Flow characteristics of pyramidal shaped small sonic nozzles

Four types of pyramidal sonic nozzles made of silicon crystal were studied experimentally. The throat sizes varied from 38 to 140 μm for type A and D nozzles and from 75 to 188 μm for type B and C nozzles. For each of the nozzle types, the results show that the discharge coefficient is proportional to the throat size, and the critical back pressure ratio for choking is insensitive to Reynolds’ number. In parallel, the flow field of a type B nozzle was investigated by numerical simulation. The effect of heat flux coming from the nozzle body was examined and the flow patterns obtained from Spalart-Allmaras and standard k−ω turbulence models were compared. The simulation results indicate the heat flux does not noticeably change the velocity field and discharge coefficient. Also, the flow downstream of the nozzle throat develops into an under-expanded supersonic jet in which expansion and oblique shock waves appear alternately.     

Accurate theoretical calculation of the discharge coefficient for sonic nozzle using geometric parameter measurements in Re=(7.33×104–1.26×106)

In order to improve the measurement accuracy and efficiency of sonic nozzles (SNs) in laminar boundary layer, a correlation model for theoretical discharge coefficient of sonic nozzle taking into account the viscous effects on the boundary layer along the nozzle wall (C_d,th,1), and the multi-dimensional characteristic effect of the core region (C_d,th,2) was proposed. The theoretical discharge coefficient is related to the measurement of geometric parameters, such as the throat diameter, d, and curvature radius, R_c. The detailed geometric measurements of sonic nozzle by 3D coordinate measuring machine were conducted. Then, the evaluation procedures of parameters d and R_c including roundness and waviness profile for designed SNs of d = 7.453 mm and d = 1.919 mm were presented in detail. The effect of waviness profile on the discharge coefficient and boundary layer transient was investigated. It indicated that waviness effect is quite complex. Finally, the validation of the theoretical calculation model of discharge coefficient was verified by the experimental data of National Institute of Metrology (NIM) and National Metrology Institute of Japan (NMIJ) based on the accurate measurements of the geometric parameters. The result showed that the consistency between the C_d,exp and the C_d,th is better than 0.11% when the effect of the heat transfer was considered within the range of Re= (7.33 × 10⁴–1.26 × 10⁶).     

Static pressure measurement error for wall taps with high Reynolds number turbulent pipe flow

An experimental study on a static pressure measurement errors in wall taps was conducted using a high Reynolds number actual flow facility (Hi-Reff). The bulk Reynolds number Re_D examined was up to 1.3 × 10⁷ and tap Reynolds number Re_t was up to 8.5 × 10⁴. The behavior of the static pressure measurement error at high Reynolds numbers was clarified experimentally. The static pressure measurement error normalized by wall shear stress increases with Reynolds number and reaches an asymptotic value. Its maximum value is 7.1 at Re_t = 8470. The asymptotic value increases with the size of the tap diameter up to 6 mm and then becomes constant for tap diameters exceeding 6 mm. The universal curve reported in previous studies is observed for only a limited range of tap Reynolds numbers of below 700 and of tap diameters below 4 mm.     

Characteristic flow patterns and aerodynamic performance on a forward-swept wing

This investigation elucidates the effects of Reynolds number (Re) and angle of attack (??) on the boundary-layer flow patterns, aerodynamic performance, flow behaviors and vortex shedding. This investigation applies a finite NACA 0012 forward-swept wing with the forward-sweep angle (??) of 15°. The Reynolds numbers were tested in the range of 4.6 × 10⁴ < Re < 10⁵. The wing chord length is 6 cm and the semi-wing span is 30 cm, such that the full-span wing aspect ratio is 10. The surface oil-flow scheme was utilized to visualize the boundary-layer flow structures. The hot-wire anemometer was applied to measure the vortex-shedding frequency behind the forwardswept wing. Furthermore, a force-moment sensor was applied to measure the aerodynamic loadings. The surface oil-flow patterns are classified into six characteristic flow modes ?? separation, separation bubble, secondary separation, leading-edge bubble, bubble extension and bluff-body wake modes. Additionally, the output of force-moment sensor and the visualized boundary-layer flow configurations indicate that the aerodynamic performance is closely related to the boundary-layer flow behaviors. Furthermore, the boundary-layer flow stalled in the leading-edge bubble mode. Moreover, the vortex-shedding frequency behind the forward-swept wing shows that the vortexshedding frequency at low ?? exceeds that at high ??.     

Interference effects of three sonic nozzles of different throat diameters in the same meter tube

For calibration of a large capacity gas flow meter, a sonic nozzle bank may be used as a reference system. International standards (ISO9300:1990) allow installation of a single nozzle in a meter tube as a flow transfer standard. For multiple nozzles in a single tube, the effect of interference between sonic nozzles and the chamber wall must be measured to predict the discharge coefficient of a nozzle array from those of single nozzles. The interference effect between neighboring nozzles can be additional error sources in mass flow measurement. Sonic nozzles with three different throat diameters (d=4.3, 8.1, and 13.4 mm) were tested in a single meter tube in three geometrical arrangements. The mass flow rate was measured against a primary gas flow standard system. Three installation plates for sonic nozzles were made to vary the distance between nozzles and distance from the chamber wall. Discharge coefficients of the three individual nozzles were in agreement with the ISO recommended equation within ±0.2%. Discharge coefficients of the nozzle bank calculated from those of the individual sonic nozzle were the same as the direct measurements within ±0.098% at the 95% confidence level for all cases. For these experiments, the results were not influenced by the proximity of the tube wall or the interaction of the nozzles.     

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 wall roughness on discharge coefficient of sonic nozzles

To research the influence of roughness on discharge coefficient of axisymmetric sonic nozzles systematically, a turbulence model was established, and standard k–ε model was used in the turbulent core region while Wall Functions was carried out in the boundary layer region. A series of numerical simulations were conducted to research discharge coefficients of 6 critical flow Venturi nozzles with throat diameter ranging from 0.5 to 100 mm when Reynolds numbers ranges from 10⁴ to 10⁹ and relative roughness from 10⁻² to 10⁻⁶. The validity of the simulation model was confirmed by both the experimental data of Stewart and ISO 9300 empirical equation. According to the simulation results and theoretical analysis, the relations between discharge coefficient and relative roughness were obtained. It is recommended that the dimensionless parameter relative roughness should be used in ISO 9300 rather than absolute roughness. Additionally, when the machining of nozzle cannot satisfy the ISO 9300 requirement or the Reynolds numbers exceed the upper limits of the ISO 9300 equation, the effect of roughness should be considered, and the relative roughness of sonic nozzle should be provided clearly in the further experiment of discharge coefficient.     

Flow visualization and transient behavior analysis of luminescent mini-tufts after a backward-facing step

Luminescent mini-tufts method has been used for surface flow visualization for a long time. One major challenging point of this method is quantitative analysis of transient flows and the dynamic structures. This study is focused on the application of luminescent mini-tufts method in transient flows. A backward-facing step (BFS) is used in this analysis, which is one classic model that consists both flow separation and re-attachment processes. In this study, the instantaneous mini-tufts recognition, image averaging and tuft inclination angle/tuft angle estimation processes are introduced for the analysis of luminescent mini-tufts for the first time on backward-facing step flow (Re_m = 2.0 × 10⁵–7.9 × 10⁵ and Re_h = 1.3 × 10⁴–5.3 × 10⁴). Detailed transient features and characterization process for the backward-facing step model are explained in this study. The combination of optical-oil flow and hot-wire anemometry methods with luminescent mini-tufts are also shown useful to give comprehensive flow field information, including the surface flow behaviors, boundary layer, re-attachment position identification, etc. In addition, the decomposition of the luminescent mini-tufts visualization data is also conducted to give the power spectral density (PSD) and characteristic frequencies for the mini-tufts behaviors under transient fluctuating flow conditions.     

Behaviors of discharge coefficients of small diameter critical nozzles

The discharge coefficients of 59 small diameter toroidal throat Venturi critical nozzles were measured by the static gravimetric method. The throat diameter is from 0.014 mm to 2.35 mm and the Reynolds number is 4 × 10² to 2 × 10⁵. These nozzles were manufactured by the normally processing method base on the same design drawing, but their discharge coefficients were scattered widely. The purpose of this paper is to explain the behavior of discharge coefficient scattered. In the correction procedure used here, while comparing the discharge coefficient obtained experimentally and the reference theoretical model, the throat diameter is corrected and the optimal radius of curvature of nozzle inlet is determined so that both discharge coefficients match. Resultantly, most of the behaviors of the discharge coefficient of 59 critical nozzles could be explained well.     

Influence of divergent section on flow fields and discharge coefficient of ISO 9300 toroidal-throat sonic nozzle

The effect of divergent section of ISO 9300 toroidal-throat nozzle on discharge coefficient was analyzed based on the inviscid transonic flow model and laminar boundary layer theory. A series of numerical simulations were conducted to verify the results of theory, and investigate the effect of divergent section length L and diffuser angle θ operated at different Reynolds numbers. Combined with the numerical results in this study and the experimental data reported by Nakao, it showed the discharge coefficient increases with the rise of diffuser angle θ or the drop of divergent section length L. A lot of new results about the effect of divergent section were obtained. It indicated that the effect of divergent section on discharge coefficient of ISO 9300 toroidal-throat nozzle should be considered when Re<1.1×10⁴. At last, a concept of effective critical flow was proposed to discuss the effect of divergent section on discharge coefficient.     

Experimental and numerical study for the cross-flow around four cylinders in an in-line square configuration

The cross-flow around four cylinders in an in-line square configuration with the spacing ratio (L/D) 1.5, 2.5, 3.5 and 5.0 have been investigated experimentally using Laser Doppler Anemometer (LDA) and Digital Particle Image Velocimetry (DPIV). The experiments were carried out in a closed-loop wind tunnel with Reynolds number 1.128× 10⁴ to 1.982× 10⁴. Mean velocity distributions are obtained by LDA. The full field instantaneous and averaged velocity and vorticity components are measured by DPIV The present experimental study indicated that several distinct flow patterns exist. Distinct vortex shedding of the upstream cylinders was suppressed forL/D < 3.5 atRe=1.128× 10⁴. The flow patterns are affected by the spacing ratio andRe. In order to capture the details of the 3-D vortices structures and obtain all the instantaneous physical information, 3-D numerical simulations of the cross-flow around the four cylinders in an in-line square configuration with the spacing ratio 1.5 and 3.5, andRe=1.50× 10⁴ are carried out using large eddy simulation (LES). The numerical results are in good agreement with the experimental results. These results provided full field instantaneous information of the flow structures, velocity field and vorticity field of cross-flow around the four cylinders in an in-line square configuration.     

The evaluation of critical pressure ratios of sonic nozzles at low Reynolds numbers

A sonic nozzle is presently used as a reference flow-meter in the area of gas flow-rate measurement. The critical pressure ratio of the sonic nozzle is an important factor in maintaining its operating condition. ISO 9300 suggested that the critical ratio of a sonic nozzle should be a function of area ratio. In this study, 13 nozzles designed according to ISO 9300, with diffuser half angles of 2°–8° and throat diameters of 0.28 to 4.48 mm were tested. The testing result for the angles of 2°–6° are similar to that of ISO 9300. But the critical ratio for the nozzle of 8° decreases by 5.5% in comparison with ISO 9300. However, ISO 9300 does not predict the critical pressure ratio at Reynolds numbers lower than 10⁵. To express the critical pressure ratio of sonic nozzles at low Reynolds numbers, it is found that the critical pressure ratio should be related as a function of Reynolds number rather than area ratio, as used by ISO 9300. A correlated relation of critical pressure ratios and low Reynolds numbers for small sonic nozzles is suggested in this investigation, with an uncertainty of ±3.2% at 95% confidence level.     

Experimental study on improving the critical back-pressure ratio using a step in a critical-flow Venturi nozzle

Critical-flow Venturi nozzles (CFVNs) are used widely as transfer standards and can measure flow rates accurately. However, previous research has reported that in some CFVNs, the pressure-recovery effect of the diffuser is poor, and it is called the premature unchoking phenomenon. In the present study, experiments were conducted to investigate the critical back-pressure ratio (CBPR) of a CFVN. Additionally, to solve the problem of premature unchoking phenomenon, we focused on the step in the diffuser and verified its effect. The diffuser step can maintain a high CBPR at values of the Reynolds number (Re) of around 22,000 and 5500. For Re = 5500, although the CBPR of a typical CFVN is 0.46, providing the step increases it to 0.75. Notably, we are able to increase the CBPR at low Re, at which previous studies could not suppress premature unchoking phenomenon. A diffuser step is believed to improve the CBPR because the shock location is fixed at the step, and the region of subsonic flow, which is important for pressure recovery, is expanded.     

Mathematical model applied to the experimental calibration results of a capillary standard leak

Gas leaks supplied through metal capillaries are nowadays largely used in industry to calibrate “in situ” leak detectors (necessary in tightness tests, versus both vacuum and atmospheric pressure) or in whatever applications in which well-known (and very low) gas flows are necessary. If the capillaries are calibrated with a primary device or a reference one, the traceability of flow measurements to the national primary standards is guaranteed. At IMGC-CNR, standard leaks are calibrated by means of two primary flowmeters, operating respectively with reference to vacuum and to atmospheric pressure. In this paper, with the aim of developing a general calculus model for a unique calibration curve in both fields of use of a capillary leak, results relative to the calibration of a particular type of an all metal, crimped-capillary leak are presented and discussed. This capillary has been calibrated for helium, sulfur hexafluoride and nitrogen with reference both to vacuum and to atmospheric pressure and for molar flows ranging from about 1×10⁻¹¹ mol/s to 5×10⁻⁷ mol/s.     

Uncertainty analysis of the high pressure closed loop gas flow standard facility in NIM

High pressure air flow standard facilities, including the pVTt facility, sonic nozzle facility and closed loop facility were built in NIM at the end of 2014. The high pressure closed loop gas flow facility was the first closed loop facility in China. The system has 4 sets of 100 mm diameter turbine meters for the reference meters with a flow range of (40–1300) m³/h and a pressure range of (190–2500) kPa. To avoid uncertainties introduced during installation, the reference meters were designed to be calibrated in situ using the sonic nozzle facility. The uncertainty in the pressure measurement was reduced by installing an absolute pressure transducer in the manifold upstream of the reference meters, with differential pressure transducers used to measure the pressure drops across the reference flow meter and the test flow meter. The relative expanded uncertainty for the test meter can reach 0.20% (k = 2) as verified by comparison the sonic nozzle facility and the closed loop facility measurements.     

Total pressure fluctuations and two-phase flow turbulence in self-aerated stepped chute flows

Current knowledge in high-velocity self-aerated flows continues to rely upon physical modelling. Herein a miniature total pressure probe was successfully used in both clear-water and air-water flow regions of high-velocity open channel flows on a steep stepped channel. The measurements were conducted in a large size facility (θ=45°, h=0.1 m, W=0.985 m) and they were complemented by detailed clear-water and air-water flow measurements using a Prandtl-Pitot tube and dual-tip phase-detection probe respectively in both developing and fully-developed flow regions for Reynolds numbers within 3.3×10⁵ to 8.7×10⁵. Upstream of the inception point of free-surface aeration, the clear-water developing flow was characterised by a developing turbulent boundary layer and an ideal-flow region above. The boundary layer flow presented large total pressure fluctuations and turbulence intensities, with distributions of turbulence intensity close to intermediate roughness flow data sets: i.e., intermediate between d-type and k-type. The total pressure measurements were validated in the highly-aerated turbulent shear region, since the total pressure predictions based upon simultaneously-measured void fraction and velocity data agreed well with experimental results recorded by the total pressure probe. The results demonstrated the suitability of miniature total pressure probe in both monophase and two-phase flows. Both interfacial and water phase turbulence intensities were recorded. Present findings indicated that the turbulence intensity in the water phase was smaller than the interfacial turbulence intensity.     

Pressure measurement technique and installation effects on the performance of wafer cone design

The present study explores novel pressure averaging technique for wafer cone flowmeter design and its robustness in the presence of double 90° bend (out-of-plane) and gate valve as a source of upstream flow disturbance. The wafer cone flowmeter is tested in a circular pipe (inside diameter of 101 mm) with water as the working medium for the flow Reynolds number ranging from 1.19×10⁵ to 5.82×10⁵. Influence of the half cone angle (α) on the coefficient of discharge (C_d) of wafer cone flowmeter is studied with this new pressure averaging technique. Half cone angles considered in this study are 30° and 45° with a constant constriction ratio (β) of 0.75. The upstream static pressure tap is located at 1D upstream of the wafer cone. The downstream pressure averaging technique comprises eight circumferential holes of diameter 2 mm on the maximum diameter step of the wafer cone. The pressure taps are communicated through the support strut which serves as a downstream static pressure tap. The disturbance causing elements are individually placed at 1.5D, 5.5D, 9.5D and 13.5D upstream to the wafer cone flowmeter. The wafer cone flowmeter is also tested with gate valve opening of 25%, 50% and 75% for all the arrangements considered. The 30° cone is found to be better than 45° cone for the range of Reynolds number covered in the present study. The results show that the 30° wafer cone flowmeter with novel downstream pressure averaging technique is insensitive to the swirl flow created by a double 90° bend (out-of-plane) and requires an upstream length of 9.5D with a gate valve as a source of flow disturbance.     

Experimental investigation on dilute gas-solid multiphase jet in crossflow

In the current study, an experimental setup was built to investigate the gas flow and particle distribution in a normal jet crossflow to a main flow in a confined test section. The experiments were conducted under two test conditions: with Re_c/Re_jet of 7.9×10⁴/3.1×10⁴ and 7.0×10⁴/1.8×10⁴. Four classes of particles were used in both tests. The planar gas flow field and particle distribution on the symmetric cross-section were measured by a DPIV system. Mean fluid velocity results and transient flow visualization images were used to analyze the jet influence on the gas flow field. The analysis of the time-average particle concentration reveal that the jet control method may set a gas barrier in the flow field, which the tiny particles are able travel around, large particles are able travel through, and only 10-micronscale particles could be successfully blocked. The results show that the wall jet control method can be applied in inertia particle separator.     

Tribological behavior of RH ceramics made from rice husk sliding against stainless steel,alumina, silicon carbide,and silicon nitride

The tribological behavior of rice husk (RH) ceramics, a hard, porous carbon material made from rice husk, sliding against stainless steel, alumina, silicon carbide, and silicon nitride (Si₃N₄) under dry conditions was investigated. High hardness of RH ceramics was obtained from the polymorphic crystallinity of silica. The friction coefficients for RH ceramics disks sliding against Si₃N₄ balls were extremely low (<0.1), irrespective of contact pressure or sliding velocity. Transfer films from RH ceramics formed on Si₃N₄ balls. Wear-mode maps indicated that the wear modes were powder formation under all tested conditions, resulting in low specific wear rates (<5×10⁻⁹ mm²/N).     

CFD analysis of the performance of elbow-meter with high concentration coal ash slurries

Elbow meter is a simple flow measuring device and its characteristics for the flow of single-phase fluids are reasonably well understood and the functional dependence of elbow meter coefficient (C_k) on parameters like Reynolds Number, radius ratio, pipe roughness etc. Is well documented in literature. Elbow meters are also being used for solid liquid flow in many industries. The present study aims to establish the characteristics of an elbow meter for high concentration coal ash slurry pipelines using validated CFD. High concentration coal ash slurries are known to behave as homogeneous fluids exhibiting behavior as Bingham plastic fluids. The validated CFD methodology has been used to predict the values of C_k for the flow of Bingham plastic fluid and establish its dependence on radius ratio, Hedstrom Number and Bingham Reynolds Number. Further, for the flow of high concentration fly ash slurry flows, C_k for any given radius ratio is observed to be independent of Hedstrom Number (over the range investigated He ≤ 10⁵). Further, in fully turbulent flows, beyond a critical Reynolds number (Re_B ≥ 5.3 × 10³), C_k remains constant and is dependent only on the radius ratio.