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.     

Choking phenomena of sonic nozzles at low Reynolds numbers

The choking phenomena of sonic nozzles were investigated for the Reynolds number range from 40 to 30 000 for nitrogen gas. The results showed that the critical back pressure ratio is a function of the Reynolds number only, with different characteristics for different nozzle shapes. In ISO-type toroidal-throat Venturi nozzles, the minimum Reynolds number satisfying the choking condition is about 40 and the critical back pressure ratio is only about 0.05 at this minimum Reynolds number. It was also found that the critical back pressure ratio has a local minimum value around Re_th=4000 and that the local maximum value is around Re_th=10 000 due to the change in characteristics of the boundary layer in the diffuser. On the other hand, the critical back pressure ratio in quadrant nozzles decreases monotonically with decreasing Reynolds number, unlike the former nozzle, and the minimum Reynolds number necessary for choking is estimated to be approximately the same as that in the Venturi nozzle.     

Theoretical discharge coefficient of a critical circular-arc nozzle with laminar boundary layer and its verification by measurements using super-accurate nozzles

The discharge coefficient of a circular-arc critical Venturi nozzle is derived theoretically by combining theories to calculate mass flow defects caused by the core flow distribution and the laminar boundary layer. The equation obtained is verified by measurements using a constant volume tank system and nozzles of similar shape machined by super accurate lathes, which achieved mirror finish without polishing thus resulting in a machining error of less than 1 μm. The agreement of the theoretical and measured discharge coefficients is better than 0.04% at Reynolds numbers larger than 8×10⁴, the minimum used. The equation derived is in an analytical form, which enables an estimation of the effects of specific heat ratio as well as nozzle shape.     

Methods to calibrate a critical nozzle and flowmeter using reference critical nozzles

Methods to calibrate a critical nozzle and a flowmeter against reference critical nozzles are developed to replace the time-consuming conventional procedures. The discharge coefficient of a critical nozzle at a low Reynolds number was measured in a series connection with a reference nozzle in the upstream position, and its Reynolds number dependence was obtained by changing the reference nozzle. The dependence of similar critical nozzles with negligible machining error measured at low pressures using the series connections and at atmospheric pressure using a constant volume tank system coincide within ±0.04%. The same configuration was employed to measure the stability of the choking flow rate, which revealed premature unchoking phenomenon. The discharge coefficient of a critical nozzle under a reference condition was measured by a combination of three series connections with two reference critical nozzles at the upstream positions. Reynolds number dependence of a critical nozzle was measured using a combination of three series connections with four reference critical nozzles. These two methods require only one pressure gauge whose sensitivity is constant in a narrow range. An air flowmeter was calibrated at various volumetric flow rates against only one critical nozzle by controlling the upstream pressure of the nozzle.     

Experimental and CFD investigation of 100 mm size cone flow elements

This paper presents performance characteristics of 100 mm line size cone flow elements having beta ratios of 0.4, 0.5, 0.6, 0.7 and 0.8. A magnetic flow meter is used as a reference standard for flow measurement in vertical test section. A series of experiments have been conducted using water at in-house Flow Calibration Facility (FCF) to cover the Reynolds number ranging from 20,000 to 200,000. The performance characteristics of 100 mm line size cone flow elements with different beta values have been evaluated experimentally. It is found that the discharge coefficient of the cone flow element is nearly independent of the specified range of Reynolds number. Testing of the cone flow element in accordance with new API 5.7 is carried out at flow calibration facility. The testing requirements in the standard explain the conditioning effect of the cone flow element having gate valve disturbance upstream of the cone at various locations. The effect of the upstream velocity profile has been investigated by placing a gate valve upstream of the cone flow element at a distance of 0D and 28D and performing experiments at 25%, 50% and 100% opening of gate valve. The value of the discharge coefficient is not affected when the cone is placed at a distance of 0D and for 100% opening of gate valve. The uncertainty results of the cone testing are discussed. For studying pressure and velocity distributions, cone elements are modeled using computational fluid dynamics (CFD) code PHOENICS. Pressure and velocity profiles for different sizes of cone elements are plotted. From the pressure profile, it can be seen that the pressure recovery downstream of the cone is within a distance of 3D. The velocity profile downstream of the cone signifies the use of flow element as a signal conditioner. For measurement of flow through a 100 mm line, differential pressure across the cone is measured using a Differential Pressure Transmitter (DPT). Experiments were repeated by replacing the cone element for obtaining different β values.     

Flow structure in critical flow Venturi nozzle and its effect on the flow rate

The flow fields in toroidal Venturi-nozzles, shaped according to the ISO-9300 Standard, have been investigated using numerical flow simulation. The present study was aimed at clarifying some of the phenomena associated with unchoking the flow in the throat. To this end, the shock structure has been studied for different Reynolds numbers and exit pressure ratios. The flow simulations were carried out in two and three dimensions. The flow fields were always unsteady, displaying a complex shock–boundary layer interaction.     

V形内锥流量计关键参数对流出系数的影响

将计算流体动力学仿真试验和实流物理试验相结合,剖析V形内锥流量计的流出系数特性,探索不同等效直径比β、前后锥角以及雷诺数等对流出系数的影响规律。湍流模型为RNG k-ε模型。针对100 mm口径,设计了β值分别为0.50、0.65、0.85,前锥角分别为40º、45º、50º,后锥角分别为120º、130º、140º,共27种组合的V形内锥体,仿真介质为水,温度为293 K。经过数值模拟试验,获得了27条内锥流量计流出系数特性曲线。为进一步验证仿真试验结果,在已有实流试验系统的基础上,建立针对V形内锥流量计的专用自动标定平台。两类试验数据比较发现：内锥流量计的流出系数不仅和雷诺数有关,还与等效直径比β及前后锥角相关。首先,β值越大,流出系数越小,且β值越大,流出系数更易受雷诺数的影响;其次,β值相同时,前锥角对流出系数具有决定性的影响,而后锥角对流出系数的线性度具有一定程度的影响;第三,较大的前锥角可减弱雷诺数对流出系数的影响。数值模拟试验预测平均误差约5%,最大值小于10%。     

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).     

叶片外部换热实验和数值研究

在短周期跨音速传热风洞上,研究不同雷诺数和压比下无气膜导叶表面换热系数分布,并在相应的数值模拟中分析叶栅通道涡结构的生成与发展,研究其对叶片换热的影响。     

Measurement of mass flow rate and evaluation of heat transfer coefficient for high-pressure pneumatic components during charge and discharge processes

Both the mass flow rate and heat transfer characteristics are significant factors to the flow behavior of the high-pressure air; however, they are not easy to be obtained by analytical model during discharge and charge processes. In this paper, the mass flow rate characteristics of high-pressure pneumatic components (HPPC) are measured by a compounding approach; two components under test with the same geometry and dimension are needed to be connected in series. Both the effective cross-section area and critical pressure ratio of HPPC are determined accurately, and only the pressure variation and the steady-state temperature of air in the chamber are utilized. The compared results between experimental and simulation data show that the accuracy of the measured effective cross-section area and critical pressure ratio of the HPPC is high when the sonic and adiabatic releasing time is less than 2 s. And then, a new combined method of calculating the heat transfer coefficient during discharging and charging processes for the high-pressure air is proposed. The computational fluid dynamics (CFD) method is used to illustrate the intensity of heat exchange between the high-pressure air inside the chamber and outer atmosphere. The dynamic flow behavior is analyzed based on the tested flow rate characteristics of HPPC, mixed heat transfer theory and numerical results. The results show that the heat-transfer coefficient during charge process is much greater than discharge process, and the forced convection heat exchange happened owing to the strong “air agitation” during the charge process. The experimental results also validate that the proposed method of calculating the transient heat transfer coefficient is more reasonable to describe the heat transfer behavior. The findings may also have general implication in the development of the design and analysis of the high-pressure pneumatic system.     

Influence of nozzle exit tip thickness on the performance and flow field of jet pump

The influence of exit tip thickness of nozzle δ _e on the flow field and performance of a jet pump was studied numerically in this paper. It is found that δ _e has influence on the distribution of turbulence kinetic energy k. If δ _e is ignored, k takes the highest value but dissipates rapidly than that of nozzle with a certain tip thickness. δ _e also affect apparently the development of tip vortex, which will occur near the exit tip of nozzle. The bigger the δ _e is, the larger the vortex is. The tip vortex develops with the increase of flow rate ratio q. When q=1 and δ _e =0.6∼0.8mm, a small vortex will be found downstream the tip vortex. And a concomitant vortex happens down the tip vortex in the case of q=1 and δ _e =0.8mm. As q increases to 2, the downstream small vortex disappears and the concomitant vortex becomes bigger. It is also found that the tip vortex might interact with the possible backflow that formed in the throat tube and parts of suction chamber. The center of backflow was affect evidently by δ _e . With the increase of δ _e , the center of backflow under the same q will go downstream. When δ _e =0.4mm, the center of backflow goes farthest. Then, as the further increase of δ _e , the center of backflow will go back some distance. Although, δ _e has relatively great influence on the flow field within the jet pump, it exerts only a little impact on the performance of jet pump. When δ _e =0.2∼0.6mm, the jet pump possess better performance. In most case, it is reasonable to ignore the nozzle exit tip thickness in performance prediction for the purpose of simplicity. This paper was presented at the 9^th Asian International Conference on Fluid Machinery (AICFM9), Jeju, Korea, October 16–19, 2007.     

高空、低速、低雷诺数对发动机部件及整机性能的影响研究

为研究FWS-9发动机作为高空无人飞行平台动力装置的可行性,在对发动机旋转部件(压气机、涡轮)雷诺数修正的基础上,研究了高空、低速、低雷诺数对发动机部件(风扇、压气机、主燃烧室和涡轮)和整机性能、稳定性的影响规律。