Non-dimensional Criterion Research Articles

Formulation of a non-dimensional criterion for stable dynamical response in coaxial magnetic gears

Formulation of a non-dimensional criterion for stable dynamical response in coaxial magnetic gears

Investigation on Heat Transfer Distribution of Rotating Two-Pass Smooth and Ribbed Channels Under Aero-Engine Simulated Conditions

Abstract Rotating significantly alters the internal cooling of turbine rotor blades by induced Coriolis force and buoyancy force, whose effects are characterized by the nondimensional rotation number (Ro) and buoyancy parameter (Bo). The present work was carried out in a new experimental rig of rotor blade internal cooling to obtain detailed heat transfer distributions when the three nondimensional criterion numbers (i.e., Re, Ro, and Bo) are similar to aero-engine operating conditions. Smooth and ribbed two-pass internal cooling channels with a 180-deg tip turn are investigated. The hydraulic diameter is 25.4 mm (1 in.), and the aspect ratio is 2:1. The Reynolds number is fixed at 25,000, with the maximum Ro and Bo of 0.316 and 0.272, respectively. The steady-state thermochromic liquid crystal (TLC) technique is used to measure detailed heat transfer distributions in the channel. Steady-state RANS simulations are also employed to resolve the flow characteristics. The effects of rotation on the flow and heat transfer characteristics are studied in this paper. The results show effects of rotation on the heat transfer distribution present apparent spatial discrepancy, especially around the bend region. The significant difference in the influence of rotation is witnessed in the smooth and the ribbed channels.

Techno-economic investigations of supercritical CO2-based partial heating cycle as bottoming system of a small gas turbine

Supercritical CO2 (sCO2) cycles represent an innovative technology especially if applied for waste heat recovery from gas turbines. This work investigates the performance of the partial heating sCO2 cycle as the bottoming cycle of a 5 MW-class gas turbine. Particular attention is paid to the selection of both minimum CO2 pressure and temperature and use of the non-dimensional criterion named Acceleration Margin to Condensation is made to prevent the formation of liquid CO2 droplets at the inlet of the compressor. Moreover, in order to avoid heavily loaded turbomachinery, considerations about the machine Mach numbers result in possible limits for the maximum cycle pressure. Single-stage radial turbomachines are selected and their efficiency calculated according to Aungier's correlations by taking actual size and running conditions into account. Focusing on the net electric power produced by the bottoming cycle and on the corresponding specific cost, a number of investigations has been carried out. After setting a limit for the compressor Mach number, around 1600 kW can be recovered by the sCO2 bottoming cycle, though a techno-economic optimization would guide towards an optimum point with slightly more than 1500 kW of power output and a specific cost for the technology of around 2000 $/kW.

An Investigation of Condensation Effects in Supercritical Carbon Dioxide Compressors

Supercritical CO2 (S-CO2) power cycles have demonstrated significant performance improvements in concentrated solar and nuclear applications. These cycles promise an increase in thermal-to-electric conversion efficiency of up to 50% over conventional gas turbines (Wright, S., 2012, “Overview of S-CO2 Power Cycles,” Mech. Eng., 134(1), pp. 40–43), and have become a priority for research, development, and deployment. In these applications the CO2 is compressed to pressures above the critical value using radial compressors. The thermodynamic state change of the working fluid is close to the critical point and near the vapor–liquid equilibrium region where phase change effects are important. This paper presents a systematic assessment of condensation on the performance and stability of centrifugal compressors operating in S-CO2. The approach combines numerical simulations with experimental tests. The objectives are to assess the relative importance of two-phase effects on the internal flow behavior and to define the implications for radial turbomachinery design. The condensation onset is investigated in a systematic manner approaching the critical point. A nondimensional criterion is established that determines whether condensation might occur. This criterion relates the time required for stable liquid droplets to form, which depends on the expansion through the vapor–pressure curve, and the residence time of the flow under saturated conditions. Two-phase flow effects can be considered negligible when the ratio of the two time scales is much smaller than unity. The study shows that condensation is not a concern away from the critical point. Numerical two-phase calculations supported by experimental data indicate that the timescale associated with nucleation is much longer than the residence time of the flow in the saturated region, leaving little opportunity for the fluid to condense. Pressure measurements in a converging diverging nozzle show that condensation cannot occur at the level of subcooling characteristic of radial compressors away from the critical point. The implications are not limited to S-CO2 power cycles but extend to applications of radial machines for dense, saturated gases. In the immediate vicinity of the critical point, two-phase effects are expected to become more prominent due to longer residence times. However, the singular behavior of thermodynamic properties at the critical point prevents the numerical schemes from capturing important gas dynamic effects. These limitations require experimental assessment, which is the focus of ongoing and future research.

Distortions introduced by normalisation of values of criteria in multiple criteria methods of evaluation

Quantitative multiple criteria decision aid (MCDA) methods of evaluation gain increasing popularity among researchers. The idea of the methods is to comprise values ofcriteria characterising each object into a single non-dimensional cumulative criterion, which reflects attractiveness or position of the object in view of an objective chosen. Normalisation of weights is a compulsory procedure whenever criteria of different dimensions are present. There several methods of normalisation available. Nevertheless, each method may introduce distortions into transformed data. The paper is devoted to exploration of problems related to such distortions and reveals particular cases.

Characteristics of Laminar Flow in Pipelines of Homogenous Alum Sludge Approximated with use of the Vočadlo Model for Viscoplastic Liquids

The study presents the manners of determination of the Darcy friction factor λ for a homogenous hydromixture of alum sludge of varied hydration and temperature for the laminar fl ow zone. The rheological evaluation of the hydromixture as a viscoplastic body has been conducted with use of measurements of viscosity. The curves of fl ow were approximated with use of the generalized Vocadlo model. The Darcy friction factor λ of the pipeline was determined with use of the non-dimensional criterion λ(Re gen ) and λ(Re, He).

Off-centered impact of water droplets on a thin horizontal wire

The current work focuses on the initial basic stage of filtering droplets. We study the factors that have an effect upon the amount of liquid trapped on a dry smooth horizontal wire. These factors include the impact velocity, impact eccentricity, initial drop size, wire thickness, and liquid thermodynamic properties. Based on elementary analysis of some simple experiments, we propose a non-dimensional criterion for the critical eccentricity for which the maximum amount of liquid is trapped by the wire.

Stratified flow through outlets

Experimental and theoretical studies of stratified flow through outlets are reviewed, focusing on limiting height of aspiration, withdrawal layer thickness, and outflow concentration. First, a new non-dimensional criterion for limiting height of aspiration is proposed. It is found that this non-dimensional criterion changes only slightly for different kinds of selective withdrawal, including two-layer flow and linearly stratified flow through outlets at different levels. Therefore, if the salinity of density current and the outflow discharge are known, the limiting height of aspiration or the withdrawal layer thickness can be estimated. Second, characteristics of the outflow concentration of turbid density currents through outlets are studied. Based on the field observations in Sanmenxia Reservoir and Guanting Reservoir in China, as well as a number of laboratory experimental data from outlets in vertical walls and bottom outlets, a simplified model is developed to analyze the empirical relationship between outflow concentration and several critical parameters including outflow discharge, inflow sediment concentration, interface elevation, and outlet elevation. These research findings are readily applicable for outlet design, especially in sediment-laden waters.

Comparison of Engine Power Exploitation between Normal and Dynamic Driving in Real Traffic Conditions

The increase of cars engine power has reached critical limits,so that further increase would make no sense, since alreadythe real traffic conditions now do not enable its reasonable exploitation.Experiments have confirmed that there is no essentialdifference between the more or less powerful cars in combinedtraffic in and near towns, particularly when fully complyingwith traffic regulations. For the evaluation of the car 'adequacy'a non-dimensional criterion number Nv was proposed.This number 1ises with the rising weight (safety), speed, lowerfuel consumption and faster acceleration. The usual Nv valuesat JOOkm!h are between 1 and 3 for the majority of ordinarycars. Statistics comprising a great number of cars in the past decadesshowed that the said criterion number turned out to be anadequate parameter for the assessment of development trends.Experiments showed that a higher criterion number value inreal traffic does not represent much advantage even in dynamicdriving.

A non-dimensional criterion and its proof for transient flow caused by fire in ventilation network

Application of 1D Transient Flow Model to a network analysis finds that the fluids in two branches (which are connected in parallel and contain no drive source) may no longer flow in a same direction while the network flow state changes from being steady into being unsteady due to a fire in the ventilation network. This phenomenon can be referred to as non-parallel flows in parallel branches. A non-dimensional criterion ξ is deduced theoretically. It is proved that for any two branches which are connected in parallel and contain no drive source, Non-parallel flows can be expected in the branches only if ξ is not equal to unity. If ξ is equal to unity, the non-dimensional flow velocities in the two branches will always be equal to each other. If ξ is not equal to unity, a prediction can be made on which one of the non-dimensional velocities in the two parallel branches will change more rapidly.

Winter time flow over and around Greenland: trajectories related to torques

Results of first steps towards a dynamically oriented climatology of winter time flow over and around Greenland are presented. The synoptic situations in the Greenland area are classified with respect to Greenland’s axial mountain torque. This torque is positive (negative) if the surface pressure at the eastern slope is higher (lower) than at the windward side. Mean trajectories are calculated from correlations of observed flows with the torque. Three classes of trajectories are formed: ‘blocked’, ‘over’ and ‘around’. It is found for low-level starting points west of Greenland, that blocked trajectories are most common for positive torques while the bulk of the trajectories is deflected around Greenland or crosses the massif for negative torques. These results are shown to be broadly consistent with the standard non-dimensional height criterion. Flow splitting is common to the west of Greenland. Stagnation points are found west of Greenland but also above the eastern slopes. Tip jets occur for negative torque events only.

The rule of affine similitude for the force coefficients of a body oscillating in a uniformly stratified fluid

This paper presents a study on affine similitude for the force coefficients of an arbitrary body oscillating in a uniformly stratified fluid. A simple formula is derived that gives a relation between the force coefficients for a body oscillating in homogeneous and uniformly stratified ideal fluids. In particular, it implies the existence of a universal nondimensional similitude criterion for a family of affinely similar bodies, namely, the bodies that can be transformed into each other by vertical dilation of the initial coordinate system. Theoretical results are verified by experiments with a set of spheroids having different length-to-diameter ratios. The experimental technique for evaluation of the frequency-dependent force coefficients is based on Fourier analysis of the time-history of damped oscillation tests.

Does the tracer gradient vector align with the strain eigenvectors in 2D turbulence?

This paper investigates the dynamics of tracer gradient for a two-dimensional flow. More precisely, the alignment of the tracer gradient vector with the eigenvectors of the strain-rate tensor is studied theoretically and numerically. We show that the basic mechanism of the gradient dynamics is the competition between the effects due to strain and an effective rotation due to both the vorticity and to the rotation of the principal axes of the strain-rate tensor. A nondimensional criterion is derived to partition the flow into different regimes: In the strain dominated regions, the tracer gradient vector aligns with a direction different from the strain axes and the gradient magnitude grows exponentially in time. In the strain-effective rotation compensated regions, the tracer gradient vector aligns with the bisector of the strain axes and its growth is only algebraic in time. In the effective rotation dominated regions, the tracer gradient vector is rotating but is often close to the bisector of the strain axes. A numerical simulation of 2D (two-dimensional) turbulence clearly confirms the theoretical preferential directions in strain and effective rotation dominated regions. Effective rotation can be dominated by the rotation rate of the strain axes, and moreover, proves to be larger than strain rate on the periphery of vortices. Taking into account this term allows us to improve significantly the Okubo–Weiss criterion. Our criterion gives the correct behavior of the growth of the tracer gradient norm for the case of axisymmetric vortices for which the Okubo–Weiss criterion fails.

Dynamic Severity Criterion for Designing Against High Cycle Fatigue

A novel approach to the interpretation of material behavior under cyclic loading is presented. In this approach a nondimensional criterion, featuring the dynamic severity of applied load, is put forward with a view to the provision of simple though confident assessment of component performance under dynamic load. The fatigue diagram based on the proposed criterion displays significant merits over previous diagrams, the presented approach thus providing an effective tool for designing against high cycle fatigue with due consideration to maximum utilization of material.