ColdStream resolution levels and when to use them?

Introduction

The meshing of cases is performed automatically by ColdStream. As a user, you do have some control over it, by selecting from a set of predefined options. The table below highlights all available options and for which case types they are applicable.

Resolution level	Simulation	Standard design	Custom design
Correlation-based estimation	Yes	Yes
CFD-reinforced estimation		Yes
Draft	Yes		Yes
Conceptual	Yes	Yes	Yes
Detailed	Yes	Yes	Yes

This article will start with the fastest mode and end with the most accurate mode.

Estimation modes

The fastest modes that ColdStream users have access to are the estimation modes. When these modes are selected, ColdStream will use correlations to estimate the performance resulting in a significant speed-up at the cost of accuracy.

ColdStream offers 2 estimation modes, these modes are always shown in a light blue box.

	Thermal hydraulic network parameter	Accuracy	Run time
Correlation-based estimation	Based on correlation	Least accurate option	Very fast
CFD reinforced estimation	Based on CFD simulation	Improved accuracy	Slightly slower

Correlation estimation

Introduction

Cases of type 'Simulation' and 'Standard design' can be submitted as a 'Correlation based estimation'. This means that instead of performing a CFD simulation to determine the flow and temperature parameters, correlations will be used to estimate them. The approach is based on setting up and calculating a thermal-hydraulic network model. The results of such a network are either shown on the platform (for simulation cases) or used to perform a standard design optimization.

A thermal-hydraulic network model consists of interconnected resistances, of which the values are based on correlations. A thermal-hydraulic network model is essentially a lumped model, similar to a resistive network for an electric circuit.
The first network (the hydraulic network) represents the fluid region(s). The thermal behavior is captured by a second, purely thermal network, representing the whole case (both fluid and solid regions). These two networks are set up and solved sequentially to estimate the flow and temperature parameters.

This article documents how both the hydraulic and thermal networks are set up and how they are based on correlations. The layout and interpretation of the thermal network on the platform are described in this article.

Hydraulic network

If one or more fluid regions are present in the case in question, a hydraulic network will be set up and calculated. For each fluid region, a subnetwork is generated, for which Bernoulli's mechanical energy equation (extended for friction) will be solved:

$$\sum_{inlets}\frac{P_{in}}{\rho}+\frac{\bar U^2_{in}}2+gz_{in}-\sum_{outlets}\frac{P_{out}}{\rho}+\frac{\bar U^2_{out}}{2}+gz_{out}=h_{l_{T}}=f\frac LD \frac{\bar U}2$$

Where:

• $P$: static pressure

• $\rho$: density

• $\bar U$: average velocity

• $g$: gravitational vector

• $z$: height

• $h_{l_T}$: total hydraulic loss

• $f$: friction factor of the complete fluid boundary

• $L$: equivalent flow length of the geometry

• $D$: equivalent diameter of the geometry

The most important result for subsequent use is the pressure drop from in- to outlet and the average flow speed in the domain. The pressure drop is of use for (purely) flow optimizations, whereas the average flow speed is an important parameter for the subsequent thermal problem.

The geometrical parameters z (height), L (length), and D (diameter) are evaluated from the geometry. The boundary conditions determine either flow or pressure (or define pressure as a function of flow in the case of fans and pumps), whereas a hydraulic correlation will be used to estimate the friction factor (f).

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Note

If a case doesn't contain any fluid regions, this step of the correlation is skipped. ColdStream will immediately continue with the thermal network.

Thermal network

A thermal network is set up for all the fluid and solid regions present in the case. All regions will have to be interconnected in one way or another.
If a case comprises only solid regions, i.e. a pure conduction case, this thermal network is generated immediately. If a case also comprises fluid regions, it is a conjugate heat transfer problem and the hydraulic network will be solved first.

Generally, the energy balance will be solved for each region:

$$\sum \dot Q_i=\sum_i\frac{T_{region}-T_{boundary,i}}{R_{th,i}}=\sum\dot Q_{source, region}$$

Where:

• $\dot Q_i$: the heat transfer from a region to a boundary

• $T_{region}$: the mean temperature of a region

• $T_{boundary}$: the mean temperature of a boundary

• $R_{th}$: the thermal resistance between the boundary and the region.

• $\dot Q_{source}$: the internal energy source of a region (if present)

The energy balance for each of the regions is coupled through the fluxes crossing the interfaces from one region to another. Both regions and boundaries are represented in the network by a node. Each node has one temperature, hence the approach being a 1D approach. The temperature of a boundary or region can be interpreted as the average temperature in the center of a boundary/region.

Whereas $T$ and $\dot Q$ are either given or calculated, the thermal resistance will be estimated based on correlations. One can distinguish three types of thermal resistances:

1. Convective thermal resistance: the thermal resistance between a solid-fluid interface and a fluid region node, being:

   $$R_{th}=\frac 1{hA}$$

   Where:

   • $h$ represents the convective heat transfer coefficient, determined by a correlation.
   • $A$ represents the heat transfer area, or the area of the interface.

2. Conductive thermal resistance: the thermal resistance between a boundary and a solid region node, being:

   $$R_{th}=\frac L{\kappa A}$$

   Where:

   • $L$ represents the length of the thermal path
   • $\kappa$ represents the thermal conductivity of the material
   • $A$ represents the heat transfer area, or the area of the interface.

3. Radiative thermal resistance: the thermal resistance due to radiation, often in parallel with a conductive/convective resistance, being:

   $$R_{th}=\frac 1{\epsilon\sigma A(T_{region}-T_{boundary,i})^3}$$

   Where:

   • $\epsilon$ represents the emissivity
   • $\sigma$ represents the Boltzmann constant
   • $A$ represents the heat transfer area, or the area of the interface

These three types of thermal resistances constitute the thermal network, which is then solved for the heat flux $(\dot Q)$ and the temperature $(T)$.

Combined network

The network that is displayed on the platform comprises the resulting information from both the hydraulic and the thermal network. For an interpretation of the thermal network, please refer to this article.

In the case of a standard design, the estimation is used to optimize the performance of the design with the given set of targets. The network is internally updated every design iteration, whereas the network shown on ColdStream is one of the final designs.

CFD reinforced estimation

As explained in the chapter above (correlation-based estimation), a thermal-hydraulic network estimation provides an easy way to get an idea about the thermal behavior of a case in a matter of minutes. The only drawback to this approach is that such results are only approximative when compared to the results of a CFD simulation.

For standard designs only, there are two submission options which are based on a thermal-hydraulic network estimation. When you press the 'Submit as a correlation-based estimation'-button, a thermal-hydraulic network is generated based on correlations, as described in the referenced article above.
Alternatively, you can submit your case by pressing the 'Submit as a CFD reinforced estimation'-button. Now, a single CFD simulation of your case setup will be performed, to get more accurate values for the thermal resistances between and the mass flows within the various regions. Secondly, the results of this CFD simulation are used to determine the thermal resistance and flow parameters within the thermal-hydraulic network estimation. Next, the standard design optimization will commence, and a new thermal-hydraulic network will be generated for each heat sink type that ColdStream tests. These thermal-hydraulic networks can be viewed by navigating to the 'Thermal network'-tab of the case in question (only the most optimal will be published).

The advantage of a CFD-reinforced estimation over a correlation-based estimation is hence that the thermal-hydraulic networks will be more accurate. This is because all the thermal resistance and flow data generated in the preceding CFD simulation (which corresponds to your specific case setup and is very accurate) is being used in the thermal-hydraulic network calculations, to improve the results.

CFD modes

To increase the accuracy of the results, the ColdStream user can opt for a full CFD simulation to be performed. ColdStream offers 3 different CFD resolutions. These options are always made available in a dark blue box.

Resolution level	Mesh count goal	body-fitted mesh?	Manufacturable design?	Accuracy	Runtime
Draft	~100k cells per region	No	Very much relaxed	Medium	Fast
Conceptual	~1M cells per region	Yes	Slightly relaxed	High	Medium
Detailed	~10M cells per region	Yes	All constraints will be met	Very high	Slow

Differences between draft, conceptual, and detailed simulations

The only difference between the 3 CFD resolutions for a simulation, is the meshing strategy:

1. For detailed cases, ColdStream will aim for about 10 million cells per region, while for the conceptual mode, this is reduced to 1 million cells per region and 100 thousand cells per region for the draft resolution.
2. Secondly, the detailed and conceptual modes will result in a body-fitted mesh. This means that the mesh elements will follow the curvature of the regions. While the draft resolution will result in a non-body-fitted mesh. This means that the mesh will be more blocked and not follow the curvature in great detail.

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Note

The higher the selected resolution, the more accurate the results will become. This comes at the price of an increased runtime.

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Important

Depending on the complexity of the geometry, the lower resolution levels may not be able to mesh your case. In this scenario, ColdStream will put your case on stalled and ask you to increase the resolution.

Differences between conceptual and detailed standard designs

The differences in resolution for standard designs are identical to simulations. The draft mode is not available for standard designs.

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Note

The higher the selected resolution, the more accurate the results will become. This comes at the price of an increased runtime.

Differences between draft, conceptual, and detailed custom designs

Custom designs by default only run using one of the CFD resolutions as a full CFD simulation is needed for every design iteration. The same differences are thus taken over from the simulation cases.
The resolution levels also have a further impact on the outcome of the custom design

	Draft	Conceptual	Detailed
Manufacturability	Manufacturing constraints are severely relaxed	Manufacturing constraints are slightly relaxed	guarantees manufacturability
Convergence of design iterations	Convergence is not required	Convergence is required	Convergence is required

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Important

Only a detailed custom design case will guarantee a fully manufacturable design. The manufacturing constraints are either severely relaxed or slightly relaxed for draft and conceptual cases.