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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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18 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

In tube condensation of low global warming potential refrigerants in an axial micro-fin aluminum tube

Environmental regulations have driven the development of refrigerants with low global warming potential (GWP). To design heat exchangers using these new refrigerants, data are needed concerning the heat transfer coefficient and pressure drop in two-phase flow. Another change is the increasing use of aluminum tubes rather than copper tubes to reduce heat exchanger cost. Hence, this study presents an experimental investigation of flow condensation using an expanded axial micro-fin aluminum tube with a fin-tip diameter of 5.96 mm. Here, the experiments included single compounds R-32, R-1234yf, and R-1234ze(E), zeotropic mixtures with low glide (R-454B), and zeotropic mixtures with high-glide (R-454C and R-455A). Experiments were conducted at condensation temperatures ranging from 40 °C to 50 °C, reduced pressures ranging from 0.21 to 0.55, and mass fluxes ranging from 150 to 350 kg/(m 2 s). Data obtained for these refrigerants constitute one of the first reports for high-glide refrigerants using axial micro-fin aluminum tubes. An evaluation of heat transfer degradation of zeotropic mixtures due to mass transfer resistance at the liquid/vapor interface is presented. This information can be used to design heat exchangers for next generation air conditioning and refrigeration systems.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

FY-24 Progress on Computational Modeling of the Water Based NSTF

This report summarizes the computational modeling of the Natural Convection Shutdown Heat Removal Test Facility (NSTF) completed in FY24. This year’s modeling campaign focuses on the continual testing of the RELAP5 model against experimental data. Several fault cases were simulated with the RELAP5 model in FY23 to study the accuracy of the model under complex flow conditions. Similarly, in FY24, a case is simulated where the chimney outlet is throttled with a valve while the flow is undergoing two-phase oscillations. The purpose of this case is to study the effects of increasing pressure drop in the two-phase region on the system behavior. Even though the model is able to capture the experimental data qualitatively, it overpredicts the pressure drops experienced by the flow in the two-phase regime. Nevertheless, the model and the experiment show that oscillations are stabilized with increased pressure drop in the two-phase region.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Extension of Clad Damage Propagation Model for Fission Gas Dispersal and Two-Phase Flow Effects in MOOSE SubChannel Module

This report presents an extension of the Clad Damage Propagation (CDAP) model implemented in the MOOSE SubChannel Module (SCM) to capture post-failure fission-gas dispersal and two-phase flow effects in sodium-cooled fast reactor assemblies. The extended model tracks discharged gas axially and radially, computes channel-averaged flow quality and void fraction using a Lockhart–Martinelli framework, evaluates two-phase frictional pressure-drop multipliers, determines inlet mass-flow degradation under fixed core pressures, and applies an intensified-void-based heat-transfer degradation to affected fuel pins. Radial plume expansion is parameterized using mineral-oil jet experiments mapped to sodium conditions via Reynolds–Weber similarity. Implementation details are documented, along with the new methods and user inputs needed to control plume mapping and two-phase behavior. Demonstration simulations for 19- and 37-pin bundles show that breach size and inlet velocity strongly influence propagation potential: small breaches (≤0.5 mm) produce limited degradation while larger breaches (~1 mm) can drive oscillatory temperature spikes and enhanced failure propagation, especially at higher velocities. These results demonstrate that the extended CDAP model provides a more complete framework for quantifying cladding damage propagation and evaluating propagation potential in transient scenarios. The approach remains computationally efficient, consistent with subchannel-level analysis, yet incorporates sufficient physics to bridge localized post-failure effects with bundle- and assembly-scale degradation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

CTF Improved Drag Model and Flow Regime Transition Criteria

The demand for accurate prediction of two-phase flow behavior in a boiling water reactor (BWR) requires a comprehensive understanding of flow regime, void fraction, heat transfer, and pressure drop. The CTF subchannel code, which is used for the Thermal/Hydraulic (T/H) solution in the Consortium for Advanced Simulation of Light Water Reactors (CASL)-developed Virtual Environment for Reactor Application (VERA) core simulator, is being further developed for BWR applications. In support of this goal, the present work highlights some of the two-phase closure model developments towards improving the CTF void fraction prediction, especially for subcooled boiling. The drift-flux approach has been well-developed for upward dispersed two-phase flows and proven to be accurate in predicting void fraction in bubbly and slug flow regimes. In this work, these kinematic constitutive relations for the drift-flux velocity have been implemented into CTF to describe the interfacial drag of bubbly flow as an alternative to the existing model for better void fraction prediction. The success of these constitutive relations also relies on a good flow regime map that accounts for flow conditions and channel geometry. A more reliable flow regime transition criteria that account for the flow condition has also been implemented in this study for modeling the flow regime transition criteria. The newly implemented models are shown to give improved void fraction predictions in comparison to experimental data.

Hizoum, Belgacem↗
DOE OSTI2026

Flow Boiling Pressure Drop Characteristics of Next-generation Refrigerants in a Micro‑fin Copper Tube

This paper presents experimental frictional pressure-drop data for flow boiling of R-410A, R-134a, and next-generation alternatives R-454C, R-455A, R-1234yf, and R-1234ze(E) in a horizontal micro-fin copper tube. Tests were conducted over a range of mass fluxes and evaporation temperatures to characterize refrigerant-dependent two-phase pressure-drop behavior. The results show that frictional pressure gradient increased with mass flux and vapor quality and generally increased as evaporation temperature decreased, with liquid viscosity strongly affecting the observed trends. Among the evaluated correlations, the Goto et al. (2001) model gave the best overall agreement with the measurements before optimization. Further optimization of the Kuo and Wang (1996) and Goto et al. (2001) models reduced the overall mean absolute deviation to below 15%, with the optimized Goto (2001) model providing the most consistent predictions across all six refrigerants. The results support improved pressure-drop prediction and evaporator design for next-generation refrigerants in micro-fin tubes.

Hu, Yifeng [ORNL] (ORCID:0000000242875185)↗
DOE OSTI2022

Loop Thermosyphon Enhanced Solar Collector

A two-phase loop thermosyphon solar collector was developed to transfer thermal energy efficiently and passively from a concentrated solar collector to a thermal desalination process. The two-phase flow in the loop thermosyphon is driven by a difference in gravitational pressure head between the liquid return line and the two-phase riser located between the evaporator and condenser. A numerical model incorporating mass, energy, and pressure drop balances was developed to predict system performance and use as a design tool. Three iterations of loop thermosyphon solar collectors were designed, fabricated, and tested to validate the numerical analysis and demonstrate system integration. Additionally, a novel solar receiver design was evaluated based on volumetric absorption of the concentrated sunlight by an optically absorptive two-phase working fluid. Life tests were performed to evaluate the working fluid thermal stability and resistance to ultraviolet degradation. A glass receiver tube and associated glass-to-metal junctions were developed. Finally, a full-scale loop thermosyphon was integrated with a parabolic trough solar collector and tested on-sun.

14 SOLAR ENERGY↗
DOE OSTI2026

Flow pattern and void fraction characterization in nitrogen/water flows through a diamond-type triply periodic minimal surface lattice

Here, this study presents, to the authors knowledge, the first experimental investigation on the void fraction and flow patterns in two-phase flows through a diamond-type Triply Periodic Minimal Surface (TPMS) lattice. An additively manufactured TPMS structure was tested under upward co-current flow of a water/nitrogen mixture. Superficial velocities varied for a total of 42 test conditions (gas: 0.01–2.4 m/s; liquid: 0.01–2.4 m/s; mass flux: 20–2370 kg/m 2 ·s). High-speed video and X-ray imaging enabled time-averaged void fraction measurements and identified six distinct flow regimes which were used to develop a flow pattern map. Comparison of the void fraction data with correlations from literature demonstrated the Rouhani and Axelsson (1970) [49] correlation modified by Steiner (1993) [52] provided the best agreement, which was improved with empirically fit coefficients. This approach predicted the void fraction with errors < ±20% for 64% of the data, with a mean absolute percent deviation (MAPD) of 23%. The measured frictional pressure drop was compared to correlations from literature which captured the observed trends but did not provide good accuracy. The best agreement was found after optimizing the empirical coefficients of the Muller-Steinhagen & Heck (1986) [56] correlation; this approach captured 33% of the data within ±20% with a MAPD of 46% over the full range and captured 71% of the data within ±20% a MAPD of 13.3% at mass fluxes >1100 kg/m 2 -s. These results provide foundational insight into TPMS two-phase flow behavior and inform modeling and design of advanced heat exchange components incorporating TPMS geometries.

42 - ENGINEERING↗
DOE OSTI2024

Design and Manufacturing of High Performance, Reduced Charge Heat Exchangers

Air-to-fluid heat exchangers (HXs) play a critical role as the main heat transfer component in Heating, Ventilation, Air-Conditioning, and Refrigeration (HVAC&R) systems. However, their airside thermal resistance significantly inhibits their overall performance. Furthermore, these HXs must be continually more compact to meet the latest refrigerant charge limits to reduce emissions. Recent literature suggests that traditional HX geometries (e.g., round or flat tubes with fins), have reached their limits, and more sophisticated shape- and topology-optimized designs are required to achieve the next jump in performance. This research sheds light on the next generation of air-to-refrigerant HXs and aims to address several practical issues to commercialization such as novelty challenges (improved performance for significant charge reduction; modeling expertise & time investment), manufacturing challenges (non-round tube manufacturing; tube-header integration; product qualification, e.g., burst pressure testing, extreme operational environment, etc.), and operational challenges (flow maldistribution, fouling & wetting, noise & vibration). For example, a >20% improvement on one (or more) HX-level performance metrics (e.g., envelope volume, airside pressure drop, face area, capacity, refrigerant charge, weight, cost, etc.) must be achieved before a HX design is considered for commercialization. We present a new, comprehensive and experimentally validated air-to-refrigerant HX optimization framework with simultaneous thermal-hydraulic performance and mechanical strength considerations for novel, non-round, shape- and topology-optimized tubes capable of optimizing single and two-phase HX designs for any refrigerant choice and performance requirement with significant engineering time savings compared to conventional design practices. The framework was exercised for a wide range of applications and refrigerants, resulting in HXs which achieved greater than 20% improved performance, 20% reductions in size, and 25% reductions in refrigerant charge. To enable non-round tube bundle use in next generation HVAC&R equipment, novel manufacturing techniques were investigated, including the development of conventional manufacturing methods for small diameter, non-round tubes and novel tube-header integration strategies. In total, ten HX prototypes were manufactured, nine using conventional methods directly attributed to this project and one using advanced additive manufacturing methods. The five-year manufacturing feasibility of the proposed HXs was found to have a good outlook. The non-round tube HX simulated performance was validated through comprehensive experimental testing, including nine in-house component-level tests, one independent component-level test at an industry partner laboratory, and in-house system-level tests of using a commercially-available, residential packaged A/C unit which was retrofitted with a non-round tube prototype HX. It was found that HX designs proposed by the new framework can successfully predict experimental thermal-hydraulic performance within ±10-20% the first time with no manual design changes, eliminating the need for time-consuming and expensive prototyping efforts. This work will accelerate design and time to market for next generation HXs while simultaneously facilitating industry transition to new refrigerants at lower charge.

42 ENGINEERING↗
DOE OSTI2022

Flow Boiling Heat Transfer Characteristics of Water for Metal-foam-filled Horizontal Tubes

The goal of this paper is to enhance the in-tube flow boiling heat transfer of water while accounting for potential increase in pressure drop. Metal foams are a class of cellular structure with large surface-area-to-volume ratio and tortuous structure which has shown promising results for various energy conversion and storage applications. The higher heat transfer area and higher nucleation sites density due to the porous media can effectively enhance the heat transfer of water in both single-phase and two-phase operations. This paper presents the local heat transfer and pressure drop measurements of water in a partially metal-foam-filled horizontal copper tube. The ranges of parameters in the experiments are: mass flux from 80 to 200 kg/s-m2, heat flux from 3.5 to 105 kW/m2, and vapor quality from subcooled to 0.3. The results in the metal-foam-filled tube are compared with that of the bare copper tube. The effect of metal foam on the thermal hydraulic characteristics is discussed and analyzed. In addition, the two-phase flow behavior in a transparent tube filled with the same metal foam was visualized and investigated by high-speed imaging system. The experiments were also conducted in the tube without the metal foam for comparison.

Nawaz, Kashif↗
DOE OSTI2022

Sockeye Heat Pipe Analysis Code Verification and Validation

Some of the most promising microreactor designs currently under development utilize heat pipe technology to transfer heat from the reactor core to the secondary side heat exchanger, due to the technology’s compactness, efficiency, passivity, and reliability. Sockeye is an engineering-scale heat pipe tool developed under the Nuclear Energy Advanced Modeling and Simulation Program to be used for the design and safety analysis of microreactors. Sockeye’s core capability lies in a 1D, two-phase, compressible flow model, used to simulate the working fluid inside the heat pipe. Sockeye is built on the Multiphysics Object-Oriented Simulation Environment framework, which allows for seamless multiphysics coupling with other Nuclear Energy Advanced Modeling and Simulation tools and can thus be used in a full-scale simulation of a microreactor assembly, which can include hundreds of heat pipes. This paper presents some initial verification and validation assessments performed for Sockeye. We demonstrate good agreement between Sockeye’s numerical results and steady-state analytic solutions for velocity and pressure drop, with differences attributable to the underlying assumptions made by the analytic solutions. We also show that Sockeye reproduces analytic predictions of key operational limits, such as the capillary limit and the sonic limit. Finally, we compare Sockeye results to experimental data for the SAFE-30 heat pipe module test.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Flow maldistribution in plate heat exchangers – Impact, analysis, and solutions

Plate heat exchangers are commonly used in various industrial applications, such as refrigeration, air conditioning, heat pumps, powerplants, and chemical industries. Plate heat exchangers are well known for their superior heat transfer performance, compactness, and low refrigerant charge. Despite offering several advantages, they suffer from flow maldistribution issues. The flow maldistribution can deteriorate both the heat transfer and pressure drop performance, ultimately resulting in a lower system efficiency where plate heat exchangers are deployed. The flow maldistribution issues become more pronounced when the heat exchanger size is relatively large and the number of plates is higher, limiting the deployment of plate heat exchangers in larger industrial systems. Consequently, analyzing and understanding the flow maldistribution behavior in plate heat exchangers and finding ways to mitigate flow maldistribution related issues become essential topics of interest. Further, this review aims to address the effect of flow maldistribution on plate heat exchanger characteristics. First, the experimental and numerical works on flow maldistribution under single-phase and two-phase conditions are detailed. Subsequently, the end-channel and end-plate effects are discussed. Then, the methods to mitigate flow maldistribution in plate heat exchangers are outlined. Finally, based on a thorough literature survey and industrial requirements, future research directions are recommended.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

Holistic energy analysis method for thermal management architectures of data centers

Modern high-performance computing (HPC) data centers (DCs), particularly those supporting energy-intensive artificial intelligence (AI) workloads, face escalating thermal management challenges that degrade performance through thermal throttling and drive up cooling power consumption and operational costs. To address this challenge, many have developed a wide variety of thermal management solutions (single-phase, two-phase, direct, indirect, hybrid, and more) which attempt to cool HPC DCs effectively while attempting to minimize overall system power consumption. However, the analysis of these solutions and methods to effectively compare one with another is lacking. Overall power usage effectiveness (PUE) and total-power usage effectiveness (TUE) provide a metric to quantify power consumption but fail to identify components in the system which require further optimization. To address this, we propose a holistic analytical framework – the waterfall diagram (WFD) – which leverages a waterfall chart methodology, offering a comprehensive visualization of both the thermal management system loop and heat flow pathways from individual server components to the outdoor ambient. Use of the WFD enables graphical estimations of power efficiency and cooling performance across each component of a DC cooling system and complements Sankey-style energy flow visualizations by additionally resolving stage-wise temperature changes and incremental TUE contributions. The framework is used in conjunction with simulation-based approaches, to conduct a detailed pressure drop and flow distribution analysis aimed at identifying the optimal coolant distribution architecture for a single-phase direct-to-chip water-cooled DC, which serves as the baseline for subsequent WFD analysis. Among the evaluated architectures, the 3 U modular coolant distribution architecture is found to demonstrate the best performance, considering minimal pressure drop and uniform flow distribution. In addition, TUE is calculated for each cooling loop component based on its associated pressure drop and corresponding pumping power, which are integrated into the WFD. This correlation between TUE and local temperature offers immediate insight into the power efficiency and thermal performance contributions of individual components, facilitating further development and optimization. Examples of WFD applications are presented under varying thermal loads and ambient conditions, demonstrating reasonable cooling strategies. Notably, the 3 U modular architecture maintains a consistent chip case temperature of 85°C, achieving a TUE of 1.016 at ambient temperature of 47°C, and a TUE of 1.026 at ambient temperature of 52°C. The WFD methodology provides an efficient, holistic, and streamlined framework for DC thermal management architecture assessment and enables design optimization which is important for addressing the thermal-fluidic energy challenges of current and next-generation DCs.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Flow Instabilities in boiling channels and their suppression methodologies—A review

Small modular reactors (SMRs) are gaining significant attention as a promising solution for clean and sustainable nuclear-power generation. However, the operation of SMRs is subject to various challenges, including two-phase flow instabilities. Flow instability has the potential to trigger flow-induced vibration and cyclic fluctuations in local thermal stress. These instabilities frequently manifest because of the complex interplay among a multitude of factors, encompassing thermal-hydraulic conditions, the geometric configuration of the steam generator, and operational parameters. These conditions could subsequently lead to premature critical heat flux, equipment malfunctions, and other safety concerns. Here, the endeavor to address steam-generator flow instabilities is of utmost importance in augmenting the sustainability and efficiency of contemporary energy production. This study offers a comprehensive review of instabilities in two-phase flow, with a particular focus on the influential factors impacting the stability of flow boiling. Furthermore, it delves into the processes of identifying, characterizing, and ameliorating these instabilities, emphasizing pivotal findings, methodologies employed, and avenues for prospective research. The primary parameters of concern encompass the efficient transfer of thermal energy, the optimization of mass-flow rates, and the establishment of favorable boundary conditions, all in the context of steam generator design to alleviate instability for water-cooled SMRs. These discernments bear substantial ramifications for enhancing reactor performance and ensuring operational safety.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Extension of the high-resolution thermal-hydraulics code ESCOT to hexagonal core geometries for multi-physics calculations

The extension of the capabilities of the pin-level nuclear reactor core thermal-hydraulics (T/H) code ESCOT to analyze hexagonal fueled cores and its performance are presented. ESCOT is an accurate yet fast core thermal-hydraulics solution aiming at high-fidelity and high-resolution multi-physics core analysis in the framework of massively parallel computing platforms. Its algorithm solution is based on the four-equation drift-flux model for two-phase calculations, these are numerically solved by applying the Finite Volume Method (FVM) and the Semi-Implicit Method for Pressure-Linked Equation (SIMPLE)-like algorithm in a staggered grid system. Constitutive models such as turbulent mixing, pressure drop, and vapor generation are employed to simulate key phenomena in subchannel-scale analysis. ESCOT is parallelized by a double (radial and axial) domain decomposition that enables its highly parallelized execution. The coupling of the code with the neutronics whole core solver for hexagonal geometries nTRACER is described. The newly implemented ESCOT features are validated by comparing single assembly and full core steady state nTRACER-ESCOT solutions with nTRACER standalone internal one-dimensional T/H solver results. The validation problems are based on the VVER 440 and VVER 1000 cores. ESCOT results show differences within an acceptable range with respect to the simple 1D nTRACER built-in solver. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

Review of heat transfer enhancement techniques in two-phase flows for highly efficient and sustainable cooling

We show that two-phase internal flow is ubiquitous to many systems due to its ability to transfer large amounts of heat effectively. Recent advances motivated by sustainability have pushed towards augmenting the heat transfer between the tube and the two-phase working fluid. Augmenting heat transfer in two-phase flows enables process intensification, and compactness leading to reduced cost and material consumption. This review investigates the effect of heat transfer enhancement techniques on different fluids including R134a, R407C, R22, etc … The techniques are categorized into passive and active and focus on durable enhancement methods which do not include surface structuring or coating. Passive techniques utilize geometrical and surface modifications to induce better mixing. Several passive techniques are analyzed including fins, inserts, and more. In analyzing these techniques, the effect of changing geometric parameters is studied, and the limitations are highlighted. Further, active techniques that enable heat transfer enhancement through applying power are also investigated. Electrohydrodynamic approaches are analyzed and compared to passive techniques. Additionally, the implications of heat exchange enhancement in the context of global energy are discussed. An energy analysis discretized by the use sector is conducted, with an emphasis on predicting the future potential for renewable and sustainable development. Moreover, although active approaches provide the highest heat transfer enhancement, due to implementation difficulties, passive techniques are more frequently adopted. The review ends with discussion of next-generation heat exchangers which will rely more on additive manufacturing due to its flexibility and reduced cost per part as the technology matures.

Nusselt number↗
DOE OSTI2021

X-ray Imaging-Based Void Fraction Measurement in Saturated Flow Boiling Experiments with Seawater Coolant

Recent studies have shown that the presence of dissolved salts in water can exhibit peculiar flow boiling and two-phase flow regimes. Two-phase flow and convective flow boiling are typically characterized with the help of void fraction measurements. To quantitatively improve our understanding of two-phase flow and boiling phenomenon with seawater coolant, void fraction data are needed, which can not be obtained from optical imaging. In this paper, we present experimental void fraction measurements of saturated flow boiling of tap water and seawater using X-ray radiography. X-rays with a maximum energy level of 40 KeV were used for imaging the exit region of the heated test section. At lower heat flux levels, the two phase flow in seawater was bubbly and homogeneous in nature, resulting in higher void fractions as compared to tap water. With an increase in heat flux, the flow regime was similar to slug flow, and void fraction measurements approached similarity with tap water. The predicted pressure drop using the measured void faction shows good agreement with the measured total pressure drop across the test section, demonstrating the validity of the measurement process.

Eckels, Seth↗
DOE OSTI2021

Evaluating the Feasibility of Measuring and Analyzing Strain Caused by Changes in Barometric Pressure in the Vadose Zone

Changes in barometric pressure propagate into the subsurface where they can affect water level measurements in wells and cause vertical strain. Previous strain sensors were developed to measure vertical strain, but they were limited to measurements at a single depth, making it difficult to evaluate strains from a migrating pressure wave. Technology known as Coherence-length-gated Microwave Photonics Interferometry (CMPI) uses optical fiber sensors to measure strain at multiple locations. It has the potential to detect strain caused by variations in barometric pressure at multiple depths in the subsurface. The goal of this study is to evaluate the feasibility of using this technology to record the changes in vertical strain in the vadose zone from small fluctuations in air pressure. Propagation of these air pressure fluctuations is affected by hydrogeological properties such as water content and permeability. A second goal of this study is to evaluate how these properties affect the air pressure distribution, strain, and gas-phase diffusivity with a long-term goal of using strain to monitor the vadose zone. The focus of this study is on a suite of laboratory experiments that used a sand-filled column with an open head space. The CMPI fiber was packaged and embedded along the axis of the column to measure the strain at multiple locations while air pressure transducers were installed through the wall of the column. Small periodic fluctuations in air pressure, similar to barometric pressure fluctuations, were created in the head space of the column using an audio driven speaker driven at 4 Hz using a sinusoidal signal created by a function generator. Then, the fluctuations propagated along the column where they were measured by the transducers and recorded as functions of time. Initial tests were conducted using dry sand, but then additional tests were conducted after injecting water into the column, which changed the hydrologic and mechanical properties. Another experiment was conducted after creating a thin barrier to air flow, which was designed to simulate a thin layer of saturated ground during rainfall. A final experiment was conducted by changing the grain size of the material to create a heterogeneity in the upper half of the column. The suite of six experiments was conducted to highlight effects of variations in water content and heterogeneities on air pressure and vertical strain. Numerical simulations were also created to evaluate the laboratory data and to provide a baseline analysis for the results. The numerical simulations used the governing equations to linear poroelasticity and two-phase flow with boundary conditions representing the experiments. The conceptual model for strain caused by barometric pressure recognizes that a fluctuating barometric pressure causes fluctuations in the air pore pressure that decrease in amplitude and lag in time with increase depth. The pressure distribution results in two different loads that cause strain: 1.) a mechanical load as the barometric pressure acts on the ground surface; and 2.) pressure loading in the pore space. The results show that the total vertical strain is a contribution of both of these loads, and this is the strain that was observed in the laboratory. The lab experiments show that both air pressure and strain vary as sinusoids that propagate with depth. The amplitude of the air pressure and strain decrease as a function of depth in all the conditions that were evaluate. For example, in the dry sand, the amplitude of the air pressure decreases from 25 Pa at the head space to 5 Pa at a depth of 70 cm, whereas the amplitude of the strain decreases from 0.15 to 0.06 µε over the same depth interval. In many cases the amplitudes decrease is approximately negative exponential functions of depth. When water was injected into the sand and the saturation increased, the amplitude of the air pressure increased in the partially saturated sand but decreased sharply to zero where the soil was saturated. The strain decreased with depth, but the transition from partially to fully saturated conditions had little effect on the strain profile, even though it had a major effect on the air pressure. This apparently is because strain is caused by variations in both water and air pressure. The fluctuating air pressure caused the water pressure to fluctuate, which caused strain throughout the column. Phase delay of the air pressure and the strain both increase as linear to bi-linear functions of depth. The phase delays indicate that pressure propagates at a velocity of 7 to 8 m/s in dry or partially saturated sand, but it drops by more than an order of magnitude in the vicinity of the capillary fringe. The phase delays indicate the strain propagates faster than the pressure. The data indicate that the strain propagates from 1.2 to more than 4x faster than the pressure. Switching from sand to silt in the column caused the velocity of the pressure to drop by roughly half for both pressures, but curiously, it had little effect on the velocity of the strain.

54 ENVIRONMENTAL SCIENCES↗