On the local anisotropy of quasi-two-dimensional forced shallow flow: An experimental study

In presently used safety valve sizing standards the gas discharge capacity is based on a nozzle flow derived from ideal gas theory. At high pressures or low temperatures real gas effects can no longer be neglected, so the discharge coefficient corrected for flow losses cannot be assumed constant anymore. Also the force balance and as a consequence the opening characteristics will be affected. In former Computational Fluid Dynamics (CFD) studies valve capacities have been validated at pressures up to 35 bar without focusing on the opening characteristic. In this thesis alternative valve sizing models and a numerical CFD tool are developed to predict the opening characteristics of a safety valve at higher pressures. To describe gas flows at pressures up to 3600 bar and for practical applicability to other gases the Soave Redlich-Kwong real gas equation of state is used. For nitrogen consistent tables of the thermodynamic quantities are generated. Comparison with experiment yielded inaccuracies below 5% for reduced temperatures larger than 1.5. The first alternative valve sizing model is the real-average model that averages between the valve inlet and the nozzle throat at the critical pressure ratio. The second real-integral model calculates small isentropic state changes from the inlet to the final critical state. In a comparison the most simple ideal model performs slightly better than the real-average model and the dimensionless flow coefficient differs less than 3% from the most accurate real-integral nozzle model. Benchmark validation test cases from which field data is available are used to investigate the relevance of the physical effects present in a safety valve and to determine the optimal settings of the CFD code ANSYS CFX. First, 1D Shock tube calculations show that strong shocks cannot be captured without oscillations, but the shock strength in a safety valve flow is small enough to be accurately computed. Second, an axisymmetric nozzle (ISO 9300) model is simulated at inlet pressures up to 200 bar with computed mass flow rate deviations less than 0.46%. Third, a supersonic ramp flow shows a dependency of the location of the separation and reattachment points on the turbulence model, where the first order accurate SST model gives the best agreement with experiment. Fourth, computations of a simplified 2D valve model by F¨ollmer show that reflecting shocks can be accurately resolved. Fifth, a comparison of mass flow rates of a pneumatic valve model results in deviations up to 5% which seems due to a 5% too high stagnation pressure at the disk front. Sixth, the computed safety valve capacities of T¨UV Rheinland Aachen overpredict the measured discharge coefficient by 18%. However, a replication of this experiment at the test facility re8 Summary duces the error to 3%. A clear reason for the large deviation with the reference data cannot be given. Lastly, the computed mass flow rates of a nozzle flow with nitrogen at pressures up to 3500 bar agrees within 5% with experiment. A high-pressure test facility has been constructed to perform tests of safety valves with water and nitrogen at operating pressures up to 600 bar at ambient temperature. The valve disk lift and flow force measurement systems are integrated in a modified pressurized protection cap so that the opening characteristics are minimally affected. The mass flow rates of both fluids are measured at ambient conditions by means of a collecting tank with a mass balance for fluids and through subcritical orifices for gases with inaccuracies of the discharge coefficient of 3 and 2.5%. Reproducible valve tests with water have been carried out at operating pressures from 64 to 450 bar. The discharge coefficient does not depend on the set pressure of the safety valve. The dimensionless flow force slightly increases with disk lift. CFD computations of selected averaged measurement points with constant disk lift show that for smaller disk lifts the mass flow rate is overpredicted up to 41%. Extending the numerical model with the Rayleigh-Plesset cavitation model reduces the errors of the mass flow rates by a factor of two. The reductions in the flow forces range from 35 to 7% at lower disk lifts. Also reproducible valve tests with nitrogen gas at operating pressures from 73 to 453 bar have been conducted. The discharge coefficient is also independent of set pressure. In contrast to the water tests, the dimensionless flow force continually decreases with disk lift. All computed mass flow rates agree within 3.6%. The computed flow forces deviate between 7.8 and 14.7%. An analysis shows that the effects of condensation, transient effects, variation of the computational domain or mechanical wear cannot explain the flow force deviation. The reason partially lies in a larger difference between the set pressure and the opening pressure of the test valve. The flow distribution around the valve spindle is sensitive to the inlet pressure and rounding of sharp edges due to mechanical wear. The cavity of the valve spindle probably causes valve chatter partially observed in the experiments and simulations. In safety valve computations with nitrogen at higher pressures up to 2000 bar and temperatures down to 175 K outside the experimentally validated region the discharge coefficient of all three valve sizing models varies less than 6% compared to the 7 bar reference value at ambient temperature. So the standardized ideal valve sizing model is sufficient for safety valve sizing. The dimensionless force, however, increases with pressure up to 34% so that the valve characteristic is affected. The influence of valve dynamics on steady state performance of a safety valve is studied by extending the CFD tool with deformable numerical grids and the inclusion of Newton’s law applied to the valve disk. The mass flow rate and disk lift are less affected, but a fast rise and collapse of the flow force due to redirection of the bulk flow has been observed during opening. Only dynamic simulations can realistically model the opening characteristic, because these force peaks have not been observed in the static approach. Furthermore, the valve geometry can be optimized without sharp edges or cavities so that redirection of the flow will result in gradual flow force changes. Then, traveling pressure waves will lead to less unstable valve operation.

Single stage electrohydraulic flow control valves are currently not suitable in high flow rate and high frequency applicaitons. This is due to the very significant flow induced forces and the power/force limitation of electromagnetic actuators that directly stokes the spool. An unstable valve has been proposed that can utilize the flow forces to achieve fast responses at high flow rate. In this paper, we model the flow forces, including both steady and transient, of a directional flow control valve for incompressible and viscous fluid. In particular, the viscosity effect and non-orifice flux are investigated. The new models have been verified by CFD analysis to be more accurate than the old models. The paper also presents a systematic experimental study on the flow forces, in particular on the steady flow forces. The estimates according to our new models, revised slightly due to the limitation of the experiment, are consistent with the experimental results. Both the experimental results and the modeling estimation show that, for an unstable valve with negative damping length, both transient and steady flow forces can help to achieve the higher spool agility. The satisfactory modeling and experimental study on the flow forces give us a grounding for the future research of unstable valve design.

Periodically forced, oscillatory fluid flows have been the focus of intense research for decades due to their richness as a nonlinear dynamical system and their relevance to applications in transportation, aeronautics, and energy conversion. Here we derive a mechanistic model of the dynamics of forced turbulent oscillator flows by leveraging a comprehensive experimental study of the turbulent wake behind a D-shaped body under periodic forcing. We confirm the role of resonant triadic interactions in the forced flow by studying the dominant components in the power spectra across multiple excitation frequencies and amplitudes. We then develop an extended Stuart-Landau model that captures the system dynamics and synchronization regions. Further, it is possible to identify the model coefficients from sparse measurement data.

The objective of this paper is to experimentally investigate the significance of the pressure transient flow force acting on hydraulic spool valves. In the past, this flow force effect has been routinely neglected due to its assumed small size. Through analytical and experimental methods, this research shows that flow forces due to pressure transient effects can be comparable in magnitude to the steady flow forces acting on the valve and that the past tradition of neglecting this effect may not always be justified. The paper also shows that the traditional steady flow force model does a fairly good job predicting the steady flow forces on the valve, but more research must be done to develop a good model for pressure transient flow forces.

To reveal the composition and distribution of the impact force of the dry granular flow against a flexible barrier, five groups of physical experiments in different slope angles have been carried out. The flow velocities, flow heights and tensile forces of the cables were measured using the high camera and the load cells. Then we developed a model to calculate the total impact force of the dry granular flow against the barrier based on the tensile force of each cable. The results show that the main components the distribution of the maximum impact force vary with the pileup characteristics of the dead zone. The distributions of the maximum impact force change from linearity to nonlinear with the increase in the proportion of the impact force of flowing layer in the maximum impact force. The hydro-static model, the hydro-dynamic model and the limit equilibrium method were using for the estimation of the maximum impact force, respectively. Compared with the estimated results, the hydro-static model is more suitable for estimating the maximum impact force of the dry granular flow when the pileup height is five times greater than the flow height. The empirical static coefficients have close relationship with the ratio of the pileup length to the pileup height.

Earthquake disasters in the United States account for $6.1 billion of economic losses each year, much of which is directly linked to infrastructure damage. These natural disasters are unpredictable and represent one of the most difficult design problems regarding constructing resilient infrastructure. Structural floor and roof diaphragms act as the horizontal portion of the lateral force resisting system (LFRS), distributing the seismically derived inertial loads out from the heavy concrete slabs to the vertical LFRS. Concrete-filled steel deck diaphragms are ubiquitously used in steel construction worldwide due to the ease of construction and cost-effective use of material. This report first presents a series of concrete-filled steel deck push-out tests that explores the effect of cyclic loading on the strength of steel headed stud anchors. The effect that cyclic loading has on structural performance is explored across different concrete densities, steel headed stud anchor placements and groupings, steel deck orientations, and edge conditions. As compared to prior tests, the push-out tests conducted in this work included four rows of studs along the length rather than the typical two rows, and an ability to impose cyclic loading. This provided novel insight into force flows, failure mechanisms, and load distribution between studs and stud groups. Most of the specimens also used lightweight concrete, as is common in high seismic zones.Secondly, this report describes a full-scale experimental concrete-filled steel deck diaphragm specimen which explored the cyclic behavior and capacity of this structural system. This experiment builds on previously reported experimental studies. This specimen demonstrated force distribution and flows in an indeterminant floor system and captured realistic boundary conditions and construction practices that affect the performance of this system in building structures. The results showed that concrete-filled steel deck diaphragms fail as expected and may have significant overstrength. Furthermore, a finite element framework is presented that can simulate cyclic fracture through the use of a high-fidelity steel material model. This framework was used and validated against nine experimental push-out specimens tested and documented as part of this research. The simulation capacity provides an avenue to further investigate this structural system through simulated parametric study.

A procedure is described for the calculation of momentum and heat transfer rates through laminar boundary layers over rotating axisymmetric bodies in forced flow. By applying appropriate coordinate transformations and Merk’s type of series, the governing momentum equations can be expressed as a set of coupled ordinary differential equations that depend on a wedge parameter and on a rotation parameter. For the energy equation, a set of ordinary differential equations is obtained which depend explicitly on the Prandtl number and implicitly on the aforementioned parameters. These equations are numerically integrated for a range of parameter values for the special case of a rotating sphere, and the local friction coefficient and the local Nusselt number are presented for values of the rotation parameter B = 1, 4, and 10 with Prandtl numbers of 1, 10, and 100. These results are then compared with previous theoretical results. It is also shown how the flow and heat transfer characteristics for a rotating disk can be readily obtained as a special case from the formulation for the rotating sphere. The disk results are also compared with previous theoretical and experimental studies.

The effect of gravity on a laminar diffusion flame established over a horizontal flat plate

Single stage valves have their main spools stroked directly by solenoid actuators. They are cheaper and more reliable. Their use, however, is restricted to low bandwidth and low flow rate applications due to the limitation of the solenoid actuators. In a previous paper, a way proposed to alleviate the need for large solenoids in single stage valves by inducing spool instability using the transient flow forces, hence, improve the spool agility. In this paper, we study the underlying premise that the transient flow forces can be controlled by the "damping length". Models for both steady and transient flow forces that include viscous effects are developed. Various models are analyzed, compared using CFD analysis and correlated to experiments. It was found that the model for the spool dynamics using the various flow force models are consistent with experimental results as long as viscous effects are taken into account. Both magnitude studies and experiments show that "damping lengths" and transient flow forces significantly affect spool agility. CFD studies also indicate that viscosity is an important factor to consider while modeling fluid flow forces.

Fluid-dynamic analysis and multi-objective design optimization of piezoelectric servo valves

In single stage electrohydraulic valves, solenoid actuators are usually used to stroke the main spools directly. They are cheaper and more reliable than multistage valves. Their use, however, is restricted to low bandwidth and low flow rate applications due to the limitation of the solenoid actuators. Our research focuses on alleviating the need for large and expensive solenoids in single stage valves by advantageously using fluid flow forces. For example, in a previous paper, we proposed to improve spool agility by inducing unstable transient flow forces by the use of negative damping lengths. In the present paper, how steady flow forces can be manipulated to improve spool agility is examined through fundamental momentum analysis, CFD analysis, and experimental studies. Particularly, it is found that two often ignored components—viscosity effect and non-metering momentum flux, have strong influence on steady flow forces. For positive damping lengths, viscosity increases the steady flow force, whereas for negative damping lengths, viscosity has the tendency to reduce steady flow forces. Also, by slightly modifying the non-metering port geometry, the non-metering flux can also be manipulated to reduce steady flow force. Therefore, both transient and steady flow forces can be used to improve the agility of single stage electrohydraulic valves. Experimental results confirm the contributions of both transient and steady flow force in improving spool agility.

Toward flow forces acting on a step-pool unit

With the springing up of freeform architectures, the key problem to structural engineers is to generate structural forms with high structural efficiency subject to the architectural space constraints during the conceptual design process. In this research, a theoretical framework for Structural Morphology has been proposed, that provides an effective solution to the problem. To enrich the proposed framework, systematic Form-Finding research on shell structures is conducted.

This paper presents experimental and numerical studies for the case of turbulent forced and mixed convection flow of water through narrow vertical rectangular channel. The channel is composed of two parallel plates which are heated at a uniform heat flux, whereas, the other two sides of the channel are thermally insulated. The plates are of 64 mm in width, 800 mm in height, and separated from each other at a narrow gap of 2.7 mm. The Nusselt number distribution along the flow direction normalized by the Nusselt number for the case of turbulent forced convection flow is obtained experimentally with a comparison with the numerical results obtained from a commercial computer code. The quantitative determination of the nor- malized Nusselt number with respect to the dimension-less number Z = (Gr/Re21/8Pr0.5) is presented with a comparison with previous experimental results. Qualitative results are presented for the normalized temperature and velocity profiles in the transverse direction with a comparison between the forced and mixed convection flow for both the cases of upward and downward flow directions. The effect of the axial locations and the parameter Gr/Re on the variation of the normalized temperature profiles in the transverse direction for both the regions of forced and mixed convection and for both of the upward and downward flow directions are obtained. The normalized velocity profiles in the transverse directions are also determined at different inlet velocity and heat fluxes for the previous cases. It is found that the normalized Nusselt number is greater than one in the mixed convection region for both the cases of upward and downward flow and correlated well with the dimension-less parameter Z for both of the forced and mixed convection regions. The temperature profiles increase with increasing the axial location along the flow direction or the parameter Gr/Re for both of the forced and mixed convection regions, but this increase is more pronounced in the case of the mixed convection flow. For the forced convection region, the velocity profile depends only on Re with no difference between the upward and downward flow directions. Whereas, for the case of mixed convection flow, the velocity profile depends on the parameter Gr/Re with a main difference between upward and downward flow. These results are of great importance for any research reactor using plate type fuel elements or for any engineering application in which mixed convection flow through rectangular channel is encountered. .

It is difficult to accurately predict the steady-state flow force of spool valve with U-grooves by the traditional theoretical formulae of flow force. To resolve the problem,a platform with high-precision experimental apparatus and system was built to investigate the steady-state flow force with a multi-way valve as objective,which aimed at obtaining the characteristics of steady-state flow force in different flow directions and the pressure and flow rate characteristics of valve notch. The flow field in the valve was also simulated with computational fluid dynamic (CFD). Both the experimental and simulation results show that the steady-state flow force with U-grooves tends to be negative,which means that the valve notch tends to be open no matter in single in/out flow direction or in double flow directions. The coupling value of the steady-state flow force in the case of single in/out flow direction of the 3/6 valve is almost the same as that in the case of double flow directions. The simulation results of the steady-state flow force together with the pressure difference matched the experimental results well.