Thermal Analysis

Introduction

The response of structures to thermal loading can be effectively simulated using both computer-aided and hand techniques. Having assessed the temperature distribution in structures and components it is then possible to derive the induced stresses.

Cyclic thermal and structural analysis can be used to optimise components or to restrict the effects of thermal loading.

The Nature of Thermal Loading

Thermal loading can arise from many sources including but not limited to;

Hot Sources: process fluid transport, hot gasses, fire, proximity to heat sources such as boilers, incinerators and engines or being contained within heat generating components such as engines.

Cold Sources: Low temperature process flow, low temperature storage, low ambient temperatures such as extreme winter temperatures and/or high altitude.

Heat Transfer Mechanisms

Heat is transmitted to, from or into a component or structure by any combination of the following mechanisms;

Radiation: the electromagnetic transfer of heat from a higher temperature source to a lower temperature target, for example in the case of a radiator heating a room.

Convection: the transfer of heat usually by the movement of a liquid or gas, for instance heating of water in a boiler.

Conduction: the transfer of heat through a solid, such as steel tubing in a boiler.

There are many instances where all three mechanisms are present, such as in the case of a jet fire playing on a steel structure or a pressurised vessel. Here there is radiation and convection within the flame itself, which transfers heat to the impinged structure. The surface of the flame radiates heat, which is absorbed by the steel, and finally, heat is transferred away from the flame-impinged area by means of conduction through the steel. The steel will also loose heat by means of convection and radiation.

When bodies receive heat by radiation, the body only absorbs a proportion of the flux; the remainder is re-radiated by reflection. The quantity of heat absorbed is governed by the emissivity of the material surface. The emissivity also has an influence on the quantity of heat radiated from a hot body.

Insulation

An effective way to protect structures from thermally induced loading is to provide insulation, this could be to prevent heat being radiated away from a source such as a high temperature steam pipe, or to prevent heat being transferred to a cold transport such as refrigerant pipework. Thermal analysis is used to assess the effect of the insulation, thus enabling design of efficient schemes.

Material Effects and Thermal Loading

With some exceptions such as water below 4° C, bodies expand as they are heated and contract as they are cooled. This change in dimension is controlled by the coefficient of linear expansion. Along with many other physical properties of a material, this coefficient can be temperature dependent. In the case of steel, its elastic modulus and yield point falls with increasing temperature, both falling to zero in the region of 1000° C. The expansion coefficient increases with temperature. The specific heat capacity rises to a peak at the Curie Point, then reduces again.

Analysis Techniques

There are several well-recognised techniques for the analysis of thermal response, leading to steady state and transient (time related) temperature profiles. The choice of steady state and transient conditions will usually be made following consideration of the temperature source and operating conditions.

Hand Calculation

Many thermal-loading conditions can be solved by hand calculation, especially where the initial conditions are simple or the body being heated is simple in nature. It is possible to look at both steady state and time dependent solutions in this manner.

Steady State Analysis

Steady state thermal analysis looks at the temperature distribution in a body at the time where the heat input to the system is equivalent to the heat output, i.e. there is no heat being used to change the temperature of the body in question. The analysis ignores the transient phase where the temperature state changes from its initial condition to the working condition. A good example would be the walls of a boiler or the crankcase of an engine.

Thermal Transient Analysis

Transient analysis allows the determination of the thermal solution with respect to time. The solution considers the rate of heat input and the mechanisms and efficiency of the heat transfer and the heat used to change the body temperature. Evidently the input parameters can be changed with time to model different boundary conditions, such as varying ambient temperatures.

Non-Linear Thermal Analysis

Non-linear thermal analysis will look at the solution of thermal systems where the material properties change with temperature. The specific heat capacity of steel for instance, rises with temperature. Other non-linear schemes will involve the change in radiative and convective properties as temperatures vary.

Combination of Thermal Loads With Other Loads

Following a thermal analysis to establish temperature distribution, whether steady state or transient, the resulting temperatures can be combined with a stress analysis.

The stress analysis can be static or dynamic, elastic or non-linear. The material non-linearities can be temperature and strain dependent, allowing the consideration of complex interactions.

Uses of Thermal Analysis

Thermal analysis is a useful tool for the determination of temperature boundary conditions, or for determining the temperatures and heat loss properties of components.

Some Typical Uses

• Temperature isolation: the analysis of thermal insulators to determine their efficiency in preventing heat transfer.
• Thermal conduction: the assessment of temperatures at given locations in structures. The temperature distribution could be calculated either as a steady state or a transient depending upon the conditions.
• Temperature induced stress: use thermal analysis to determine temperature distribution. Use the resulting distribution as the temperature distribution in a stress analysis, which can combine thermal expansion and the effects on material properties.
• Fire protection: thermal analysis can be used to establish the temperature/time relationship influencing a structure subjected to fire. The analysis can take account of fire barriers and protective materials such as intumescent coatings and fireboards.
• Heat sinks: in many applications heat sinks can be used to control temperature rise. Analysis can determine the effect of different heat sinks and help to determine the best design. Examples would be additional mass of material, and static or moving water or oil.
• Heat loss: the influence of heat loss mechanisms can be investigated, such as the movement of air over heated surfaces to proved intentional or un-intentional cooling.
• Radiation loss: the determination of radiative heat transfer from surfaces to enable assessments to be made of the effect on other neighbouring processes or personnel.
• Mixed materials: study the influence of different materials in the heat transfer path, the inclusion of insulators or improved conductors for instance.

Design Optimisation Techniques

(Simulated Prototyping)

(What If? Studies)

Design optimisation is the name given to techniques primarily designed to optimise components. Optimisation is not the only use for this technique, since it can be used to tune or de-tune systems, provide a basis for design development and to look at the influence of various parameters on a design. In the computer application of the method it is not necessary to give full control of the process to the program, the engineer can control the process at all steps.

Optimisation of structures and systems leads to more effective use of material to reduce cost and/or improve performance. Optimisation can be used to find the best means of preventing heat gain or heat loss, or conversely finding the best means of achieving heat gain or heat loss. Once the mechanisms for heat transfer are determined, then they can be represented parametrically, which then allows automatic or semi-automatic adjustment to find the optimal values.

The optimisation can then be passed onto structural analysis. One large-scale application is the optimisation of fire protection measures on structures. The thermal analysis is used to assess the temperature distribution in the frame taking account of the flame temperatures. This would be a time dependent study, therefore the rise and decay of the fire can be modelled. The thermal analysis would also take account of the locations and properties of fire barriers and protective coatings.

The time related temperature distribution is then passed to the structural analysis and a time to collapse can be determined. This technique which helps in ensuring that structures can be safely evacuated is used in the offshore oil and gas industry.

The techniques used in design optimisation can be used to prototype designs. This helps to reduce the time to bring products to market by cutting out the need to build a series of prototypes. Whilst prototyping will not be entirely eradicated, fewer prototypes will be required. Results of testing on prototypes can be fed back into the analysis for the next design cycle.

Trouble Shooting

Thermal effects can often lead to structural problems without being readily suspected. In systems that include temperature and displacement, the support requirements for each of the loading schemes are mutually exclusive. A structure designed to restrict displacement-induced stresses due to vibration will often not be supported correctly for the reduction of thermally induced stresses. A combined thermal and structural analysis will help to balance the requirements.

CREA Consultants can study failed components to attempt to determine the cause of failure. These studies can be combined with design optimisation techniques to rapidly determine design modifications.