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DOE OSTI2025

Modeling a Sodium Heat Pipe Experiment at SPHERE Using Sockeye

The Single Primary Heat Extraction and Rejection Emulator (SPHERE) facility at Idaho Na- tional Laboratory was recently utilized to generate data for the startup and steady operation of a high-performance, sodium heat pipe over the course of 1000 hours, as a test of detrimental, long-term effects of heat pipe operation. The setup consists of a single, sodium heat pipe enclosed in a stainless-steel vacuum chamber, heated radiatively via a cylindrical ceramic fiber heater configuration and cooled via a water-cooled calorimeter. Measurements include temperatures at several axial locations along the outer surface of the heat pipe, the power provided to the heaters, and the heat removal rate of the calorimeter. In this work, this data is utilized to validate heat pipe models in the heat pipe application Sockeye, which is based upon the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework. Sockeye provides various heat pipe models at an engineering scale appropriate for the multiphysics simulation of microreactors, which may feature several hundred heat pipes. This work details models of this experiment in SPHERE using various heat pipe models with Sockeye, including heat conduction-based models and compressible flow models of the heat pipe interior. These models are compared to the experimental data to assess the accuracy of several aspects of heat pipe modeling, including frozen startup, the effect of non-condensable gases, and the coupling of the heat pipe to its environment.

97 - MATHEMATICS AND COMPUTING↗

NASA NTRS1992

Thermostructural applications of heat pipes for cooling leading edges of high-speed aerospace vehicles

Heat pipes have been considered for use on wing leading edge for over 20 years. Early concepts envisioned metal heat pipes cooling a metallic leading edge. Several superalloy/sodium heat pipes were fabricated and successfully tested for wing leading edge cooling. Results of radiant heat and aerothermal testing indicate the feasibility of using heat pipes to cool the stagnation region of shuttle-type space transportation systems. The test model withstood a total seven radiant heating tests, eight aerothermal tests, and twenty-seven supplemental radiant heating tests. Cold-wall heating rates ranged from 21 to 57 Btu/sq ft-s and maximum operating temperatures ranged from 1090 to 1520 F. Follow-on studies investigated the application of heat pipes to cool the stagnation regions of single-stage-to-orbit and advanced shuttle vehicles. Results of those studies indicate that a 'D-shaped' structural design can reduce the mass of the heat-pipe concept by over 44 percent compared to a circular heat-pipe geometry. Simple analytical models for heat-pipe startup from the frozen state (working fluid initially frozen) were adequate to approximate transient, startup, and steady-state heat-pipe performance. Improvement in analysis methods has resulted in the development of a finite-element analysis technique to predict heat-pipe startup from the frozen state. However, current requirements of light-weight design and reliability suggest that metallic heat pipes embedded in a refractory composite material should be used. This concept is the concept presently being evaluated for NASP. A refractory-composite/heat-pipe-cooled wing leading edge is currently being considered for the National Aero-Space Plane (NASP). This concept uses high-temperature refractory-metal/lithium heat pipes embedded within a refractory-composite structure and is significantly lighter than an actively cooled wing leading edge because it eliminates the need for active cooling during ascent and descent. Since the NASP vehicle uses cryogenic hydrogen to cool structural components and then burns this fuel in the combustor, hydrogen necessary for descent cooling only, when the vehicle is unpowered, is considered to be a weight penalty. Details of the design of the refractory-composite/heat-pipe-cooled wing leading edge are currently being investigated. Issues such as thermal contact resistance and thermal stress are also being investigated.

Camarda, Charles J.↗

NASA NTRS1971

Arterial and grooved cryogenic heat pipes.

Tests were conducted on two cryogenic heat pipes using nitrogen as the working fluid. Both pipes are 1.27 cm in diameter. The first pipe is 141 cm long and uses longitudinal grooves in the aluminum wall as the wick structure. The second pipe is 91 cm long and has an arterial wick adjacent to the wall. In addition, circumferential screw threads are machined along the entire length of the inside pipe wall. Both heat pipes primed with no difficulty in the horizontal position. Start-up after burn-out was obtained repeatedly. However, more testing is required to determine whether the artery pipe is as reliable as the grooved pipe with respect to priming. Once primed, the artery heat pipe is much less sensitive to elevation than the grooved design and, consequently, offers a significant advantage with respect to ground testing. Heat-transfer characteristics of the two pipes were comparable, with both pipes achieving the initial goal of 1000 watt-cm of heat-transport capability.

Brennan, P.↗

NASA NTRS1988

Development of an integrated heat pipe-thermal storage system for a solar receiver

An integrated heat pipe-thermal storage system was developed as part of the Organic Rankine Cycle Solar Dynamic Power System solar receiver for space station application. The solar receiver incorporates potassium heat pipe elements to absorb and transfer the solar energy within the receiver cavity. The heat pipes contain thermal energy storage (TES) canisters within the vapor space with a toluene heater tube used as the condenser region of the heat pipe. During the insolation period of the earth orbit, solar energy is delivered to the heat pipe. Part of this thermal energy is delivered to the heater tube and the balance is stored in the TES units. During the eclipse period of earth orbit, the stored energy in the TES units is transferred by the potassium vapor to the toluene heater tube. A developmental heat pipe element was constructed that contains axial arteries and a distribution wick connecting the toluene heater and the TES units to the solar insolation surface of the heat pipe. Tests were conducted to demonstrate the heat pipe, TES units, and the heater tube operation. The heat pipe element was operated at design input power of 4.8 kW. Thermal cycle tests were conducted to demonstrate the successful charge and discharge of the TES units. Axial power flux levels up to 15 watts/sq cm were demonstrated and transient tests were conducted on the heat pipe element. Details of the heat pipe development and test procedures are presented.

Keddy, E.↗

NASA NTRS2004

Working Fluids for Increasing Capacities of Heat Pipes

A theoretical and experimental investigation has shown that the capacities of heat pipes can be increased through suitable reformulation of their working fluids. The surface tensions of all of the working fluids heretofore used in heat pipes decrease with temperature. As explained in more detail below, the limits on the performance of a heat pipe are associated with the decrease in the surface tension of the working fluid with temperature, and so one can enhance performance by reformulating the working fluid so that its surface tension increases with temperature. This improvement is applicable to almost any kind of heat pipe in almost any environment. The heat-transfer capacity of a heat pipe in its normal operating-temperature range is subject to a capillary limit and a boiling limit. Both of these limits are associated with the temperature dependence of surface tension of the working fluid. In the case of a traditional working fluid, the decrease in surface tension with temperature causes a body of the liquid phase of the working fluid to move toward a region of lower temperature, thus preventing the desired spreading of the liquid in the heated portion of the heat pipe. As a result, the available capillary-pressure pumping head decreases as the temperature of the evaporator end of the heat pipe increases, and operation becomes unstable. Water has widely been used as a working fluid in heat pipes. Because the surface tension of water decreases with increasing temperature, the heat loads and other aspects of performance of heat pipes that contain water are limited. Dilute aqueous solutions of long-chain alcohols have shown promise as substitutes for water that can offer improved performance, because these solutions exhibit unusual surface-tension characteristics: Experiments have shown that in the cases of an aqueous solution of an alcohol, the molecules of which contain chains of more than four carbon atoms, the surface tension increases with temperature when the temperature exceeds a certain value. There are also other liquids that have surface tensions that increase with temperature and could be used as working fluids in heat pipes. For example, as a substitute for ammonia, which is the working fluid in some heat pipes, one could use a solution of ammonia and an ionic surfactant.

Chao, David F.↗

DOE OSTI2025

Modeling a Sodium Heat Pipe Experiment at SPHERE Using Sockeye

The Single Primary Heat Extraction and Rejection Emulator (SPHERE) facility at Idaho National Laboratory was recently utilized to generate data for the startup and steady operation of a high-performance, sodium heat pipe over the course of 1,000 hours to test the detrimental, long-term effects of heat pipe operation. The setup consisted of a single, sodium heat pipe enclosed in a stainless-steel vacuum chamber, heated radiatively via a cylindrical ceramic-fiber heater configuration and cooled via a water-cooled calorimeter. Measurements included temperatures at several axial locations along the outer surface of the heat pipe, the power provided to the heaters, and the heat removal rate of the calorimeter. In this work, we use this data to validate heat pipe models in Sockeye, a heat pipe application based on the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework. Sockeye provides various heat pipe models at an engineering scale appropriate for the multiphysics simulation of microreactors, which may feature several hundred heat pipes. This work details models of this experiment at SPHERE using various heat pipe models with Sockeye, including heat-conduction-based and compressible flow models of the heat pipe interior.

97 - MATHEMATICS AND COMPUTING↗

NASA NTRS1974

Design, development and testing of a cryogenic temperature heat pipe for the icicle system

An analytical model was formulated for a cryogenic heat pipe, and thermal and transport analyses were developed to predict the performance characteristics of various heat pipe designs. These analyses permitted optimization of various design parameters. A series of four breadboard heat pipes were fabricated and tested to provide inputs such as internal film coefficients, minimum capillary radii, and wick permeabilities which are required for the analyses. The results of instrumentation, charging, and testing of cryogenic heat pipes were applied to the prototype heat pipes. After a thorough design analysis of three potential heat pipe wicks (slab, artery, and axial groove), the first two were chosen for application to two prototype heat pipes. Detailed designs were made of the two heat pipes and the units were fabricated. Tests were conducted which verified the integrity and safety margin of the design to withstand the internal pressure at ambient temperature and fatigue of thermal cycling. During the acceptance testing in the vacuum chamber, no difficulty was experienced in priming the slab-wick heat pipe and it met the performance design requirements. The artery-wick heat pipe would not prime with nitrogen working fluid for any test conditions.

Trimmer, D. S.↗

NASA NTRS1991

Thermion: Verification of a thermionic heat pipe in microgravity

The Idaho National Engineering Laboratory (INEL) is conducting intensive research in the design and development of a small excore heat-pipe-thermionic space nuclear reactor power system (SEHPTR). The SEHPTR spacecraft will be able to supply 40 kW of power in any given orbit. The key components in this reactor are the thermionic heat pipes. The heat pipes have two major functions: (1) to convert heat energy into electrical energy, and (2) to radiate the excess heat to space. Thermionic power conversion is the process of converting heat energy into electrical energy with no moving parts. Heat is applied to the cathode surface. This heat will boil off electrons that will jump across the gap to the cooler surface of the anode, which will cause a potential difference between the two plates and induce a current through the load. Thermionic power conversion is incorporated as part of the heat pipe. The heat pipe, which is being developed by Thermacore Inc., is actually two heat pipes. It uses a radial heat pipe, called the emitter, and an axial heat pipe collector. The emitter heat pipe will pass the heat from the nuclear core to the cathode surface. The collector heat pipe keeps the anode surface cooler by transferring the heat from the anode surface and radiating it to space.

Source record↗

NASA NTRS2004

An Overview of Long Duration Sodium Heat Pipe Tests

High temperature heat pipes are being evaluated for use in energy conversion applications such as fuel cells, gas turbine re-combustors, and Stirling cycle heat sources; with the resurgence of space nuclear power, additional applications include reactor heat removal elements and radiator elements. Long operating life and reliable performance are critical requirements for these applications. Accordingly long-term materials compatibility is being evaluated through the use of high temperature life test heat pipes. Thermacore International, Inc., has carried out several sodium heat pipe life tests to establish long term operating reliability. Four sodium heat pipes have recently demonstrated favorable materials compatibility and heat transport characteristics at high operating temperatures in air over long time periods. A 3l6L stainless steel heat pipe with a sintered porous nickel wick structure and an integral brazed cartridge heater has successfully operated at 650 to 700 C for over 115,000 hours without signs of failure. A second 3l6L stainless steel heat pipe with a specially-designed Inconel 60 I rupture disk and a sintered nickel powder wick has demonstrated over 83,000 hours at 600 to 650 C with similar success. A representative one-tenth segment Stirling Space Power Converter heat pipe with an Inconel 718 envelope and a stainless steel screen wick has operated for over 41 ,000 hours at nearly 700 0c. A hybrid (i.e. gas-fired and solar) heat pipe with a Haynes 230 envelope and a sintered porous nickel wick structure was operated for about 20,000 hours at nearly 700 C without signs of degradation. These life test results collectively have demonstrated the potential for high temperature heat pipes to serve as reliable energy conversion system components for power applications that require long operating lifetime with high reliability, Detailed design specifications, operating hi story, and test results are described for each of these sodium heat pipes. Lessons learned and future life test plans are also discussed.

Rosenfeld, John H.↗

NASA NTRS2019

Operation of a Heat Pipe with Multiple Heat Loads Under Reflux Mode

"Heat pipes are being used on many spacecraft to acquire heat dissipated by the payload and transport the heat to a remote radiator. In instrument-level or spacecraft-level ground testing, many heat pipes are placed in a gravity-driven reflux mode where the condenser is well above the evaporator, resulting in the formation of a liquid pool at the bottom of the heat pipe. If a head load is applied to a site that is in contact with the liquid pool, the generated vapor will flow upward to the condenser and the condensate will fall back to the evaporator due the influence of gravity. Hence, the heat pipe can operate steadily under reflux mode because the heated site always has sufficient liquid supply to sustain the fluid flow. In contrast, when a heat load is applied to a site remote from the liquid pool, the heat pipe will be unable to transfer heat through liquid evaporation unless the heated site has a chance to be in contact with liquid. This can be accomplished by applying an additional heat load to the liquid pool to establish a reflux flow so that the remote site can capture the falling condensate. An experimental investigation was conducted to study the effect of gravity on the thermal performance of a heat pipe under reflux mode with multiple heat loads. An aluminum ammonia heat pipe with internal axial grooves was placed in a vertical position. Cooling was provided to the top of the heat pipe, and heat was applied to three sites below the condenser with various heat distributions. One of the heated sites was above the liquid pool, and two were in direct contact with the liquid pool. Test results showed that when a heat load was applied to either one or both of the lower sites, the heat pipe could run steadily under reflux mode. After a reflux flow had been established, a heat load could be applied to the upper site. If the upper site could capture sufficient liquid falling from the condenser to handle its heat load solely by liquid evaporation, the heat pipe could reach steady operation. Otherwise, the temperature of the upper site would oscillate due to its intermittent contact with the falling liquid. For a given heat load to the upper site, the amplitude of temperature oscillation decreased with an increasing heat load to the lower sites because there was more falling condensate available for the upper site to capture. Moreover, the temperature oscillation disappeared completely when the total heat loads to lower sites exceeded a threshold power, and the threshold power increased with an increasing heat load to the upper site."

Ku, Jentung↗

DOE OSTI2025

Phenomena Identification and Ranking Table (PIRT) for Heat Pipes

This Phenomena Identification and Ranking Table (PIRT) report provides an evaluation of key phenomena affecting the performance and operational regimes of heat pipes, particularly in the context of heat pipe microreactors (HPMRs). Heat pipes are advanced passive thermal management devices that utilize phase change and capillary action to achieve efficient heat transfer. However, due to the complexity of the phenomena coupled in the heat pipe, including phase change, turbulent transition, and compressibility effects, among others, there is high uncertainty in identifying and ranking the important phenomena affecting the operation of heat pipes and the current knowledge for their modeling and simulation and experimental measurements and instrumentation. This PIRT exercise, conducted as a collaborative effort involving the Department of Energy (DOE) Microreactor Program (MRP), the Nuclear Regulatory Commission (NRC), and university partners systematically identifies, reviews, and prioritizes critical phenomena affecting the operation of heat pipes based on their importance and knowledge levels. The report analyzes phenomena with high importance and low knowledge, such as wick de-wetting, critical heat flux, contact angles, and pressure dynamics, discussing challenges and future research directions for improving their modeling and simulation and experimental measurements. Additionally, the report addresses phenomena with low knowledge that could impact heat pipe operation during non-normal or transient operation, including frozen startup, laminar to turbulent transition, geysering, wick priming, underfilling conditions, surface roughness of the wick, NCGs trapped in the wick, and the timescales of startup and shutdown. This comprehensive evaluation serves as a valuable resource for guiding future research and development efforts, supporting the successful integration of heat pipes into critical applications such as nuclear reactors, and contributing to the advancement of heat pipe technologies in safety-critical industries.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗

NASA NTRS1978

Heat pipes in space and on earth

The heat pipe is a closed tube whose inner surfaces are lined with a porous capillary wick. The wick is saturated with the liquid phase of a working fluid. The heat supplied at one end of the tube, the evaporator, causes evaporation of the working fluid. The vapor will pass to the other end of the tube, the condenser, where it will condense and release the latent heat of vaporization to a heat sink in that section of the pipe. Problems concerning a design of heat pipes for space applications are related to certain difficulties regarding the prediction of device performance under zero-g conditions. Heat pipes are usually tested on the ground under the influence of gravity, and then their performance is extrapolated to space. A description is presented of the approaches used to insure good heat pipe performance in space. Attention is given to an international heat pipe experiment conducted to accumulate zero-g performance data for several new and unique heat pipe designs, heat pipes for ATS-6, cryogenic heat pipes, and future activities.

Ollendorf, S.↗

NASA NTRS1979

NEP heat pipe radiators

This paper covers improvements of heat pipe radiators for the thermionic NEP design. Liquid metal heat pipes are suitable as spacecraft radiator elements because of high thermal conductance, low mass and reliability, but the NEP thermionic system design was too large and difficult to fabricate. The current integral collector-radiator design consisting of several layers of thermionic converters, the annular-tangential collector heat pipe, the radiator heat pipe, and the transition zone designed to minimize the temperature difference between the collector heat pipe and radiator heat pipe are described. Finally, the design of micrometeoroid armor protection and the fabrication of the stainless steel annular heat pipe with a tangential arm are discussed, and it is concluded that the heat rejection system for the thermionic NEP system is well advanced, but the collector-radiator heat pipe transition and the 8 to 10 m radiator heat pipe with two bends require evaluation.

Ernst, D. M.↗

NASA NTRS1995

Liquid metal micro heat pipes for space radiator applications

Micromachining is a chemical means of etching three-dimensional structures, typically in single-crystalline silicon. These techniques are leading toward what is coming to be referred to as MEMS (micro electro mechanical systems), where in addition to the ordinary two dimensional (planar) microelectronics, it is possible to build three-dimensional micromotors, electrically-actuated microvalves, hydraulic systems, and much more on the same microchip. These techniques become possible because of differential etching rates of various crystallographic planes and materials used for semiconductor microfabrication. The University of Cincinnati group in collaboration with NASA Lewis formed micro heat pipes in silicon by the above techniques. Work is ongoing at a modest level, but several essential bonding and packaging techniques have been recently developed. Currently, we have constructed and filled water/silicon micro heat pipes. Preliminary thermal tests of arrays of 125 micro heat pipes etched in a 1 inch x 1 inch x 250 micron silicon wafer have been completed. These pipes are instrumented with extremely small P-N junctions to measure their effective conductivity and their maximum operating power. A relatively simple one-dimensional model has been developed in order to predict micro heat pipes' operating characteristics. This information can be used to optimize micro heat pipe design with respect to length, hydraulic diameter, and number of pipes. Work is progressing on the fabrication of liquid-metal micro heat pipes. In order to be compatible with liquid metal (sodium or potassium), the inside of the micro heat pipes will be coated with a refractory metal (such as tungsten, molybdenum, or titanium).

Gerner, F. M.↗

NASA NTRS2008

Cold Start of a Radiator Equipped with Titanium-Water Heat Pipes

Radiator panels utilizing titanium-water heat pipes are being considered for lunar applications. A traditional sandwich structure is envisioned where heat pipes are embedded between two high thermal conductivity face sheets. The heat pipe evaporators are to be thermally connected to the heat source through one or more manifolds containing coolant. Initial radiator operation on the lunar surface would likely follow a cold soak where the water in the heat pipes is purposely frozen. To achieve heat pipe operation, it will be necessary to thaw the heat pipes. One option is to allow the sunlight impinging on the surface at sunrise to achieve this goal. Testing was conducted in a thermal vacuum chamber to simulate the lunar sunrise and additional modeling was conducted to identify steady-state and transient response. It was found that sunlight impinging on the radiator surface at sunrise was insufficient to solely achieve the goal of thawing the water in the heat pipes. However, starting from a frozen condition was accomplished successfully by applying power to the evaporators. Start up in this fashion was demonstrated without evaporator dryout. Concern is raised over thawing thermosyphons, vertical heat pipes operating in a gravity field, with no wick in the condenser section. This paper presents the results of the simulated cold start study and identifies future work to support radiator panels equipped with titanium-water heat pipes.

Jaworske, Donald A.↗

NASA NTRS2011

Transient Response to Rapid Cooling of a Stainless Steel Sodium Heat Pipe

Compact fission power systems are under consideration for use in long duration space exploration missions. Power demands on the order of 500 W, to 5 kW, will be required for up to 15 years of continuous service. One such small reactor design consists of a fast spectrum reactor cooled with an array of in-core alkali metal heat pipes coupled to thermoelectric or Stirling power conversion systems. Heat pipes advantageous attributes include a simplistic design, lack of moving parts, and well understood behavior. Concerns over reactor transients induced by heat pipe instability as a function of extreme thermal transients require experimental investigations. One particular concern is rapid cooling of the heat pipe condenser that would propagate to cool the evaporator. Rapid cooling of the reactor core beyond acceptable design limits could possibly induce unintended reactor control issues. This paper discusses a series of experimental demonstrations where a heat pipe operating at near prototypic conditions experienced rapid cooling of the condenser. The condenser section of a stainless steel sodium heat pipe was enclosed within a heat exchanger. The heat pipe - heat exchanger assembly was housed within a vacuum chamber held at a pressure of 50 Torr of helium. The heat pipe was brought to steady state operating conditions using graphite resistance heaters then cooled by a high flow of gaseous nitrogen through the heat exchanger. Subsequent thermal transient behavior was characterized by performing an energy balance using temperature, pressure and flow rate data obtained throughout the tests. Results indicate the degree of temperature change that results from a rapid cooling scenario will not significantly influence thermal stability of an operating heat pipe, even under extreme condenser cooling conditions.

Mireles, Omar R.↗

NASA NTRS2003

Small, Untethered, Mobile Robots for Inspecting Gas Pipes

Small, untethered mobile robots denoted gas-pipe explorers (GPEXs) have been proposed for inspecting the interiors of pipes used in the local distribution natural gas. The United States has network of gas-distribution pipes with a total length of approximately 109 m. These pipes are often made of iron and steel and some are more than 100 years old. As this network ages, there is a need to locate weaknesses that necessitate repair and/or preventive maintenance. The most common weaknesses are leaks and reductions in thickness, which are caused mostly by chemical reactions between the iron in the pipes and various substances in soil and groundwater. At present, mobile robots called pigs are used to inspect and clean the interiors of gas-transmission pipelines. Some carry magnetic-flux-leakage (MFL) sensors for measuring average wall thicknesses, some capture images, and some measure sizes and physical conditions. The operating ranges of pigs are limited to fairly straight sections of wide transmission- type (as distinguished from distribution- type) pipes: pigs are too large to negotiate such obstacles as bends with radii comparable to or smaller than pipe diameters, intrusions of other pipes at branch connections, and reductions in diameter at valves and meters. The GPEXs would be smaller and would be able to negotiate sharp bends and other obstacles that typically occur in gas-distribution pipes.

Wilcox, Brian↗

NASA NTRS2003

Detecting Conductive Liquid Leaking from Nonconductive Pipe

A method that can be implemented with relatively simple electronic circuitry provides a capability for detecting leakage of an electrically conductive liquid from an electrically nonconductive underground pipe. Alternatively or in addition, the method can be applied to locate the pipe, whether or not there is a leak. Although the method is subject to limitations (some of which are described below), it is still attractive as an additional option for detecting leaks and locating pipes without need for extensive digging. The method is based on capacitive coupling of an alternating electrical signal from the liquid to a portable electronic unit that resembles a metal detector. A signal voltage is applied to the liquid at some convenient point along the pipe: for example, the signal could be coupled into the liquid via an aboveground metal pipe fitting, the interior surface of which is in contact with the liquid. The signal is conducted through the liquid in the pipe; in the case of diffusive leak of liquid into the surrounding ground, the signal is conducted through the leak, into the portion of the adjacent ground that has become soaked with the liquid. (A drip leak cannot be detected by this method because there is no conductive path between the liquid inside and the liquid outside the pipe.) The portable unit includes an electrically conductive plate connected to the input terminal of an amplifier. When the plate is brought near the pipe or the leaked liquid, a small portion of the signal power is coupled capacitively from the liquid to the plate. The user scans the plate near the ground surface to find the locus of maximum signal strength. The leak can be identified as a relatively wide area, contiguous with the location of the pipe, over which the signal is detectable.

Youngquist, Robert C.↗