The convergence of virtual reality, parallel processing, and Internet access is enabling computational-fluid-dynamics (CFD) codes to model complex problems in the process and petroleum industries. Improved user interfaces are making it easier for non-specialists to use CFD to investigate the conditions under which flammable or poisonous gases, to investigate the conditions under which flammable or poisonous gases, for example, might build up around an oil platform. CFD rests on the sure foundation of the scientific laws that deal with mass, momentum, and energy. Engineers used CFD in the design of a coal-fired furnace whose burners produce a swirling flow, enhancing the efficiency of the combustion process. CFD codes simulate the processes in four key stages: ignition, laminar-flame propagation, turbulence generation, and turbulence-controlled combustion. The ignition process is usually represented by the sudden temperature increase of a small body of gas, such as in a single computational cell. Most CFD codes seeking to simulate explosions use variants of one of these models.
In the process and petroleum industries, computational fluid dynamics (CFD) can reduce development time scales and costs by replacing lengthy and ex- pensive laboratory investigation with numerical predictions. Yet some companies are unwilling to use CFD because of the cost of software and hardware, the need for in-house CFD expertise, and the time required to solve complex simulations. Several recent advances in computing, however, have enabled firms without vast computing power or extensive expertise to obtain solutions to complex CFD problems using virtual-reality methods via the Internet.
Many different types of simulation are relevant to the petroleum and process industries, including mixing and projected vessels; the combustion of solid and gaseous fuels within furnaces, and the subsequent formation of soot and NOx; the separation of mixtures of oil, gas, and water; fluid flow through pumps and valves; and gas dispersion. Computer simulations provide insight into these processes and many more; in some cases, they represent essential tools for a fuller understanding.
Of particular importance are cases in which safety is being investigated. As an ex ample, consider the safety of oil platforms and the risk of explosions. As is well known, combustible gases may leak into oil- platform modules, forming combustible mixtures with air. These mixtures may be inadvertently ignited, leading to explosive flame propagation. The pressures generated by explosions result in loading on the platform structure. Damage to and partial destruction of the platform may cause missiles to be projected, and consequent penetration of vessels containing liquid fuel may lead to spills and the spread of fire.
How high the structural forces, how severe the damage, and how lethal the missiles will be are all difficult to estimate, as are the fires that will spread. Yet all of these factors must be estimated if the adequacy of safety precautions is to be assessed 'and approvals to build and operate are to be given. Computer simulations provide a means of making such estimates by predicting the gas-dispersion and mixing process; the ignition, flame-acceleration, and explosion phenomena; the load on the platform structure; missile formation and motion resulting from structural damage; and the spread of fire resulting from subsequent oil spillage.
Several CFD packages can perform the necessary simulations. The specialist codes are applicable to only one of the processes mentioned; general-purpose packages are designed to perform simulations of all five kinds.
A Virtual Approach
CFD has an important role in many areas of the process industry, but it is often seen as technically demanding, computationally intensive, and expensive. One recent development in computing that is helping to change those ideas is parallel computing. CFD is ideally suited to parallel computers, since each processor can be used for a different section of the computational domain almost completely independently of the others. This means complex simulations can be solved much more quickly. Parallel computers are expensive, however, and many companies cannot justify the expense of a parallel-processing machine purely for CFD use.
Another development is the use of the Internet to connect computers that may be separated by a considerable physical distance. A third is in virtual reality (VR), because it is now possible to view and move around virtual worlds where the displayed view is as close to "reality" as the user desires.
These three advances have led to the establishment of a VR-based consulting service developed by the London-based company CHAM. Users set up their problems in a limited VR environment on their PC, and use the Internet to transmit their geometry and associated information to a network of parallel computers that can quickly provide a solution. Virtual reality makes CHAM's PHOENICS CFD code accessible to non-CFD experts, and it lets the engineer concentrate on solving the problem. Tills system requires only a PC, an Internet connection, and a knowledge of the process under consideration. Remote computing makes it possible to access the necessary computing power to solve the problem from a Pc.
PHOENICS runs on PCs and Unix platforms, but it performs its calculations in a way that has proved economical for use on either shared-memory or distributed-memory parallel computers. The technique is called domain decomposition, which implies the whole geometry to be simulated is cut into imaginary slices, with a PHOENICS-carrying processor devoted to each. Domain decomposition permits simulations to be performed with computational grids that are fine enough to represent the simulations adequately.
In the PHOENICS VR interface, dialogue boxes enable users to choose and alter material properties, models, and boundary and initial conditions, and to enter any other information applicable to the problem. Users can also move around their chosen geometry and view it from any angle. Objects can be at any orientation, and entire geometries can be imported from a standard CAD file. The PHOENICS results viewer can be used to plot a wide range of results in the virtual-reality environment, including streamlines, vectors, and contours on planes, iso surfaces, and x-y plots.
Laws and Models
CFD rests on the sure foundation of the scientific laws that deal with mass, momentum, and energy. However, the rigorous calculations needed to work out the implications of all these laws would vastly overstretch modern computational power, even that of parallel processors. Shortcuts (usually called models) must be used. CFD therefore also rests on the less secure foundation of models of turbulence, radiation, and chemical reaction. These models are embodied in sets of mathematical equations, similar in form to those for the conservation of mass and momentum, which purport to describe the most significant aspects of the phenomena in question.
The turbulence models now in use derive mainly from research projects performed at Imperial College in London in the 1970s. Additions with respect to combustion have come from the University of Trondheim in Trondheim, Norway. New advances have resulted in two models of turbulence, both of which can be activated by PHOENICS. One is known as LVEL, which is derived from L, the distance from the nearest wall, and VEL, the local velocity. The second is a multifluid approach to turbulence, which allows quantitative computation of what had to be guessed at before-namely, the probability-density function that describes the fluctuations of temperature, concentration, and the like.
Although explosion processes occur too rapidly for the radiative transfer of heat to exert much influence, quite the opposite is true of the spread-of-fire process, which may take place later. Radiation is a complex process that is expensive to compute exactly. The challenge, therefore, has been to invent a more economical (albeit less rigorous) formulation that is approximately correct.
The Immersol model that CHAM has developed and incorporated into PHOENICS simultaneously handles radiation between solid surfaces, heat conduction within those solids, and convective and radiative interactions with the surrounding fluids. The validation of this method is still in progress. At this stage, we can assert that it gives exactly correct results in simple circumstances and plausible results otherwise.
Chemical reaction is another expensive process to compute exactly. What may be expressed simply as a single step-fuel plus air results in carbon dioxide plus steam plus heat-actually proceeds by way of hundreds of individual reactions involving scores of distinct individual species, such as H, 0, OH, CO, and NO.
Fortunately, in contrast to some other applications CFD is used for (such as furnaces, gas-turbine combustors, and reciprocating engines), single-step models suffice for explosion and fire-spread simulation. It is far more important to represent the turbulence properly than to refine the chemical-kinetic description.
In evaluating the safety precautions and the risk of explosion on an offshore oil platform, leakage of combustible gas at a certain minimum rate may be regarded as inevitable (or at least possible). This assumption leads to several questions. Will gas-air mixtures arise that are within the limits of flammability? How large a volume of such a flammable mixture can accumulate in the module? Will that volume be located near a source of possible ignition? Such questions are easy for CFD to resolve if the location and rate of the leakage are specified and if enough is known about the ventilation conditions.
Faced with such a task, CFD will take into account the motion of the air, under the combined influences of ventilation induced by exposure to the external atmosphere; buoyancy (density differences interacting with gravity, whether driven by temperature or concentration); the momentum of the gas jet, if this is appreciable; any internal-ventilation fans; the resistance exerted by the solid objects in the module; the turbulence generated by the flow past the solid objects; and the resulting evening of composition differences.
In 1988, an explosion on Piper Alpha, an oil rig in the North Sea, resulted in a fire that completely destroyed the platform, killing 167 people and costing millions of dollars in lost revenue each day. PHOENICS has generated results that include the influence of a crosswind (neglected in some earlier studies) on the distribution of combustible gas within a module of the platform. One focus, the concentration of gas from a leaking flange joint, enabled us to explore the assumption that the wind entering the open end of the module is aligned with the module axis. PHOENICS also shows that the gas concentration when the wind is from the left has a component along the inlet face of the module. The two concentration profiles are markedly different, because of the different velocity profiles.
Had such computer simulations been done at the time of the British government's public inquiry into the Piper Alpha disaster (as they could have been, albeit less easily than today), the simulations would have provided a more accurate picture of what happened. The investigation instead relied on physical model experiments, and these took no account of the side wind effect, even though the wind direction was known to be oblique to the module end on the night of the disaster. The inquiry, however, ultimately did result in new regulations that set high standards for the safety of offshore platforms.
CFO and Explosions
What if an ignition source exists within the region in which CFD predicts that a flammable mixture will form? Will the flame be extinguished before spreading, or will it propagate with increasing speed and violence, leading to a fully developed explosion? Such are the questions to which a CFD code can supply answers that are probably correct. Of special interest are the pressure differences across damage-prone confining walls: What will they be, and how will they vary with time?
The physical and chemical processes under consideration are flame propagation in unconfined gas mixtures, pressure rise in fully confined gas mixtures, the generation of turbulence by the flame, and the effect of pressure gradients. When a spark ignites a flammable mixture that is initially at rest, a thin spherical flame spreads from it at a speed (relative to the unburned gas) of between 0.1 and 1 meter per second, depending on the fuel and its concentration. Although such flames might have a bad thermal effect by reason of their high temperature, they can scarcely damage structures, because pressure differences are approximately equal to the density multiplied by the square of the velocity. The density of unburned gas is approximately 1 kilogram per cubic meter, and the velocity is-at most-10 meters per second. Therefore, no pressure differences in excess of 100 newtons per square meter (0.1 atmosphere) are likely to arise.
To consider the other extreme, suppose that the combustible mixture is completely confined within a fixed volume enclosure, raising the gas temperature within from, say, 300K to 2,100K. Then, no matter how rapidly the flame propagates, the pressure rise will be approximately 2,100/300:1, or 6 atmospheres. This is enough to fracture many structural elements. Unfortunately, this is not even the worst case.
If the gas mixtures in offshore-platform modules burn, they must be regarded as partially confined. They are present in spaces between solid obstacles, both large (such as compressor housings) and small (such as tubes within a tube bank). The influence of these restrictions to flow is to distort the shape of the flame in such a way as to promote the mixing of hot, burned gas and cold, still-to-be-burned gas. This increases the volumetric burning rate, so the flame speed (insofar as this concept has any clear meaning) rises by one or two orders of magnitude.
When we view the progression of an explosion in a vented, baffled enclosure, the flame propagates around each pair of baffles and accelerates along the center of the enclosure. The shape of the flame closely matches experimental images obtained by the British health and safety executive as part of the Piper Alp ha investigation, using high-speed video techniques.
The motion of gas through the succession of restrictions and enlargements represented by the solid objects in an oil-platform module creates shear layers or regions exhibiting steep variations of velocity. Turbulence is created in these layers; this turbulence promotes the further mixing between burned and u n- burned gases, which leads to further combustion.
Like velocity gradients, pressure gradients can lead to flame acceleration. They act by accelerating the less-dense hot-gas fragments more easily than the denser unburned fragments. The former are therefore thrust vigorously into the latter, forming new sources of ignition. This process can lead to detonations, or explosive waves, in which the pressure exceeds even the constant- volume-burning pressure. CFD codes simulate the processes in four key stages: ignition, laminar-flame propagation, turbulence generation, and turbulence-controlled combustion.
The ignition process is usually represented by the sudden temperature increase of a small body of gas, such as in a single computational cell. Until the flame meets• the first obstacle, it is represented as progressing as a thin front at the speed known from laboratory experiments. Differential equations are usually solved for the energy and the length scale of the subsequently generated turbulence. These may contain special, empirically derived terms for the effect of obstacles, particularly restricted ones. The rate of gas burning is then taken as proportional to the rate of energy dissipation, i.e., to the square root of the energy divided by the length scale.
This practice is called the eddy-breakup model. A modification is known as the eddy-dissipation concept. Most CFD codes seeking to simulate explosions use variants of one of these models. All such practices rely on the notion that there are two distinguishable gases at each location, one significantly hotter than the other. They can be classified as two-fluid models. PHOENICS embodies the recent generalization called the multifluid model.
On an offshore oil platform, leakage of combustible gas may be regarded as inevitable (or at least possible).
A well-known but often neglected fact about CFD calculations is that, unless the number of space and time intervals is sufficiently numerous, numerical errors render their results dubious. How many intervals are enough? The only way to find out for certain is to repeat the calculations with a greater number of intervals, so as to determine whether the physically significant results are appreciably altered. This rule is accepted but rarely observed, because the expense of finer-grid calculations may be hard to tolerate. PHOENICS is no different from other codes in this respect. However, because it can run on parallel machines, the cost of the finer-grid runs is more affordable.
Furthermore, the predictions are intended to answer questions that are not always sufficiently realistic. Thus, a uniform stoichiometric mixture of gas and air may be postulated as prevailing throughout the module in which the explosion is to be simulated, yet this initial condition could never be attained in practice. Or wind conditions external to the module may be supposed irrelevant and therefore inserted with little thought, whereas in fact a• crosswind may greatly influence gas mixing within a module. Finally, the making of initial-condition postulates about the locations of gas leaks and ignition sources involves much guesswork; with so much uncertainty, we can argue that some numerical or scientific deficiencies can be tolerated.
Models of turbulence, chemical reaction, and radiation properly have science-based uncertainty attached to them. This doubt is quantitatively substantial; in the case of explosions in offshore modules, it could mean that the predicted peak pressure, for example, is correct within ± 50 percent. Only extensive comparisons between predictions and experiments can reveal the size of the errors. Given the expense of these experiments, it may be many years before the question is adequately answered.
This article is adapted from a paper presented at the ASME Asia '97 Congress and Exhibition, held in Singapore Sept. 30-Oct. 2, 1997