Discharge coefficients of CFVN predicted for high Reynolds numbers based on low-Re-calibration

In 2016, PTB introduced a function for the representation of the discharge coefficient c_D of critical flow venturi nozzles (CFVN) (versus the Reynolds number Re) which covers the operating range for both laminar and turbulent boundary layers. It contains the parameters a for the impact of the core flow, b_lam for the Re-dependency in case of laminar and b_turb in case of turbulent boundary layers. These parameters are not independent from each other but have the fixed relation of b_turb = 0.003654b_lam^1.736.Furthermore, the parameter a and the parameter b_lam are both direct functions of the local curvature radius R_c,throat of the nozzle at the throat. These relationships to R_c,throat are described by theoretical models. Consequently, the overall dependency of the discharge coefficient c_D on Reynolds number Re can be derived from only one parameter.The paper describes how these relationships can be used to extrapolate the calibration values of a CFVN determined with atmospheric air to high pressure gas flow applications covering a Reynolds range of about 1:60. It is shown in detail by examples and the reliability is demonstrated by comparison data for low and high pressure for 33 nozzles. Finally, aspects of preconditions for such extrapolation and uncertainties are discussed.     

Influence of flow conditions on the corrosion of AISI 304L stainless steel

Hydrodynamic and electrochemical noise measurements (ENMs), of AISI 304L stainless steel, were made in a pipe test section of 28 mm inside diameter for a range of flow regimes from laminar to turbulent. Mean flow velocities through the test section were controlled at 0.04, 0.07, 0.11, 0.36, 1.8 and 2.7 m s⁻¹, equivalent to Reynolds numbers of 1000, 2000, 3000, 10 000, 50 000 and 75 000, respectively. Standard hydrodynamic parameters were employed to characterise and evaluate the complex interrelationship between the mass transfer rate of oxygen and momentum transfer through turbulence to the metal/solution interface. For AISI 304L stainless steel, pitting typically occurs in the form of metastable pits which either repassivated before achieving stability or grow to become stable pits. Metastable pitting was evident under all flow regimes. The fluid flow, whether laminar or turbulent, had little overall effect on the nucleation rates of metastable pitting events. Conversely, stable pit growth was most evident during laminar flow immediately before the transition to turbulent flow and close to the critical velocity (∼1.5 m s⁻¹).     

A numerical study on the transient aspects of porous flows and the applicability of Darcy’s friction flow relation

In recent developments of shale reservoirs, it is important to estimate the permeabilities of hydraulic fractures accompanying the Non- Darcy effects and geometric changes. Accordingly, a new permeability estimation method that considers the varying geometric features under different flow regions is demanded. To this end, the present study introduces the generalized Darcy’s friction flow relation, especially for examining the friction factor-Reynolds number (f · Re) relationship of porous flow, which is originally used in general internal friction flow analyses. Moreover, simple hydraulic fractures comprising structured microbeads are simulated via computational fluid dynamics during fracture aperture variations under different flow conditions from laminar to turbulent. Frictional flow features, e.g., the preservation characteristics of f · Re values, are examined under different geometry and flow conditions, and the transient flow characteristics are investigated using streamline analyses. Consequently, it is verified that the f · Re values vary slightly in proportion to the geometric changes caused by aperture reduction in each medium. Even though the variations in the f · Re values are much smaller than the permeability variations, it seems to be contrary to our expectation. Otherwise, the almost linear-variation aspects of f · Re values were observed in both directional flow cases. The linear-variation aspect of f · Re values is expected to be useful in the permeability-variation estimations in porous media with changing basic geometric factors, such as hydraulic fracture closing. Moreover, it is demonstrated that regardless of aperture reduction in the same type of medium, each porous flow has a very similar power-law relation between f and Re values when the flow velocity changes from the laminar to the turbulent condition. This aspect can be effectively used for obtaining permeability estimations of the varied media, particularly under different flow conditions.     

混合流态下径向滑动轴承的静态特性研究

以无限宽径向滑动轴承为研究对象,考虑油膜中同时存在层流和紊流两种流态,基于层流、紊流润滑理论,联立求解雷诺方程、能量方程和温黏方程,分析油膜中流态变化,得到压力分布、承载力、摩擦力和最高温度等特性参数。结果表明:随着转速的升高和偏心率的增大,油膜内流体从完全层流转变为完全紊流要经过一个复杂的流态变化过程;与单一层流流态相比,混合流态下油膜承载力和摩擦力较大,温升较高,黏度变化较大,这表明流态的改变和热效应对轴承特性有着不可忽略的影响,在计算轴承特性时,应准确判断油膜中流态,并考虑热效应的影响。     

Investigation of a novel Couette flow with cylindrical baffles

The high-precision measure instrument for flow velocity is essential for industrial applications because the high-precision velocity can well reflect the physical characteristic of the flow. A restricted laminar Couette flow with cylindrical baffles, using a synthetic heat conduction liquid, was designed to obtain a steady vortex flow and wider work scope, according to Couette flow and Suspension flow characteristics. The heat transfer mechanism was investigated with a laminar flow model by the Fourier law. The research indicates that the heat transfer enhancement is related to the Temperature Boundary Layer (TBL). The TBL is affected by the Velocity Boundary Layer (VBL). The TBL thickness and Nusselt number (Nu) have a dependent relationship. The Reynolds number (Re) and the gap between the baffle and plate wall (Δh/h) can further affect Nu. The vortex flow generated by Couette flow can significantly enhance the heat transfer performance by a double spiral structure, which can rapidly mix heat fluxes and make the temperature converge to uniform. There is a sensitive and stable relationship between flow velocity and heat transfer. Notably, it is linear when Δh/h or Re is small, which can be used to design a high-precision thermal flow velocity meter.     

Laminar and turbulent channel flow simulation using residual based variational multi-scale method

We present a residual-based isogeometric variational multiscale method to solve laminar and turbulent channel flow. Residual-based variational multiscale method is a new finite element formulation for solving turbulent flows using a large-eddy simulation type modeling. Isogeometric analysis, a new finite element method using CAD blending functions as its basis functions, is employed for higher order approximation of the solution. First, laminar flow with Re _τ 0.55 = through flat channel is considered and linear, quadratic and cubic basis functions, which are C ⁰, C ¹, and C ²-continuous across element boundaries, respectively are employed and their accuracy is presented by the comparison with analytical result. Next, same methodology is applied to the turbulent channel flow with Re_r = 180. Current results are validated by the comparison of turbulence statistics using available DNS data.     

Discharge coefficient equation for critical-flow toroidal-throat venturi nozzles covering the boundary-layer transition regime

A single, simple correlating equation between the discharge coefficient of critical-flow Venturi nozzles (CFVNs) having an ISO 9300 toroidal throat and their Reynolds number is proposed in the Reynolds number range from 2.1×10⁴ to 3.2×10⁷. The equation covers the whole Reynolds number range from laminar to turbulent boundary-layer regimes and can thus be used instead of the two correlating equations defined in ISO 9300 : 2005. The deviation of the discharge coefficients of well-made CFVNs is expected to be less than ±0.2% throughout the Reynolds number range. Tolerances for the diffuser length, inlet curvature and inlet diameter are also proposed. It is shown that the widely-accepted theories that estimate the core flow distribution result in significant error when the inlet curvature is small and that removing the third term in Hall׳s equation results in very good agreement with the experimental data regardless of the magnitude of the inlet curvature. The use of CFVNs with the inlet curvature of 1.0D is discussed in order to reduce the uncertainty owing to undefined boundary-layer transition Reynolds number. A possibility is shown that such a CFVN may not have an apparent boundary-layer transition in the investigated Reynolds number range from 1.5×10⁴ to 2.0×10⁶.     

Stability of a rigid rotor in turbulent hybrid porous journal bearings

Stability characteristics of hybrid porous journal bearings with a turbulent fluid film have been investigated theoretically following Constantinescu's turbulent lubrication theory. The stability curves have been drawn for different Re, eccentricity ratios, slenderness ratios and bearing speed parameters. In the absence of any experimental data, laminar flow results obtained by this analysis have been compared and found to be in excellent agreement with the previous results. It is observed that turbulence deteriorates the stability of the rotor and for better performance the value of the bearing feeding parameter, β, should be kept small.     

A quality control method by ultrasonic vibration energy and diagnosis system at trimming process

To investigate a relation between vortex clusters and large-scale structures in the outer layer of wall turbulence, direct numerical simulations of turbulent channel flows have been conducted up toRe _τ = 1270. The vortex clusters in the outer layer consist coherent fine scale eddies (CFSEs) of which diameter and maximum azimuthal velocity are scaled by the Kolmogorov length and the Kolmogorov velocity. The CFSE clusters are inside the large-scale structure, which contributes to the streamwise velocity deficit The scale of those clusters tends to be enlarged with the increase of a distance from the wall. The CFSE clusters are composed of the relatively strong CFSEs, which play an important role in the production of the Reynolds shear stress and the dissipation rate of the turbulent kinetic energy. The most expected maximum azimuthal velocity of the CFSEs in these low-momentum regions of the outer layer is 30–70% fester compared with those of the CFSEs in unconditioned regions (i.e. all regions of the outer layer), while the most expected diameter of the CFSEs is not changed greatly.     

Discharge equation for the gabion weir under through flow condition

A gabion weir is considered to be more environmentally friendly as compared to an impermeable weir, as its permeability allows substances and aquatic life to pass through it. Also, gabion weirs offer an alternative design with low afflux that could be adopted for flash flood mitigation. In the present study, a series of laboratory experiments were performed on flow through gabion weir of various sizes and for varying boulder sizes and discharges. Collected data were used to check the accuracy of the existing relationships between hydraulic gradient and flow velocity for highly porous material like gabion filled with boulders. It is found that Ergun's equation predicts the hydraulic gradient more accurately than the other available equation. Ergun's equation is extended to calculate the flow through the gabion weir. The derived discharge equation for flow through gabion weir was validated with the collected data. A qualitative performance of the present model indicates that it has the highest coefficient of correlation (R = 0.956) and the lowest MAPE (16.902), RMSE (0.002), AAD (15.52). It was found that the derived equation computes discharge within a maximum of ±10% error for almost all data sets, which can be considered satisfactory from practical consideration. Sensitivity analysis reveals that the discharge through the gabion weir is more sensitive to the boulders diameter and upstream depth as compared to the downstream depth of the gabion weir.     

板坯连铸结晶器流场的格子法模拟

给出一种与现有传统数值方法不同的计算流体动力学介观模型。在该模型中,建立描述流体微团运动及碰撞规律的格子Boltzmann方程以及平衡分布函数,并依此求解出流体微团的分布函数,而流场的速度、压力等物理量可直接根据流体微团的分布函数统计求和而得。在此基础上计算了板坯连铸结晶器中心面内的二维流动,模拟出流场在高雷诺数条件下流动模态随时间的变化过程,得到与试验结果一致的流场结构,较真实地反映高雷诺数条件下结晶器内湍流的有漩性、非对称性及非定常性。结果表明随着流场雷诺数的提高,流动中物理量脉动成分的显著增强,打乱了原有对称性的大涡结构,使得流动呈现非对称性及非定常性。     

Numerical simulation of turbulent flow of hydraulic oil through 90° circular-sectional bend

Oil flow through pipe bends is found in many engineering applications. However, up to now, the studies of oil flow field in the pipe bend appear to be relatively sparse, although the oil flow field and the associated losses of pipe bend are very important in practice. In this paper, the relationships between the turbulent flow of hydraulic oil in a bend and the Reynolds number Re and the curvature ratio ? are studied by using computational fluid dynamics (CFD). A particular emphasis is put on hydraulic oil, which differs from air or water, flowing through 90° circular-sectional bend, with the purpose of determining the turbulent flow characteristics as well as losses. Three turbulence models, namely, RNG k-? model, realizable k-? model, and Reynolds stress model (RSM), are used respectively. The simulation results in the form of contour and vector plots for all the three turbulence models for pipe bends having curvature ratio of ??0.5, and the detailed pressure fields and total pressure losses for different Re and ? for RSM are presented. The RSM can predict the stronger secondary flow in the bend better than other models. As Re increases, the pressure gradient changes rapidly, and the pressure magnitude increases at inner and outer wall of the bend. When ? decreases, two transition points or transition zones of pressure gradient arise at inner wall, meanwhile, the transition point moves towards the inlet at outer wall of the bend. Owing to secondary flow, the total pressure loss factor k increases as the bend tightens, on the contrary, as Re increases, factor k decreases due to higher velocity heads, and the rapid change of pressure gradient on the surface of the bend leads to increasing of friction and separation effects, and magnified swirl intensity of secondary flow. A new mathematical model is proposed for predicting pressure loss in terms of Re and ? in order to provide support to the one-dimensional simulation software. The proposed research provides reference for the analysis of oil flow with higher Re in the large bends.     

Numerical investigation of fluid flow and heat transfer characteristics in a helically-finned tube

In order to investigate the characteristics of flow and heat transfer rate in a Helically-finned tub (HFT), we used continuity, momentum and energy equations under a steady, three-dimensional and incompressible fluid flow assumptions. For the performance metrics, we considered the Darcy friction factor, Colburn j-factor, volume goodness factor and area goodness factor of the HFT. We could also evaluate the effect of geometry parameters on the results of local pressure coefficient, fluid vorticity and Nusselt number of the HFT. We carried out the CFD calculation for a range of laminar flow (Re = 100) and turbulent flow (Re = 2000 and 10000). In a laminar and turbulent flow regime, the friction factor increases with increasing the each geometric parameter. While the Colburn j-factor decreases as increasing these geometric parameters. Consequently, the thermal performance of HFT is poorer than that of single straight circular tube type because of having a small volume and area goodness factor as increasing the Reynolds numbers.     

Flow velocity estimation using a fish-shaped lateral line probe with product-moment correlation features and a neural network

Environmental studies on fish require measurements of highly turbulent flows in both the laboratory and in the field. A fish-shaped bioinspired flow measuring device is applied in conjunction with data processing workflow which leverages the interactions between the body and the surrounding flow field for velocity estimation in turbulent flows. Our objective is to develop a robust velocity estimation methodology relevant for studies of fish behavior using a bioinspired fish-shaped artificial lateral line probe (LLP). We show that the device is capable of covering the range of flow velocities from 0 to 1.5 m/s. Three different sets of experiments performed in a closed flow tunnel, a model vertical slot fishway and laboratory open channel flume were collected and combined to provide time-averaged flow velocity and LLP measurements under fully turbulent flow conditions. Based on the experimental results, a signal processing workflow using Pearson product-moment correlation coefficient (PCC) features in conjunction with an artificial neural network (ANN) is presented. Using PCC features provides a simple data fusion methodology exploiting the use of the LLP's as a simultaneous collocated sensing array. In this work we show that (1) the PCC-ANN workflow provides the first LLP velocity estimator without repeated calibration across the full span of 0–1.5 m/s, (2) using all pressure sensors results in the best performance with R²=0.917, but requires a PCC feature matrix of 55 dimensions and (3) a stepwise reduction of the PCC feature matrix allows for the use of as few as 11 dimensions, and results in R²=0.911, indicating that a modest reduction in LLP velocity estimation performance can be gained by a large reduction in dimensionality. A surprising finding was that after stepwise reduction, the best performing sensor pair combinations were not the expected pitot-like anteroposterior couples spanning from nose to body. Instead, it was found that optimal velocity estimation using the LLP exploited a network of sensor pairs. It is shown that the LLP can be implemented similar to an ADV for highly turbulent flows over the range of 0–1.5 m/s, and in addition provides body-centric pressure distributions which may aid in the interpretation of fish hydrodynamic preferences in future environmental studies.     

Convective heat transfer in ventilated space with various partitions

The laminar convective heat transfer in ventilated space with various horizontal partitions was studied numerically and experimentally. For the numerical study, the governing equations were solved by using a finite volume method for various numbers Re, Gr, Pr and partition numbers. The experimental study was conducted by using a holographic interferometer. The isotherms and velocity vectors have been presented for various parameters. As the number and length of partition ncreased, convective heat transfer decreased. Based on the numerical data, correlation equations were obtained for the mean Nusselt number in term of Gr/Re². In the region ofGr/Re²<-1, the mean Nusselt number was small, but in the region ofGr/Re²>1, the mean Nusselt number was constant.     

Pressure field estimation from ultrasound Doppler velocity profiler for vortex-shedding flows

A novel algorithm of pressure field estimation based on ultrasound velocity profiler (UVP) is developed. The method consists of UVP measurement of velocity distribution in fluid flows and numerical analysis of the measured data using fluid dynamics equations. We introduce equation of continuity, incompressible Navier-Stokes equation and proper orthogonal decomposition (POD) into the basic algorithm, so that pressure field of space-time two-dimensional unsteady fluid flow is fully reconstructed. Since UVP is based on ultrasound Doppler principle, the local instantaneous pressure distribution is obtained non-intrusively. The performance of an algorithm is evaluated for vortex shedding flow behind a circular cylinder at Re = 1000. Considering the specification of UVP, the optimal method of experimental data conversion to pressure information is proposed. We have found that the one-dimensional velocity measurement by UVP upon Taylor's frozen hypothesis is suitable for evaluation of pressure field in wake of the cylinder. The present algorithm is also demonstrated for opaque fluid flows by considering vortex flow in milk.     

Approximate velocity scale for primary and secondary dual-inlet side-dump flows

Effects of the bulk inlet velocity on the characteristics of dual-inlet side-dump flows are numerically investigated. Non-reacting subsonic turbulent flow is solved by a preconditioned Reynolds-averaged Navier-Stokes equation system with low-Reynolds number k − ɛ turbulence model. The numerical method is properly validated with measured velocity distributions in the head dome and the combustor. With substantial increase in the bulk inlet velocity, general profiles of essential primary and secondary flows normalized by the bulk inlet velocity are quantitatively invariant to the changes in the bulk inlet velocity. This paper was recommended for publication in revised form by Associate Editor Do Hyung Lee Seung-chai Jung received his B.S. degree in Mechanical Engineering from Yonsei University, Korea, in 2001. He then received his M.S. degree in Mechanical Engineering from Yonsei University, Korea, in 2005. Mr. Jung is currently a Ph. D. candidate at Yonsei University, where he is majoring in Mechanical Engineering. Mr. Jung’s research interests include propulsion system and particle-surface collision dynamics. Byung-Hoon Park received his B.S. degree in Mechanical Design and Production Engineering from Yonsei University in 2003. He is currently a Ph.D. candidate in Yonsei University in Seoul, Korea. His research interests include performance design of propulsion systems and nu-merical analysis of instability in multiphase turbulent reacting flow-fields. Hyun Ko received his B.S. degree in Aerospace Engineering from Chonbuk National University, Korea, in 1996. He then received his M.S. degree in Mechanical Design from Chonbuk National University, Korea, in 1998. In 2005, he obtained his Ph.D. degree from Yonsei University, where he majored in mechanical engineering. Dr. Ko is currently a Principal Research Engineer of the MicroFriend Co., Ltd. in Seoul, Korea. His research interests include propulsion related systems and computational fluid dynamics. Woong-sup Yoon received his B.S. degree in Mechanical Engineering from Yonsei University, Korea, in 1985. He then received his M.S. degree from University of Missouri-Rolla in 1989. In 1992, he obtained his Ph.D. degree from the University of Alabama in Huntsville, where he majored in mechanical and aerospace engineering. Dr. Yoon is currently a professor at the School of Mechanical Engineering at Yonsei University in Seoul, Korea. His research interests include propulsion system and particle-related environmental/ thermal engineering.     

Study on the parallel pressure differential type gas laminar flow sensing technique

Parallel pressure differential (PPD) type laminar flow sensing technique was invented several years ago to reduce nonlinear effect in a traditional laminar flow element (LFE). In this paper, the internal flow of each branch in a PPD LFE is numerically simulated for gas flow. The results show that the relative deviation of the pressure drops of the two branches in a PPD LFE is within ±0.05% as inlet mass flow being the same, indicating that the flow resistance characteristics of the two branches are consistent, which means that the hypothesis of a same flow rate for the two branches in a real PPD LFE is tenable. There is little difference, ±0.01%, in the local pressure losses of the two upstream capillaries outlet flows, which can be ignored in a real measurement, further verifying that the theoretical analysis of the PPD principle is reliable. Capillary length effect in a PPD LFE is also examined. The bigger capillary length, the higher measurement precision can be achieved for a certain length range. For instance, it is suggested that the length of the short components should not be shorter than the laminar flow dimensionless entrance length defined by X_e (L_e/d/Re, where L_e is the entrance length) = 0.035, for flow measurement uncertainty within ±1.0%. The simulation and experiment results of gas flow show that the suitable value of K_exp is 1, and in the flow range of (0.0256–5.2985) m³/h measurement error of a PPD LFE is within ±0.8% only with expansion correction, indicating that the PPD laminar flow measurement technique is suitable for the gas flow.     

Utilization of I–Q signals of ultrasound Doppler velocimeter to obtain 1-D turbulence quantities in pipe flow

A new method based on using inphase–quadrature (I–Q) ultrasound (US) signals was developed in order to overcome time resolution limitations encountered in turbulent flow measurements by ultrasound Doppler velocimetry (UDV). First, mathematical relations to be used in obtaining probability density function (PDF) and auto correlation function (ACF) of randomly fluctuating velocity (u) in the probe direction were derived in the form of the experimental I–Q signals. The results were evaluated with respect to those obtained by UDV or other conventional techniques whenever possible. In terms of general trend, velocity PDFs obtained from analytical relation along with the I–Q signals and from UDV compare well with each other for Reynolds numbers (N_Re) of 16730 and 26300 at the pipe center. Smaller standard deviation of velocity PDF from spectrum of I–Q US signals than that of UDV measurements was the only major difference that could be attributed to the enhanced time resolution of the former technique. Effect of increased time resolution was also observed in the measurement of velocity auto correlation coefficients (ACC). Time correlations of the velocity fluctuations could be captured by using I–Q signals as opposed to UDV that resulted in correlations going to zero in one or two time steps.ACC from I–Q signals was used to get turbulence spectrum at the pipe center. In addition Reynolds number and radial position dependency of integral and Taylor microlength scales, Kolmogorov length scale, rate of energy dissipation and eddy diffusion coefficient were also established.     

Three-dimensional MHD simulations of the electromagnetic flowmeter for laminar and turbulent flows

The interaction between an electrically conducting fluid and an external magnetic field in an ideal cylindrical electromagnetic flowmeter is numerically investigated for both laminar and turbulent flows. Induced electric potential in the fluid, and the difference in potential at the measuring electrodes are directly obtained by including MHD effects in the CFD simulations. Fully developed laminar and turbulent flows are simulated. The computed electric potential difference on the electrodes agrees with analytical values for small Hartmann number cases, where the induced Lorentz force is small. Turbulent flow produces a more uniform electric potential distribution in the flow meter cross-section than laminar flow. These integrated MHD/CFD simulations couple the MHD effect with flow dynamics without deriving a weighting function with an assumed velocity profile, which will be necessary for electromagnetic flow meters when the Hartmann number is not small.