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RELEVANCE. Vertical cone diffusers are used in various technical applications: heat exchangers, gas cleaning units, boilers, industrial furnaces, dryers, ventilation devices, nozzle systems and others. For their efficient operation, it is necessary to ensure a uniform supply of the working medium to the device, which is determined by the characteristics of the flow in thediffuser. Thus, the study of the aerodynamics of technological devices with conical diffusers is an urgent task for gas-dynamic improvement and the search for ways to control flow characteristics. THE PURPOSE. To establish the evolution of the velocity field along the height of the cylindrical part of the diffuser for different configurations of the supply tubes, and also to determine the magnitude of the change in the intensity of turbulence along the height of the diffuser under different initial conditions based on experimental data on the instantaneous values of the air flow velocity. METHODS. Measurement of instantaneous values of air flow velocity is carried out using a constant temperature hot-wire anemometer. The article provides data on velocity fields and turbulence intensity along the height and along the diameter of the cylindrical part of the diffuser when air is supplied through tubes of different configurations. Feed tubes with cross sections in the form of a circle, a square and an equilateral triangle were used. RESULTS. The article provides a detailed description of the experimental stand (including key geometric dimensions), instrumentation and measurement system, and data processing techniques. The ranges of changes in the initial conditions for the experiments are presented. A comparison of the aeromechanical characteristics of flows in a vertical diffuser when air issupplied through different tube configurations is carried out. CONCLUSION. It is shown that in the diffuser there is a drop in the average velocity upstream, which is typical for all configurations of the supply tubes. It has been established that profiled tubes influence the shape of the velocity field. It was found that the values of turbulence intensity vary from 0.05 to 0.39 (the highest values were typical when air was supplied through profiled tubes). It is shown that the intensity of turbulence has its maximum values at a height of 300-350 mm, which is typical for all investigated tube configurations.

Conical diffusers of various configurations are used in many kinds of technical equipment and manufacturing processes. Therefore, it is a relevant objective to obtain reliable experimental and mathematical data on the aerodynamic characteristics of diffusers. This article presents experimental data on the aerodynamics of stationary flows in a vertical conical diffuser when air is supplied through tubes with various cross sections (circle, square, and triangle). Instantaneous values of air flow velocity are measured with a constant-temperature hot-wire anemometer. Data are obtained on the velocity fields and turbulence intensity along the height and the diameter of the diffuser's cylindrical part when air is supplied through tubes of various configurations. It is established that air supply through profiled tubes has a significant effect on the shape of the velocity field and turbulence intensity in a vertical conical diffuser. For example, higher values of turbulence intensity are typical of air supplied through profiled tubes (the differences reach 50%). A mathematical formulation (linear and exponential equations) of the change in the average speed and intensity of air flow turbulence along the height of the diffuser's cylindrical part for various initial conditions and supply tube configurations is presented. The obtained findings will make it possible to refine mathematical models and update algorithms for engineering the design of diffusers for various engineering processes and pieces of technical equipment. [ABSTRACT FROM AUTHOR]

In this paper we continue our analysis of the stationary flows of M component, coupled KdV (cKdV) hierarchies and their modifications. We describe the general structure of the t 1 and t 2 flows, using the case M = 3 as our main example. One of our stationary reductions gives N degrees of freedom, superintegrable systems. When N = 1 (for t 1) and N = 2 (for t 2), we have Poisson maps, which give multi-Hamiltonian representations of the flows. We discuss the general structure of these Poisson tensors and give explicit forms for the case M = 3. In this case there are 3 modified hierarchies, each with 4 Poisson brackets. The stationary t 2 flow (for N = 2) is separable in parabolic coordinates. Each Poisson bracket has rank 4, with M + 1 Casimirs. The 4 × 4 "core" of the Poisson tensors are nonsingular and related by a "recursion operator". The remaining part of each tensor is built out of the two commuting Hamiltonian vector fields, depending upon the specific Casimirs. The Poisson brackets are generalised to include the entire class of potential, separable in parabolic coordinates. The Jacobi identity imposes specific dependence on some parameters, representing the Casimirs of the extended canonical bracket. This general case is no longer a stationary cKdV flow, with Lax representation. We give a recursive procedure for constructing the Lax representation of the stationary flow for all values of M , without having to go through the stationary reduction. [ABSTRACT FROM AUTHOR]