Non-invasive temperature measurement of turbulent flows of aqueous solutions and gases in pipes

Abstract Accurate and responsive non-invasive temperature measurements are enablers for process monitoring and plant optimization use cases in the context of Industry 4.0. If their performance is proven for large classes of applications, such measurement principles can replace traditional invasive measurements. In this paper we describe a two-step model to estimate the process temperature from a pipe surface temperature measurement. This static case model is compared to and enhanced by computational fluid dynamic (CFD) calculations to predict transient situations. The predictions of the approach are validated by means of controlled experiments in a laboratory environment. The experimental results demonstrate the efficacy of the model, the responsiveness of the pipe surface temperature, and that state of the art industrial non-invasive sensors can achieve the performance of invasive thermowells. The non-invasive sensors are then used to demonstrate the performance of the model in industrial applications for cooling fluids and steam.


Introduction -The relevance of non-invasive temperature measurement in process industries
Digitalization and Industry 4.0 have created a new industrial environment for sensors [1]. Flexible measurement solutions for monitoring and optimization that can be cost effectively and reliably installed in existing plants are key sources of new insights into industrial processes [2].
With temperature being one of the fundamental and often critical process parameters, this paper demonstrates a non-invasive approach to measuring the process temperature in a large number of common industrial processes. Such an approach can greatly simplify the engineering and implementation of temperature measurement while significantly enhancing the safety over traditional invasive approaches. The ability to infer the process temperature without the need for a penetration in the piping eliminates leak points, and minimizes the risks and costs associated with shutting down a running process to install a new measurement point. Critically, the temperature inference has to provide comparable, if not better, performance than traditional invasive approaches in terms of accuracy, repeatability and responsiveness to changes in the process temperature.
The current state of the art in temperature measurement that does not penetrate the piping are skin type or surface temperature sensors. Such sensors are widely used in the process industry and other contexts [3,4,5,6]. However, they are considered to be less accurate and slower to respond than invasive measurements in a thermowell. In addition, the measurements can easily be influenced by ambient conditions such as convective currents, radiation or even outdoor effects [6]. The questions that need to be posed are whether their performance is a result of their construction and usage or if the inaccuracy and slower response are physically represented in the interaction of the pipe with the fluid.
In an industrial context, Gorman et al. [7] describe an approach to understand the measurement deviations of a surface measurement by considering the interaction of an uninsulated pipe carrying a process fluid with a surrounding ambient environment. Through dimensional analysis, a considerable number of parameters are organized to give an estimate that demonstrates a range of process conditions where a surface measurement is adequate. Nouri et al. [8] propose an elaborated shielded cable sensor setup for achieving reliable accuracy indicating clearly that the performance of the sensors can be improved with careful design.
However, what seems to be lacking is a validation of the application space for non-invasive measurements that considers both the static and dynamic requirements in industry.
In this paper we address this gap by first describing, in Section 2, a step wise model-based procedure for estimating the process temperature, with the surface temperature of the pipe as the primary physical measurement point.
In Section 3, analytical and CFD methods are developed to predict the temperature difference between a surface measurement on a pipe and the average bulk temperature of a flowing process medium. Organization of the use cases and the parameter sets for error estimates are done from an industrial end user's point of view. This means we aim at reducing the parameter space by imposing boundary conditions and parameters of relevant use cases. For the scope of this paper, we look primarily at important industrial cases where the analysis yields that the boundary layer resistance can be neglected.
Use case examples are considered in Section 4. Static and dynamic predictions of the models are tested first under controlled conditions on a test rig with water as the process medium. The performance of the models is then validated using results from real industrial applications of non-invasive sensors mounted in close proximity to traditional invasive ones.

Two-step measurement approach
The setup for a non-invasive temperature measurement in an industrial context is often similar to the one shown in Figure 1. A process medium is conveyed in a pipe that is protected against ambient conditions by one or several layers of insulating material. The outer surface of the insulation interacts with the ambient via convection and ra-diation. The fluidś thermal interaction with the pipeś inner surface can often effectively be described by a thermal boundary layer with certain properties.
The situation is axisymmetric at this stage, and the thermal behavior of the setup in a steady state can be described by a linear chain of thermal resistances (see e. g. [5,8] for previous work on this approach). Details of our specific formulation and use of the model are given in Section 3.1. We will call this the process model. If the parameters are known to sufficient accuracy, as well as two temperatures along the chain, an estimate of the medium temperature can be calculated. Among the challenges when using this model is knowing the thermal characteristics of the boundary layer.
The approach to determine an estimate of the medium temperature can therefore be divided into two steps. Having set up the process model, the next task is to accurately measure two temperatures, e. g. those of the pipe surface and the ambient.
In particular, finding a good estimate of the pipe surface temperature T s is important and a challenge. Restricting ourselves to contact temperature sensors such as resistance temperature detectors or thermocouples, the sensor element, packaged for industrial environments, in some way has to be immersed in the insulation in order to make contact to the pipe surface. To some extent, the cylindrical symmetry characterizing the process model will be broken by conduction paths through the sensor in contact. Therefore, a specific type of model is needed to infer a good estimate of the surface temperature T s , e. g., as indicated in Figure 1, from sensor readings T primary and T reference . We will call this the device model. Details on the device model and the efficacy of devices using this approach can be found in previous publications (e. g. [9]) and will not be covered further. However, measurements using devices that incorporate this model will be shown and analyzed in later sections of this paper. The next section covers the development of analytical and numerical process models.

Process models, analytical and numerical
Models of the temperature measurement process can be used in different ways. First it is important to understand the physical situation of given use cases in order to determine applicability of a measurement concept. Some models can be embedded in intelligent devices (devices which have internal computation capabilities) for online measurement correction. Second, larger-scale offline simula- tions, e. g. involving CFD, can be used for benchmarking the embedded models. They are also relevant for understanding transient phenomena.

Analytical models and correlation formulae
Thermal interaction of fluid conveying pipes with their ambience has been extensively considered in literature (see, e. g., [10], and references therein). Assuming cylindrical symmetry one arrives at a one-dimensional description of the situation. It is shown schematically in Figure 2. In the figure, T m is the fluid mean temperature, the target of the measurement process. T m is generally defined via the convective heat flowq in the pipe, and the local flow of heat capacity c P ρ v is used as weight function when taking the mean over the pipe cross section A: For a homogeneous flow (ρ = const and c P = const) the mean temperature is simply correlated to the flows of heat, mass and volume: T wi is the temperature at the inner wall surface. The temperature field is assumed to be continuous there. T s is the temperature at the pipe surface. We assume that the contact resistance between insulation and pipe is negligible as compared to the insulation resistance. T ins is the temperature at the outer surface of the insulation. T amb denotes the ambient reservoir temperature in a certain distance from the isolation. q i , i = 1, 2, 3 denote the heat flow densities at corresponding values of the radial variable r.
To describe the thermal layer resistances (which we define as temperature difference per heat flux), we start with the pipe flowś boundary layer. We use the definition of the Nußelt number where κ f is the fluidś heat conductivity and h 1 is the hypothetical contact conductivity between fluid and inner wall surface (the conductivity of the fluid boundary layer). The pipe diameter D is taken as characteristic length scale. We then have for the heat flow density across the inner pipe surface giving as the boundary layer resistance. For the temperature difference across the wall, the radial heat equation leads to with R w as the layer resistance for the wall. The resistance of the insulation layer is, analogously, At the external surface of the insulation we generally may have convection with a coefficient h 3 and radiation where σ and ε are Stefan-Boltzmann constant and surface emissivity, respectively. The combined resistance R cr of convection and radiation is In many cases, a detailed consideration of radiation can be avoided, since e. g. metallic low-emissivity covers can be used to ensure that radiative effects do not significantly contribute to heat transfer or can be included in an effective convection factor. Then we end up with just The total resistance R tot of the chain is given by From the definitions and the chain setup we arrive at the equation for calculation of T m from measured quantities T s and T amb and known or estimated parameters: As an example for a reasonable treatment of the boundary layer in turbulent flow range: For liquids as well as for gases, in this study we use the modified Petukhovformula as proposed in [11,12,13,14] Nu turb for 4000 < Re < 10 6 and 0.1 < Pr < 10 3 .
The application range covers, e. g., large classes of water and gas flows. For the purpose of this work, effects of the entry length L are neglected. ξ should be calculated according to Konakov's formula [15]: This formula is valid in turbulent flows in approximately smooth pipes. For laminar flow (Re < 2300) the Nußelt number approaches Nu D,lam ≈ 4, the exact value depending on thermal boundary conditions. The transition region 2300 < Re < 4000 can be covered by a linear interpolation. For industrial purposes it is often of interest to consider the expected relative deviation Δθ: It can now be estimated for a given use case, if medium, geometry and operation point for an industrial application are known. Certain parameters, e. g. regarding the insulation, can also be provided for the measurement points as a standard. In particular, regions can be determined where Δθ is small enough so that an online compensation for it is not necessary. In a water application with a stainless steel pipe and mineral wool insulation of a prescribed thickness d ins , for example, one may determine the range of allowed Δθ for a process run at approximately 60 ∘ C as a function of pipe diameter D and flow velocity v. Δθ and the validity region with Δθ < 2 % are plotted in Figure 3.
These results are in good agreement with experiments and calculations given in Sections 4.2 and 4.3.
A full investigation of measurement uncertainties for the noninvasive measurement concept is beyond the scope of this paper. Nevertheless it makes sense to study the mea-  surement uncertainty associated to the model in Equ. 12 for an operation point which is representative for the experiments and use cases described in this article. Following [16], we perform a Type-B assessment with estimated uncorrelated uncertainties of the inputs in the model. As operation point we use the parameter set as given in Figure 3, now specifically for a DN80 pipe with a medium flow velocity of v ≈ 2 m s −1 . This corresponds to a typical situation in the experiments described in Section 4.1. For simplicity and physical clarity, the uncertainty analysis is done on the level of temperatures and resistances. As inputs for the calculation, we assume standard uncertainties for the temperatures and relative uncertainties for the resistances. The calculation of the uncertainty u c (T m ) of the medium temperature measurement is given in Table 1.
We find that u c (T m ) is dominated here by the measurement uncertainty of the surface temperature T s . It has been assumed to be 0.2 K. The model correction T m − T s for the case is remarkably small, in the range of 10 mK. The situation is quite common for industrial processes with aqueous solutions as process medium, and for many others, too, such as steam applications. In particular, the analysis applies qualitatively to the experimental situations as described in Sections 4.1, 4.3 and 4.4.

Setup of CFD models
The correlation formulae used in the process model above are based on heuristics and experience from a large num-  ber of measurements reported in literature. However, a drawback of these models is the inability to predict the thermal response of piping to changes in the temperature of the fluid. An well-known option is to do CFD calculations for studying conjugate heat transfer in pipes [17]. We use them here not only as a sanity check for the heuristic approach but also to understand transient phenomena.
The model solves equations of mass, momentum and energy conservation within the computational domain to calculate the flow and temperature fields. The k-εequations are additionally solved to resolve turbulent effects within the fluid. The flow was simulated to be hydrodynamically fully developed by imposing a power law velocity profile at the inlet. A mesh which was found to yield good convergence and stable results for this calculations is shown in Figure 4. Wall functions incorporated in the k-εformulation were imposed at the pipe wall, to resolve flow complexity there. In this way, the necessity of further nearwall mesh refinement can be avoided. The pipe model has a length of 4 m. Analyses of the radial temperature distributions have been done across a transverse section of the fluid and pipe, at the center of the 4 m pipe length. At the pipe outlet ambient pressure (gauge pressure equal to zero) was prescribed as the boundary condition. The velocity field within the pipe, as expected for turbulent flow, is almost uniform across the pipe, drastically reducing to zero at the wall.
In the next section, we compare and contrast some results from these inference models to measurements under test rig and real industry conditions.

Experimental results and industrial use cases
In this section, experiments from a test rig with water flow are described, and performance predictions for noninvasive measurements are analysed using the data. After that, we consider and evaluate test results for a water and a steam flow taken from measurement points in industrial plants.

Experimental setup: Turbulent flow of water in metal pipes
A set of experiments were carried out on a flow process test rig at ABB Corporate Research Germany. The flow rig consists of a system of tanks with the capability of pumping water through metal piping with standard flow rates ranging from 5 l/s to 20 l/s from one tank to another in a continuous closed loop system. The temperature of the fluid in the tanks is controlled by circulating a portion of the fluid contained in a tank through a heat exchanger system. Much like an industrial process facility, the rig is controlled by a distributed control system (ABB 800xA) and all sensor data are collected over a profibus DP system and stored in operational data historians. For the purposes of validating the performance of the process models, a comprehensive set of sensors were installed on a DN80 stainless steel pipe with a wall thickness of approximately 3 mm. The sensors are as follows (see -Invasive measurement with standard 6 mm inset rods, without thermowell, approximately at the inlet and outlet of the straight measurement section, -a standard 3G thermowell, mounted according to the state of the art, located 50 cm downstream of the start of the section, -an ABB non-invasive temperature sensor with a device model located 1.5 m downstream of the thermowell, -Pt100 sensors glued to the pipe surface below 5 cm of insulation, mounted approximately 50 cm upstream and downstream of the ABB non-invasive temperature sensor.
The experiments were started from ambient conditions in a climate controlled environment of 20 ∘ C with the piping filled with water at close to the ambient temperature. The inlet and outlet valves were then closed and the water in the tank before the inlet heated to 65 ∘ C. The pump was then started with the valve to the measurement section still closed until the set speed was achieved. The inlet valve was then opened with the pump pushing in hot water to replace the ambient temperature water in the piping such that the flow rises in an approximate stepwise manner. The valve opening time is in the range of 0.5 s to 1 s and the flow rate was approximately ≈ 10 l s −1 , which corresponds to a flow velocity of ≈ 2 m s −1 .
The response of all sensors was logged over the bus system with a logging frequency of 1 s. The experiments are carried out with a curtain separating the measurement setup from the rest of the room thereby creating an environment around the piping solely with natural convective currents. The experiments were run at a continuous process temperature of 65 ∘ C for at least 1.5 h thereby ensuring that both the static and dynamic cases were adequately represented.

Comparison of models and experimental results
We start with the steady state response and then address the dynamic responses. Figure 6 shows the situation after complete thermalization of the rig. The maximum variation among all sets of measurements is less than ±0.5 ∘ C. On this small scale, the deviation of one of the Pt100 sensors can be attributed to small differences in the glue-fixation to the pipe. Of particular interest is that the deviation between the measurement insets without the thermowell differs by less than 0.1 ∘ C from the ABB noninvasive sensor and the Pt100s. This difference is generally insignificant in industrial applications. The close coincidence of surface measurements and fluid temperature is in line with predictions from the heuristic process model in Section 3.1 and CFD-calculations as outlined in Section 3.2.
Model results are shown in Figure 7. Predicted differences between wall and water temperature are in the range of 0.01 ∘ C. Both models start from the same pipe surface temperature. The analytical model estimate for the tempera- ture difference to the process is ≈ 0.003 K larger than the CFD prediction. We now examine the dynamic response. The results shown in Figure 8 demonstrate that the surface Pt100 measurements show the fastest response. The unshielded insets, surprisingly, are slower by about 5 s to 10 s. The response time T 90 of the thermowell is ≈ 30 s to 35 s which agrees with specification for an optimally installed 3G thermowell. T 90 for the non-invasive device is in the range of 35 s to 40 s with the device model designed to ensure no overshoot. The thermowell reaches standard accuracy of ±1 ∘ C after about 35 s. The non-invasive device needs about 45 s, largely due to a remaining slow time constant in the setup. Both insets and the Pt100 register a slight ringing of the temperature signal which comes from the recirculation of room temperature water which was present downstream of the pump reentering the tank and cooling the incoming water slightly. This happens over a time scale that is faster than the response time of both the thermowell and the ABB non-invasive sensor.
Shown in the graph is also the predicted dynamic response of the CFD model showing a remarkably good match between rise time of the experimental measurements and that of the model. These results would indicate that CFD models could be used to predict the dynamic thermal response of non-invasive measurements for common process fluids.
In the next section, we present industrial use cases where the ABB non-invasive sensor is used as the reference of the surface response and is compared against invasive thermowells.

Industrial use case -Cooling water
Water and other cooling or heating fluids are widely used in heat exchangers in the process industry and naturally temperature is one of the critical parameters for control and monitoring purposes. For many of such use cases not all parameters for estimating the performance of a noninvasive measurement need to be known. By way of example, it suffices to know that a water-like is flowing and in a turbulent regime to know that a non-invasive temperature measurement is promising. A successful example has been investigated in long-term tests on a DN300 cooling water pipe. Based on the results in Figure 3 we expect good agreement with invasive measurements already for moderate flows. A snapshot of the results is given in Figure 9. Testing over several months, the average difference between the non-invasive and the thermowell measurement was 0.14 ∘ C with a standard deviation of 0.13 ∘ C. As demonstrated in this case, the non-invasive measurement meets the requirements of the application. A few data points show a large deviation from invasive measurements. They are connected to low-flow situations or even shutdowns where the thermal field starts to get highly inhomogeneous, and where both temperature measurements, therefore, are not representative.

Industrial use case -Steam measurements
Analytical correlation formulae and CFD calculations also suggest that there are certain classes of gas flows for which a non-invasive temperature measurement is promising. Due to its widespread and common use as a heating medium, we selected steam for a more detailed investigation. Here we present data from a district heating application where a non-invasive approach makes it easier to add distributed temperature measurements in the network without significant shutdowns. In this use case, we consider a DN125 steam process pipe, insulated and conveying superheated steam at about  250 ∘ C and approx. 10 bar and a flow rate between 1 t/h and 5 t/h. Table 2 shows that the predicted deviations differ, but are in the same acceptable order of magnitude.
In particular, the total expected deviation is less than 1 % of the temperature difference between process and ambience. Figure 10 shows an accuracy analysis of a corresponding benchmark test under industrial conditions. The noninvasive device is compared to an existing invasive temperature measurement which complies to the industry's standards. Although insulation was removed locally for this (indoor) test, the correspondence of thermowell and noninvasive measurement is remarkably good with an average of less than 0.1 ∘ C difference between the two. The non-invasive device, interestingly, shows generally a slightly higher value than the invasive one. Among the reasons that could lead to this effect are heat conduction errors in the thermowell installation [3,18], similar to those which have been studied in recent literature [19]. Of course, the remaining spread in the data can also be connected to the lack of a local insulation at the measurement point. The latter often is shielded quite well already by the stainless steel device adapter and small air gaps in the setup (shown in Figure 1). Nevertheless, if ambient effects are expected such as radiation, wind or generally time variations of the convective/radiative situation, a suitable insulation is recommended.

Conclusions
A two-step approach to non-invasive temperature measurement on pipes has been proposed. It incorporates a process-pipe model based on well-known principles and heuristic thermo-hydrodynamic correlation formulae. The model is basically applicable in turbulent, transition and laminar ranges of process flow.
Two large classes of applications (with water and steam, respectively, as process media) have been addressed where process and pipe surface temperature can be estimated to be very close. Using CFD models, the analytical results could be cross-checked and predictions on transient behavior could be made for a temperature step in a water flow example.
In a corresponding test-rig experiment, responsiveness has been compared for a state-of-the-art industrial non-invasive device, a state-of-the-art thermowell, uncovered insets immersed in the water stream, and Pt100 sensors attached to the pipe surface. As predicted by CFD, the pipe surface temperatures react faster than even the uncovered insets. This shows the performance potential of surface measurements in this important type of application, which is obviously not limited by the physics of the boundary layer or pipe. The industry-compliant non-invasive device has been found in this test to be close in performance to the thermowell installations.
In a real-world cooling water application, long-term tests show that non-invasive and thermowell installation indeed deliver measurement results which are very close. A similarly good correspondence for a steam pipe measurement has been predicted analytically and by CFD. Subsequent measurements in an industrial steam use case confirmed the applicability of the concept.
Future work will include exploration of further use cases, according to their relevance, achievable accuracy and repeatability. Of particular interest for industry applications would be to investigate the robustness of measurement compensation in cases where R bl can not be neglected, e. g. for gaseous processes at low flow and pressure.