Particle Image Velocimetry Images Research Articles

Theoretical description of PIV measurement errors

Expressions for particle image velocimetry (PIV) mean error and error variance are derived for iterative deformation method algorithms. The analytical expressions explicitly account for the role of in- and out-of-plane displacements, displacement gradients, particle image diameter, fill factor of the imaging sensor, image noise, light sheet intensity distribution, seeding particle concentration, the interpolation function used to deform PIV images, and the interrogation window size and weighting window. The newly derived analytical expressions show good agreement with errors estimated using synthetic image sets.

High Spatial Resolution 2C-2D PIV Measurements Using A 47 MPx Sensor Of High Reynolds Number Turbulent Boundary Layer Flow

In the past decade, advances in electronics technology have made larger imaging sensors available to the experimental fluid mechanics community. These advancements have enabled the measurement of 2-component 2-dimensional (2C-2D) velocity fields using particle image velocimetry (PIV) with much higher spatial resolution than previously possible using a single camera. Although previously reported experiments have incorporated multiple-camera arrays to acquire high spatial resolution PIV, using a single large camera can greatly reduce the complexity of the experimental setup as well as the error introduced by the calibration between the cameras. In this paper, the ability of a single large sensor for high spatial resolution PIV is demonstrated by performing the measurement of a zero-pressure-gradient turbulent boundary layer (ZPG-TBL). In post-processing the PIV images, the lens distortion error is of particular importance, as the lens distortion error increases with the size of the imaging sensor. The third-order polynomial functions are used to model the lens distortion in this study, and the correction is performed on the PIV vectors to save computational cost. The first- and second-order statistics are calculated and compared with the profiles captured by small camera arrays, and the result shows that the corrected profiles agree well with the previously acquired data, therefore, the lens distortion error can be corrected.

Analysis Of PIV Images Of Transonic Buffet Flow By Recurrent Deep Learning Based Optical Flow Prediction

In the past few years, several algorithms have been proposed that leverage deep learning techniques within the data analysis workflow of particle-image velocimetry (PIV) experiments. This emerging body of work has shown that deep learning has the potential to match or outperform state-of-the-art classical algorithms in terms of efficiency, accuracy, and spatial resolution. Due to the significant relevance of PIV experiments in the broader fluid mechanics community, progress in PIV processing approaches based on state-of-the-art machine learning tools has a major impact across a range of problems in applied physics and engineering where velocity components of flow fields need to be determined. In contrast to existing methods, these approaches are general, near-automated and yield per-pixel flow estimates. Primary work on deep learning for PIV is promising, but important questions concerning the application to challenging engineering problems remain open and more scientific analyses are necessary to substantiate the general confidence amongst practitioners in such neural network based tools. This motivates us to employ a novel deep learning based PIV approach called RAFT-PIV to a challenging application of a recent research subject. That is, we use our neural optical flow approach to evaluate Background-Oriented Schlieren (BOS) and PIV images obtained by measurements of the transonic flow around a supercritical DRA-2303 profile and demonstrate that it can be used as a direct one-to-one replacement for standard cross-correlation based counterparts.

Fluorescent particle image velocimetry using atomized liquid particles

Aerosolized fluorescent particles of Kiton Red 620 dye in a water/glycol fluid are generated using a Venturi-type atomizer and shown to provide effective flow seeding for fluorescent particle image velocimetry (PIV), which can mitigate the detrimental effects of laser reflections from surfaces. Ninety two percent of particles by number concentration were found to be <1 μm in diameter, an acceptable size threshold for gas-flow PIV purposes. A PIV application was conducted in a wind tunnel (freestream velocity U ∞ = 27 m s−1), using the particles for measurement of the boundary layer flow approaching a forward-facing step (approach boundary layer momentum thickness Reynolds number of . Particles were generated from solutions with dye molar concentrations of and mol l−1, and PIV images were obtained for both elastic Mie scattering and filtered, Stokes-shifted fluorescent light. Raw images indicate that the fluorescence yield of the mol l−1 solution provides PIV images with high contrast, even in the near-surface regions where Mie scattering image contrast is highly affected by surface reflections. Boundary layer profiles are processed in the region of adverse pressure gradient leading up to the forward-facing step, where the fluorescent PIV was found to perform comparably to the most optimized Mie scattering PIV; both approaches obtained data as near to the wall as 30 μm, or two viscous wall units in our flow of interest. These results indicate that the new seeding method holds promise for near-surface measurement applications with more complicated three-dimensional geometries, where it is impossible to arrange PIV cameras to reject surface-scattered light.

Vacuum-induced lateral deformation around a vertical drain in dredged slurry

The horizontal strain in the vacuum preloading/dewatering of dredged slurry is significant to the apparent clogging effect and estimation of surface settlement around a drain; however, it has seldom been investigated in previous studies. In this study, a vacuum consolidation model test assisted by particle image velocimetry (PIV) technology was conducted. The displacement vector field was obtained through PIV analysis and image processing; it was used to visually observe the deformation features around a drain. Based on the displacement field, the vertical/horizontal strains at varied radial distances were calculated to explain the ‘soil pile’ and apparent clogging effect. From the strain distribution with radial distances, a significant lateral compression zone near the drain and an extension zone at farther areas were confirmed. Furthermore, a simple explicit model was established to evaluate the horizontal strain within a prefabricated vertical drain unit cell considering a horizontal attenuated vacuum and compression/extension zone. Finally, this method was applied to predict the horizontal displacement in the model test. The results showed that the proposed method can estimate the lateral displacement of soft clay slurry fairly well.

Application of partial wire mesh and particle image velocimetry for rectangular phase change material containers as efficient thermal energy storage systems

AbstractAn experimental setup is built to improve the charging process of a bio‐based phase change material inside a rectangular latent heat thermal energy storage (LHTES) system. In addition to experimenting with different porosities of full‐coverage wire mesh, a novel method of partial wire mesh placement at a proper location is used for improving conduction and maintaining natural convection, proven by the particle image velocimetry (PIV) method. Although acquiring PIV images from coconut oil is challenging because of the laser reflection, the image capturing and processing have been completed successfully. Temperatures inside the enclosure were measured using four K‐type thermocouples, and the melt fraction was calculated using captured images. The full‐size mesh results in a more uniform temperature distribution, and its charging time for porosities of 88% and 82% is decreased by 41% and 52%, respectively. The results of partial wire mesh placements indicate that a top‐only approach leads to a time reduction of only 7%. However, the bottom‐only approach yields a time reduction of 34% and the value of 3.8 for the charging time reduction over the porosity reduction parameter, which is the highest among all experiments. Additionally, this placement eliminates sudden temperature spikes, which improves the performance of the LHTES system and results in an economical and practical configuration. Moreover, the PIV test shows sustained convective velocities at the top half of the enclosure with a partial mesh at the bottom, demonstrating improved natural convection compared to that of a full‐size mesh implementation which weakens convection. Therefore, contrary to full‐size meshes used in previous works, a bottom‐only mesh placement can enhance conduction and convection simultaneously, which can be utilized in practical applications.

Diffeomorphic Particle Image Velocimetry

The existing particle image velocimetry (PIV) do not consider the curvature effect of the non-straight particle trajectory, because it seems to be impossible to obtain the curvature information from a pair of particle images. As a result, the computed vector underestimates the real velocity due to the straight-line approximation, that further causes a systematic error for the PIV instrument. In this work, the particle curved trajectory between two recordings is firstly explained with the streamline segment of a steady flow (diffeomorphic transformation) instead of a single vector, and this idea is termed as diffeomorphic PIV. Specifically, a deformation field is introduced to describe the particle displacement, i.e., we try to find the optimal velocity field, of which the corresponding deformation vector field agrees with the particle displacement. Because the variation of the deformation function can be approximated with the variation of the velocity function, the diffeomorphic PIV can be implemented as iterative PIV. That says, the diffeomorphic PIV warps the images with deformation vector field instead of the velocity, and keeps the rest as same as iterative PIVs. Two diffeomorphic deformation schemes -- forward diffeomorphic deformation interrogation (FDDI) and central diffeomorphic deformation interrogation (CDDI) -- are proposed. Tested on synthetic images, the FDDI achieves significant accuracy improvement across different one-pass displacement estimators (cross-correlation, optical flow, deep learning flow). Besides, the results on three real PIV image pairs demonstrate the non-negligible curvature effect for CDI-based PIV, and our FDDI provides larger velocity estimation (more accurate) in the fast curvy streamline areas. The accuracy improvement of the combination of FDDI and accurate dense estimator means that our diffeomorphic PIV paves a new way for complex flow measurement.

An experimental study of the unsteady vortex structures of a clapping-wing micro air vehicle

It is a challenge to explore the unsteady vortex structures of flexible flapping wings of X-shaped flapping-wing micro air vehicles (also known as clapping-wing micro air vehicles (CWMAVs)). The objective of this paper is to obtain the influence of wind speed, flapping frequency, and angle of attack (AoA) on the instantaneous and average force coefficients of CWMAVs, investigate flow visualization of the leading-edge vortex (LEV), trailing-edge vortex (TEV) and wake vortex (WV) structures and identify some novel flow mechanisms of flapping propulsion. This paper proposes a mechanics and particle image velocimetry (PIV) measuring platform in a low-speed tunnel. In addition, cross-correlation peak analysis and kriging image reconstruction are applied for postprocessing to enhance PIV image recognition. Combining the time evolution of the forces, the force coefficients, and the flow visualization, we find the evolution and effects of LEV, TEV and WV structures.

A novel method based on the Otsu threshold for instantaneous elimination of light reflection in PIV images

The base of particle image velocimetry (PIV) is the maximization of the correlation between the distribution of particle images in an interrogation window or a volume separated by an instant of time. In real images, the unwanted reflection of light on fixed walls or moving objects can directly interfere with the correlation, deteriorating the PIV quality. In this work, a new method for generating instantaneous masks based on the Otsu threshold for instantaneous elimination of light reflection in PIV images is proposed. This method separates the saturated image caused by the unwanted scattering of light from the tracer particles images through the Otsu threshold combined with the Gauss filter and Wiener adaptive local filter. This new method, called Otsu–Gauss–Wiener (OGW), was first tested using synthetic PIV images. In these tests, the authors analyzed the reflection caused by an object regarding different sizes, shapes, and intensities to evaluate the performance of the proposed method. Later, the OGW method was tested in PIV experimental cases with real adversities, for example, scattering of light on a fixed wall in a channel with periodic hills (case B—4th PIV challenge), strong reflection in a centrifugal impeller (case C—1st PIV challenge) and light scattering caused by an out-of-plane motion of the diaphragm of a pulsatile pediatric ventricular assist device. The results show that the method can remove the reflections by static and moving objects using an automatic mask generated for each instantaneous image.

Deep particle image velocimetry supervised learning under light conditions

Particle image velocimetry (PIV) is an important fluid visualization technology which extracts the velocity field from two successive particle images. Recently, some researchers have begun to use convolutional neural network (CNN) to tackle the PIV problem successfully. Some supervised learning methods make use of the PIV dataset with ground truth for network training. However, the existing dataset is composed of pairs of particle images under ideal light conditions and does not take into account the changes in actual experimental conditions. In this paper, we firstly generated a new and more challenging dataset called Light-PIV which fully simulates the change of the brightness of particle images in the real PIV experiment. Secondly, we present here a novel approach for fluid motion estimation which is based on an optical flow network LiteFlowNet. The proposed approach is verified by the application to a diversity of synthetic and experimental PIV images. We not only improve the structure, but also combine the traditional prior assumptions knowledge with the loss function to better guide the network training. The proposed approach is verified by the application to a diversity of synthetic and experimental PIV images. The experimental results show that our proposed method has advantages of high accuracy, obtaining detailed information and strong robustness in our PIV dataset compared with classical PIV methods such as HS optical flow and WIDIM, and even outperforms these existing approaches in some flow cases.

A particle-based image segmentation method for phase separation and interface detection in PIV images of immiscible multiphase flow

Particle image velocimetry (PIV) is a valuable tool for experimentally studying multiphase flows. In order to distinguish the flow dynamics of each individual phase, proper image segmentation must be performed. In immiscible multiphase flows, the fidelity of phase segmentation is directly linked to the accuracy of the interface detection. This paper reports a novel method for robust phase separation and phase boundary identification applicable to particle images acquired via PIV. The method, which requires a seeding density differentiation between the phases, is based on particle detection and triangular meshing. In this method, tracer particles in all seeded phases are first identified, and the coordinates of the particle locations are then used to formulate a 2D unstructured mesh, where the triangular grids provide the basis for phase separation and the outer edges provide a basis for interface detection. This paper presents a parametric analysis on synthetic particle images to assess the performance of the method and to compare the results to existing approaches. In addition, an application to experimentally generated images is reported. These results show that this method can successfully track the complex interface evolution in a particularly challenging flow system consisting of immiscible multiphase flow in porous media.

A phantom study comparing radial trajectories for accelerated cardiac 4D flow MRI against a particle imaging velocimetry reference.

Radial sampling is one method to accelerate 4D flow MRI acquisition, making feasible dual-velocity encoding (Venc) assessment of slow flow in the left ventricle (LV). Here, two radial trajectories are compared in vitro for this application: 3D radial (phase-contrast vastly undersampled isotropic projection, PC-VIPR) versus stack of stars (phase-contrast stack of stars, PC-SOS), with benchtop particle imaging velocimetry (PIV) serving as a reference standard. The study contained three steps: (1) Construction of an MRI- and PIV-compatible LV model from a healthy adult's CT images. (2) In vitro PIV using a pulsatile flow pump. (3) In vitro dual-Venc 4D flow MRI using PC-VIPR and PC-SOS (two repeat experiments). Each MR image set was retrospectively undersampled to five effective scan durations and compared with the PIV reference. The root-mean-square velocity vector difference (RMSE) between MRI and PIV images was compared, along with kinetic energy (KE) and wall shear stress (WSS). RMSE increased as scan time decreased for both MR acquisitions. RMSE was 3% lower in PC-SOS images than PC-VIPR images in 30-min scans (3.8 vs. 3.9 cm/s) but 98% higher in 2.5-min scans (9.5 vs. 4.8 cm/s). PIV intrasession repeatability showed a RMSE of 4.4 cm/s, reflecting beat-to-beat flow variation, while MRI had intersession RMSEs of 3.8/3.5 cm/s for VIPR/SOS, respectively. Speed, KE, and WSS were overestimated voxel-wise in 30-min MRI scans relative to PIV by 0.4/0.3 cm/s, 0.2/0.1 μJ/mL, and 36/43 mPa, respectively, for VIPR/SOS. PIV is feasible for application-specific 4D flow MRI protocol optimization. PC-VIPR is better-suited to dual-Venc LV imaging with short scan times.

Deep-learning-based liquid extraction algorithm for particle image velocimetry in two-phase flow experiments of an object entering water

Particle image velocimetry (PIV) enables the study of instantaneous fluid kinematics through flow visualization, which promotes the study of an object entering a liquid surface. However, even with PIV, the accurate extraction of the liquid phase region remains elusive due to the unsteady hydrodynamic forces involved. Therefore, we present a deep-learning network based on U-Net to solve the problems. The network, named MRes-Att-Unet, combines the mechanisms of residual connectivity and attention, which is proven to be effective in medical image segmentation. Considering the use of a training of network in supervised learning, we created a corresponding dataset based on the PIV experiment of an object entering water in two-phase flow and tested the images of an object entering water in an isolated wave crushing experiment. The results showed that the MRes-Att-UNet improved the segmentation accuracy of the gas–liquid boundaries, with especially enhanced results in a wide range of laser scattering, fuzzy bubbles, splash, and other complex interferences. Moreover, a WIDIM method is used to process the segmented and original images, and the results show that a deep learning method is feasible for segmenting PIV images and can effectively reduce the error vector of two-phase flow boundary.

Experimental investigation of sonic transverse jets in Mach 5 crossflow

An experimental investigation of sonic transverse jets in Mach 5 cross flow over a flat plate with a sharp leading edge was carried out. Jet to free stream momentum flux ratio, J, was varied from 1.16 to 5.30. Schlieren visualisation provided information regarding mean flow features such as Mach disc height, h, separation length, xsep as well as inherent unsteadiness. Steady wall pressure measurements diagnosed the interaction region between the jet and the incoming cross flow developing on the flat plate. To assess the jet penetration characteristics and trajectories, two-component Particle Image Velocimetry (PIV) measurements were carried out at the centreplane of the flat plate. Raw PIV image analysis was used to specify jet penetration boundaries. Ensemble-averaged streamwise and transverse velocity contours revealed the mean flow structures. The barrel shocks and the Mach disc forming the jet boundary can be easily seen and were visualised/quantified using PIV measurement technique. Maximum turbulence occurred above the Mach disc due to the presence of the shear layer and at the intersection of the windward side of the barrel shock and bow shock.

Measurement of the air bubble size and velocity from micro air bubble generation (MBG) in diesel using optical methods

In this paper, we determine the bubble size and velocity from air bubble generation (MBG) in a diesel using optical methods. A KTM Series Pump was used to generate micro air bubbles in diesel. The air bubble radius and velocity measurements can be useful parameters to optimize the bubble generation process. Two optical systems were used for measurement air bubble sizes and their velocities in diesel. First, the optical system without an objective lens was used to determine the velocity of air bubbles in diesel. Another optical system with a 10× objective lens was used to obtain the size distribution of air bubbles generated in diesel. An available optical system with a 10× objective lens can detect a bubble diameter greater than 3.3 µm that air bubble images were processed using the ImageJ program. We measured the size distribution of air bubbles generated using the ImageJ program. The micro air bubble radius measured in diesel was found to be 6.26 µm in the sample after a month from air bubble generation. In addition, the particle image velocimetry (PIV) technique was used to measure the velocity field. Then, we used the OpenPIV program for PIV image processing. The highest velocity distribution was determined to be 90 mm/s for diesel without air bubbles and 20 mm/s for diesel with air bubbles after a month of the bubble generation.

On the feasibility of selective spatial correlation to accelerate convergence of PIV image analysis based on confidence statistics

This paper presents a method which allows for a reduced portion of a particle image velocimetry (PIV) image to be analysed, without introducing numerical artefacts near the edges of the reduced region. Based on confidence intervals of statistics of interest, such a region can be determined automatically depending on user-imposed confidence requirements, allowing for already satisfactorily converged regions of the field of view to be neglected in further analysis, offering significant computational benefits. Temporal fluctuations of the flow are unavoidable even for very steady flows, and the magnitude of such fluctuations will naturally vary over the domain. Moreover, the non-linear modulation effects of the cross-correlation operator exacerbate the perceived temporal fluctuations in regions of strong spatial displacement gradients. It follows, therefore, that steady, uniform, flow regions will require fewer contributing images than their less steady, spatially fluctuating, counterparts within the same field of view, and hence the further analysis of image pairs may be solely driven by small, isolated, non-converged regions. In this paper, a methodology is presented which allows these non-converged regions to be identified and subsequently analysed in isolation from the rest of the image, while ensuring that such localised analysis is not adversely affected by the reduced analysis region, i.e. does not introduce boundary effects, thus accelerating the analysis procedure considerably. Via experimental analysis, it is shown that under typical conditions a 44% reduction in the required number of correlations for an ensemble solution is achieved, compared to conventional image processing routines while maintaining a specified level of confidence over the domain.Graphic abstract

Aerodynamic Performance and Flow Structure Investigation of Contra-rotating Wind Turbines by CFD and Experimental Methods

Wind tunnel experiment was carried out to measure mechanical power of the contra-rotating wind turbine (CRWT) and single rotor wind turbine (SRWT) under various working conditions. Particle Image Velocimetry (PIV) device was employed to measure the transient flow field on the meridional plane of the rotors. The azimuthal velocity vector, magnitude and streamline were obtained by the average PIV image of ten intervals in a rotation cycle. CFD model of steady flow was developed to predict aerodynamic performance and flow structure of the CRWTs using S-A turbulent model. The single channel model was employed with periodic boundary condition. CFD results were validated with wind tunnel test in literature and experiment in this paper. Results show that CFD method has a satisfied accuracy in power prediction, with a relative error less than 34%. The azimuthal average velocity distributions predicted by experimental and CFD methods are close and the maximum value are approximate to each other. Results demonstrate a high velocity zone at the outside of the front rotor tip and a low velocity zone near the middle of the rear rotor. CRWT has a complicated flow structure. Particularly at the rear rotor, flow becomes uneven and streamline curvatures are more ununiformed.

Development and validation of a PIV processing routine for two-phase index-matched flows

Implementing particle image velocimetry (PIV) in particle-laden flows is a challenging task due to the optical effects of the added particles. The addition of particles reduces optical access in the measurement region, degrades image quality and increases the experimental uncertainty. One method for reducing this effect is by using refractive index matching (RIM) which matches the index of refraction of the fluid and added particles rendering the particles optically transparent. Exact matching of the refractive index is difficult to achieve in practice. Even slight mismatches in the refractive indices lead to degradation of the image quality which will impact the higher-order statistics. Comparisons of statistics between loading levels are difficult under these conditions. In this work, the effect of processing methodology on RIM PIV images is investigated. RIM is achieved through the use of superabsorbent hydrogel materials in water. Two processing methods are investigated. The baseline method is a basic PIV correlation process without any pre- or post-processing. The refined process utilizes image pre-processing, data post-processing, and experimental error compensation. The goal for the refined method was to optimize and implement a more sophisticated PIV processing routine using existing commercial software on a particle-laden flow to reduce progressive error artifacts. Images from a fully turbulent channel flow with particle loading levels of 0–15% are utilized. Past literature indicates that turbulence levels will be attenuated for the particles used. Turbulence levels calculated using the baseline method show a linear increase with increasing loading, which is a non-physical result. The refined processing method shows a slight attenuation of turbulence which is consistent with expectations. The study highlights the need for careful processing and interpretation of results in cases where changes in image quality can be expected between different experimental conditions.

Application of a zonal hybrid URANS/LES turbulence model to high and low-resolution grids for engine simulation

A zonal hybrid unsteady Reynolds-averaged Navier–Stokes/large eddy simulation (URANS-LES) Zonal detached-eddy simulation (ZDES) model is applied to internal combustion engine (ICE) simulation and comparisons of predicted flow morphology and variability are carried out against on the transparent combustion chamber (TCC-III) particle image velocimetry (PIV) data set for motored conditions. To this aim, a previously developed model derived from a standard seamless-detached eddy simulation (DES) formulation is adopted for two different grid resolutions. In particular, two zonalization choices are evaluated based on previous single-grid results, in order to assess the model outcomes based on the joint turbulence treatment/grid density: the seamless-DES mode is applied (1) only to the cylinder (TCC-Z1) and (2) to the cylinder and intake port (TCC-Z2). Multi-cycle simulations (50 samples) are carried out and the results are compared to experimental data in terms of PIV images using multiple quality indices on multiple planes ( Y = 0 and X = 0). Finally, comparison of predicted mean flow fields is extended to standard URANS mode. Results show that the use of a cylinder-only seamless-DES treatment on a relatively coarse grid results in a quantitative agreement between simulated and measured (PIV) flow fields, both in terms of average morphology and flow variability, whereas the extension of the DES mode to the intake port does not introduce relevant variations. Quality indicators seem to be moderately sensitive to the grid resolution, thus confirming the adaptive potential of a ZDES–like model and promoting the use of DES–type turbulence modelling even on relatively low-resolution grids. The analysis of average fields compared to URANS simulations highlights the benefit for both grids of a scale-resolving ZDES modelling when the same underlying turbulence model ( k-ε RNG) is used. This study reinforces the recommendation in the use of hybrid URANS-LES models to simulate ICE flows. The adopted ZDES formulation based on the two-equation k-ε RNG model shows that high-quality results can be obtained even on engineering-grade grids, both in terms of average and cycle-to-cycle variation. The numerical results obtained using the two grids with variable resolution are consistent, and this further promotes a wider adoption of this class of models to simulate engine flows in industrial applications.

Uncertainty analysis of PIV measurements in bubbly flows considering sampling and bubble effects with ray optics modeling

In this paper, a modeling-based approach is developed to investigate the external sources of uncertainty in particle image velocimetry (PIV) measurements for two-phase bubbly flows. Primarily relied on ray optics modeling, this study focuses on the uncertainty in PIV measurements due to bubble-induced light distortion. In addition, the uncertainty due to sampling is also considered through synthetic PIV images generated from Monte Carlo sampling. Based on a PIV-planar laser induced florescence (PLIF) measurement system, three case studies are performed and discussed, considering respectively the sampling effect, bubble effect, and the combination of these two effects. These case studies confirm the validity of the ray optics modeling in obtaining accurate particle images through a benchmark test. Furthermore, it is also found that the bubble effect could significantly influence the particle images. On the other hand, the result of the case study with synthetic PIV images indicates that the bubble effect on particle images can be minimized by removing “outliers” in the obtained velocity vector field through a multi-pass post-processing procedure. However, the uncertainty of the velocity measurements will still increase.