Numerical Investigation of Cavitating Flows for Diesel Applications

Principal Investigator:
Theresa Trummler, Steffen Schmidt

Institute of Aerodynamics and Fluid Mechanics, Technische Universität München

Local Project ID:

HPC Platform used:
SuperMUC of LRZ

Date published:


During the past decade, European legislative bodies have imposed significant restrictions on the emission level of Diesel injections systems, thus challenging car manufacturers and suppliers to reduce pollution. Improvement of the combustion process and spray quality has become a main objective in fulfilling those policies, which is mainly achieved by increasing injection pressures.

Small geometric dimensions of orifices, coupled with rail pressures of up to 3000 bar, lead to high flow accelerations inside nozzles and promote formation of vapor cavities.

If the surrounding static pressure is higher than the saturation pressure of the liquid, vapor cavities collapse. The collapse of a cavity produces extremely high pressure pulses and leads to the formation of shock waves. Repeated collapses in the proximity of solid walls will produce high surface loads that can eventually lead to material erosion. The erosive processes can thus alter the initial nozzle design and affect overall injector performance.

Therefore, understanding internal nozzle flows has become a key aspect in designing efficient and durable Diesel injection systems. Due to the high spatial and temporal resolution required, quantitative experimental investigations are challenging. High rail pressures and complex geometrical shapes are further limiting factors for the in situ measurements. Hence, investigations are usually conducted at reduced pressure levels using planar nozzles or enlarged transparent models and provided results are more of a qualitative nature. To the authors’ knowledge, there are no quantitative experimental data available for realistic injection pressures exceeding 2000 bar and throttle diameters on the order of several hundred micrometers operating in a submerged environment.

Assessing erosion damage from experiments can provide information about areas sensitive to cavitation erosion and the frequency of erosive events, but still fails to connect it with the underlying flow dynamics. Computational fluid dynamics (CFD) can complement experimental findings by providing additional information about the flow topology.

Description of the Project

The present research project focuses on the detailed assessment of cavity dynamics and identification of cavitation erosion mechanisms in various geometries using a CFD approach. Wave dynamics, interaction of cavitation and turbulence as well as non-condensable gas have important effects on cavitation erosion and need to be accounted for.

Within this project and its extension, the cavitation dynamics and the erosion potential in the following configurations were investigated:

  1. Simplified valve chamber of a common rail injection system
  2. Converging diverging nozzle
  3. Cavitating jet above a target plate to assess the cavitation erosion prediction

For a more generic configuration of single bubble collapses the Gasmodelling and the effect of gas was investigated.

  1. Gasmodelling

Ad. (1) Valve chamber of a common rail injection system

Due to the high pre-processing and computational costs associated with the set-up and simulation of flow in the realistic valve chamber, a simplified chamber model is developed. The generic model enables investigation of canonical flow configurations at the reduced computational effort [6]. For this configuration the following points were investigated and evaluated:

  • the influence of viscosity as well as the mutual interaction between cavitation and turbulence,
  • the influence of non-condensable gas during the injection cycle,  
  • the cavitation erosion potential of various geometries and
  • the effect of the step-hole diameter on the cavitating flow field and the predicted cavitation erosion.

The results of this investigation were presented in the previous status report in detail, are published in Atomization and Sprays [1] and were presented on a conference [2]. Fig. 1 visualizes the cloud fragmentation in the step hole and the emitted pressure wave and Fig. 2 shows the pressure distribution on the surface for two different step-hole diameter.

Ad. (2) Converging-diverging nozzle flow

During the investigations of the cavitation dynamics in the valve, we observed that different shedding mechanism occur for the detachment of clouds as the shedding can be initiated either by a re-entrant jet or by a condensation shock [9, 10]. In order to further investigate the cavitation dynamics, we performed numerical simulations of the cavitating flow in a converging-diverging nozzle featuring two operating points. Fig. 3 shows a time series with the vapor structures for a re-entrant jet governed operating point. Preliminary results to this investigation were presented on the Cavitation Conference CAV2018 [3].

Ad. (3) Cavitating jet above a target plate to assess the cavitation erosion prediction

Erosion prediction is a central part of our research. Our fully compressible approach enables us to capture the shockwaves after a collapse of a vapor structure and thus to evaluate collapse induced pressure loads. The investigations performed for the micro-throttle (objective 1) have demonstrated that  surface loads can be well predicted, see Figure 2. Using a collapse detection algorithm [7] we are able to detect the collapse events and thus directly assess the maximum pressure occurring after an event. However, so far, the actual material damage can not be predicted based on the simulation results. This is due to the grid dependency of the numerically predicted surface load [7] and the fact that materials have different yield strengths and often nonlinear responses to pressure loads. Thus, one objective of this project is to improve the cavitation erosion prediction and make a step towards predicting actual material damage.

For this subproject, we have chosen a cavitating jet which is experimentally well documented [8] and has a relatively simple geometry. The configuration is a throttle with a conical outlet where shear layer cavitation takes place and leads to the formation of a cavitating jet. When the jet reaches the target, the vapor structures collapse, and the target surface is damaged by the collapse induced pressure loads. From experimental investigations, it is known, that a ring-shaped erosion damage occurs. Depending on the driving pressure difference, the cavitating jet shows different erosion potentials. We have investigated the following aspects

  • Grid dependency of the wall pressure
  • Evaluation of different post-processing methods for erosion prediction
  • Development of a generic erosion prediction method
  • Correlation and detailed analysis of the temporal and spatial occurrence of collapse events and the evolution of the vapor content.

With these studies we continue with the research of B. Beban [1,13] during the first project phase. At the moment we postprocess and analyse the data of this simulation.

Ad (4) Gasmodelling

During the first project phase, we have investigated the influence of non-condensable gas on the cavitation dynamics by using a gas model including free gas in the liquid. This investigations and other numerical investigations with gasentrainment into the nozzle showed that free gas can affect the cavitation dynamics by suppressing vapor formation and also potentially decrease the cavitation erosion potential by damping the collapse intensities. In order to investigate the effect of free gas in more detail, we perform numerical simulations of collapsing single bubbles with a varying amount of free gas inside the bubble. Therefore, we derived a new thermodynamic modelling approach [4], which enables us to model bubbles containing condensable vapor and non-condensable gas. After a successful validation of the model for spherical gas bubbles, we applied the model to aspherical collapses close to a wall [5]. 

The results of this investigation were presented on two international conferences [4,5].

Project Team

Nikolaus Adams1 (Institute Head), Steffen Schmidt1, Theresa Trummler1 (PI)

Project contributor(s)

Bruno Beban1, Polina Gorkh1

1 Institute of Aerodynamics and Fluid Mechanics, Technische Universität München

List of publications


[1]  Bruno Beban, Steffen J. Schmidt, and Nikolaus A. Adams, 2017. Numerical study of submerged cavitating throttle flows. Atomization and Sprays, 27(8), 723–739.

Contributions to Collections

[2]  Bruno Beban, Stefan Legat, Steffen J. Schmidt, and Nikolaus A. Adams, 2015. On instationary mechanisms in cavitating micro throttles. Journal of Physics: Conference Series, 656, 012079.

[3]  Polina Gorkh, Steffen J. Schmidt, and Nikolaus A. Adams, 2018. Numerical investigation of cavitation-regimes in a converging-diverging nozzle. Proceedings of the 10th International Symposium on Cavitation (CAV2018).

[4] Theresa Trummler, Lukas Freytag, Steffen J. Schmidt, and Nikolaus A. Adams, 2018. Large eddy simulation of a collapsing vapor bubble containing non-condensable gas. Proceedings of the 10th International Symposium on Cavitation (CAV2018).

[5]  Theresa Trummler, Steffen J. Schmidt, and Nikolaus A. Adams, 2019. Numerical simulation of a collapsing vapor bubble containing non-condensable gas. 10th International Conference on Multiphase Flow.

Theses completed within the project

[6]  Bruno Beban, 2019 PhD  Numerical Simulation of Submerged Cavitating Throttle Flows

Additional References:

[7]  Mihatsch, M. S., Schmidt, S. J., & Adams, N. A. (2015). Cavitation erosion prediction based on analysis of flow dynamics and impact load spectra. Physics of Fluids, 27(10), 103302.

[8]  Fujisawa, N., Kikuchi, T., Fujisawa, K., & Yamagata, T. (2017). Time-resolved observations of pit formation and cloud behavior in cavitating jet. Wear, 386-387, 99–105.

[9]  Budich, Bernd, S. J. Schmidt, and Nikolaus A. Adams. "Numerical simulation and analysis of condensation shocks in cavitating flow." Journal of Fluid Mechanics 838 (2018): 759-813.

[10] Trummler, T., Schmidt, S. J., & Adams, N. A. (2020).Investigation of condensation shocks and re-entrant jet dynamics in a cavitating nozzle flow by Large-Eddy Simulation. International Journal of Multiphase Flow.

[11] Theresa Trummler, expected 2020. Numerical simulations of cavitating multicomponent flows. PhD, Technische Universität München. In preparation.

Scientific Contact

Theresa Trummler, M.Sc.
Lehrstuhl für Aerodynamik und Strömungsmechanik
Technische Universität München
Boltzmannstr. 15, D-85748 Garching bei München (Germany)
e-mail: theresa.trummler [@]

LRZ project ID: pr92ho

March 2020