cylindrical chamber was simulated for both normal and flash-boiling conditions using the KIVA-3V code implemented with the present model. In addition, the model was applied to a realistic gasoline direct injection engine.

Unsteady convective surface heat flux measurements on cylinder for CFD code validation

The surface convective heat transfer rates to a cylinder have been measured using platinum thin film gauges in a shock tube and the results have been used to validate two numerical codes. The investigations have been carried out at different incident shock Mach numbers and flow Reynolds numbers. The measured and simulated results give an insight into the transient flow fields around the model in the shock tube and are a valuable means of complementing the numerical and experimental techniques used in this study.

Comparison of Laser- and Pressure-Driven Thrust Response of HMX

The laser- and pressure-driven thrust response functions of HMX (cyclotetramethylene tetranitramine) at pressures near 1 atm were measured during laser-supported combustion at mean CO 2 laser heat fluxes of 35 and 60 W/cm 2 . During laser-driven testing, the laser flux was modulated at ′15 W/cm 2 at driving frequencies ranging from 4 to 250 Hz. Pressure-driven thrust measurements were made with a 10% peak-to-peak variation about the mean chamber pressure at driving frequencies ranging from 4 to 100 Hz. Measured steady-state temperature profiles and numerical predictions of the temperature profiles in the gas-phase reaction zone were used to estimate steady and unsteady heat feedback, respectively. Trends in the experimental results are consistent with a condensed-phase response to the unsteady heat fluxes and with results in the literature from similar experiments. Differences in trends with changing mean heat flux between the laser- and pressure-driven results are explained using the unsteady heat feedback estimates. The experimental results are compared to an analytical model, which used one-step reactions in the condensed phase and gas phase, and numerical modeling results that used detailed gas-phase chemistry. The agreement between the analytical model and the data was found to be better than that between the numerical modeling results and the data.

Recursive solution of inverse natural convection problems by means of mode reduction

A recursive method based on the Kalman filtering is developed to solve inverse natural convection problems of estimating the unsteady nonuniform wall heat flux from temperature measurements in the flow. By employing the Karhunen–Loeve Galerkin procedure that reduces the Boussinesq equation to a small set of ordinary differential equations, the computational difficulties associated with the Kalman filtering for the partial differential equations are overcome. The present method is assessed through several numerical experiments, and is found to yield satisfactory results.

Dusty Supersonic Flow Past a Blunt Body: Viscous and Nonstationary Effects

High-speed space- or aircrafts travelling through a dusty atmosphere may meet dust clouds in which the particles are often distributed very nonuniformly. Such nonuniformities may result in the onset of unsteady effects in the shock and boundary layer and (that is of prime interest) unsteady heat fluxes at the stagnation region of the vehicle. In the nearwall region of high-speed dusty-gas flow, there may take place regimes with and without particle inertial deposition, which require essentially different mathematical models for describing the heat transfer [1]. The present paper deals with two problems, considered within the framework of the two-fluid model of dusty gas [2]: (i) determination of the limits of the particle inertial deposition regime and the distribution of dispersed-phase parameters near the frontal surface of a sphere immersed in dusty supersonic flow (Mach number M = 6) at moderate flow Reynolds numbers (102 ≤ Re ≤ ∞); (ii) effect of free-stream nonuniformities in the concentration of low inertial (non-depositing) particles on the friction and heat transfer at the stagnation point of the body at high Re and M.

Pulsatile blood flow effects on temperature distribution and heat transfer in rigid vessels.

The effect of blood velocity pulsations on bioheat transfer is studied. A simple model of a straight rigid blood vessel with unsteady periodic flow is considered. A numerical solution that considers the fully coupled Navier-Stokes and energy equations is used for the simulations. The influence of the pulsation rate on the temperature distribution and energy transport is studied for four typical vessel sizes: aorta, large arteries, terminal arterial branches, and arterioles. The results show that: the pulsating axial velocity produces a pulsating temperature distribution; reversal of flow occurs in the aorta and in large vessels, which produces significant time variation in the temperature profile. Change of the pulsation rate yields a change of the energy transport between the vessel wall and fluid for the large vessels. For the thermally important terminal arteries (0.04-1 mm), velocity pulsations have a small influence on temperature distribution and on the energy transport out of the vessels (8 percent for the Womersley number corresponding to a normal heart rate). Given that there is a small difference between the time-averaged unsteady heat flux due to a pulsating blood velocity and an assumed nonpulsating blood velocity, it is reasonable to assume a nonpulsating blood velocity for the purposes of estimating bioheat transfer.

Measurement of Thermophysical Properties of Fire Testing Materials.

An unsteady heat flux method was used to determine the thermophysical properties of Polymethyl methacrylate (PMMA) and cellulose, both of which are commonly used as standard sample materials in flame spread tests. The analysis is based on an analytical solution to a heat conduction equation with periodic heat flux. The effective thermal conductivity and diffusivity for a packed bed of each sample material were simultaneously determined from the amplitude and phase delay of the temperature response for periodic heat flux. Experiments were performed for a range of heating rates, particle sizes and apparent densities. The variation in thermophysical properties with temperature was obtained, and the effects of pyrolysis for cellulose, and phase transition for PMMA, on the thermophysical properties of these materials were investigated.