Pressure Field Research Articles

Investigation of geometric structure on energy performance and flow characteristics in underwater hydraulic machinery

PurposeFor underwater hydraulic machinery, the unique structure significantly enhances the three-dimensional non-uniformity of turbulence within the flow domain and high Reynolds number turbulence introduces complex effects on the machinery. Therefore, studying the turbulent flow characteristics in underwater hydraulic machinery is crucial for system stability.Design/methodology/approachThis paper conducts a numerical analysis on a specific type of underwater hydraulic machinery. A numerical calculation model is established under stable inflow conditions to analyze the flow trends and pressure changes at different flow speeds. Subsequently, structural modifications are made to the underwater hydraulic machinery, and the characteristics of the velocity field, pressure field and vorticity distribution under different model parameters are analyzed.FindingsThe results indicate that changes in internal structure have a certain impact on flow characteristics. When the structural changes are significant, the fluid flow becomes more complex and pressure fluctuations become more intense. The research findings provide a scientific basis and theoretical guidance for the structural design of underwater hydraulic machinery and have significant research implications for controlling fluid-induced noise.Originality/valueAffected by the inherent structural characteristics of the flow channel structure, the flow direction of the high-speed water flow changes drastically in the flow channel, so it is of great significance to study its flow characteristics for the stability of the system.

Abstract B033: Towards magnetic resonance microscopy for liquid biopsy in cancer therapy monitoring

Abstract The advancement of liquid biopsy techniques promises to revolutionize cancer diagnostics and therapy monitoring, by offering a minimally invasive approach to track tumor progression and treatment efficacy. One central issue preventing advancements are innovations in sensor technology, necessary to enable the detection of molecular and cellular biomarkers with sufficient precision. Over the past decade, atomic-scale quantum sensors have emerged as powerful detectors, offering the ability to perform precise measurements of temperature, pressure, and magnetic fields on the single cell scale. These sensors, based on the interaction of spin qubits with their environment, have the unique capability to amplify and exploit environmental interactions for highly accurate detection, making them ideal for complex biological applications. In this context, we present an advanced quantum sensing platform specifically tailored for liquid biopsy applications in cancer therapy monitoring. This platform integrates the capabilities of optical microscopy with magnetic resonance imaging (MRI) techniques, utilizing nitrogen-vacancy (NV) centers in diamond as quantum sensors by converting magnetic resonance signals into optical signals, which are subsequently captured by a high-speed camera. Our platform offers a novel approach, promising quantitative analysis of single cancer cells from liquid samples with unprecedented accuracy. Unlike traditional MRI, our method captures signals over a wide field of view directly in real space. Each camera pixel records a magnetic resonance spectrum, providing detailed multicomponent information about the sample, such as molecular concentration, diffusion, and relaxation behavior, which are critical for understanding the tumor’s microenvironment. Our quantum sensing technology holds significant potential for enhancing the sensitivity of liquid biopsies. By capturing detailed molecular information from blood or other body fluids, it will enable in-depth analysis of Circulating Tumor Cells (CTCs), circulating tumor DNA (ctDNA), exosomes, and other biomarkers. Citation Format: Karl D. Briegel, Robin D. Allert, Dominik B. Bucher, Julia D. Draeger, Nick R v. Grafenstein, Linyan Nie. Towards magnetic resonance microscopy for liquid biopsy in cancer therapy monitoring [abstract]. In: Proceedings of the AACR Special Conference: Liquid Biopsy: From Discovery to Clinical Implementation; 2024 Nov 13-16; San Diego, CA. Philadelphia (PA): AACR; Clin Cancer Res 2024;30(21_Suppl):Abstract nr B033.

Noise Source Identification for the Unsteady Low-Pressure Turbine Flow Fields

Abstract The article presents a data processing methodology to identify the noise sources in low-pressure turbine (LPT) stages and their relative importance. Scale adaptive simulation (SAS) has been carried out on a geometry reproducing the midspan blade section of an entire LPT stage. The proper orthogonal decomposition (POD) is applied to data matrices constructed with the velocity and the pressure fields in order to distinctly extract the coherent structures responsible for velocity fluctuations and pressure waves (i.e., POD modes from the corresponding kernel), their temporal evolution and energies. The cross-correlation matrices of the pressure modes and the velocity modes reveal the degree of coupling between pressure and velocity oscillations, thus highlighting the modes linked to the same flow phenomena. The results show that the periodic vortex shedding at the stator trailing edge emits strong pressure waves, and the upstream-propagating waves reflect against the adjacent stator suction surface. The POD modes related to the rotor–stator interaction show peak amplitudes at the blade passing frequency and its harmonics and their shapes mimic the potential interaction in the stator domain and the migration of viscous wakes in the rotor domain. The POD modes with lower energy content correspond to the stochastic turbulent structures originated from the turbulent boundary layers as well as those carried by the vane and blade wakes. The biggest noise sources of the current flow fields are identified to be the von Karman vortex street downstream the stator trailing edge and the rotor–stator interaction.

The Development of Machine Learning Models for Radial Compressor Monitoring With Instability Detection

Abstract Modern radial compressors are designed to operate with high performance and a wide range of applications while minimizing their environmental impact. It is necessary to study the machine near the stability limit and gain a comprehensive understanding of the fluid dynamic mechanisms that trigger the instability in the system to extend the operating range at high efficiency. Machine learning aids in developing pattern identification models for detecting compressor instability. In a prior study, a two-stage radial compressor for refrigerant gas underwent extensive simulation, capturing unsteady RANS conditions and generating a substantial dataset of pressure signals from multiple probes. Selected signals, coupled with detailed computational fluid dynamics (CFD) post-processing, revealed fluid dynamic structures near surge conditions. This study utilizes all pressure signals to assess the stage's operational state (stable, transient, or unstable/surge). An additional goal is to develop an algorithm predicting flow patterns in different stage sections with minimal pressure signals at the rotor inlet. This is a preliminary step toward the development of a smart monitoring and diagnostic model for the compressor installed in a plant. The developed model consists of three submodels, trained with CFD results obtained from unsteady Reynolds averaged Navier–Stokes (URANS) simulations. The three submodels are a regression submodule, a classification submodule, and a forecasting algorithm. The regression submodule predicts diffuser static pressure fields, the classification submodule categorizes whether the compressor is in a critical condition or not, and the forecasting algorithm predicts the inducer pressure signals in the future impeller rotations according to the actual operation history. These sub-modules work together to forecast whether the compressor, according to the operation strategy, is going into instability conditions.

THE EVOLUTION OF A CLAY CRUST IN A BOREHOLE

Based on the previously proposed quasi-stationary model of clay crust formation when drilling wells in depth intervals with permeable rocks, software was created and computational experiments were performed, which made it possible to clarify the contribution of various physical parameters to the process of its growth.Based on the analysis of the results of computational experiments, the contribution of the physical parameters of the formation and clay crust to the dependence of its size on time has been clarified. The model assumes that the filtration pressure fields are described by stationary piezo conductivity equations. This made it possible to construct explicit dependences of pressure, thickness of the clay crust, radius of the zone of pressure disturbances in the reservoir during drilling and other parameters on time. Simple approximate formulas have been found for the dependence of the thickness of the clay crust, the filtration rate and the radius of the pressure disturbance zone in the reservoir on time, which describe their evolution with high accuracy.Based on the analysis of the calculation results, it was found that the thickness of the clay crust significantly depends on the permeability of the reservoir and repression, and these parameters determine the process of its formation. The porosity of the collector makes a smaller contribution, and the filtration and capacitance parameters of the clay crust have little effect on its thickness.New possibilities for estimating the physical parameters of reservoirs based on cavernometry have been identified. The solution of this problem is especially important for horizontal wells, in which the clay crust intervals have a significant length, and its formation occurs under conditions of a wide range of reservoir properties of the formation. The considered problem is of practical importance, since the zone of penetration of drilling mud filtrate into the formation has a screening effect on the use of geophysical methods to determine reservoir saturation. The results obtained can be used both to improve the interpretation of geophysical methods and to develop those.When conducting computational experiments using an exact formula, the stochastic behavior of the calculated curves was found. It was found that the noted effect is associated with rounding error, and in this sense is a manifestation of the features of the processor. An approach is proposed to eliminate the detected stochastic errors.

Optimising hydrofoils using automated multi-fidelity surrogate models

ABSTRACT Lifting hydrofoils are gaining importance, since they drastically reduce the wetted surface area of a ship, thus decreasing resistance. To attain efficient hydrofoils, the geometries can be obtained from an automated optimisation process. However, hydrofoil simulations are computationally demanding, since fine meshes are needed to accurately capture the pressure field and the boundary layer on the hydrofoil. Simulation-based optimisation can therefore be very expensive. To speed up the fully automated hydrofoil optimisation procedure, we propose a multi-fidelity framework which takes advantage of both an efficient low-fidelity potential flow solver dedicated to hydrofoils and a high-fidelity RANS solver enhanced with adaptive grid refinement and dedicated foil-aligned overset meshes, to attain high accuracy with a limited computational budget. Both solvers are shown to be reliable for automatic simulation, and remarkable correlation between potential-flow and RANS results is obtained. Two different multi-fidelity frameworks are compared for a realistic hydrofoil: only RANS based and potential-RANS based. According to the optimisation results, the drag is able to be reduced by 17% and 8% in these frameworks, within a realistic time frame. Thus, industrial optimisation of hydrofoils appears possible. Finally, critical areas of future improvement regarding the robustness and efficiency of the optimisation procedure are discussed in this study.

Diffusion-driven flows in a nonlinear stratified fluid layer

Diffusion-driven flow is a boundary layer flow arising from the interplay of gravity and diffusion in density-stratified fluids when a gravitational field is non-parallel to an impermeable solid boundary. This study investigates diffusion-driven flow within a nonlinearly density-stratified fluid confined between two tilted parallel walls. We introduce an asymptotic expansion inspired by the centre manifold theory, where quantities are expanded in terms of derivatives of the cross-sectional averaged stratified scalar (such as salinity or temperature). This technique provides accurate approximations for velocity, density and pressure fields. Furthermore, we derive an evolution equation describing the cross-sectional averaged stratified scalar. This equation takes the form of the traditional diffusion equation but replaces the constant diffusion coefficient with a positive-definite function dependent on the solution's derivative. Numerical simulations validate the accuracy of our approximations. Our investigation of the effective equation reveals that the density profile depends on a non-dimensional parameter denoted as $\gamma$ representing the flow strength. In the large $\gamma$ limit, the system is approximated by a diffusion process with an augmented diffusion coefficient of $1+\cot ^{2}\theta$ , where $\theta$ signifies the inclination angle of the channel domain. This parameter regime is where diffusion-driven flow exhibits its strongest mixing ability. Conversely, in the small $\gamma$ regime, the density field behaves like pure diffusion with distorted isopycnals. Lastly, we show that the classical thin film equation aligns with the results obtained using the proposed expansion in the small $\gamma$ regime but fails to accurately describe the dynamics of the density field for large $\gamma$ .

Localized topological states beyond Fano resonances via counter-propagating wave mode conversion in piezoelectric microelectromechanical devices

A variety of scientific fields like proteomics and spintronics have created a new demand for on-chip devices capable of sensing parameters localized within a few tens of micrometers. Nano and microelectromechanical systems (NEMS/MEMS) are extensively employed for monitoring parameters that exert uniform forces over hundreds of micrometers or more, such as acceleration, pressure, and magnetic fields. However, they can show significantly degraded sensing performance when targeting more localized parameters, like the mass of a single cell. To address this challenge, we present a MEMS device that leverages the destructive interference of two topological radiofrequency (RF) counter-propagating wave modes along a piezoelectric Aluminum Scandium Nitride (AlScN) Su-Schrieffer-Heeger (SSH) interface. The reported MEMS device opens up opportunities for further purposes, including achieving more stable frequency sources for communication and timing applications.

Strengthening by {110} and {112} edge dislocations in BCC high entropy alloys

Abstract Mechanical tests and microscopy studies on body-centered cubic (BCC) high entropy alloys reveal transitions from screw to edge dislocation slip and from {110} to {112} slip plane activity. Here, a strengthening theory for BCC edge dislocation slip on {112} planes is thus developed that parallels a recent theory for {110} slip. Using the atomistic dislocation pressure fields for four BCC elements (Nb, Ta, Mo, W) as proxies to span the range of likely alloy cores, theory predicts that the zero temperature yield strength for {112} slip is slightly lower (0%–20%) than that for {110} slip but that the associated energy barrier is slightly (0%–20%) higher. This leads to cancelling effects, and hence very similar strengths, at finite temperatures and strain rates. Full atomistic results on selected dilute binary alloys show some shifts in these trends, but with similar magnitudes and cancelling effects. The close strengths of {110} and {112} slip modes indicate that subtle aspects beyond the scope of the theory will determine which slip system controls the observed strengthening. This closeness in strength cements the use of the {110} edge theory for guiding alloy design independent of actual slip system.

Waves Generated by the Horizontal Motions of a Bottom Disturbance

Waves generated by a horizontally moving disturbance on the seabed have been studied by developing two numerical models, namely, the Navier–Stokes and the Green–Naghdi equations. Various geometries of the bottom disturbances are considered, and waves generated due to a single motion and multiple oscillatory motions of the bottom disturbances are investigated by the two models. Discussion is provided on how the motion of the disturbance on the seafloor results in the generation of surface waves. The wave-field parameters investigated include the surface elevation, velocity, pressure fields and wave celerity. A parametric study is conducted to assess the effect of the geometry of the disturbance and the kinematic characteristics on the wave generation. It is shown that both linear and nonlinear waves can be generated by a horizontally moving disturbance on the seabed. Long waves, followed by a series of dispersive waves, are produced by the single motion of the bottom disturbance. It is also found that, under appropriate conditions, there would be a balance between nonlinearity and dispersion, such that the generated waves propagate over a flat seafloor with little to no change in their form and shape.

Chuprov invariant for vector-scalar fields of multipole sources in a shallow sea

A computational and theoretical study of the properties of the well-known waveguide invariant S.D. Chuprova (IC) was carried out in a plane-parallel Pekeris waveguide. Unlike earlier works, in which predominantly non-directional (monopole) sources were used as a source, and sound pressure fields (scalar fields) were studied, in this work not only scalar, but also vector fields formed in the waveguide by directional - combined multipole sources with directivity in both horizontal and vertical planes. A differential equation has been obtained that makes it possible to fairly accurately calculate the IC values under different conditions of signal propagation and different depths of sources and receivers. This makes it possible, in a simpler way than “full computer modeling,” to predict the invariance (stability) of the IC when varying both the hydrophysical conditions in the waveguide and the geometry of the experiment. It is shown that the directionality of sources in the horizontal plane has virtually no effect on the properties of the IC, and the directionality in the vertical plane leads to a shift in the fan structure of the signal amplitude fields, but has little effect on the IC values. The properties of the fan structure change in a similar way when using vertical projections of the oscillatory velocity vector - despite the fact that another analytical relation, different from scalar fields, is used to calculate the IC, the IC value is close to (+1) at all frequencies and distances, except those at which new modes or dislocations arise. At these frequencies and in these zones, alternating emissions with different signs and magnitudes occur. It is concluded that the stability of IC allows the application of signal processing algorithms developed for scalar fields and non-directional sources to vector-scalar fields generated, including using directional sources.

A local synergy angle of velocity, temperature and pressure fields for enhancement of comprehensive heat transfer performance

The field synergy principles for convective heat transfer and flow resistance are integrated in this study. A local three-field synergy angle of velocity, temperature and pressure fields is proposed to evaluate the local comprehensive performance of heat transfer and pumping power consumption. The angle is based on the polar angle of a plot with dot products of velocity and enthalpy/total pressure gradients, respectively, as coordinates. The polar angle is then shifted by the observation that the enhancement of heat transfer rate at the cost of pumping power decreases from the second quadrant to the forth quadrant. The application of the synergy angle is demonstrated by examples of flow and heat transfer in channels with different fin structures. Inspired by the distribution of the synergy angle, Airfoil-Rect fin and Rhom-Rect fin structures are designed, which can improve the heat transfer rate with constraints of pumping power consumption. The present study provides a possible approach for heat transfer enhancement.

Course control in a self-consistent model of cuttlefish movement

We developed a simulation model to mimic cuttlefish movement. We developed a simulation model to mimic cuttlefish movement, representing an elongated body with two undulatory fins that generate propulsive forces for underwater movement. Our mathematical model concurrently solved equations for both body mechanics and fluid dynamics, using the Navier–Stokes equations to describe the latter. To implement this self-consistent model, we utilized deformable mesh techniques. This enabled us to compute both the apparatus’s movement performance characteristics and hydrodynamic flow parameters, such as vorticity and pressure fields. Our study focused on examining how oscillations of the left and right fins, each with different parameters, impact the apparatus’s maneuverability. We found that differences in frequencies between the left and right fins resulted in a peak turning angle velocity. We also explored how the interplay between hydrodynamic forces influences the apparatus’s course control.

Investigation on flow–acoustic resonance behaviors inside ducts with tandem cavities using a high-order spectral/hp element method

This study numerically investigates the flow–acoustic resonance behaviors inside ducts with tandem cavities, containing the flow-excited acoustic eigenmodes and elevated flow dynamics under self-sustained acoustic forcing. An advanced high-order spectral/hp element method integrated with implicit large-eddy simulations was utilized to solve the nonlinear compressible Navier–Stokes equations, which effectively identified the fully coupled self-sustained flow–acoustic resonance fields. The benchmark shallow cavity configuration with a length-to-depth (L/D) ratios of 2 was motivated by the experimental findings from Shaaban and Ziada [“Fully developed building unit cavity source for long multiple shallow cavity configurations,” Phys. Fluids 30, 086105 (2018)], in which the intensive flow–acoustic resonance was occurred at a Reynolds number of 1.3×105, and we further investigated three deeper cavity configurations with L/D of 1, 2/3, and 1/2 for numerical validation and further comparison. Subsequently, aeroacoustic characteristics were assessed by analyzing the wall pressure fluctuations, indicating broader resonance regions and augmented pressure pulsation amplitudes extending from main duct to local cavity volumes with larger cavity depths. As feedback, the intensified acoustic forcing can modulate the cavity flow dynamics into stronger fluctuation levels. Furthermore, the spectral proper orthogonal decomposition analysis was conducted on the pressure fields and velocity fields, respectively. The significant fluctuations in acoustic pressure were linked to transitional acoustic modes that were present as global modes in the main duct and local modes in tandem cavities. As for velocity analysis, coherent vortex structures were extracted along the cavity entrances. These vortex structures caused progressively amplified velocity fluctuations and classified the shear layers into two dynamic motions, i.e., a flapping motion in shallow cavities and a rolling-up motion in deep cavities.

Experimental synthesis of random pressure fields based on Transfer-Matrix analysis on 1D arrays

Synthesizing random pressure fields with loudspeaker arrays in a laboratory setting requires acquiring a global transfer matrix of all channels between the loudspeaker array and the microphone array. This inevitably involves measuring a large and unwieldy number of transfer functions. Therefore, we propose a prediction method for the transfer matrix under free-field conditions, combining a substantially reduced number of measurements with specific predictions based on segmented acoustic centers. In free-field conditions, if only three sets of transfer functions are measured for each loudspeaker and the remaining entries in the global transfer matrix are predicted using analytical expressions, the results show that the normalized error between the predicted and measured transfer matrices can be less than -13 dB. The experimental results indicate that, based on a one-dimensional loudspeaker array in a standard anechoic chamber, this prediction method shows promise for accurately reproducing random pressure fields, such as a diffuse acoustic field and the pressure field in the spanwise direction of a turbulent boundary layer. Additionally, the prediction method demonstrates the potential for extension to two-dimensional synthesis.

A comparative study of multi-tentacled underwater robot with different self-steering behaviors: Maneuvering and cruising modes

Based on the concept of same structure but different laws, we propose two driving modes, maneuvering and cruising, using multiple tentacles of cephalopods as biomimetic prototypes. These two modes are distinguished by transient or continuous kinematic laws and can achieve self-steering behaviors with different features. The computational evolution process between this underwater robot and the flow field is solved on the OpenFOAM platform. We nest the secondary developed solver with dynamic overlapping mesh technology and integrate multiple functional modules. The numerical results show that for the maneuvering mode, the robot achieves rapid turning by collectively generating high-intensity pressure and vorticity fields during the upstroke of tentacles. This mode is suitable for application scenarios that require real-time direction adjustment, such as obstacle avoidance and emergency response. For the cruising mode, the robot relies on continuous asymmetric swing of their tentacles to generate stable yaw moment, and the navigation trajectory presents a fan-shaped pattern with serrated edges. This mode is suitable for purposeful application scenarios such as anti-interference stability and advance prediction.

Toward aerodynamic surrogate modeling based on β-variational autoencoders

Surrogate models that combine dimensionality reduction and regression techniques are essential to reduce the need for costly high-fidelity computational fluid dynamics data. New approaches using β-variational autoencoder (β-VAE) architectures have shown promise in obtaining high-quality low-dimensional representations of high-dimensional flow data while enabling physical interpretation of their latent spaces. We propose a surrogate model based on latent space regression to predict pressure distributions on a transonic wing given the flight conditions: Mach number and angle of attack. The β-VAE model, enhanced with principal component analysis (PCA), maps high-dimensional data to a low-dimensional latent space, showing a direct correlation with flight conditions. Regularization through β requires careful tuning to improve overall performance, while PCA preprocessing helps to construct an effective latent space, improving autoencoder training and performance. Gaussian process regression is used to predict latent space variables from flight conditions, showing robust behavior independent of β, and the decoder reconstructs the high-dimensional pressure field data. This pipeline provides insight into unexplored flight conditions. Furthermore, a fine-tuning process of the decoder further refines the model, reducing the dependence on β and enhancing accuracy. Structured latent space, robust regression performance, and significant improvements in fine-tuning collectively create a highly accurate and efficient surrogate model. Our methodology demonstrates the effectiveness of β-VAEs for aerodynamic surrogate modeling, offering a rapid, cost-effective, and reliable alternative for aerodynamic data prediction.

Comparative analysis of Zero Pressure Geometry and prestress methods in cardiovascular Fluid-Structure Interaction

Background and Objective:Modelling patient-specific aortic biomechanics with advanced computational techniques, such as Fluid–Structure Interaction (FSI), can be crucial to provide effective decision-making indices to enhance current clinical practices. To effectively simulate Ascending Thoracic Aortic Aneurysms (ATAA), the stress-free configuration must be defined. The Zero Pressure Geometry (ZPG) and the Prestress Tensor (PT) are two of the main approaches to tackle this issue. However, their impact on the numerical results is yet to be analysed. Computed Tomography Angiography (CTA) and Magnetic Resonance Imaging (MRI) data were used to develop patient-specific 2-way FSI frameworks. Methods:Three models were developed considering different tissue prestressing approaches to account for the reference configuration and their numerical results were compared. The selected approaches were: (i) ZPG, (ii) PT and (iii) a combination of the PT approach with a regional mapping of material properties (PTCAL). Results:The pressure fields estimated by all models were equivalent. The estimation of Wall Shear Stress (WSS) based metrics revealed good correspondence between all models except the Relative Residence Time (RRT). Regarding ATAA wall mechanics, the proposed extension to the PT approach presented a closer agreement with the ZPG model than its counterpart. Additionally, the PT and PTCAL approaches required around 60% fewer iterations to achieve cycle-to-cycle convergence than the ZPG algorithm. Conclusion:Using a regional mapping of material properties in combination with the PT method presented a better correspondence with the ZPG approach. The outcomes of this study can pave the way for advancing the accuracy and convergence of ATAA numerical models using the PT methodology.

Characterizing surface pressure and wind fields of typhoons approaching Hong Kong

In this paper, 17 severe typhoons that have affected Hong Kong are simulated using an advanced numerical atmospheric simulation system - Weather Research and Forecasting model (WRF). The simulated surface pressure and wind fields of these typhoons are validated against a wide range of field observations. Then azimuth-dependent models for the radius of maximum winds and the Holland parameter are established statistically at the surface level. It is observed that the shape parameter of the Holland pressure model is smaller at the surface than that at the gradient level. And the Holland wind field model cannot well reproduce the simulated radial wind profiles due to the complexities of nonuniform surface conditions and typhoon dynamics. It is found that the modified Rankine model provides satisfactory estimates of typhoon wind speeds in Hong Kong. Additionally, wind field asymmetries of typhoons approaching Hong Kong are highly correlated with the typhoon track velocity, vertical wind shear and the angle between them. The proposed statistical models and identified characteristics of wind field asymmetries of typhoons will provide useful information for rapidly assessing typhoon wind hazards.

Mesh topology-based spurious pressure stabilization in 3D finite elasticity using Voronoi tessellations

AbstractIn this paper, we present a mesh topology-based stabilization approach to suppress spurious pressure modes in 3D nearly-incompressible finite elasticity. The focus lies on a mixed formulation with lowest-order approximation for the displacement and pressure fields. Motivated by the fact that the popular H1/P0 element does not fulfill the inf-sup condition, all possible local spurious pressure modes are derived on a patch of elements. The nullspace method is used to determine all spurious pressure solutions. From this, the topological requirements of the finite element mesh are established. We conclude that no more than four elements are allowed to intersect in the same vertex to overcome local checkerboarding. To fulfill this requirement, we employ non-degenerate 3D Voronoi diagrams with several different site distributions. These result in random, centroidal, and honeycomb Voronoi meshes. The resulting convex polyhedral elements are discretized by a polyhedral mixed finite element based on the lowest possible interpolation pair. The numerical examples illustrate that spurious pressure modes do not occur for any degree of mesh refinement as long as the topological mesh requirements are met. Furthermore, it is shown that the numerical inf-sup test is passed. By violating the topological requirements, it is shown that a stable pressure field cannot be guaranteed and the checkerboard phenomenon is provoked.