Heat Exchange in Staggered Threaded Pipe Banks with Similar Developed Surface Patterns under Natural Draft Conditions

Helical pipes with similar developed surface patterns efficiently operate under forced convection conditions. The available literature describes their essential advantages over the tubes of a round-ribbed profile and the possibility of their application as a heat-exchanging section for the air-cooling unit. However, the peculiarities of the operation of such units require checking an opportunity for the use of helical pipes with similar developed surface patterns under natural draft conditions. The purpose of the research is to get new data on the flow structure in the intertube space of the staggered banks of such pipes under natural draft conditions. These data are required for the in-depth analysis of the appropriateness of the use of such pipes for “dry” air cooling systems. The methods of investigation included the use of the academic licensed software package ANSYS Student for numerical computations. It was established that the heat exchange in ribbed pipes under natural draft conditions is specified first of all by the parameters of the staggered bank (longitudinal and transversal pitches of the arrangement of pipes in the bank) and the geometric parameters of the pipes, in particular the pitch between the humps and the dents on the tube surface that form its helical surface. Design ratios were suggested for the determination of the averaged heat exchange in the staggered banks of the single-thread helical pipes with similar developed surface patterns. It was shown that the pitch characteristics of the banks have the greatest effect on the similarity equation. A preliminary validation was carried out for the methods adopted for the design of helical pipes and the known methods used for the computation of the staggered banks of smooth cylindrical pipes. The obtained research data can be used for the evaluation of the intensification of the heat exchange and for the flow analysis in order to increase the efficiency of the heat-exchange equipment.

Performance of similarity explicit group iteration for solving 2D unsteady convection-diffusion equation

In this paper, a similarity finite difference (SFD) solution is addressed for thetwo-dimensional (2D) parabolic partial differential equation (PDE), specifically on the unsteady convection-diffusion problem. Structuring the similarity transformation using wave variables, we reduce the parabolic PDE into elliptic PDE. The numerical solution of the corresponding similarity equation is obtained using a second-order central SFD discretization schemeto get the second-order SFD approximation equation. We propose a four-point similarity explicit group (4-point SEG) iterative methodasa numericalsolution of the large-scale and sparse linear systems derived from SFD discretization of 2D unsteady convection-diffusion equation (CDE). To showthe 4-point SEG iteration efficiency, two iterative methods, such as Jacobiand Gauss-Seidel (GS) iterations, are also considered. The numerical experiments are carried out using three different problems to illustrate our proposed iterative method's performance. Finally, the numerical results showed that our proposed iterative method is more efficient than the Jacobiand GS iterations in terms of iteration number and execution time.

Design Guidelines for Axial Turbines Operating With Non-Ideal Compressible Flows

The impact of non-ideal compressible flows on the fluid-dynamic design of axial turbine stages is examined. First, the classical similarity equation (CSE) is revised and extended to account for the effect of flow non-ideality. Then, the influence of the most relevant design parameters is investigated through the application of a dimensionless turbine stage model embedding a first-principles loss model. The results show that compressibility effects induced by the fluid molecular complexity and the stage volumetric flow ratio produce an offset in the efficiency trends and in the optimal stage layout. Furthermore, flow non-ideality can lead to either an increase or a decrease of stage efficiency up to 3–4% relative to turbines designed to operate in dilute gas state. This effect can be predicted at preliminary design phase through the evaluation of the isentropic pressure–volume exponent. Three-dimensional (3D) RANS simulations of selected test cases corroborate the trends predicted with the reduced-order turbine stage model. URANS computations provide equivalent trends, except for case study niMM1, featuring a non-monotonic variation of the generalized isentropic exponent. For such turbine stage, the efficiency is predicted to be higher than the one computed with any steady-state model based on the control volume approach.

Design Guidelines for Axial Turbines Operating With Non-Ideal Compressible Flows

The impact of non-ideal compressible flows on the fluid-dynamic design of axial turbine stages is examined. First, the classical similarity equation is revised and extended to account for the effect of flow non-ideality and compressibility. Then, the influence of the most relevant design parameters is investigated through the application of a dimensionless turbine stage model embedding a first-principles loss model. The results show that the selection of optimal duty coefficients is scarcely affected by the molecular complexity of the working fluid, whereas compressibility effects produce an offset in the efficiency trends and in the optimal flow coefficient. Furthermore, flow non-ideality can lead to either an increase or a decrease of stage efficiency of the order of 2–3% relative to turbines designed to operate in dilute gas state. This effect can be predicted at preliminary design phase through the evaluation of the isentropic pressure-volume exponent. 3D RANS simulations of selected test cases corroborate the trends predicted with the reduced-order turbine stage model.

Studying heat transfer in freon-oil mixture boiling in evaporator tubes in ship refrigerating units

The paper describes small-capacity irrigation evaporators that improve the performance of a refrigeration unit, as they exclude the release of liquid freon into the compressor suction pipe under sharp increasing of heat load or during ship rolling. The relevance of studying heat transfer at freons boiling in a moving film has been proved. The results and analysis of experimental data on average heat transfer coefficients are presented. The graph shows the dependence of the average heat transfer coefficients on the heat flux density at various irrigation densities. There are presented the results of special experiments determining the effect of irrigation density on heat transfer. It has been stated that the effect of pressure or saturation temperature in the modes of evaporation and developed boiling manifests itself in different ways. With developed boiling, the beam pitch does not have a significant effect on heat transfer. The experiments were carried out on two stands: small-row and multi-row. The pipes were heated with an internal electric heater. It has been inferred that heat transfer in the film is more intense than in volume, therefore, smooth steel pipes can be used in irrigation evaporators instead of finned copper tubes, which are used in flooded devices. The boiling process in a film can be described by equations valid for a large volume, taking into account quantitative differences. The values of a constant coefficient and the criteria exponents are given; the similarity equation for the regime of developed bubble boiling of freons is derived. The calculated dependencies can be applied in evaluating the operation of irrigation evaporators of ship refrigeration units.

Thermal and Aerodynamic Researches of Staggered Bundles for Choice of an Effective Spacing of Round-Finned Tubes

The results of an experimental study of local modeling of convective heat transfer and aerodynamic resistance of staggered six-row bundles of bimetallic tubes with spiral knurled aluminum fins under transverse air flow in the range of its velocity alteration in a compressed bundle section of 1.9−11.0 m/s are presented. The velocity range covers the possible modes of operation of industrial air coolers (AVO). The fins with a diameter of approximately 57 mm are rolled on a steel supporting tube with an outer diameter of 25 mm. Tube finning ratio j = 19.26. Such tubes are widely used in the heat exchange sections of AVO of natural gas, in particular, at “Gribanovskii Engineering Plant” JSC (Russia). To measure the reduced heat transfer coefficients, an electric calorimeter had been developed by the authors with a power input of 600−1300 W. The temperature of the wall surface at the base of the fins did not exceed the range of 77–92 °C. The transverse tube spacing in bundles S1was 64.0 or 68.0 mm, while the longitudinal spacing S2 was 54.4 or 50.0 mm. The heat transfer of each transverse row of six-row bundles was measured, as well as the average heat transfer and aerodynamic drag, which are summarized by the similarity equation of a power type. The heat transfer rate of the last transverse row in the direction of air movement is 0–5 % lower than the heat transfer rate of the stabilized rows, and here new features of heat transfer variations in the insufficiently studied area of spacing changes S1 and S2 have been found. The thermal contact resistance (TCR) was measured in the range of the average temperature of the contact surfaces tк = (79–95) оС, and no dependence of the value of TCR on tк for the specified interval was found. The numerical average value of TCR was Rк = 2,13 × 10–4 m2×K/W, which is typical for reliable mechanical connection of the finned aluminum shell with the supporting steel tube made of carbon steel. The results of variant thermal and aerodynamic calculations with the use of the obtained data established the technical and economic feasibility of placing tubes at the vertices of an isosceles triangle with spacing S1 = 68–69 mm and S2 = 55 mm with failure to use the location of the tubes along an equilateral triangle with S1 = S2' = 64 mm (where S2' – is diagonal spacing). With Q = idem and other conditions being equal, the number of tubes on AVO decreases by 5.7 % with a decrease in power consumption to 4.0 %.

Criterion similarity equation for determining the drops diameter of artificial rain

Development and implementation of water-saving technologies into irrigation agriculture aimed at increasing the efficiency of irrigation water use, is one of the priorities for achieving guaranteed and stable yields of agricultural crops. Study of parameters of artificial rain is one of the key moments in design of irrigation equipment. Research of the rain formation process is necessary in order to avoid negative effect on soil cover and vegetation, and also to increase efficiency of artificial irrigation, also reducing the power consumption. At the same time, one of the key characteristics is the diameter of drops created by rain-forming devices, which directly affects the other main characteristics of artificial rain and depends on the physical and mechanical properties of water, parameters of working fluid flow and geometric parameters of rain- forming devices. Based on the theoretical studies, a criterion similarity equation was obtained, allowing to calculate the drop diameter using parameters characterizing the process of artificial rain formation, to predict the size of drops when designing sprinkling equipment. The parameters having greatest effect on drop diameter are determined. It was revealed that, in accordance with the criterion equation obtained, the process of formation of artificial rain drops can be characterized by a geometric similarity criterion, as well as by Ohnezorge and Froude number. Calculations on the proposed formulas are well correlated with the results of other authors’ experiments. The studies conducted further allow to significantly improve the accuracy of determining the diameter of drops for various types of sprinkling nozzles, match design parameters and operating fluid flow parameters for the specified conditions.

MODEL MATEMATIKA ALIRAN TAK TUNAK PADA NANO FLUID MELEWATI BOLA TERIRIS DENGAN PENGARUH MEDAN MAGNET

Model matematika adalah suatu representasi sederhana dari suatu fenomena atau peristiwa alam yang terjadi untuk disajikan dalam konsep matematis. Dari fenomena tersebut maka terbentuklah persamaan matematika yang lebih sederhana dan mudah untuk diselesaikan. Nano fluid adalah salah satu fluida baru yang memiliki keunikan karakteristik tersendiri. Komponen nano fluid adalah campuran fluida cair dengan partikel nano yang memiliki ukuran antara 1-100 nm. Terdapat sifat karakteristik dari fluida nano yaitu densitas fluida nano, viskositas, kalor spesifik fluida nano, dan konduktifitas termal. Pada penelitian ini, bertujuan untuk memperoleh sebuah model matematika aliran tak tunak pada nano fluid melewati bola teriris dengan pengaruh medan magnet. Untuk memperoleh model tersebut maka dibentuklah persamaan pembangun berdimensi dari persamaan kontinuitas, persamaan momentum, dan energy equation. Dari dimensional equation ditransformasikan ke dalam bentuk non-dimensional equation. Kemudian diklasifikasikan dalam bentuk similarity equation menggunakan teori pada lapisan batas. Hasil dari penelitian ini adalah diketahui pengaruh medan magnet pada aliran tak tunak nano fluid yang melewati bola teriris.

On Magnetohydrodynamic Unsteady Flows with Induced Field Over A Stretching Surface

The problem of unsteady, incompressible, laminar electrically conducting flow part a continuously stretching surface is investigated based on a time depended length scale. Similarity conditions for the stretching surface flow velocity and induced magnetic field functions are denied. The governing partial differential equations are first transformed to ordinary ones using similarity transformation. The governing system of equation includes the continuity equation, magnetic continuity equation, Maxwell’s equation, momentum equation and magnetic equations. The resulting similarity equation is then obtained through the use of Maple software. Effects of the unsteadiness parameter A, magnetic force parameter β and the reciprocal of the magnetic prandtl number ë on the velocity and magnetic induction functions are displayed graphically.

Spatial structure of shock formation

The formation of a singularity in a compressible gas, as described by the Euler equation, is characterized by the steepening and eventual overturning of a wave. Using self-similar variables in two space dimensions and a power series expansion based on powers of $|t_{0}-t|^{1/2}$, $t_{0}$ being the singularity time, we show that the spatial structure of this process, which starts at a point, is equivalent to the formation of a caustic, i.e. to a cusp catastrophe. The lines along which the profile has infinite slope correspond to the caustic lines, from which we construct the position of the shock. By solving the similarity equation, we obtain a complete local description of wave steepening and of the spreading of the shock from a point. The shock spreads in the transversal direction as $|t_{0}-t|^{1/2}$ and in the direction of propagation as $|t_{0}-t|^{3/2}$, as also found in a one-dimensional model problem.