Stagnation Region Heat Transfer Research Articles

Experimental investigation of heating augmentation by particle kinetic energy conversion in dust-laden supersonic flows

The presence of particles in supersonic flows can cause significant increases in stagnation point heat fluxes (Dunbar et al. in AIAA J 13:908–912, 1975). This effect is commonly named ‘particle-induced heat flux augmentation’ or just ‘heating augmentation.’ Heating augmentation can be described as the sum of the conversion of kinetic energy of the particles into thermal energy, characterized by the energy conversion efficiency, also called accommodation coefficient, and the increase of convective heat flux (Polezhaev et al. in High Temp 30:1147–1153, 1992; Vasilevskii and Osiptsov in Experimental and numerical study of heat transfer on a blunt body in dusty hypersonic flow 33rd thermophysics conference, American Institute of Aeronautics and Astronautics, 1999). Although the accommodation coefficient is fundamental for heating augmentation characterization, there is only a small number of experimental datasets for it. This work focusses on the experimental determination of the accommodation coefficient in flow regimes at Mach number 2.1, Reynolds number, based on the probe nose diameter, from approx. 6e5 to 1.8e6, and nominal particle sizes of approx. 20 µm. The decrease of particle velocity and kinetic energy flux in the shock layer is measured with highly resolved shadowgraphy for individual particles. The particle kinetic energy flux is decreased by 29% on average by particle deceleration in the shock layer. Negligible kinetic energy fluxes of rebounded particles were measured. The accommodation coefficient is approx. 0.36 for Al2O3 and SiO2 particles, while it is approx. 0.09 for MgO particles. Hence, it is significantly smaller than the widely used value of 0.7, based on the study of (Fleener and Watson in Convective heating in dust-laden hypersonic flows 8th thermophysics conference, 1973), but in good agreement with values given in (Hove and Shih in Reentry vehicle stagnation region heat transfer in particle environments 15th aerospace sciences meeting, 1977) and (Molleson and Stasenko in High Temp 55:87–94, 2017. https://doi.org/10.1134/S0018151X1701014X ). No difference between erosive and elastic particle reflection mode was detected on the conversion efficiency. The data from a simplification of the modeling approach of the conversion efficiency for elastic particle reflection by Molleson and Stasenko (2017) are in poor agreement with experimental data.

Single- and two-phase water jet impingement heat transfer on a hot moving surface

In this study, the laminar flow and heat transfer of water jet impingement on a hot moving plate is investigated. A similarity solution is applied to momentum and energy equations formulating the single-phase forced convection in order to determine the flow velocity and heat transfer. The heat flux in flow boiling regime is predicted by a superposition approach which is based on the combination of the single-phase and nucleate pool boiling components. The effects of surface motion and arbitrary surface temperature distribution on important forced convection and nucleate boiling heat transfer parameters for both stationary and moving plates are examined in the stagnation line and its nearby region. The results show that surface motion does not affect the rate of heat transfer in stagnation region when surface temperature is constant, while this motion is found to decrease heat transfer for a non-uniform surface temperature distribution state. However, it is observed that in fully developed nucleate boiling regime, the parameters including the surface velocity, the surface temperature gradient and the local distance from the stagnation line have negligible effect on the rate of heat transfer from the surface.

Discussion: “Heat and Mass Transfer Analysis in the Stagnation Region of Maxwell Fluid With Chemical Reaction Over a Stretched Surface,” [T. Hayat, M. I. Khan, M. Imtiaz, and A. Alsaedi, 2018, ASME J. Thermal Sci. Eng. Appl., 10(1), p. 011002

Discussion: “Heat and Mass Transfer Analysis in the Stagnation Region of Maxwell Fluid With Chemical Reaction Over a Stretched Surface,” [T. Hayat, M. I. Khan, M. Imtiaz, and A. Alsaedi, 2018, ASME J. Thermal Sci. Eng. Appl., 10(1), p. 011002

Self-similarity of heat transfer characteristics in laminar submerged and free-surface slot jet impingement

Laminar slot jet impingement of free-surface and submerged jets is investigated numerically regarding self-similar behavior in local heat transfer. Two different scaling behaviors, one for the stagnation region and one for the fully developed wall-jet region are shown, and the validity of the scaling is confirmed by fully resolved numerical simulations. Within the stagnation region, self-similarity is obtained if the relaxation process of the velocity profile is considered, which is described by the dimensionless nozzle-to-plate distance h/W·ReW as introduced in Rohlfs et al. (2014) for circular jets. Further, it is shown that the Prandtl number dependency can be well described by an analytical relationship obtained by solving the classical similarity solution of a viscous flow near stagnation point. For the wall-jet region, we first derive the scaling behavior based on the work of Watson (1964) for circular free surface jets. This analysis leads to an additional stretching of the spatial coordinate in the wall-tangential direction by the Reynolds number, e.g. x∗=x/(W·ReW).Finally, correlations for the stagnation region heat transfer are introduced for free-surface and submerged slot jets, dependent on the dimensionless nozzle-to-plate distance and constant heat flux/wall temperature, valid over a wide range of laminar flow conditions (i.e., 0.07⩽Pr≤1307,100⩽ReW⩽1000 and 4⩽h/W⩽20). Thereby, analytic Prandtl dependencies for stagnation point flows are employed and corresponding correlations for impinging slot jets are presented, valid in a very broad range (0.0005⩽Pr⩽4500).

Stagnation Region Heat Transfer Augmentation at Very High Turbulence Levels

Current land-based gas turbines are growing in size producing higher approach flow Reynolds numbers at the leading edge of turbine nozzles. These vanes are subjected to high intensity large scale turbulence. This present paper reports on the research which significantly expands the parameter range for stagnation region heat transfer augmentation due to high intensity turbulence. Heat transfer measurements were acquired over two constant heat flux test surfaces with large diameter leading edges (10.16 cm and 40.64 cm). The test surfaces were placed downstream from a new high intensity (17.4%) mock combustor and tested over an eight to one range in approach flow Reynolds number for each test surface. Stagnation region heat transfer augmentation for the smaller (ReD = 15,625–125,000) and larger (ReD = 62,500–500,000) leading edge regions ranged from 45% to 81% and 80% to 136%, respectively. These data also include heat transfer distributions over the full test surface compared with the earlier data acquired at six additional inlet turbulence conditions. These surfaces exhibit continued but more moderate acceleration downstream from the stagnation regions and these data are expected to be useful in testing bypass transition predictive approaches. This database will be useful to gas turbine heat transfer design engineers.

Stagnation Region Heat Transfer of Axisymmetric Impinging Jets on Solid Surfaces

AbstractA theoretical model is proposed to evaluate the heat transfer characteristics of axisymmetric impinging fluid jets on the horizontal hot surface in the stagnation region using the energy integral method. A generalized expression involving various modeling parameters such as Nusselt number, nozzle‐to‐plate distance, Prandtl number, Reynolds number, and the modeling parameter k is obtained from the analysis. Present predictions are found to agree well with the test data involving a wide range of coolant type, Reynolds number, and nozzle‐to‐plate distance. In addition, a mechanistic correlation is suggested between the modeling parameter k and flow parameter, i.e., Reynolds number.

Influence of viscous flow relaxation time on self-similarity in free-surface jet impingement

Self-similar behavior in laminar free-surface jets regarding the velocity profile, its evolution, and the influence on stagnation-region heat transfer is presented. Approximate theoretical analysis shows that there are two regions with different scaling: a free-jet region where viscous relaxation dominates and an impingement region where a potential solution applies. Using the dimensionless time scale found for the first region, H/(D·Re), self-similarity is obtained for the axial velocity and its development. Fully resolved numerical simulations are performed to identify the crossover between the regions. It is further shown that the velocity profile at the cross-over point directly dictates the heat transfer distribution in the stagnation zone. The conditions under which this distribution has a central or off-center peak are found to be related to specific velocity profiles. Numerical results are used to find approximate closed-form relations tying the jet emergence velocity to the heat transfer distribution. A new comprehensive correlation is subsequently formulated for the heat transfer incorporating this new time scale, covering the range of velocity profiles emerging from pipe-type (parabolic) to orifice-type nozzles (uniform). A well-known analytical Prandtl dependency for stagnation flows is employed, yielding strong agreement with the numerical results. Agreement is observed for a very wide range of liquid and laminar flow conditions (i.e., 0.07<Pr<1307,73<Re<2000, and 4<H/D<110).

The effects of stroke length and Reynolds number on heat transfer to a ducted confined and semi-confined synthetic air jet

Heat transfer to three configurations of ducted jet and un-ducted semiconfined jets is investigated experimentally. The influence of the jet operating parameters, stroke length (L0/D) and Reynolds (Re) number on the heat transferred to the jet is of particular interest. Heat transfer distributions to the jet are reported at H/D = 1 for a range of experimental parameters Re (1000 to 4000) and L0/D (5 to 20). Secondary and tertiary peaks are discernable in the heat transfer distributions across the range of parameters tested. It is shown that for a fixed Re varying the L0/D has little effect on the magnitude of the stagnation region heat transfer but does effect the position and magnitude of the secondary and tertiary peaks in the heat transfer distribution. It is also shown that for a fixed L0/D increasing the Re has a significant effect on the magnitude of the stagnation region heat transfer but has little impact on the position of the secondary and tertiary peaks in the heat transfer distributions. Ducting is added to the configuration to improve heat transfer by drawing cold air from a remote location into the jet flow. Ducting is shown to increase stagnation region and area averaged heat transfer across the range of jet parameters tested when compared with an un-ducted jets of equal confinement. Increasing the stroke length from L0/D = 5 to 20 for a Reynolds number of 2000 reduces the enhancement in stagnation region heat transfer provided by the ducting from 35% to 10%; the area averaged heat transfer provided by the ducting also changes from a 42% to a 21% enhancement. This is shown to be partly due to relative magnitude of the peaks in heat transfer outwith the stagnation region; at low stroke lengths, the difference in the magnitude of these peaks is large and reduces with increasing L0/D. It is also shown that as L0/D is increased the stagnation region heat transfer to the un-ducted jets increases while for the ducted jets stagnation region heat transfer decreases with increasing L0/D. Increasing Reynolds number from 1000 to 4000 for a stroke length from L0/D = 10 increases the increase in stagnation region heat transfer provided by the ducting from 10 % to over 50 % and increases the increase in area averaged heat transfer provided by the ducting from 15 % to 45 %. This is shown to be primarily due to the magnitude of the stagnation region heat transfer. While the heat transfer increases with Re for all configurations of jet the increase is much more significant for the ducted jets.

촉매벽 효과를 고려한 무딘 물체 주위의 열화학적 비평형 유동에 대한 수치적 연구

A computational study has been performed to examine the effects of catalytic walls on stagnation region heat transfer. Boundary Conditions for none, finite, and fully catalytic walls have been incorporated into a Multi-Block Compressible Navier-Stokes code, known as Eilmer3. Both chemical and thermal nonequilibrium effects were included. Flows over several blunt bodies model at 0 deg angle of attack were simulated by varying surface catalytic recombination rates. A full range of catalycities was explored in the context of a surface energy balance and a constant wall temperature assumption. Detailed information on species concentrations, temperature, and surface heat flux are presented. Comparison with experimental surface heat flux data obtained using a shock tube is also made. Using the data obtained in a shock tube experiment, the catalytic efficiency of copper oxide was about 0.005, while copper had an efficiency of about 0.07.

Impingement Heat Transfer Enhancement on a Cylindrical, Leading Edge Model With Varying Jet Temperatures

Stagnation region heat transfer coefficients are obtained from jet impingement onto a concave surface in this experimental investigation. A single row of round jets impinge on the cylindrical target surface to replicate leading edge cooling in a gas turbine airfoil. A modified, transient lumped capacitance experimental technique was developed (and validated) to obtain stagnation region Nusselt numbers with jet-to-target surface temperature differences ranging from 60 °F (33.3 °C) to 400 °F (222.2 °C). In addition to varying jet temperatures, the jet Reynolds number (5000–20,000), jet-to-jet spacing (s/d = 2–8), jet-to-target surface spacing (ℓ/d = 2–8), and impingement surface diameter-to-jet diameter (D/d = 3.6, 5.5) were independently varied. This parametric investigation has served to develop and validate a new experimental technique, which can be used for investigations involving large temperature differences between the surface and fluid. Furthermore, the study has broadened the range of existing correlations currently used to predict heat transfer coefficients for leading edge jet impingement.

Effect of Thermal Boundary Condition on Heat Dissipation due to Swirling Jet Impingement on a Heated Plate

This paper reports on experimental research conducted to investigate the convective heat transfer characteristics for jet impingement with and without swirl. A series of different nozzle to surface heights, ranging from 0.5D to 10D, and Reynolds numbers, ranging from 8000 to 20000, were examined to determine their influence on the heat transfer characteristics for varying degree of swirl. Two separate experimental setups, having different thermal boundary conditions, were used in order to determine the effect that the thermal boundary condition might have on the findings. The results obtained indicate that the Nusselt number distributions are largely similar for the two boundary conditions considered, with the method based on a uniform wall temperature with hot-film sensor measurements showing greater local variation and spatial resolution in the stagnation region. For the range of parameters tested, the stagnation region heat transfer is enhanced with the addition of swirl to the jet flow.

The Influence of Leading Edge Diameter on Stagnation Region Heat Transfer Augmentation Including Effects of Turbulence Level, Scale, and Reynolds Number

Stagnation region heat transfer measurements have been acquired on two large cylindrical leading edge test surfaces having a four to one range in leading edge diameter. Heat transfer measurements have been acquired for six turbulence conditions including three grid conditions, two aero-combustor conditions, and a low turbulence condition. The data have been run over an eight to one range in Reynolds numbers for each test surface with Reynolds numbers ranging from 62,500 to 500,000 for the large leading edge and 15,625 to 125,000 for the smaller leading edge. The data show augmentation levels of up to 110% in the stagnation region for the large leading edge. However, the heat transfer results for the large cylindrical leading edge do not appear to infer a significant level of turbulence intensification in the stagnation region. The smaller cylindrical leading edge shows more consistency with earlier stagnation region heat transfer results correlated on the TRL parameter. These results indicate that the intensification of approaching turbulence is more prevalent with the more rapid straining of the smaller leading edge. The downstream regions of both test surfaces continue to accelerate the flow but at a much lower rate than the leading edge. Bypass transition occurs in these regions providing a useful set of data to ground the prediction of transition onset and length over a wide range of Reynolds numbers and turbulence intensity and scales.

The Physical Mechanism of Heat Transfer Augmentation in Stagnating Flows Subject to Freestream Turbulence

Experiments have been performed in a water tunnel facility to examine the physical mechanism of heat transfer augmentation by freestream turbulence in classical Hiemenz flow. A unique experimental approach to studying the problem is developed and demonstrated herein. Time-resolved digital particle image velocimetry (TRDPIV) and a new variety of thin-film heat flux sensor called the heat flux array (HFA) are used simultaneously to measure the spatiotemporal influence of coherent structures on the heat transfer coefficient as they approach and interact with the stagnation surface. Laminar flow and heat transfer at low levels of freestream turbulence (Tux¯=0.5–1.0%) are examined to provide baseline flow characteristics and heat transfer coefficients. Similar experiments using a turbulence grid are performed to examine the effects of turbulence with mean streamwise turbulence intensity of Tux¯=5.0% and an integral length scale of Λx¯=3.25 cm. At a Reynolds number of ReD¯=U∞¯D/υ=21,000, an average increase in the mean heat transfer coefficient of 64% above the laminar level was observed. Experimental studies confirm that coherent structures play a dominant role in the augmentation of heat transfer in the stagnation region. Calculation and examination of the transient physical properties for coherent structures (i.e., circulation, area averaged vorticity, integral length scale, and proximity to the surface) shows that freestream turbulence is stretched and vorticity is amplified as it is convected toward the stagnation surface. The resulting stagnation flow is dominated by dynamic, counter-rotating vortex pairs. Heat transfer augmentation occurs when the rotational motion of coherent structures sweeps cooler freestream fluid into the laminar momentum and thermal boundary layers into close proximity of the heated stagnation surface. Evidence in support of this mechanism is provided through validation of a new mechanistic model, which incorporates the transient physical properties of tracked coherent structures. The model performs well in capturing the essential dynamics of the interaction and in the prediction of the experimentally measured transient and time-averaged turbulent heat transfer coefficients.

Analysis and Prediction of the Thermal Performance of Piezoelectrically Actuated Fans

An experimentally validated numerical model is developed to analyze the operation of a piezoelectrically actuated cantilever vibrating close to a heated surface. The vibrating cantilever acts as a fan and provides localized cooling. The numerical results for the flow field and heat transfer show satisfactory agreement with experiments. The numerical model is used to develop fan curves for the piezoelectric fans, using a methodology similar to that used in constructing pump or fan curves for conventional fans. A simplified model based on stagnation region heat transfer in impingement flows is also proposed to estimate the heat transfer from a piezoelectric fan. The velocities obtained from the piezoelectric fan curves generated are used in this impingement heat transfer model, and the predictions are found to agree with measured stagnation zone Nusselt numbers with an average deviation of 17%.

Çarpan dikdörtgen bir hava jetinde türbülans modellerinin karşılaştırılması ve ilgili parametrelerin ısı transferine etkileri

Impinging jets have been used in a wide range of applications such as heating, cooling and drying due to its ability to enhance heat transfer. In this study, heat transfer characteristics of a heated plate in a cooling process with an impinging slot air jet are investigated numerically. Conservation equations are solved with ANSYS-FLOTRAN Galerkin Finite Element Code by assuming steady, turbulent, 2D, incompressible flow. Obtained results by using the std. k–e, RNG k–e, k–ω and SST turbulent models are compared with experimental results and better results are obtained with SST model. Then, the effects of jet-to-target distance and Re number, turbulence intensity, thermophysical property variation with buoyancy, and different heat flux values on the heat transfer are analyzed by using SST model. Computations are performed in the Reynolds number range of 4000 ≤ Re ≤ 12000 and the jet-to-target distance range of 4 ≤ z / Dh ≤ 12. Results showed that the local Nusselt number increases with increasing Reynolds number and decreasing z/Dh values. Also, stagnation region heat transfer is increased with increasing turbulence intensity.

Sensitivity analysis of freestream turbulence parameters on stagnation region heat transfer using a neural network

A neural network has been used to predict stagnation region heat transfer in the presence of freestream turbulence. The neural network was trained using data from an experimental study to investigate the influence of freestream turbulence on stagnation region heat transfer. The integral length scale, Reynolds number, all three components of velocity fluctuations and the vorticity field were used to characterize the freestream turbulence. The neural network is able to predict 50% of the test data within ±1%, while the maximum error of any data point is under 3%. A sensitivity analysis of the freestream turbulence parameters on stagnation region heat transfer was performed using the trained neural network. The integral length scale is found to have the least influence on the stagnation line heat transfer, while the normal and spanwise turbulence intensities have the highest influence.

Breakdown of similarity between momentum and energy transfer in a stagnation-region with free-stream turbulence

A direct numerical simulation of turbulent stagnation-region heat transfer with free-stream turbulence is performed. The temperature field in the 'damping' regime is mildly disturbed and that in the 'attached amplifying' regime is organised. In the 'detached amplifying' regime, the temperature field becomes turbulent. The temperature field is stretched in the x direction near the wall. The surface contours reveal that the temperature field is influenced significantly by streamwise vorticity. The enhancement of wall heat transfer by free-stream turbulence is similar to that in the previous results of the organised inflow disturbances. This indicates that the effect of large-scale eddies on the enhancement of wall heat transfer is important in the turbulent stagnation-region heat transfer. The breakdown of similarity between momentum and energy transfers in the stagnation-region with free-stream turbulence is analysed. The wall blocking and the pressure fluctuations are found to be responsible for the dissimilarity.

Turbulent Augmentation of Internal Convection Over Pins in Staggered-Pin Fin Arrays

The objective of this research was to investigate pin fin midline heat transfer in terms of our understanding of stagnation region heat transfer for cylinders in cross flow and turbine airfoils. An experimental investigation was conducted in a staggered-pin fin array at Reynolds numbers of 3000, 10,000, and 30,000 based on the maximum velocity between cylinders. Midline distributions of static pressure and heat transfer were acquired for rows 1 through 8 at the three Reynolds numbers. Turbulence measurements and velocity distributions were acquired at the inlet and in between adjacent pins in rows using hot wire anemometry. One-dimensional power spectra were calculated to determine integral and energy scales. Midline heat transfer distributions are reported as the Nusselt number divided by the square root of the Reynolds number as a function of angle. In these terms, heat transfer was found to increase through row 3 for a Reynolds number of 30,000. After row 3, heat transfer diminished slightly. The Reynolds number for each row was recast in terms of an effective approach velocity, which was found to be highest in row 3 due to the upstream blockage of row 2. Based on this effective velocity the Nusselt number divided by the square root of the Reynolds number increased through row 4. These data indicate that heat transfer is highest in row 3 pins due to the highest effective velocity, while heat transfer augmentation due to turbulence is highest in row 4 and beyond. Hot wire measurements show higher turbulence intensity and dissipation rates upstream of row 4 compared to upstream of row 3. Generally, pressure, heat transfer, and turbulence measurements were taken at all rows, providing a better understanding of turbulent transport from pin fin arrays.

Direct numerical simulation of stagnation region flow and heat transfer with free-stream turbulence

A direct numerical simulation is performed for stagnation-region flow with free-stream turbulence. A fully implicit second-order time-advancement scheme with fourth-order finite differences and an optimized scheme are employed. The optimized scheme is developed to save computational cost. The free-stream turbulence is a precomputed field of isotropic turbulence. The present DNS results in the “damping” and “attached amplifying” regimes are found to be similar to those of the organized inflow disturbances. Emphasis is placed on the flow and temperature fields in the “detached amplifying” regime. The contours of instantaneous flow field illustrate that streamwise vortices are stretched in the streamwise direction by mean strain rate. The temperature field is also stretched in the streamwise direction near the wall. The surface contours reveal that the temperature field is influenced significantly by streamwise vorticity. Due to the dominance of the mean strain, the log-law region is not observed for ū and T̃, the inner scaling fails, but the outer scaling works. The single-point turbulence statistics and the turbulent statistics budgets are obtained. The flow statistics reflect the typical characteristics of stagnation-region flow which are generically different from those of other canonical shear flows. One of the typical features of the budgets is that the velocity pressure correlation and the turbulent transport play significant roles in the stagnation-region flow. Finally, the present simulation data are compared with experimental results. It is found that the effect of large-scale eddies on the enhancement of wall heat transfer is substantial in the turbulent stagnation-region heat transfer.

Stagnation Line Heat Transfer Augmentation Due to Freestream Vortical Structures and Vorticity

Abstract An experimental study has been performed to investigate the effect of freestream vortical structures and vorticity on stagnation region heat transfer. A heat transfer model with a cylindrical leading edge was tested in a wind tunnel at Reynolds numbers ranging from 67,750 to 142,250 based on leading edge diameter of the model. Grids of parallel rods were placed at several locations upstream of the heat transfer model in orientations where the rods were perpendicular and parallel to the stagnation line to generate freestream turbulence with distinct vortical structures. All three components of turbulence intensity, integral length scale and the spanwise and transverse vorticity were measured to characterize the freestream turbulence. The measured heat transfer data and freestream turbulence characteristics were compared with existing empirical models for the stagnation line heat transfer. A new correlation for the stagnation line heat transfer has been developed that includes the spanwise fluctuating vorticity components.