Modeling — Heat Transfer
Heat transfer analyses commonly arise when an estimate of the fire resistance rating for an unlisted structural component is required or when the fire exposure is expected to deviate significantly from the standard test exposures. Heat transfer analyses also are used to predict the thermal response of combustibles or other objects for which a temperature increase could have an adverse effect and to provide temperature data as input to structural response models. The goal of any heat transfer analysis is usually the same: to predict the transient temperature response of a solid region given a known or prescribed fire exposure. Depending on what is evaluated, the transient temperature field in an object may be one-, two-, or three-dimensional and the boundary conditions may include convection, thermal radiation, or even a contact resistance.
Hughes Associates has the capability to perform multi-dimensional heat transfer analyses in Cartesian, cylindrical, spherical, or mixed coordinate systems involving steady-state and transient fire exposures. A heat transfer model may include one or multiple materials, and each material may have constant or time, temperature, or spatially varying thermal material properties. Materials may also undergo an endothermic or exothermic reaction such as dehydration. Hughes Associates uses two commercially available heat transfer models for most applications: HEATING, a finite difference model developed at the Oak Ridge National Laboratories and SINDA, a combined finite difference-finite element model with developmental origins at NASA. SINDA has the additional capability to optimize a design over one or more parameters, such as a dimension. The optimization process may be used to extract thermal material properties from well constrained tests. Both SINDA and HEATING provide as output spatial and temporal temperature, data that may be graphed or plotted as contours. Animations are readily made of the contour plots to visualize the heating process.
HEATING has undergone Quality Assurance (QA) validation for use in the commercial nuclear industry and has been validated and verified for use with DOD projects. SINDA is currently undergoing a similar validation and verification process.
Customized thermal models have been developed at Hughes for applications that fall beyond the capabilities of many commercial transfer models including HEATING and SINDA. One notable example is the development of a one-dimensional decomposition model that predicts the heat and mass flow through a composition material. The model has been successfully used to predict the thermal performance of materials protected with an intumescent coating. Customized heat transfer models could be developed or extended on a case-by-case basis using in-house expertise from a wide range of disciplines.
Selected Project Examples
- Great Platte River Road Monument
- Analysis of Embedded Electrical Conduits
- Temperature Response of an Aluminum Floor Assembly
Great Platte River Road Monument
The Great Platte River Road Monument (GPRRM) is a bridge like museum structure that spans Interstate 80 in Kearny, Nebraska. During the design and construction of the GPRRM, Hughes Associates was contracted to develop a passive fire protection strategy for the external portions of the bridge structure that would meet the requirements of the Uniform Building Code. The architectural design called for unprotected Cor-Ten weathering steel on the exterior to replicate the appearance of a rustic wood-like bridge. Accordingly, one of the primary constraints on the passive fire protection design was to minimize the amount of external steel that would have to be covered with a fire protection material.
Because the structure is at least 30 ft above the road surface, it was apparent that the code required ASTM E 19 Time-Temperature enclosure fire would not be representative of external fire threats. The structure spans a major east-west interstate on which flammable liquids are routinely transported in single and tandem tanker trucks. Consequently, the most severe fire exposure to the structure would be associated with a tanker truck fuel spill under or adjacent to the bridge structure. A fire hazards analysis was conducted and it was concluded that the structure could achieve passive fire protection if the underside were protected and flame shields were installed to prevent exposure of the supporting arches from below. The extent of the flame shield structure and the type and thickness of fire insulation on the underside of the structure were calculated using a two-dimensional heat transfer analysis with the finite element model FIRES-T3. The design goals were to limit the peak and average steel temperatures given a hydrocarbon pool fire exposure to levels permitted by ASTM E 119. The goal of the flame shield was to deflect the flame and reduce the intensity of the radiant heat flux on the primary structural chords of the arch structure. The passive fire protection design was presented to the Nebraska State Fire Marshal and approved for implementation based on the results of the heat transfer modeling and the fire hazards analysis.
Analysis of Embedded Electrical Conduits
Typical temperature contour plot in the vicinity of steel conduit in contact with rebar.
The goal of this project was to assess the time concrete-embedded conduit would reach a pre-defined critical temperature given exposure of the concrete surface to the ASTM E 119 Standard Time-Temperature Profile. It had been presumed by a utility that the concrete cover over the conduit would provide adequate fire resistance defined as the continuity of the circuit(s) contained within the conduit. The analysis was general insofar as no specific wall, floor or ceiling was considered. The conduit embed depths ranged from 1.25 – 7 in, but the outermost rebar mesh was always nearer the exposed surface than the conduit. The size of the rebar varied with the thickness of the concrete boundary but, per design specification, required at least 0.75 in concrete cover. The conduit was either schedule 80 PVC or galvanized steel; conduit diameters varied from 1 – 6 in.
The focus of the analysis was to establish a limited number of cases that could be used to represent all others. Once such cases were identified, a series of curves could be produced plotting the time to reach the critical conduit temperature against the embed depth. A two-dimensional thermal analysis was conducted using HEATING to identify the critical parameters affecting the temperature field. It was found that the flow field was two-dimensional for steel conduit and nearly one-dimensional for the PVC conduit. In addition, it was determined that a small diameter conduit bound the results of a large diameter conduit, and that conduit placed behind and in contact with rebar was bounding. From these findings, a series of plots were constructed presenting the time to reach the critical temperature as a function of the embed depth. These plots could then be used in the field to determine, on a case-by-case basis, which conduit would be subject to failure given the required ASTM fire resistance required for a given area.
Temperature Response of an Aluminum Floor Assembly
A three-dimensional heat transfer analysis was conducted on an aluminum floor assembly exposed to a radiant flux from a hydrocarbon pool fire exposure with the intent of estimating the time at which the assembly would reach a critical temperature. The dominant feature of the floor assembly was a complex three-dimensional radiation and convection heat transfer within multiple cavities. The exposure profile was symmetric about the hydrocarbon pool fire and decreased inversely with the square of the distance from the pool fire origin. The project included a three-dimensional transient heat transfer analysis conducted using the finite difference model SINDA. The specific objective of the analysis was to provide the times at which certain portions of the aluminum floor assembly would reach a pre-defined critical temperature. The results were provided as input to a subsequent structural analysis. A visualization of a typical temperature response of the floor assembly is provided in the attached movie file. The animation depicts the temperature development in a quarter section of the floor assembly given a pool fire exposure from above. Heat enters the system from an imposed heat flux on the top surface that varies with the distance from the corner. Heat conducts into the stiffeners and radiates to the various steel surfaces forming the cavity boundaries. For perspective, the stiffeners are about three inches wide. The three-dimensional effects on the floor surface temperature caused by the conduction into the stiffeners is clearly shown in this animation as lower temperature zones.
Click to watch SINDA animation.
For more information contact:
Sean Hunt
shunt@haifire.com
410-737-8677 x254
