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At least 595 records · Page 33

Low-frequency dynamics of quasi-geostrophic waves in a midlatitude channel and the effects of tropical influence

Both zonal mean flow and stationary waves in the stratosphere have large variabilities from month to month and from year to year. One plausible mechanism that can account for these variabilities is the interaction between the forced stationary waves and the mean zonal flow. Given the large energy source contained in the stationary waves which are forced in the lower atmosphere, they are probably responsible for inducing the bulk of the variability in the mean flow in the stratosphere. Variability in the mean flow can in turn produce variability in the stationary wave amplitudes due to the possible sensitivity of wave response in the stratosphere to the configuration of the wave guide determined by the mean flow. The likely causes for the low-frequency variability of the stationary waves-mean flow system in extratropical latitudes are assessed. The causes of variability are divided into internal and external ones. Internal mechanisms include transition between equilibria and vacillation cycles, while mechanisms external to the midlatitude system include eddy heat and momentum fluxes from the tropics and the Hadley circulation forced in the tropics.

Tung, K. K.↗

The effects of forced air flow and oxygen concentration on flammability, smoke density, and pyrolytic toxicity

The question is posed whether forced air flow should be incorporated into flammability tests as a relevant variable. A test apparatus is described which permits tests to be conducted on small test specimens in a forced flow which is (continuously) variable over flow velocities from zero to 300 feet per minute (1.52 m/s). The effects of air-flow rate and oxygen concentration on flame propagation rate, maximum smoke density, and pyrolytic product toxicity were measured for a single material and were statistically evaluated. Regression analysis was used to graph the resulting relationships. It is concluded that air velocity is an important variable for laboratory flammability testing.

Sauers, D. G.↗

Correlation of boundary layer quantities for hypersonic laminar flows with zero pressure gradient for several gases

The laminar boundary layer has been theoretically studied for six gases for flows over cold walls with zero pressure gradient at Mach numbers between 5.5 and 12.5 to correlate boundary layer quantities for the various gases. The flow conditions considered correspond to those that can be generated in test facilities such as the shock tunnel and the expansion tube. Computed results obtained using real gas properties indicate that the Eckert number based on edge conditions serves to correlate the results in terms of the wall shear stress and enthalpy gradient, the Stanton number, and the momentum thickness for the various gases within plus or minus 10 per cent for Te = Tw and Te approximately 3Tw. Computed Reynolds analogy factors exhibit very good agreement with those predicted by the Colburn analogy. Velocity and displacement thicknesses correlate well with Eckert number for Te = Tw, but fail to correlate for Te approximately 3Tw. Differences in results are traced to property variations. Results show that the Eckert number is a significant correlating variable for the flows considered.

Cook, W. J.↗

Perceived Noise Analysis for Offset Jets Applied to Commercial Supersonic Aircraft

A systems analysis was performed with experimental jet noise data, engine/aircraft performance codes and aircraft noise prediction codes to assess takeoff noise levels and mission range for conceptual supersonic commercial aircraft. A parametric study was done to identify viable engine cycles that meet NASA's N+2 goals for noise and performance. Model scale data from offset jets were used as input to the aircraft noise prediction code to determine the expected sound levels for the lateral certification point where jet noise dominates over all other noise sources. The noise predictions were used to determine the optimal orientation of the offset nozzles to minimize the noise at the lateral microphone location. An alternative takeoff procedure called "programmed lapse rate" was evaluated for noise reduction benefits. Results show there are two types of engines that provide acceptable mission range performance; one is a conventional mixed-flow turbofan and the other is a three-stream variable-cycle engine. Separate flow offset nozzles reduce the noise directed toward the thicker side of the outer flow stream, but have less benefit as the core nozzle pressure ratio is reduced. At the systems level for a three-engine N+2 aircraft with full throttle takeoff, there is a 1.4 EPNdB margin to Chapter 3 noise regulations predicted for the lateral certification point (assuming jet noise dominates). With a 10% reduction in thrust just after clearing the runway, the margin increases to 5.5 EPNdB. Margins to Chapter 4 and Chapter 14 levels will depend on the cumulative split between the three certification points, but it appears that low specific thrust engines with a 10% reduction in thrust (programmed lapse rate) can come close to meeting Chapter 14 noise levels. Further noise reduction is possible with engine oversizing and derated takeoff, but more detailed mission studies are needed to investigate the range impacts as well as the practical limits for safety and takeoff regulations.

Turbofans↗

A wave-envelope of sound propagation in nonuniform circular ducts with compressible mean flows

An acoustic theory is developed to determine the sound transmission and attenuation through an infinite, hard-walled or lined circular duct carrying compressible, sheared, mean flows and having a variable cross section. The theory is applicable to large as well as small axial variations, as long as the mean flow does not separate. The technique is based on solving for the envelopes of the quasi-parallel acoustic modes that exist in the duct instead of solving for the actual wave, thereby reducing the computation time and the round-off error encountered in purely numerical techniques. The solution recovers the solution based on the method of multiple scales for slowly varying duct geometry. A computer program was developed based on the wave-envelope analysis for general mean flows. Results are presented for the reflection and transmission coefficients as well as the acoustic pressure distributions for a number of conditions: both straight and variable area ducts with and without liners and mean flows from very low to high subsonic speeds are considered.

Nayfeh, A. H.↗

The MOOSE fluid properties module

The fluid properties module in MOOSE~\cite{lindsay2022moose} serves a variety of fluid simulation applications based on MOOSE, including the MOOSE Navier Stokes module~\cite{moose_ns}, Pronghorn~\cite{pgh}, the MOOSE thermal hydraulics module, SAM~\cite{sam}, RELAP-7~\cite{relap7}, Sockeye~\cite{sockeye}, Pronghorn-subchannel~\cite{subchannel} and the MOOSE porous flow module~\cite{porous}. These applications are used to solve coarse mesh multi-dimensional thermal-hydraulics~\cite{pgh}, 1D systems analysis~\cite{sam,relap7} in nuclear reactor analysis, heat pipe modeling~\cite{sockeye} and porous flow simulations~\cite{porous} for underground gas storage and water seepage. The use of consistent fluid properties across fluid flow applications facilitates coupled flow simulations~\cite{anl_sam_pgh,osti_1889653}. Each application has historically driven the implementation of several fluid properties, which were later extended to be compatible with other applications. The unique diversity of applications of the module, due to its presence in MOOSE, has driven its expansion to new fluids, such as advanced nuclear reactor coolants and, more recently, arbitrary functions or tables-based property definitions, as detailed in section~\ref{content}, as well as numerous thermophysical properties and variable sets, as detailed in subsection~\ref{sec:prop}. The need for different discretizations of flow equations based on the compressibility of the fluid has motivated support for both primitive (pressure- and temperature-based) and conservative (internal energy- and specific volume-based) flow variables in the module. Thermodynamic relations are used to convert between these two formulations, as needed. The module serves a dual purpose of providing fluid properties for direct use in flow simulations and facilitating the implementation of user-specific fluid properties. Contributions of new properties for existing fluids or new fluids are strongly encouraged.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

A provisional analysis of two-dimensional turbulent mixing with variable density

A predictive method for the titled flows based on the Prandtl energy method was developed and assessed by comparing predicted results with experimental results. For constant-density flows, both gross properties such as spreading rate and maximum turbulent kinetic energy and detailed properties such as mean shear stress distributions are shown to be well predicted. For variable-density flows, considerable attention is devoted to the inclusion in the analysis of the added effect of pressure fluctuations and of the variation in the several extant empirical parameters on the turbulent kinetic energy. It is found that a variation with Mach number of the characteristic Reynolds number for turbulent transport is needed to account for the observed decrease in spreading rate. The predictions which result from these considerations are compared with the limited experimental data presently available for the two crucial cases: compressible adiabatic mixing and low-speed isothermal mixing of two dissimilar gases.

Libby, P. A.↗

Analytical Model for Steady Flow through a Finite Channel with One Porous Wall with Arbitrary Variable Suction or Injection

This paper presents an exact solution of two-dimensional laminar flow through a finite length channel with one porous wall. It improves upon previous solutions by (1) satisfying the no-slip boundary condition at the channel dead end, (2) adding a turbulent term to the porous wall boundary condition, (3) allowing for arbitrary variable suction or injection across the porous wall, and (4) model validation against new cryogenic liquid hydrogen and oxygen experimental data. Of particular interest in the current work is the modeling of cryogenic propellant flow through a porous liquid acquisition device (LAD) screen and channel inside a propellant tank. First, a detailed review of the literature is presented for previously attempted solutions to channel flow with one porous wall. Next, the governing equations, boundary conditions, and model assumptions are used to derive the analytical flow solution and present general model results for pressure and velocity fields within the channel. Then, the model solution is compared with horizontal LAD channel flow data in liquid oxygen as well as vertical LAD channel flow data in an inverted outflow configuration in liquid hydrogen. Model results are used to update the static cryogenic bubble point pressure model with a dynamic bubble point term which factors in enhanced convection and cooling at the screen during propellant outflow. Convective heat transfer at the LAD screen during outflow is also quantified by comparing model and data. The new analytical flow solution with the dynamic bubble point model is shown to compare well with available cryogenic experimental data

Navier Stokes Equations↗

Effect of including variable gas properties and entrained particles in the flow analysis of the ASRM nozzle

The objective of this study is to determine the effect of using constant gas properties for the analysis of the Advanced Solid Rocket Motor (ASRM) nozzle and to gain more understanding concerning those types of analysis which might require this additional complexity. Kinetics data for viscosity, thermal conductivity, specific heat, and specific heat ratio are extracted from the Solid Propellant Rocket Motor Performance Prediction Computer Program (SPP) and tabulated as a function of temperature. These tables are added to the Aerovisc computational fluid dynamics (CFD) code in place of the constant gas property values. The results of a CFD analysis of the ASRM 48 inch motor with constant gas properties will be compared with an analysis which uses variable gas properties. Mach number, surface pressure, and torque plots are presented. A full scale ASRM analysis using SPP with and without particle flow is presented.

Clayton, Curtis D.↗

A real-time distributed solid oxide electrolysis cell (SOEC) model for cyber-physical simulation

System integration and dynamic operability between SOEC and balance-of-plant (BoP) components are major technical challenges before realizing rapid load following of SOEC systems. Cyber-physical simulation (CPS) is a leading-edge digital engineering approach and is regarded as the next step beyond Digital Twins. CPS approach can be used to research SOEC system integration and develop dynamic controls prior to actual pilot testing without using a real SOEC. To seamlessly couple with BoP hardware and access non-observable operational parameters (e.g., local temperature gradient) during transients, a distributed one-dimensional (1D) real-time SOEC model was developed. Its real-time execution was demonstrated for 20 to 640 nodes at the fixed time step of 5 ms. A higher excess air ratio enabled smaller local temperature gradients on SOEC solid materials and faster transients upon current density step change from 0.15 to 0.55 A cm -2 . During the transients, the magnitude of the peak temperature gradient nearly doubled in 10 s from -3.5 to -5.9 °C cm -1 . This represents a significant operating risk that can impact the dynamic operability of SOEC systems. In addition, the local temperature gradient was found to change directions on all nodes in SOEC solid materials, with the greatest impact on the upstream nodes. The SOEC model was also tested at the thermal neutral voltage using actual process air flow parameters as variable model inputs. Variable process air temperatures were found to induce alternating local temperature gradients on SOEC solid materials. These are new operational mechanisms for SOEC degradation relevant for load following operational modes yet distinct from previous reports. To mitigate these unfavorable features, the SOEC can be operated at voltages that are slightly (±20 mV) deviated from the thermal neutral voltage. Here, the corresponding net thermal energy change was less than 1.6% of the electric power consumption. This 1D real-time SOEC model established the basis of cyber-physical simulation of SOEC hybrid systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A Case Study on Pathogen Transport, Deposition, Evaporation and Transmission: Linking High-Fidelity Computational Fluid Dynamics Simulations to Probability of Infection

A high-fidelity, low-Mach computational fluid dynamics simulation tool that includes evaporating droplets and variable-density turbulent flow coupling is well-suited to ascertain transmission probability and supports risk mitigation methods development for airborne infectious diseases such as COVID-19. A multi-physics large-eddy simulation-based paradigm is used to explore droplet and aerosol pathogen transport from a synthetic cough emanating from a kneeling humanoid. For an outdoor configuration that mimics the recent open-space social distance strategy of San Francisco, maximum primary droplet deposition distances are shown to approach 8.1 m in a moderate wind configuration with the aerosol plume transported in excess of 15 m. In quiescent conditions, the aerosol plume extends to approximately 4 m before the emanating pulsed jet becomes neutrally buoyant. A dose–response model, which is based on previous SARS coronavirus (SARS-CoV) data, is exercised on the high-fidelity aerosol transport database to establish relative risk at eighteen virtual receptor probe locations.

59 BASIC BIOLOGICAL SCIENCES↗

The MOOSE Thermal Hydraulics Module

The Multiphysics Object-Oriented Simulation Environment (MOOSE) is an open-source object-oriented finite element framework written in C++ (Lindsay et al., 2022). The Thermal Hydraulics Module (THM) is an optional MOOSE physics module that provides capabilities for studying thermal hydraulic systems. Its core capability lies in assembling a network of coupled components, for instance, pipes, junctions, and valves. THM provides several new systems to MOOSE to enable and facilitate thermal hydraulic simulations, most notably the Components system, which provides a higher-level syntax to MOOSE’s lower-level objects. This system is extensible by the user, but the current library primarily includes components based on a one-dimensional, single-phase, variable-area, compressible flow model, as well as heat conduction.

42 ENGINEERING↗

Enhanced Control, Optimization, and Integration of Distributed Energy Applications (ECO-IDEA)

With support from the U.S. Department of Energy Solar Energy Technologies Office, the National Renewable Energy Laboratory (NREL) partnered with Xcel Energy, Schneider Electric, Varentec, and Electric Power Research Institute (EPRI) to meet the goals of the Enabling Extreme Real-Time Grid Integration of Solar Energy (ENERGISE) program. This project developed and validated an innovative data-enhanced hierarchical control architecture that enables the efficient, reliable, resilient, and secure operation of future distribution systems with a high penetration of distributed energy resources like solar energy. The architecture enables a hybrid control approach where a centralized control layer is complemented by distributed control algorithms for solar inverters and autonomous control of grid edge devices. It is fully interoperable and includes all the cybersecurity aspects necessary for reliable and secure system operation. The hybrid approach can seamlessly integrate multiple voltage-regulation technologies, both at central and grid-edge levels, which enables reliable and efficient system operation in the face of unpredictable conditions. The overarching goal of the Eco-Idea project is to develop, validate, and deploy a unique and innovative Data-Enhanced Hierarchical Control (DEHC) architecture that comprehensively addresses the formidable challenges associated with proliferation of high penetration of distributed PV such as reverse power flows, transients from variability of PV systems, feeder load balancing, and voltage stability. These issues are exposing the weaknesses of existing grid operations and controls - including, but not limited to, lack of grid situational awareness, heuristic and slow-acting control actions, latency of control for emergency situations, and points of failure in communications. The proposed architecture will comprehensively resolve the deficiencies of current operational settings - where monitoring and control solutions proposed across industry and academia may not be interoperable and may not coexist in the same system - and will enable an efficient, reliable, resilient, and secure operation of future distribution systems with penetration of solar energy well beyond current limits. The DEHC architecture was developed and validated rigorously through hardware-in-loop simulations in the laboratory environment and deployed on the field.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Analysis of HolosGen Sub-Scale Simulator with Plant Dynamics Code

The Subcritical Power Module Sub-scale Simulator (SPM-SS) has been designed and constructed by HolosGen LLC under the ARPA-E MEITNER program to simulate the thermal-hydraulic and heat transfer behavior of the full-scale Holos-Quad Subcritical Power Modules (SPMs). Four coupled SPMs, each rated at 5.5MW, form the Holos-Quad gas-cooled microreactor design. The SPM-SS represents a substantially scaled-down system with a power rating less than 40 kW, equipped with an electrically heated fuel cartridge heat exchanger, an electrically heated compressor heat exchanger, and a valve actuated turbine heat exchanger, in addition to a recuperator and a cooler heat exchanger. The fuel cartridge represents a portion of the full-scale SPM core, the compressor heat exchanger mimics the temperature changes resulting from the compressor’s turbomachinery inefficiencies, the turbine heat exchanger mimics the expansion process normally occurring through the turbine, while the recuperator and cooler heat exchangers complete the subscale simulator loop. The heaters equipping the fuel cartridge and the compressor heat exchangers are electronically controlled to simulate normal and off-normal SPM operating conditions. The full-scale Holos-Quad SPM design eliminates the traditional balance of plant and executes thermal-to-electric energy conversion by means of an intercooled Brayton cycle with decoupled compressor-turbine turbomachinery. The Holos-Quad full-scale design is equipped with a multi-stage axial Low- and High-Pressure compressor, and a multistage axial turbine. The SPM-SS is designed for testing and validation of selected components which are instead coupled by a traditional balance of plant. The SPMSS is not equipped with turbo-machinery (compressor and turbine) as the development of these components were excluded from the scope of work under the ARPA-E MEITNER funding program. The SPM-SS balance of plant enables modifications, replacement and testing of individual components with different working fluids and is designed to include the turbo-machinery components that will be developed in future research . The SPM-SS can be operated with different gases, variable mass-flow-rates, pressures, and temperatures to obtain test data for selected components, whose performance can be scaled to validate the computer model of the full-scale SPM at various conditions (e.g., start-up, transients conditions). The SPM-SS can operate at the maximum Holos-Quad design pressure of 7 MPa, and a maximum temperature limited to 650 °C by the electrical heaters. Several SPM-SS tests have been conducted and analyzed with the Plant Dynamics Code (PDC) developed at the Argonne National Laboratory (ANL). These tests aimed at validating the PDC modeled predictions of the full-scale Holos-Quad design with data from selected SPM-SS components. In order to address SPM-SS specific characteristics, such as components heat losses and absence of turbomachinery components, some modifications to the PDC have been implemented to factor the design differences from the full-scale Holos-Quad SPM to the SPM-SS. As the PDC offers capabilities to analyze systems with different working fluids, air, nitrogen, and helium were utilized as the SPM-SS working fluids. Air was utilized to fine-tune the SPM-SS Systems Structures and Components (SSCs), nitrogen was utilized to pressure test the SPM-SS loop at the SPMs design maximum pressure of 7MPa. Helium was utilized as the working fluid circulating through the SPM-SS SSCs for specific tests to validate the PDC predictions of the fuel cartridge heat exchanger. SPM-SS tests data were also analyzed with both the steady-state and transient analysis capabilities offered by the PDC. This report describes the PDC analysis of the SPM-SS tests data, including the necessary code modifications and comparison of the code results with the experimental data. Based on the results, a discussion is presented on how the analysis supports design and transient calculations of the full-scale Holos-Quad microreactor. Also based on the results of this work, recommendations are made for future optimizations of the SPM-SS components and PDC model development needs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Identifying Hydropower Operational Flexibilities in Presence of Streamflow and Net-load Uncertainty (Final Technical report)

In the existing operations, hydropower contributions to future system flexibility are generally modeled while maintaining traditional operating rules and constraints in supporting grid operation, such as the balancing of variable renewable energy production. Moreover, operation of large scale hydropower systems on major rivers has been investigated for decades, utilizing various systems engineering approaches, with the evolving electric grid, as the result of renewable resources integration, compounded by the changing climate (variability of river flows, intensification of hydrologic cycle resulting in more frequent extreme events) affecting water availability, the need for more advanced stochastic modeling and effective uncertainty analysis approaches have become necessary. The research results supported by this funding and presented in this report provide a new look at hydropower operational flexibility enforced by the changes identified above. Understanding how hydropower operates in response to the underlying uncertainties with respect to the system constraints is crucial in identifying its operational flexibility potentials. In this project, the flexibility of the operating hydropower facility is described by capturing uncertainties in both water and power system and formulating the operations as a multistage stochastic optimization problem. The proposed approach supports short- to seasonal-term operations and planning decision horizons.

13 HYDRO ENERGY↗

Photoinitiated Reactions of Molecules and Radicals in Molecular Beams

The UV photochemistry of organic molecules is a fundamental process that governs reactions in the atmosphere, synthetic chemistry, processing of organic aerosols, and biological damage in living tissues. In many organic molecules, the ensuing evolution involves pathways that are in competition, giving rise to different products, isomerization, coupling to other electronic states, and secondary reactive collisions. Because photodissociation is usually fast (picoseconds to microseconds), these processes are far from equilibrium and are controlled by kinetic competition and dynamical forces. The work accomplished was focused primarily on the photochemistry of alpha-keto carboxylic acids, a group of acids produced from natural sources, which are implicated in aerosol formation and biological processes. In the atmosphere, they are destroyed mainly by solar radiation. Studying their photochemistry has been surprisingly difficult because of the complexity of their excited electronic states, and the effect of collisions and secondary reactions. The second project investigated the lifetime of excited electronic states of pyrazine and picoline and had both experimental and theoretical aspects. The work focused on a model molecule, pyruvic acid (PA), because it was hypothesized that it should be a good source of the unstable carbene, methylhydroxycarbene (MHC). PA has an internal hydrogen bond that controls the evolution of its decomposition. The decomposition was studied following excitation to two of its lowest excited states reached by laser irradiation at 351 and 193 nm. The photodissociation dynamics in the absence and presence of collisions was monitored and compared. Understanding the UV photochemistry requires the use of complementary experimental approaches. Two methods were enlisted, which together generated a comprehensive and detailed set of results: (i) The time-sliced velocity map imaging (SVMI) instrument at USC was exploited to determine kinetic energy release of fragments, fast dissociation timescales, and internal state distributions of fragments for which Resonance Enhanced Multiphoton Ionization (REMPI) schemes exist; and (ii) The multiplexed photoionization mass spectrometer (MPIMS) setup developed at the Sandia Combustion Research Facility was used for product discovery, achieved by exploiting tunable narrowband VUV radiation at the Advanced Light Source (ALS), and to follow in real time their subsequent unimolecular and bimolecular reactions. The experimental conditions ranged from collisionless molecular beams to study nascent products to flow reactors of variable pressures to study subsequent bimolecular reactions of the products. The goals stated above were successfully accomplished. By exciting PA to its lowest excited state, MHC was identified as the only primary product and its isomerization to vinylalcohol and acetaldehyde was directly observed in real time. Moreover, we reported the first bimolecular reaction of MHC, which was with acetaldehyde, and identified its reaction product. This paves the way for the study of other reactions of this important carbene intermediate. When excitation was carried out at 193 nm, which imparted much higher energy to PA, many more products were directly observed in real time, some deriving from three-body dissociation. Quantitative branching ratios and secondary reactions of radical products were also determined and analyzed. The studies of pyrazine and picoline focused on the second excited state of these molecules and showed (via ionization studies) that their excited states were very short lived (<100 fs) because of efficient couplings to lower electronic states via vibronic coupling. Theoretical work on modeling the absorption spectrum and decay mechanisms of the excited states are in progress in collaboration with theoreticians.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Components of aircraft life support systems interact with each other and the user

The life support system in a tactical aircraft provides necessary supplemental oxygen to the aircrew. However, interactions among its various components may generate unexpected breathing loads. We focus here on the interactions between a regulator and breathing mask commonly used together in the U.S. Navy, the CRU-103 regulator and MBU 23/P mask, and some effects of the interactions on the user. The data reported were collected during a larger research effort examining potential physiological and cognitive effects of low regulator inlet pressures. Seventeen participants completed a series of tasks under mild exercise while breathing 40% O 2 (balance N 2 ) from an MBU-23/P mask supplied by a CRU-103 regulator with supply pressures 10, 6, 4, and 2 psig (CRU-103 specifications are for inlet pressures from 5 to 120 psig). Variables measured included flow to the mask and pressures at the regulator supply, in the hose to the mask, and in the mask. In addition to restricting inspiratory flow, low inlet pressure to the CRU-103 caused a counterintuitive overshoot in gas delivery pressure at end-inspiration, a mean increase of 1.5 cm H 2 O between the 10- and 2 psig conditions. The added pressure to the exhalation valve increased the expiratory threshold, the pressure to start expiratory flow, by approximately 2 cm H 2 O, increasing the effort needed to exhale.

60 APPLIED LIFE SCIENCES↗

Calculation of turbulent boundary layers with heat transfer and pressure gradient utilizing a compressibility transformation. Part 1: Summary report

The analysis uses a compressibility transformation and utilizes higher order closure rules to complete the transformation. By requiring that the momentum equations in differential form be satisfied at the wall and at the sublayer edge, correspondence rules are obtained which relate the variable property (VP) flow to a constant property (CP) flow in which mass transfer and pressure gradient occur simultaneously. A new CP formulation is developed and numerical results for a variety of cases are presented. Comparisons with earlier forms of the transformation and with experiment are included. For the zero pressure gradient case some differences between the various predictions are observed. For the several pressure gradient cases examined, the results are found to be essentially identical to those given by first order closure rules; i.e., by a form of transformation which relates the VP flow to a CP flow with pressure gradient but zero mass transfer.

Economos, C.↗