Theta Transition Research Articles

A comprehensive comparison of film cooling characteristics of shaped holes on the leading edge of rotating blade

This study numerically investigates the cooling characteristics and flow features of various hole geometries on the rotating blade leading edge. A comprehensive comparison of cooling effectiveness, heat transfer coefficients, net heat flux reduction, and discharge coefficients is conducted among laidback fan-shaped, fan-shaped, laidback, cone holes, and cylindrical holes with two different diameters. Detailed flow and thermal field analysis reveals the impact of geometry on cooling performance. The blade rotational speed is 600 rpm, with a Reynolds number of 12.4 × 104, blowing ratios from 0.5 to 2.0, and fixed injection and spanwise angles at 90° and 30°. Shaped holes share a uniform hole exit-to-inlet area ratio, and cylindrical holes match their inlet or exit areas. The RANS equations were closed using the SST k-ω turbulence model coupled with the Gamma Theta transition model, and an unstructured grid of 13.0 million cells was employed to attain relatively accurate predictive results. Results show that the lateral expansion on the leading edge significantly enhances cooling performance, with fan-shaped holes outperforming others, especially at high blowing ratios. Additionally, cooling effectiveness and discharge coefficient on the leading edge correlate strongly with hole geometric parameters. Shaped holes with equal area ratios show similar discharge coefficients. Cooling effectiveness at high blowing ratios is proportional to the effective exit width, provided that the coolant flows smoothly without severe lift-off.

Influence of Wake Intensity on the Unsteady Flow Characteristics of the Integrated Aggressive Interturbine Duct

The interturbine transition duct (ITD), located between the high-pressure (HP) and low-pressure (LP) turbines of aeroengines, tends to be designed as an aggressive ITD integrated with wide-chord struts to meet the requirements of civil aeroengines for high bypass ratios and thrust–weight ratios. This paper presents a detailed unsteady numerical investigation of the effects of the HP rotor trailing-edge radius on the unsteady flow characteristics in the integrated aggressive interturbine transition duct (AITD), including the transport and dissipation of HP rotor wakes, the control mechanism of HP rotor wakes on flow separation and the influence of wake parameters. A sweeping rod, with a nondimensional diameter ranging from d/s = 0.056~0.143 (based on the pitch (s) of wide-chord struts at the midspan) and a reduced frequency (f) of 1.07, is used to simulate the HP rotor wake to decouple its influence from other secondary flows. Using the k-ω SST turbulence model and gamma–theta transition model, a structured grid with 6.3 million nodes can achieve similar global results. The wake in the lower part of the AITD channel dissipates rapidly because of the stretching between its own circumferential motion and the radial upward secondary flow, especially for a small d/s. Only the residual wake in the upper part can reach wide-chord struts in the case with large d/s. A sweeping rod with a large d/s can reduce the radial pressure gradient in the AITD, inhibit the internal secondary flow to a certain extent, reduce the dissipation rate of the wake, enhance its suppression effect on flow separation on a wide-chord strut, and decrease the flow loss. However, the wake can also enhance the passage vortex due to the increasing circumferential pressure gradient in the wide-chord strut channel, resulting in increasing blade profile loss. In the scope of this study, the aerodynamic gain of the wake is still not enough to compensate for its loss increment (including its own dissipation loss). Therefore, selecting a small trailing-edge radius of the HP rotor is conducive to improving the aerodynamic performance of the integrated AITD.

Моделювання течії в співвісному гвинтовентиляторі з управлінням примежовим шаром

The development and improvement of turboprop engines are one of the important tasks of modern aircraft engine building. Propeller performance significantly affects the overall efficiency of turboprop engines. An important issue is to increase the trust of the propeller or propfan. In this matter, promising energy methods for increasing lift deserve special attention. Energy methods for increasing the lift force are based on the use of additional energy from the power plant to improve the flow around the blade and increase its bearing properties. The purpose of this work is to assess the influence of the boundary layer control on the blades of a coaxial propfan on the thrust. A coaxial propfan was chosen as the object of research. The rotor fan consists of two rows of blades, the first row has eight blades, the second - six. The peripheral diameter of the blades of the propfan is the same and amounts to 4.5 m. The cruise mode of operation was selected for the study. Modeling the flow in a coaxial propfan was based on the solution of the Navier-Stokes system of equations, which was closed by the SST Gamma Theta Transition model of turbulent viscosity. The computational grid consisted of 20 million cells, type-block, structured and unstructured with an adaptation of the boundary layer. In this study, an active boundary layer control method was chosen. The boundary layer was controlled only on the blades of the first row of the propfan. In the peripheral region of the blade, an additional mass of air was blown out through the slot, at a distance of 70 % of the profile chord. Blowing out a thin jet near the blade wall to increase the flow energy serves as an effective means of controlling the flow separation and increasing the bearing capacity of the propfan blade. Analysis of the simulation of the flow in a propfan with control of the boundary layer showed that the addition of energy to the boundary layer contributes to the filling of the velocity profile in the boundary layer, leads to a decrease in resistance and an increase in the thrust of the propfan. The results of the study showed that for the studied scheme of blowing out an additional mass of air on the propeller blades, it is possible to increase the thrust force up to 100 N. In the future, it is planned to investigate other schemes for controlling the boundary layer to increase the thrust of the coaxial propfan.

Удосконалення характеристик кільцевого вхідного пристрою авіаційної силової установки з гвинтовентилятором

The article considers the method of improving the characteristics of the ring inlet device, taking into account the influence of the propeller of an aircraft power plant with a turboprop engine. It is shown that increasing the total pressure loss in the inlet device by 5% increases, approximately, the specific fuel consumption by 3% and reduces engine thrust by 6%, and uneven flow at the inlet to the engine is the cause of unstable compressor of the turboprop engine. It is proposed to improve the characteristics of the input device by modifying the shape of its shell and channel. Evaluation of the influence of the shape of the shell and the channel of the annular axial VP on its main aerodynamic characteristics, taking into account the non-uniformity of the flow on the fan in the calculated mode of operation of the SU is carried out by calculating the full pressure recovery factor. The object of the study is an annular axial input device in front of which is a coaxial fan turboprop fan. The process of modeling the influence of the shape of the shell and the channel on the recovery factor of total pressure, circular and radial non-uniformity of the flow through the input device is implemented in the software system of finite element analysis ANSYS CFX. Geometric models of coaxial screw fan, fairing and inlet device are built in ANSYS SpaceClaim and transferred using the built-in import function in ANSYS Workbench. Block-structured grid models of air propellers of the first and second rows of the fan in the amount of 1.9 million, fairing and inlet device, in the amount of 3.9 million, are built in the ANSYS TurboGrid environment. The standard Stern (Shear Stress Transport) Gamma Theta Transition was used to close the Navier-Stokes equation system. Based on the results of mathematical modeling of flow in coaxial fans and subsonic ring inlet device on the maximum cruising mode of the turboprop engine, the full pressure recovery factor is calculated and it is established that the most influential factor that increases its full pressure recovery factor.

Laminar-Turbulent Transition Flows of Non-Newtonian Slurries: Models Assessment

In this study, a qualitative assessment of transitional velocity engineering models for predicting non-Newtonian slurry flows in a horizontal pipe was performed using data from a wide range of pipe diameters (25–268 mm). In addition, the gamma theta transition model was used to compute selected flow conditions. These models were used to predict transitional velocities in large pipe diameters (up to 420 mm) for slurries. In general, it was observed that most of the current engineering models predict transitional velocities conservatively. Based on the gamma theta transition model results, for large Hedström numbers (He ≳ 105), other methods should be used to predict transitional velocities if a change in the pipe diameter (scale-up) results in an order of magnitude increase in the He value. It was also found that the gamma theta transition model predicted a laminar flow condition in the fully developed region for flow conditions with a small plug region (low-yield stress-to-wall shear stress ratio), which is contrary to what has been observed in some experiments. This is attributed to the local fluid rheological parameters values, which might be different from those reported. However, the gamma theta transition model results are in good agreement with the experimental data for flow conditions that have a large plug region (high-yield stress-to-wall shear stress ratio).

Loose, Flat Knots in Collapsed Polymers

We consider single ring polymers which are confined on a plane but maintain a fixed three-dimensional knotted topology. The equilibrium statistics of such systems is studied on the basis of a model on square lattice in which the configurations are represented by N-step polygons with a number of self-intersections restricted to the minimum compatible with the topology. This allows to define the size, s, of the flat knots and to study their localization properties. Due to the presence of both excluded volume and attractive interactions, the model undergoes a theta transition. Accurate Monte Carlo results show that, while in the high temperature swollen regime both prime and composite knot components are localized (〈s〉 N ∼N t , with t=0), in the low temperature, compact phase they are fully delocalized (t=1). Right at the theta transition weak localization prevails (t=0.44±0.02). Part of the results can be interpreted by taking into account a dominance of figure eight shapes for the coarse grained knotted polymer configurations, and by applying the scaling theory of polymer networks of fixed topology. In particular t=3/7 can be conjectured as an exact exponent characterizing the weak knot localization at the theta point.

Mechanical unfolding of directed polymers in a poor solvent: critical exponents.

We study the thermodynamics of an exactly solvable model of a self-interacting, partially directed self-avoiding walk in two dimensions when a force is applied on one end of the chain. The critical force for the unfolding is determined exactly, as a function of the temperature, below the Theta transition. The transition is of second order and is characterized by new critical exponents that are determined by a careful numerical analysis. The usual polymer critical index nu on the critical line, and another one which we call zeta, takes a nontrivial value that is numerically close to 2/3.

Structural properties of self-attracting walks.

Self-attracting walks (SATW) with attractive interaction u>0 display a swelling-collapse transition at a critical u(c) for dimensions d>or=2, analogous to the Theta transition of polymers. We are interested in the structure of the clusters generated by SATW below u(c) (swollen walk), above u(c) (collapsed walk), and at u(c), which can be characterized by the fractal dimensions of the clusters d(f) and their interface d(I). Using scaling arguments and Monte Carlo simulations, we find that for u<u(c), the structures are in the universality class of clusters generated by simple random walks. For u>u(c), the clusters are compact, i.e., d(f)=d and d(I)=d-1. At u(c), the SATW is in a new universality class. The clusters are compact in both d=2 and d=3, but their interface is fractal: d(I)=1.50+/-0.01 and 2.73+/-0.03 in d=2 and d=3, respectively. In d=1, where the walk is collapsed for all u and no swelling-collapse transition exists, we derive analytical expressions for the average number of visited sites <S> and the mean time <t> to visit S sites.

Swelling-collapse transition of self-attracting walks

We study the structural properties of self-attracting walks in d dimensions using scaling arguments and Monte Carlo simulations. We find evidence of a transition analogous to the Theta transition of polymers. Above a critical attractive interaction u(c), the walk collapses and the exponents nu and k, characterizing the scaling with time t of the mean square end-to-end distance <R2> approximately t(2nu) and the average number of visited sites <S> approximately t(k), are universal and given by nu=1/(d+1) and k=d/(d+1). Below u(c), the walk swells and the exponents are as with no interaction, i.e., nu=1/2 for all d, k=1/2 for d=1 and k=1 for d>/=2. At u(c), the exponents are found to be in a different universality class.

Sequence Randomness and Polymer Collapse Transitions

Contrary to expectations based on Harris' criterion, chain disorder with frustration can modify the universality class of scaling at the theta transition of heteropolymers. This is shown for a model with random two-body potentials in 2D on the basis of exact enumeration and accurate Monte Carlo results. When frustration grows beyond a certain finite threshold, the temperature below which disorder becomes relevant coincides with the theta one and scaling exponents definitely start deviating from those valid for homopolymers.

Θ-point universality of random polyampholytes with screened interactions

By an efficient algorithm we evaluate exactly the disorder-averaged statistics of globally neutral self-avoiding chains with quenched random charge $q_i=\pm 1$ in monomer i and nearest neighbor interactions $\propto q_i q_j$ on square (22 monomers) and cubic (16 monomers) lattices. At the theta transition in 2D, radius of gyration, entropic and crossover exponents are well compatible with the universality class of the corresponding transition of homopolymers. Further strong indication of such class comes from direct comparison with the corresponding annealed problem. In 3D classical exponents are recovered. The percentage of charge sequences leading to folding in a unique ground state approaches zero exponentially with the chain length.

Luminescence Characterization of Chromium‐Containing theta‐Alumina

Characteristic photostimulated luminescence (fluorescence) in the visible range is reported from theta transition alumina prepared by using a variety of methods. The luminescence is associated with trace concentrations of chromium and can be intensified by intentional chromium doping. The luminescence from theta‐alumina is similar to, albeit considerably weaker than, the R‐line luminescence from alpha‐alumina. The theta‐alumina spectrum is characterized by a doublet at ∼14575 and 14645 cm−1 at 77 K and is blue‐shifted from the R‐lines of alpha‐alumina by ∼150 cm−1. The doublet is attributed to Cr3+ ions in octahedral coordination and can be used for phase identification in microstructural characterization.

Thin animals

Lattice animals provide a discretized model for the theta transition displayed by branched polymers in solvent. Exact graph enumeration studies have given some indications that the phase diagram of such lattice animals may contain two collapsed phases as well as an extended phase. This has not been confirmed by studies using other means. We use the exact correspondence between the q --> 1 limit of an extended Potts model and lattice animals to investigate the phase diagram of lattice animals on phi-cubed random graphs of arbitrary topology (``thin'' random graphs). We find that only a two phase structure exists -- there is no sign of a second collapsed phase. The random graph model is solved in the thermodynamic limit by saddle point methods. We observe that the ratio of these saddle point equations give precisely the fixed points of the recursion relations that appear in the solution of the model on the Bethe lattice by Henkel and Seno. This explains the equality of non-universal quantities such as the critical lines for the Bethe lattice and random graph ensembles.

Critical behavior at the theta point of self-avoiding walks on a Manhattan lattice

The authors study the collapse of self-attracting self-avoiding walks on a Manhattan lattice, by means of phenomenological renormalization group techniques. Their results support a recent prediction of nonuniversality for the entropic exponent gamma . The surface exponents are in the same universality class as the theta transition on undirected lattices, thus differing from those of the theta ' point. They use a two-parameter renormalization group to obtain estimates of the crossover exponent.

The effect of attractive monomer-monomer interactions on adsorption of a polymer chain

The authors have used transfer matrix techniques to study a model of polymer adsorption and collapse. They consider the conventional model of a self-avoiding walk with attractive nearest-neighbour interactions on the square lattice and introduce adsorbing boundaries. The numerical results are consistent with the existence of a multicritical point where the adsorption and collapse transitions coincide and suggest that the adsorption transition of a collapsed polymer chain in first order. There is also clear evidence that the collapse transition lowers the adsorption temperature. Estimates of the surface scaling dimensions at the ordinary- Theta transition support the conjecture of Seno and Stella (1988) that the surface critical behaviour at the Theta and Theta ' points belong to different universality classes.

Tricritical points of trails, their Euler digraphs and graphs: exact results on the Sierpinski gasket

The collapse transitions of trails, their oriented graphs and silhouettes (Eulerian digraphs and graphs, respectively), as the fugacity for crossings is increased, are investigated by exact decimation on the 2D Sierpinski gasket. Recursion relations between the generating functions for the three basic configurations on consecutive levels are derived. For all models the authors find tricritical points which move along a line in a four-dimensional parameter space, as the fugacity is varied, and terminate at a decoupled first- or second-order multicritical point. It suggests these models belong to distinct universality classes which differ from that of self-attracting polymer chains which do not undergo a collapse Theta transition on this fractal lattice.