Minimum Flow Resistance Research Articles

On deriving Murray’s law from constrained minimization of flow resistance

Murray’s law, which states that the cube of the radius of a parent vessel equals the sum of the cubes of the radii of the daughter vessels, was originally derived by minimizing the cost of operation of blood flow in a single cylindrical tube. An alternative widely cited derivation by Sherman is based upon the optimization problem of minimizing the total flow resistance subject to a material constraint, and that study claimed that “Conservation of the sum of the cubes of the radii is the condition for minimal resistance whether the parent vessel divides symmetrically or asymmetrically, and whether it divides into two, three, four, or, presumably, any number of daughter vessels.” In this paper we show that Sherman’s analysis is flawed, since with N daughter vessels there are 2N-N-1 sets of vessel radii which satisfy Murray’s law but which do not yield minimal total flow resistance. Moreover, we show that when there are N daughter vessels, each with the same radius, the minimal total flow resistance is an increasing function of N for N⩾1. Since N=1 corresponds to the degenerate case of no branching at all, our result implies that bifurcation (N=2) achieves the minimal total flow resistance. Our analysis thus offers an explanation for the preponderance of bifurcations (as opposed to trifurcations or higher level branchings) in many biological systems.

Numerical study on maximizing heat transfer and minimizing flow resistance behavior of metal foams owing to their structural properties

Despite many research works considering metal foams largely involving heat exchange applications, an overall comprehensive view on the performance of metal foams based on their structural properties is hitherto unaddressed in the literature. In the present work, an air forced convection-laminar flow in a vertical channel is considered in which a heated plate along with metal foam is placed at the center. The plate is subject to constant heat flux condition to assess the performance of aluminum metal foam based on their degree of inclination towards maximizing heat transfer and minimizing flow resistance behavior in a vertical channel corresponding to the combination of structural properties they possess. Heat transfer and flow phenomena pertaining to the metal foam are numerically modeled using Local Thermal Non-Equilibrium (LTNE) and Darcy–Forchheimer flow models, respectively to obtain key thermo-hydrodynamic parameters. Both the independent and the combined effects of foam structural parameters viz., porosity and pore density on Nusselt number and friction factor are discussed justifying the effects of interfacial specific surface area and interfacial heat transfer coefficient of fluid saturated foam samples. The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) a multi attribute decision-making technique is applied to solve the multi objective function to determine the performance of metal foams measured on a scale of 0 to 1. Five distinct criteria are studied involving distributed weights of 0:1, 0.25:0.75, 0.5:0.5, 0.75:0.25 and 1:0 each representing amplitudes of varying importance given to maximizing heat transfer and minimizing flow resistance characteristics of metal foams. Global performance charts are obtained, featuring performance abilities of metal foam samples covering wide ranges of porosity ranging from 0.8 to 0.97 and pore densities ranging from 5PPI to 45PPI corresponding to a given criteria involving a specific weight distribution scenario. The present work provides performance characteristics of available as well as possible foam samples with an overview idea on the range of structural aspects of foam samples, where the enhanced ability of the foam to perform best in meeting the given criteria is witnessed.

Assessment of Cerebrovascular Reserve in the Heart Failure Patients Supported with the HeartMate3

We previously showed that cerebrovascular reactivity (CVR) is reduced in heart failure (HF) patients and does not improve after left ventricular assist device (LVAD) HeartMate II (HMII) implantation, possibly because of low pulsatile physiology. Therefore, it is possible that the artificial pulse of the latest generation LVAD, the HeartMate3 (HM3), restores normal CVR. HM3 patients will have an increased CVR to a CO2-retention challenge compared with HF and HMII. A total of 79 subjects (17 healthy, 30 HF, 15 HMII and 17 HM3) underwent angle-corrected transcranial Doppler sonography. Middle cerebral artery (MCA) velocity profiles were recorded before and at the end of a 30s breath hold. Mean flow velocity (MFV), peak flow velocity (Vmax), minimal flow velocity (Vmin), Pulsatility Index (PI) and Resistance Index (RI) were quantified. Statistical differences were determined using 2-way ANOVA (Breathhold x group). At baseline, HF patients with and without LVAD implantation had a decreased Vmax, MFV, PI and RI compared to healthy (all P < 0.05). With CO2-retention the absolute and relative increase in MFV was highest in the HM3 group significantly compared with HMII (7.8±2.4 vs 1.6±2.1 cm/s; +16% vs +3%, p<0.01). HM3 and HF subjects exhibited similar absolute and relative changes in MFV and both were lower than health controls. Similar results were seen for Vmax and Vmin, however, there was no change PI or RI in any groups (Fig. 1). The change with MFV with breath-holding was not different when considering HF subjects on inotropes, or when comparing beats with and without artificial pulse in HM3 patients. HM3 patients have a significantly improved CVR to a CO2-retention challenge compared with HMII patients. However, the acute CVR is not altered by the artificial pulse. Since CVR of HM3 patients remains reduced compared with healthy controls, further research is needed to understand the pathophysiology of cerebrovascular complications in LVAD.

P103 Improved Metabolic Vasoreactivity in the Brain of HM3 Patients and its Underlying Microcirculatory Mechanisms

BackgroundThe MOMENTUM3 trial1 has revealed superiority of the novel HeartMate3 (HM3) left ventricular assist device (LVAD) compared with the HM2, with a significantly reduced occurrence of cerebrovascular accidents. Thus, cerebral autoregulation may be improved in HM3 compared with HM II patients, possibly because of altered microcirculatory haemodynamics associated with the in-built speed modulation (‘pulsatility’) of the HM3 device.MethodsAngle-corrected Doppler ultrasound images of the middle cerebral artery (MCA) were recorded before and at the end of a 30s breathhold test in healthy controls (n = 17), heart failure (HF n = 18), HM2 (n = 10) and HM3 (n = 17) patients. Microcirculatory haemodynamics as represented by the central retinal artery (CRA) were also quantified (Controls = 33, HF = 27, HM2 = 23, HM3 = 31). Data were analysed for Time-Averaged Maximum flow velocity (TAMAX), peak flow velocity (Vmax), minimum flow velocity (Vmin), Pulsatility Index (PI) and Resistance Index (RI, Table 1).ResultsBreathhold significantly increased TAMAX, Vmax and Vmin in all groups except HM II patients (Figure 1A). Conversely, PI decreased slightly in all groups while RI was maintained. The greater breathhold response in HM3 compared with HM2 patients was not attributable to the in-built pump-speed modulation (Figure 1B), however, HM3 had a consistently lower RI in the MCA and CRA.ConclusionAlthough reduced compared with healthy controls, HF and HM3 patients have a significantly greater metabolic cerebral vasoreactivity compared with HM2 patients. The 60% greater diastolic flow velocity in the microcirculation of both LVAD groups compared to healthy controls may alter gas exchange in the microcirculation. Future studies should examine the role of altered RI in HM3 patients.Table 1Haemodynamics in the middle cererbral artery (MCA) and the central retinal artery (CRA) between HeartMate2 and HeartMate3 patientsHealthy controls (n = 33)Heart failure (n = 27)HeartMate II (n = 23)HeartMate3 (average) (n = 31)HeartMate3 (no speed modulation) (n = 31)HeartMate3 (with speed modulation) (n = 31)Middle cerebral arteryTAMAX (cm/s)58 ± 1548 ± 1345 ± 1548 ± 1948 ± 1946 ± 18Vmax (cm/s)92 ± 2278 ± 2055 ± 19*#55 ± 21*#54 ± 21*#55 ± 22*#Vmin (cm/s)39 ± 1229 ± 1137 ± 1639 ± 1444 ± 16#32 ± 13Pulsatility index0.88 ± 0.181.05 ± 0.31*0.40 ± 0.24*#0.34 ± 0.14*#0.21 ± 0.12*#$0.56 ± 0.24*#Resistance index0.57 ± 0.070.60 ± 0.110.29 ± 0.14*#0.16 ± 0.09*#$0.17 ± 0.10*#$0.14 ± 0.09*#$Central retinal arteryTAMAX (cm/s)6 ± 15 ± 26 ± 37 ± 37 ± 46 ± 4Vmax (cm/s)12 ± 311 ± 68 ± 4*8 ± 4*8 ± 4*8 ± 4*Vmin (cm/s)3 ± 13 ± 15 ± 25 ± 36 ± 3*#4 ± 4Pulsatility index1.60 ± 0.451.42 ± 0.400.58 ± 0.26*#0.49 ± 0.21*#0.32 ± 0.17*#0.79 ± 0.35*#Resistance index0.75 ± 0.090.70 ± 0.110.38 ± 0.15*#0.22 ± 0.11*#$0.24 ± 0.12*#$0.20 ± 0.13*#$*p < 0.05 compared with healthy controls; #p < 0.05 compared with Heart Failure; $p < 0.05 compared with HeartMate II.Figure 1(A) Time-averaged maximum flow velocity in the middle cerebral artery of healthy controls and patient groups in response to a 30-s breathhold test. (B) Breakdown of the responses in HM3 patients, comparing beats with and without added pulsatility.

New concept of 3D bio-inspired solar thermal collector

The aim of the present work was to develop a new type of solar thermal collector tree shape in three dimensions. It is a Solar Thermal Tree (STT) whose branches and trunk consist of tubular absorbers glazed or not. The article presents the validation of the concept with a medium-scale prototype. The numerical modeling of the STT is first described, then the comparison of the experimental and numerical results, the evaluation of the performances based on dimensionless equations, and finally the multi-criteria optimization. The model has been used to identify the dimensionless equations (thermal efficiency and pressure drop) from a small number of parameters. These equations can be used to design the STT for different applications. It also enabled to define optimal solutions (Pareto) by considering the two performance functions in a configuration close to that of the prototype. Optimal solutions are compared with the experiment using the prototype, a solution that minimizes the creation of entropy generated by flow and heat transfer, and a solution based on the Hess-Murray law that minimizes flow resistance in laminar or turbulent flow. The optimization criterion based on entropy generation is the most relevant because the entropy generated by the air flow is very low compared to heat transfer. Also, optimization leads to maximizing thermal efficiency. Finally, the design of a 4 m2 STT that can be used to preheat the building's fresh air (0 °C) has been optimized. This new configuration, based on vacuum tubes has a thermal efficiency of 58%.

Influences of structure parameters on performance of tree-shaped ground heat exchanger

During long-term operation of ground source heat pump (GSHP) system, heat accumulation is a common problem leading to the increase of soil temperature and the degradation of operating efficiency. The tree-shaped ground heat exchanger (GHE) showed great potential to eliminate heat accumulation and maintain soil temperature. In this paper, the influences of structure parameters on flow and heat transfer performance of GHE are explored. The results indicate that the diameter ratio adopting design method of minimum flow resistance has better comprehensive performance than that of minimum thermal resistance. For two sub-tubes, the comprehensive performance of GHE increases as the rise of asymmetry ratio and reaches maximum when the sub-tube is symmetric. Meanwhile, for tree-shaped GHE with bifurcation level of 1, the optimal length ratio is 1.

Numerical–experimental research on the influence of inclined angle on the flow characteristics of angle seat valve

The influence of inclined angle on the flow characteristics of angle seat valve is investigated by the numerical and experimental study. The accuracy of numerical modelling and calculation is verified by comparing the flow coefficients obtained from numerical simulation and experiments under the different pressure difference at the inclined angle of 45° and 60°. The experiment results showed that the highest flow velocity, the maximum flow coefficient, and the minimum flow resistance exist as the inclined angle is 45°. The flow coefficient increases as the increase of inclined angle when it ranges from 45° to 60°, and the flow resistance decreases correspondingly. The observed result is discussed and explained by the computational fluid dynamics (CFD) method. The calculation results indicated that the flow coefficient mainly depends on the maximum flow velocity in the angle seat valve. Moreover, the flow capacity is also affected by the flow direction near the sealing surface, and the number, locations and intensities of flow vortex.

Non-invasive evaluation of cerebral hemodynamic and intracranial pressure in pediatric neuroinfections

The study of intracranial pressure (eICP), cerebral perfusion pressure (eCPP), cerebral blood flow index (CFI), zero flow pressure (ZFP) in 49 children hospitalized in the intensive care unit with severe course of neuroinfections was carried out. The level of consciousness was determined by the Glasgow pediatric scale. Monitoring of central and peripheral hemodynamics (ECG, heart rate, systolic, diastolic and mean blood pressure, and cardiac output), pulse oximetry, capnography, hemoglobin, hematocrit, total protein, urea, creatinine, lactate, glucose and serum electrolytes was done. An ultrasound scanner was used to perform ultrasound duplex scanning of blood flow in the left and middle cerebral artery (MCA), measuring maximum, minimum and average blood flow velocities, pulsation index (PI), and resistance index (RI). Based on the formulae of Edouard et al. indicators of eCPP, ZFP, CFI, eICP were calculated. The eSCP was also determined by the formulae of Kligenchöfer et al. and Bellner et al. All patients were divided into group I with RI &gt; 1.3 and group II with RI &lt; 1.3. It was found that eCPP in the group I was significantly less (29.5 ± 1.3 mm Hg) than in the II group (41.6 ± 1.7 mm Hg). Despite the lack of a reliable difference in blood pressure between groups I and II, the difference in eCPP was found due to a significant difference in eICP 34.6 ± 1.4 and 27.6 ± 0.89 mm Hg in I and II groups respectively. ZFP in group I was significantly higher than in group II. The indexes of the Glasgow coma scale was significantly lower in group I and 7.8 ± 0.6 points. There were observed direct moderate correlations between systolic blood pressure, cardiac output and eSRP and CFI, presumably associated with a loss of autoregulation. CFI in the group I was lower than in the group II. Thus, non-invasive examination of cerebral flow in MCA by duplex sonography revealed that PI &gt; 1.3 is an informative marker of intracranial hypertension and reduction of cerebral perfusion, which is common in children with neuroinfections. To determine the eSRP and CFI it is advisable to use the formula of Edouard et al. and to determine the eICP the formula of Kligenchöfer et al. The obtained data can be useful for objectifying the severity of the condition, predicting the outcomes of neuroinfections, choosing the directions of intensive care and evaluating its effectiveness.

Influences of the Preparation Temperature on the Acoustic Parameters of Polyurethane

In this paper, the influence of the preparation temperature on the absorption coefficient and acoustic parameters of polyurethane was studied. Best sound absorption coefficient of polyurethane at high frequency is at 50℃, followed is 30℃ and 40℃,70℃ is lowest. Between 20~50℃, the flow resistance increased rapidly with the temperature increasing, the minimum flow resistance at 50℃, maximum value at 70℃.The trend of porosity with temperature is similar to that with flow resistance. With the temperature increasing, the porosity decreases first and then increases, minimum value at 50℃. Flow resistance dominating the flow resistance of the sound absorption performance.

Theoretical and computational investigation of optimal wall shear stress in bifurcations: a generalization of Murray’s law

In this study, the optimal distribution of Wall Shear Stress (WSS) in a bifurcation and its effect on the morphology of blood vessels were investigated. The optimal WSS was obtained through minimization of energy loss due to friction and metabolic consumption. It was shown that the optimal WSS is a function of metabolic rate, fluid properties, diameter, and flow regime. For fully developed laminar and turbulent flows different patterns of WSS were observed. For laminar flows WSS is constant but for turbulent flows WSS is a function of diameter such that the exponent of diameter varies by tube relative roughness. Based on the optimal WSS and conservation of mass, the optimal relationship between diameters of mother and daughters’ vessels was obtained for different flow regimes. Also, it was theoretically shown that the optimal distribution of WSS in a bifurcation minimizes flow resistance as well as energy loss. In addition, it was demonstrated that the specific relationship between the length and diameters of a blood vessel and optimal relationship between diameters lead to optimal WSS distribution. Finally, the numerical simulation was used to investigate the effect of Reynolds number on the optimal WSS and flow resistance, and to verify the theoretical formula predictions, obtained in this work.

Attenuation of Sounds in a Pipe with Shear Flow Using Layered Metamaterials

This study presents a simulation of interactions between sound and a surrounding pipe structure conveying fluid flows. A sound-attenuating structure using layered metamaterials of cylindrical shells is proposed and verified. Numerical simulations based on the finite difference method after considering steady fluid flow in the pipe were performed. The effective wave speed and density of the fluid required to determine acoustic characteristics were calculated from the transfer matrix method. This enabled estimation of noise reduction capability. The metastructure layers were lined parallel to the pipe walls to minimize flow resistance. The effective density was negative near the resonance frequency of the layers. The transmission loss predicted for a moving fluid medium was smaller than that for a stationary medium due to boundary layer formation. The proposed method can be used to design silencers to reduce the transmitted noise in pipe systems.

Numerical simulation of heat transfer for microelectronic heat sinks with different fin geometries in tandem and staggered arrangements

The heat transfer in heat sinks of microelectronic components has been numerically analyzed for different heat sink geometries in tandem and staggered arrangements. The present numerical study addresses cooling of fins with forced air convection in single micro channel heat sink using Ansys FLUENT software. Maximum heat transfer flux with minimum flow resistance was considered as the selection criteria for different heat sinks. Standard and staggered fins of uniform thickness are considered for all the heat sinks to analyze heat transfer performance. Quality factors corresponding to different geometries were calculated and compared with experimental and numerical results available in open literature. The present numerical results ensure the better performance of staggered heat sinks over standard ones. It has been noticed that staggered fins with conic section provide enhanced quality factors at flow Reynolds number range of 450–900 whereas staggered fins with rounded leading edges provide better thermal performances for Reynolds number beyond 900.

Optimization strategies of heat transfer systems with consideration of heat transfer and flow resistance

Performance optimization of heat transfer systems with consideration of both heat transfer and flow resistances is critical for energy conservation. This paper compares two different optimization strategies to trade off heat transfer enhancement and flow resistance reduction. One is to convert multiple objectives to a single one by some individual optimization criteria, such as minimization of entropy generation and other dimensionless entropy generation-based numbers, and the other is to select the maximum heat transfer rate or the minimum flow resistance as the objective directly and adapt the others as constraints by Pareto Optimality. After optimizing a practical multi-loop heat exchanger network (HXN), the optimized results by the former strategy with individual optimization criteria are probably unsuitable for practical operations. Nevertheless, it needs the energy conservation and heat transfer equations of all heat exchangers as the constraints, which makes the optimization more complex. Oppositely, the latter strategy provides a series of maximum heat transfer rates with different flow resistances, i.e. Pareto front, which can be applied according to different practical requirements. The equivalent thermal circuit diagram offers the systematical constraint without involving any intermediate fluid temperatures. The systematic constraint shows advantages and convenience to optimize HXN with consideration of heat transfer and flow resistance, which is pivotal and general for the synergy of heat transfer enhancement and flow resistance reduction in heat transfer system optimization.

Fuel filtration properties and mechanism of a novel fibrous filter produced by a melt-process

A porous filter comprised of polypropylene (PP)/polyamide 6 (PA6) micro-/nano-fibers has been produced from a novel melt-based plastics co-extrusion and exfoliation process technology for the separation of microscale water droplets from diesel fuel. The filter media have a mean pore size of 11µm, a porosity greater than 85%, a surface area of more than 12x the value for an electrospun medium, tough mechanical properties, and a contact angle of 124°, all of which make the co-extruded filter a superior fuel filter. An improvement in water-separation from diesel fuel feed stream from 62–85% water-removal was achieved by the co-extruded and exfoliated PP/PA6 fibrous media in comparison to a commercial fuel filter under identical test conditions and pressure drop. The fuel/water separation mechanism was identified as a capture-coalescence-release process. It has been found that the highest performance fuel filter required small pore sizes and large surface area for droplet capture, due to the hydrophobic nature of materials required for successful droplet release, and a high porosity for minimizing flow resistance. In addition to the proof of concept water separation demonstration, studies into (a) the effect of increasing the barrier substrates thickness and (b) surface corona treatment to alter the hydrophilicity of media surfaces on the filtration efficiency co-extruded, exfoliated filters are reported.

Design optimization with computational fluid dynamic analysis of β-type Stirling engine

The real performance of Stirling engine always deviates from prescribed theoretical potential. This is mainly because of complex interaction of different engine parameters, heat transfer process of oscillating flows and fluid dynamics. In order to develop an effective methodology to optimize geometric design of Stirling engines a beta-type rhombic drive Stirling engine was investigated whose initial experimental efficiency and output power was relatively low. This paper presents a sensitivity analysis of β-type Stirling model and proposed a combined method to carry out multi-objective optimization of a Stirling engine using detailed information of pressure and volume provided by CFD analysis. The geometric parameters of heat exchangers including heater and cooler tubes diameter with length, regenerator length, matrix mesh and wire diameter were considered for maximizing thermal efficiency, output power and minimizing flow resistance power loss in Stirling engine. CFD analysis covers a detailed study of real and optimized model with best experimental agreement. The CFD results include the detailed description of Stirling cycle with temperature contour, velocity vectors and pressure–volume variation in compression and expansion spaces. The proposed modification results an increase of 2 percentage points in thermal efficiency and more than 80W in power output when the dead volume of heater, cooler and regenerator is reduced up to 54%, 42% and 24% respectively. The additional dead volume leads to a phase shift of the pressure which is also the main reason of lowering output results.

MPS 08-07 CEREBROVASCULAR RESISTANCE INDEX AND COGNITIVE IMPAIRMENT IN ESSENTIAL HYPERTENSIVE PATIENTS

Objective: To evaluate the relationship between parameters of cerebral blood flow and cognitive function in pts with essential hypertension (EH). Design and Method: Doppler ultrasonography, 24 h blood pressure monitoring were performed in 141 pts (61.8 ± 0.94 years; 78 males) with EH. We measured blood flow velocities (BFV) in media (MCA), anterior (ACA), posterior (PCA) cerebral arteries and calculated cerebrovascular resistance index (CVRI) for each artery. Cognitive function was assessed in all pts by Montreal cognitive assessment (MoCA) test. All patients were divided into 2 groups depending on the MoCA results: group I (n = 79) – MoCA score ≥26, group II (n = 62) - MoCA score < 26. Results: Patients of II gr. had significantly lower BFV min in MCA, ACA, PCA (accordingly: MCA – 0.46 ± 0.03 vs 0.62 ± 0.04 m/s, p < 0.05, ACA – 0.34 ± 0.02 vs 0.45 ± 0.03 m/s, p < 0.05, PCA – 0.25 ± 0.01 vs 0.36 ± 0.02 m/s, p < 0.05) and significantly higher CVRI than pts of I gr. (accordingly: MCA – 169.21 ± 10.28 vs 130.47 ± 8.47 mmHg/m/s, ACA – 271.65 ± 21.32 vs 180.16 ± 20.25 mmHg/m/s, PCA – 407.12 ± 24.28 vs 252.03 ± 21.58 mmHg/m/s, p < 0.05). Changes of BFV max and mean were not significant. MoCA results were related to MCA BFV min (r = −0.46; p < 0.01), CVRI (r = 0.52; p < 0.05). The same relations were between MoCA results and BFV parameters of ACA and PCA. After adjustment for 24 h SBP and DBP, 24hI SBP, variability of nighttime SBP and DBP these relationships were not significant. Multiple regression analysis has shown that CVRI is predictor of cognitive impairment in pts with EH. Conclusions: Cognitive function in patients with EH related to increase vascular resistance manifesting through decrease minimal blood flow and increase vascular resistance indexes in media, anterior, posterior cerebral arteries. These changes are caused by high 24 h SBP and DBP, variability of nighttime SBP and DBP, low SBP 24 h index. CVRI is predictor of cognitive impairment in pts with EH.

Principle-based design of distributed multiphase segmented flow

The design of systems incorporating multiphase flows remains a significant challenge for applications including lab-on-chip and microreactors. Segmented two-phase flow is used for the purpose of distributing biological samples from one site to many, enhancing heat and mass transport over laminar single phase flow and rapid chemical synthesis. This paper examines hierarchical designs, regularly utilised in such applications, that transport a segmented gas–liquid flow over an area with maximal thermodynamic performance. Fundamental design rules, predicted using the constructal method, minimize flow resistance of elemental bifurcations. The predicted geometric configuration follows an alternative to the established Murray’s law (or Hess–Murray law) when the global pressure difference is dominated by short liquid slugs and dispersed gas phase. Breakup of phases in the junction region was examined numerically with a volume-of-fluid approach to develop a general criteria where junction losses are non-negligible. Although this loss is periodic, the interfacial pressure during the necking stage of the dispersed phase dominates. Using the findings for an elemental bifurcation, multiple scale hierarchical configurations for combined fluid and heat transport were assessed. The multiple scale tree-shaped design can be advantageous for low thermal resistance and pumping power requirements compared to a single scale serpentine layout. The principle-based method and results can reduce the design space in high-fidelity investigations of microscale segmented flows.

Optimization of an enclosed gas analyzer sampling system for measuring eddy covariance fluxes of H&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;O and CO&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;

Abstract. Several initiatives are currently emerging to observe the exchange of energy and matter between the earth's surface and atmosphere standardized over larger space and time domains. For example, the National Ecological Observatory Network (NEON) and the Integrated Carbon Observing System (ICOS) are set to provide the ability of unbiased ecological inference across ecoclimatic zones and decades by deploying highly scalable and robust instruments and data processing. In the construction of these observatories, enclosed infrared gas analyzers are widely employed for eddy covariance applications. While these sensors represent a substantial improvement compared to their open- and closed-path predecessors, remaining high-frequency attenuation varies with site properties and gas sampling systems, and requires correction. Here, we show that components of the gas sampling system can substantially contribute to such high-frequency attenuation, but their effects can be significantly reduced by careful system design. From laboratory tests we determine the frequency at which signal attenuation reaches 50 % for individual parts of the gas sampling system. For different models of rain caps and particulate filters, this frequency falls into ranges of 2.5–16.5 Hz for CO2, 2.4–14.3 Hz for H2O, and 8.3–21.8 Hz for CO2, 1.4–19.9 Hz for H2O, respectively. A short and thin stainless steel intake tube was found to not limit frequency response, with 50 % attenuation occurring at frequencies well above 10 Hz for both H2O and CO2. From field tests we found that heating the intake tube and particulate filter continuously with 4 W was effective, and reduced the occurrence of problematic relative humidity levels (RH &gt; 60 %) by 50 % in the infrared gas analyzer cell. No further improvement of H2O frequency response was found for heating in excess of 4 W. These laboratory and field tests were reconciled using resistor–capacitor theory, and NEON's final gas sampling system was developed on this basis. The design consists of the stainless steel intake tube, a pleated mesh particulate filter and a low-volume rain cap in combination with 4 W of heating and insulation. In comparison to the original design, this reduced the high-frequency attenuation for H2O by ≈ 3∕4, and the remaining cospectral correction did not exceed 3 %, even at high relative humidity (95 %). The standardized design can be used across a wide range of ecoclimates and site layouts, and maximizes practicability due to minimal flow resistance and maintenance needs. Furthermore, due to minimal high-frequency spectral loss, it supports the routine application of adaptive correction procedures, and enables largely automated data processing across sites.

Constructal entropy generation rate minimization for asymmetric vascular networks in a disc-shaped body

Based on constructal theory, the vascular networks with asymmetric pairing in a disc-shaped body are optimized by taking the minimizations of the dimensionless entropy generation rate and dimensionless entropy generation ratio as optimization objectives, respectively. The results show that there exist optimal tube lengths and angles which lead to the minimum dimensionless entropy generation rate and dimensionless entropy generation ratio of the vascular networks with two and three levels of asymmetric pairing, respectively. The optimal constructs of the vascular networks based on asymmetric and symmetric designs are different. For the specified heat flow per unit length on each tube surface, when the number of outlets N=24 and the dimensionless mass flow rate M1∗=10-2, the dimensionless entropy generation rate with two levels of pairing based on asymmetric design is decreased by 7.80% than that based on symmetric design; when the number of outlets N=24 and the dimensionless pumping power W̃2∗=1, the dimensionless entropy generation rate with three levels of pairing based on asymmetric design is decreased by 6.78% than that based on symmetric design. Moreover, the performance improvements of the vascular networks with asymmetric design can also be found for the specified heat flux on each tube surface. The optimization results of the vascular networks based on minimum flow resistance are special cases of those based on minimum entropy generation rate in this paper.

The natural emergence of asymmetric tree-shaped pathways for cooling of a non-uniformly heated domain

Here, we show that the peak temperature on a non-uniformly heated domain can be decreased by embedding a high-conductivity insert in it. The trunk of the high-conductivity insert is in contact with a heat sink. The heat is generated non-uniformly throughout the domain or concentrated in a square spot of length scale 0.1 L0, where L0 is the length scale of the non-uniformly heated domain. Peak and average temperatures are affected by the volume fraction of the high-conductivity material and by the shape of the high-conductivity pathways. This paper uncovers how varying the shape of the symmetric and asymmetric high-conductivity trees affects the overall thermal conductance of the heat generating domain. The tree-shaped high-conductivity inserts tend to grow toward where the heat generation is concentrated in order to minimize the peak temperature, i.e., in order to minimize the resistances to the heat flow. This behaviour of high-conductivity trees is alike with the root growth of the plants and trees. They also tend to grow towards sunlight, and their roots tend to grow towards water and nutrients. This paper uncovers the similarity between biological trees and high-conductivity trees, which is that trees should grow asymmetrically when the boundary conditions are non-uniform. We show here even though all the trees have the same objectives (minimum flow resistance), their shape should not be the same because of the variation in boundary conditions. To sum up, this paper shows that there is a high-conductivity tree design corresponding to minimum peak temperature with fixed constraints and conditions. This result is in accord with the constructal law which states that there should be an optimal design for a given set of conditions and constraints, and this design should be morphed in order to ensure minimum flow resistances as conditions and constraints change.