Trade-off analysis of high-aspect-ratio-cooling-channels for rocket engines

High performance liquid rocket engines are often characterized by rectangular cooling channels with high aspect ratio (channel height-to-width ratio) because of their proven superior cooling efficiency with respect to a conventional design. However, the identification of the optimum aspect ratio is not a trivial task. In the present study a trade-off analysis is performed on a cooling channel system that can be of interest for rocket engines. This analysis requires multiple cooling channel flow calculations and thus cannot be efficiently performed by CFD solvers. Therefore, a proper numerical approach, referred to as quasi-2D model, is used to have fast and accurate predictions of cooling system properties. This approach relies on its capability of describing the thermal stratification that occurs in the coolant and in the wall structure, as well as the coolant warming and pressure drop along the channel length. Validation of the model is carried out by comparison with solutions obtained with a validated CFD solver. Results of the analysis show the existence of an optimum channel aspect ratio that minimizes the requested pump power needed to overcome losses in the cooling circuit.     

Experimental studies of adiabatic flow boiling in fractal-like branching microchannels

Experimental results of adiabatic boiling of water flowing through a fractal-like branching microchannel network are presented and compared to numerical model simulations. The goal is to assess the ability of current pressure loss models applied to a bifurcating flow geometry. The fractal-like branching channel network is based on channel length and width ratios between adjacent branching levels of 2^−1/2. There are four branching sections for a total flow length of 18 mm, a channel height of 150 μm and a terminal channel width of 100 μm. The channels were Deep Reactive Ion Etched (DRIE) into a silicon disk. A Pyrex disk was anodically bonded to the silicon to form the channel top to allow visualization of the flow within the channels. The flow rates ranged from 100 to 225 g/min and the inlet subcooling levels varied from 0.5 to 6 °C. Pressure drop along the flow network and time averaged void fraction in each branching level were measured for each of the test conditions. The measured pressure drop ranged from 20 to 90 kPa, and the measured void fraction ranged from 0.3 to 0.9. The measured pressure drop results agree well with separated flow model predictions accounting for the varying flow geometry. The measured void fraction results followed the same trends as the model; however, the scatter in the experimental results is rather large.     

Influence of the aspect ratio on boiling flows in rectangular mini-channels

This article presents experiments conducted with two single rectangular mini-channels of same hydraulic diameter (1.4 mm) and different aspect ratios for conditions of horizontal boiling flow. The Forane® 365 HX used was subcooled (ΔT_sub = 15 °C) for all the boiling curves presented in the paper. Local heat transfer coefficients were measured for heat flux ranging from 25 to 62 kW m⁻² and mass flux from 200 kg m⁻² s⁻¹ to 400 kg m⁻² s⁻¹. The boiling flows were observed with two different cameras (depending on the flow velocity) through a visualization window. The flow patterns in the two channels were compared for similar conditions. The results show that the boiling heat transfer coefficient and the pressure drop values are different for the two single mini-channels. For low heat flux condition, the channel with lowest aspect ratio (H/W = 0.143) has a higher heat transfer coefficient. On the other hand, for high heat flux condition, the opposite situation occurs, namely the heat transfer coefficient becomes higher for the channel with highest aspect ratio (H/W = 0.43). This is probably due to the earlier onset of dryout in the channel with lowest aspect ratio. For the two cases of heating, the pressure drop for the two-phase flow remains lower for the channel with lowest aspect ratio. These results show that the aspect ratio plays a substantial role for boiling flows in rectangular channels. As for single-phase flows, the heat transfer characteristics are significantly influenced (even though the hydraulic diameter remains the same) by this parameter.     

Experimental evaluation of cooling performance of circular heat sinks for heat dissipation from electronic chips using nanofluid

In this work, an experimental investigation on cooling performance of using nanofluid to replace the pure water as the coolant in a minichannel heat sink is conducted. The heat sink comprises of four circular channels with hydraulic diameter of 6 mm. Thermal and hydraulic performances of the nanofluid cooled minichannel heat sink are evaluated from the results obtained for the Nusselt number, friction factor, thermal resistance and pumping power, with the volume flow rate ranging from 0.3 to 1.5 L/min. The experimental results show that the nanofluid cooled heat sink outperforms the water-cooled one, having significantly higher average heat transfer coefficient. Despite the marked increase in dynamic viscosity due to dispersing the nanoparticles in water, the friction factor for the nanofluid-cooled heat sink is found slightly increased only.     

Flow boiling enhancement of FC-72 from microporous surfaces in minichannels

The microporous coatings can remarkably enhance the liquid boiling heat transfer. Therefore, they are promising to be introduced into minichannels in the design of the cooling system of high-power microchips. However, the flow boiling heat transfer characteristics from microporous surfaces in the minichannels have not been extensively studied, and the pertinent knowledge is rather fragmentary. The present research is an experimental investigation on flow boiling of a dielectric fluid FC-72 from microporous coating surfaces in horizontal, rectangular minichannels of 0.49, 0.93 and 1.26 mm hydraulic diameter. Effects of coating structural parameters, such as the particle diameter and coating thickness, were investigated to identify the optimum microporous coating for heat transfer enhancement. All microporous surfaces in this paper were found to significantly enhance FC-72 flow boiling heat transfer in minichannels. With the optimum coating, the heat transfer coefficients could be 7-10 times those of the uncoated surface, and the boiling wall temperature was reduced by about 10 K. The flow boiling phenomena in the present minichannels were distinctly different from those in conventional-sized channels, due to the wall confinement effect on vapor bubbles. The confinement effect was evaluated by taking the contributions of the liquid mass flux and channel size into consideration. It was found that the very strong confinement effect was unfavorable with respect to flow boiling enhancement of the microporous coatings in the minichannels.     

Adiabatic two phase flow distribution and visualization in scaled microchannel heat sinks

The present work investigates the characteristics of adiabatic two-phase flow, and compares the flow distribution in two different multi-channel configurations. One is a standard straight channel design, and the second is similar, except that it has two cross-linked paths located at one-third and two-thirds of the channel length. Each test section consists of 45 rectangular channels with a hydraulic diameter of 1.59 mm and is fabricated out of acrylic to enable flow visualization. The test facility operates with water and air as the working fluids. Gas and water superficial velocities range from 0.03 to 9.93 and 0.04 to 0.83 m/s, respectively, corresponding to a flow quality between 0 and 0.25, whereby the mass flux range is from 41 to 834 kg/m²s. Four channels were selected for flow distribution tracking, and the results showed that the straight and cross-linked designs both have unequal flow distributions. Flow patterns are presented in terms of a fractional time function to gain insight into the flow characteristics. Compared to a single channel flow regime map, the intermittent flow regime was observed 65 to 85% of the times expected, whereas the dispersed flow regime only occurred ∼40% of the times expected for both designs. Further discussion on flow distribution and flow patterns are also documented.     

Flow pattern based correlations of two-phase pressure drop in rectangular microchannels

Numerous pressure drop correlations for microchannels have been proposed; most of them can be classified as either a homogeneous flow model (HFM) or a separated flow model (SFM). However, the predictions of these correlations have not been compared directly because they were developed in experiments conducted under a range of conditions, including channel shape, the number of channels, channel material and the working fluid. In this study, single rectangular microchannels with different aspect ratios and hydraulic diameters were fabricated in a photosensitive glass. Adiabatic water-liquid and Nitrogen-gas two-phase flow experiments were conducted using liquid superficial velocities of 0.06–1.0 m/s, gas superficial velocities of 0.06–72 m/s and hydraulic diameters of 141, 143, 304, 322 and 490 μm. A pressure drop in microchannels was directly measured through embedded ports. The flow pattern was visualized using a high-speed camera and a long-distance microscope. A two-phase pressure drop in the microchannel was highly related to the flow pattern. Data were used to assess seven different HFM viscosity models and ten SFM correlations, and new correlations based on flow patterns were proposed for both HFMs and SFMs.     

Characterization of wettability effects on pressure drop of two-phase flow in microchannel

The Characterization of the effects of surface wettability and geometry on pressure drop of slug flow in isothermal horizontal microchannels is investigated for circular and square channels with hydraulic diameter (D _h ) of 700 μm. Flow visualization is employed to characterize the bubble in slug flow established in microchannels of various surface wettabilities. Pressure drop increases with decrease in surface wettability, while the channel geometry influences slug frequency. It is observed that the gas–liquid contact line in advancing and receding interfaces of bubble change with surface wettability in slug flows. Flow resistance, where capillary force is important, is estimated using Laplace–Young equation considering the change of dynamic contact angles of bubble. The experimental study also demonstrates that the liquid film presence elucidates the pressure drop variation of slug flows at various surface wettabilities due to diminishing capillary effect.     

Numerical simulation of particle migration in asymmetric bifurcation channel

In this work we provide numerical validation of the particle migration during flow of concentrated suspension in asymmetric T-junction bifurcation channel observed in a recent experiment [1]. The mathematical models developed to explain particle migration phenomenon basically fall into two categories, namely, suspension balance model and diffusive flux model. These models have been successfully applied to explain migration behavior in several two-dimensional flows. However, many processes often involve flow in complex 3D geometries. In this work we have carried out numerical simulation of concentrated suspension flow in 3D bifurcation geometry using the diffusive flux model. The simulation method was validated with available experimental and theoretical results for channel flow. After validation of the method we have applied the simulation technique to study the flow of concentrated suspensions through an asymmetric T-junction bifurcation composed of rectangular channels. It is observed that in the span-wise direction inhomogeneous concentration distribution that develops upstream persists throughout the inlet and downstream channels. Due to the migration of particles near the bifurcation section there is almost equal partitioning of flow in the two downstream branches. The detailed comparison of numerical simulation results is made with the experimental data.     

Simulation of non‐hydrostatic,density‐stratified flow in irregular domains

A numerical model has been developed for simulating density‐stratified flow in domains with irregular but simple topography. The model was designed for simulating strong interactions between internal gravity waves and topography, e.g. exchange flows in contracting channels, tidally or convectively driven flow over two‐dimensional sills or waves propagating onto a shoaling bed. The model is based on the non‐hydrostatic, Boussinesq equations of motion for a continuously stratified fluid in a rotating frame, subject to user‐configurable boundary conditions. An orthogonal boundary fitting co‐ordinate system is used for the numerical computations, which rely on a fourth‐order compact differentiation scheme, a third‐order explicit time stepping and a multi‐grid based pressure projection algorithm. The numerical techniques are described and a suite of validation studies are presented. The validation studies include a pointwise comparison of numerical simulations with both analytical solutions and laboratory measurements of non‐linear solitary wave propagation. Simulation results for flows lacking analytical or laboratory data are analysed a posteriori to demonstrate satisfaction of the potential energy balance. Computational results are compared with two‐layer hydraulic predictions in the case of exchange flow through a contracting channel. Finally, a simulation of circulation driven by spatially non‐uniform surface buoyancy flux in an irregular basin is discussed. Copyright © 2000 John Wiley & Sons, Ltd.     

Flow pattern based correlations of two-phase pressure drop in rectangular microchannels

Numerous pressure drop correlations for microchannels have been proposed; most of them can be classified as either a homogeneous flow model (HFM) or a separated flow model (SFM). However, the predictions of these correlations have not been compared directly because they were developed in experiments conducted under a range of conditions, including channel shape, the number of channels, channel material and the working fluid. In this study, single rectangular microchannels with different aspect ratios and hydraulic diameters were fabricated in a photosensitive glass. Adiabatic water-liquid and Nitrogen-gas two-phase flow experiments were conducted using liquid superficial velocities of 0.06–1.0 m/s, gas superficial velocities of 0.06–72 m/s and hydraulic diameters of 141, 143, 304, 322 and 490 μm. A pressure drop in microchannels was directly measured through embedded ports. The flow pattern was visualized using a high-speed camera and a long-distance microscope. A two-phase pressure drop in the microchannel was highly related to the flow pattern. Data were used to assess seven different HFM viscosity models and ten SFM correlations, and new correlations based on flow patterns were proposed for both HFMs and SFMs.     

Pressure drop and heat transfer characteristics of boiling water in sub-hundred micron channel

The current work focuses on the pressure drop, heat transfer and stability in two phase flow in microchannels with hydraulic diameter of less than one hundred microns. Experiments were conducted in smooth microchannels of hydraulic diameter of 45, 65 μm, and a rough microchannel of hydraulic diameter of 70 μm, with deionised water as the working fluid. The local saturation pressure and temperature vary substantially over the length of the channel. In order to correctly predict the local saturation temperature and subsequently the heat transfer characteristics, numerical techniques have been used in conjunction with the conventional two phase pressure drop models. The Lockhart–Martinelli (liquid–laminar, vapour–laminar) model is found to predict the two phase pressure drop data within 20%. The instability in two phase flow is quantified; it is found that microchannels of smaller hydraulic diameter have lesser instabilities as compared to their larger counterparts. The experiments also suggest that surface characteristics strongly affect flow stability in the two phase flow regime. The effect of hydraulic diameter and surface characteristics on the flow characteristics and stability in two phase flow is seldom reported, and is of considerable practical relevance.     

Flux‐corrected transport technique for open channel flow

In modeling flow in open channels, the traditional finite difference/finite volume schemes become inefficient and warrant special numerical treatment in the presence of shocks and discontinuities. The numerical oscillations that arise by making use of a second‐ and higher‐order schemes require some additional smoothing mechanism. A characteristic feature of high‐resolution schemes lies in smooth capturing of the shock fronts. This paper provides a general formulation for a flux‐corrected transport algorithm to the one‐dimensional open channel flow equations. The preliminary results presented show that the present algorithm is an efficient, conservative and robust tool that can be easily coded. To demonstrate the robustness of the present formulation, results are compared with other published numerical results, experimental data and analytical solutions when available. In particular, a comprehensive study on the effect of the source term, dry bed, variable width channel, steep sloping channel and flow with mixed flow conditions (as in a hydraulic jump) has been carried out to test the efficacy of the present algorithm. Copyright © 1999 John Wiley & Sons, Ltd.     

Comparative evaluation of three heat transfer enhancement strategies in a grooved channel

 Results of a comparative evaluation of three heat transfer enhancement strategies for forced convection cooling of a parallel plate channel populated with heated blocks, representing electronic components mounted on printed circuit boards, are reported. Heat transfer in the reference geometry, the asymmetrically heated parallel plate channel, is compared with that for the basic grooved channel, and the same geometry enhanced by cylinders and vanes placed above the downstream edge of each heated block. In addition to conventional heat transfer and pressure drop measurements, holographic interferometry combined with high-speed cinematography was used to visualize the unsteady temperature fields in the self-sustained oscillatory flow. The locations of increased heat transfer within one channel periodicity depend on the enhancement technique applied, and were identified by analyzing the unsteady temperature distributions visualized by holographic interferometry. This approach allowed gaining insight into the mechanisms responsible for heat transfer enhancement. Experiments were conducted at moderate flow velocities in the laminar, transitional and turbulent flow regimes. Reynolds numbers were varied in the range Re = 200–6500, corresponding to flow velocities from 0.076 to 2.36 m/s. Flow oscillations were first observed between Re = 1050 and 1320 for the basic grooved channel, and around Re = 350 and 450 for the grooved channels equipped with cylinders and vanes, respectively. At Reynolds numbers above the onset of oscillations and in the transitional flow regime, heat transfer rates in the investigated grooved channels exceeded the performance of the reference geometry, the asymmetrically heated parallel plate channel. Heat transfer in the grooved channels enhanced with cylinders and vanes showed an increase by a factor of 1.2–1.8 and 1.5–3.5, respectively, when compared to data obtained for the basic grooved channel; however, the accompanying pressure drop penalties also increased significantly. Received on 5 April 2001     

Mathematical expression of pressure gradient in the flow of spherical capsules less dense than water

This study yielded a mathematical expression to calculate the pressure gradient (ΔP/L)_m of the flow of a spherical capsule train. An experimental investigation was carried out to determine pressure drops of two-phase mixture flow of spherical ice capsules and water inside the pipelines of cooling systems. Instead of ice capsules, spherical capsules made of polypropylene material whose density (870 kg/m³) is similar to that of ice were used in the experiments. Flow behavior of the spherical capsules, 0.08 m outer diameter, was observed in the measuring section inside plexiglass pipes, 0.1 m inner diameter (ID) and 6 m in length; pressure drops were measured on the 4 m section. The investigation was carried out in the 1.2 × 10⁴ < Re < 1.5 × 10⁵ range and under transport concentration (C_tr) by 5–30%. Dimensionless numbers of the physical event were found out by conducting a dimensional analysis, so that mixture density was expressed in terms of specific gravity and in situ concentration. After arriving at certain conclusions based on the relevant experimental findings and observations, empirical and mathematical models which can be used for calculation of the pressure gradient were developed. Comparison of the mathematical model with the experimental findings revealed that pressure drop values deviated by 2.7% on average for 2.5 × 10⁴ < Re < 1.5 × 10⁵.     

Numerical characterization of micro heat exchangers using experimentally tested porous aluminum layers

A microporous heat exchanger device is being developed for cooling high-power electronics. The device uses a mechanically compressed aluminum porous layer to improve the heat transfer at the coolant/solid interface and to provide more uniform cooling of the electronics. The hydraulic characteristics (porosity, permeability, and Forchheimer coefficient) of nine distinct compressed layers are obtained experimentally. These layers have porosity from 0.3 to 0.7 and permeability from 1.8 × 10⁻¹⁰ m2 to 1.2 × 10⁻⁹ m2. The inertia coefficient varies from 0.3 to 0.9. These hydraulic characteristics are used in the numerical simulations of a real microporous heat exchanger for cooling phased-array radars in development. Thermal and hydraulic performances are illustrated in terms of total pressure drop across the heat exchanger, maximum temperature difference in the direction transverse to the electronic modules, and maximum temperature within the coolant passage. Results indicate that the proposed design is capable of achieving a maximum transverse temperature difference of 2°C using polyalphaolephin as coolant.     

An experimental and three-dimensional numerical study on the convective heat transfer inside a trapezoidal duct under constant wall temperature

In this study, steady-state forced convection heat transfer and pressure drop characteristics for hydrodynamically fully developed thermally developing three-dimensional turbulent flow in a horizontal smooth trapezoidal duct with corner angle of 75° and hydraulic diameter of 0.043 m were both experimentally and numerically investigated in the Reynolds number range from 2.6 × 10³ to 67 × 10³ for isothermal conditions. Results have shown that there is a good agreement between the present experimental and numerical results.     

Flow division at a channel crossing with subcritical or supercritical flow

The passage of an extreme storm over an urban area can lead to the flooding of the streets if the rainfall intensity exceeds the design value and/or the drainage system is not functional. The study of flow distribution in street networks thus is important for the design of flood protection measures. The flow distribution is affected by the junction flow characteristics, inflow discharges and downstream water depths. To reduce the degree of empiricism, a 3D Reynolds‐averaged Navier–Stokes equations model has been implemented in this study to investigate the flow phenomena in a cross junction. The Spalart–Allmaras model is used for turbulence closure. The numerical model utilizes the split‐operator approach, in which the advection, diffusion and pressure propagations are solved separately. The numerical model predicts accurately the flow distribution in a channel crossing under different subcritical flow conditions, for which experimental data are available. Recirculation zones exist at both the downstream channels and the associated contraction coefficient varies linearly with the ratio of the discharges at the two inlets. Secondary currents are apparent for the flow with strong asymmetric outlet conditions. Under supercritical inflow conditions, the model reproduces the hydraulic jump and hydraulic drop phenomena and predicts accurately the relationship between the input power ratio and the outflow discharge ratio of the street crossing. Copyright © 2009 John Wiley & Sons, Ltd.     

An inverse boundary value problem for Maxwell's equations

We consider steady, two-dimensional motions of an incompressible, Newtonian fluid flowing under gravity down an inclined channel. If the bottom of the channel is flat, the flow is the classical Poiseuille-Nusselt flow and the free surface is then a plane parallel to the bottom. Motivated by the recent experimental and numerical studies of Pritchard, Scott & Tavener, we look at bottom configurations which possess some localized, non-uniform structure. We present an existence theory for steady, highly viscous flow over such configurations. An important consequence of our theory is that the steady flows whose existence is established decay exponentially rapidly to the unperturbed Poiseuille-Nusselt flow away from the local variation in the channel bottom profile.