Stagnation Line Research Articles

Numerical study on unsteady film cooling performance of turbine rotor considering influences of inlet non-uniformities and upstream coolant

High-pressure turbine (HPT) rotor blades work in a harsh environment with high temperature and rotational speed. Affected by blade row interaction and inlet non-uniformities, the rotor flow field behaves with significant unsteady characteristics. In order to study the unsteady film cooling performance of the rotor blade, unsteady numerical simulations were conducted on the film-cooled first stage vane and blade of GE-E3 engine HPT. Time-resolved results of cases with hot streak (HS) and combined HS and swirl were compared to the case with uniform inlet total temperature and velocity to investigate the effect of inlet non-uniformities. A simulation with non-film-cooled stator vane (NFCS) was also studied to reveal the impact of stator film coolant. The results showed that unsteady film cooling effectiveness fluctuations at the leading edge (LE) region are the most significant, with the mean-to-peak fluctuation amplitude reaching over ±100%. LE cooling air unsteady excursion induced by the stagnation line oscillation is the main cause of this behavior. Vane coolant and inlet non-uniformities have shown a distinguished influence on the coolant attachment and migration at LE, thus affecting the film cooling effectiveness. At blade pressure side (PS) and suction side (SS), vane coolant and inlet non-uniformities affect the fluctuation amplitude of film cooling effectiveness by changing the static pressure perturbation behavior. Simultaneously, the existence of HS will decrease the SS time-averaged film effectiveness by a factor of 10%. In comparison, swirl has shown a negative effect on PS film effectiveness by a factor of 6%.

Emission and absorption coefficients of diatomic gases in air plasmas produced by Earth entry

Accurate radiative properties data are required for the further calculations of radiative transfer in thermodynamic nonequilibrium plasmas produced by Earth entry. However, most of the published radiative properties were determined using the outdated spectroscopic constants, transition probabilities, and partition functions, some of which are less accurate and may deviate from the experimental results. In this paper, the spectral emission and absorption coefficients of diatomic molecules in air plasmas are thoroughly calculated based upon the exact line by line approach. In this scheme, the accurate spectroscopic constants and Franck–Condon factors were selected from the recent publications to reconstruct the rotational structure of spectral lines. Moreover, the level populations were determined by means of our newly reported two-temperature partition functions. The required thermodynamic parameters of each species were obtained by simulating a hypersonic flow field of the RAMC II vehicle. The calculated radiative properties were verified by the experimental and numerical equilibrium radiative source strength and the results show good consistency with measured and theoretical values in the available literature. Based upon the obtained flow field parameters, we finally predicted the distributions of nonequilibrium source strength along the stagnation line. Estimates and analysis were also made for the contributions of each transition system of the diatomic molecule to the total source strength.

A surrogate-based optimal likelihood function for the Bayesian calibration of catalytic recombination in atmospheric entry protection materials

This work deals with the inference of catalytic recombination parameters from plasma wind tunnel experiments for reusable thermal protection materials. One of the critical factors affecting the performance of such materials is the contribution to the heat flux of the exothermic recombination reactions at the vehicle surface. The main objective of this work is to develop a dedicated Bayesian framework that allows us to compare uncertain measurements with model predictions which depend on the catalytic parameter values. Our framework accounts for uncertainties involved in the model definition and incorporates all measured variables with their respective uncertainties. The physical model used for the estimation consists of a 1D boundary layer solver along the stagnation line. The chemical production term included in the surface mass balance depends on the catalytic recombination efficiency. As not all the different quantities needed to simulate a reacting boundary layer can be measured or known (such as the flow enthalpy at the inlet boundary), we propose an optimization procedure built on the construction of the likelihood function to determine their most likely values based on the available experimental data. This procedure avoids the need to introduce any a priori estimates on the nuisance quantities, namely, the boundary layer edge enthalpy, wall temperatures, static and dynamic pressures, which would entail the use of very wide priors. Furthermore, we substitute the optimal likelihood of the experimental measurements with a surrogate model to make the inference procedure both faster and more robust. We show that the resulting Bayesian formulation yields meaningful and accurate posterior probability distributions of the catalytic parameters with a reduction of more than 20% of the standard deviation with respect to previous works. We also study the implications of an extension of the experimental procedure on the improvement of the quality of the inference.

Numerical Analysis of the Take-Off Performance of a Seaplane in Calm Water

Nowadays, with the escalating tensions in maritime dispute and the development of marine economy, there has been renewed interest in seaplanes for their special capacity of taking off and landing on water. Prediction of take-off performance, involving aerodynamic analysis and hydrodynamic analysis, is a main challenge in seaplane design, while the prediction methods have been little improved since the 1960s. This paper aims to investigate the attitude and resistance characteristics of a seaplane at different speeds during the take-off by numerically modeling the air-water flow field using RANS equations with VOF method. The trim and heave motion of seaplane in response to aerodynamic forces, hydrodynamic forces, hydrostatic forces, and propeller thrust was realized by solving rigid body dynamics equations and adopting dynamic overset mesh technique. The variations in heave, trim angle, and resistance characteristics during the takeoff were investigated, and their inherent relationships with the aerodynamic, hydrodynamic, and hydrostatic performance were revealed. Particular investigation on the hydrodynamic resistance indicates that the stagnation line located at the convex bow would contribute a considerable increase of pressure resistance at the first hump, and the trim angel of a seaplane should be operated in an optimum trim range, typical between 4–6 deg, to minimize the hydrodynamic resistance at the second hump. Additionally, the dynamic motion convergence study proves that the utilization of damping terms was an effective way to accelerate the convergence of the dynamic motion ending with a quasi-static state.

Effect of microchannel on combined impingement and film cooling of a concave surface

In this work, a micro-channel-based wall cooling approach is investigated. The cooling efficiency of curved surfaces is determined by employing a computational study for conjugate heat transfer. A semi-circular curved body depicting the turbine blade leading edge, with a microchannel placed in the solid wall of the body and three rows of film holes, is considered for the study. The film holes are positioned along a stagnation line and either side of the stagnation line at an angle of 25o. The steady-state solver with a realizable k-ε turbulence model is used to study the heat transfer results for film cooling in a 3D geometry. Simulations were carried out, and subsequently, parametric analysis was performed to observe the effect of varying blowing ratio and temperature ratio. The temperature distribution is observed to be more uniform due to the presence of the microchannel, resulting in a lesser thermal gradient on the curved surface. It is also noted that overall effectiveness increases with the blowing ratio. The maximum increase in overall effectiveness due to placing the microchannel is found to be ~16% for the blowing ratio of three.

Shape factor effect of radiative Cu–Al2O3/H2O hybrid nanofluid flow towards an EMHD plate

This paper aims to analyze the effects of different nanoparticles shape factor, EMHD and radiation parameters for the Cu–Al2O3/H2O nanofluid flow towards a stretching/shrinking Riga plate. The model is simplified into a set of ordinary (similarity) differential equations using the similarity transformation while the existing correlations are used to estimate the thermophysical properties for Cu–Al2O3/H2O. The comparison with previous results is in a good agreement with 0% error. Second solution is found and only exist in certain value of the shrinking parameter which reflects the unstableness of the solution. From the streamlines plot, the second solution dislocates the stagnation line far away from the wall surface to the reverse flow region as compared to the first solution. An increase of 1% EMHD parameter extends the separation value by 0.4%. This reflects the potential of EMHD parameter in delaying the separation process. Further, the heat transfer rate slightly increases with the rise of EMHD, radiation and shape factor parameters. The maximum heat transfer rate is acquirable for the ascendance nanoparticle concentration using blade-shape while the sphere-shape produce the lowest thermal rate. These findings are important in long run where we can plan for the heat transfer optimization of the cooling/heating applications.

Hole arrangement effect to film cooling performance on leading edge region of rotating blade

The effect of relative position of two rows of film holes on film cooling performance was experimentally and numerically investigated on each side (suction side and pressure side) of rotating blade leading edge. The film cooling performance was measured by pressure sensitive paint and phase-locked techniques. The numerical simulation was also employed to improve the understanding of flow filed. The first row of film holes is fixed at α1 = ±10° downstream of stagnation line and is followed by the second row of holes with staggered arrangement. The span-wise relative positions between two rows of holes, P2/P1, are ranged from 1/4 to 3/4. Meanwhile, the stream-wise location of second row of holes is varied from α2 = ±25° to ±40°. Five blowing ratios ranged from 0.5 to 2.0 are also employed. The results indicate that the effect of relative position of two rows on film cooling is different on the two sides of leading edge. On the suction side, the relative position between two rows of holes significantly affects the interaction between the adjacent jets from two rows, which determines the distribution and value of film cooling effectiveness. When it comes to the leading edge pressure side, closer distance between two adjacent holes in two rows produces better film cooling performance. Meanwhile, the effect of relative position between two rows of holes is mainly located in the near hole region.

Performance Prediction of a Hard-Chine Planing Hull by Employing Different CFD Models

This paper presents CFD (Computational Fluid Dynamics) simulations of the performance of a planing hull in a calm-water condition, aiming to evaluate similarities and differences between results of different CFD models. The key differences between these models are the ways they use to compute the turbulent flow and simulate the motion of the vessel. The planing motion of a vessel on water leads to a strong turbulent fluid flow motion, and the movement of the vessel from its initial position can be relatively significant, which makes the simulation of the problem challenging. Two different frameworks including k-ε and DES (Detached Eddy Simulation) methods are employed to model the turbulence behavior of the fluid motion of the air–water flow around the boat. Vertical motions of the rigid solid body in the fluid domain, which eventually converge to steady linear and angular displacements, are numerically modeled by using two approaches, including morphing and overset techniques. All simulations are performed with a similar mesh structure which allows us to evaluate the differences between results of the applied mesh motions in terms of computation of turbulent air–water flow around the vessel. Through quantitative comparisons, the morphing technique has been seen to result in smaller errors in the prediction of the running trim angle at high speeds. Numerical observations suggest that a DES model can modify the accuracy of the morphing mesh simulations in the prediction of the trim angle, especially at high-speeds. The DES model has been seen to increase the accuracy of the model in the computation of the resistance of the vessel in a high-speed operation, as well. This better level of accuracy in the prediction of resistance is a result of the calculation of the turbulent eddies emerging in the water flow in the downstream zone, which are not captured when a k-ε framework is employed. The morphing approach itself can also increase the accuracy of the resistance prediction. The overset method, however, overpredicts the resistance force. This overprediction is caused by the larger vorticity, computed in the direction of the waves, generated under the bow of the vessel. Furthermore, the overset technique is observed to result in larger hydrodynamic pressure on the stagnation line, which is linked to the greater trim angle, predicted by this approach. The DES model is seen to result in extra-damping of the second and third crests of transom waves as it calculates the stronger eddies in the wake of the boat. Overall, a combination of the morphing and DES models is recommended to be used for CFD modeling of a planing hull at high-speeds. This combined CFD model might be relatively slower in terms of computational time, but it provides a greater level of accuracy in the performance prediction, and can predict the energy damping, developed in the surrounding water. Finally, the results of the present paper demonstrate that a better level of accuracy in the performance prediction of the vessel might also be achieved when an overset mesh motion is used. This can be attained in future by modifying the mesh structure in such a way that vorticity is not overpredicted and the generated eddies, emerging when a DES model is employed, are captured properly.

The effect of spray deflection on the performance of high speed craft in calm water

Hydrodynamic analysis of high speed craft is a complex problem. Naval architects have been improving the efficiency of high speed hulls by introducing hard chines, warping, adding spray rails and steps, or forcing air ventilation. Spray deflectors is a novel spray redirection technology inspired by spray rails. It has shown potential for further improving the performance of high speed craft. Spray deflectors run parallel to the stagnation line from the keel to the chine through the spray area. Previous numerical and experimental studies focusing on spray deflectors have been unable to draw definite conclusions regarding the efficiency and optimal design of the deflectors. This paper aims to experimentally investigate, through towing tank testing, the effect on the total resistance using spray deflectors to redirect the spray. Three spray deflectors were designed for different design speeds, tested, and compared in terms of the resulting bare hull for resistance, trim, and heave response. The new deflector designs did not affect the running position of the hull, allowing for an unequivocal resistance comparison. Deflectors reduced resistance by up to 5% with the highest reduction achieved when the stagnation line crossed the deflector at about a quarter beam from the chine.

Stagnation line due to colliding wall jets of two liquid impinging jets on a horizontal surface

When two free liquid jets impinge on a planar surface with their wall jets colliding, a stagnation line is formed between the two wall jets. The location and shape of the stagnation line depend on the free jet flow conditions, fluid properties, impingement orientation of each free jet, and relative positioning of the two free jets. Experiments are conducted to observe and measure stagnation lines formed by two free jets impinging on the upper surface of a transparent plate, and a camera is placed under the plate to take the images of stagnation lines. It is found that changing the fluid and the position and orientation of the two jets causes the stagnation line to change. A theoretical model consisting of momentum analysis of a singe wall jet and momentum balance of two wall jets is derived to predict the stagnation line. It is hypothesized that, when two unequal liquid wall jets collide, the stagnation takes place where the momentum balance between the two jets within the thinner thickness is satisfied. Based on the hypothesis, the developed theoretical model shows good agreement with the experimental results.

Showerhead film cooling injection orientation design on the turbine vane leading edge considering representative lean burn combustor outflow

The heat transfer performance of showerhead film cooling on the vane leading edge was numerically investigated considering representative lean burn combustor swirling outflow. Three cases with different inflow conditions (uniform inflow, positive swirling inflow, and negative swirling inflow) and three cases with different film injection angles (45°, 90°, and 135°) were studied. As the first study to explore the showerhead film design principle under swirling inflow, a newly designed asymmetrical counter-inclined (45° and 135°) film cooling was also proposed. To examine the design principles, the cooling effectiveness, heat transfer augmentation, and heat flux reduction of the newly designed asymmetrical case were evaluated compared with the traditional symmetrical case. The results show that the swirling inflow introduces obvious radial pressure gradient on the vane. The radial pressure gradient is the key influence factor to deflect the coolant migration, decrease the cooling effect, and degrade the homogeneity. The film with opposite orientation to the radial pressure gradient can weaken the deflect effect. The radial pressure gradient direction differs in different regions, making it impossible for the film with congruent injection orientation to simultaneously resist the pressure gradient on the entire vane. For the new design, the boundary line of the counter-inclined holes is consistent with the twisted stagnation line to guarantee that the injection orientation of all the film holes is opposite to the radial pressure gradient. As expected, the new design can effectively weaken the deflection effect and show uniform film distribution. The higher coolant mass ratio provides more obvious enhancement effect. At coolant mass ratio 3.71% and 4.56%, the overall area-averaged heat flux reduction (Δ q) is increased by 0.311 and 0.576, and the overall area-averaged relative standard deviation is reduced by 12.17 and 11.66 compared with the traditional design. The results have confirmed the adaptability of the film design principle under swirling inflow.

Numerical simulation of hypersonic reaction flows with nonlinear coupled constitutive relations

As all known, there exists extremely thermal and chemical non-equilibrium phenomenon in hypersonic flows. Much effort has been put into the development of computational models for the prediction of such non-equilibrium flow. In order to obtain the real physical solution of the challenging non-equilibrium problems, Eu proposed a set of generalized hydrodynamic equations (GHE) from the viewpoint of generalized hydrodynamics. Based on Eu's GHE equations, Myong developed an efficient computational model, named as the nonlinear coupled constitutive relations (NCCR). The present study is based on the 3-D FVM NCCR model in conjunction with 7-species chemical reaction model to consider the reacting gas effect for hypersonic reentry vehicles. For further examining the performance of the proposed computational model, the typical engineering cases of Radio Attenuation Measurements (RAM)-C II vehicle are adopted. The flow contours, distribution profiles along stagnation line and surface properties are compared between nonlinear coupled constitutive model and those of the Navier-Stokes equation. The accuracy and physical consistency of the NCCR model are critically examined and validated for hypersonic reaction flow in the continuum region. For the near continuum region, the NCCR model can predict non-equilibrium phenomenon more accurately than NS equation through the comparison of shock stand-off distance and electron number density. The comparisons between NCCR model with one component perfect gas and multi-species reacting gas effect are also made to show the importance of chemical reaction source term.

Experimental investigation of inclination angle effect on unsteady film coverage of double-row staggered-holes at vane leading edge using time-resolved quantitative light sheet technique

Turbine vane leading edge features the highest heat load and is effectively protected by multi-row film-ejections. In present work, time-resolved planar quantitative light sheet (QLS) technique was proposed to acquire unsteady behaviors of film coverage and jet-trajectory caused by fluid-interaction. Under proper calibrations, the uncertainty of transient concentration measurement was controlled below 4.5%. Leading edge zone of a typical film-cooled vane was simplified into a cylinder with double-row staggered cylindrical-holes. One row locates at the stagnation line and the other is in the downstream. The effect of inclination angle of film-holes on the unsteady film coverage and the concentration-interactions of two rows was of concern. Transient tests revealed that row-to-row interaction can generate higher time-averaged film cooling effectiveness; however, improve the unsteadiness of film outflow, an adverse factor of component durability. Relative to the downstream hole-row, the ejections in stagnation line dominated much stronger unsteadiness. The angle effect on film cooling unsteadiness in stagnation line was significant; however, in the downstream was nearly non-sensitive. Along the vane span, the irregular relationships of unsteadiness with hole-location and hole-angle can be found. Consequently, some new suggestions of film cooling design in stagnation region were proposed based on the aforementioned unsteadiness analysis.

Blackout analysis of Mars entry missions

Abstract

An exploratory study on using Slippery-Liquid-Infused-Porous-Surface (SLIPS) for wind turbine icing mitigation

An experimental study was conducted to explore the potentials of using a Slippery-Liquid-Infused-Porous-Surface (SLIPS) for wind turbine icing mitigation. The SLIPS was prepared by infusing a lubricant oil into a nanofibrous membrane, which can stick firmly to the surface of a turbine blade model. While the SLIPS was found to effectively suppress impact ice accretion on the blade surface where strong aerodynamic forces are exerted, ice was still found to accrete in the vicinity of the blade stagnation line where aerodynamic forces are at their minimum. A novel hybrid anti-/de-icing strategy to integrate the SLIPS with a minimized leading-edge heating was demonstrated to effectively remove the ice accretion over entire blade surface. An comprehensive experimental study was also performed to evaluate the durability of the SLIPS to resist wearing away of the substrate materials and depletion of the infused lubricant oil due to “rain erosion” effects, in considering its practical usage for wind turbine icing mitigation. It was found that the “rain erosion” effects would induce significant surface wettability degradation, substantial ice adhesion increment and even structural failures to the SLIPS as the duration of the rain erosion testing increases.

The Combined Influences of Film Cooling and Thermal Barrier Coatings on the Cooling Performances of a Film and Internal Cooled Vane

This paper presents a numerical investigation on the combined influences of film cooling and thermal barrier coatings (TBCs) on the cooling performances of a NASA C3X guide vane. The results show that: (1) film cooling on the pressure side is more effective than suction side, especially on the trailing edge where multiple cooling and thermal protection techniques include internal cooling and TBCs are necessary. (2) TBCs show positive and negative roles in improving cooling performance at the same time for the coated vane with or without film cooling. Without film cooling, TBCs show negative roles on the regions with lower temperature external hot gas, which is caused by flow acceleration from the stagnation line of the suction side. (3) Internal cooling improvement caused by coolant introduction leads to a larger cooling effectiveness inclement due to TBCs near coolant plenums and film cooling holes. However, the influence of TBCs on cooling effectiveness increment goes down and even shows negative roles on the regions away from coolant plenums and under the effective coverage of the film cooling. (4) Improving the convective heat transfer of coolant with the wall of coolant plenums and film cooling holes is the guarantee of improving the cooling performance of a coated vane.

Pumping flow model for couple stress fluids with a propagative membrane contraction

A pumping flow model induced by propagative and non-propagative wall contraction is presented to examine the pumping and flow characteristics. A couple stress fluid model is considered to see the effect of couple stress parameter. An inelastic single membrane is used in upper wall of the channel with rhythmic contraction to produce unidirectional flow which can be applied in many physiological transports. Governing equations are derived using basic conservation principles of mass and momentum. Furthermore scaling analysis is made to introduce the lubrication theory (typical length scale δ=(H/λ)≪1 and low Reynolds number approximation). The influence of the couple stress parameter, propagative shape membrane, and the time variation on axial velocity, volumetric flow rate, local shear stress, pressure gradient, and streamline distribution are evaluated with aid of in-house code in Matlab. The significant stagnation line in the flow streamline with the membrane parameter is computed where the pressure gradient is zero. This study is relevant in the simulation of fluid dynamics of duodenum and intestine and other physiological systems. Novel smart biomimetic pumping devices are relatively easy to engineer using this pumping mechanism.

The Discrete Green's Function for Convective Heat Transfer—Part 2: Semi-Analytical Estimates of Boundary Layer Discrete Green's Function

Abstract This is the second paper in a set that defines the discrete Green's function (DGF). This paper focuses first on the turbulent boundary layer and presents two different methods to estimate the DGF. The long-element formulation defines the DGF with just two simple algebraic equations, but it is not quantitatively accurate for short element lengths. A short element correction is derived, but must be recalculated for each selection of flow parameters and element lengths. A similarity solution is derived that allows accurate estimates of the DGF diagonal elements for laminar boundary layers and for turbulent boundary layers discretized with short element lengths. To illustrate other methods to derive DGFs in more complex flows, a low-resolution DGF for laminar stagnation line boundary layers is determined using the skin-friction formulation combined with similarity solutions for two different thermal boundary conditions. Stagnation line flow is shown to be highly sensitive to the thermal boundary condition, and this can be analyzed effectively using the DGF.

Bio-Inspired Icephobic Coatings for Aircraft Icing Mitigation: A Critical Review

A critical review is provided to summarize our recent efforts to utilize the state-of-the-art bio-inspired icephobic coatings/surfaces, i.e., 1). Lotus-leaf-inspired superhydrophobic surfaces (SHS) and 2). Pitcher-plant-inspired slippery liquid-infused porous surfaces (SLIPS) for aircraft icing mitigation. By leveraging the unique Icing Research Tunnel of Iowa State University (i.e., ISU-IRT), an experimental campaign was performed to evaluate the effectiveness of using SHS and SLIPS coatings to suppress impact ice accretion over the surfaces of typical airfoil/wing models. While both SHS and SLIPS were found to be able to suppress ice accretion over the airframe surfaces where strong aerodynamic forces are exerted, ice was still found to accrete in the vicinity of the airfoil stagnation line where the aerodynamic forces are at their minimum. A novel hybrid anti-/de-icing strategy concept to combine icephobic coatings with minimized surface heating near airfoil leading edge was demonstrated to effectively remove impact ice accretion over entire airfoil/wing surfaces. An experimental investigation was also conducted to examine the durability of the icephobic coatings/surfaces to resist "rain erosion" effects (i.e., the damage to the surface coatings due to continuous impingement of water droplets at high speeds) in considering the practical usage for aircraft icing mitigation. The rain erosion effects were characterized based on the variations of the ice adhesion strengths and surface morphology of the eroded test surfaces coated with SHS and SLIPS. The research findings are very helpful to elucidate the underlying physics for the development of novel and robust anti-/de-icing strategies for aircraft icing mitigation.

Coolant Jets Blowing Across the Airfoil Stagnation Line to Enhance Film Effectiveness

Abstract A novel airfoil leading edge film cooling design has been investigated, and its performance over conventional alternatives quantified. In conventional designs, the region near the geometric stagnation line is typically between the two most upstream film hole rows, which each emit coolant in the downstream direction on their respective sides of the airfoil. This region is thus relatively starved of coolant flow and adequate cooling is achieved inefficiently with a high density of holes expelling a large amount of coolant in order to dilute the nearby mainstream flow. Drawing inspiration from recent literature on reverse-blowing film cooling holes, several film cooling geometries have been designed and tested with a view to improving upon this situation by blowing coolant from each side of the airfoil geometric stagnation line to the other in a criss-cross pattern. This is found to be capable of producing much higher film effectiveness near the stagnation line than a series of more conventional designs which were also tested, without decreasing downstream film effectiveness. A method is also described for using experimental film effectiveness data to estimate two novel measures of the efficiency of leading edge film coolant usage: the proportion of the mainstream which interacts with leading edge film coolant and the proportion of coolant from the two most upstream film hole rows which reaches the stagnation line.