Pressure pulsations in piping system excited by a centrifugal turbomachinery taking the damping characteristics into consideration

Pressure pulsations excited by a centrifugal turbomachinery such as compressor, fan or pump at the blade passing frequency may cause severe noise and vibrations in piping system. Therefore, the practical evaluation method of pressure pulsations is strongly recommended. In particular, the maximum pressure amplitude under the resonant conditions should be appropriately evaluated. In this study, a one-dimensional excitation source model for a compressor or pump is introduced based on the equation of motion, so as to incorporate the non-linear damping proportional to velocity squared in the total piping system including the compressor or pump. The damping characteristics of the compressor or pump are investigated by using the semi-empirical model. It is shown that the resistance coefficient of the compressor or pump depends on the Reynolds number that is defined using the equivalent velocity of the pulsating flow. The frequency response of the pressure amplitude and the pressure distribution in the piping system can be evaluated by introducing the equivalent resistance of the compressor or pump and that of piping system. In particular, the relation of the maximum pressure amplitude in piping system to the location of the excitation source under resonant conditions can be evaluated. Finally, the reduction of the pressure pulsations by use of an orifice plate is discussed in terms of the pulsation energy loss.     

On the Similarity of Pulsating and Accelerating Turbulent Pipe Flows

The near-wall region of an unsteady turbulent pipe flow has been investigated experimentally using hot-film anemometry and two-component particle image velocimetry. The imposed unsteadiness has been pulsating, i.e., when a non-zero mean turbulent flow is perturbed by sinusoidal oscillations, and near-uniformly accelerating in which the mean flow ramped monotonically between two turbulent states. Previous studies of accelerating flows have shown that the time evolution between the two turbulent states occurs in three stages. The first stage is associated with a minimal response of the Reynolds shear stress and the ensemble-averaged mean flow evolves essentially akin to a laminar flow undergoing the same change in flow rate. During the second stage, the turbulence responds rapidly to the new flow conditions set by the acceleration and the laminar-like behavior rapidly disappears. During the final stage, the flow adapts to the conditions set by the final Reynolds number. In here, it is shown that the time-development of the ensemble-averaged wall shear stress and turbulence during the accelerating phase of a pulsating flow bears marked similarity to the first two stages of time-development exhibited by a near-uniformly accelerating flow. The stage-like time-development is observed even for a very low forcing frequency; \(\omega ^{+}=\omega \nu /{\overline {u}}_{\tau }^{2}=0.00073\) (or equivalently, \({l}_{s}^{+}=\sqrt {2/\omega ^{+}}=52\)), at an amplitude of pulsation of 0.5. Some previous studies have considered the flow to be quasi-steady at \({l}_{s}^{+}=52\); however, the forcing amplitude has been smaller in those studies. The importance of the forcing amplitude is reinforced by the time-development of the ensemble-averaged turbulence field. For, the near-wall response of the Reynolds stresses showed a dependence on the amplitude of pulsation. Thus, it appears to exist a need to seek alternative similarity parameters, taking the amplitude of pulsation into account, if the response of different flow quantities in a pulsating flow are to be classified correctly.     

A study of pulsating flow in automotive catalyst systems

Conversion efficiency, durability and pressure drop of automotive exhaust catalysts are dependent on the flow distribution within the substrate. This study examines the effect of pulsating flow on the flow distribution within these systems. The flow distribution was measured for a range of flow rates at pulsation frequencies of 16, 32, 64 and 100 Hz. It was shown that the flow uniformity at 16 Hz was similar to the steady equivalent whereas improved uniformity was seen at the higher frequencies resulting in a reduced pressure drop. It was further found that flow maldistribution under pulsating conditions was less sensitive to increases in flow rate compared to steady-state flow. Downstream of the monolith strong pulses were observed although the pulse shapes changed across the substrate diameter. Flow maldistribution correlated well with a non-dimensional parameter derived from the inlet flow velocity, pulsation frequency and diffuser length.     

Pulsating slurry flow in pipelines

An experimental study on pulsating turbulent flow of sand-water suspension was carried out. The objective was to investigate the effect of pulsating flow parameters, such as, frequency and amplitude on the critical velocity, the pressure drop per unit length of pipeline and hence the energy requirements for hydraulic transportation of a unit mass of solids. The apparatus was constructed as a closed loop of 11.4 m length and 3.3 cm inner diameter of steel tubing. Solid volumetric concentrations of up to 20% were used in turbulent flow at a mean Reynolds number of 33,000–82,000. Pulsation was generated using compressed air in a controlled pulsation unit. Frequencies of 0.1–1.0 Hz and amplitude ratios of up to 30% were used. Instantaneous pressure drop and flow rate curves were digitized to calculate the energy dissipation associated with pulsation. The critical velocity in pulsating flow was found to be less than that for the corresponding steady flow at the same volumetric concentration. Energy dissipation for pulsating flow was found to be a function of both frequency and amplitude of pulsation. A possible energy saving was indicated at frequencies of 0.4–0.8 Hz and moderate amplitudes ratios of less than 25%.List of symbols A cross-section area of the tube (m²) - C _D drag coefficient of sand particles - C _v volumetric concentration (%) - D inner diameter of test-section pipe (m) - F frequency (Hz) - f friction factor - g gravitational constant (m/s²) - J energy dissipation of suspension (W/m)/(kg/s) - J _p energy dissipation of pulsating suspension (W/m)/(kg/s) - J _s energy dissipation of steady component of suspension (W/m)/(kg/s) - J _w energy dissipation of pure water (W/m)/(kg/s) - L length of test-section (m) - m mass flow rate (kg/s) - P pressure drop in test-section (N/m²) - S specific gravity of sand - V instantaneous flow velocity (m/s) - V _c steady flow critical velocity (m/s) - V _cp pulsating flow critical velocity (m/s) - V _F settling velocity of particles (m/s) - V _s steady component of mean flow velocity (m/s) - dynamic viscosity (g/cm sec) - _m mean density of suspension (kg/m³) - angular velocity (rad/sec) - amplitude ratio (V — V _s)/V - nondimentional factor equal to - nondimentional factor equal to (V–V _s/V - NI nondimentional factor equal to (V ²C _d/g D(S – 1)) - Re Reynolds number (V ²C _d/C _v g D(S – 1))     

Effect on the flow and heat transfer characteristics for sinusoidal pulsating laminar flow in a heated square cylinder

Two-dimensional numerical simulation is performed to understand the effect of flow pulsation on the flow and heat transfer from a heated square cylinder at Re = 100. Numerical calculations are carried out by using a finite volume method based on the pressure-implicit with splitting of operators algorithm in a collocated grid. The effects of flow pulsation amplitude (0.2 ≤ A ≤ 0.8) and frequency (0 ≤ f _p  ≤ 20 Hz) on the detailed kinematics of flow (streamlines, vorticity patterns), the macroscopic parameters (drag coefficient, vortex shedding frequency) and heat transfer enhancement are presented in detail. The Strouhal number of vortices shedding, drag coefficient for non-pulsating flow are compared with the previously published data, and good agreement is found. The lock-on phenomenon is observed for a square cylinder in the present flow pulsation. When the pulsating frequency is within the lock-on regime, time averaged drag coefficient and heat transfer from the square cylinder is substantially augmented, and when the pulsating frequency in about the natural vortex shedding frequency, the heat transfer is also substantially enhanced. In addition, the influence of the pulsating amplitude on the time averaged drag coefficient, heat transfer enhancement and lock-on occurrence is discussed in detail.     

Influence of particles on turbulent flow in channels

In this work, the equations of balance of the second single-point moments of pulsations of the carrier phase are used to analyze the influence of particles on the intensity of pulsation motion. Besides dissipation due to pulsation phase slip, these equations take account the effect of dissipation of small-scale vortices on the particles and also of the additional transfer of pulsations by particles due to the particles being drawn into the pulsating motion and the migration of particles across the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 40–48, January–February, 1985.     

Steady and pulsating flow characteristics in straight tubes with and without a lateral circular protrusion

 Flow characteristics in straight tubes with and without a lateral circular protrusion had been investigated using Particle Image Velocimetry over a range of Reynolds numbers from 400 to 1400, and at Womersley number of 65. The practical interest of the flows considered lies mainly in blood flows through arteries with saccular aneurysm. Both steady and pulsating flow experiments had been conducted. It was found that under the steady flow conditions, a recirculating vortex would be formed inside the circular protrusion. The maximum strength of the vortex would be as low as 10% of the bulk mean velocity in the main tube at the highest Reynolds number tested (i.e. at 1400). Under the pulsating flow conditions, the vortex appeared and disappeared at different phase of a cycle. The sequence was only punctuated by quasi-inviscid flow behavior. The steady flow results only resembled those of the pulsating ones for about 1 10 of the time at each cycle. Received: 13 August 1997/Accepted: 30 June 1998     

Response of viscoelastic fluids in extensional flow generated by a pulsating sphere

A simple analysis of the periodic extensional flow generated by a pulsating sphere in an infinite sea of viscoelastic fluid has been carried out. The general procedure is illustrated by two specific constitutive equations: the corotational Jeffreys fluid and the Oldroyd fluid model B. The response of these fluids is reflected in the temporal variation of the pressure on the surface of the sphere, with Reynolds and Deborah numbers and parameters of the constitutive equations as independent variables. For the case of pulsation with infinitesimal amplitude the fluid response is summarised in the form of pressure amplitude and phase lag versus Deborah number plots. The role of the pulsating flow in the characterisation of viscoelastic fluids and the extension of the procedure to other constitutive equations are briefly discussed.     

Einfluß der Kanalgeometrie auf die pulsierende Druckströmung viskoelastischer Flüssigkeiten

Zusammenfassung Hiermit wird die in der Arbeit [1] dargestellte theoretische Erfassung der pulsierenden Strömung viskoelastischer Flüssigkeiten im kreisförmigen Kanal auf Breitschlitz- und Ringspaltkanäle verallgemeinert. Unabhängig von der Kanalgeometrie lassen sich sowohl die relative Amplitude der Ausstoßschwankungen als auch die relative Veränderung des mittleren Ausstoßes in einer einheitlichen Form ausdrücken, indem die Schergeschwindigkeit an der Kanalwand in der stationären Strömung passend definiert wird.

---

A theoretical approach to the pulsating flow of viscoelastic liquids through a circular channel presented earlier has been generalized to include the case of slit and annular ducts. Irrespective of the geometry of the channel, both the relative amplitude of pulsation of the output and the relative change in the average output can be presented in a uniform manner by an appropriate definition of the shear rate at the wall of the channel under steady flow conditions.

     

ROUTE TO SURGE FOR A THROTTLED COMPRESSOR — A NUMERICAL STUDY

Aerodynamic instabilities of axial compressors are investigated numerically and compared with experimental results. The compressor flow in the interblade-row spaces is simulated by means of 2-D Euler equations while the blade rows are modelled as quasi-steady actuator disks. The coupling of different unbladed regions of the compressor by actuator disks, which is characterized by the influence of stator and rotor, is captured in terms of conservation laws and source terms by means of compressor characteristics. At inflow and outflow nonreflecting boundary conditions are used in order to avoid any nonphysical reflections at the boundary. Numerically simulating this model for selected initial and boundary conditions, we observe that for increasing values of the imposed exit pressure the compressor flow undergoes several qualitative changes. At some critical value of exit pressure a primary stable steady state losses stability to several coexisting time-periodic states with a number of rotating stall cells. While for these time-periodic states the mass flow does not depend on time, all solution branches lead finally to surge, i.e., to states with an oscillation of mass flow in time if the exit pressure is sufficiently large. In addition, the numerical results are compared with experimental measurements.     

Effect of a pulsating flow on hydrodynamics and fluid catalytic cracking chemical reaction in a circulating fluidized bed riser

The three-dimensional computational fluid dynamics (3D-CFD) of a pulsating flow applied to the fluid catalytic cracking (FCC) reaction was investigated in the riser of a circulating fluidized bed reactor. The kinetic parameters of the FCC and coke burning reactions for predicting the reactant conversion and product yield percentages were applied. To increase the reactant conversion level and product yield, the effect of the pulsating flow operating parameters was considered using a 2^k statistical experimental design with four factors (amplitude, frequency, types of the waveform, and amplitude ratio). The 3D-CFD simulation was successfully validated from the experimental literature data. The frequency and type of the waveform were found to be the significant operating parameters. The expression of the fitted regression model and response surface contour were derived and revealed that the pulsating flow provides a higher reactant conversion level and product yield percentages compared to a non-pulsating or steady flow.     

Experimental study on the effect of pulsating inflow to an enclosure for improved mixing

Optimal control of inlet jet flows is of broad interest for enhanced mixing in ventilated rooms. The general approach in mechanical ventilation is forced convection by means of a constant flow rate supply. However, this type of ventilation may cause several problems such as draught and appearance of stagnation zones, which reduces the ventilation efficiency. A potential way to improve the ventilation quality is to apply a pulsating inflow, which has been hypothesised to reduce the stagnation zones due to enhanced mixing. The present study aims at testing this hypothesis, experimentally, in a small-scale two-dimensional water model using Particle Image Velocimetry with an in-house vortex detection program. We are able to show that for an increase in pulsation frequency or alternatively in the flow rate the stagnation zones are reduced in size and the distribution of vortices becomes more homogeneous over the considered domain. The number of vortices (all scales) increases by a factor of four and the swirl-strength by about 50% simply by turning on the inflow pulsation. Furthermore, the vortices are well balanced in terms of their rotational direction, which is validated by the symmetric Probability Density Functions of vortex circulation (Γ) around Γ = 0. There are two dominating vortex length scales in the flow, namely 0.6 and 0.8 inlet diameters and the spectrum of vortex diameters become broader by turning on the inflow pulsation. We conclude that the positive effect for enhanced mixing by increasing the flow rate can equally be accomplished by applying a pulsating inflow.     

Localised dynamics of laminar pulsatile flow in a rectangular channel

The exploitation of flow pulsation in low-Reynolds number micro/minichannel flows is a potentially useful technique for enhancing cooling of high power photonics and electronics devices. Although the mechanical and thermal problems are inextricably linked, decoupling of the local instantaneous parameters provides insight into underlying mechanisms. The current study performs complementary experimental and analytical analyses to verify novel representations of the pulsating channel flow solutions, which conveniently decompose hydrodynamic parameters into amplitude and phase values relative to a prescribed flow rate, for sinusoidally-pulsating flows of Womersley numbers 1.4 ≤ Wo ≤ 7.0 and a fixed ratio of oscillating flow rate amplitude to steady flow rate equal to 0.9. To the best of the authors’ knowledge, the velocity measurements – taken using particle image velocimetry – constitute the first experimental verification of theory over two dimensions of a rectangular channel. Furthermore, the wall shear stress measurements add to the very limited number of studies that exist for any vessel geometry. The amplification of the modulation component of wall shear stress relative to a steady flow (with flow rate equal to the amplitude of the oscillating flow rate) is an important thermal indicator that may be coupled with future heat transfer measurements. The positive half-cycle time- and space-averaged value is found to increase with frequency owing to growing phase delays and higher amplitudes in the near-wall region of the velocity profiles. Furthermore, the local time-dependent amplification varies depending on the regime of unsteadiness: (i) For quasi-steady flows, the local values are similar during acceleration and deceleration though amplification is greater near the corners over the interval 0 – 0.5π. (ii) At intermediate frequencies, local behaviour begins to differ during accelerating and decelerating periods and the interval of greater wall shear stress near the corners lengthens. (iii) Plug-like flows experience universally high amplifications, with wall shear stress greater near the corners for the majority of the positive half-cycle. The overall fluid mechanical performance of pulsating flow, measured by the ratio of bulk mean wall shear stress and pressure gradient amplifications, is found to reduce from an initial value of 0.97 at Wo = 1.4 to 0.28 at Wo = 7.0, demonstrating the increasing work input required to overcome inertia.     

涡旋式压缩机排气系统气流脉动现象研究

研究了涡旋式空气压缩机排气系统的气流脉动现象，首次提出了排气孔口侵入现象及计算方法。由一维非定常流动理论建立了排气系统气流脉动的计算模型，利用匀熵修正理论进行了边界条件处理，并运用Ｌ－Ｗ两步计算法进行了数值计算。试验样机的实测结果与数值计算结果吻合较好。研究内容对于新型压缩机——涡旋式空气压缩机的设计具有指导意义。     

PIV investigation of the flow induced by a passive surge control method in a radial compressor

Due to recent emission regulations, the use of turbochargers for force induction of internal combustion engines has increased. Actually, the trend in diesel engines is to downsize the engine by use of turbochargers that operate at higher pressure ratios. Unfortunately, increasing the impeller rotational speed of turbocharger radial compressors tends to reduce their range of operation, which is limited at low mass flow rate by the occurrence of surge. In order to extend the operability of turbochargers, compressor housings can be equipped with a passive surge control device such as a ??ported shroud.?? This specific casing treatment has been demonstrated to enhance the surge margin with minor negative impact on the compressor efficiency. However, the actual working mechanisms of the system remain not well understood. Hence, in order to optimize the design of the ported shroud, it is crucial to identify the dynamic flow changes induced by the implementation of the device to control instabilities. From the full dynamic survey of the compressor performance characteristics obtained with and without ported shroud, specific points of operation were selected to carry out planar flow visualization. At normal working, both standard and stereoscopic particle imaging velocimetry (PIV) measurements were performed to evaluate instantaneous and mean velocity flow fields at the inlet of the compressor. At incipient and full surge, phase-locked PIV measurements were added. As a result, satisfying characterization of the compressor instabilities was provided at different operational speeds. Combining transient pressure data and PIV measurements, the time evolution of the complex flow patterns occurring at surge was reconstructed and a better insight into the bypass mechanism was achieved.     

Effect of high-amplitude flow pulsations on heat transfer

We present results of an experimental study of the effect of flow pulsations on turbulent heat transfer in the transverse direction in propagation of sound waves. A significant increase in heat-transfer intensity was recorded at mean-square pressure pulsation amplitude p=168–180 dB at frequency f=100–150 Hz. The dependence of heat-transfer intensity on acoustic field characteristics is obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 169–172, March–April, 1975.     

Prediction of the drag reduction effect of pulsating pipe flow based on machine learning

Prediction of drag reduction effect caused by pulsating pipe flows is examined using machine learning. First, a large set of flow field data is obtained experimentally by measuring turbulent pipe flows with various pulsation patterns. Consequently, more than 7000 waveforms are applied, obtaining a maximum drag reduction rate and maximum energy saving rate of 38.6% and 31.4%, respectively. The results indicate that the pulsating flow effect can be characterized by the pulsation period and pressure gradient during acceleration and deceleration. Subsequently, two machine learning models are tested to predict the drag reduction rate. The results confirm that the machine learning model developed for predicting the time variation of the flow velocity and differential pressure with respect to the pump voltage can accurately predict the nonlinearity of pressure gradients. Therefore, using this model, the drag reduction effect can be estimated with high accuracy.     

Heat transfer characteristics of pulsated turbulent pipe flow

Heat Transfer characteristics of pulsated turbulent pipe flow under different conditions of pulsation frequency, amplitude and Reynolds number were experimentally investigated. The pipe wall was kept at uniform heat flux. Reynolds number was varied from 5000 to 29 000 while frequency of pulsation ranged from 1 to 8 Hz. The results show an enhancement in the local Nusselt number at the entrance region. The rate of enhancement decreased as Re increased. Reduction of heat transfer coefficient was observed at higher frequencies and the effect of pulsation is found to be significant at high Reynolds number. It can be concluded that the effect of pulsation on the mean Nusselt numbers is insignificant at low values of Reynolds number. Received on 29 June 1998     

轴流压气机机匣处理研究进展及评述

喘振和旋转失速裕度等稳定性问题是压气机设计者所关心的主要问题之一, 不稳定 流动大多数情况下都是从压气机端部区域开始的, 如果能够延迟端部区域的失速, 就能提高压气机的稳定工作范围. 在过去的30多年中,许多种型式的处理机匣结 构被用于改善端部区域流动, 提高压气机的稳定工作范围. 从机匣处理的实验 研究、理论分析和数值模拟3个方面对轴流压气机机匣处理的研究进行了回顾, 讨 论了处理机匣内部流动机理及其对轴流压气机性能和稳定性的影响, 并指出了机匣 处理研究的发展趋势.     

Investigation of the specific mass flow rate distribution in pipes supplied with a pulsating flow

A pulsating flow is typical of inlet and exhaust pipes of internal combustion engines and piston compressors. Unsteady flow phenomena are especially important in the case of turbocharged engines, because dynamic effects occurring in the exhaust pipe can affect turbine operation conditions and performance.One of the basic parameters describing the unsteady flow is a transient mass flow rate related to the instantaneous flow velocity, which is usually measured by means of hot-wire anemometers. For the flowing gas, it is more appropriate to analyze the specific mass flow rate φ_m = ρv, which takes into account also variations in the gas density. In order to minimize the volume occupied by measuring devices in the control section, special double-wire sensors for the specific mass flow rate (CTA) and temperature (CCT) measurement were applied. The article describes procedures of their calibration and measurement. Different forms of calibration curves are analyzed as well in order to match the approximation function to calibration points. Special attention is paid to dynamic phenomena related to the resonance occurring in a pipe for characteristic frequencies depending on the pipe length. One of these phenomena is a reverse flow, which makes it difficult to interpret properly the recorded CTA signal. Procedures of signal correction are described in detail. To verify the measurements, a flow field investigation was carried out by displacing probes radially and determining the profiles of the specific mass flow rate under the conditions of a steady and pulsating flow. The presence and general features of a reverse flow, which was identified experimentally, were confirmed by 1-D unsteady flow calculations.