Thermal Boundary Layer Effects Research Articles

A computational and experimental study of the effects of thermal boundary layers and negative coefficient chemistry on propane ignition delay times

Experimental measurements of low-temperature ignition often exhibit higher uncertainties and scatter compared with ignition measurements at higher temperatures. One source of experimental variability and uncertainty is the effect of negative temperature coefficient (NTC) chemistry in thermal boundary layers at low-temperature conditions. The objective of the current work was to evaluate the effects of NTC chemistry and thermal boundary layers on propane ignition delay times using a combined modeling and experimental approach. A two-zone “balloon” model was developed where the core zone represented the high-temperature region of an experimental facility and an annulus zone represented the cooler thermal boundary-layer region. Independent initial conditions and elementary reaction chemistry was used in each zone. The effects of boundary-layer size were evaluated using different volume fractions (Vcore/Vtotal). At high initial temperatures (Tcore > 1000 K), there was negligible effect of NTC chemistry on the predicted ignition delay time for propane compared with a single-zone model, and the core region dominated the ignition characteristics for all sizes of thermal boundary layer. However, for lower initial temperature conditions (e.g., Tcore = 800 K), the thermal boundary layer was predicted to ignite first and all ignition delay times, regardless of the size of the boundary layer, were faster than the single-zone prediction for 800 K by up to 25%. Based on the results of the modeling study, propane ignition experiments were conducted using two rapid compression facilities (Vcore/Vtotal ≅ 0.9). at core temperatures of 744–1044 K and pressures of 9.8–25.4 atm for stoichiometric propane-air mixtures. While the measured ignition delay times were within the uncertainties of the both the single- and two-zone model predictions, high-speed imaging showed clear transition from ignition initially in the annulus region at lower temperatures to ignition in the core region at higher temperatures. The results of the study provide important new insights into the effects of NTC chemistry on ignition studies and support the use of diagnostics that can resolve core and boundary layer ignition behavior, particularly for experiments conducted in the NTC region. The two-zone model is also a valuable new tool for assessing the impact of NTC chemistry on previous and planned ignition delay time measurements.

Method for Determining Adiabatic Film Effectiveness in Presence of Thermal Boundary Layer

Abstract In this paper, we present a new method for determining adiabatic film effectiveness in film cooling experiments with nonuniform inlet temperature distributions, in particular the situation of an inlet thermal boundary layer. This might arise in a quasi-steady experiment due to loss of heat from the mainstream flow to the inlet contraction walls, for example. In this situation, the thermal boundary layer would be time-varying. Adiabatic film effectiveness is generally normalized by the difference between mainstream and coolant gas temperatures. Most importantly, these temperatures are generally assumed to be spatially—and, possibly temporally—uniform at the system inlet. In experiments with nonuniform inlet temperature, the relevant hot gas temperature for a particular point of interest on a surface is not easily determined, being a complex function of both the inlet temperature profile and the flow field between the inlet and the point of interest. In this situation, adiabatic film effectiveness cannot be uniquely defined using conventional processing techniques. We solve this problem by introducing the concept of equivalent mainstream effectiveness, a nondimensional temperature for the mainstream that can be used to represent the thermal boundary layer profile at the inlet plane, or the effective temperature of the mainstream gas—which we refer to as the equivalent mainstream temperature—entrained into the mixing layer affecting the wall temperature at a particular point of interest. By using data from two or more time instants during an experiment, we simultaneously solve for equivalent mainstream effectiveness and true adiabatic film effectiveness, that is, the adiabatic film effectiveness that we would measure in an experiment with both steady and uniform inlet temperature. This is an important transformation because the true adiabatic effectiveness has a clear physical interpretation and is a more transportable quantity between systems (comparisons between different experiments, between experiment and computational fluid dynamics (CFD), etc.). The proposed method is experimentally demonstrated using full-surface infrared (IR) thermography measurements of a cooled rotor blade platform, operated in a transonic linear cascade facility at matched engine conditions. Film effectiveness measurements processed in the conventional way suffer from inlet thermal boundary layer effects, rendering them both time-varying (as heat is released to the walls of the tunnel) and, in certain regions, nonphysical in magnitude. The proposed technique renders the same data insensitive to time, and everywhere within physically reasonable limits. By demonstrating independence to the particular (time-varying) inlet temperature profile, we demonstrate the advantages of the proposed technique.

Thermal boundary layers in critical flow venturis

We improve the usefulness of small (diameter < 10 mm) critical flow venturis (CFVs) as transfer standards for gas flow by measuring and explaining how their discharge coefficients depend on the temperature T of their environment. At Reynolds numbers Re < 2.5 × 105 (e.g., a 2 mm diameter throat; inlet air at 1 MPa), CFVs exhibit sensitivity to the environmental temperature of approximately 0.02 % K−1 due to biased measurements of the stagnation temperature T0 (temperature “sampling” error) and from ignoring the low-density, annular, thermal boundary layer generated by heat transfer from the CFV's body to the gas flowing through the CFV. To reduce temperature sampling errors, we used a non-metallic approach pipe and a temperature sensor with a low stem-conduction error. To correct for thermal boundary layer effects on the flow, we used Geropp's functional form: CT=1+KTRe−1/2ΔT/T0 where ΔT is the difference between the CFV's inner wall temperature and the stagnation temperature. For CFVs made of stainless steel and copper with diameters of d = 0.56 mm, 1.1 mm, and 3.2 mm we measured KT ≈ −7 while theoretical predictions of KT by Geropp and Ding et al. are −1.7 and −3.845 respectively. Introducing the correction for room temperature changes (CT) measured in this work, reduces the room temperature sensitivity of the flow measured with the 0.56 mm diameter CFVs from 0.02 % K−1 to less than 0.003 % K−1. Smaller, but significant, improvements are achieved with larger CFVs.

Towards a dTDLAS-Based Spectrometer for Absolute HCl Measurements in Combustion Flue Gases and a Better Evaluation of Thermal Boundary Layer Effects

This work presents a mid-IR direct tunable diode laser absorption spectroscopy (dTDLAS)-based HCl spectrometer, which is specially designed and optimized to measure HCl concentration in combustion exhaust gas matrices (i.e. elevated gas temperatures, high water vapour and CO2 contents). The work is motivated by (legal) requirements for monitoring combustion emissions from large-scale power stations or biomass burning domestic boilers. In our novel dTDLAS HCl spectrometer we use a low power room temperature mid-IR ICL diode laser to access the HCl P5 line at 2775.76 cm−1 in the 1-0 vibrational band which was especially selected for gas matrixes with high CO2 and H2O admixtures. With this set-up we demonstrate at 77 cm path length, total pressure from 320 hPa to 954 hPa, room temperature and at 110 s of signal averaging an optimal precision of 0.17 µmol/mol (ppm). Gas monitoring in combustion applications and elevated gas temperatures are prone to systematic errors caused by spectroscopic falsifications in colder gas boundary layers (BL) unavoidable in the high temperature gas ducts. These BL lead, e.g. to temperature, matrix composition or target gas concentration gradients near walls, which also influence the spectroscopic raw signal via their temperature and collision partner dependence. Depending on the chosen spectral line these can cause significant systematic deviations in in-situ, line-of-sight (LOS) laser spectrometers. For an improved understanding of the quantitative effects of thermal BL on our LOS HCl dTDLAS spectrometer and better representing real BL, we expanded our spectroscopic BL simulation model to allow for continuous (linear) instead of the previous stepwise changes. From the new simulation results, we deduce systematic relative deviations in the extracted HCl-concentration to be up to 10% depending on the magnitude of the BL changes and the choice of the “representative” single temperature measurement. With this simulation model, a user can now derive the system’s systematic deviation based on assumptions on the present temperature gradients. The model also helps the user to choose the gas temperature measurement location in his process, in order to minimize the spatial heterogeneity effects.

A Model for the Fast Determination of Modal Sound Transmission of Large Rectangular Opening

Abstract The existence of openings affects the sound insulation performance of structures significantly. The determination of sound transmission through large rectangular openings is often time-consuming, because of the large number of modes, especially if there is a need to go to high frequencies. A model is proposed and detailed based on three-dimensional wave equations, the transfer matrix method, and modal superposition. The viscous and thermal boundary layer effects have been concerned; hence, the model accuracy for narrow slits was improved. The computational effort is significantly decreased by neglecting the cross-modal sound transmission. The accuracy of this model is validated by comparing it with the existing model, the measurement, and the acoustic finite element method. The study of sound transmission behavior of higher-order modes is performed. The modal sound transmission is predicted and compared for several modes. The phenomenon that is different from that of the plane wave situation is found and discussed.

Revisiting Forced Convection Flow Through a Porous Medium Saturated Channel Using Singular Perturbation Analysis

Abstract Accounting for the fact that thermal conductivity of fluid is much less than the thermal conductivity of solid in most of the porous medium-related applications, this study applies perturbation approach in analyzing forced convection through a parallel plate channel under local thermal nonequilibirum (LTNE) condition by denoting the thermal conductivity ratio of fluid to solid as the small parameter, suggesting leading order solutions to solve the two-equation energy model, by incorporating Darcy model and Brinkman model for large porous medium shape factor, respectively, in the presence of heat generation in both fluid and solid. This study provides important fluid temperatures, solid temperatures, and heat transfer coefficient approximations, which enables further analysis on the fluid and solid temperature gradient at the boundary and hence delineate the roles of thermal conductivities and interfacial heat transfer in LNTE mode. The results signify competition between the heat conduction from the wall through fluid conduction and interfacial heat transfer from solid to fluid in the thermal boundary layer. The effect of thermal boundary layer is intensified with the attendant increase in porous medium shape factor and heat generation in solid. The results for Brinkman model also establish conditions for temperature bifurcations to take place whereby in such cases, an increase in viscous dissipation in fluid attributes to the detachment of thermal boundary layer as the porous medium shape factor, S decreases. The phenomenon caused by insufficient convection rate to overcome viscous dissipation bears much resemblance to the separation point in the momentum boundary layer.

Large Eddy Simulation of a particle-laden flow around a cylinder: Importance of thermal boundary layer effects for slagging and fouling

This work presents a detailed and novel ash deposition model predicting early deposit formation validated with measurements conducted in a full-scale suspension fired boiler considering inertial impaction, eddy impaction, thermophoresis and condensation as deposition mechanisms. A cooled deposition probe, exposed for one week in the furnace region, is modeled using an isolated tube and Large Eddy Simulations. The flow field is validated against literature data using isothermal and non-isothermal cases. Fly ash is described using measured particle size distribution and CCSEM data. Particles with various chemical compositions are injected in the domain and the role of thermophoresis on impaction and sticking efficiency is investigated. The ash deposition model uses a detailed sticking criterion based on the particle kinetic energy, the impact angle and its viscosity. The model is able to predict an increased iron content in the initial deposit layer. Results indicate a high sensitivity towards the viscosity model with best agreement for the model of Senior and Srinivasachar, who implemented a low temperature regime. This approach can predict selective deposition of certain ash particles with low viscosity values such as Fe-rich particles or particles with low kinetic energy, e.g. small Al-Si particles. Depending on the selected model, thermophoresis increased impaction efficiency for small particles by three to four orders of magnitude, and accounted for 5 up to 75% of deposit formation. Condensation on the tube surface is not observed at given temperatures and vapor concentrations. It is shown that boundary effects and particle cooling are crucial effects during early stages of deposit formation.

Thermal boundary layer limitations on the performance of micromachined microphones.

This work examines the extent to which thermal boundary layer effects limit the performance of micromachined microphones. The acoustic impedance of the cavity formed by the microphone enclosure is calculated using both analytical and finite-element methods. A thermal correction to the cavity impedance is included to account for the transition of compression and expansion within the enclosure from adiabatic to isothermal when the thermal boundary layer that forms at the walls of the enclosure becomes large compared to the enclosure dimensions. The thermal correction to the cavity impedance contains a resistive term that results from thermal relaxation losses and contributes thermal-acoustic noise to the system. A lumped-element network model for the microphone response which includes the thermally corrected enclosure impedance is presented and compared to measured results for a case study device. The relative noise power contribution of each noise source considered in the model is calculated. It is shown that the noise due to the resistive term of the enclosure cavity impedance becomes significant when the enclosure volume is small. This sets a theoretical limit on the noise floor that can be achieved by a micromachined microphone with given enclosure dimensions.

Acoustic boundary layers as boundary conditions

The linearized, compressible Navier–Stokes equations can be used to model acoustic wave propagation in the presence of viscous and thermal boundary layers. However, acoustic boundary layers are notorious for invoking prohibitively high resolution requirements on numerical solutions of the equations. We derive and present a strategy for how viscous and thermal boundary-layer effects can be represented as a boundary condition on the standard Helmholtz equation for the acoustic pressure. This boundary condition constitutes an O(δ) perturbation, where δ is the boundary-layer thickness, of the vanishing Neumann condition for the acoustic pressure associated with a lossless sound-hard wall. The approximate model is valid when the wavelength and the minimum radius of curvature of the wall is much larger than the boundary layer thickness. In the special case of sound propagation in a cylindrical duct, the model collapses to the classical Kirchhoff solution. We assess the model in the case of sound propagation through a compression driver, a kind of transducer that is commonly used to feed horn loudspeakers. Due to the presence of shallow chambers and thin slits in the device, it is crucial to include modeling of visco-thermal losses in the acoustic analysis. The transmitted power spectrum through the device calculated numerically using our model agrees well with computations using a hybrid model, where the full linearized, compressible Navier–Stokes equations are solved in the narrow regions of the device and the inviscid Helmholtz equations elsewhere. However, our model needs about two orders of magnitude less memory and computational time than the more complete model.

Thermal Boundary Layer Effects on Line-of-Sight Tunable Diode Laser Absorption Spectroscopy (TDLAS) Gas Concentration Measurements.

The effects of thermal boundary layers on tunable diode laser absorption spectroscopy (TDLAS) measurement results must be quantified when using the line-of-sight (LOS) TDLAS under conditions with spatial temperature gradient. In this paper, a new methodology based on spectral simulation is presented quantifying the LOS TDLAS measurement deviation under conditions with thermal boundary layers. The effects of different temperature gradients and thermal boundary layer thickness on spectral collisional widths and gas concentration measurements are quantified. A CO2 TDLAS spectrometer, which has two gas cells to generate the spatial temperature gradients, was employed to validate the simulation results. The measured deviations and LOS averaged collisional widths are in very good agreement with the simulated results for conditions with different temperature gradients. We demonstrate quantification of thermal boundary layers' thickness with proposed method by exploitation of the LOS averaged the collisional width of the path-integrated spectrum.

Thermal boundary layer limitations on the performance of micromachined microphones

The extent to which thermal boundary layer effects limit the performance of micromachined microphones is examined. A lumped element network model for a micromachined microphone is presented which includes a ladder network in parallel with the adiabatic back volume compliance to account for the transition of the enclosure from adiabatic to isothermal conditions when the thermal boundary layer becomes large compared to the enclosure dimensions. The thermal correction to the cavity impedance contains a resistive component which contributes thermal-acoustic noise to the system. The model results are compared to measurements taken from commercially available microphone units with various back volume sizes, and the simulated relative noise power contribution of each acoustic noise source is calculated. The impedance of the back volume, including the thermal correction factor, is compared to the adiabatic compliance and the impedance derived from thermoacoustic finite element analysis. It is shown that the noise due to the thermal component of the back volume impedance becomes significant in microphones with small back volumes and effectively sets an upper bound on the signal-to-noise ratio of a microphone of given package dimensions.

Numerical study of bubbles rising and merging during convective boiling in micro-channels

A three dimensional numerical study on bubble growth and merger in a micro-channel with diameter of 0.64 mm has been conducted. The working fluid is R134a and the wall material is steel. The inlet Reynolds number is set at 549 in order to keep the flow in laminar regime. Two different heat fluxes (14 and 28kWm2) are supplied to the wall to heat up the fluid. The coupled level set and volume of fluid (CLSVOF) method is used to capture the distorted two-phase interface. An evaporation model is also implemented through UDF (User defined function). The combination of these two methods has successfully eliminated spurious velocities which is a common problem in two phase flow simulation. The boiling and merger processes are well-predicted by the simulation. It is found that the whole process can be divided into three sub-stages: sliding, merger, and post-merger. The dynamics and heat transfer are found to be different in these stages. The evaporation rate is much higher in the first two stages due to the thermal boundary layer effects.

A continuous flow microfluidic calorimeter: 3-D numerical modeling with aqueous reactants

A computational analysis of the reacting flow field, species diffusion and heat transfer processes with thermal boundary layer effects in a microchannel reactor with a coflow configuration was performed. Two parallel adjacent streams of aqueous reactants flow along a wide, shallow, enclosed channel in contact with a substrate, which is affixed to a temperature controlled plate. The Fluent computational fluid dynamics package solved the Navier–Stokes, mass transport and energy equations. The energy model, including the enthalpy of reaction as a nonuniform heat source, was validated by calculating the energy balance at several control volumes in the microchannel. Analysis reveals that the temperature is nearly uniform across the channel thickness, in the direction normal to the substrate surface; hence, measurements made by sensors at or near the surface are representative of the average temperature. Additionally, modeling the channel with a glass substrate and a silicone cover shows that heat transfer is predominantly due to the glass substrate. Finally, using the numerical results, we suggest that a microcalorimeter could be based on this configuration, and that temperature sensors such as optical nanohole array sensors could have sufficient spatial resolution to determine enthalpy of reaction.

Heat transfer enhancement with liquid–gas flow in microchannels and the effect of thermal boundary layer

Heat transfer coefficient of air–water two-phase flow in a microchannel was experimentally studied and the effect of the thermal boundary layer on the heat transfer process was elucidated. Air stream was injected into liquid water flow in a 210μm deep and 1.5mm wide horizontal microchannel, and the heat transfer coefficients due to the presence of bubbles were measured through an array of heaters and resistance temperature detectors (RTDs) inside the channel. Using different configurations of heated areas in the channel, the mixing effect of the bubbles and the interaction with the thermal boundary layer were studied for a range of liquid and gas flow rates. With two-phase flow, enhancement of up to 100% in the heat transfer coefficient was observed compared to single-phase flow. The enhancement was observed to be more significant for thermally developing flow with thicker thermal boundary layers.

Miniaturized electrostatic receiver with small-sized backing electrode

A miniaturized electrostatic receiver design, having a central cylindrical backing electrode of small radius surrounded by a flat annular cavity behind the circular membrane, can lead to both a higher sensitivity and a larger frequency bandwidth compared to the ones achieved with other designs, while bringing a geometrical simplicity which is advantageous from the point of view of microfabrication. An appropriate computational method, relying on a specific 2-D axisymmetrical simulation using an adaptive mesh and accounting for both viscous and thermal boundary layer effects, provides results against which analytical results can be tested. An analytical approach, which leads to solutions based on the eigenmode expansion of the membrane displacement, the acoustic pressure field depending on the radial coordinate in the central fluid gap but being assumed quasi-uniform in the annular cavity, is much faster in terms of running time and appears to be sufficiently accurate to achieve final optimization of this kind of devices.

Thermal boundary layer effects on the acoustical impedance of enclosures and consequences for acoustical sensing devices

Expressions are derived for the acoustical impedance of a rectangular enclosure and of a finite annular cylindrical enclosure. The derivation is valid throughout the frequency range in which all dimensions of the enclosure are much less than the wavelength. The results are valid throughout the range from adiabatic to isothermal conditions in the enclosure. The effect is equivalent to placing an additional, frequency-dependent complex impedance in parallel with the adiabatic compliance. As the thermal boundary layer grows to fill the cavity, the reactive part of the impedance varies smoothly from the adiabatic value to the isothermal value. In some microphones, this change in cavity stiffness is sufficient to modify the sensitivity. The resistive part of the additional cavity impedance varies as the inverse square root of frequency at high frequencies where the boundary layer has not grown to fill the enclosure. The thermal modification gives rise to a thermal noise whose spectral density varies asymptotically as l/f(3/2) above the isothermal transition frequency.

Shock tube/time-of-flight mass spectrometer for high temperature kinetic studies

A shock tube (ST) with online, time-of-flight mass spectrometric (TOF-MS) detection has been constructed for the study of elementary reactions at high temperature. The ST and TOF-MS are coupled by a differentially pumped molecular beam sampling interface, which ensures that the samples entering the TOF-MS are not contaminated by gases drawn from the cold end wall thermal boundary layer in the ST. Additionally, the interface allows a large range of postshock pressures to be used in the shock tube while maintaining high vacuum in the TOF-MS. The apparatus and the details of the sampling system are described along with an analysis in which cooling of the sampled gases and minimization of thermal boundary layer effects are discussed. The accuracy of kinetic measurements made with the apparatus has been tested by investigating the thermal unimolecular dissociation of cyclohexene to ethylene and 1,3-butadiene, a well characterized reaction for which considerable literature data that are in good agreement exist. The experiments were performed at nominal reflected shock wave pressures of 600 and 1300 Torr, and temperatures ranging from 1260 to 1430 K. The rate coefficients obtained are compared with the earlier shock tube studies and are found to be in very good agreement. As expected no significant difference is observed in the rate constant between pressures of 600 and 1300 Torr.

An explanation for the shape of Earth's gravity spectrum based on viscous mantle flow models

The Earth's gravity spectrum can be used as an observational constraint on geophysical modelling. Here we show how the spectrum up to degree l = 31 can be explained to a large part by viscous mantle flow in combination with a very simple model of random mantle density anomalies. Efforts to make the calculation more “realistic” by considering effects of thermal boundary layers, or using density anomalies based on tomography, or geodynamic modelling, tend to worsen the fit. Results are rather sensitive to assumptions on density anomalies in the upper thermal boundary layer. We suggest that, in combination with other observations, the shape of the Earth's gravity spectrum can serve to better constrain radial viscosity structure, density anomalies and flow in the Earth's mantle. Appropriate treatment of the lithosphere and of lateral viscosity variations will be the main challenges in modelling this spectrum.

Airborne thermal remote sensing for water temperature assessment in rivers and streams

Airborne remote sensing methods are needed to assess spatial patterns of stream temperature at scales relevant to issues in water quality and fisheries management. In this study, we developed an airborne remote sensing method to measure spatially continuous patterns of stream temperature and evaluated the physical factors that influence the accuracy of thermal remote sensing of flowing waters. The airborne thermal infrared (TIR) system incorporated an internally calibrated thermal imager (8–12 μm) aligned with a visible band camera in a vertically mounted, gimbaled pod attached to the underside of a helicopter. High-resolution imagery (0.2–0.4 m) covering the entire channel and adjacent floodplains was recorded digitally and georeferenced in-flight along 50- to 60-km river sections ranging from 2 to 110 m in width. Radiant water temperature corresponded to kinetic water temperature (5–27°C) in a range of stream environments within ±0.5°C. Longitudinal profiles of radiant water temperature from downstream to headwater reaches provided a spatial context for assessing large-scale patterns of thermal heterogeneity and fine-scale thermal features such as tributaries and groundwater inputs. Potential sources of error in remote measurements of stream temperature included reflected longwave radiation, thermal boundary layer effects at the water surface, and vertical thermal stratification. After taking into account the radiative properties of the surrounding environment and the physical qualities of the stream, thermal remote sensing proved highly effective for examining spatial patterns of stream temperature at a resolution and extent previously unattainable through conventional methods of stream temperature measurement using in-stream data recorders.

Thermal boundary layer effects in an annular acoustic Stirling engine

A stability and transport analysis is performed for a simplified model of a strongly coupled thermoacoustic prime mover stack in an annular resonator. The result demonstrates that, even in the limit that other flow impedances of the resonator and stack can be ignored, there is a thermal impedance mismatch created in the boundary region at the ends of the stack. This can cause the gain predicted for the wave traversing the interior of the stack to differ significantly from the gain that drives sound in the resonator. The analysis is used to derive scaling relations between the heat and mass transport around the annulus, and to show how different scaling regimes relate to the maximum sound intensity that the stack can induce in the absence of other losses.