In advanced heat transfer courses, a technique exists for reducing a partial differential equation, where the dependent variable is a function of two independent variables, to an ordinary differential equation where that same dependent variable becomes a function of only one. The key to this technique is finding out what the functional form of the similarity variable is to make such a transformation. The difficulty is that the form of the similarity variable is not intuitive, and many heat transfer textbooks do not reveal how this variable is found in classical problems such as viscous and thermal boundary layer theory. It turns out that one way to find this variable is by utilizing the integral technique. By employing the integral technique to boundary layer theory, it will be shown that when the approximate functional relationship for the dependent variable (temperature, velocity, etc) can be represented by an nth order polynomial, the similarity variable can be found very simply. This is seen to be a good tool especially in heat transfer education, but may have applications in research as well. The approach described here is a variation of a well-known technique used for isothermal momentum boundary layer consideration.

The paper presents a new solution for the wind turbine profile shape modeling based on the concept of the maximum lift force, capable to be produced at different values of the wind velocities. The profile is designed and realized in accordance with the new concept emerged in the last decade, on the operation of the wind turbines with maximum lifting force. The purpose is to provide a low-noise during operation because a negative effect on the medium and long-term operation of the wind turbines (wind farms) is the noise that affects the flight of birds, terrestrial animal life, and especially human communities. Various sources generate independent acoustic emissions on wind profiles, such as the turbulent flow, the interaction of the turbulent boundary layer area of the trailing edge, the flow separation, and the boundary layer separation of vortices formed in the zone of the trailing edge. There is also considered the influence of the apparent wind on the incidence variation of the profile. In order to maintain an optimum angle of attack relative to the wind velocity, a fixed blade inclination must increase its speed to be proportional to the wind. Thus, to maximize the aerodynamic performance, the rotor must spin faster when the wind intensity increases. Measurement of the acoustic signal requires electronic devices that operate on electric signals obtained from the conversion of the pressure variations in voltage or variations in electrical current. The noise caused by the turbulent flow is generated primarily by the sharply pointed leading edge and cannot be diminished. There are presented some numerical results correlated with the measurements made in the field.

Turbine airfoils are subject to strong secondary flows that produce total pressure loss and high surface heat transfer in the airfoil passage. The secondary flows arise from the high overall flow turning acting on the incoming boundary layer, as well as the generation of a horseshoe vortex at the leading edge of the airfoil. Prediction of the effects of secondary flows on endwall heat transfer using steady Reynolds-averaged Navier-Stokes (RANS) approaches has so far been somewhat unsatisfactory, but it is unclear whether this is due to unsteadiness of the secondary flow, modeling assumptions (such as the Boussinesq approximation and Reynolds analogy), strongly non-equilibrium boundary layer behavior in the highly skewed endwall flow, or some combination of all. To address some of these questions, and to determine the efficacy of higher-fidelity computational approaches to predict endwall heat transfer, a low pressure turbine cascade was modeled using a wall-modeled Large Eddy Simulation (LES) approach. The result was compared to a steady Reynolds-stress modeling (RSM) approach, and to experimental data. Results indicate that the effect of the unsteadiness of the pressure side leg of the horseshoe vortex results in a broad distribution of heat transfer in the front of the passage, and high heat transfer on the aft suction side corner, which is not predicted by steady RANS. However, the time-mean heat transfer is still not well predicted due to slight differences in the secondary flow pattern. Turbulence quantities in the blade passage agree fairly well to prior measurements and highlight the effect of the strong passage curvature on the endwall boundary layer, but the LES approach here overpredicts turbulence in the secondary flow at the cascade outlet due to a thick airfoil suction side boundary layer. Overall, more work remains to identify the specific model deficiencies in RSM or wall-modeled LES approaches.

To improve the airfoils performances placed in supersonic flow is proposed a method of optimization for their shapes, in order to minimize the effect of the landing vortices. The theoretical modeling starts with the Navier-Stokes equations applied for thin layers, supplemented with additional conditions related to the profile shape. For a proper estimation of efficiency and responses at different flow regime’s conditions, were considered four aerodynamics airfoils, with different shapes and functioning characteristics. Two of them are special shapes of supersonic profiles and the other two deduced by theoretical assessments with an efficient behavior at high Reynolds numbers. The main purpose of this selection was to identify the essential aspects needed to be considered in numerical modeling of the airfoil’s wing shapes, as to assure an optimization of their behavior for different flow conditions. In the supersonic flow, the cross-sections of the wings are thin profiles, mainly symmetric, as to reduce the drag coefficient and to maximize, as possible, the lift coefficient. A supplementary method for the shape calculation of the aerodynamic profiles with small curvature, based on the Fredholm integral equation of the second kind, with a good behavior in the supersonic flow, is presented. Some aspects referring to unsteady flows and air compressibility are considered, as to simulate as much as possible the real, natural conditions. All profiles were tested, firstly, into a subsonic wind tunnel at incidences between 0 0 – 4 0 for different values of wind velocity, and secondly, into a supersonic wind tunnel, at the same incidences. The objective was to better understand and analyze the main factors, which influence the aerodynamic of shapes with curvature, and to assure an optimization of their behavior. The purpose of testing these profiles was to estimate a solution to improve the main characteristics, especially into the trailing and leading edges zones. There were also considered the effects of the attack angle, the influence of the wind velocity, air viscosity, and the shape’s curvature, on the vortices development. The obtained results allow a better functioning in supersonic flow regime, by eliminating the adverse pressure gradient and the boundary layer separation, assuring an optimum behavior especially into the leading edge zone.

Offshore wind turbines are mega structures that span a critical section of the lowest part of atmospheric boundary layer while experiencing significant wind shear. A detailed knowledge of the wind field through a wind farm as part of the atmospheric boundary layer is essential to design efficient farm layouts and estimate power production for grid integration. To address these needs, we present a micro-scale wind prediction model based on a large-eddy simulation paradigm. We consider actuator disk models with and without rotation to simulate the influence of turbines on the wind field and apply our computational capability to the well-known Horns Rev offshore wind farm in Denmark to estimate power production. Instead of using manufacturers power curve to estimate power production, we propose an alternative approach based on the control volume analysis of kinetic energy conservation around turbines.

This experiment measures the temperature and the velocity field synchronously in the boundary layer in a rotating smooth, wall-heated channel using hot-wire. The Reynolds number based on the bulk mean velocity and hydraulic diameter is 19000 and the rotation numbers are 0, 0.07, 0.14, 0.21, 0.28 and 0.35. Four streamwise stations (X/D = 4.06, 5.31, 6.56, 7.81) were investigated. To calibrate the parallel-array hot-wire probe, a heating section is added to the original wind tunnel that could only calibrate the hot-wire at room temperature. Different gas temperatures at the outlet could be obtained by changing the heating power of the heating section. The velocity profiles and the temperature profiles are obtained. It can be seen that the viscous sublayer also exists when the wall is heated, thus the viscous sublayer profile method is also valid when the wall is heated. It is found that the velocity profile near the leading side is more sensitive to the change of rotation number and X/D than the velocity profile near the trailing edge. The critical rotation number phenomenon of velocity profile has also been found in present work. By comparing with the previous work without the wall heated, the influence of both kinds of buoyancy under this condition is discussed. Some explanations are given for the experimental results.

In the current study, the influence of different rotation conditions on the flow behavior is experimentally investigated by a new system which is designed for time-resolved PIV measurements of the smooth channels at rotation conditions. The Reynolds number equals 15000 and the rotation number ranges from 0 to 0.392 with an interval of 0.098. This new time-resolved Particle Image Velocimetry system consists of a 10 Watts continuous laser diode and a high-speed camera. The laser diode can provide a less than 1mm thickness sheet light. 6400 frames can be captured in one second by the high-speed camera. These two parts of the system are fixed on a rotating disk. In this case, the relative velocity of flows in the rotating smooth square channel can be measured directly to reduce the measurement error. This system makes high-speed camera close to the rotating channel, which allows a high resolution for the measurements of main stream. In addition, high accuracy and temporal resolution realize a detailed analysis of boundary layer characteristics in rotation conditions. Based on this system, experimental investigation has been undertaken. Results are presented of the evolution of velocity and boundary layer thickness at various rotation numbers and different circumferential positions.

In this study, the tribological behavior of the Trihexyl tetradecylphosphonium-bis(2,4,4-trimethylpentyl)phosphinate [THTDP][Phos] ionic liquid with and without single-wall carbon nanotubes (SWCNT) dispersion as a thin boundary layer was intended for investigation. However, the surface heat treatment process was not sufficient to form a thin film on the sample surfaces. Thus, in each test condition, the lubricating agents were used as external (liquid) lubricants. Specifically, [THTDP][Phos] and ([THTDP][Phos]+0.1 wt.% SWCNT) boundary film layers were applied on 6061-T6 aluminum alloy disk samples and tested under sliding contact with 1.5 mm diameter 420C stainless steel balls using a ball-on-flat linearly reciprocating tribometer. A commercially available Mobil Super 10W-40 engine oil (MS10W40) was also tested and used as this investigation’s datum. The tribological behavior of [THTDP][Phos] and ([THTDP][Phos]+SWCNT) boundary film layers was analyzed via wear volume calculations from optical microscopy measurements, as well as by observation of the transient coefficient of friction (COF) obtained through strain gauge measurements made directly from the reciprocating member of the tribometer. Results indicate the potential for reduction of wear volume and coefficient of friction in the IL lubricated steel-on-aluminum sliding contact through (SWCNT) dispersion in the ionic liquid. Wear results are based on measurements obtained using optical microscopy (OM). Results discussed display improved tribological performance for both [THTDP][Phos] and ([THTDP][Phos]+SWCNT) over baseline MS10W40 oil lubricant for both roughness values tested for the steel-on-aluminum contact. No measurable improvements were observed between [THTDP][Phos] and ([THTDP][Phos]+SWCNT) tests.

Current CFD models fail to accurately predict boundary layer asymmetry on spin-stabilized projectiles, particularly in the transonic and subsonic flow regimes. Consequently, these models cannot accurately characterize the Magnus moment, a key component in aerodynamic behavior. This work seeks to capture boundary layer thickness asymmetry, an indicator of Magnus effects, around a spinning projectile using Magnetic Resonance Velocimetry (MRV). The MRV technique allows for collection of three-dimensional, non-intrusive, high-resolution velocity field measurements that can be used for comparison to and validation of current computational models. In this experiment, a modified M80 projectile was designed to thicken the hydrodynamic boundary layer for technique validation. The scaled projectile was mounted in a custom-designed test rig at a 2° nosedown angle of attack. The apparatus rotated the projectile at various spin rates in a constant flow of copper-sulfate solution. Initial results revealed azimuthal differences in boundary layer thickness for three different cases — no spin, nominal spin, and double spin — particularly in the tapered rear (boattail) region of the projectile. The introduction of spin shifted the boundary layer thickness in the spin direction resulting in lateral boundary layer asymmetry in the boattail region, a phenomenon that likely affects the stability of spin-stabilized projectiles.

Organic Rankine cycle (ORC) has gained an increasing worldwide attention due to its high efficiency in converting low-grade thermal energy into electricity. The expander is the most critical component in the ORC system. Among the influential factors that define the performance of the expander, the velocity coefficient of the nozzle is crucial. This work numerically investigates the effects of the nozzle height, length, surface roughness, outlet geometric angle, and expansion ratio, on the velocity coefficient of the nozzle in the ORC turbine with hexamethyldisiloxane (MM) as working fluid. In the 3-D viscous numerical analysis, the shear stress transports k-ω turbulence model is employed and the numerical method is verified by the experimental data of the nozzle with pressured air based on hotwire technology. The numerical results show that the velocity coefficient is almost independent of expansion ratio compared to other factors due to the relatively small flow boundary layer and high Reynolds number. Since the existing correlations for the gas nozzle cannot well predict the velocity coefficient of the organic nozzle, an empirical equation is proposed according to the numerical results with the maximum deviation of 3.0%.

The growth in renewable energy generation highlights a demand for an effective energy storage system for future power grid. Energy storage systems have a crucial role in balancing the power grid and compensating for intermittency of renewable energy sources. The state-of-the-art of grid-scale energy storage technologies (e.g., pumped-hydro and conventional compressed air energy storage) require special topological considerations; however, thermal energy storage remains as a scalable technology for storing the energy from solar thermal plans and the power grid. In this paper elemental sulfur is further investigated as a storage medium for its driving low cost and high energy storage density capabilities. Presented work numerically investigates the heat transfer behavior between elemental sulfur and an internal heat source that is placed within the thermal energy storage element. The heat transfer from the internal heat source to the thermal storage medium (elemental sulfur) is investigated computationally to understand the heat transfer behavior during charge cycle. The computations were performed with a commercial CFD package (ANSYS FLUENT) using variable properties for the storage medium. A comprehensive grid refinement study was performed to ensure the accuracy of the computational results. The results of this study show that buoyancy-driven flow induced by the internal heat source forms a rising jet toward the top of the thermal energy storage element and enhances the mixing of the boundary layer leading to enhanced heat transfer from the internal heat source.

DBD plasma actuators have several applications within the field of active flow control. Separation control, wake control, aircraft noise reduction, modification of velocity fluctuations or boundary layer control are just some examples of their applications. They present several attractive features such as, their simple construction, very low mass, fast response, low power consumption and robustness. Besides their aerodynamic applications, these devices have also possible applications within the field of heat transfer, for example film cooling applications. However, due to the extremely high electric fields in the plasma region and consequent impossibility of applying intrusive techniques, there is a relative lack of information about DBDs thermal characteristics. In an attempt to contradict this scenario, this work describes the thermal behaviour of DBD plasma actuators. The total power consumed, the fraction of power that is dissipated as heat energy and the dielectric temperature variation due to the plasma operation are some parameters with great interest in any plasma actuator applications. Thus, these parameters were quantified and the results were presented and discussed. Infra-red thermography measurements were performed in order to obtain the temperature distribution of the dielectric layer. During this work we analysed DBD plasma actuators with different dielectric thicknesses and also with different dielectric materials, whose thermal behaviour was not reported in the literature yet. Conclusions were taken in order to extend the fundamental knowledge on the thermal aspects of the DBD plasma actuators.

Proper Orthogonal Decomposition (POD) analysis of high-resolution Particle Image Velocimetry (PIV) measurements is used to identify the most energetic coherent structures of the turbulent flow field resulting from the interaction of a turbulent boundary layer with a shallow cavity. The PIV measurements capture the flow structure and turbulence, upstream, over, and downstream of a shallow open cavity. Two sets of PIV measurements corresponding to a turbulent incoming boundary layer and a cavity length-to-depth ratio of four are used. The cavity depth based Reynolds numbers are 21,000 and 42,000. The first six POD modes are found to contain a substantial percentage of the overall turbulent energy, approximately 45.2% and 45.7% for Reynolds numbers of 21,000 and 42,000, respectively. The overall spatial and modal energy content distribution are almost identical for both Reynolds numbers. The spatial flow characteristics of POD modes 1–6 reveal the existence of vortical structures, developing in the mixing region, that grow in size as they approach the trailing edge of the cavity. POD mode number one, containing approximately 20% of the overall turbulent energy, represents non-impinging vortices interaction with the cavity trailing edge, while POD modes 2–6 capture various stages of the impinging vortices type of interaction.

A vortex cell is a cylindrical aerodynamic cavity that traps separated vortices to prevent the formation of large-scale vortex shedding. Due to the presence of complex vortical structures, regions with varying turbulent intensities, and rotation-curvature effects on turbulent structure; the flow inside a vortex cell is a valuable test case for newly proposed turbulence models and numerical schemes. In the present study, numerical simulations were carried using a Reynolds-averaged Navier-Stokes (RANS) turbulence model and two hybrid RANS/large-eddy-simulation (LES) models. The computational domain consists of a cylindrical cavity with an incoming transitional boundary layer and a Reynolds number of 9.4 × 10 4 based on the diameter of the cavity. Results indicate that the RANS model provides general information about the flow characteristics, while the hybrid RANS-LES models predict the flow characteristics with more accuracy but suffer inaccuracies due to the details of the RANS to LES transition. Most significantly, the dynamic hybrid RANS-LES (DHRL) model in combination with a low-dissipation numerical scheme overpredicts the turbulent mixing in the vortex cell and fails to provide an accurate representation of the physics of the trapped vortex. It is concluded that the hybrid RANS-LES models used in this study need further work to be able to fully and accurately predict the flow in a vortex cell.

Formation of the boundary layer in the laminar flow of Herschel–Bulkley fluid between parallel plates is taken into consideration. In particular, the study is focused on the flow of the shear thinning and shear thickening fluids past a partial vertical wall in between the plates. Upon numerically solving the continuity and momentum equations the flow is analyzed throughout the domain using a finite volume scheme. The shear stress at the wall together with velocity distribution are evaluated and compared with experimental results for several values of Herschel-Bulkley coefficients for fluidity and flow behavior index.

With advances in computing power and Computational Fluid Dynamics (CFD) algorithms, the complexity of CutCell based simulation models has significantly increased. In this study three dimensional numerical simulations were carried out for steady incompressible flow around an airfoil shape. The authors extended their previous work on more complex geometries; a NACA-23012 wing with 20 percent C Clark Y flap was used for this study. The boundary layer thickness, mesh expansion ratio, and mesh density variation parameters were examined. The skin friction coefficient vanishes where the flow separation starts. Although there is no experimental data available to compare the simulation work the results can be subjected to future work experimentally.

The complete understanding of the aerodynamics of wings and blades under transonic conditions represents a substantial challenge in the design of modern airplanes and turbomachinery. Transonic flow over airfoils may result in appearance of shock waves, which lead to increase in drag if not properly considered during the design stage. Therefore, it is a major challenge to design transonic airfoils such that potential appearance of shock waves is foreseen and negative drag effects are minimized. This paper presents the computational study of the SC(2)-0714 airfoil, focusing on its aerodynamics characteristics at Reynolds number of 35 × 10 6 and angle of attack of 2 and 10 degrees which are the most common operational conditions of transonic wings using this airfoil. The study was undertaken at free-stream Mach 0.72. The numerical simulation was conducted using the finite volume method on platform ANSYS CFX™ and solving the Reynolds-Averaged Navier-Stokes, mass conservation and energy equations. Mesh verification and model validation are presented. The latter is developed by using two different isotropic turbulence models: k-ω and Shear Stress Transport (SST) and the comparison of results with NASA experimental data to determine the best among the treated models. Thereafter, effects of local boundary-layer suction on shock wave strength and characteristics during transonic speed are analyzed for the two aforementioned angles of attack. Two suction slots were placed along the airfoil contour to determine their control effectiveness when compared to standard closed-contour airfoil. Suction slots were placed at the leading edge and in the middle of the upper camber of the airfoil with inflow in the normal direction to the surface. The slot length was 2.5 % of the chord with inflow velocity of 30%, 40% and 50% of free-stream velocity. Effects of suction slots were assessed on the wake region and by computing the resulting lift-to-drag ratio. Concluding remarks on the turbulence model and global aerodynamics performance of the airfoil are presented.

Active flow control by plasma actuators is a topic of great interest by worldwide scientific community. These devices are mainly used for boundary layer control in order to improve the aerodynamic performance of aerial vehicles. Plasma actuators are simple devices that produces a wall bounded jet which allow to control the adjacent flow without moving mechanical parts. Recently, new geometries have been proposed by different authors in an attempt to improve the performance of these devices. In this work, some of these new configurations will be studied and compared considering its ability for boundary layer control applications. Dielectric Barrier Discharge (DBD) plasma actuator, Plasma Synthetic Jet (PSJ) actuator, Multiple Encapsulated Electrodes (MEE) plasma actuator and Curved plasma actuator (or 3D plasma actuator) will be experimentally studied in this work. Plasma actuators power consumption was measured by two different experimental methods. Results for power consumption and power losses of different plasma actuators geometries were presented and discussed.

This study presents a numerical simulation of a 3D viscous subsonic flow in the VKI-Genoa turbine cascade taking into account the laminar-turbulent transition. The numerical simulation is performed using the Reynolds-averaged Navier-Stokes (RANS) equations and the low-Reynolds k -ω SST turbulence model. The Langtry’s algebraic Production Term Modification (PTM) model is applied for modeling the laminar-turbulent transition. The governing equations are integrated using the second-order accurate Godunov’s type implicit ENO scheme. Computations of both fully turbulent and transitional flows are carried out. Much attention is given to the comparison between the present numerical results and the existing experimental data. The comparison was based on the surface distributions of the isentropic velocity, the friction velocity, the flow acceleration parameter, the displacement thickness, the shape-factor, and the momentum thickness Reynolds number. Velocity profiles upstream and downstream of the transition onset were compared also. The numerical results obtained show an influence of the transition on the secondary flow pattern. In the case of the transitional flow, when compared with the fully turbulence flow case, the endwall boundary layer cross-flow starts upstream, and it is more intensive, but less massive due to a thinner boundary layer in the laminar flow region.

High frequency fluidic oscillators have been of scientific interest for many decades. Especially over the last couple of years fluidic oscillators became more important for active flow control applications. At the Institute of Jet Propulsion of the University of the German Federal Armed Forces Munich studies on different kinds of flow control methods were carried out on aerodynamically highly loaded low pressure turbine blades. On the basis of these studies, the most efficient way to trigger transition at low Reynolds numbers was found to be with fluidic oscillators at frequencies up to 10 kHz. Still, it is an open issue whether it is most efficient to trigger Tollmien-Schlichting waves, stimulate Kelvin-Helmholtz instabilities or simply induce a frequency independent disturbance in form of a periodic impulse for boundary layer control on aero-dynamically highly loaded low pressure turbine blades. To find an answer to these questions, a high frequency master-slave fluidic oscillator is introduced with an independent frequency and mass flow characteristic. Any frequency from the master oscillator’s characteristic can be chosen and the mass flow rate can be controlled with the slave oscillator. Contrary to concepts with fast switching valves or piezo actuators, this actuator is based on a working principle without the necessity of any moving and life limited parts. Based on experimental results, the characteristics of the master as well as the coupled oscillator are shown. The predictable operation of the coupled device is demonstrated in detail for a constant overall mass flow rate at discrete frequencies of 5 and 6 kHz. In addition, it is also shown that the mass flow can be varied with one master-slave arrangement by a factor of six while keeping the frequency constant at 5 or 6 kHz, respectively. Besides proof of concept these investigations focus on relevant parameters for active boundary layer and transition control. The frequency and velocity spectra of the coupled device are presented for constant frequency and constant mass flow operating points. Based on these results the improvement potential of the coupled oscillator for fundamental research on this topic is discussed.