Igor V. Shevchuk

Convective heat and mass transfer in rotating disk systems

General Characteristic of Rotating-Disk Systems.- Modelling of Fluid Flow and Heat Transfer in Rotating-Disk Systems.- Free Rotating Disk.- Unsteady Laminar Heat Transfer of a Free Rotating Disk.- External Flow Imposed over a Rotating Disk.- Outward Underswirled and Overswirled Radial Flow Between Parallel Co-rotating Disks.- Laminar Fluid Flow and Heat Transfer in a Gap Between a Disk and a Cone that Touches the Disk with Its Apex.- Heat and Mass Transfer of a Free Rotating Disk for the Prandtl and Schmidt Numbers Larger than Unity.

Review of fluid flow and convective heat transfer within rotating disk cavities with impinging jet

Fluid flow and convective heat transfer in rotor-stator configurations, which are of great importance in different engineering applications, are treated in details in this review. The review focuses on convective heat transfer in predominantly outward air flow in the rotor-stator geometries with and without impinging jets and incorporates two main parts, namely, experimental/theoretical methodologies and geometries/results. Experimental methodologies include naphthalene sublimation techniques, steadystate (thin layer) and transient (thermochromic liquid crystals) thermal measurements, thermocouples and infra-red cameras, hot-wire anemometry, laser Doppler and particle image velocimetry, laser plane and smoke generator. Theoretical approaches incorporate modern CFD computational tools (DNS, LES, RANS etc). Geometries and results part being mentioned starting from simple to complex elucidates cases of a free rotating disk, a single disk in the crossflow, single jets impinging onto stationary and rotating disk, rotor-stator systems without and with impinging single jets, as well as multiple jets. Conclusions to the review outline perspectives of the further extension of the investigations of different kinds of the rotor-stator systems and their applications in engineering practice.

Self-similar analysis of fluid flow and heat-mass transfer of nanofluids in boundary layer

Processes of heat, momentum, and concentration transport in a boundary layer of a nanofluid near a flat wall were studied. The study was performed by means of numerical analysis of boundary layer equations in a self-similar form. Self-similar forms of these equations were obtained based on symmetry properties (Lie groups). In doing so, dependence of physical properties (viscosity, thermal conductivity, and diffusion coefficient) on concentration of nanofluids and temperature were taken into account. Effects of concentration of the nano-particles on velocity and temperature profiles, as well as on the relative Nusselt numbers and skin-friction coefficients, were elucidated.

Symmetry analysis and self-similar forms of fluid flow and heat-mass transfer in turbulent boundary layer flow of a nanofluid

Heat, momentum, and mass transport in turbulent boundary layer nanofluid flow over a flat plate were investigated. Boundary layer equations were reduced to self-similar forms and solved numerically. The Lie group technique, which is based on the symmetry properties of governing equations, was used to derive self-similar forms of these equations. Turbulent viscosity was predicted using the mixing-length model. Also, dependences of physical properties (viscosity, thermal conductivity, and diffusion coefficients) on the nanofluid concentration and temperature were accounted for. Influences of different dimensionless parameters and nanoparticle concentration on the velocity and temperature profiles, as well as on the relative Nusselt number and skin-friction coefficient, were investigated.

Symmetry of turbulent boundary-layer flows: Investigation of different eddy viscosity models

SummaryThe symmetrical properties of the turbulent boundary-layer flows and other turbulent flows are studied utilizing the Lie group theory technique. The self-similar forms of the indepedent variables and the solution function for the turbulent boundary layer flows with three different models of the turbulent (eddy) viscosity are obtained. Proceeding from this analysis, a simple numerical method for computation of turbulent flows is developed.

Effect of the Wall Temperature on Laminar Heat Transfer in a Rotating Disk: An Approximate Analytical Solution

* = 41.0 0.0 0.1305 0.2352 0.3221 0.3963 0.5180 0.6159 0.6982 0.76930.9 0.0 0.1217 0.2204 0.3029 0.3737 0.4905 0.5849 0.6643 0.73310.8 0.0 0.1124 0.2046 0.2824 0.3495 0.4608 0.5513 0.6276 0.69390.72 0.0 0.1045 0.1911 0.2647 0.3286 0.4352 0.5223 0.5959 0.65990.71 0.0 0.1035 0.1893 0.2624 0.3259 0.4319 0.5185 0.5918 0.65550.6 0.0 0.0917 0.1691 0.2358 0.2943 0.3929 0.4742 0.5433 0.60360.5 0.0 0.0802 0.1490 0.2091 0.2623 0.3531 0.4287 0.4935 0.55020.4 0.0 0.0675 0.1267 0.1792 0.2263 0.3078 0.3767 0.4362 0.48870.3 0.0 0.0536 0.1017 0.1452 0.1849 0.2550 0.3153 0.3682 0.41530.2 0.0 0.0381 0.0732 0.1058 0.1362 0.1912 0.2400 0.2838 0.32340.1 0.0 0.0204 0.0399 0.0586 0.0766 0.1104 0.1417 0.1709 0.1981

Turbulent Heat Transfer of Rotating Disk at Constant Temperature or Density of Heat Flux to the Wall

Conclusions1. The approximation of the velocity and temperature profiles [8-10], used in this study, enabled us to obtain an expression for the Nusselt number which agrees with the experimental data atqw = const andTw = const much better than the well-known Dorfman formula (4).2. The difference between the solution obtained and formula (4) increases with the deviation of the exponent in the wall temperature distribution (1) from the value n * = 2 toward negative values.3. The obtained solution makes it possible to vary the exponent on the number Reω. A comparison with the data with the exponent 0.83 [7] revealed good agreement of these results with the obtained solution.

An analytical and numerical study on the start-up flow of slightly rarefied gases in a parallel-plate channel and a pipe

The paper presents results of an investigation of the response of an incompressible fluid in a circular micropipe and a parallel-plate microchannel to a sudden time-independent pressure drop. Solutions of the problem were obtained analytically using the Laplace transform technique and numerically using the lattice Boltzmann method. The unsteady velocity profiles in the pipe and in the channel were obtained with the help of the infinite series solutions validated against numerical simulations. In line with the expectations, the flow asymptotically tends to the fully developed pattern, which is attained quicker for smaller Knudsen numbers. The solution enabled also obtaining relations to estimate the hydraulic resistance coefficient.

Validation and Analysis of Numerical Results for a Two-Pass Trapezoidal Channel With Different Cooling Configurations of Trailing Edge

The fact that thermal efficiency of the gas turbine is related directly to the gas entry temperature has led to the operation of gas turbines at elevated temperatures. It is therefore necessary for the first stage vanes and blades to withstand temperatures higher than the melting point of the components. Air from the compressor is fed to the internal channels of the vanes/blades to keep the metal temperatures below the melting point. The channel is usually divided into three parts as leading edge, midspan, and trailing edge sections. The trailing edge region is difficult to cool as it is narrow and has very little space for coolant to flow. The treatment is difficult not only due to heat transfer problems but also due to the aerodynamic losses. The aerodynamic losses associated with the trailing edge enforce the requirement of a narrow and smooth trailing edge. Therefore a compromise is forced between blade cooling and aerodynamic losses. The conventional method of cooling the trailing edge is to provide the trailing edge slots where from the coolant leaves the blade. This ejected coolant mixes with the gas path and not only reduces the temperature of the main flow but also adds to the aerodynamic losses. On the other hand, the internal cooling for the trailing edge has limitations like small flow area. A better design of the internal cooling of the trailing edge is therefore required. In the case of internal cooling, the coolant is fed to the two-pass channels which are cast in the blade. The phenomenon like impingement, flow separation, and recirculation are characterized by the flow in such channels. The heat transfer enhancement is obtained on expense of the pressure drop. An acceptable two-pass channel requires optimized heat transfer enhancement and pressure drop. The literature survey has shown that these are modeled as rectangular or trapezoidal channels depending upon their location in the blade. Metzger and Sahm [1] varied the divider location and the gap at the 180 deg turn in a two-pass smooth rectangular channel and studied forced convection. They observed a nonuniform enhancement of heat transfer at the bend region due to flow characteristics at the bend. Park and Lau [2] studied the effect of sharp turning flows in a two-pass square channel and found very large spanwise variation in heat transfer at the turn and upstream of the outlet pass. Han et al. [3] and Liou et al. [4] showed that heat transfer enhances in a two-pass channel after the turn and this is due to the secondary flow generated by the centrifugal force at the turn. Many researchers [5–9] have studied the effect of channel aspect ratio on heat transfer characteristics. They concluded that heat transfer and pressure drop is influenced by the aspect ratio of channel. It was found that the pressure drop in a wide channel is more than the narrow channel. The two-pass channels are turbulated with ribs to enhance heat transfer. This leads to an increase in pressure drop as well. There have been many fundamental studies to understand the heat transfer enhancement phenomena by the flow separation caused by ribs. Han [10,11] studied the effect of rib pitch to rib height ratios (P/e) in stationary channels of different aspect ratios and found that a rib pitch to rib height ratio of 10 is optimum for heat transfer in these channels. Chandra et al. [12] showed that increase in the number of ribbed walls reduces the heat transfer performance. Wright et al. [13] studied the thermal performance of three different types of ribs (45 deg angled, V- and W-shaped) in a high aspect ratio (W/H = 4:1) channel with Reynolds number varied from 10,000 to 40,000. They found that W-shaped ribs performed better than the other two types of ribs. The shape of the trailing edge is such that it can be modeled as the trapezoidal channel. Taslim et al. [14] modeled the trailing edge as trapezoidal channel and studied the effect of bleed holes and tapered ribs on the heat transfer and pressure drop. Taslim et al. [15] found that in a trapezoidal channel, half-length ribs on two opposite walls enhance the heat transfer on the two walls with full-length ribs. Moon et al. [16] studied the local distributions of the heat transfer coefficient on all of the walls at the turn of a smooth two-pass channel with a trapezoidal cross section for various rates of airflow through the channel. The heat transfer was found to be higher at the turn and the outlet pass. The lowest flow rate resulted in highest heat transfer due to turn. Lee et al. [17] used naphthalene sublimation technique to study the heat (mass) transfer distribution in a two-pass trapezoidal channel with a 180 deg turn. The results were obtained over a range of Reynolds numbers for the channel with smooth walls and with ribs on one wall and on two opposite walls. They found that for all cases, the average heat transfer was higher on the downstream of the turn compared to that on the upstream of the turn. In addition, the shape of the local heat transfer distribution was found to be unaffected by the variation in flow rates. The trapezoidal shape of the cross-section of two-pass channels results in differences in the 3D fluid flow and heat transfer patters in them as compared to the square or rectangular two-pass channels. Cravero et al. [18] analyzed the flow field and heat transfer in a three-pass trapezoidal channel and showed that the geometry of the channel has a strong influence on flow field, especially at the regions of flow separation and recirculation. Taslim et al. [19] investigated trapezoidal cooling channels and showed that the trapezoidal channel has higher thermal performance compared to the square channel. It was concluded that the stronger interaction of the adjacent walls results in the increased heat transfer of the trapezoidal duct. Ekkad et al. [20] and Murata and Mochizuki [21] investigated heat transfer in straight and tapered (from hub-to-tip) two-pass ribbed channels. They found that at low Reynolds number, the heat transfer augmentation in the inlet pass is comparable in both cases, but at high Reynolds numbers the acceleration effect in the tapered channel leads to higher heat transfer as compared to the straight channel. At the outlet pass, the heat transfer was found to be comparable. Kiml et al. [22] studied the rib-induced secondary flow structure inside a trapezoidal channel with rib height proportional to the channel cross-section (proportional ribs) and constant height ribs (nonproportional ribs) at four rib inclinations, i.e., 90 deg, 75 deg, 60 deg, and 45 deg. They concluded that the proportional ribs offer less pressure losses, but they deteriorate the strength of the secondary flow rotational momentum as a result of wider space for the air flow between the rib and the opposite wall. Furthermore, the strength of the secondary flow rotational momentum increases with change of rib inclination from 90 deg to 45 deg. There have been many numerical studies performed to analyze the flow and heat transfer in the two-pass channel with a 180 deg bend. Lucci et al. [23] studied the performance of k-ɛ, k-ω, and RSM (Reynolds Stress Model) in the computation of the turbulent flow in a two-pass smooth channel. For the Reynolds number 100,000, all three models showed similar results. Su et al. [24] applied the RANS (Reynolds-averaged Navier–Stokes) approach in combination with a near wall, second moment turbulence closure to validate experiments performed at Re = 100,000. Pape et al. [25] successfully modeled a two-pass channel with a 180 deg bend and 45 deg ribs at Re = 100,000 using the realizable version of k-ɛ model with enhanced wall treatment. Shevchuk et al. [26] used the same model for a varying aspect ratio two-pass channel. The inlet channel aspect ratio (W/H) was 1:2, while for the outlet channel it was 1:1. The channels were roughened with 45 deg ribs and connected together with a 180 deg bend. The simulations were performed for Re = 100,000. They found the model to be effective and time efficient for high Reynolds number flows. To get more accurate results, advanced numerical methods like LES (Large Eddy Simulation) and DES (Detached Eddy Simulation) were used by Sewall and Tafti [27] and Viswanathan and Tafti [28]. They concluded that due to computational economy, it is more practical to use RANS methods based on turbulence models to study heat transfer in the convective cooling channel. In the present study, three different configurations of two-pass trapezoidal channels have been studied, keeping the trailing edge as the focus. Table ​Table11 shows the details of the three configurations. Table 1 The three configurations for augmented heat transfer at trailing edge The purpose of this study is to analyze the effect of placing ribs at the trailing edge on heat transfer and pressure drop in the channel for the three configurations. The results of this study should help gas turbine designers to improve the thermal performance of the gas turbine.

Dean instability of nanofluids with radial temperature and concentration non-uniformity

The paper focuses on an investigation into instability of Dean flows of nanofluids in curved channels restricted by two concentric cylinders. The flow is caused by a constant azimuthal pressure gradient. Critical values of the Dean number, which serves as the instability criterion, were found numerically by the collocation method. Functional dependencies of the critical Dean number on the ratio between the radii of the concave and convex walls (0.1…0.99), as well as dimensionless parameters describing the temperature gradient (−3…6), the relative density of the nanoparticles (0…4), the ratio of the Brownian and thermophoreticdiffusion (0.1…0.9), Prandtl (0.1…10) and Schmidt (10…100) number were revealed. It was shown that an increase in the relative density of the nanoparticles, the ratio of the Brownian and thermophoreticdiffusion, and Schmidt number causes instability under conditions of either positive or negative temperature gradients. An increase in the Prandtl number enforces flow stability for the negative temperature gradient and deteriorates stability for the positive temperature gradient. In light of the complexity of the physical problem in the present paper, only axisymmetric perturbations are considered as the first step to be further developed in future investigations.