On velocity and temperature distribution in turbulent flow between parallel plates

Summary By means of mixing-length and turbulent Prandtl number hypothesis we solved the problem of parallel turbulent flow at constant density, both from the dynamic and thermal point of view; we then analyzed the fit with experimental data of various mixing-length formulas, and also the dependence of temperature profiles on the value of the turbulent Prandtl number.This critical analysis allowed the choice of the most suitable mixing-length formula and the value for the turbulent Prandtl number. On the basis of these results we extended the study discarding the condition of constant density; in particular we considered the case of liquids whose density was taken dependent on temperature changes across the walls, but independent of the pressure changes in flow direction.The study belongs to the case of fully developed temperature and velocity profiles.

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Sommario Mediante l'introduzione del numero di Prandtl turbolento e della lunghezza di miscelamento nelle equazioni di Reynolds, viene risolto il problema della distribuzione di velocità e temperatura in un fluido a densità costante, in moto turbolento tra due piani paralleli. Le distribuzioni di velocità, ottenute con diverse espressioni della lunghezza di miscelamento, vengono poi confrontate con i dati sperimentali, allo scopo di scegliere la più opportuna di queste lunghezze; infine viene esaminata l'influenza del numero di Prandtl turbolento sulla distribuzione di temperatura.In accordo con le suddette scelte, lo studio è successivamente esteso al caso di densità dipendente dalla sola temperatura, ritenendo trascurabili le variazioni di densità per effetto del gradiente di pressione. In altri termini si limita lo studio ai liquidi.Tutti i risultati ottenuti si riferiscono a moti stabilizzati in velocità e temperatura.

     

Two-phase flow distribution of air–water annular flow in a parallel flow heat exchanger

The air and water flow distribution are experimentally studied for a round header – flat tube geometry simulating a parallel flow heat exchanger. The number of branch flat tube is 30. The effects of tube outlet direction, tube protrusion depth as well as mass flux, and quality are investigated. The flow at the header inlet is identified as annular. For the downward flow configuration, the water flow distribution is significantly affected by the tube protrusion depth. For flush-mounted configuration, most of the water flows through frontal part of the header. As the protrusion depth increases, more water is forced to the rear part of the header. The effect of mass flux or quality is qualitatively the same as that of the protrusion depth. Increase of the mass flux or quality forces the water to rear part of the header. For the upward flow configuration, however, most of the water flows through rear part of the header. The protrusion depth, mass flux, or quality does not significantly alter the flow pattern. Possible explanations are provided based on the flow visualization results. Negligible difference on the water flow distribution was observed between the parallel and the reverse flow configuration.     

Flow pattern analysis of linear gradient flow distribution

This paper uses the Oseen transformation to solve the differential equations governing motion of the vertical linear gradient flow distribution close to a wall surface. The Navier-Stokes equations are used to consider the inertia term along the flow direction. A novel contour integral method is used to solve the complex Airy function. The boundary conditions of linear gradient flow distribution for finite problems are determined. The vorticity function, the pressure function, and the turbulent velocity profiles are provided, and the stability of particle trajectories is studied. An L_x-function form of the third derivative circulation is used to to simplify the solution. Theoretical results are compared with the experimental measurements with satisfactory agreement.     

The effects of flow split ratio and flow rate in manifolds

This paper reports a combined experimental and numerical investigation of three-dimensional steady turbulent flows in inlet manifolds of square cross-section. Predictions and measurements of the flows were carried out using computational fluid dynamics and laser Doppler anemometry techniques respectively. The flow structure was characterized in detail and the effects of flow split ratio and inlet flow rate were studied. These were found to cause significant variations in the size and shape of recirculation regions in the branches, and in the turbulence levels. It was then found that there is a significant difference between the flow rates through different branches. The performance of the code was assessed through a comparison between predictions and measurements. The comparison demonstrates that all important features of the flow are well represented by the predictions.     

Refrigerant distribution in a parallel flow heat exchanger having vertical headers and heated horizontal tubes

Refrigerant R-410a flow distribution is experimentally studied in a test section simulating a parallel flow heat exchanger having vertical headers with two pass configuration. Tubes are heated to yield a test section outlet superheat of 5 °C with inlet quality of 0.3. Mass flux is varied from 50 kg/m² s to 70 kg/m² s. Effects of inlet and outlet locations are investigated in a search for an optimum configuration. Results show that, significant liquid flows through bottom channels, and less liquid is supplied to top channels. As for the inlet location, better flow distribution (pressure drop as well) is obtained for top inlet as compared with middle inlet. As for the outlet location, top or bottom outlet is better than middle outlet. Correlations are developed for the fraction of liquid or gas taken off by downstream channel as a function of header gas Reynolds number at immediate upstream. The correlations may be used to predict the liquid or gas distribution in a parallel flow heat exchanger having vertical headers. A novel thermal performance evaluation method, which accounts for tube-side flow mal-distribution is proposed.     

Experiments on two-phase flow distribution inside parallel channels of compact heat exchangers

Uneven distribution in heat exchangers is a cause of reduction in both thermal and fluid-dynamic performances. Many papers have dealt with single-phase flow and both flow distribution data and analytical or numerical models are available for header design. With regard to two-phase flow, phase separation in manifolds with several outlets is so complicated that, to date, there is no general way to predict the distribution of two-phase mixtures at header-channel junctions. The design of headers for new generation compact heat exchangers and multi-microchannel evaporators is still based on an empirical approach, as a number of variables act together: geometrical parameters and orientation of the manifolds and of the channels, operating conditions, fluid physical properties.     

Simulations of two-phase flow distribution in communicating parallel channels for a PEM fuel cell

Numerical simulations utilizing computational fluid dynamics (CFD) with a volume of fluid (VOF) method has been employed to investigate two-phase flow distribution in inter-connected parallel flow channels. The interconnections resemble gas and liquid communications in fuel cell flow fields due to the inherent or artificial structures of gas diffusion layers (GDLs). The simulation results showed that communication between parallel channels could have a great impact on the two-phase flow pattern, gas and water distribution and flow maldistribution. Wide communication channels provide a pathway for gas to short-circuit the liquid, leading to a worsened gas flow distribution. However, when the communication channels are narrow enough, they are helpful for mitigating the flow maldistribution by redistributing the liquid among the parallel flow channels through the communication channels. The simulation results were also verified by comparing the predicted and measured normalized pressure drop and the gas flow ratios at the entrance section of experimental parallel channels.     

Squeezing flow between parallel plates

Summary The flow between two parallel plates (rectangular or circular) approaching or receding from each other symmetrically is analysed. The Xavier-Stokes equations have been transformed into an ordinary differential equation using a similarity transformation and the resulting equations are solved numerically. Results for the velocity components, pressure distribution and shearing stress on the wall are presented. In the case of squeezing flow between two circular plates the load supporting capacity of the upper plate has been calculated.

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Quetschströmung zwischen parallelen Platten

Übersicht Untersucht wird die Strömung zwischen zwei parallelen Rechteck- bzw. Kreisplatten, die sich einander nähern oder entfernen. Die Navier-Stokes-Gleichungen werden durch eine Ähnlichkeitstransformation in eine gewöhnliche Differentialgleichung überführt. Die Lösung erfolgt numerisch. Ergebnisse für die Geschwindigkeitskomponenten, die Druckverteilung und die Wandschubspannung werden vorgestellt. Für die Quetschströmung zwischen zwei Kreisplatten wird die Tragkraft bestimmt.

     

Laminar heat transfer in parallel plate flow

An exact solution for the fluid temperature due to laminar heat transfer in parallel plate flow is found. The formulas obtained are valid for an arbitrary velocity profile. The basic problem encountered involves finding certain expansion coefficients in a series of nonorthogonal eigenfunctions. This problem is solved by passing to a vector system of equations having orthogonal eigenvectors. The method is applicable to more general problems.     

Countercurrent gas-liquid flow in parallel vertical tubes

The subject of this paper is the flow between an upper reservoir, containing a liquid, and a lower reservoir, containing a gas, interconnected by parallel vertical tubes. The characteristics of the combined system are predicted from a knowledge of the behavior of flow in individual tubes. Numerous modes of possible operation are described analytically and demonstrated experimentally. The effects of system geometry, changes in gas supply characteristics, operating procedure and two-phase flow regimes on the transitions between modes and system stability are presented. Predictions are made for the limiting case of a large number of identical parallel channels.     

Experimental study on the performance of a novel structure for two-phase flow distribution in parallel vertical channels

Uniform flow distribution is critical to obtain high thermal performance in many heat and mass transfer devices. It especially plays an important role in a compact heat exchanger. In this paper, a two-phase flow distributor is proposed for the evaporator unit of the plate-fin heat exchanger to alleviate the phase maldistribution in the multiphase flow. Air and water mixture was adopted as two-phase medium and distributions into ten parallel channels were measured in detail. The results show that the proposed distributor can improve the two-phase flow distribution of the plate-fin heat exchanger.     

Flow characteristics in flow networks

A flow network is a system of mutually intersecting holes in a plate or an assembly of plates. The flow at each intersection is characterized by a collision of two flow streams, resulting in complex flow patterns through the downstream holes. In the case of multiple intersections, the flow is periodically disrupted at each succeeding intersection, thus preventing the formation of a fully-developed flow through the holes.An experimental study is presented in this paper to determine flow characteristics in flow networks with various geometry. The intersecting pressure loss coefficient which represents the performance of flow networks is defined and its magnitude empirically determined as functions of geometric and flow conditions. A method is developed to measure the ramming loss in an intersection tube. Flow visualization by means of hydrogen bubble method is applied to observe flow patterns and mixing behavior in the flow network. A physical model is developed to predict the intersection pressure loss in flow networks.List of symbols A total section area of the flow network holes - a section are a of one hole in the flow network - a _t throat area of the orifice - b semi-minor axis of the intersection throat ellipse (Fig. 8) - C _d overall flow discharge coefficient with intersection - C _do overall flow discharge coefficient in the absence of intersection - D _h hydraulic diameter of the flow channel - d hole diameter - f flow friction coefficient - FF compressible flow function - H major axis of the intersection ellipse (Fig. 8) - K _b, K₀ pressure loss coefficients for the miter bend, and quadrant-edged orifice, respectively - K _c, K_e, K_x flow contraction, expansion, and intersection coefficients, respectively - L length of the hole in the flow network, i.e. flow length inside holes - L _e equivalent length of a pipe for the miter bend pressure loss - N _h number of holes in the flow network - N _x number of intersections for each hole - p pitch distance between holes - P _a, P_s, P_t total pressure in the plenum, the ambient pressure, and absolute total pressure in the plenum, respectively - _Pb, p₀ pressure losses in the miter bend and through the quadrant-edged orifice, respectively - p _T, p_H pressure drops in the flow network and its half unit, respectively - Q, Q flow rates passing through the test section equivalent to standard condition and in operating conditions, respectively - R univeral gas constant - s test plate thickness - T, T _t air temperature in the plenum and the absolute temperature of air, respectively - V fluid flow velocity - W mass flow rate of air - diameter ratio in the quadrant-edged orifice - dynamic viscosity of fluid - kinematic viscosity of fluid - intersection angle between holes - fluid density     

Magnetohydrodynamic pipe flow with reverse motion

An exact solution of the Magnetohydrodynamic pipe flow equations is found in terms of elementary functions. As the Hartmann number increases from zero reverse motion in the pipe occurs and eventually separates from the boundary. With further increase in the Hartmann number the vorticity on the boundary continuously changes sign and the flow is analogous to laminar separation in field free hydrodynamics.Sponsored by the United States Army under Contract No. DA-31-124-ARO-D-462.     

Oscillating radial flow between parallel plates

An analysis is presented for laminar radial flow due to an oscillating source between parallel plates. The source strength varies according to Q=Q ₀ cos ωt, and the solution is in the form of an infinite series in terms of a reduced Reynolds number, R _a ^* =Q ₀/4πνa/(r/a)². (Q ₀ = amplitude of source strength, ω = frequency, a = half distance between plates, r = radial coordinate, t = time, and ν = kinematic viscosity.) The results are valid for small values of R _a ^* and all values of the frequency Reynolds number, α=ωa ²/ν. The effects of the parameters R _a ^* and α are discussed.     

Starting flow in a rotating parallel plate channel

The starting flow due to a suddenly applied pressure gradient in a parallel plate channel which is rotating as a system is studied. Exact analytic series solutions to the unsteady Navier-Stokes equations are found by both the Laplace transform method and the separation of parameters method, the latter is shown to be superior. Rotation not only induces a secondary transverse flow but also alters the character of the transient flow rate and velocity profiles. Back flow and inertial oscillations occur, especially at higher rotation rates.