Dear Hemanth Gurumurthy ,

Rate release rate can be related to rate of change in pressure and volume using 1st law of thermodynamics.

HRR = gamma*P*(dV/dt)/(gamma-1) + V*(dP/dt)/(gamma-1)

It's not, strictly, a question of formula... (and, depending on exactly what you want to know, you'll need a sophisiticated model -- possibly/ideally numerical, with combustion dynamics... and with lots of formulae...)

In principle, this is just the most basic question of conservation of energy. However, there are complications...

It's a question of what exactly do you want to know (e.g., thermal efficiency) and what you *can* measure reliably (and exhaust temperature is not nearly enough).

Theoretically, it's very easy... in practice, not so much...

But first, you need to specify what "rate of heat release" are you referring to. The rate of heat release of the combustion itself? (that one is 'relatively' easy) Or the rate of heat release of the engine to the surroundings? (i.e. the heat 'released' by the combustion minus the mechanical work done by the engine)

Let's say you know the enthalpy of combustion of gasoline in ideal stoichiometric/lean conditions, i.e., perfect combustion, no CO products (you can find this info easily). Then, if you know the average mass flow of gasoline into the engine, it's a straightforward calculation... The compression ratio and the heat tranfer to the combustion chamber are irrelevant in this case: it only matters if you want to estimate the temperature of combustion (which you can model and, possibly, even measure) and/or the instantaneous heat release (for which you would need a model). If the combustion conditions are not 'ideal' (i.e., incomplete combustion due to rich mixture or heterogeneous charge, etc.), things get complicated. You would need to know the composition of the exhaust gases and use a combustion model.

If you want to know the *instantaneous* heat released by the combustion process, measuring the exhaust temperature is definitely not enough. There's a correlation, obviously. But there are numerous factors that influence exhaust temperature (heat 'leaked' into the head/block/piston walls, expansion ratio, expansion speed, compression ratio, rpm, gas mixture composition of the exhaust, etc... etc...).

If, on the other hand, you want to address the thermal efficiency, the mechanical work done by the engine is the difference between the enthalpy of combustion of the burned fuel (assuming near ideal combustion conditions, this is relatively easy to find) and the heat dissipated to the environment, of which the heat lost on the exhaust is just a part. The advantage of measuring the exhaust is that it's technologically easy to measure its temperature, composition and mass flow... in case you want to know the heat dissipated by other means (i.e., radiation and convection).

Sorry about the long reply. You need to be more specific, in order for me to be able to help you better and be more focused on the answer.

@Luis Sousa Rodrigues. As a part my study i need to analyse the rate of heat release as the result of fuel combustion to be related to the exhaust temperature measured before turbocharger.

We can measure the IMEP and the rate of heat release itself. However, i know that I need to accommodate for the heat lost to the surrounding from the engine before the exhaust gas reaches the point before the turbocharger where the temperature is measured.

Coming back to the question. Is there any mathematical equations or previous literature that studied the relationship among exhaust temperature before turbocharger, the rate of heat release and heat lost to the surroundings.

@Henanth,

The short answer to your question (if read strictly and literally) «Is there any mathematical equations (…) (for computing) the relationship among exhaust temperature (…) (and) the rate of heat release and heat lost to the surroundings?» is: no.

However, there is an obvious direct correlation between the amount of heat (i.e., thermal energy) released and the EGT:

(H_combustion – Q_loss) = m_gases x (cp_exhaust x EGT – cp_mixture x T_intake).

But not the rate (power).

I.e., if you mean to ask if there is a simple analytical relationship between the heat release rate (HRR) of a combustion reaction inside the combustion chamber of an ICE and the exhaust gas temperature (EGT) (before the turbocharger turbine is irrelevant for the current purpose), the answer is clearly no. You see: since exhaust happens after combustion is complete (not strictly true in every case, but… let’s simplify), the HRR (or the “quickness” that heat is released with) has no direct relation with EGT (which doesn’t mean that there is no correlation; there is a correlation, but it’s minimal and more complicated).

The HRR surely influences the amount of heat dissipated through the combustion chamber walls, since this depends on time (of exposure). But this is not easy to model at all. The highly dynamic and non-adiabatic internal environment of an ICE combustion chamber is still very difficult to model with precision. Also, the number of variables that might influence EGT in an non-adiabatic chamber is massive, e.g.: area, volume, geometry, temperature, thermal conductivity and heat capacity of the chamber boundaries (which are not uniform, btw), rate of expansion (directly from the RPM and engine geometry)… etc… not to speak of combustion dynamics and fluid dynamics, which are another “can of worms” altogether…

Adiabatic models are much simpler and can, frequently, give us adequate results, within their clear limitations. However, if we ignore the heat dissipated through the combustion chamber boundaries, then the EGT has nothing to do with the combustion HRR, whatsoever…

Concluding, there’s no quick and straightforward way to compute/calculate the HRR solely on the EGT or vice-versa. Even if that is virtually possible, you would have to build a rather complex model, based on several differential equations only solvable by numeric (iterative) methods. Quite a mess…

Nevertheless, it would be virtually possible to fit an empirical mathematical model to a *specific* engine, once it is sufficiently tested and measured, and the relevant covariates are identified. But I have serious doubts about the feasibility of such endeavor…

I may, however, have misunderstood you. I’m still not 100% sure I got you right. If that’s the case, please let me know.

@Luis Sousa Rodrigues Thank you for the detailed answer. Your understanding of the question is right. Now I have known what are the complexities and requirements for the modelling. I will give it a try to model with a data that are available.