Computation of Pressure Distribution Using PIV Velocity Data
Computation of Pressure Distribution Using PIV Velocity Data
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发表时间：
2002
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通讯作者：
D. Rubinstein;U. Shavit
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作者：
D. Rubinstein;U. Shavit
粒子图像测速（PIV）可用于压力评估。这种非侵入式测量方法提供了使用压力传感器时无法获得的高空间分辨率。利用速度矢量信息反求解Navier-Stokes方程，得到Neumann边界条件所需的压力梯度。然后再次利用速度数据求解压力泊松方程。测试了两种流动问题，一种是水在有收缩的管道中流动，另一种是空气射流的冲击。选择收缩流来表示压力变化较大的层流问题。结果与无粘溶液比较。并考察了空间分辨率的影响。选取撞击气流来表示紊流问题。将撞击板上的压力分布与文献报道的数据进行了比较，并对时间平均的一些方面进行了讨论。还有湍流。当需要计算力时，当需要与压力表进行比较时，以及当需要更好地理解流动问题时，层流和湍流中的压力场都是有用的。用于压力测量的压力表是膨胀的，尺寸大，需要与流体实际接触。当进行侵入性测量时，流量和压力会受到过程本身的影响（例如，在冠状动脉手术中使用导管时）。因此，建议利用非侵入式粒子图像测速法产生的速度数据计算压力场，以避免这一困难。在本研究中，我们给出了基于粒子图像测速获得的瞬时速度场的压力场计算结果。压力场的计算是通过对不可压缩牛顿Navier-Stockes方程应用散度算子得到的压力泊松方程来确定的。简介粒子图像测速（PIV）在二维流动问题的横截面上生成v 2p = -PV {v mb的瞬时速度图。如果执行得当，测量的空间分辨率和精度被认为是高的。测得的速度可以用于广泛的范围，其中P是平面压力，V是速度矢量，P是密度。方程1在直角坐标系下的二维形式表示为，处理计算，包括速度duav的大小和方向、速度梯度、2 ={(+ 2（—）+ [z)~} a)粘性剪切、流函数、涡度等。可以基于多种实现计算平均分量和波动分量来表示不稳定的统计参数，其中u和v分别是v的x分量和y分量。公式1的右侧可以直接从PIV系统产生的速度矢量场中计算出来。Gresho和Sani（1987）指出，物理边界条件是由动量守恒，即Navier Stokes方程推导出来的。因此，不可压缩流动的正确边界条件是诺伊曼边界条件而不是迪切雷边界条件。与泊松方程（方程l）的右侧类似，粒子图像测速可以通过在边界I？式中，p为动力粘度，t为时间。当分析定常层流或定常平均湍流时，时间导数dV/dt为零，PIV数据可用于计算p{v ~VV)和pv2V项。当对湍流感兴趣时，将雷诺应力项加到式1和式2中。通过求解时间平均湍流方程得到了诺依曼边界条件，由此得到了湍流泊松方程I。水在有收缩和撞击气流的管道中流动。选择收缩流来表示压力变化较大的层流问题。结果与无粘溶液进行了比较，并考察了空间分辨率的影响。选取撞击气流来表示紊流问题。将撞击板上的压力分布与文献报道的数据进行了比较，并对时间平均的一些方面进行了讨论。图1测量区域。采用指标表示法，实验收缩流量A恒定蒸馏水i， j = 1,2,3， ui和xi分别表示360 rnllmin的流量，即循环速度和位置。其中，V为20内径玻璃管时间平均速度矢量。内径为10的笛卡尔曲线。V d/& （ulu;）的表示是，5pm将聚酰胺种子颗粒（PSP-5, Dantec）溶液加入蒸馏水中，得到浓度为116毫升。采用160mJ /脉冲Nd:YAG双激光系统（Quantel）、互相关lKxlK CCD相机（Kodak, MEGAPLUS ES 1.0）、图像采集系统（OFS）和自制分析软件进行粒子图像测速。采用科里奥利加速度流量计（Micro-Motion）测量质量流量。水采用离心泵和恒水头容器进行循环，以保持稳定的流量。入口长度为21直径时，实现了充分发展的流动。为避免气泡积聚和沉降，管的取向为垂直，流向为向上。图1为玻璃管。速度矢量场在图1所示的两个矩形框架内互相关生成。校正后的微米像素比为14.347 pdpixel。审问区采用32x32像素（459.1 pm x 459.1pm）和64x64像素（918.2pm x 918.2pm）。通过每4、8、16、32和64像素（57.4、114.8、229.6、459.1和918.2 m）重复PIV分析来测试测量分辨率的影响。结果表明，该方法无需向量验证和滤波。滤波器如信噪比和局部核比较导致零抑制。获得了40个瞬时速度场的实现，并对每个实验取平均值。碰撞空气实验装置由送风系统、气溶胶发生器、混合室和会聚段、圆形光滑玻璃管（长300mm，内径29.5 mrn）组成。圆形平板（直径200mm）垂直于管道出口下游1、3、5个管径处安装。流速为6.83e4 m3/s，满足Peper et. a1（1997）的流动条件，采用基于微动科氏流量计进行测量。用拉斯金气溶胶发生器产生丙二醇颗粒，其平均直径为0.75毫微米（Echols和Young， 1963）。选择32 × 32像素的正方形审问区域，57.8 mp /像素比率，每16像素重复PIV分析，在57.3 mm × 58.3 mm的视场中得到3906个向量。对于管出口与板之间的每个距离（Idi， 3di和5di，其中di代表喷嘴直径），测量了130个瞬时速度场的实现。矢量验证由信噪滤波器和局部核比较滤波器获得，平均拒绝率约为5%。一个这样的速度图如图2所示。图2冲击射流速度矢量图。图3 A管速度矢量图。-30 -25 -20 -15 -10 - 50
Particle image velocimetry (PIV) can be used for pressure assessment. This non intrusive measurement method provide a high spatial resolution which is unavailable when using pressure transducers. The velocity vector information was used to solve inversely the Navier-Stokes equation to provide the pressure gradient needed for the Neumann boundary condition. Then the velocity data was used again to solve the pressure Poisson equation. Two flow problems were tested, water flow in a pipe with a constriction and an impinging air jet. The constriction flow was chosen to represent laminar flow problem where pressure is changing significantly. Results were compared with an inviscid solution. and the effect of spatial resolution was examined. The impinging air jet was chosen to represent a turbulent flow problem. The pressure distribution on the impingement plate was compared with reported data from the literature and some aspects of time averaging were discussed. and turbulent flows. The pressure field in both laminar and turbulent flows is useful when forces are to calculated, when comparison with pressure gauging is required, and when better understanding of the flow problem is desired. Pressure gauges used for pressure measurement are expansive, large in their size, and require an actual contact with the fluid. When the measurement is performed intrusively the flow and pressure are affected by the procedure itself (e.g. while using a catheter for coronary procedures). It was suggested, therefore, to avoid such difficulties by computing the pressure field from the velocity data generated by the non intrusive particle image velocimetry method. In the current study we present calculation results of pressure fields based on the instantaneous velocity fields obtained by particle image velocimetry. The calculation of the pressure field is determined by using the pressure Poisson equation which is derived by applying the divergence operator on the incompressible Newtonian Navier-Stockes equations, Introduction Particle Image Velocimetry (PIV) generates v 2 p = -PV {V mb in Q (1) instantaneous velocity maps in a two dimensional cross section of flow problems. The spatial resolution and the accuracy of the measurement, if performed adequately, are considered to be high. The measured velocity can then be used for a wide range of post where P is the piazometric pressure, V is the velocity vector, and p is density. The representation of the two dimensional form of Eq. 1 in Cartesian coordinates is, processing calculations, including velocity duav magnitude and direction, velocity gradient, 2 = { ( + 2 ( --) + [ z )~ } a) viscous shear, stream function, vorticity, and others. Mean and fluctuating components can ayh be calculated based on multiple realizations to represent the statistical parameters of unstable where u and v are the x and y components of V. The right hand side of Eq. 1 can be directly calculated fiom the velocity vector field generated by the PIV system. Gresho and Sani (1987) have pointed out that the physical boundary conditions are to be derived from the conservation of momentum, namely the Navier Stokes equations. The correct boundary conditions for incompressible flow are, therefore, the Neumann boundary conditions rather than the Dirchelet conditions. Similar to the right hand side of the Poisson equation (Eq. l), particle image velocimetry can be used to provide the required boundary pressure conditions by applying the Navier Stokes equations on the boundary, I?, as follows, where p is the dynamic viscosity and t is time. When either steady laminar flow or steady mean turbulent flow are to be analyzed, the time derivative, dV/dt, is zero and the PIV data can be used to compute the p{v ~VV) and pv2V terms. When turbulent flows are of interest, the Reynolds stress term is added to both Eqs. 1 and 2. The Neumann boundary conditions are obtained by solving the time average turbulent eauations and the turbulent Poisson eauation I is hence, The pressure field calculation was tested for two flow problems; water flow in a pipe with a constriction and an impinging air jet. The constriction flow was chosen to represent laminar flow problem where pressure is changing significantly. Results were compared with an inviscid solution and the effect of spatial resolution was examined. The impinging air jet was chosen to represent a turbulent flow problem. The pressure distribution on the impingement plate was compared with reported data from the literature and some aspects of time averaging were discussed. Fig. 1 The measurement regions. index notation was used such that Experimental Constriction Flow A constant distilled water i, j = 1,2,3 and ui and xi represent the flow rate of 360 rnllmin was circulated velocity and location. Here V denotes the though a 20inner diameter glass tube time averaged velocity vector. The Cartesian with a 10inner diameter constriction. A representation of V d/& (ulu;) is, 5pm Polyamid seeding particles (PSP-5, Dantec) solution was added to the distilled water, resulting in a concentration of 116 mgll. A 160mJ per pulse Nd:YAG double laser system (Quantel), a cross correlation lKxlK CCD camera (Kodak, MEGAPLUS ES 1.0), an image acquisition system (OFS), and a home made analysis software was used for the particle image velocimetry. Mass flow rate was measured using a Coriolis acceleration flow meter (Micro-Motion). Water was circulated using a centrifugal pump and a constant head container to maintain a steady flow rate. Fully developed flow was achieved using an entry length of 21 diameters. The tube orientation was vertical and flow direction was upwards to avoid accumulation of air bubbles and sedimentation. Fig. 1 shows the glass tube. The velocity vector field was generated by cross correlation within the two rectangular frames shown in Fig. 1. Calibration resulted in a micron to pixel ratio of 14.347 pdpixel. Interrogation areas of 32x32 pixels (459.1 pm x 459.1pm) and 64x64 pixels (918.2pm x 918.2pm) were used. The effect of measurement resolutionwas tested by repeating the PIV analysis every 4, 8, 16, 32, and 64 pixels (57.4, 114.8, 229.6, 459.1, and 918.2 m ) . Results showed that vector validation and filtering was unnecessary. Filters such as signal to noise ratio and a local kernel comparison resulted in zero rejection. Forty realizations of the instantaneous velocity fields were obtained and averaged for each experiment. Impinging air iet The experimental setup consists of an air supply system, an aerosol generator, a mixing chamber and a convergence section, and a round smooth glass tube (length 300 mm, inner diameter 29.5 mrn). A round flat plate (200 mm in diameter) was installed perpendicular to the flow, 1, 3, and 5 tube diameters downstream from the tube exit. A flow rate of 6.83e4 m3/s was used to meet the flow conditions of Peper et. a1 (1997) and was measured using a Micro-Motion coriolis based flow meter. Propylene-glycol particles were generated by a Laskin aerosol generator resulting in an average diameter of 0.75 mp (Echols and Young, 1963). A choice of 32x32 pixels square interrogation areas, a 57.8 mp /pixel ratio, and repeating the PIV analysis every 16 pixels resulted in 3906 vectors in a field of 57.3 mm by 58.3 mm. For each distance between the tube exit and the plate (Idi, 3di, and 5di, with di representing the nozzle diameter), 130 realizations of the instantaneous velocity fields were measured. Vector validation was obtained by a signal to noise filter and a local kernel comparison filter resulting in an average rejection rate of approximately 5%. One such velocity map is shown in Fig. 2. Fig. 2 An impinging jet velocity vector map. Fig. 3 A tube velocity vector map. -30 -25 -20 -15 -10 -5 0 I